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   =
   =
BEAVER VALLEY POWER STATION, UNIT 1 TABLE OF CONTENTS (Cont)
BEAVER VALLEY POWER STATION, UNIT 1 TABLE OF CONTENTS (Cont)
  ._;
         ;  Section        Title                                                                                        E.a.gg 5.0  COMPARISON OF RESULTS.        . . . . . . . . . . . . . . . . .                            . . . .      5-1 1
         ;  Section        Title                                                                                        E.a.gg 5.0  COMPARISON OF RESULTS.        . . . . . . . . . . . . . . . . .                            . . . .      5-1 1
5.1  REFUND / FRIDAY VS PLAXLY.        . . . . . . . . . . . . . . . . . . . .                              . 5-1 5.2  FSAR EARTHQUAKE VS REGULATORY GUIDE 1.60 EARTHQUAKE.                            . . . . . .            . 5-2 i
5.1  REFUND / FRIDAY VS PLAXLY.        . . . . . . . . . . . . . . . . . . . .                              . 5-1 5.2  FSAR EARTHQUAKE VS REGULATORY GUIDE 1.60 EARTHQUAKE.                            . . . . . .            . 5-2 i
Line 145: Line 144:
I ix
I ix


                                                      ,                                  ;              .
                                                                                                   '                                                                                              '*              'x
                                                                                                   '                                                                                              '*              'x
               - ~
               - ~
Line 232: Line 230:
5
5
_t    -
_t    -
              , ..;.        %.      #              **
e,y ,            .
e,y ,            .
y  >      8 '
y  >      8 '
Line 251: Line 248:


A' BEAVER VALLEY POWER STATION, UNIT 1 m
A' BEAVER VALLEY POWER STATION, UNIT 1 m
4
4 j          2.2  SOIL PROFILES The soil beneath the plant consists of medium to dense sand and gravels that
    ;
j          2.2  SOIL PROFILES The soil beneath the plant consists of medium to dense sand and gravels that
=
=
extend from the shale bedrock at El. 620 to plant grade at                                              El. 735. The
extend from the shale bedrock at El. 620 to plant grade at                                              El. 735. The
Line 297: Line 292:
's-
's-
       !                                                                  2253 025
       !                                                                  2253 025
'M 2-3
'M 2-3 2
;
2
         =---                                                                - - - . . - . . , , , - . - . - . , , , , . . .
         =---                                                                - - - . . - . . , , , - . - . - . , , , , . . .


Line 373: Line 366:
     )  methods agree closely.      The shear wave velocity profile for small strain values used in the present free-field SHAKE analysis is                  shown in Figure 2-6 i
     )  methods agree closely.      The shear wave velocity profile for small strain values used in the present free-field SHAKE analysis is                  shown in Figure 2-6 i
j    and is basically the same as that presented by Whitman in the curve on Tigure 2-5.
j    and is basically the same as that presented by Whitman in the curve on Tigure 2-5.
    ;
k      2.4.2    Strain Dependent Modulus and Damping m
k      2.4.2    Strain Dependent Modulus and Damping m
j    The calculation of strain dependent modulus and damping profiles is discussed
j    The calculation of strain dependent modulus and damping profiles is discussed
Line 420: Line 412:
record. The peak acceleration of the El Centro record at the base layer after
record. The peak acceleration of the El Centro record at the base layer after
   ;      deconvolution to El 620 feet was .090g.
   ;      deconvolution to El 620 feet was .090g.
1                                                                                                    2253 032
1                                                                                                    2253 032 4
-_;
4
_.                                                                      2-10 J
_.                                                                      2-10 J


Line 505: Line 495:
,-                                  shear wave velocities determined from cross-hole data i
,-                                  shear wave velocities determined from cross-hole data i
_i i
_i i
V          = coefficient of variation of G/Gmax from SW-AJA curves C/Gmax
V          = coefficient of variation of G/Gmax from SW-AJA curves C/Gmax j                              (Figure 5-2) j                                                                                      2253 037 8
        ;
j                              (Figure 5-2) j                                                                                      2253 037 8
I
I
     ^,
     ^,
Line 795: Line 783:
         ;                                                                                                                                                              wwmm Il                                                                  4 W1 J
         ;                                                                                                                                                              wwmm Il                                                                  4 W1 J
a Ee w  -
a Ee w  -
                                       =        0 0
                                       =        0 0 2
                                                                        ;
0?23
2 0?23
                                                                                         .          3
                                                                                         .          3
                                                                                                                         %2**        S: 2              uo==.
                                                                                                                         %2**        S: 2              uo==.
Line 879: Line 866:
. OOgz 4
. OOgz 4
5    N e        6'i.    ,, os ., s,          7    2*
5    N e        6'i.    ,, os ., s,          7    2*
                                                                        .;;,
                                                                               ,E6foeg61S                      6;r;      P,;; y P.
                                                                               ,E6foeg61S                      6;r;      P,;; y P.
s                                    2 s*                      T8            2g62I                2 1
s                                    2 s*                      T8            2g62I                2 1
Line 960: Line 946:
         =
         =
7t = 130 p c f b    .
7t = 130 p c f b    .
100        (Q)                                              o Vs (FPS)
100        (Q)                                              o Vs (FPS) n
      ;
n
=
=
i J
i J
Line 995: Line 979:
_                                              VS= 50:.'0 'PS
_                                              VS= 50:.'0 'PS
?
?
I j                                                                      2253 066
I j                                                                      2253 066 i
;
e L
i e
q l
L q
1 A
l 1
3                                                    FIGURE 2-6 i                                            FREE FIELD SOIL PROFILE r                                                        BEAVER VALLEY POWER STATION-UNIT 1 m
A 3                                                    FIGURE 2-6 i                                            FREE FIELD SOIL PROFILE r                                                        BEAVER VALLEY POWER STATION-UNIT 1 m


+
+
Line 1,040: Line 1,023:
j                          665    -
j                          665    -
SAND a GRAVEL 655  -
SAND a GRAVEL 655  -
:;
645              # T= 136 PCF I.
645              # T= 136 PCF I.
635    -
635    -
Line 1,097: Line 1,079:
i
i
     -)
     -)
  ;
FIGURE 2-10 i                                  SERVICE BUILDING SOIL PROFILE
FIGURE 2-10 i                                  SERVICE BUILDING SOIL PROFILE
   ,                                  BEAVER VALLEY POWER STATION-UNIT 1
   ,                                  BEAVER VALLEY POWER STATION-UNIT 1
Line 1,159: Line 1,140:
SA,ND 8                                        I 655                              GRAVEL
SA,ND 8                                        I 655                              GRAVEL
[
[
645                                  I = 136 PCF
645                                  I = 136 PCF T
          ;
T
    ;
635              -
635              -
i J      625              -
i J      625              -
Line 1,171: Line 1,149:
2253 073 I_
2253 073 I_
5 i
5 i
;
e
e
     -i
     -i
Line 1,218: Line 1,195:
I                              FIGURE 2-16 I                              INTAKE STRUCTURE SOIL PROFILE BEAVER VALLEY POWER STATION-UNIT 1 I
I                              FIGURE 2-16 I                              INTAKE STRUCTURE SOIL PROFILE BEAVER VALLEY POWER STATION-UNIT 1 I


  ;
i E
i E
2253 077                                      :
2253 077                                      :
Line 1,313: Line 1,289:
34., W / /^//MI4'SWAA /                                                  @M\                      Mf5W/                      /\ /\ \ Mf5      '
34., W / /^//MI4'SWAA /                                                  @M\                      Mf5W/                      /\ /\ \ Mf5      '
4.,
4.,
  ;
     ,.,    R$88W/AM*'^' $h@M30(M'/\                                                                                                              830(        ,.,
     ,.,    R$88W/AM*'^' $h@M30(M'/\                                                                                                              830(        ,.,
l E ,.. MYd$k!$)@M@N$3MA M2$$5                                                                                                                            ...
l E ,.. MYd$k!$)@M@N$3MA M2$$5                                                                                                                            ...
Line 1,348: Line 1,323:
                                                         /,z, g
                                                         /,z, g
s ml  s 3 > Z ?,_.
s ml  s 3 > Z ?,_.
s; i 3 f){779
s; i 3 f){779 z san? > Z/3 s                            '
                                                                                                    ' ;,,
z san? > Z/3 s                            '
                                                                                                                                                     /; -
                                                                                                                                                     /; -
3 3
3 3
Line 1,577: Line 1,550:
_ M                /\                            8 / EN c.'k / \ $)(NMV\                                                            _)h(N Nb AkkN N4kkkhNbkk$h
_ M                /\                            8 / EN c.'k / \ $)(NMV\                                                            _)h(N Nb AkkN N4kkkhNbkk$h
* h    \ Y<        s                            .,  ,
* h    \ Y<        s                            .,  ,
r , , , i, x                                                ., ,,,,1, N                  4 ,  ,, , - ,  ie
r , , , i, x                                                ., ,,,,1, N                  4 ,  ,, , - ,  ie ir                        ,                                                                      ,        ,
;
ir                        ,                                                                      ,        ,
                                                                                                                         ,,,,;,,,j ARTirICI AL CARTHQUAKE SSE                              8VP3 FREE FIELD 735-620 DECONVOLUT 2                                                                '"'"* lelf,ilu#"" '
                                                                                                                         ,,,,;,,,j ARTirICI AL CARTHQUAKE SSE                              8VP3 FREE FIELD 735-620 DECONVOLUT 2                                                                '"'"* lelf,ilu#"" '
o 2253 086 O! 0.030
o 2253 086 O! 0.030
Line 1,616: Line 1,587:
             !! N'/                        \        *%$RRS884V//N                            M3O?M', /N                                      *%$R l          !          Nb                4$k$$(5Mb 2$$$I Mbskk$$(5 54                                '/                                                Qjj } g
             !! N'/                        \        *%$RRS884V//N                            M3O?M', /N                                      *%$R l          !          Nb                4$k$$(5Mb 2$$$I Mbskk$$(5 54                                '/                                                Qjj } g
                                                                                                                                                     )j(
                                                                                                                                                     )j(
N'g
N'g m
;
m
                                   /
                                   /
                             \ // / /^ A>
                             \ // / /^ A>
Line 1,673: Line 1,642:
,            included. An earthquake with a specified amplitude and frequency content at 4          the site surface is not necessarily a reasonable input to the detailed model in the second step.
,            included. An earthquake with a specified amplitude and frequency content at 4          the site surface is not necessarily a reasonable input to the detailed model in the second step.
E
E
;
!            A multiple-step analysis need not re'ly upon finite element representations of m
!            A multiple-step analysis need not re'ly upon finite element representations of m
,)
,)
Line 1,694: Line 1,662:
The frequency-dependent stiffnesses of a rectangular footing founded at the
The frequency-dependent stiffnesses of a rectangular footing founded at the
   ~1 surface of a layered medium are computed with the program REFUND, discussed in L9          Section 10.3. The program solves the problem of forced vibration of a rigid plate on a viscoelastic, layered stratum using numerical solutions to the L
   ~1 surface of a layered medium are computed with the program REFUND, discussed in L9          Section 10.3. The program solves the problem of forced vibration of a rigid plate on a viscoelastic, layered stratum using numerical solutions to the L
;
l                                                                    2253 090
l                                                                    2253 090
           !                                                  4-2 i
           !                                                  4-2 i
Line 1,705: Line 1,672:
j j                1. calculations of frequency-dependent soil stiffnesses 4              2. modification of the specified surface motion to account for structure l                    embedment
j j                1. calculations of frequency-dependent soil stiffnesses 4              2. modification of the specified surface motion to account for structure l                    embedment
]
]
    -;
       ;        3. interaction analysis i;
       ;        3. interaction analysis i;
2      These steps are illustrated in Figure 4-1 (see Reference 2).
2      These steps are illustrated in Figure 4-1 (see Reference 2).
Line 1,733: Line 1,699:
~
~
admissible;          for a layered stratum, however, only a numerable set of values of k (each one with a corresponding propagation mode)                                  satisfies the. boundary I
admissible;          for a layered stratum, however, only a numerable set of values of k (each one with a corresponding propagation mode)                                  satisfies the. boundary I
   !    conditions.                There are thus, at a given frequency, an infinite but numerable set of propagation modes and wave numbers k that can be found by solving a
   !    conditions.                There are thus, at a given frequency, an infinite but numerable set of propagation modes and wave numbers k that can be found by solving a i
  ;
transcendental eigenvalue problem.                  For each eigenfunction the distribution of l    stresses can be determined up to a multiplicative constant, the participation i-factor of        the mode.              By combining these modal stresses to match any given 1
i transcendental eigenvalue problem.                  For each eigenfunction the distribution of l    stresses can be determined up to a multiplicative constant, the participation i-factor of        the mode.              By combining these modal stresses to match any given 1
j      distributi'sn of stresses at the boundary, the participation factors and the corresponding                dynamic stiffness function relating boundary stresses                      to i
j      distributi'sn of stresses at the boundary, the participation factors and the corresponding                dynamic stiffness function relating boundary stresses                      to i
boundary displacements can be determined.
boundary displacements can be determined.
Line 1,771: Line 1,736:
i d
i d
i                              SEAVER VALLEY POWER STATION, UNIT 1 4
i                              SEAVER VALLEY POWER STATION, UNIT 1 4
;
   !    computes the cylindrical displacement components for the two leading cases, and determines the cartesian flexibility matrix T under the load (axis),      at i
   !    computes the cylindrical displacement components for the two leading cases, and determines the cartesian flexibility matrix T under the load (axis),      at i
)        the boundary. and at selected points beyond the boundary.
)        the boundary. and at selected points beyond the boundary.
Line 1,781: Line 1,745:
where U is the global displacement vector satisfying the rigid body condition.
where U is the global displacement vector satisfying the rigid body condition.
It follows that U is of the form
It follows that U is of the form
;
  ;
?_
?_
j              U - TV i
j              U - TV i
Line 1,805: Line 1,767:
Ignoring the rotational component would result in an unconservative solution.
Ignoring the rotational component would result in an unconservative solution.
Note that the modified motion at the base of the foundation is not equivalent to a deconvolution.              The specified surface motion is modified so that F(n) cos(  )  , f 5 0.7 fn y, (t) = IFT (F(D) 0.453 , f > 0.7 fn ond fF(a) 0.257(1- cos 11)/R      , f 5 fn g            k(t) = IFT (F(n) 0.257/R , f > fn l
Note that the modified motion at the base of the foundation is not equivalent to a deconvolution.              The specified surface motion is modified so that F(n) cos(  )  , f 5 0.7 fn y, (t) = IFT (F(D) 0.453 , f > 0.7 fn ond fF(a) 0.257(1- cos 11)/R      , f 5 fn g            k(t) = IFT (F(n) 0.257/R , f > fn l
;
1 J            F(G)    = Fourier Transform of surface motion l
1 J            F(G)    = Fourier Transform of surface motion l
IFT      = inverse transform 7
IFT      = inverse transform 7
J R        = foundation radius i
J R        = foundation radius i
  ]              f        = fundamental shear beam frequency of the column of soil between the embedment level and the free surface
  ]              f        = fundamental shear beam frequency of the column of soil between the embedment level and the free surface 2                                                                                                22ST 098
;
2                                                                                                22ST 098
  -:                                                                4-9
  -:                                                                4-9


Line 1,825: Line 1,784:
       ,    convolution of the transfer functions and the Fourier transform of the input i
       ,    convolution of the transfer functions and the Fourier transform of the input i
         . excitation. The dynamic equilibrium equations can be written in matrix l      not cion as:
         . excitation. The dynamic equilibrium equations can be written in matrix l      not cion as:
  ;
2253 099 j
2253 099 j
j                        -
j                        -
Line 1,888: Line 1,846:
BEAVER VALLEY POWER STATION, UNIT 1 s
BEAVER VALLEY POWER STATION, UNIT 1 s
-i The procedure consists                              then of determining the dyna::ic stiffness matrix K d' solving Eq 6 for the six loading cohditions H =                                H  ,  determining the six
-i The procedure consists                              then of determining the dyna::ic stiffness matrix K d' solving Eq 6 for the six loading cohditions H =                                H  ,  determining the six
                                                                                         ~    f
                                                                                         ~    f Fourier              transforms of the input components F =if)]', and performing the inver 1          transformation (Eq 9), which corresponds formally to:
;
Fourier              transforms of the input components F =if)]', and performing the inver 1          transformation (Eq 9), which corresponds formally to:
J                                _ _ _ _ -
J                                _ _ _ _ -
     ;          O=h                            HF elW' dw i
     ;          O=h                            HF elW' dw i
Line 1,897: Line 1,853:
=
=
The level of detail in mathematical models of s ructures is determined by consideration of the following:
The level of detail in mathematical models of s ructures is determined by consideration of the following:
      ;
e
e
_                1.                  distribution of mass in the building
_                1.                  distribution of mass in the building
Line 1,909: Line 1,864:
       ;        The  models                    used in the analysis,    typically,  are generalized,  three-dimensional, multi-mass representations.                    The total number of degrees of freedom included is more than sufficient to encompass all significant frequencies; the number of masses being governed, as a practical matter,                      by the locations at which amplified response spectra (ARS) are required.
       ;        The  models                    used in the analysis,    typically,  are generalized,  three-dimensional, multi-mass representations.                    The total number of degrees of freedom included is more than sufficient to encompass all significant frequencies; the number of masses being governed, as a practical matter,                      by the locations at which amplified response spectra (ARS) are required.
e
e
;
_              Eccentricity between the center of mass and center of stiffness at every level i
_              Eccentricity between the center of mass and center of stiffness at every level i
is included, except where insignificant.                  As a result, the effects of torsion
is included, except where insignificant.                  As a result, the effects of torsion
Line 1,966: Line 1,920:
t l                                        )
t l                                        )
J:                                                \                        /
J:                                                \                        /
  ;
uy
uy
  ~
  ~
Line 2,025: Line 1,978:
                                                           ;;,,  N                            O
                                                           ;;,,  N                            O
                                                       <                      A-*              r
                                                       <                      A-*              r
        ;
                                                   <*N w_              ^
                                                   <*N w_              ^
                                                                         =:::
                                                                         =:::
Line 2,032: Line 1,984:
                     *6-                              "3  %        N                      oO' N        %
                     *6-                              "3  %        N                      oO' N        %
7 i              ~                  N              I      H            2
7 i              ~                  N              I      H            2
              ;'
                                 \                                                          <m            O N                                                    n                  e M*
                                 \                                                          <m            O N                                                    n                  e M*
Ww            5
Ww            5
Line 2,098: Line 2,049:
       =
       =
u 0 Q80  --
u 0 Q80  --
                                                                                                                          ;
4                                                                                                      I a              c60                                                                  ^ ^                              \              AA j                                                                                    [I                          \/S            I \
4                                                                                                      I a              c60                                                                  ^ ^                              \              AA j                                                                                    [I                          \/S            I \
2                                                                            A                                                            J    %,
2                                                                            A                                                            J    %,
Line 2,110: Line 2,060:
                                 ----- 2 D MODEL
                                 ----- 2 D MODEL
   $                                                                                                                                                                2253 113
   $                                                                                                                                                                2253 113
__                                                                                                                                    FIGURE 4-7 SEISMIC ANALYSIS OF
__                                                                                                                                    FIGURE 4-7 SEISMIC ANALYSIS OF MAIN STEAM VALVE BUILDING HORIZONTAL SSE EW HORIZONTAL RESPONSE SPECTRUM 4
  -;
MAIN STEAM VALVE BUILDING HORIZONTAL SSE EW HORIZONTAL RESPONSE SPECTRUM 4
AT MAT j                                                                                                                                      BEAVER VALLEY POWER STATION-UNIT 1 J
AT MAT j                                                                                                                                      BEAVER VALLEY POWER STATION-UNIT 1 J
N                                                    mummimummim----si---ime---    ui smmi-,m-----------ni      nyniumio  u
N                                                    mummimummim----si---ime---    ui smmi-,m-----------ni      nyniumio  u
Line 2,124: Line 2,072:
?                O j                g1.20 9
?                O j                g1.20 9
U                                k        :
U                                k        :
       .          m 1.00
       .          m 1.00 hJ                              A 3      ,  1
;
hJ                              A 3      ,  1
                                                       ' 'j
                                                       ' 'j
$                0 0.80 j                <
$                0 0.80 j                <
Line 2,164: Line 2,110:
       !    <r j                                                  ['''
       !    <r j                                                  ['''
O.60                                  i                  A m
O.60                                  i                  A m
  ;                                              ;
r!  '
r!  '
Wrj 0.40                                                                  "
Wrj 0.40                                                                  "
Line 2,183: Line 2,128:
4 J
4 J
t 1
t 1
    ;
ELEVATION ABOVE MAT                                      ACCELERATION (FEET)                                          (G) 177.50 C                                      O.245 7
ELEVATION ABOVE MAT                                      ACCELERATION (FEET)                                          (G) 177.50 C                                      O.245 7
I J                                                                                                          ELEVATION        ACCELERATION (FEET)              (G) 0.174                                            136.@ C            O.228 132.10 0 111. 7 5 O                                  O.15 4                                            g g ,000        O.19 4 91.40 0                                    0.134 86.00 O          O.157 71.050                                      0.11 2
I J                                                                                                          ELEVATION        ACCELERATION (FEET)              (G) 0.174                                            136.@ C            O.228 132.10 0 111. 7 5 O                                  O.15 4                                            g g ,000        O.19 4 91.40 0                                    0.134 86.00 O          O.157 71.050                                      0.11 2
Line 2,286: Line 2,230:
   =
   =
.-                                                                                                2253 122 L
.-                                                                                                2253 122 L
a i                                                        5-3
a i                                                        5-3 l,
;
l,


+
+
Line 2,360: Line 2,302:
i
i
.~
.~
___;                                                      -
                                                                                                             .      2253 125
                                                                                                             .      2253 125
   ,                LEGEND                                                                                                      ,
   ,                LEGEND                                                                                                      ,
Line 2,379: Line 2,320:
O s        i g"'
O s        i g"'
                                               /A              Ng d
                                               /A              Ng d
    ;
jfrx
jfrx
                                             /
                                             /
Line 2,392: Line 2,332:
O.30                    -
O.30                    -
   "                                i j                                    -
   "                                i j                                    -
3
3 m0
  ;
m0
                       -        /, s                                                                    tR f        ./                                                                                          ,
                       -        /, s                                                                    tR f        ./                                                                                          ,
0.10
0.10 0.0 OD      OJO Q20    Q30    0.40    0.50  0.60  Q70  0.80                      Q90  1.00  I.10    I.20 j                                                  PERIOD-SECONOS                                                        -
        ;
0.0 OD      OJO Q20    Q30    0.40    0.50  0.60  Q70  0.80                      Q90  1.00  I.10    I.20 j                                                  PERIOD-SECONOS                                                        -
LEGEND                                                                            2253 126
LEGEND                                                                            2253 126
   $                                REFUND / FRIDAY                                                      ~-
   $                                REFUND / FRIDAY                                                      ~-
Line 2,440: Line 2,376:
   }          $ 'So                                              yv^\ k 075                                    \      h/
   }          $ 'So                                              yv^\ k 075                                    \      h/
() i^^
() i^^
      ;
sp ."                                        k.
sp ."                                        k.
   !_            m                                    hAl                                                  kA i                                              p                                                                                        N.
   !_            m                                    hAl                                                  kA i                                              p                                                                                        N.
Line 2,451: Line 2,386:
REGULATORY GUIDE l.60 EARTHQUAKE 3% DAMPING                                      --
REGULATORY GUIDE l.60 EARTHQUAKE 3% DAMPING                                      --
i L
i L
  ;
j                                                                                                                          2253 128 1.
j                                                                                                                          2253 128 1.
t FIGURE 5-5
t FIGURE 5-5
Line 2,458: Line 2,392:
     ,                                                                              ARS AT OPERATING FLOOR BEAVER VALLEY POWER STATION- UNIT I 5
     ,                                                                              ARS AT OPERATING FLOOR BEAVER VALLEY POWER STATION- UNIT I 5


m'
m' a
    ;
a
  't              5.0
  't              5.0
   )
   )
Line 2,475: Line 2,407:
                                                       , f            vp                                                              -
                                                       , f            vp                                                              -
T            "'                      .  ,                                          $& mmw      i                              s u                      --; AM,pu i        O.0
T            "'                      .  ,                                          $& mmw      i                              s u                      --; AM,pu i        O.0
_!                O.00      0.10  0.20              0.30    0.40                    0.50    Q60  0.70  0.80    0.90  1.0 0 1.10    1.20 l                                                                                      PERIOD-SECONDS
_!                O.00      0.10  0.20              0.30    0.40                    0.50    Q60  0.70  0.80    0.90  1.0 0 1.10    1.20 l                                                                                      PERIOD-SECONDS FSAR EARTHOUAKE 1% DAMPlNG 2253 129  .
      ;
FSAR EARTHOUAKE 1% DAMPlNG 2253 129  .
:,                  ----- REGULATORY GUIDE 1.60 EARTHOUAKE 2% DAMPING                                          - - -
:,                  ----- REGULATORY GUIDE 1.60 EARTHOUAKE 2% DAMPING                                          - - -
                             -      REGULATORY GulDE 1.60 EARTHOUAKE 3% DAMPING                                  --
                             -      REGULATORY GulDE 1.60 EARTHOUAKE 3% DAMPING                                  --
Line 2,507: Line 2,437:


   .        2.50 2.25 DAMP 1.0 %
   .        2.50 2.25 DAMP 1.0 %
2.00 I.75
2.00 I.75 O
;
y1.50 e
O y1.50 e
      ;
tim 1.25
tim 1.25
     ~
     ~
Line 2,523: Line 2,451:
j FIGURE 5-8 COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS l
j FIGURE 5-8 COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS l
HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION-UNIT I
HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION-UNIT I
;


e i
e i
Line 2,534: Line 2,461:
:  LM
:  LM
_.,      J
_.,      J
   -          IDO O.75
   -          IDO O.75 050 5*
;
050 5*
azs                m yaqq
azs                m yaqq
[.8:D              e-              -
[.8:D              e-              -
Line 2,575: Line 2,500:
_~                      - L AST ITERATION FROM SHAKE                                                                        2253 133 r
_~                      - L AST ITERATION FROM SHAKE                                                                        2253 133 r
u FIGURE 5-10
u FIGURE 5-10
  "                                                                                      COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE S PECTRUM AT OPERATING FLOOR BEAVER VALLEY POWER STATION-UNIT 1
  "                                                                                      COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE S PECTRUM AT OPERATING FLOOR BEAVER VALLEY POWER STATION-UNIT 1 r
;
r


I 2.50 2.25 DAMP 1.00%
I 2.50 2.25 DAMP 1.00%
Line 2,633: Line 2,556:
   ~
   ~
FIGURE 5-13
FIGURE 5-13
'_                                                                                      COMPARISON OF ARS FOR
'_                                                                                      COMPARISON OF ARS FOR i
;
SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM 1                                                                                        AT SPRINGLINE j                                                                                    BEAVER VALLEY POWER STATION-UNIT I semi-i----i-ii iim -
i SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM 1                                                                                        AT SPRINGLINE j                                                                                    BEAVER VALLEY POWER STATION-UNIT I
;
semi-i----i-ii iim -


3 2.50 2.25 e            2.0                                                                                                          DAMP 1.00%
3 2.50 2.25 e            2.0                                                                                                          DAMP 1.00%
Line 2,667: Line 2,587:
                                                                                                               }}}} l}7 w
                                                                                                               }}}} l}7 w
y h
y h
        ;
[  1 FIG U R E 5- 14 COMPARISON OF ARS FOR l                                                                            SOIL PARAMETER VARI ATIONS HORIZONTAL RESPONSE SPECTRUM AT SPRINGLINE
[  1 FIG U R E 5- 14 COMPARISON OF ARS FOR l                                                                            SOIL PARAMETER VARI ATIONS HORIZONTAL RESPONSE SPECTRUM AT SPRINGLINE
     ]                                                                                  BEAVER VALLEY POWER STATION- UNIT 1
     ]                                                                                  BEAVER VALLEY POWER STATION- UNIT 1
Line 2,673: Line 2,592:
=
=
e j            2.50 2.25 DAMP 3.00%
e j            2.50 2.25 DAMP 3.00%
2.00 1.75
2.00 1.75 1.50
    ;
1.50
     }
     }
       !      9 a: 1.25 3
       !      9 a: 1.25 3
Line 2,686: Line 2,603:
s LEGEND LOW STRAIN Guax
s LEGEND LOW STRAIN Guax
-                            ---- FIRST ITERATION FROM SHAKE
-                            ---- FIRST ITERATION FROM SHAKE
      ;                          -
                                                 - LAST ITERATION FROM SHAKE
                                                 - LAST ITERATION FROM SHAKE
                                                                                                             }}}} j}}
                                                                                                             }}}} j}}
Line 2,699: Line 2,615:
_            O
_            O
           ?            i 50
           ?            i 50
    ;
_8
_8
     --            N g 1.25
     --            N g 1.25
Line 2,719: Line 2,634:
                                                                                                                                                   ~
                                                                                                                                                   ~
1
1
  .a
  .a 7!                                                                                                  FIGURE 5-16 J                                                                                                    COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS 7                                                                                                    HORIZONTAL RESPONSE SPECTRUM AT MAT j                                                                                                    BEAVER VALLEY STATION-UNIT 1
;
7!                                                                                                  FIGURE 5-16 J                                                                                                    COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS 7                                                                                                    HORIZONTAL RESPONSE SPECTRUM AT MAT j                                                                                                    BEAVER VALLEY STATION-UNIT 1
- m; I
- m; I
mn-s-imini-nn--uni-i
mn-s-imini-nn--uni-i
Line 2,731: Line 2,644:
-.        o
-.        o
[    E 1.50 O
[    E 1.50 O
P i    <t j l.25
P i    <t j l.25 w
          ;
u
w u
       ,, N 100 O.75 3
       ,, N 100 O.75 3
         -    0.50                                            - ^                          -
         -    0.50                                            - ^                          -
Line 2,750: Line 2,662:
(                                            G + 50% FROM SHAKE                                        - --
(                                            G + 50% FROM SHAKE                                        - --
-f
-f
;
                               -- CAST ITERATION FROM SHAKE G - 50% FROM SHAKE
                               -- CAST ITERATION FROM SHAKE G - 50% FROM SHAKE
                                                                                                   }}}-}-]-fQ
                                                                                                   }}}-}-]-fQ
Line 2,758: Line 2,669:
       !                                                      FIGURE 5-17
       !                                                      FIGURE 5-17
/                                                            COMPARISON OF ARS FOR
/                                                            COMPARISON OF ARS FOR
,                                                            SOIL PAR AMETER VARIATIONS l                                                      HORIZONTAL RESPONSE SPECTRUM AT MAT
,                                                            SOIL PAR AMETER VARIATIONS l                                                      HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION- UNIT 1
;
BEAVER VALLEY POWER STATION- UNIT 1


2.50          >
2.50          >
Line 2,821: Line 2,730:
j          2.0 0 1.75 0
j          2.0 0 1.75 0
E 1.50 o                                              f      Il ct: 1.25                                            h. A g
E 1.50 o                                              f      Il ct: 1.25                                            h. A g
   ,          1.00
   ,          1.00 0.75                              '
  ;
0.75                              '
1 l}
1 l}
L    m
L    m
Line 2,885: Line 2,792:
0 ,.25                                              :              :,.        J, 3            g                                                  h; in l    ;                      .,
0 ,.25                                              :              :,.        J, 3            g                                                  h; in l    ;                      .,
_              1.00 j      ,,l
_              1.00 j      ,,l
                                                                                                                 .I 0.75
                                                                                                                 .I 0.75 y'      .
                                                                                    ;
y'      .
;
                                                       \
                                                       \
f,I                        ~
f,I                        ~
Line 2,926: Line 2,830:
i                        A                        -
i                        A                        -
3
3
;                                .
                                   .        ))                ./                            %%y a
                                   .        ))                ./                            %%y a
0.2 - p    x 7y J Ly bN J                                                                              %%
0.2 - p    x 7y J Ly bN J                                                                              %%
Line 2,932: Line 2,835:
* G-50% FROM SHAME
* G-50% FROM SHAME
       =
       =
      ;
FIGURE 5-23 3                                                                        COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS j                                                                          HORIZONTAL RESPONSE SPECTRUM AT SPRINGLINE BEAVER VALLEY POWER STATION-UNIT l
FIGURE 5-23 3                                                                        COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS j                                                                          HORIZONTAL RESPONSE SPECTRUM AT SPRINGLINE BEAVER VALLEY POWER STATION-UNIT l


Line 3,014: Line 2,916:
  -m              7          14.952        0.0669                                  0.0207                              0.0207 8      -
  -m              7          14.952        0.0669                                  0.0207                              0.0207 8      -
18.873        0.0530                                  0.02703                            0.02703 9          22.013        0.0454                                  0.0279                              0.0279  Vertical
18.873        0.0530                                  0.02703                            0.02703 9          22.013        0.0454                                  0.0279                              0.0279  Vertical
',              10          22.293        0.0448                                  0.0213                              0.0213
',              10          22.293        0.0448                                  0.0213                              0.0213 11          26.015        0.03844                                0.0207                              0.0207 12          26.749        0.03738                                0.0202                              0.0002
          ;
11          26.015        0.03844                                0.0207                              0.0207 12          26.749        0.03738                                0.0202                              0.0002
~
~
13          30.226        0.0331                                  0.0249                              0.0249  Vertical 14          31.037        0.0322                                  0.0200                              0.0200 15          34.511        0.0289                                  0.0206                              0.0206
13          30.226        0.0331                                  0.0249                              0.0249  Vertical 14          31.037        0.0322                                  0.0200                              0.0200 15          34.511        0.0289                                  0.0206                              0.0206
Line 3,203: Line 3,103:
;              The. resulting family of ARS at the operating ficar are enveloped by the DBE spectrum, demonstrating that the effects of the DBE are not exceeded by those of smaller earthquakes (Figure 8-2).                                                Therefore, it can be concluded that the stresses in piping due to the DBE are not exceeded by those due to smaller I              earthquakes.
;              The. resulting family of ARS at the operating ficar are enveloped by the DBE spectrum, demonstrating that the effects of the DBE are not exceeded by those of smaller earthquakes (Figure 8-2).                                                Therefore, it can be concluded that the stresses in piping due to the DBE are not exceeded by those due to smaller I              earthquakes.
l 2253 159 i
l 2253 159 i
m
m 4            -
;
4            -
;
8 i
8 i
_a l:                                                                                              8-2 l
_a l:                                                                                              8-2 l
Line 3,220: Line 3,117:
O  .02        .04              .06  .08        .I O    .12 HOR I ZO N TA L      ACCELERATION, g's 2253 160 1
O  .02        .04              .06  .08        .I O    .12 HOR I ZO N TA L      ACCELERATION, g's 2253 160 1
2
2
;
  )                                                  FIGURE 8-1 VARIATION OF SHEAR MODULUS
  )                                                  FIGURE 8-1 VARIATION OF SHEAR MODULUS
  ,                                                  WITH GROUND ACCELERATION j                                                    BEAVER VALLEY POWER STATION-UNIT I i                                                                                          i
  ,                                                  WITH GROUND ACCELERATION j                                                    BEAVER VALLEY POWER STATION-UNIT I i                                                                                          i


    ;
1 5
1 5
2.0 i
2.0 i
1.8 1.6 l.4
1.8 1.6 l.4 O
    ;
jb Z
O jb Z
il i.2 i    e H
il i.2 i    e H
f1        ,
f1        ,
Line 3,262: Line 3,156:
                         .... . . . . . . . . . ~ O. O l G              .
                         .... . . . . . . . . . ~ O. O l G              .
3 J
3 J
      ;
  ~
  ~
FIGURE 8-2 SEISMIC AN ALYSIS OF CONTAINMENT s                                                                                      HORIZONTAL SSE HORIZONTAL RESPONSE SPECTRUM 3
FIGURE 8-2 SEISMIC AN ALYSIS OF CONTAINMENT s                                                                                      HORIZONTAL SSE HORIZONTAL RESPONSE SPECTRUM 3
Line 3,296: Line 3,189:
i
i
       ;      The use of low strain shear moduli Gmax values for soil is not appropriate in developing ARS because earthquake-induced soil strain levels are approximately J          2 orders of magnitude higher than low strain levels.
       ;      The use of low strain shear moduli Gmax values for soil is not appropriate in developing ARS because earthquake-induced soil strain levels are approximately J          2 orders of magnitude higher than low strain levels.
-;
The use of lov strain shear moduli values equal to 150 percent of the Gmax to e
The use of lov strain shear moduli values equal to 150 percent of the Gmax to e
j            serve as a basis for developing a range of values                        in the strain compatible
j            serve as a basis for developing a range of values                        in the strain compatible
Line 3,311: Line 3,203:
2253 164
2253 164
     =
     =
      ;
9-2 a
9-2 a


  ;
BEAVER VALLEY POWER STATION, UNIT 1
BEAVER VALLEY POWER STATION, UNIT 1
=
=
Line 3,332: Line 3,222:
       =
       =
calculated on the basis of the FSAR committed ground response spectra 2253 165 4
calculated on the basis of the FSAR committed ground response spectra 2253 165 4
          ;
9-3
9-3


Line 3,341: Line 3,230:
       ]
       ]
J through 5-24 using strain compatible soil properties from the last 1
J through 5-24 using strain compatible soil properties from the last 1
j            iteration of SHAKE based upon (a) the low strain shear modulus (Gmax) g
j            iteration of SHAKE based upon (a) the low strain shear modulus (Gmax) g input to SHAKE, (b) Gmax plus 50 percent input to SHAKE, and (c) Gmax J            minus 50 percent input to SHAKE show some variation in amplitude and i
        ;
input to SHAKE, (b) Gmax plus 50 percent input to SHAKE, and (c) Gmax J            minus 50 percent input to SHAKE show some variation in amplitude and i
   ]i        frequency of the maximum response, i
   ]i        frequency of the maximum response, i
h j        5. Changes in the shear modulus of the soil change the frequencies at i
h j        5. Changes in the shear modulus of the soil change the frequencies at i
   ,          which the amplification function has                                          its peaks. This  shift in i
   ,          which the amplification function has                                          its peaks. This  shift in i
)            frequency is evident in the general shapes of the response spectra i:    for different values of G. The exact frequencies                                      of the specific individual peaks are influenced by the frequency content of the artificial earthquake, so that each individual peak appears in all spectra. However,  the essential phenomenon displayed is a shift in
)            frequency is evident in the general shapes of the response spectra i:    for different values of G. The exact frequencies                                      of the specific individual peaks are influenced by the frequency content of the artificial earthquake, so that each individual peak appears in all spectra. However,  the essential phenomenon displayed is a shift in 2253 166 i
        ;
2253 166 i
         ~
         ~
9-4
9-4
Line 3,360: Line 3,245:
structure.
structure.
: 7. Spectra calculated using the three-step method, the PSAR earthquake, i
: 7. Spectra calculated using the three-step method, the PSAR earthquake, i
   -                    and the strain compatible free-field soil properties are an adequate
   -                    and the strain compatible free-field soil properties are an adequate basis for analysis of piping systems when peak broadened 225 percent.
;
            ;
basis for analysis of piping systems when peak broadened 225 percent.
b Additional conservatism was directed by the NRC in the period range
b Additional conservatism was directed by the NRC in the period range
=l                    from                    .4 see to  .55 see where amplitudes will be increased by W                                            P 20 percent in accordance with their position confirmed in a letter d                    dated May 25, 1979.
=l                    from                    .4 see to  .55 see where amplitudes will be increased by W                                            P 20 percent in accordance with their position confirmed in a letter d                    dated May 25, 1979.
        -;
9.6  APPLICATION OF SEISMIC INPUT TO PIPE STRESS ANALYSIS m
9.6  APPLICATION OF SEISMIC INPUT TO PIPE STRESS ANALYSIS m
The application of seismic input to pipe stress analysis as defined in J    Section 6 of this report is conservative and serves as an adequate basis for
The application of seismic input to pipe stress analysis as defined in J    Section 6 of this report is conservative and serves as an adequate basis for
Line 3,396: Line 3,277:
                                                                 . - - .          -~                e i
                                                                 . - - .          -~                e i
]
]
  }                                            3EAVER VALLEY POWL1 STATION, UNIT 1
  }                                            3EAVER VALLEY POWL1 STATION, UNIT 1 10.1 SHAKE 3
  ;
10.1 SHAKE 3
   ;      SHAKE is a public domain computer program developed at the University of California and described by Schnabel, Lysmer, and Seed.''' Stone & Webster has
   ;      SHAKE is a public domain computer program developed at the University of California and described by Schnabel, Lysmer, and Seed.''' Stone & Webster has
]          made a few changes in the program, principally the addition of plotter J
]          made a few changes in the program, principally the addition of plotter J
Line 3,414: Line 3,293:
b 10.1-2
b 10.1-2


      ;
E i
E i
1 3
1 3
Line 3,429: Line 3,307:
           *1                                N;wr DL              i a~o
           *1                                N;wr DL              i a~o
   ]                                                                        ,
   ]                                                                        ,
I        2      3 4  5 6  7  8  9  10 11    12 13  14 15 FREQUENCY IN CPS O NUMERICAL OUTPUT-SHAKE RUN M72532OI
I        2      3 4  5 6  7  8  9  10 11    12 13  14 15 FREQUENCY IN CPS O NUMERICAL OUTPUT-SHAKE RUN M72532OI 2253 172 i
;
2253 172 i
    -;
=
=
_                                              FIGURE 10.1-1 AMPLIFICATION FUNCTION OF SOIL
_                                              FIGURE 10.1-1 AMPLIFICATION FUNCTION OF SOIL
Line 3,438: Line 3,313:
  =-
  =-


    ;
2 LAYER i                  n 2
2 LAYER i                  n 2
3
3
Line 3,485: Line 3,359:
e d
e d
5
5
    ;


3EAVER VAUEY PO'JER STATION, UNIT 1 Tor purposes of comparison, the results of PLAXLY and those of a similar program in the public domain, TLUSH (CDC Version 2.2),                are shown in
3EAVER VAUEY PO'JER STATION, UNIT 1 Tor purposes of comparison, the results of PLAXLY and those of a similar program in the public domain, TLUSH (CDC Version 2.2),                are shown in
Line 3,493: Line 3,366:


i Ja L
i Ja L
    ;
O.7  -
O.7  -
PLAXLY
PLAXLY
Line 3,514: Line 3,386:
a
a
                                     ,    ,        ,                          ,    ,                        e o
                                     ,    ,        ,                          ,    ,                        e o
                                                               ,      ,                                i        i
                                                               ,      ,                                i        i 0.8  0.9
                                                                                                                      ;
0.8  0.9
         ~
         ~
O            O.1 0.2      0.3          0.4    0.5    0.6  0.7                            1.0 PERIOD (SECONDS) 1 j  _
O            O.1 0.2      0.3          0.4    0.5    0.6  0.7                            1.0 PERIOD (SECONDS) 1 j  _
Line 3,527: Line 3,397:
COMPUTE FOURIER TRANSFORM i
COMPUTE FOURIER TRANSFORM i
( PRIMARY NONLINEARITY                                              :
( PRIMARY NONLINEARITY                                              :
YES
YES COMPUTE 1-D AMPLIFICATION
      ;                              ,  ,
COMPUTE 1-D AMPLIFICATION
         ,                (DECONVOLUTION)
         ,                (DECONVOLUTION)
COMPUTE 1-D SHEAR STRAIN
COMPUTE 1-D SHEAR STRAIN
                                         , r                                                  3 r
                                         , r                                                  3 r
      ;
         ,                                                                    2253 177 i
         ,                                                                    2253 177 i
4 i.
4 i.
3 FIGURE 10.2-2 (SH.10F 3)
3 FIGURE 10.2-2 (SH.10F 3)
                                         'PLAXLY' FLOW DIAGRAM BEAVER VALLEY POWER STATION - UNIT 1
                                         'PLAXLY' FLOW DIAGRAM BEAVER VALLEY POWER STATION - UNIT 1
  ;


                                                                                         - . ~ ~ _            .      .._m ,
                                                                                         - . ~ ~ _            .      .._m ,
Line 3,587: Line 3,453:
A
A


        ;
3EAVER VALLEY p0WER STATION, UNIT 1 N
3EAVER VALLEY p0WER STATION, UNIT 1 N
10.3 RETUND AND EMBED 1
10.3 RETUND AND EMBED 1
-; .
The computer program RETUND is used for computation of the dynamic stiffness functions (impedance functions) of a rigid, massless, rectangular plate velded to the surface of a viscoelastle, layered stratum. The subgrade stiffness
The computer program RETUND is used for computation of the dynamic stiffness functions (impedance functions) of a rigid, massless, rectangular plate velded to the surface of a viscoelastle, layered stratum. The subgrade stiffness
  ]
  ]
matrix is evaluated for all six degrees of freedom for the range of l            frequencies specified by the user. Embedment effects are applied subsequently J                                                                              __.
matrix is evaluated for all six degrees of freedom for the range of l            frequencies specified by the user. Embedment effects are applied subsequently J                                                                              __.
by the program EMBED.
by the program EMBED.
   --1
   --1 a
        ;
The program reads the topology and material properties, assembles the subgrade
a The program reads the topology and material properties, assembles the subgrade
_          flexibility matrix, and determines the foundation impedances by inversion.
_          flexibility matrix, and determines the foundation impedances by inversion.
         =
         =
Line 3,650: Line 3,513:
J I
J I
J 2253 183 j
J 2253 183 j
        ;
i FIGURE 10.3-1 LUC 0'S TWO-LAYER PROBLEM j
i FIGURE 10.3-1 LUC 0'S TWO-LAYER PROBLEM j
BEAVER VALLEY POWER STATION - UNIT 1 1
BEAVER VALLEY POWER STATION - UNIT 1 1
      ;


_ ~ _ .  . . _ . . . . _ . . . .. .
_ ~ _ .  . . _ . . . . _ . . . .. .
Line 3,686: Line 3,547:


=.                      .-
=.                      .-
        ;
d J
d J
k
k
Line 3,721: Line 3,581:
l                                                                                FIGURE 10.3-4 J                                                                                      HORIZONTAL STIFFNESS COMPARIS0N -
l                                                                                FIGURE 10.3-4 J                                                                                      HORIZONTAL STIFFNESS COMPARIS0N -
:                                                                                      REAL PART BEAVER VALLEY POWER STATION - UNIT 1
:                                                                                      REAL PART BEAVER VALLEY POWER STATION - UNIT 1
          ;
?
?
J
J
Line 3,766: Line 3,625:
l o.2
l o.2
                   )
                   )
o f
o f O      1  2  3  4    5    6    7    8      c, 2253 189 FIGURE 10.3-7 VERTICAL STIFFNESS COMPARISON -
                                                                  ;
O      1  2  3  4    5    6    7    8      c, 2253 189 FIGURE 10.3-7 VERTICAL STIFFNESS COMPARISON -
IMAGINARY PART BEAVER VALLEY POWER STATION - UNIT 1
IMAGINARY PART BEAVER VALLEY POWER STATION - UNIT 1


Line 3,794: Line 3,651:
u
u
   $                                                    READ FOUNDATION GEOMETRY                                    _
   $                                                    READ FOUNDATION GEOMETRY                                    _
.;                                                                          '
READ REFUND OUTPUT                                  _. _
READ REFUND OUTPUT                                  _. _
_                                                            STIFFNESSES e
_                                                            STIFFNESSES e
Line 3,803: Line 3,659:
c                    -
c                    -
u OUTPUT (PRINT / PUNCH)
u OUTPUT (PRINT / PUNCH)
'.i
'.i v
  ;                                                                                                              -
i_
v i_
END i
END i
L_
L_
Line 3,811: Line 3,666:
   ~
   ~
                                                                             ' REFUND' AND ' EMBED' FLOW DIAGRAMS BEAVER VALLEY POWER STATION - UNIT 1 j
                                                                             ' REFUND' AND ' EMBED' FLOW DIAGRAMS BEAVER VALLEY POWER STATION - UNIT 1 j
;
                                                                                                                                     =
                                                                                                                                     =
i
i
Line 3,833: Line 3,687:
Us)
Us)
                             $=C(Us E 2253 192
                             $=C(Us E 2253 192
    ;
?
?
w                                                                        10.4-1 i
w                                                                        10.4-1 i
Line 4,081: Line 3,934:


7 -__ . p__ . 7_ _                                              -7 *---)      ,  y        ,    - -- ) i l
7 -__ . p__ . 7_ _                                              -7 *---)      ,  y        ,    - -- ) i l
l                      l
l                      l TABLE 2                              '
                                                                                                                                          ;
TABLE 2                              '
                                               .              IN-SITU VEIDCITY MEASUREMENTS i
                                               .              IN-SITU VEIDCITY MEASUREMENTS i
i apu          mgu Have          Wave                                          Shear                Young's              Bulk            -
i apu          mgu Have          Wave                                          Shear                Young's              Bulk            -

Revision as of 05:32, 22 February 2020

Soil-Structure Interaction in Development of Amplified Response Spectra.
ML19269D833
Person / Time
Site: Beaver Valley
Issue date: 06/11/1979
From:
STONE & WEBSTER, INC.
To:
Shared Package
ML19269D832 List:
References
NUDOCS 7906200158
Download: ML19269D833 (203)
v • d • e


Text

{{#Wiki_filter:_ . _ _ 

;                                            BEAVER VALLEY POWER STATION, UNIT 1 7

j TABLE OF CONTENTS 21 g Section Title 23.gg j

1.0 INTRODUCTION

.           . . .. .. . . . . . . . . . . . . . . . . . . . .                                               1-1 m

j 2.0 SOIL PROPERTIES. . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 2.1 SuBSURrACE DATA. ... .. . . . . . . . . . . . . . . . . . . . . 2-1 9 2.2 SOIL PROFILES. . ... .. . . . . . . . . . . . . . . . . . . . . 2-2 d ll 2.3 SOIL PARAMETERS. ... ... . . . . . . . . . . . . . . . . . . . 2-2 _m_ 2.4 MODULUS AND DAMPING PROFILES . . . . . . . . . . . . . . . . . . . 2-7 

 ;;          2.4.1    Small Strain Modulus and Damping . . . .                       . . . . . . . . . . . .                                2-8 2.4.2    Strain Dependent Modulus and Damping .                         . . . . .                             . . . . . . . 2-8 2.5

SUMMARY

ON SOIL PROPERTIES . . . . . . . . . . . . . . . . . . . . 2-16

2.6 REFERENCES

. . . .... . . . . . . . . . . . . . . . . . . . . .                                                          2-18
-            3.0   EARTHQUAKE GROUND MOTION .                . . . . . . . . . . . . . . . . . . . .                                        3-1 7          3.1   DESIGN BASIS EARTHQUAKE (DBE) AND OPERATING BASIS

_j EARTHQUAKE (OBE) ' 

                                               .... . . . . . . . . . . . . . . . . . . . . .                                               3-1 3.2 GROUND RESPONSE SPECTRA.                 . . . . . . . . . . . . . . . . . . . . .                                         3-2

= 3.3 ARTIFICIAL TIME HISTORY. . . . . . . . . . . . . . . . . . . . . 3-2 3.4 GROUND RESPONSE SPECTRA AT BASE Cl CONTAINMENT . . . . . . . . . . 3-3

3.5 REFERENCES

.             . . .. . . . . . . . . . . . . . . . . . . . . . . .                                              3-4 a

4.0 AMPLIFIED RESPONSE ANALYSIS. . . . . . . . . . . . . . . . . . . . 4-1 

       =

4.1 DESCRIPTION

OF THREE-STEP ANALYSIS . . . . . . . . . . . . . . . . 4-2 m 4.1.1 Frequency-Dependent Soil Stiffness . . . . . . . . . . . . . . . 4-1 4.1.2 Embedment Correction . . . . . . . . . . . . . . . . . . . . . . 4-7 4.1.3 Kinematic Interaction. . . . . . . . . . . . . . . . . . . . . . 4-8 = 

  --         4.1.4    Interaction Analysis . . . . . . . . . . . . . . . . . . . . . .                                                      4-10 4.2    STRUCTURAL MODELING.             . .. . . . . . . . . . . . . . . . . . . . .                                           4-15 4.3   RESULTS.    . . . . ... .. . . . . . . . . . . . . . . . . . . . .                                                       4-17 2

4.4 REFERENCES

.           . . . . . . . . . . . . . . . . . . . . . . . . . . .                                             4-18
    -a 7906200158 i

2253 009 O 

 =

BEAVER VALLEY POWER STATION, UNIT 1 TABLE OF CONTENTS (Cont) 

       ;   Section         Title                                                                                         E.a.gg 5.0  COMPARISON OF RESULTS.        . . . . . . . . . . . . . . . . .                            . . . .       5-1 1

5.1 REFUND / FRIDAY VS PLAXLY. . . . . . . . . . . . . . . . . . . . . . 5-1 5.2 FSAR EARTHQUAKE VS REGULATORY GUIDE 1.60 EARTHQUAKE. . . . . . . . 5-2 i j 5.3 VARIATION OF SOIL PROPERTIES . . . . . . . . . . . . . . . . . . . 5-3 1 6.0 APPLICATION OF SEISMIC INPUT TO PIPE STRESS ANALYSIS . . . . . . . 6-1 i 

  ~

6.1 AMPLIFIED RESPONSE SPECTRA . . . . . . . . . . . . . . . . . . . . 6-1 6.2 BUILDING DISPLACEMENTS . . . . . . . . . . . . . . . . . . . . . . 6-2 7.0 SOIL STRUCTURE INTERACTION ANALYSIS IN l THE ORIGINAL DESIGN. . . . . . . . . . . . . . . . . . . . . . . . 7-1 4 8.0 INVESTIGATION OF THE EFFECTS OF EARTHQUAKES SMALLER THAN THE DBE . . . . . . . . . . . . . . . . . . . . . . . . 

                                                                                              . .                      . 8-1
        =

9.0 CONCLUSION

S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1 8 9.1 USE OF SOIL-STRUCTURE INTERACTION. . . . . . . . . . . . . . . . . 9-1 = 9.2 SOIL PROPERTIES. . . .. . . . . . . . . . . . . . . . . . . . . . 9-1 9.3 GROUND RESPONSE. . . . . . . . . . . . . . . . . . . . . . . . . . 9-2 

     =     9.4   AMPLIFIED RESPONSE ANALYSIS.           . . . . . . . . . . . . . . . . . .                            . 9-2
 ~

9.5 COMPARISON OF RESULTS. . . . . . . .. . . . . . . . . . . . . . 9-3 m 9.6 APPLICATION OF SEISMIC INPUT TO PIPE STRESS ANALYSIS . . . . . . . 9-5 s 9.7 SOIL-STRUCTURE INTERACTION ANALYSIS. . . . . . . . . . . . . . . . 9-6 -j 9.8 EFFECTS OF EARTHQUAKES SMALLER THAN THE DBE. . . . . . . . . . . . 9-6 7 i 9.9 COMPUTER PROGRAM VERIFICATION. . . . . . . . . . . . . . . . . . . 9-6 E. 10.0 APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1-1 1 10.1 SHAKE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1-1 

 =

10.2 PLAXLY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2-1 10.3 REFUND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3-1 = it 22S3 010

BEAVER VALLEY POWER STATION, UNIT 1 TABLE OF CONTENTS (Cont) Section h Eagg 10.4 KINACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4-1 10.5 FRIDAY. .... . . . . . . . . . . . . . . . . . . . . . . . . 10.5-1 10.6 IN SITU SEISMIC VELOCITY MEASUREMENTS . . . . . . . . . . . . . . 10.6-1 2253 011 iii

BEAVER VALLEY POWER STATION, UNIT 1 LIST OF TABLES Table Title 2-1 Strain Compatible Poisson's Ratios - Tree Field - Elevation 735 2-2 Strain Compatible Soil Properties - Free Field - Elevation 735

2. Strain Compatible Soil Properties - Reactor Building 2-4 Strain Compatible Soil Properties - Safeguard Building 2-5 Strain Compatible Soil Properties - Auxiliary Building 2-6 Strain Compatible Soil Properties - Service Building 2-7 Strain Compatible Soil Properties - Cable Vault (Main Steam Building) 2-8  ::: rain Compatible Soil Properties - Diesel Generator Building 2-9 Strain Compatible Soil Properties - Tuel Building I 2-10 Strain Compatible Soil Properties - Tree Field - Elevation 645 (North of Intake Structure)

I 2-11 Strain Compatible Soil Properties - Free Field - Elevation 675 (South of Intake Structure) 2-12 Strain Compatible Soil Properties - Main Intake Structure 2-13 Strain Compatible soil Properties - DBE (Gmax plus 50%) - Free Field 

       - Elevation 735 2-14  Strain Compatible Soil Properties - DBE (Gmax minus 50%) - Free Field Elevation 735 2-15  Strain Compatible Soil Properties - DBE (Gmax plus 50%) - Reactor Building 2-16  Strain Compatible Soil Properties - DBE (Gmax minus 50%) - Reactor Building I 7-1   Modal Damping Ratios Used in the Time History Analysis Using Soil Spring Stiffness I                                                       2253 012 I                                     iv I

i J BEAVER VALLEY F0WER STATION, UNIT 1 j LIST OF FIGURES = Firure Title a 2-1 3cring Location Plan Category 1 Area 

  ;      2-2    East-West Soil Profile - Section 1-1 2-3    North-South Soil Profile - Section 2-2 2-4    Measured and Computed Values of Shear Wave Velocity i

2-5 Properties Used for Whitman's Analysis j 2-6 Free Field Soil Profile a 2-7 Reactor Building Soil Profile 2-8 Safeguard Building Soil Profile 2-9 Auxiliary Building Soil Profile 2-10 Service Building Soil Profile 2-11 Cable Vault Soil Profile 2-12 Diesel Generator Building Soil Frofile 2-13 Fuel Building Soil Profile s 2-14 Free Field Soil Profile - Soeth of Intake Structure 2-15 Tree Field Soil Profile - North of Intake Structure 2-16 Intake Structure Soil Profile r = 3-1 Response Spectra 0.125 G DBE 

    ^
 ~

3 3-2 Response Spectra 0.06 G OBE-L 3-3 Response Spectra Artificial Earthquake - 2 Percent Damping r- 

     =

3-4 Ground Response Spectra Average Gmax __ 3-5 Ground Response Spectra Average Gma:: +50 Percent 

  ]       3-6   Group Response Spectra Average Gmax -50 Percent a

v 2253 013 m

BEAVER VALLEY POWER STATION, UNIT 1 LIST OF FIGURES (Cont) Firure Title 4-1 The Three-Step Sclution 4-2 The 3oussinesq and Cerruti Problems 4-3 Idealization of the Basic REFUND Solution for Concentrated Loads I 4-4 REFUND Coordinate System 4-5 Kinematic Interaction 4-6 Generali:ed Dynamic Model of a Category 1 Structure 4-7 Seismic Analysis of Main Steam Valve Building Horizontal SSE EW Horizontal Response Spectrum at Mat 4-8 Seism!.c Analysis of Main Steam Valve Building Horizontal SSE EW Hori: ental Response Spectrum at Top I 4-9 Seismic Analysis of Main Steam Valve Building Horizontal NS Hori: ental Response Spectrum at Mat 4-10 Seismic of Main Steam Valve Building Horizontal NS I Analysis Horizontal Response Spectrum at Top 4-11 Typical Acceleration Profiles I 4-12 Typical Displacement Profiles I 5-1 Comparison of REFUND / FRIDAY and PLAXLY - AF.S at Mat 5-2 Comparison of REFUND / FRIDAY and PLAXLY - ARS at Operating Floor 5-3 Comparison of REFUND / FRIDAY and PLAXLY - ARS at Springline 5-4 Comparison of the FSAR and Regulatory Guide 1.60 Earthquakes - ARS at the Mat I 5-5 Comparison of FSAR and Regulatory Guide 1.60 Earthquakes - ARS at Operating Floor 5-6 Comparison of FSAR and Regulatory Guide 1.60 - ARS at Springline 5-7 Comparison of ARS for Soil Parameter Variations - Hori: ental Response Spe_: m at Mat - Damp : 0. 50:: 2253 014 g I

BEAVER VALLEY PCUEP. STATION, UNIT 1 LIST OF FIGURES (Cont) I Finure 5-8 Title Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Mat - Damp = 1.0 : 5-9 Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Mat - Damp : 3.0% 5-10 Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Operating Floor - Damp : 0.5% 5-11 Comparison of ARS for soil Parameter Variations - Horizontal Response Spectrum at Operating Floor - Damp = 1.0% 5-12 Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Operating Floor - Damp : 3.0% I 5-13 Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Springline - Damp : 0.5% 5-14 Comparfson of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Springline - Damp : 1.0% 5-15 Comparison of ARS for Soil Parameter Variations - Horizontal Response I 5-16 Spectrum at Springline - Damp : 3.0% Comparison of ARS for Soil Parameter Variations - Hori: ental Response Spectrum at Mat - Damp = 0.5% 5-17 Comparison of ARS for Soil Parameter Variations - Hori: ental Response Spectrum at Mat - Damp : 1.0% , 5-13 Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Mat - Damp = 3.0% 5-19 Co=parisor. of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Operating Floor - Damp : 0.5% 5-20 Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Operating Floor - Damp : 1.0% 5-21 Comparison of ARS for Soil Parameter Variations - Horizontal Response Spectrum at Operating Floor - Damp : 3.0% 5-22 Comparison of ARS for Soil Paramet.'r Variations - Horizontal Response Spectrum at Springline - Damp 0.5% 5-23 Comparison of ARS for Soil Parameter Variations - Horizontal F.esponse Spectrum at Springline - Damp : 1.0% g ,11 2253 015 I .

BEAVER VALLfY POWER STATIO!i, U!iIT 1 LIST OF FIGURES (Cont) Figure Title 5-24 Comparison of ARS for Soil Parameter Variations Horizontal Response Spectrum at SprinSline - Damp = 3.0% 7-1 Comparison of ARS at the Operating Floor by Time History, Method 7-2 Comparison of ARS at the Springline by Time History Method 8-1 Variation of Shear Modulus with Ground Acceleration I 8-? Seismic Analysis of Centainment Horizontal SSE, Horizontal Response Spectrum at Operating Floor 10.1-1 Amplification Function of Soil 10.1-2 Soils Profile 10.2-1 Comparisen of ARS by PLAXLY and FLUSH at Operating Floor 10.2-2 PLAXLY Tiov Diagram 10.3-1 Luco's Two-Layer Problem 10.3-2 Rccking Stiffness Comparison - Real Part I 10.3-3 Rocking Stiffness Comparison - Imag.inary Part 10.3-4 ~ Horizontal Stiffness Comparison - Real Part 10.3-5 Horizontal Stiffness Comparison - Imaginary Part 10.3-6 Vertu al Stiffness Comparison - Real Part , 10.3-7 Vertical Stiffness Comparison - Imaginary Part 10.3-8 REFU:iD and EM3ED Flow Diagrams I 10.4-1 Translational Response Spectra at 3ase of Rigid, Massless Foundation 10.4-2 Rotational Response Spectrum at Base of Rigid, Massless Foundation 10.4-3 KI!!ACT Flow Diagram I viii 2253 016

BEAVER VALLEY F0WER STATION, UNIT 1 LIST OF FIGURES (Cont) ricure Title 10.5-1 Comparisen of FRIDAY AND STARDYNE - ARS at the Roof 1,0. 5 -2 STARDYNE Model I 10.5-3 FRIDAY Flow Diagram I 2253 017 I I I I I I ix 

                                                                                                  '                                                                                               '*              'x
             - ~
                     's.            .

8i . _ _ . . . - . . . - _ . 

                                                                                                    ._.,-._,_,....__.._.........x....,_.._..
                                                                                                                                                          . .__ _ . _ _ _ . . _ __ _ . _ . .. _ . ..._...m_

C W O *e O C 

   ,!                                                                                                                                                                                                                            0 :

t

  • i il t

4 09 -s l-2253 018 

                                                                                                                                                                                                                                                 \
                                                                                                                                                                                                                                      .s
    • p. w s

e E u 'h 

  .g g                                                                                                                                                                                                                                               m
                                                                                                                                                                                                                                      " '      t A

b 9 _ _ _ _ _ _ . = _ _ . . _ ,.' . _ . . _ . . . . . _ _ _ _ _ . _ _ . _ . _ _ . . . . 78 4 . ', " Ki- a e-

BEAVER VALLEY POWER STATION, UNIT 1

1.0 INTRODUCTION

On March 13, 1979 the Nuclear Regulatory Commission (NRC) issued an Order to Show Cause to the Duquesne Light Company. The order required shutdown of the Beaver Valley Power Station Unit I within 48 hours after receipt of the order. The order required all piping systems originally seismically analyzed using algebraic summation of intramodal responses to be reanalyzed using methodology currently acceptable to the NRC staff. In carrying out this reanalysis, I amplified response spectra, deve&oped using soil-structure interaction (SSI) techniques, have been used. Soil-structure interaction has been the subject of much dialogue between the Staff, DLC, and Stone & Webster since the Order, the fundamental purpose of which was to agree on the details of the SSI methodology for use in developing I suitable amplified response spectra and subsequent pipe stress analysis. Over the course of numerous discussions, the NRC staff asked for documentation in a number of areas, and it is the purpose of this report to reply in detail to the NRC staff's requests. I This report describes the basis for performing soil-structure interaction analyses to develop amplified response spectra for use in reevaluating the I 2253 019 l-1 I

BEAVER VALLEY POWER STATION, UNIT 1 I

1.0 INTRODUCTION

I On March 13, 1979 the Nuclear Regulatory Commission (NRC) issued an Order to Show Cause to the Duquesne Light Company. The order required shutdown of the Beaver Valley Power Station Unit 1 within 48 hours after receipt of the order. I The order required all piping systems originally seismically analyzed using algebraic summation of intramodal responses to be reanalyzed using methodology currently acceptable to the NRC staff. In carrying out this reanalysis, amplified asponse spectra, developed using soil-structure interaction (SSI) techniques, have been used. I Soil-structure interaction has been the subject of much dialogue between the Staff, DLC, and Stone & Webster since the Order, the fundamental purpose of which was to agree on the details of the SSI methodology for use in developing suitable anp11fied response spectra and subsequent pipe stress analysis. I Over the course of numerous discussions, the NRC staff asked for documentation in a number of areas, and it is the purpose of this report to reply in detail to the NRC staff's requests. I This report describes the basis for performing soil-structure interaction analyses to develop amplified response spectra for use in reevaluating the I 2253 020 I .

BEAVER VALLEY POWER STATION, UNIT 1 I pipe stress and support loads. The soil properties are developed from subsurface data into a soil profile, in which each stratum has its own soil parameters. The required dynamic properties in each layer are described first by the small strain values of shear modulus, and then site response analysis I is used to develop values of damping and shear modulus that are compatible with the strains to be expected during an earthe.uake. The design basis earthqt!ake (DBE) and the operating basis earthquake (OBE) are described by ground response spectra and by artificial time histories that give response spectra enveloping the ground response spectra. The analysis of soil-I structure interaction is performed by tuo methods: a one-step, finite element method, and a three-step, analytically based method. The report describes how these methods, including the structural representation, are derived and how they are used in the present case. I Results for different methods and for different input are compared, and their application to pipe stress analysis is discussed. The results show that the three-step (REFUND /TRIDAY) method gives conservative results that are consistent with the present state-of-the-art of soil-structure interaction. 

                                             ~

g . 2253 021 I I I I 

                                                                               ~
                                                                                                  *                                            ~

y  %= = -

. - __ . -_ ?, ' ?. ;- . .b ,
u. j

___e_ w _ _ . . _ _ , _ _ _ _ _ _ __ _ , _ _ _ 4 _ _,g g,, fe i 

                                                                                                                                                                                       /

r f g _ o i= 30 

                                                                                                                                                 ,                            9 ^
                                                                                                                                                                              -s               .

T 1, ph 

                                                                                                                                                                                   ;e *.
                                                                                                                                                                                   .q
    .                                                                                                                                                                              al,
        .                                                                                            2253 022                                                                      ,

T 1 h A et 9 I i 1 

                                                                                                                                                                                        +

3 4 I e 'N ' " 5 _t - e,y , . y > 8 ' 

                                                                                                                              ,,                 g

i BEAVER VALLEY POWER STATION, UNIT 1 a l _} 2.0 SOIL PROPERTIES The soil properties developed for use in the soil-structure interaction analyses are presented in this section of the report. The computer program SHAKE developed by Schnabel, Lysmer, and Seed8 and discussed in Section 10.1 a was used to calculate strain compatible shear moduli and damping from low g strain values determined from field testing and empirical formulae based on laboratory test data. Although most of the data are included in reports previously submitted to the NRC for completeness, the data are summarized =,, below. 2.1 SUBSURFACE DATA 3 Subsurface information was obtained from several sources, which include the Beaver Valley Power Station (BVPS) Unit 1 FSAR,'28 the Geotechnical Design j Criteria for Unit 2,585 and the report on the Soil Densification Program for h Unit 2. The pre-construction borings under the Category 1 structures aro l located as shown in Figure 2-1. The logs for these borings are included in 

 ]      Appendix 2r of the Unit 1 FSAR. Two seismic cross-hole surveys were performed by Weston Geophysical Laboratory, the first in 1968 and the second in 1977, in j        conjunction with the Unit 2 Soil Densification Program.                        The     1977 report

] summarizing both cross-hole surveys is included as Appendix 10.6 of this i report. 3 

    ,                                                                          2253 023 j                                                        2-1 h

_l

A' BEAVER VALLEY POWER STATION, UNIT 1 m 4 j 2.2 SOIL PROFILES The soil beneath the plant consists of medium to dense sand and gravels that = extend from the shale bedrock at El. 620 to plant grade at El. 735. The + interbedded sands and gravels are alluvial deposits that occur as terraces d along the Ohio River Valley. The terraces are the result of cyclic 

 ,            aggradation and degradation of local materials and glacial outwash by the Ohio
 ~

River drainage system during the Pleistocene Epoch. Normal groundwater at the 

          ~

site is at El. 665 and closely reflects the pool elevation of the Ohio River. The groundwater elevation chosen for analysis is El. 675, some 10 feet higher 

       ;      than normal.      Figures 2-2 and 2-3 show two typical soil profiles through the site area. Figure 2-2 is an east-west profile encompassing Borings 114,                                            104,
 -]

103, 115, and 116; Figure 2-3 is a north-south profile emcompassing Borings 102, 115 and 101. Included on the profiles are the Standard 

  =

Penetration Test (SPT) blow counts (N) and Unified Soil Classification System 4 (USCS) symbols for each sample, s J E- 2.3 SOIL PARAMETERS h (_ The soil underlying BVPS is granular. From the surveys and field 

,j             investigations mentioned above, various soil parameters have been calculated.

USCS classifications and SPT blow counts are presented on each boring log in i Appendix 2F of the Unit 1 FSAR. Values of void ratio (e), specific gravity 7 [[ 2253 024 2-2 m s

i k BEAVER VALLEY POWER STATION, UNIT 1 (SG), and in-situ dry densities (yd) are those presented for in situ soil in 

     ;      the Beaver Valley Unit 2 Geotechnical Design Criteria.'s* Values of yd and e

~ i vere calculated from the results of in situ soil testing performed during l e Unit I construction. These values are: n. y yd = 117 PCF 

                       ~

_ e = 0.40 4 SG = 2.65 .= To calculate the values of total density (yy above the water table an average a water content (W n) of 6.5 percent was assumed. 1 i 

  ;                      1+W yT *         (SG) yw = 126 PT 1+e J

I Below the water table, 100 percent saturation (S) was assumed giving 2 i SG + (s/100)e w = 136 PCF YT" 1 +e q A 

        =

j Values of shear wave velocity (V s) and compression wave velocity (Vp ) for low !;? strain were based on the 1977 Weston Geophysical Laboratory Survey (Appendix 10.6, Table I). 's- 

      !                                                                  2253 025

'M 2-3 2 

       =---                                                                 - - - . . - . . , , , - . - . - . , , , , . . .

Y b BEAVER VALLEY POWER STATION, UNIT 1 3 b ) Values of Poisson's ratio (U) were calculated both above and below the water table based on the relationship between V and V p. ] s e Above the water table, an average Vs = 800 fps and an average Vp = 2,500 fps _a were used. 3 

  ,                since:

1 - 2r 

      .                  V=

2 - 2r where i l sO p then '= 

   ~

f s y = 0.44 i Values of dynamic Poisson's ratio below the water table for both the Operating i j Basis Earthquake (OBE) and Design Basis Earthquake (DBE) were calculated using 4 the free-field strain compatible shear modulus (Gave) determined from the 2 3 

      ^

2253 026 i j 2-4 

                                                                        -....i

BEAVER VALLEY POWER STATION, UNIT 1 , SHAKE analyses discussed in the next section and the shear modulus values (Gmax) as determined from Weston's cross hole surveys. For the DBE: i G  : ,000 KSF ave m and V = fps a where p 0.136/32.2 Kip-Sec/ft" 

   , giving V = 843 fps Below the water table, the strain compatibiu compression wave velocity (V )p was calculated as either the compressional wave velocity of water m

2253 027 2-5

I BEAVER VALLEY POWER STATION, UNIT 1 I V : 5.000 fps I or as V =V (Gave)**' P p (Gmax) I where , i V 6400 fps (from Weston's report) p If the value of V calculated from Gave, Gmax and V was less than 5,000 fps, p p the compressional wave velocity of water was used. I Therefore for the DBE: I r = (V s'Yp )2 = 0.028 2253 028 I V, = 5, - ,,s ane u-4: 2;-o.4, y 2-6 i

e BEAVER VALLEY POWER STATION, UNIT 1 -a =_A_ e 5 Table 2-1 presents the strain co=patible Poisson's ratio for each layer for Gmax, Gmax plus 50 percent and Gmax minus 50 percent. 1 i Analyses have shown that there is an adequate factor of safety agair.st 

    'J liquefaction of the granular materials beneath the site.                                  The results of the liquefaction analyses are eresented in reports previously submitted to the NRC.,6,F' J
'?       2.4 MODULUS AND DAMPING PROPILES Soil profiles were developed for the free-field and under each Category 1 s      structure. These profiles, presented in Tables 2-2 through 2-16, are based on the soil profiles discussed in Section 2.2.                       Small strain values of modulus
^

and damping were developed from cross-hole seismic surveys conducted at both 

~~

i Units 1 and 2. Additional analyses were conducted at Gmax values of plus and 

   }     minus   (t) 50 percent.                     The results of these studies are discussed in
                                                                                                            ~

Section 2.4.3. 2253 029 E + .=- d 2-7

BEAVER VALLEY POWER STATION, UNIT 1 ) 4 3 2.4.1 Small Strain Modulus and Damping The values of small strain shear modulus and damping were based on the results of the Weston Geophysical's Survey (Appendix 10.6). The results of the study were analyzed by Dr. R.V. Whitman and his recommendations are included in his j report in Appendix 2D to the TSAR. In summary, Dr. Whitman compared the 

   =

results of the Westen survey with values of V, calculated using the Hardin and Blacki relationship. As can be seen in Figure 2-4, the results from both a 

    )  methods agree closely.       The shear wave velocity profile for small strain values used in the present free-field SHAKE analysis is                  shown in Figure 2-6 i

j and is basically the same as that presented by Whitman in the curve on Tigure 2-5. k 2.4.2 Strain Dependent Modulus and Damping m j The calculation of strain dependent modulus and damping profiles is discussed 

   =    in detail in tr.e following sections.
   )    2.4.2.1   Summary of SHAKE Analysis
   's

") The computer program SHAKEt was used to obtain values of shear nodulus and damping at strain levels compatible with those induced during the DBE and OBE. The time histories from the El Centro 1940 (North-South component) and Kern 

   ]                                                                            2253 030

_, 2-8 _= e

J BEAVER VALLEY POWER STATION, UNIT 1 1 County (Taft 569E) earthquakes were normalized to a peak acceleration of .125g g and .06g for the DBE and OBE, respectively. These motions were input at the 

     ~i ground surface (El 735 feet) and deconvolved in the free field down to bedrock through the soil profile in Figure 2-6.                The deconvolved time history was then amplified up through the soil profile to the base of                         the structure.

3 Iterations of shear modulus and damping with strain were performed internally f; by SHAKI in both the free field and under the structures. The values obtained from the final iteration were tabulated for each layer in the soil profile, and the average valuus of shear modulus and damping using El Centro and Taft acceleregrams as input were used in soil-structure interaction calculations. a Strain compatible shear modulus and damping values for the DBE and OBE are 7 included in Tables 2-2 to 2-16. 2.4.2.2 Earthquake Accelerograms 1 

 -)          Two strong motion time-history accelerograms vere used in the SHAKE analyses
        ;     to determine strain compatible soil properties:               the 1940 El Centro earthquake (North-South component) and the 1952 Kern County earthquake (S69E component of a      -

the Taft record). The El Centro earthquake record was chosen because it is representative of the strongest motions available from deep soil sites, i 

 $           whereas Taft was chosen because of its vide frequency range and strong motion
  =

characteristics. 2 2253 031 N _=. s 2-9 M

l i~ BEAVER VALLEY POWER STATION, UNIT 1 1 7 I j The Taft S69E record, from the 1952 Kern County earthquake, has a maximum 3 acceleration of .179g at a time of 3.70 see and a mean square frequency of i 2.95 Hz. Each value of the accelerogram was multiplied by a factor of .698 to scale the record to a peak acceleration of .125g for the DBE at Beaver Valley. A similar scaling technique was used to obtain the Taft record for the OBE. 1 J Frequencies over 20 Hz vere excluded frcm the time history input at ground 

      , surface in order to allow convergence of the iterations when deconvoluting in the free field and to maintain deconvoluted time histories with mean square m

frequencies close to the original Taft record in each of the layers of the soil profile. The time history at the base layer, El 620 feet in this 

    ;   analysis, was shored for later use in amplification analyses under each of the q        structures. The peak acceleration of the Taft record at the base layer after deconvolution to El 620 feet was .059g.

i _i The 1940 El Centro earthquake, North-South record, was also used in the SHAKE F 

      ! analyses. The maximum recorded acceleration at El Centro was .349g at a time
of 2.12 sec, with a mean square frequency of 3.18 Hz. Each value of the J

acceleregram was multiplied by a factor of .358 to scale the El Centro record 

  }     to the Beaver Valley DBE. Frequencies above 20 Hz vere cut off the El Centro e

record. The peak acceleration of the El Centro record at the base layer after 

 ;      deconvolution to El 620 feet was .090g.

1 2253 032 4 _. 2-10 J 

 =i BEAVER VALLEY POWER STATION, UNIT 1 4

s 2.4.2.3 Soil Profile 4 A horizontally layered, idealized soil profile was established for the SHAKE analysis based on previous studies discussed in Section 2.2. A description of the profile and relevant soil properties for each layer are included in -1 ' j Figures 2-2 to 2-16 for the free field case and for each structure. 

 'I The structures themselves have been represented as "pseudoscils" in the SHAKE analysis. These soils are described by unit weights and shear wave volocities a

that are compatible with the structure. For the equivalent unit weight, the

total weight of the structure was divided by the volume of the pseudosoil layer. The shear wave velocity was computed using the equation for the first
    =

harmonic natural period of the structure, which is: - 

 =

a 3 j V s" = where: 

       )           Vg    equivalent shear wave velocity for structure H : thickness of pseudoscil layer T = natural period of the structure

, 2253 033 3 9 5 2-11 -N

i BEAVER VALLEY F0WER STATION, UNIT 1 i 3 2.4.2.4 Strain Dependency Relationships The variation of shear modulus with strain is input into SHAKE using the shear 1 i modulus factor K varying with strain. For Beaver Valley, K is an empirical i factor relating shear modulus to confining stress for the underlying granular 

  ;             material. The shear modulus is calculated freq the shear modulus factor K by 7           the folleving equations:

3 For sands: J G = 1000K (cielo .s y where: .i G = shear modulus in ksf i r R : shear modulus factor for sands He : effective octahedral stress in ksf J Fg : scaling factor of low strain shear modulus value h The decrease of shear modulus with increasing shear strain is presented in j terms of K to conform with the input format required in the SHAKE program. The strain dependency . relationships of K. Plotted with sh;ar strain, are presented in SW-AJA, specifically Figure 5-2. These curves are based on 5 f 4_ 2253 034 ,; 2-12 =

l - ~ BEAVER VALLEY PO'JER STATION, UNIT 1 J empirical data plotted by Seed and Idriss. The factor F is calculated internally by the program, using the small strain values of shear modulus and K input into the program. This calculated value of F is used in subsequent iterations to compute the new shear modulus based on a K vs shear strain curve that has been shifted from the empirical curve by the factor F to account for i a site conditions as defined by Gmax. The increase of damping ratio for sands with increasing shear strain is based on Figure 5-9 of the Shannon and Wilson Report.<** This curve is based on data plotted by Sesd and Idriss. The curves were modified by the use of a damping 4 correction factor, which accounts for the variability of damping with depth: s . FD = 2.53 - 0.45 log Ev i where: i FD = factor modifying damping curves j ov = vertical effective overburden stress in psf 1, 1 < e j 2253 035 

      'E-m 2-13 i   -
                                                               ----i----

I BEAVER VALLEY POWER STATION, UNIT 1 I 2.4.2.5 Strain Compatible Shear Moduli and Damping I The shear, moduli and damping values corresponding to the shear strain induced by the DBE and OBE are presented in tabular form for each structure analyzed and for the free field case in Tables 2-2 through 2-16. The results represent values obtained from the last iteration of shear moduli and damping. Criteria for convergence of iterations were established at plus or minus 5 percent of the previously iterated value. The data include strain-compatible moduli and damping ratios calculated from the two earthquake accelerograms described in Section 2.4.2.2, i.e., El Centro North-South and Taft S69E. An average value was calculated for each soil layer and used to model the soil in subsequent soil-structure interaction analyses. I 2.4.2.6 Variation of Shear Modulus The effect of increasing and decreasing the low strain shear moduli (Gmax) by 50 percent was evaluated using SHAKE. The El Centro and Taft earthquake records, normalized for the DBE, were input at the ground surface in the free field, deconvoluted to the base layer and then amplified up through the soil to the containment structure. All soil parameters other than the low strain shear moduli remained unchanged. I 2253 036 I 2-14 I

1 i BEAVER VALLEY POWER STATION, UNIT 1 l, 

    =

i J-- The strain compatible soil properties for G plus 50 percent and G minus max max 50 percent are listed on Tables 2-13 through 2-16, for the free field and I 

 =

under tha reactor containment, respectively. Poisson's ratio, calculated for these cases using small strain values and strain compatible values from the DBE and OBE, are listed on Table 2-1. Strain compatible soil properties for 

        . G      are included in Tables 2-2 and 2-3 for the free field                     'rui containment,
    =           max

-, respectively. To determine the variation of G, which is a function of the product of Gmax and G/G , it is assumed that Gmax and G/G are uncorrelated. Thus max max R _i Y 7 G *Ydmax

  • Yb/h
  • Y b Yb/ h 1

i 4

where i

k W ki V Gmax

coefficient of variation of in situ Gmax values from

,- shear wave velocities determined from cross-hole data i _i i V = coefficient of variation of G/Gmax from SW-AJA curves C/Gmax j (Figure 5-2) j 2253 037 8 I 

   ^,

__ 2-15 L__ l 

              -           r,    ,,                       , ,           ,   ,              m
                                         ,--w BEAVER VALLEY POWER STATION, UNIT 1 i

3 Vg  : coelficient Jf variation of G values at various shear st - . levels l Trom V, g the expected variation as a parcentage of the average G value for a a particular shear strain level can be estimated. This variation was 1 3 28.4 percent at low shear strains and ranged from 146.1 to 177.8 percent of 3 the average shear modulus at a shear strain level of 2 x 10-8 to 6 x 10-' percent, the range of shear strain levels generated by the DBE and OBE at m the site. Although the percentage variation of the average G value is higher j at higher shear strain levels, the actual range of moduli values is 4 g approximately the same as at low strain levels. 

        =

i 2.5

SUMMARY

ON SOIL PROPERTIES 

    =

Procedures followed to obtain soil properties for the soil-structure interaction analyses and their use in developing amplified response spectra are summarized as follows. 

       =
First, a small strain soil profile was' developed from the best available soil data, including cross hole seismic shear wave velocity measurements, as well

'l 

       !  as data from borings and samples.

2253 038 7 _= 2-16 Q

I EEAVER VALLEY POWER STATIC'J. UNIT 1 I Second, the effect of an earthquake in the free field was evaluated using the SHAKE computer program. The control motion was specified at the surface of the free field; two real records were used - El Centro and Taft - normalized to the acceleration level of the specified design earthquake (OBE or DBE). The program iterated to obtain values of shear modulus and damping compatible with the levels of strain developed during the earthquake. The average of the results from the two records was used in further analyses and is here called I the strain compatible, free field profile. I Third, the moduli and material damping for the strain compatible, free field profile were used for the REFUND / FRIDAY analyses. I Fourth, the motion at the base of the profile obtained in the SHAKE analysis of the free field was input to several profiles representing thu soil column under the Category I buildings. The top layers of these profiles had masses and fundamental periods equivalent to those,of the corresponding buildings. The small strain values of soil shear moduli were adjusted to account for the I additional static stresses imposed by the buildings. The computer program SHAKE was run to obtain strain compatible moduli and damping values for each building profile. The average of results for the two time histories established each profile. 2253 039 g I I  :-17 I

BEAVER VALLEY FCWER STATION, UNIT 1 Fifth, the strain compatible properties under each building vere used in the . finite element dynamic analyses as soil properties directly under the corresponding buildings. The strain compatible, free field soil properties were used for the elements representing the free field. Strain compatible a soil properties were interpolated between these values for two columns of elements adjacent to the building. Sixth, no further iteration on soil properties was performed in either the i REFUND / FRIDAY or the finite element analysis. j 

 -1 j

2.6 REFERENCES

1. Schnabel, P.B., Lysmer, J., and Seed, H.B. SHAKE, A Computer Program for
 ]                   Earthquake Response Analysis of Horizontally Layered Sites.                    Earthquake Engineering Research Center,                  Report    No. EERC72-12 December 1972 (as modified for SWEC Computer System in Prt. tam ST211 Version 2 Levol 0).
2. Beaver Valley Power Station-Unit 1, Final Safety Analysis Report,

[- Appendix B, Section B.1.2 Seismic Design. 

       =

M

3. Geotechnical Design Criteria, BVPS Unit 2. 2BVM-80, Stone & Webster

_. Engineering Corp, Boston, issued 6/23/77, revised 3/15/78, p. 4. 

 +

1 2 2253 040 2-18 _---=;

BEAVER VALLEY POWER STATION, UNIT 1

4. Report of Soil Densific& tion Program, BVPS Unit 2. Stone & Webster Engineering Corp, Boston, 9/23/76.
5. Supplemer,t to Soil .>.cdy - Category I Structures, BVPS Unit 1. Duquesne Light Co., Pittsburgh, January 13, 1976.
6. Supplement No. 2 to Soil Study -

Category I Structures, BVPS Unit 1. Duquesne Light Co., Pittsburgh, April 30, 1978.

7. Soil Analysis of Turbine Building and Northern Yard Area, BVPS Unit No. 1.

Duquesne Light Co., Pittsburgh, April 30, 1979.

8. Soil Behavior Under Earthquake Loading Conditions. USAEC SW-AJA, January 1972.
9. Hardin, B.O. and Black, W.L., Closure to Vibration Modulus of Normally Consolidated Clays. Journal of Soil Mechanics and Foundations Division, ASCE Volume 95, SM 6, November 1969.

2253 041 0 e 2-19

I TABLE 2-1 STRAIN COMPATIBLE POISSON'S RATIOS free TLeLd - EL. 735 I Top of Gmax Gmax + 50% Gmax - 50% Layer A Laver El. E m DBE DBE 1 735 0.440 0.440 0.440 0.440 I 2 3 4 725 715 705 0.440 0.440 0.440 0.440 0.440 0.440 0.440 0.440 0.440 0.440 0.440 0.440 695 0.440 0.440 0.440 0.440 I 5 6 690 0.440 0.440 0.440 0.440 7 685 0.440 0.440 0.440 0.440 8 675 0.490 0.480 0.473 0.493 9 665 0.490 0.480 0.473 0.493 'I 10 655 0.490 0.480 0.473 0.493 11 645 0.490 0.480 0.473 0.493 I 12 13 14 635 625 620 0.490 0.490 0.480 0.480 0.473 0.473 0.493 0.493 I l 2253 042 I I I I I I I I 1e1 I

IO N T' M " N 'NN " " " N TABLE 2-2 STRAIN COMPATIDLE So1L PROPERTIES Free Field - Elevation 735 DDE = .125 g OBE = 0.06 o Top Iow Strain Total Shear Modulus Shear Modulus Thick- of Values . Unit (ksf) Damping Ratio (ksf) Damping Ratio

  • Idyer ness Layer Cs Wt Tatt ElCentro Aver- Taft ElCentro Aver- Taft ElCentro Aver- Taf t ElCentro Aver-No. (ft) Elev. (f ps) (kef) Material S69E 1940 NS age S69E 1940 NS age S69E 1940 NS age S69E 1940 NS aqe 1 10 735 600 .125 Sand 1095 1091 1093 .041 .041 .041 1242 1240 1241 .025 .026 .026 2 10 725 800 .125 Sand 1728 1701 1715 .054 .055 .055 2074 2062 2068 .033 .034 .034 3 10 715 950 .125 Sand 2369 2285 2327 .057 .060 .059 2859 2813 2836 .036 .038 .037 4 10 705 950 .125 Sand 2114 1979 2047 .068 .074 .071 2685 2624 2655 .043 .046 .045 5 5 695 1100 .125 Sand 3024 2820 2922 .062 .069 .066 3724 3612 3668 .040 .043 .042 6 5 690 1100 .125 Sand 2880 2696 2788 .066 .073 .070 3637 3529 3583 .042 .046 .044 7 10 685 1100 .125 Sand 2694 2564 2629 .073 .077 .075 3520 3434 3477 .046 .049 .048 8 10 675 1100 .136 Sand 2837 2714 2775 .076 .079 .078 3766 3702 3734 .048 .050 .049 9 10 665 1200 .136 Sand 3490 3417 3454 .073 .075 .074 4538 4471 4505 .046 .048 .047 10 10 655 1200 .136 Sand 3327 3267 3297 .077 .079 .078 4428 4396 4412 .049 .050 .050 11 10 645 1200 .136 Sand 3207 3192 3200 .080 .080 .080 4342 4322 ;332 .051 .052 .052 12 10 635 1200 .136 Sand 3124 3142 3133 .082 .082 .082 4277 4270 4274 .053 .053 .053 13 5 625 1200 .136 Sand 3083 3119 3101 .083 .082 .083 4239 4257 4248 .054 .053 .054 14 620 5000 .160 Rock NOTE:

Ground water table at El. 675 N N Ln u 

                                            -h U

1 of 1

E E E E E E EvM EONMT E E E E E E E N TABLE 2-3 STRAIN COMPATIBLE SOIL PROPERTIES Reactor Building DbE = .125 o OBE = .06 o Top Lcw Strain Total shear Modulus Shear Modulus Thick- of values Unit (ksf1 Damping Ratio (kst) Damping Ratio Layer ness Layer Cs Wt Taf t ElCentro Aver- Taft blCentro Aver- Taf t E1 Centro Aver- Taf t ElCentro Aver-No. (ft) Elev. (f ps) (kct) Material S69E 1940 HS age S69E 1940 NS ace S69E 1940 NS ace S69E 1940 NS ace 1- 10 735 1091 .138 Reactor Building Pseudo-soll 2 10 725 1091 .138 Reactor Building Pseudo-soil 3 10 715 1091 .138 Reactor Building Pseudo-soil 4 10 705 1091 .138 Reactor Building Pseudo-soil 5 10 695 1091 .138 Reactor Duilding Pseudo-soil 6 4 685 1091 .138 Reactor Building Pseudo-soil 7 6 681 1100 .125 Sand 2416 2111 2264 .082 .092 .087 3319 3:32 3276 .052 .055 .054 8 10 675 1100 .136 Sand 2651 2366 2509 .081 .050 .086 3616 3529 3573 .052 .055 .054 9 10 665 1200 .136 Sand 3352 3090 3221 .076 .083 .080 4416 4295 4356 .049 .052 .051 1C> W 10 655 1200 .136 Sand 3192 3030 3111 .080 .085 .083 4340 4207 4274 .051 .054 .053 1 !4 11 10 645 1200 .136 Sand 3045 3030 3037 .084 .085 .085 4266 4133 4200 .053 .056 .055 CD 4 4 1 of 2

W M M M M M MEAvMufmTl&M M M M - M M M TABLE 2-3 (Cont) LEE = .125 g OBE = 0.06 q Top Low Strain Total Shear Modulus Shear Modulus Thick- of Values Unit Iksi) Damping Ratio (kst) Damping Ratio Layer ness Layer Ca Wt Taf t ElCentro Aver- Taf t ElCentro Aver- Taf t ElCentro Aver- Taf t ElCentro Aver-No. fft) Elev. (fps) ikef) Material S69E 1940 NS age S69E 1940 NS age S69E 1940 NS age S692 1940 is age 12 10 635 1200 .116 Sand 2945 3039 2992 .087 .084 .086 4212 4079 4146 .054 .057 .056 13 5 625 1200 .136 Sand 2908 3008 2958' .088 .085 .087 4182 4071 4127 .055 .058 .057 14 620 5000 .160 Rock inrE: Ground water table at El. '675 N Ln U CD 4 LM 2 of 2

gfygyg@ ' W W W W W ~~M M TABLE 2-4 STRAIN COMPATIDLE SOIL PROPERTIES Safeguards Building DDE = 0.125 g OBE = 0.06 q 

                 'Ib p Iow Strain Total                Shear Modulus                                                                 Stear Modulus Thick- of      Values    Unit                     (kst)             Damping Ratio                                                Iksf1            Damping Ratio Layer ness   Layer   Cs          Wt            Taf t ElCentro Aver- Tatt ElCentro Aver- Taf t E1 Centro Aver- Taf t ElCentro Aver-tio.   (ft) Elev.    (f ps) , (kef) Material S69E 1940 NS age         S69E 1940 NS age                         S69E 1940 NS age                     S69E 1940 MS age 1    11.5   735     1243      .137 Safeguard Bldg.

Pseudo-Eoil 2 8.5 723.5 800' .125 Sand 1654 1587 1621 .058 .062 .060 2007 1961 1984 .037 .040 .039 3 10 715 950 .125 Sand 2292 2141 2216 .060 .067 .064 2801 2708 2755 .039 .042 .041 4 10 705 950 .125 Sand 2008 1826 1917 .073 .081 .077 2629 2521 2575 .046 .050 .048

  • 5 5 695 1100 .125 Sand 2629 2675 2802 .065 .073 .069 '3663 3504 3584 .041 .046 .044 6 5 690 1100 .125 Sand 2794 2547 2671 .069 .078 .074 3588 3419 3504 .044 .049 .047 7 10 685 1100 .125 Sand 2624 2420 2522 .075 .082 .079 3479 3322 3401 .047 .052 .050 8 10 675 1100 .136 Sand 2786 2601 2694 .077 .083 .080 3734 3594 3664 .049 .053 .051 9 10 665 1200 .136 Sand 3460 3354 3407 .074 .076 .075 4504 4356 4430 .047 .051 .049 10 10 655 1200 .136 Sand 3309 3223 3266 .077 .080 .079 4394 'J 283 4339 .050 .053 .052 11 10 645 1200 .136 Sand 3204 3194 3199 .080 .080 .080 4308 4213 4261 .052 .054 .053 12 10 635 1200 .136 Sand 3138 3135 3137 .082 .082 .082 4244 4172 4208 .053 .055 .054 13 5 625 1200 .136 Sand 3114 3144 3129 .083 .082 .082 4210 4170 4190 .054 .055 .055 14 620 5000 .160 Rock N

N NOTE: U1 U Ground water table at El. 675 C') Ch 1 of 1

M M M M M MrA#AMMTr&1M M M M M M M TABLE 2-5 STRAIN COMPATIBLE SOIL PROPHtTIES Auxiliary Duilding DBE = .125 q OBE = 0.06 q Top Low Strain Total shear Modulus Shear Modulus Thick- of Values Unit (ksi) Damping Ratio (ksf) Damping Ratio Layer ness Layer Cs Wt Taf t E1 Centro Aver- Taft ElCentro Aver- Taf t ElCentro Aver- Taf t E1 Centro Aver-No. fft) Elev. (fps) (kef) Material S698 1940 NS age S69E 1940 NS age S69E 1940 NS age S698 1940 NS age 1 10 735 1105 .179 Auxiliary Building Pseudo-soil 2 11 725 1105 .179 Auxiliary Building Pseudo-soil 3 9 714 950 .125 Sand 2024 1822 1923 .072 .081 .077 2594 2539 2567 .047 .050 .049 4 10 705 950 .125 Sand 1786 1578 1682 .083 .092 .088 2453 2393 2423 .053 .056 .055 5 5 695 1100 .125 Sand 2707 2444 2576 .072 .081 .077 3465 3364 3415 .048 .051 .050 6 5 690 1100 .125 Sand 2626 2369 2498 .075 .084 .080 3413 3296 3355 .049 .053 .051 7 10 685 1100 .125 Sand 2518 2272 2395 .079 .087 .083 3348 3215 3282 .051 .055 .053 8 10 675 1100 .136 Sand 2755 2577 2666 .078 .084 .081 3654 3501 3578 .051 .055 .053 9 10 665 1200 .136 Sand 3467 3347 3407 .073 .076 .075 4488 4268 4378 .048 .052 .051 10 10 655 1200 .136 Sand 3336 3302 3319 .077 .078 .078 4436 4212 4324 .049 .054 .052 11 10 645 1200 .136 Sand 3247 3234 3241 .079 .079 .079 4376 4171 4274 .050 .055 .052 12 10 635 1200 .136 Sand 3189 3212 3201 .081 .080 .081 4314 4142 4228 .052 .056 .054 13 5 625 1200 .136 Sand 3152 3153 3153 .082 .082 .082 4280 4147 4214 .053 .056 .055 14 N 620 5000 .160 Rock N U'l u - CD 4 N t of 1 

                                            'A
                                             .                          TI       It1 TAnLE 2-6 STRAIN COMPATIBLE SOIL PROPERTIES Service Building DDE = .*25 g                                OBE = 0.06 q Top Iow Strain %tal                    shear :-naulus                              Shear Modulus Thick- of      Values   Unit                       (ksf)              Daraping Ratio            (kst)              Daraping Ratio Iayer ness   Layer   Cs         Wt No. Eft) 1. lev. E p ls Taft E1 Centro Aver- Tatt ElCentro Aver- Taft E1 Centro Aver- Taft ElC m tro Aver-(kcf) Material S R 1940 NS age            S69E 1940 NS age     3623 1940 NS age        669E 1940 NS age 1    to     735      2372    .072 Service Building Pseudo-soil 2    15.5   725      2372    .072 service Euilding Pseudo-soil
  • 3 4.5 709.5 950 .125 Sand 2525 2551 2538 .050 2993
                                                                                .049   .050 2980             2987   .031     .031   .031 4    10     705        950   .125 Sand         2247    2315     2281   .062            .061 2768    2826
                                                                                .059                         2797   .040     .038   .039 5     5     695       1100   .12; Sand         3099    3189     3144   .059     .056   .058 3772    3881     3827   .038     .035   .037 6     5     690       1100   .125 Sand         2918    3049     2984   .065     .061   .063 3672    3787     3730   .041     .038   .040 7    10     685       1100   .125 Sand        2697     2835     2766   .073     .068                3675
                                                                                       .071 3553             3614   .045     .041   .043 8    10     675       1100   .136 Sand        2782     3011     2897   .077     .070   .074  3816   3978     3897   .046     .042   .044 9    10     665       1200   .136 Sand        3364     3727     3546   .076     .067   .072 4624    4768     4696   .044     .041   .043 10    10     655      1200    .136 Sand        3136     3555     3346   .082    .071    .077 4536    4607     4572   .046     .045   .046 11    10     645      1200    .136 Sand        2974     3403     3189   .086     .075   .081 4476    4482     4479   .048     .048   .048 12    10     635      1200    .136 Sand        2870     3279     3075   .089     .078   .084 4422    4386     4404   .049     .050   .050 13     5     625      1200    .136 Sand       2825      3231     3028   .090     .079   .085 4398    4350     4374   .050    .051    .051 14           620      5000    .160 Rock N

N Ln u a l of 1 4 00

g--- "-' W - unums y mumm ummum maums assus TABLE 2-7 STRAIN CCEPATIBLE SOIL PROPERTIES Cable Vault (Main Steam Building) DBE = 0.125 o OBE = 0.06 o Top Iow Strain Total Shear Modulus Shear Modulus Thick- of values Unit (ksf) Dainping Ratio (ksf) Damping Ratio Layer ness Layer Cs Mt Tatt ElCentro Aver- Tatt ElCentro Aver- Taf t ElCentro Aver- Taf t E1 Centro Aver-No. fft) Elev. Ifps) (kef) Haterial S698 1940 NS ago S69E 1940 NS age S69E 1940 NS , age S69E 1940 NS E 1 10 735 1135 .101 cable Vault Pseudo-Soil 2 12 725 1135 .101 Cable vault Pseudo-Soil 3 8 713 950 .125 Sand 2399 2419 2409 .055 .055 .055 2884 2986 2935 .035 .031 .033 4 10 705 950 .125 Sand 2100 2005 2093 .069 .069 .069 2691 2775 2733 .043 .039 .041 5 5 695 1100 .125 Sand 2975 2969 2972 .063 .063 .063 3723 3787 3755 .040 .037 .039 6 5 690 1100 .125 Sand 2829 2834 2832 .068 .068 .068 3646 3682 3664 .042 .040 .041 7 10 685 1100 .125 Sand 2638 2641 2640 .075 .075 .075 3544 3562 3553 .045 .044 .045 8 10 675 1100 .136 Sand 2767 2798 2783 .078 .077 .078 3788 3800 3794 .047 .046 .047 9 10 665 1200 .136 Sand 3403 3518 3461 .075 .072 .074 4562 4591 4577 .046 .045 .046 10 10 655 1200 .136 Sand 3236 3361 3299 .079 .076 .078 4439 4520 4480 .049 .046 .048 11 10 645 1200 .136 Sand 3111 3274 3193 .083 .078 .081 4339 4427 4383 .051 .049 .050 12 10 635 1200 .136 Sand 3033 3172 3103 .085 .081 .083 4266 4390 4328 .053 .049 .051 13 5 625 1200 .136 Sand 3003 3158 3081 .085 .081 .083 4228 4386 4307 .054 .049 .052 14 N 620 5000 .160 Rock N LT1 u CD 4 4 1 of 1

g g 'UN M ' M M W W W TABLE 2-8 STRAIN CCEPATIBLE SOIL PROPERTIES Diesel Generator Building DBE = .125 o OBE = 0 *6 a Top Low Strain Total Shear Modulus Shear Modulus Thick- of Values Unit (ksf) Damping Ratio (kst) Damping Ratio Layer ness Layer Cs Wt Taf t Elcentro Aver- Taft ElCentro Aver- Taft ElCentro Aver- Taf t E1 Centro Aver-No. (ft) Elev. (fps) (kef) Material S69E 1940 HS age S69E 1940 NS age S69E 1940 NS age S69E 1940 NS age 1 4.5 735 514 .357 Diesel Generator Building Pseudo-soil 2 5.5 730.5 600 .125 Sand 643 592 618 .091 .098 .095 975 938 957 .053 .057 .055 3 10 725 800 .125 Sand 1360 1223 1292 .077 .086 .082 1837 1760 1799 .047 .052 .050 4 10 715 950 .125 Sand 2016 1831 1924 .072 .081 .077 2633 2496 25'5 6 .046 .051 .049 5 10 705 950 .125 Sand 1797 1650 1724 .082 .089 .086 2503 2345 2424 .051 .058 .055 6 5 695 1100 .125 Sand 2726 2511 2619 .072 .079 .076 3509 3301 3405 .046 .053 .050 7 5 690 1100 .125 Sand 2637 2446 2542 .075 .081 .078 3453 3231 3342 .048 .055 .052 8 10 685 1100 .125 Sand 2530 2376 2453 .078 .083 .081 3384 3147 3266 .050 .058 .054 9 10 675 1100 .136 Sand 2791 2668 2730 .077 .081 .079 3685 3418 3552 .050 .058 .054 10 10 665 1200 .136 Sand 3554 3366 3460 .071 .076 .074 4513 4179 4346 .047 .055 .051 11 10 655 1200 .136 Sand 3457 3287 3372 .074 .078 .076 4462 4116 4289 .048 .057 .053 12 10 645 1200 .136 Sand 3382 3237 3310 .076 .079 .078 4393 4086 4240 .050 .057 .054 13 10 635 1200 .136 Sand 3325 3206 3266 .077 .080 .079 4347 4076 4212 .051 .057 .054 14 5 625 1200 .136 Sand 3293 3210 3252 .078 .080 .079 4324 4078 4201 .052 .057 .055 N 15 620 5000 .160 Rock N LM u O Ln

  • O 1 of 1

E E U E O V M ER N IO IT TADLE 2-9 STRAIN CCHPATIDLE SOIL FROPERTIES Fuel Building DBE = .125 o OBE = 0.06 o hp Low Strain Total Shear Modulus Shear Modulus Thick- of values Unit (ksti Damping Ratio (ksf) Damping Ratio Layer ness Layer Cs Wt Taf t ElCentro Aver- Tatt ElCentro Aver- Taf t ElCentro Aver- Taf t ElCentro Aver-No. fft) Elev. (fps) (kcfl Material S69E 1990 NS age S69E 1940 NS age S69E 1940 NS age S69E 1940 NS age 1 13 735 1092 .296 Fuel Bldg. Pseudo-Soil 2 7 722 800 .125 Sand 1093 1063 1078 .094 .097 .096 1702 1531 1617 .055 .066 .061 3 10 715 950 .125 Sand 1738 1678 1708 .085 .088 .087 2502 2322 2412 .351 .059 .055 4 10 705 950 .125 Sand 1563 1501 1532 .093 .097 .095 2004 2170 2287 .055 .066 .061 5 5 695 1100 .125 Sand 2430 2254 2342 .062 .088 .085 3408 3149 3219 .'J 4 9 .057 .053 6 5 690 1100 .125 Sand 2361 2185 2273 .084 .090 .087 3371 3100 3236 .051 .059 .055 7 10 685 1100 .125 Sand 2275 2110 2193 .087 .092 .090 3322 3007 3165 .052 .062 .057 8 10 675 1100 .13b Sand 2523 2310 2417 .085 .092 .089 3623 3293 3458 .052 .062 .057 9 10 665 1200 .136 Sand 3247 2855 3051 .079 .089 .084 4443 4114 4279 .049 .057 .053 10 10 655 1200 .136 Sand 3161 2681 2921 .081 .094 .088 4400 4070 4235 .050 .058 .054 11 10 645 1200 .136 Sand 3075 2573 2824 .084 .098 .091 4373 4055 4214 .050 .058 .054 12 10 635 1200 .136 Sand 3002 2510 2756 .085 .102 .094 4358 4033 4193 .051 .059 .055 13 5 625 1200 .136 Sand 2943 2485 2714 .087 .103 .095 4353 4016 4185 .051 .059 .055 14 620 5000 .160 Rock N N L71 u O l.J1 1 of 1

6YM STM,' W1 W W N W W W W TABLE 2-10 STRAIN COMPATIBLE SOIL PROPERTIES Free Field - Elevation 645 (North of Intake Structure) DDE = .125 o onE = .06 o __ Top Low Strain Total Shear Modulus Shear Modulus Thick- of values Unit Iksi) Damping Ratio (ksf) Damping Ratio Layer ness Layer Cs Mt Taf t E1 Centro Aver- Taf t ElCentro Aver- Tait E1 Centro Aver- Tait ElCentro Aver-No. (ft) Elev. (fps) (kef) Haterial S69E 1940 NS age S69E 1940 NS age S69E 1940 NS age S69E 1940 NS age 1 5 645 1200 .136 Sand 5917 5853 5885 .014 .015 .015 6052 5925 5989 .012 .014 .013 2 10 640 1200 .136 Sand 5402 5211 5307 .025 .030 .028 5804 5465 5635 .016 .024 .020 3 10 630 1200 .136 Sand 4911 4635 4773 .037 .044 .041 5535 5124 5330 .022 .032 .027 4 620 5000 .160 Rock N&rP,: Ground water table at El. 675 N LT1 tra CD LT1 N 1 of 1

_= _. ._.. .. . . TABLE 2-11 STRAIN COHPATIBLE SOIL PROPERTIES Free Field - Elevation 675 (South of Intake Structure) LBE = .125 g OBE = 0,16 a 

                 'Ibp Low Strain Total                   Shear Modulus                                    Shear Modulus Thick- of       Values   Unit                       (knf)             Damping Ratio                   Iksf)              Dampinq Ratio layer neos    Layer   Cs          Mt              Tatt ElCentro Aver- Tait ElCentro Aver- Taf t ElCentro Aver- Taf t E1 Centro Aver-No. Eft)   Elev.   (fps)     (kef) Material S69E 1940 NS _ age _ S69E 1940 NS _ age           p6,9E 69   1940 NS age      S69E 1940 NS age 1       10      675     600   .136 Sand          1028     960     994   .057     .064      .061 1167       1172     1170  .043    .043   .043 2       10     665    1100    .136 Sand          3642    3489    3566   .051     .056      .053 4095       4238    4167   .038    .034   .036 3       10      655   1100     .136 Sand         3162    2832    2977   .066     .076      .071 3685       3919    3802   .050    .043   .047 4       10      645   1200     .136 Sand         3651    3274    3463   .069     .078      .074 4301       4583     4442  .052    .045   .049 5       10      635   1200    .136 Sand          3413    3013    3213   .075     .085      .080 4142       4436    4289 .056      .049   .353 6         5     625   1200    .136 Sand          3311    2868    3090 .077       .089      .083 4083       4388    4236   .057    .050   .054 7               620   5000     .160 Rock                                 ,

NOTE: Ground water table at El. 675 N N LT1 u O LT1 u 1 of 1

M 'W W Wluur W W W W TABLE 2-12 STRAIN CQiPATIDLE SOIL PROPERTIES Main Intake structure DDE = .125 o OBE = 0.06 o Top Mw Strain Total Shear Modulus Shear Modulus Thick- of Values Unit (ksf) Damping Ratio iksf) Damping Ratio Layer ness Layer Cs Wt Taf t ElCentro Aver- Taft ElCentro Aver- Taft E1 Centro Aver- Taf t ElCentro Avez-No. (ft) Elev. (fps) (kef) Material S69E 1940 NS age S69E 1940 NS. age S69E 1940 NS age S698 1940 NS age 1 55 730 1910 .063 Intake Struc-ture - Pseudo-soil 2 40.5 675 1910 .063 Intake Struc-ture - . Pseudo- . soil 3 9.5 634.5 1200 .136 Sand 2781 2720 2751 .091 .093 .092 4063 3788 3926 .058 .065 .062 4 5 625 1200 .136 Sand 2676 2630 2653 .094 .095 .095 4011 3701 3856 .059 .067 .063 5 620 5000 .160 Rock

  • NLEE t Ground water table at El. 675 N

Ln u CD U'1 4 1 of 1

BEAVER VALLEY POWER STATION, UNIT 1 TABLE 2-13 STRAIN COMPATII.LE SOIL PROPERTIES - DBE Gmax + 50% - Free Field - Elevation 735 Top Total Shear Modulus Thick- of Low Strain Unit - (ksf) Damoinn Ratio Layer ness Layer Values Ut laft E1 Centro Aver- Iaft E1 Centro Aver-No. (ft) Elev. G(ksf) (Fef) Haterial 119E 1940 NS ace li2g 1940 NS age 1 10 735 2097 .125 Sand 1791 1794 1793 0.031 0.030 0.031 2 10 725 3726 .125 Sand 2870 2882 2876 0.043 0.042 0.043 3 10 715 3255 .125 Sand 3891 3947 3911 0.047 0.046 0.047 4 10 705 5255 .125 Sand 3586 3670 3628 0.056 0.053 0.055 5 5 695 7046 .125 Sand 4977 5096 5037 0.052 0.050 0.051 6 5 690 7046 .125 Sand 4838 4985 4912 0.055 0.052 0.054 7 10 685 7046 .125 Sand 4646 4843 4745 0.059 0.055 0.057 8 10 675 7667 .136 Sand 4940 5159 5050 0.062 0.057 0.061 9 10 665 9123 .136 Sand 6054 6195 6125 0.058 0.056 0.057 10 10 655 9123 .136 Sand 5798 5973 5886 0.063 0.060 0.062 11 10 645 9123 .136 Sand 5604 5749 5677 0.066 0.064 0.065 12 10 635 9123 .136 Sand 5484 5566 5525 0.068 0.067 0.068 13 5 625 9123 .136 Sand 5394 5452 5423 0.070 0.069 0.070 14 620 Rock l!91E: p) Ground water table at El. 675 N Ln U CD Ln Ln 1 of 1

O E MN OM E E N W E M BEAVER VALLEY POWER STATION, UNIT 1 M M M E NO E TABLE 2-14 STRAIN COMPATIBLE SOIL PROPERTIES - DBE Gmax Minus 50% - Free Field - Elevation 735 Top Total Shear Modulus Thich- of Low Strain Unit (ksi) Damping Ratio Layer r.ess Layer Valugi__ Wt Taft E1 Centro Aver- Taft ElCentro Aver-No. (ft) Elev. G(ksf) (Fef) Material 1125 1940 NS age 1125 1940 NS pge 1 10 735 699 .125 Sand 450 454 452 .062 .061 .062 2 10 725 1242 .125 Sand 605 653 629 .086 .080 .083 3 10 715 1752 .125 Sand 796 883 840 .092 .084 .088 4 10 705 1752 .125 Sand 684 722 703 .109 .102 .106 5 5 695 2349 .125 Sand 1028 1069 1049 .094 .092 .093 6 5 690 2349 .125 Sand 988 1014 1001 .099 .096 .098 7 10 685 2349 .125 Sand 960 968 964 .103 .102 .103 8 10 675 2555 .136 Sand 1073 1070 1072 .099 .100 .100 9 10 665 3041 .136 Sand 1436 1422 1429 .089 .090 .090 10 10 655 3041 .136 Sand 1442 1435 1439 .089 .089 .089 11 10 645 3041 .136 Sr.nd 1482 1470 1476 .086 .C87 .087 12 10 635 3041 .136 Sand 1475 1494 1485 .087 .086 .087 13 5 625 3041 .136 Sand 1411 1494 1453 .090 .086 .088 14 620 Rock E9IL: h[j Ground water table at El. 675 w u CD w CB 1 of 1

Y Y &N &M Y M & M M W & M O' S W W M BEAVER VALLEY POWER STATION, UNIT 1 TABLE 2-15 STRAIN COMPATIBLE SOIL PROPERTIES - DBE Gmax Plus 50% - Reactor Building Top Low Strain Total Shear Mcdulus Thick- of Values Unit (ksf) Dampinn Ratio 

         ' Layer ness   Layer     G         Ut             Taft E1 Centro Aver- Taft E1 Centro Aver-No.    (ft) Elev.    (ksf)     (Fcf) Haterial Eh25 1940 NS. ane      1h25 1940 NS age 1        10    735    5101     .138 Reactor Building Pseudo-soil 2        10    725    5101     .138 Reactor Building Pseudo-soil 3        10    715    5101     .138 Reactor Building Pseudo-soil 4        10    705    5101     .138 Reactor Building Pseudo-soil 5        10    695    5101     .138 Reactor Building Pseudo-soil 6          4   685    5101     .138 Reactor Building Pseudo-soil 7          6   681    7046     .125 Sand        4215    4103   4159  .069    .071   .070 r\)     8         10   675    7667     .136 Sand        4564    4435   4500  .069    .072   .071 N

LJ1 9 10 665 9123 .136 Sand 5658 5487 5573 .065 .068 .067 10 10 655 9123 .136 Sand 5380 5231 5306 .070 .073 072 C3 11 10 645 ?l23 .136 Sand 5171 5019 50?5 .074 .076 .075 LJ1 N 1 of 2

Y Y & W M' O Y & M M & BEAVER VALLEY POWER STATION, UNIT 1 

                                                                         $      $$             Y   & &W TABLE 2-15 (Cont)

Top Low Strain Total Shear Modulus Thick- of Values Unit (ksf) Dampine Ratio Layer ness Layer G Wt Taft E1 Centro Aver- Taft E1 Centro Aver-No. (ft) Elev. (ksf) 1.ts.f.)_ Material gh_2X 1940 NS age 562X 1940 NS age 12 10 635 9123 .136 Sand 5058 4850 4954 .076 .079 .078 13 5 625 9123 .136 Sand 4943 4743 4843 .078 .081 .080 14 620 .160 Rock [LO.II: Ground water table at E1. 675 N N Ln ' u CD Ln CD 2 of 2

M M W W W W W BEAVER W W mmW VALLEY POWER STATION, UNIT 1 W W W W W M M TABLE 2-16 STRAIN COMPATIBLE SOIL PROPERTIES - DBE Gmax Hinus 50% - Reactor Building Top Low Strain Total Shear Modulus Thick- of Values Unit (ksf) Dampinn Ratio Layer ness Layer G Wt Taft E1 Centro Aver- Taft E1 Centro Aver-No. (ft) Lim (ksf) Ikg_O, Material 'Ef9_E 1940 NS are 112X 1940 NS MJL. I 10 735 5101 .138 Reactor Building Pseudo-soil 2 10 725 5101 .138 Reactor Building Pseudo-soil 3 10 715 5101 .138 Reactor Building Pseudo-soil 4 10 705 5101 .138 Reactor Building Pseado-soil 5 10 695 5101 .138 Reactor Building Pseudo-soil 6 4 685 5101 .138 Reactor Building pg) Pseudo-pg) soll LJ' 7 6 681 2349 .125 Sand 859 972 916 .116 .101 .109 U 8 10 675 2556 .136 Sand 972 1058 1015 .112 .101 .107 CD (y, 9 10 665 3041 .136 Sand 1290 1341 1316 .098 .094 .096 sC) 10 10 655 3041 .136 Sand 1332 1286 1309 .094 .098 .096 11 10 645 3041 .136 Sand 1334 1250 1292 .094 .102 .098 1 of 2

N NM M M O M M M M M M E M' N E O E M BEAVER VALLEY POWER STATION, UNIT 1 

            .                               TABLE 2-16 (Cont)

Top Low Strain Total Shear Modulus Thick- of Values Unit (ksf) Damoine Ratio Layer ness Layer G Ut Taft E1 Centro Aver- Taft E1 Centro Aver-No. (ft) Elev. (ksf) (kef) Haterial S.S.21 1940 NS age Effl 1940 NS E 12 10 635 3041 .136 Sand 1312 1241 1277 .096 .103 .100 13 5 625 3041 .136 Sand 1268 1245 1257 .100 .103 .102 14 620 Rock ILOJI: O Ground water table at El. 675 N tri u O CF C 2 of 2 

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t :: . # . . . . . i.f: 1.:l. . ..j::. - d Gs= 2.70 

.........;;ti f'\

620 SHALE . N N FIGURE 2-4

  • MEASURED AND COMPUTED VALUES OF SHEAR WAVE VELOCITY o BEAVER VALLEY POWER STATION-UNIT 1 4

j i a i d i O 500 I000 1500 O n 

   .1 20                                             --

79 = 120 pcf p 40 ta. t 

           %60                                                                          o

_= CL td a a 0 80 

       =

7t = 130 p c f b . 100 (Q) o Vs (FPS) n = i J n 2253 065 

 =

~~ FIGURE 2-5 PROPERTIES USED FOR WHITMAN'S ANALYSIS BEAVER VALLEY POWER STATION-UNIT 1 m 4 

 ?

1 

   }

3 Vs (FPS) j o 500 1000 1500 735 i i 725 - 

   )                             715  -   SAND 8 j                                      GRAVEL 705  -

q V7 = 125 PCF p 695 _ u. 

                               ~

z 685 - 9 g 675 w S 

    ~

_J W 665 - 

-                                           SAND &

GRAVEL 655 645 - 

                                               # T= 136 PCF

] .J-635 - 625-k 620 ,,,,,,,,,,,,,,y - yyn ,,quagagsp ~~ BEDROCK V7 :160 'iF _ VS= 50:.'0 'PS ? I j 2253 066 i e L q l 1 A 3 FIGURE 2-6 i FREE FIELD SOIL PROFILE r BEAVER VALLEY POWER STATION-UNIT 1 m

+ Vs (FPS) O 500 1000 1500 735 , , , 725 - 

-=

REACTOR 

     =,         715 -

BUILDING 

     =

705 YT = 138 PCF _; 695-I 1 z 685 - i 9 F 

             % 675 w

S 665 - SAND a GRAVEL 

     }         655   -

- 645- 3 T =I56 PCF ~ 635 - 

      ,        625    -

620 ,,,,,,,ie,,ngiam,,,_g,winnin warmpeg BEDROCK V7 :160 PCF Vs= 5000 FPS s

2253 067 4

i FIGU R E 2-7 7 REACTOR BUILDING SOIL PROFILE B EAVER VALLEY POWER STATION-UNIT 1 _] 7 

  =
-%i Vs (FPS) o             500                             1000      1500 y                            735                  i                               i SAFEGUARD
                                                                      'f = 137 PCF 725 - BUILDING b

715 - SAND 8 g GRAVEL 705 - YT = 125 PCF g 695 u. _ i 685 9 

 -i                      H
                         % 675     -

8-1 $ j 665 - SAND a GRAVEL 655 - 645 # T= 136 PCF I. 635 -

625 -

620 ,,,,,,,,,,,,,,,,wamn,ne,en.s wasars BEDROCK V7 :160 PCF [ Vs=5000 FPS 2253 068 

    ~

m... m I B w A FIGURE 2-8 -=' SAFEGUARD BUILDING SOIL PROFILE BEAVER VALLEY POWER STATION-UNIT 1 y

I: V3 (FFS) O 500 1000 1500 735 , , i AUXILIARY 725 - BUILDING 4T =179 PCF 715 - SAND & GR AVEL 705 - 

      -                                YT= 125 PCF j            g                695 -
            'tz           685     -
       !    9
 =

w 

            % 675-                     3-1          'iW J                             665  -

SAND 8 GRAVEL 

 ]                           655  -

-. 645 - DT= 136 PCF a I 635 - 625 - 620 un ,,,,, ,,,,,,nemn,,,,,qnnmaimp BEDROCK YT =l60 PCF Vs=5000 FPS a 2253 069 D

FIGURE 2-9

'; AUXILI ARY BUILDING SOIL PROFILE

BEAVER VALLEY POWER STATION-UNIT 1 i

m M

1, d 

  ,                                 Vs (FPS) o             500         1000                    1500     2000 3

735 , , , , 1 

                   ~

SERVICE BUILDING 1 T =72 PCF 715 - 705 - SAND E. GRAVEL 

  ,                       YT= 125 PCF 695 -

I z 685 - 3 9 t- 

        .   % 675-        S i  '
            "i 665  -

SAND 8 655 GRAVEL [. j 645 - # T= 136 PCF _i 635 - 

  )            625-620 , .,,,,,,,,,,,,_,,,,, _ ,,,,,,,,, , _
 ;                      BEDROCK YT =l60 PCF Vs=5000 FPS N

2253 070 2 1 2 i 

   -)

FIGURE 2-10 i SERVICE BUILDING SOIL PROFILE 

 ,                                   BEAVER VALLEY POWER STATION-UNIT 1
 -_=

m

I E Vs (FPS) O 500 1000 1500 I 735 i i i CABLE VAULT 725 - V =101PCF 715- 

                ^           ^

705 YT=125 PCF I z 685-I e 

 % 675-         S
 'i I
  • 665 -

SAND & GRAVEL 655 - 645 - 

                   # T= 136 PCF I    635 625  -

6 20 ,,-,,,,,,,,,,,,,,-,,, . , ,,,, ,. . ,a BEDROCK V7 :160 PCF Vs= 5000 FPS I 2253 071 l , I . . I I FIGURE 2-11 CABLE VAULT SOIL PROFILE BEAVER VALLEY POWER STATION-UNIT t l I

i 4 DIESEL GENERATOR Vs (FPS) 

      !                          o                        500         1000           1500 Ty=357 PCF 4                        725       -

715 - SAND a w GRAVEL 705-YT = 125 PCF 695 - =- I z 685 - 

     -     o P

m y 675 - S 

   ~
        . 5
  • 665 -

SAND 8 GRAVEL 655 645 - 

                                              # T= 136 PCF
  =

'_ 635 - 

     .-i 625    -

L, 6 20 ,,,,,,, ,,,,,,,,, n . .,,,,,nn,,,,,--g i [ BEDROCK V 7 =l60 PCF Vs= 5000 FPS 5 2253 072 h 

        -s f

_3 E, FIGURE 2-12 ( DIESEL GENERATOR BUILDING SOIL PROFILE l BEAVER VALLEY POWER STATION-UNIT 1 N

i j m j Vs (FPS) l o 500 1000 1500 735 , , i FUEL BUILDING J 725 - 4T = 125 715 - SAND & j GRAVEL 705 - Y7= 125 PCF 2 g 695 u. z 685 - 9 

            % 675                                3-S
  • 665 -

SA,ND 8 I 655 GRAVEL [ 645 I = 136 PCF T 635 - i J 625 - 620 ,,na,,manniuiawemmennimn urarangs 

 ~f BEDROCK YT =l60 PCF Vs= 5000 FPS i

1 

          =

2253 073 I_ 5 i e 

    -i
         =

a i FIGURE 2-13 

         ;                                                   FUEL BUILDING SOIL PROFILE

,1 B EAVER VALLEY POWER STATION-UNIT 1

I I I I I - Vs (FPS) O 500 1000 1500 665 2 655 - SAND AND GRAVEL 427 136 PCF k 645

j 635 -

625 - 

        //M/M/M/M/M/M/hV/h BEDROCK     YT=160 PCF Vs = 5000 f ps I

I l 2253 074 I I I Fleuee 2-,4 FREE FIELD SOIL PROFILE I SOUTH OF INTAKE STRUCTURE BEAVER VALLEY POWER STATION-UNIT 1 I

I . I I I I I Vs (FPS) o soo toco isoo l g3 _!. 640 - 6 S AND AND GRAVEL I k 63o - T8T 136 PCF l d 52o<av/4v/4vav/Averv/Avea BEDROCK VT = 160 PCF Vs = 5000 f ps E I g 2253 075 I I I I rieuRE z-se FREE FIELD SOIL PROFILE I NORTH OF INTAKE STRUCTURE BEAVER VALLEY POWER STATION-UNIT 1 I

I I I I V3 (FPS) 00 1000 1500 2000 730 i i I 725 715 - INTAKE STRUCTURE T2T 63 PCF 695 - I 685 - I 2 ti> 675 - I j 665 - 655 - 645 - 635 SAND AND GRAVEL 625 - T Ts 136 P C l" I, 620 fgggg yfyfAxpANffy/Av/A I g 2253 076 I I FIGURE 2-16 I INTAKE STRUCTURE SOIL PROFILE BEAVER VALLEY POWER STATION-UNIT 1 I

i E 2253 077  : E 3 m

BEAVER VALLEY POWER STATION, UNIT 1 I 3.0 GROUND RESPONSE I The selection of seismic design parameters has been discussed in detail in the Beaver Valley Unit 1 PSAR. This section discribes the smoothed ground response spectra. I 3.1 DESIGN BASIS EARTHQUAKE (DBE) AND OPERATIONAL BASIS EARTHQUAKE COBE) I ~ The design basis earthquake (DBE) for the Beaver Valley site has a peak acceleration of 0.125g at the ground surface elevation of 735 feet. This acceleration level was established by considering an intensity V to VI earthquake with peak bedrock acce1eration of 0.035g amplified from bedrock elevation '620 feet through the overlying soil to elevation 735 feet. The amplification factor is 3.5. Smoothed response spectra were then normalized to the amplified acceleration. . I Accordingly, the design is based on a DBE normalized to 0.125 g at the ground surface (El. 735) and for the OBE normalized to 0.06 g at the same elevation. , Vert 1ca1 acc.1erations accelerations. ar. taken as t.o-ehires o, th. hori.onta1 l 2253 078 I I 3-1 I

BEAVER VALLEY POWER STATION, UNIT 1 I 3.2 GROUND R.'SPONSE SPECTRA I The ground responce spectra shown in Figure 3-1 (DBE) and Figure 3-2 (OBE) are the bases for the d6 sign of all ground supported structures, equipment, and piping. The design is based on a DBE normalized to 0.125 g and for the OBE normalized to 0.06 g. Dynamic amplification factors used for these spectra are such as to give a' maximum spectral acceleration of 0.45 g for two percent damping for the DBE with appropriate relative values for other amounts of damping. The spectra are flat from 2 to 5 Hz (0.2 to 0.5 see period) and reduce to an amplification ratio of unity for frequency exceeding 20 Hz. Amplified response spectra are used for the design of equipment, piping, and instrumentation supported from structures. 3.3 I ARTIFICIAL TIME HISTORY The artificial time histcry has a total duration of 15 seconds, with about 3.5 seconds cach of rise and fall time, whose ground response spectra are forced to fit the specified site spectrum. An artificial accelerogram which reproduces the frequency content displayed either in a response spectrum or in a power spectral density function is simulated statistically by using a stochastic model as described in Reference 1. In this model, the earthquake motion is considered to be a wide-band stationary process whose spectral density function, duration, and maximum acceleration are specified. The I 2253 079 3-2 I

BEAVER VALLEY POWER STATION, UNIT 1 artificial motion is generated by matching the target or site spectrum for several specified percentages of critical damping at 125 oscillator periods distributed from 0.0204 (49 Hz) to 5.0 (0.2 Hz) seconds. For a detailed treatment of the modeling procedurs, see References 2 and 3. The acceleration time history yields ground response spectra at damping values of 0.5, 1, 2, 5, 7, and 10 percent that envelop the smoothed site design ground response spectra for those damping values (see Figure 3-3, for example). 3.4 GROUND RESPONSE SPECTRA AT BASE OF CONTAINMENT The ground response spectra at the base of the reactor containment structure were calculated and plotted using SHAKE. The artificial earthquake developed for the Beaver Valley site was normalized to the DBE maximum acceleration of 0.125 g and input at the ground surface of the free-field profile. The earthquake motion was deconvoluted to the base of the profile and the computed motion at the El 681 feet, the containment founding grade, was used to compute the real velocity and acceleration response spectra and the tripartite plot of I real displacement, pseudovelocity, and pseudoacceleration vs. frequency. These spectra are plotted for damping ratios of .5, 1.0, and 3.0 percent. I 2253 080 3-3 I

I BEAVER VALLEY POWER STATION, UNIT 1 I I Response spectra were calculated for three soil profiles, represented by the shear modulus (Gmax) calculated from seismic cross-hole surveys, Gmax plus 50 percent, and Gmax minus 50 percent. The spectra for each soil profile are plotted on Figures 3-4, 3-5, and 3-6, respectively. Also plotted on these figures is the ground response spectrum for .5 percent damping presented in the Beaver Valley Unit 1 FSAR. 3.5 REFERE! ICES I 1. Hou, S.N., Earthquake Simulation Models and their Applications. Research Report R68-17, Department of Civil Engineerix , MIT, 1968.

2. Rascon, 0.A. and, Cornell, C.A., Strong Motion Earthquake Simulation.

Research Report R68-15, Department of Civil Engineering, MIT, 1968. I 3. Trat, N.C., Spectrum Compatible Motions for Design Purposes. Journal of Engineering Mechanics Division, ASCE, Vol 98, No. EM2, Rev. 4, Paper 8807, April 1972, p 345-35o. g 2253 081 I I 3-4 I

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a _- BEAVER VALLEY F0WER STATION, UNIT 1 l 4.0 AMPLITIED RESPONSE ANALYSIS i Soil-structure interaction analysis can be perfor=ed using a direct finite 

    ;      element solution in which the dynamic model is                                                            composed of    detailed
 ~

i representations of both the structure and the supporting medium. In a direct intoraction analysis, the effects of embedmont upon stiffness and control motion are automatically included. Although such a procedure may appear to be 1 j efficient, anilyses become more difficult to manage when large, complex structures are founded upon stratified media. Also, this procedure does not 1 produce any intermediate results, which are often useful in making engineering s assessments. = 

 =
 ;         Many different procedures may be used to reduce such an analysis to more 9           manageable steps. For example, a detailed finite element soil model can be
      ~

used to compute frequency-dependent stiffnesses that are then used in a second step for seismic analysis of a detailed structural model. For embedded structures, however, some method that redefines the control motion must be , included. An earthquake with a specified amplitude and frequency content at 4 the site surface is not necessarily a reasonable input to the detailed model in the second step. E ! A multiple-step analysis need not re'ly upon finite element representations of m ,) soil. The three-step solution described below is based upon the theory of ?' 4-1 2253 089 r - , , - - . . . . - - . .

BEAVER VALLEY POWER STATION, UNIT 1 j elasticity, and includes a solution for the prcblem of definition of the control motion in the case of embedded structures.

4.1 DESCRIPTION

OF THE THREE-STEP ANALYSIS 

    =                                                                     -

j The solution of soil-structure interaction problems can be reduced to the following three steps:

1. calculations of frequency-dependent soil stiffnesses a 2. modification of the specifie'd surface motion to account for structure embedment
3. interaction analysis These steps are illustrated in Figure 4-1 (see Reference 2).

A 

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4.1.1 Trequency-Dependent Soil Stiffness 

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The frequency-dependent stiffnesses of a rectangular footing founded at the 

  ~1 surface of a layered medium are computed with the program REFUND, discussed in L9           Section 10.3. The program solves the problem of forced vibration of a rigid plate on a viscoelastic, layered stratum using numerical solutions to the L

l 2253 090 

         !                                                   4-2 i

M

BEAVER VALLEY POWER STATION, UNIT 1 elasticity, and includes a solution for the problem of definition of the control motion in the case of embedded structures, a

4.1 DESCRIPTION

OF THE THREE-STEP ANALYSIS The solution of soil-structure interaction problems can be reduced to the 1 following three steps: j j 1. calculations of frequency-dependent soil stiffnesses 4 2. modification of the specified surface motion to account for structure l embedment ] 

      ;         3. interaction analysis i;

2 These steps are illustrated in Figure 4-1 (see Reference 2). 4.1.1 Frequency-Dependent Scil Stiffness The frequency-dependent stiffnesses of a rectangular footing founded at the 

    .'      surface of a layered medium are computed with the program RETUND, discussed in 1       Section 10.3.              The program solves the problem of forced vibration of a rigid plate on a viscoelastic, layered stratum using numerical              solutions to the i,

j u-2 2253 091 4 

      =

i BEAVER VALLEY POWER STATION, UNIT 1 l - J generali:ed problems of Cerruti and Boussinesq (see Figure 4-2). The effects 

      ;    of unit harmonic horizontal and vertical point loads are combined by superposition to produce the behavior of a rectangular plate.

_= I Solutions to the problem of a point lead on the surface of continuum require i an assumption about the behavior of the medium directly under the load; for example, see Timoshenko and Goodier. ' In RETUND, a solution directly under the load is achieved by employing a column of elements for which a linear displacement function is assumed. Away from this central column, in the "far-i field," the salution for a viscoelastic layered medium is obtained (see

  • Tigure 4-3).
    =

~ If the central column under the point load is removed and replaced by equivalent distributed forces corresponding to the internal stresses, the dynamic equilibrium of the far field is preserved. Since no other prescribed i forces act on the far field, the displacements at the boundary (and any other point in the far field) are uniquely defined in terms of these boundary forces. The problem is thus to find the relations between these brundary forces and the corresponding boundary displacements. It is always possible to express the displacements in the far field in terms of eigenfunctions corresponding to the natural modes of wave propagation in the stratum, each having a characteristic wave number k. In an unbounded u I 2253 092 , 4-3 

 ~.
                                     ,     BEAVER VALLEY POWER STATION, UNIT 1 A

i i i medium, any value of the wave number k, and hence any vavelength, is ~ admissible; for a layered stratum, however, only a numerable set of values of k (each one with a corresponding propagation mode) satisfies the. boundary I 

 !     conditions.                 There are thus, at a given frequency, an infinite but numerable set of propagation modes and wave numbers k that can be found by solving a i

transcendental eigenvalue problem. For each eigenfunction the distribution of l stresses can be determined up to a multiplicative constant, the participation i-factor of the mode. By combining these modal stresses to match any given 1 j distributi'sn of stresses at the boundary, the participation factors and the corresponding dynamic stiffness function relating boundary stresses to i boundary displacements can be determined. I In REFUND's cylindrical coordinates, loads and displacements are expanded in a _j Fourier series around the axis: i e = 

 !          ur : EO u" cos n6                   p, = 1 p" cos nB O

e m Tl u y=Eu" ces nB p, = E p," cos n6 o o e e lj u6 = 0E-u6 sin n6 pg= E-p6 o sin n6 i i For the problem at hand, only the first two components of the series are needed. The (unit) vertical force case corresponds to the Fourier component of order zero (n=0), and the horizontal unit force case corresponds to the I 

 =

2253 093 1 4-4

, BEAVER VALLEY PC'a*ER STATION, UNIT 1 

       !    Fourier component of order                             one     (n 1). The      cartesian     displacement a

(flexibility) matrix (T) at a point then follows from the cylindrical l _; displacement components: d 

   =_

i f(uj+ uh) + f(ul-uj)cos 26 u' cos 6 h(u -ug) sin 26 uycos 6 u'y u'y sin 6 f 1 f(uf - u8) sin 26 u' sin 6 f (ul + u'8 ) - (u - u'6 ) c s 26 = and the displacement vector for arbitrary leading is U = FP a -, where i*u i pal l xl l l U= u y) P= py) I,uJ {,p,J U is the displacement vector at a point (x,0,z) while P is the load vector at ~ (0,0,0). The coordinate system is illustrated in Figure 4-4. For points along the free surface, the reciprocity theorem requires that

UO

U Hence, F is chessboard symmetric /antisymmetric. REFUND then r y. q 2253 094 l 4-5 

 =

i d i SEAVER VALLEY POWER STATION, UNIT 1 4 

  !     computes the cylindrical displacement components for the two leading cases, and determines the cartesian flexibility matrix T under the load (axis),       at i

) the boundary. and at selected points beyond the boundary. s ~ To compute the subgrade stiffness functions for a rigid, rectangular plate, the program discreti es the foundation into a number of points and computes 

,       the global flexibility matrix T from the nodal subcatrices T using the 4

technique just described. Imposing then the conditions of unit ri.gid body j displacements and rotations, it is possible to solve for the global load vector from the equation 1 FP = U u where U is the global displacement vector satisfying the rigid body condition. It follows that U is of the form ?_ j U - TV i i where V is a (6xt) vector containing the rigid body translations or rotations

of the plate and T is linear transformation matrix assembled with the 1

i 2253 095 4-6 e s I

BEAVER VALLEY POWER SIATION, UNIT 1 coordinates of the nodal points. The stiffness functions are then obtained from 2=Tp T which corresponds formally to 2 = T F'*TV A comparison of REFUND results with another method is shown in section 10.3. 4.1.2 Embedment Correction The effects of foundation embedment on the impedances are included by employing correction factors described by Kausel et al.'2' These correction factors are determined from parametric studies of cmbedded foundations and are of the form Ca = (1 + iC ()(1 + C2 h)(1 + C3 h) 2253 096 in which 4-7

__ BEAVER VALLEY PO'4ER STATION, UNIT 1 C = correction factor R R = foundation radius E  : embedment depth H  : depth to bedrock Ci  : constants, different values for each degree of freedom. The frequency dependent stiffnesses, K, determined by REFUND are modified to become K = K x Ca 4.1.3 Kinematic Interaction In the second step of the analysis shown in Figure 4-1, " kinematic interaction" modifies the purely translational input specified at the surface of the stratum to both a translational and rotational motion at the base of the rigid, massless foundation. The existence of the additional input can be inferred from Figure 4-5. In a strftum undergoing trarslational motion only, 2253 097 - 4-8

BEAVER VALLEY POWER STATION, UNIT 1 

   =

the boundary conditions at the " excavation" require the foundation to rotate. 

~

~~ Ignoring the rotational component would result in an unconservative solution. Note that the modified motion at the base of the foundation is not equivalent to a deconvolution. The specified surface motion is modified so that F(n) cos( ) , f 5 0.7 fn y, (t) = IFT (F(D) 0.453 , f > 0.7 fn ond fF(a) 0.257(1- cos 11)/R , f 5 fn g k(t) = IFT (F(n) 0.257/R , f > fn l 1 J F(G) = Fourier Transform of surface motion l IFT = inverse transform 7 J R = foundation radius i 

]               f        = fundamental shear beam frequency of the column of soil between the embedment level and the free surface 2                                                                                                 22ST 098
-:                                                                4-9

s 3EAVER VALLEY POWER STATION, UNIT 1 l These relationships are taken from Kausel et al.'28 j 

   !      A finite element analysis of a rigid, massless, embedded foundation provides a demonstration that the relations above are reasonable and conservative.      Such a comparison is shown in Section 10.4 (KINACT).

i 4.1.4 Interaction Analysis 4 The third step of the procedure illustrated schematically in Figure 4-1 is the analysis of the structural model supported on the frequency-dependent springs 

 ~

from Step 1 for the modified seismic input from Step 2. The solution is achieved using the program FRIDAY. l FRIDAY evaluates the dynamic response of an assembly of cantilever structures 3 4 supported by a common mat and subjected to a seismic excitation. The support 

] j of the mat can be rigid, or it can consist of frequency-dependent / independent springs and dashpots (subgrade stiffnesses). The equations of motion are solved in the frequency domain,       determining response time histories by
     ,     convolution of the transfer functions and the Fourier transform of the input i
        . excitation. The dynamic equilibrium equations can be written in matrix l       not cion as:

2253 099 j j - 4-10 m 1 i

BEAVER VALLEY POWER STATION, UNIT 1 MO+C + KY = 0 (1) where M, C, K are the mass, damping and stiffness matrices, respectively, and U, Y are the absolute and relative (to the moving support) displacement vectors. These two vectors are related by: U = Y + EU s (2) where U is the base excitation vector (3 translations and 3 rotations), and E is the matrix: I Ti O I I T2 E= 0 I 

                                 ,                                                     (3)

I Tn 2253 100 O I 4-11

LEAVER VALLEY P0b'ER STATION, UNIT 1 I where I is the (3x3) identity matrix, O is the null matrix, and f 0 Z t - Zo -(Yt - Yo)] I i

  • Tt = ( -(Z t- Zo) O Xt - Xo )

I ( Y -t Yo -(X t- Xo) O j vith xg, y ,g:1 being the coordinates of the corresponding mass point; x o, yo,

o are the coordinates of the common support.

In the frequency response method, the transfer functions are determined by setting, one at a time, the ground motion components equal to a unit harmonic i of the form uf = e "U. It follows then that U, Y are also harmonic: O: Hjel ** I Y = (H g - Eg ) e "' U=1twHjeI *' i = 1(Hj-tw Eg)e twt (4) I U = -wi Hj eI "' Y = -wh(H) - Eg le "' I I th where Hg=Hg (w) is the vector containing the transfer functions for the j ch column of E in Eq. 3. input ground motion, and Eg is the j Substitution of Eq 4 into Eq 1 yields I 2253 101

l. 4-u I
  =

BEAVER VALLEY PO'n'ER STATION, UNIT 1 (w2 M + twC+ K)Hj = (twC + K)Ej C3) T If the damping matrix is of the form C = hD,whichcorrespondstoalinear hysteretic damping situation, the equation reduces to 4 l (- w2 M + K + LD)Hj = (K + ID)El (6) 4 ,J _j In view of the correspondence principle, it is possible to generalize the equation of motion allowing at this stage elements in the stiffness matrix K .- vith an arbitrary variation with frequency. This enables the use of E frequency-dependent stiffness functions or impedance (inverse of flexibility functions or compliances). E 

     ?
,        Defining the dynamic stiffness matrix:

Kd K + 10 -way (7) 3 n The solution for the transfer functions follows formally from: 2J 2253 102 4-13

3EAVER VALLEY POWER STATION, UNIT 1 I I Hj = - K~j (K + 1D) Ej I = -(1 + w 2Kg M)Ej I I Note that the dynamic stiffness matrix K does not depend on the loading condition E i. Also, for W = 0 H g(O) : E. g Having found the transfer functions, the acceleration time-histories follow then from the inverse Tourier transformation: I . r las , (9) Hjfjfe twt dw i b

  • 2r ',
                  -m I

where, ft

ft (w) is the Tourier transform of the j th input acceleration component:

B T fj :- jj ,-lwt di O I 2253 103 4-14

BEAVER VALLEY POWER STATION, UNIT 1 s -i The procedure consists then of determining the dyna::ic stiffness matrix K d' solving Eq 6 for the six loading cohditions H = H , determining the six 

                                                                                       ~     f Fourier               transforms of the input components F =if)]', and performing the inver 1           transformation (Eq 9), which corresponds formally to:

J _ _ _ _ - 

    ;           O=h                             HF elW' dw i
    !      The dynamic equations are solved in FRIDAY by Gaussian elimination, and the Fourier transforms are computed by subroutines using the Cooley-Tuckey FFT (fast Fourier transform) algorithm.                                 A comparison of the results of FRIDAY vith another solution is shown in Section 10.5.

4.2 STRUCTURAL MODELING = The level of detail in mathematical models of s ructures is determined by consideration of the following: e _ 1. distribution of mass in the building

2. symmetry / asymmetry of building arrangement 3.

locations at which output is required 4 approximate frequency content of input 

   -=

2253 104 4-15 3 

      'h h

BEAVER VALLEY POWER STATION, UNIT 1 li 

     ;        The   models                     used in the analysis,    typically,   are generalized,   three-dimensional, multi-mass representations.                    The total number of degrees of freedom included is more than sufficient to encompass all significant frequencies; the number of masses being governed, as a practical matter,                      by the locations at which amplified response spectra (ARS) are required.

e _ Eccentricity between the center of mass and center of stiffness at every level i is included, except where insignificant. As a result, the effects of torsion 

}             upon the modes and frequencies is automatically determined.                      A typical model is shova in Figure 4-6.                     The generalized dynamic members connecting the
~

j centers of mass have stiffness matrices determined by tensor transformation 

        ;     from the matrices of the structural elements connecting the centers of 9              stiffness.

= 4 e To demonstrate the effects of torsion on the results, a comparison was made a j between the analyses using a generalized three-dimensional model and a planar 

   ,          model of the main steam valve building. This building has one open side and 1

relatively large eccentricities between centers of mass and rigidity. The l results of this comparison are shown in Figures 4-7 to 4-10 and indicate that j for this site the effects of torsion are not significant. i 3 2253 105 1-4-16 

                                           .ii                                     ,       ,

BEAVER VALLEY POWER STATION, UNIT 1 4.3 RESULTS Output from the third step FRIDAY includes structural response as well as ARS for all , coordinates in each structure analyzed. In general, a structural coordinate coincides with a building floor level. Typical structural acceleration and displacement profiles are shown in Figures 4-11 and 4-12. ARS are generated for two orthogonal horizontal and the vertical directions at each structural coordinate for both OBE and DBE earthquakes. Typical ARS are shown in Section 5. For use in pipe stress problems, ARS peaks are automatically broadened 225 percent to account for variations in soil and structural material properties. Comparisons of AhS generated by the three-step REFUND / FRIDAY method and the finite element PLAXLY method as well as those based on the FSAR earthquake and the Regulatory Guide 1.60 earthquakes were made at the request .of the NRC. The ARS generated for these comparisons used strain compatibic soil parametere from the last iteration of the SHAKE program. Comparisons were also made of ARS generated from the REFUND / FRIDAY programs for a variety of soil parameters as requested by the NRC. All ARS comparisons are described in Section 5. 2253 106 4-17

3EAVER VALLEY POWER STATI0!i, U!!IT 1 I 4.4 RETEREliCES

1. Timoshenko & Goodier, Theory of Elasticity, 3rd Edition. McGraw-Hill Book I

Co., p 97-109..

2. Kausel, Whitman, Morray, & Elsabee, The Spring Method for Embedded Foundations. tiuclear Engineering and Design 48(1978): 377-392.

I I I I I I g .. I I 2253 107 I I 4-18 I 

                                               -- w - m        ummer   -      unums   ummus   ummu ammar   ammums
 $(t)                 [K[nxn   '

O M f(t) O r O  % C ,u(t) ,f(t) F 

                             *                                       +

O(t) J 

                                                                                   'f "W"         "*74                           " " "/

[' fY nxn FREQUENCY KIN EMATIC INTERACTION DEPENDENT INTERACTION ANALYSIS STIFFNESS REFUND KINACT FRIDAY w u FIGURE 4-1 THE THREE STEP SOLUTION BEAVER VAL. LEY POWER STATION - UNIT 1

t i 3 

                                                                          /z               '

J-y,,lat , u 

                                                                                       ~

j i \ i \ t l ) J: \ / uy 

~

BOUS SINESQ 

                                                                                   )
              ~

z

H=e lDt i & --;m-- X
                                                                                /

, \ . t,

-i y
,                                                              Y cesauri UE 10
 'l L,                                                                  FIGURE 4-2 THE BOUSSINESQ AND CERRUTl PROBLEMS 7

j BEAVER VALLEY POWER STATION -UNIT 1 )

I b 

                                                             ~

I \ \ 

                                              \

g g  :=N i s 

     ~^" ' ' " ~ " ^ " '
                                                   \

I I - I FIGURE 4-3 IDEALIZATION OF THE BASIC ' REFUND' SOLUTION FOR CONCENTRATED LOADS BEAVER VALLEY POWER STATION - UNIT 1 I - I Uz Ux r "UY Z 

               -           Bi e X I

I 2253 110 I FIGURE 4-4 I ' REFUND' C0 ORDINATE SYSTEM BEAVER VALLEY POWER STATION - UNIT 1 I .

b "X -

  • W A z x =

I N<:n. z 

                                      %                                                              o 35                                                                                   p
 ,                     -xM               N    -
                                                                                                   =m i$

h i A - 2 Hw a: 

                       ~
                                         -~                                                        U M o.

w H >= i 

                                                                                                   =W U

c> i W25 aw> uue b k 

,      -                                               < =-

w 

                                                  ^       ::=.              c:

E >' 

                                                          =
                                                                   ==::::

w 

                                                          ;;,,   N                             O
                                                      <                      A-*               r
                                                  <*N w_              ^
                                                                       =:::

A H< 

                                                                                          <c2 4                                                N 2 3 g
                   *6-                               "3   %        N                      oO' N        %

7 i ~ N I H 2 

                               \                                                          <m            O N                                                     n                   e M*

Ww 5 

                                                          ,                w              JJ            4 g
                                                      =3           ==$.                   WM            y I     g                                                                            UM J                                                                                         U<            d 4 g:
                                                                                               ~

W O 1 y - O 

                                                                                          <b            <

i 2O d O- 

                                                                                          - 0:          4 H             Z 4L            O JO            -

m H zW < 1 <W H O 1 e< Qll H in se is (j  :: . 

                                                                                         ==

ed 

                                                                                                      = $-

J 4 2253 111

_1 l __ y 

                                                                                                                 )L

[ ' 

                                                                                                                    'X g M5 (3.20,73.0, -14.32) i                                                  \                                                          /
     !                                                 \                                                      Z
                                                         \

2 \ j \ 

                                                                  \

l  : 

                                                                            \
      ,                                                                              N 2                                                                                             \ NCS     [

l 

                                                                      /CS l M4 (44.13,51.33,702)
                                                                                             .        /

1 - 

                                                                                    /
                                                                            /
                                                                     /
                                                                       /

M3 ( 32.26, 7.0,-1.63) i 1 _. 1 LCS I M2( 34.76,18.25,0.21) 

                                                                                                    /

_l lfCS l \ / M1 ( 30.0, OD ) ~ 

                                                                      /

h STRUCTURAL ELEMENTS CONNECTING g CENTERS OF STIFFNESS, CS 

          --- GENERALIZED DYN AMIC MEMBER 2253 112 CONNECTING CENTER OF MASS, M i
 =

-1 FIGURE 4 -6 GENERALIZED DYNAMIC MODEL OF A CATEGORY 1 STRUCTURE BEAVER VALLEY POWER STATION - UNIT 1 l T

I 2.00 1.80 DAMP 2.0% 

   ~

1.60 

     ,                140 O

5 l1 8 20 

     -            P
                  $ 1.00 w
     =

u 0 Q80 -- 4 I a c60 ^ ^ \ AA j [I \/S I \ 2 A J  %, J 060 - A - f i WK--N ~ - /, 

 ,                  0.20 j

Ad 

            \              -- :

O.0 EB O.00 0.10 0.20 0.30 0.40 a50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 

       ,                                                                                                                               PERIOD-SECONDS LEGEND 3-D MODEL
                               ----- 2 D MODEL
 $                                                                                                                                                                 2253 113

__ FIGURE 4-7 SEISMIC ANALYSIS OF MAIN STEAM VALVE BUILDING HORIZONTAL SSE EW HORIZONTAL RESPONSE SPECTRUM 4 AT MAT j BEAVER VALLEY POWER STATION-UNIT 1 J N mummimummim----si---ime--- ui smmi-,m-----------ni nyniumio u

2.00 

       ~

1.80 , DAMP 2.00 % 1.60 4 5 1.40 ? O j g1.20 9 U k  : 

      .          m 1.00 hJ                              A 3      ,   1
                                                     ' 'j

$ 0 0.80 j < [V V1 w k_f 1 60 N p A{sk s o,40 I m u .. _ n/N n l 

                                                                                               %d~~v\% /

j s f __ . Q20 

,                        r_.7 0.0 s                0.00         0.10    0.20     0.30   0.40  0.50    0.60  0.70            0.80  Q90  1.00 1.10    1.20 j                                                                  PERIOD-SECONDS
      !                     LEGEND 3D MODEL
                                   ----- 2D MODEL 2253 114 f

i FIGURE 4-8 i SEISMIC ANALYSIS OF 3 MAIN STEAM VALVE BUILDING HORIZONTAL SSE l EW HORIZONTAL RESPONSE SPECTRUM AT TOP J BEAVER VALLEY POWER STATION -UNIT 1 2 

   ~ - - - - -

I I 2.00 1.80 DAMP 2.00% 1.60 1.40 I ? 1.20 I 5, i.OO e I 0.80 l a60 T 

                    )

e 

                                    \ A g    0.20 p                                -

x _ 

         .00   0.10 0.20   0.3 0 0.40 0.50   0.60  0.70   080  0.90    1.00 1.10 1.20 P E RIOD -SECONDS I             LEGEND 3-D MODEL                                                    '
              ---- D MODEL g                                                              2253 115 I                                        FIGURE 4-9 g                                        SEISMIC ANALYSIS OF MAIN STEAM VALVE BUILDING HORIZONTAL SSE I                                        NS HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION -UNIT I I                                                                       .

                         -i.._..i_..-.

d 2 2.00 1.80 DAMP 2.00% 1.60 1.40 O ]~ f 1.20

9 3 m 1.00 w

w , 8 0.80 ,A 

      !     <r j                                                   [

O.60 i A m r! ' Wrj 0.40 " 

                                                                                                ~Nm 0.20                     ,

L. M

= 0.0 O.00 0.10 0.20 0.30 O.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

{ PERIOD-SECONDS N LEGEND 3-D MODEL 

                                       ------- 2-D MOD E L
                                                                                   ~

a 33 116 5 F FIGURE 4-10 =. SEISMIC ANALYSIS OF 1 MAIN STEAM VALVE BUILDING HORIZONTAL SSE 

   '                                                             NS HORIZONTAL RESPONSE SPECTRUM AT TOP BEAVER VALLEY POWER STATION- UNIT I
   --                                                                     -ii-.i

               ,     .                                                     m                                         ,,,

4 J t 1 ELEVATION ABOVE MAT ACCELERATION (FEET) (G) 177.50 C O.245 7 I J ELEVATION ACCELERATION (FEET) (G) 0.174 136.@ C O.228 132.10 0 111. 7 5 O O.15 4 g g ,000 O.19 4 91.40 0 0.134 86.00 O O.157 71.050 0.11 2 

                                                                                                                                  *I a              5(170()                                     O.095 30.350                                   )   0.090                                               35.00()          O.I O 8
 ,               0.00--O                                    0.082                                                0.O(y- h        O.082 SHELL                                                                                       INTERNALS i
-a d
 ;                                                                                                                       2253 117
   -l 1._

FIGURE 4-11 l TYPICAL ACCELERATION PROFILES ~ BEAVER VALLEY POWER STATION -UNIT 1 2

I I I ELEVATION ABOVE MAT DISPLACEMENT ( FEET) (INCH E S) 177.50C O.28695 I ELEVATION (FEET) 136.000 DIS P L A CEMENT (INCHES) 0,2558 132.10() 0.21429 111.7 5() 0.18806 l 11.00( ) 0.2 213 91.4 0() 0.!6135 I 71.0 5() 50.70() 0.13454 0.10814 5 7.00 t ) 0.1430 3025(,) O.08355 I O.0 0.06838 0.0 0.0684 SHELL INTERNALS I I l 2253 118 I I FIGURE 4-12 TYPICAL DISPLACEMENT PROFILES BEAVER VALLEY POWER STATION-UNIT I I 

                                         ~
        ; .-x_-_- L__'L___

_ .. _=_l _ _- - . .- . . 

                                                    + . _.     .
                                                                   * ,   ...______2

( 1 Y I 

               =

P - it e e 2253 119 

     +

x s* 

     't    [

S - E 

                                                                                        =

3 

                                                                                        $ l *-

I BEAVER VALLEY POWER STATION, UNIT 1 

          ?

_i 3 j 5.0 COMPARISONS OF RESULTS 4 

~

Comparisons of amplified response spectra (ARS) f,or the DBE vere prepared for 1 the following cases: a _f 1. Methodology - RETUND/TRIDAY vs PLAXLY 

~
2. Earthquake - TSAR vs Regulatory Guide 1.60 A

A

3. Soil Parameter Variation - low strain, first and last iterations from
   ^

_j~ SHAKE; 150 percent variation of low strain input to SHAKE. 2 5.1 RETUND/TRIDAY VS PLAXLY 

    =

The contain=ent structure was analyzed two ways for purposes of comparison using strain compatible soil parameters from the SNAKE program. Y u

1. A one-step analysis using the finite element program PLAXLY k -

._ 2. A three-step analysis using the methodology described in Section 4.1 

      -f

} The following observations can be made about the ARS shown in Figures 5-1 I through 5-3.: t_ 2253 120 4 5-1 L. i

j BEAVER VALLEY POWER STATICK, UNIT 1

1. At the mat level, the results of the two methods are very close.

[ 2. With increasing elevation, the RETUND/TRIDAY results become more conservative with respect to the PLAXLY results. This is a [ i consequence of the conservative assumption made about the rotational part of the input in the kinematic interaction step (see, for -_- example, Tigure 10.4-2). _I i 5.2 TSAR EARTHQUAKE VS REGULATORY GUIDE 1.60 EARTHQUAKE Additional analyses were performed at the request of the NRC using the three- , step method (RETUND/TRIDAY) to compare the design earthquake in the TSAR to that specified by Regulatory Guide 1.60. The ARS shown in Figures 5-4 through 

         , 5-6 are comparisons of consistent piping analysis bases; that is, the spectra for equipment dampings associated with the Regulatory Guide 1.60 earthquake (2 j       and 3 percent)                    are displayed with' the               1 percent spectra for the TSAR

) earthquake. The soil shear moduli and damping used for these analyses ars = from the last iteration of the SHAKE program. L Even though the Re gulatory Guide 1.60 earthquake is significantly more 

  $        energetic than the TSAR earthquake, the results are very close.

2253 121 

      $                                                                     5-2 I

t O

BEAVER VALLEY POWER STATION, UNIT 1 7 N 5.3 VARIATION OT SOIL PROPERTIES 4 At- the request of the NRC, ARS vere generated for a range of soil shear f modulus and damping ratio: r i 

       ;          1. The low-strain soil shear modulus                             (Gmax) with scil damping ratio 3                     equal to 0.05.

i

2. Shear modulus and damping after one iteration in SHAKE, starting from a

L{ the low-strain modulus (Gmax), d e 3. Shear modulus and damping consistent with earthquake amplitude, but i calculated by the program SHAKE starting from 1 1/2 times the low-strain modulus Gmax +50 percent. s J 4 Shear modulus and damping consistent with earthquake amplitude, but calculated by SHAKE starting from 1/2 times the low-strain modulus Gmax -50 percent. J [, _

5. Shear modulus and damping from the last iteration of SHAKE, starting s with the low-strain modulus (Gmax).
  =

.- 2253 122 L a i 5-3 l,

+ E BEAVER VALLEY POWER STATION, UNIT 1 s i i The ARS for Cases 1, 2, and 5 are compared in Figures 5-7 through 5-16 for piping damping ratios of .005, .010, and .030. They indicate that the analysis is sensitive to extreme variations in parameters but that, within the i limits of the iterations of SHAKE, both the amplitudes and frequency content ~. are well-behaved. 

 ,       The ARS for Cases 3, 4 and 5 are shown in Figures 5-16 through 5-24 for piping 4

3 damping ratios of .005, .010, and .030. Beginning the SHAKE analysis with 1/2 3 the low-strain modulus results in extremely low moduli for the final iteration. Again, while apparently sensitive to extreme variations of input parameters, the amplified response analysis is relatively insensitive to variations of modulus and damping in the reasonable middle range of values. s [ 

   ?

[ 2253 123 a h [ 5 f 5-4 1 aur

_1 h 1 0.80 }. DAMP 3.OO*/o O.70 3 0.60 

  !     C 1          *O 8 50

- N m 0.40 

                                                                                           \     '

O.30 d' < \/ \  % 

  ^!-

O.20 

                                            '                #                                                '           ^
                                                                                                                  ~

h 1 O.10 y . h O.0 

    ,           QO                     O.10   0.20   0.30    0.40  0.50                 0.60   0.70  0.80   0.90        LOO    LIO      1.20 PERIOD- SECONDS
  ^

= i LEGEND .' REFUN0/ FRIDAY ---- 

                                ---- PLAXLY                                                                           -

f ? 5 

    !~

i. i m { FIGURE 5-1 COMPARISON OF REFUND / FRIDAY i AND PLAXLY - ARS AT MAT j BEAVER VALLEY POWER STATION- UNIT I 

 ? =

_i 

?
            '00

_ i j DAMP 100% 0.90 ~_ o.80 . I 0.70 

                                            \

h,h I i o.60 k 

       . 5 5 0.50                           un      /T.

. d , se . O g,4n i. , \n A 

  >      <                     ym                          ~y                     v a               O\    .                                      Ih-
                                                                                                                'N'L 3 f \/

~ p n/ ojo i s i o.0 clo 020 030 0.40 aso oso 070 nao 090 1.00 tio 1.20 PERIOD-SECONDS 

 =

i .~ 

                                                                                                           .       2253 125
  ,                LEGEND                                                                                                      ,

i REFUNo/ FRIDAY --,-- 

 ~

j ---- PLAXLY - - - - - 

  ,                                                      FIGURE 5-2 j                                                        COMPARISON OF REFUND / FRIDAY l

AND PLAXLY- ARS s AT OPERATING FLOOR -2 BEAVER VALLEY POWER STATION-UNIT I 7 

 --N                                                             . _ _ . - - - - - - - , , , , , ,   , , ,

    }

i i 11 0 i DAMP 3.00% IM g . 

    .         Q,0
 -J           O20 O.70         ,                               ,

O s i g"' 

                                             /A              Ng d

jfrx 

                                           /

g 

                                                         \        \

w 0.50 , 

                                                          )

o l i l 0.40 \ 2 

                                                                  \       \_

O.30 - 

 "                                 i j                                    -

3 m0 

                     -         /, s                                                                     tR f        ./                                                                                          ,

0.10 0.0 OD OJO Q20 Q30 0.40 0.50 0.60 Q70 0.80 Q90 1.00 I.10 I.20 j PERIOD-SECONOS - LEGEND 2253 126 

 $                                 REFUND / FRIDAY                                                       ~-

U ---- PL AXLY 

    -5
 ~)                                                     FIGURE 5-3
 ~~

COMPARISON OF REFUND / FRIDAY 

 -,                                                     AND PLAXLY-ARS AT SPRINGLINE BEAVER VALLEY POWER STATION-UNIT I

1 J N 2.0 3 8

  • 1.8 J 1.6 J 1.4 4

O y 1.2 O 

=.      Q m 1.0 u

y 0.8 0.6 

     =
                                                                        'N 0.4 NSWDAd 3
           ,,                  ,                    .h-g [. 4 9                            //D,%                        V/
                   ,       g*
                           /

c O.0 i O.00- O.10 0.20 Q30 0.40 0.50 0.60 0.70 0.80 Q90 1.00 1.10 1.20 j PERIOD-SECONDS LEGEND FSAR EARTHQUAKE 1% DAMPING I\ -~~- REGULATORY GUIDE l.60 EARTHQUAKE 2% DAMPfNG h - REGULATORY GUIDE I.60 EARTHQUAKE 3%DAMPfNG -- 1 [  : 2253 127 A .. FIGURE 5-4 COMPARISON OF FSAR AND REGULATORY GUIDE I.60 1 EARTHQUAKES- ARS AT M AT d BEAVER VALLEY POWER STATION - UNIT 1 m 

'F'

. - , r, u i i i 2.50 

  ?   t d            2.25 l

J 2.00 . . - ..- ( l 1.75 +-+ O y 1.50 e ) 12.5 I A "i 

             -                                                   t4 ))t
 }           $ 'So                                              yv^\ k 075                                    \      h/

() i^^ sp ." k. 

 !_             m                                     hAl                                                  kA i                                               p                                                                                        N.

y se -- - 0.0 

 ';                  O.00'                 O.lO     O.20     0.30      0.40                   0.50       0.60    0.70  0.80 Q90         1.00       1.10 1.20 j                                                                                              PERIOD-SECONDS 1

1 I LEGEND FSAR EARTHQUAKE 1% DAMPING - - - - 

                                           ---- REGULATORY GUIDE L60 EARTHQUAKE 2% DAMPfNG
 )

REGULATORY GUIDE l.60 EARTHQUAKE 3% DAMPING -- i L j 2253 128 1. t FIGURE 5-5 

  ]

COMPARISON OF FSAR AND REGULATORY GUIDE I.60 EARTHQUAKES- 

    ,                                                                              ARS AT OPERATING FLOOR BEAVER VALLEY POWER STATION- UNIT I 5

m' a 

't              5.0
 )

4.5 3e 4.0 

      .                        i 3.5 7

m i 3.0 s g r 4 g 2.5 3 

             "i w

82.0 

             <                                             T i

i.5 i L y . io (: ~ 

                                                     , f             vp                                                              -

T "' . , $& mmw i s u --; AM,pu i O.0 _! O.00 0.10 0.20 0.30 0.40 0.50 Q60 0.70 0.80 0.90 1.0 0 1.10 1.20 l PERIOD-SECONDS FSAR EARTHOUAKE 1% DAMPlNG 2253 129 .

, ----- REGULATORY GUIDE 1.60 EARTHOUAKE 2% DAMPING - - -
                           -      REGULATORY GulDE 1.60 EARTHOUAKE 3% DAMPING                                   --

FIGtJRE 5-6 h, COMPARISON OF FSAR AND REGULATORY GUIDE I.60- ARS AT 

 ;                                                                                         SPRINGLINE J                                                                                         BEAVER VALLEY POWER STATION-UNIT 1 1

l 

   =

g 2.50 2.25 y DAMP O.50% 2.00 1.75 o p 1.50 9 

   =

a: 1.25 i W

a w

u 1.00 0.75 h 

                                      , .g //g..         / *   %/                   W%

NN O.25 .9, h[/ 

                                        .v    .

i 

                    /

O.O QOO O.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 L20 PERIOD-SECONDS a i LEGEND 

 !                                   LOW STRAIN Gun
                        -- -- FIRST ITERATION FROM SHAKE LAST ITERATION FROM SH AKE                                2253 130 k

( l j 

   -                                                     FIGURE 5-7 COMPARISON OF ARS' FOR T                                                       SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION - UNIT 1 F

2 

  .        2.50 2.25 DAMP 1.0 %

2.00 I.75 O y1.50 e tim 1.25 

   ~

u.i 8 LOO 

     !. 4 O.75 MS          A O.25                '
                                    'V 4/
   ~

i M 0.0 

,                0.0   0.10   0.20   Q30    0.40   0.50   0.60  0.70              0.80 0.90   LOO  l.lO   1.20 i                                             PERIOD-SECONDS

_1 LEGEND LOW STRAIN Guax 

   ]                   ---- FIRST ITERATION FROM SHAKE                                     2253 131 LAST ITERATION FROM SHAKE i

j FIGURE 5-8 COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS l HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION-UNIT I

e i =. 2.50 2.25 DAMP 3.00% ~ 2.00 1.75 g .50 1 9 4 

     . Q: L25
LM

_., J 

  -          IDO O.75 050 5*

azs m yaqq [.8:D e- - m - 

                                                                                                    ~
                                                                                                        ~

_i <- QO O.10 0.20 0.30 0.40 0.50 a60 0.70 0.80 0.90 LOO 1.10 1.20 PERIOD-SECONDS LEGEND LOW STRAIN Guax 

                       ---- FIRST ITERATION FROM SHAKE j                           -

LAST ITERATION FROM SHAKE 2253 132 h FIGURE 5-9 COMPARISON OF ARS FOR ? SOIL PARAMETER VA'tIATIONS

-- HORIZONTAL RESPONSE EPECTRUM AT MAT BEAVER VALLEY POWER STATION-UNIT 1
  +
     !                                                                                                          I j

4 

    =

2.50 ~ 2.25 DAMP O.5% 1 2.00 gg a, 1.75 l 1.50 

       $                                                         y      1 3

1.25 ' I i W  ! .I 2 d l 8 1.00 1/ /' 

       <                                               l   j!                ~^g.s l

0.75 ' A 

     ;                            .                  "#!                                                  V n                           i 0.50
 =
                                                                                                                         ^

O.25 ' - j'4 , 0.0 0.00 0.10 O.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 PER100-SECONDS 'e' LEGEND LOW STRAIN Guax 

                   -- -- FIRST ITERATION FROM SHAKE

_~ - L AST ITERATION FROM SHAKE 2253 133 r u FIGURE 5-10 

"                                                                                      COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE S PECTRUM AT OPERATING FLOOR BEAVER VALLEY POWER STATION-UNIT 1 r

I 2.50 2.25 DAMP 1.00% 2.00 1.75 e . n. I hin i [r-a m s 

                                     /      b g 1.0                      ,          . 9 l  \   ;f
                                       /        .
                           !  t  !;              \.\cs
     .50 lJ a

sAk ms s \ 

     .25         y
                    #                                                                  w%_

v I 0.20 0.30 0.40 0.50 0.60 0.70 0.90 1.00 1.10 1.20 O.00 0.10 0.80 PERIOD-SECONDS LEGEND LOW STRAlH Gnx 

              ------ FIRST ITER ATION FROM SHAKE
                    -           LAST ITERATION FROM SHAKE I

I FIGURE 5-11 COMPARISON OF ARS FOR l SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM AT OPERATING FLOOR BEAVER VALLEY POWER STATION -UNIT 1 I

I P_50 2.25 DAMP 3.00% 2.OC 1.75 e , g tsO I. m 4 

  $ 125 I  d 1.OC
                                /l      A-j  r-   bij s

n !/ a" V 0.25 j QQ._x , D- _ f- -- I 00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 f.OO l.10 1.20 PERIOD-SECONDS I LEGEND LOW STRAIN Guax 

                ----- FIRST ITERATION FROM SHAKE L AST ITERATION FROM SHAKE
                                                                           }}}} j}}

I I FIGURE 5-12 COMPARISON OF ARS FOR l SOIL PAR AMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM AT OPER ATING FLOOR BEAVER VALLEY POWER STATION-UNIT 1 I 

                                                           ,,                                                                        r 1

1 2.50 i l,l DAMP O.5 % 2.00

1.75 N, i J l .

4 j' l j ~ 1 5 '50 j I E I i a:125 i.j b l b l.00 ' 

                                                                                   -- ^

4 

                                                         $l l' In
                                                                                   \

og ,f :g Mt A a a50 7 a25 fV N \)  %% O.0 0.00 0.10 0.20 Q30 0.40 Q50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 "; PERIOD-SECONDS j LEGEND ~ LOW STRAIN Guax 

                         ---- F1RST ITERATION FROM SHAKE LAST ITERATION FROM SHAKE
                                                                                                                                                         }}}} j}{
 ~

FIGURE 5-13 '_ COMPARISON OF ARS FOR i SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM 1 AT SPRINGLINE j BEAVER VALLEY POWER STATION-UNIT I semi-i----i-ii iim -

3 2.50 2.25 e 2.0 DAMP 1.00% j-1.75 I e "l . 

     ?    e                                                       ( j'l !
f. i.5 u iA O -

l C 7[4 1.25 ( l d ,8 / I - 

                                                             '    /               \

O 1.0 2 m 8 =, e./ s U O.75  ! '- \, 0.75 - 

                                               )
    -;                                              \)l x

_j O.25 

                   ; py
                         ^-
                                                                                                                  %-    ~.

j O.0 000 0.10 0.20 0.30 0.40 0.50 Q60 0.70 0.80 0.90 1.00 1.10 L2O 

]                                                                                     PERIOD-SECONDS 9

LEGEND j - LOW STRAIN Gesu 

                                  - - FIRST. lTERATION FROM SHAKE
                                                - LAST ITERATION FROM SHAKE
                                                                                                             }}}} l}7 w

y h [ 1 FIG U R E 5- 14 COMPARISON OF ARS FOR l SOIL PARAMETER VARI ATIONS HORIZONTAL RESPONSE SPECTRUM AT SPRINGLINE 

   ]                                                                                  BEAVER VALLEY POWER STATION- UNIT 1

= e j 2.50 2.25 DAMP 3.00% 2.00 1.75 1.50 

   }
      !       9 a: 1.25 3

w s o 1.00 . i l' G75 #' A 8' 

                                                                               ""\

O.50 # b kJ / V% I Y O.25 pr -v- g 0.0 0.00 0.10 G20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 PERIOD-SECONDS M s LEGEND LOW STRAIN Guax - ---- FIRST ITERATION FROM SHAKE 

                                               - LAST ITERATION FROM SHAKE
                                                                                                           }}}} j}}

5 FIGURE 5-15 -7 COMPARISON OF ARS FOR 1~ SOIL PAR AMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM 3 AT SPRINGLINE j BEAVER VALLEY POWER STATION - UNIT 1 J

1 2.50 m 5 J 2.25 DAMP O.5 % _j 2.00 h ' 1.75 _ O 

         ?            i 50

_8 

   --             N g 1.25
 =;

y 

   -5             8 1.00 4.

7 0.75 s A A 5 v v g 0.25 

                                        .3          ,! gI(ftyy~
                                                   ,- m T

7 e m.A ~ h% ~x - ~ i h,% O.0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80' O.90 1.00 1.10 0.20 ] PERIOD-SECONDS d LEGEND G + 50% FROM SHAKE - 

                                  ---- LAST ITER ATION FROM SH AKE                                                                   - - -
                                  - - G- 50% FROM SHAKE
                                                                                                                                                  ~

1 

.a 7!                                                                                                  FIGURE 5-16 J                                                                                                    COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS 7                                                                                                    HORIZONTAL RESPONSE SPECTRUM AT MAT j                                                                                                    BEAVER VALLEY STATION-UNIT 1

- m; I mn-s-imini-nn--uni-i

-s f 2.50 2.25 l DAMP 1.0 % 2.00 $ 1.75 -. o [ E 1.50 O P i <t j l.25 w u 

      ,, N 100 O.75 3
       -    0.50                                             - ^                          -

g / O.25 - s 

                                                                  ^

v l'- h - - - - ~ q ,7W\'/ Ny '- - w _y :..' . ./ i O.O } O.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

. PERIOD-SECONDS t

LEGEND ( G + 50% FROM SHAKE - -- -f 

                              -- CAST ITERATION FROM SHAKE G - 50% FROM SHAKE
                                                                                                  }}}-}-]-fQ

= 1 i .] 

      !                                                      FIGURE 5-17

/ COMPARISON OF ARS FOR , SOIL PAR AMETER VARIATIONS l HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION- UNIT 1

2.50 > 2.25 DAMP 3.0% 2.00 1.75 o y 1J50 9 cr 1.25 8100 

             *C
                 .75
                  .50 2S

_ ., 7

  • V.
                                                                  /*                       vt y'" ~*A          .sCWm
                                                            .       .   ,. J                                            :. _. a
                 .00   &ff 0.00  0.10                0.20    0.30    0.40   0.50   0.60             0.70 0.80  0.90    1.00 1.10    1.20 PERIOD-SECONDS LEGEND G + 50% FROM SHAKE                                        --

LAST ITERATION FROM SHAKE G- 50% FROM SHAKE 

                                                                                                           }}}}- ) .)

FIGURE 5-18 COMPARISON OF ARS FOR 

  ~

SOIL PAR AMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM AT MAT BEAVER VALLEY POWER STATION-UNIT 1

_^ 2.50 

;            2.25
--                                                                                                                    DAMP O.5%

2.00 

   -j         l.75                                     !', f
                                                          ,1
     =
-i             1.50                                  11
    ;     2                                         II       i I
!! ' zs l l l
 -        W                             l ,i        l            6 l.00
    ]                                       ;     ,                  43 J         <-                                 j i

I g5 ' 

                                                 /

e 

                                                                         /st. U,     ,I 0.75 3                                                ,                     j         i, '

O SO - p' y. 7  % 0.25 - j',.f !

. .6;-

i 0.0 g 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 j PE RIOD - S ECONDS LEGEND: q J G + 50% FROM SHAKE 

                       ----- LAST ITER ATION FROM SH AKE
                       - -+-* G- 50% FROM SHAKE                                                                    :]}}    j(}

J 7  : a l = 

~

FIGUR E 5-19 n COMPARISON OF ARS FOR e S0ll PAR AMETER VARI ATIONS HORIZONTAL RESPONSE SPECTRUM 1 AT OPERATING FLOOR A BEAVER VALLEY POWER STATION- UNIT 2 m n

g i 

    =

2.50 I

2.25

_ D AMP 1.0% j 2.0 0 1.75 0 E 1.50 o f Il ct: 1.25 h. A g 

 ,          1.00 0.75                               '

1 l} L m 

                                                                         ^   ^
  ~

O 50 0.25 s' 

                   - d y

rj j sf- w N 0.0 0.00 0.10 .O.20 0.30 0.40 0.50 0. 8.3 0.70 0.80 0.90 1.00 1.10 1.20 

]                                                                      PERIOD-SECONDS
 ,    1 J                LEGEND G + 50% FROM SHAME                             - - --

f ---- LAST ITERATION FROM SHAKE 7 G - 50% FROM SHAKE - -} FIGURE 5-20 COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS HOREONTAL RESPONSE SPECTRUM AT OPERATING FLOOR _i BEAVER VALLEY POWER STATION-UNIT 1 l 

    ]

l' 250 i 21s = DAMP 3.0% 2.00 

     .=
      .              l.75 O
  ]              gISO e                                                                                             -

Q a: L25 w w 8 oo ) -= 0.75 h I h 

                                            /

l / I P lf YI 

                                                    /

i og i azs JI j 

                                            '{'          F'
                                                             )              %                                 s  ~

A 1 1 g# - 

                                                                                                                                                  ^

0.0 

      .                  - 0.0   0.10    0.20      0.30      0.40   0.50   0.60                   0.70             0.80 0.90            1.00   1.10   1.20 j                                                                   PERIOD-SECONDS i

i LEGEND G + 508/o FROM SHAKE - - - - - 

                                 ---- LAST ITERATION FROM SHAKE                                                          2 2 5 -3 1 4 4 G - 50 */o F ROM SHAKE                                                           . - - - -

i J FIGURE 5-21 

     ?                                                               COMPARISON OF ARS FOR
     >                                                                Soll PARAMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM AT 1                                                                  OPERATING FLOOR j                                                                  BEAVER VALLEY POWER STATION-UNIT I n

M

j. _ _ _ _

3.00 2 2.75 DAMP O.5% 2.50 2.25 , j 2.00 b glk.!' , 11 l l 

       -                                                                   It !$

a z 1.75 9 I 

                                                                           !u-a                                                       i       df y             $ 1.50
                                                                                                                             ~

j s i 

                                                                   , ,l       )

p\ 0 ,.25  :  :,. J, 3 g h; in l  ; ., _ 1.00 j ,,l 

                                                                                                               .I 0.75 y'      .
                                                      \

f,I ~ 

                                                                                                             ~

o.50 

                                                                                                                             %4
                                                                                                                                    ^
                                                                          ./
                                                      ) $i
                                                    ^     '

0.25 

 -                    aT*=r

! ' O.co 0.10 0.20 0.30 0.40 0.50 0.so o.70 0.80 0.90 1.00 1.10 1.20 =. PERIOD-SECONDS J 

                        'E ""
    )                                                         G + 50% FROM SH AKE 2253 145 r
                               -~~~-- LAST ITERATION FROM SHAKE G -50% FROM SHAKE                                                         --

FIGURE 5-22 l COMPARISON OF ARS FOR J SOIL PARAMETER VARIATIONS HORI2ONTAL RESPONSE SPECTRUM i AT SPRINGLINE BEAVER VALLEY POWER STATloN-UNIT 1 7 

        .1

3 1 

    ;       2.50 i

j 2.25 DAMP 1.00% )~ 1 s i 1.75  ; A f 1.5C -i i r I(i I I l y ' [ W hjS ; 

                                                                      \#.

o / -, O l.00 I e /g\ t > \. x  : i A - 3 

                                  .        ))                 ./                             %%y a

0.2 - p x 7y J Ly bN J  %% i 0.00 0.00 O.10 0.20 0.3O O.40 0.50 0.6O O.70 0.80 0.90 1.00 1.10 1.20 2 PERIOD-SECONDS l LEGEND E G+ 50*/o FROM SHAKE m ----- LAST ITERATION FROM SHAXE 2253 146 j *

  • G-50% FROM SHAME
      =

FIGURE 5-23 3 COMPARISON OF ARS FOR SOIL PARAMETER VARIATIONS j HORIZONTAL RESPONSE SPECTRUM AT SPRINGLINE BEAVER VALLEY POWER STATION-UNIT l

1 

 -          2.50 l            2.25

. DAMP 3.0% 2.00 1.75 , o l 4 1.50 9 w 1 $ 1.25

  • i w a
                                                    \

a 

                                                        )

U '00 )lb l E l \ W / \ oy3 .I u 

                                                              \4"N       .

l L o' j . , ,/\ \ 0.50 > 1 m% % 5 *  ! L/ .. 6 r ,.f' Y - 

                                                                                                                    ~           .n n_2s g7 s,                   v.r                                                                    -w~--                 ,
     ^i 0.0 0.00             0.10 0.20       0.30      0.40   0.50    0.60                     0.70 0.80    0.90      1.00    1.10 1.20 PERIOD-SECONDS
       ;             LEGEND G +50% FROM SHAKE                                                         2253 147
                             ---- LAST ITERATION FROM SHAKE                                                           -

j - G-50% FROM SHAKE e FIGURE 5-24 COMPARISON OF ARS FOR J SOIL PARAMETER VARIATIONS HORIZONTAL RESPONSE SPECTRUM i AT SPRINGLINE j BEAVER VALLEY POWER STATION UNIT 1 d,

4 

              !E si 11 EN 2253 148

r BEAVER VALLEY POWER STATION, UNIT 1 6.0 APPLICATION OP SEISMIC INPUT TO PIPE STRESS ANALYSIS In general, seismic input to pipe stress analysis consists of inertia loads obtained through the application of amplified response spectra, and building seismic displacements applied appropriately at support points in accordance with the design load combinations for each piping system. 6.1 AMPLIFIED RESPONSE SPECTRA Amplified response spectra for pipe stress analysis are developed and peak broadened as described in Section 4 of this report. Damping values for piping systems are 0.5 percent for the OBE and 1.0 percent for the D3E. When all support points of a piping problem are located within the same structure, the amplified response spectrum which is closest to and higher in elevation than the center of mass of the piping system is applied in the analysis. Por piping routed between buildings, an enveloped response spectrum representing the highest aceleration for all periods is used. 2253 149 6-1

BEAVER VALLEY POWER STATION, UNIT 1 6.2 BUILDING DISPLACEMENTS Relative seismic structural displacements within a building, as determined from the building seismic analysis, are used as inputs to support motion of piping systa=s and are considered as static boundary displacements in the piping analysis. Por piping running between buildings, the relative support motion includes the effect of each building's motion taken out of phase; this is the most conservative approach. 2253 150 g I I I I I I - .- I I I e-2 I

-i --- RE 

               =E na 2253 151

BEAVER VALLEY POWER STATION, UNIT 1 I 7.0 SOIL STRUCTURE INTERACTION ANALYSIS IN THE ORIGINAL DESIGN This section is included because of a request by the Nuclear Regulatory Commission, Division of Operating Reactors, during meetings held with the I Stone & Webster Engineering Corporation at Bethesda, Md. on March 16 and 17, 1979. The basis for material presented in this section is described in Section B.1.2, entitled " Seismic Design" of Appendix B of the Beaver Valley Power Station FSAR.8 I This section provides comparisons of ARS for the containment structure at the operating floor (Figure 7-1) and springline (Figure 7-2) calculated by (1) the time history method using a maximum modal damping of 7 percent, shown by the

d. ashed line, and (2) by the time history method using modal damping but including radiation damping due to soil structure. interaction, shown by the solid line. The analysis used to compute radiation damping is in accordance with procedures described by Whitman.828 Table 7-1 shows weighted modal damping values used in the time history analyses which were performed to calculate the ARS. These modal damping values were calculated in the manner suggested by Biggs and Whitman.'88 The spring connected lu= ped mass model (including soil springs) used in these analyses is similar to that depicted in the FSAR, Figure B.1-1.

I 2253 152 7-1 I 

                                                      ~

BEAVER VALLEY POWER STATION, UNIT 1 I The Helena E-U earthquake record normalized to .125 g was used as input in accordance with studies referenced in the TSAR, Appendix 3. I 

                                                                  ~

7.1 RETERENCES I

1. Beaver Valley Power Station Unit 1 Final Safety Analysis Report, Appendix B, Section B.1.2, Seisnic Design.

I

2. Whitman, R. V. Vibrations in Civil Engineering. Proceedings of a Symposium Organized by the British National Section of the International Association for Earthquake Engineering.

I- 3. Biggs, J. M. and Whitman, R.V. Soil Structure Interaction la Nuclear Power Plants, Fluid Japanese Symposium on Earthquake Engineering, Nov. 1970. 2253 153 I I I - I 7-2 I 

                                                         . . . . -                                 .... .. . _ . = -

i d BEAVER VALLEY POWER STATION, UNIT 1

TABLE 7-1
MODAL DAMPING RATIOS USED IN TH1: TIME HISTORY ANALYSIS

_) USING SOIL SPRING ST.*FTNESSESM l Modal Damping Hgd3 Freo (cos) Period (see) Case I Case II i 1.61 0.622 0.07 0.1565 

          ;     2           2.847        0.3512                                  0.07                                0.6536  Vertical 3           3.83         0.2611
                                                     ~

0.07 0.3059 4 5.525 0.1843 0.041 0.041 

 ;              5          11.933        0.0838                                  0.022                               0.022 6          14.255        0.0701                                  0.0224                              0.02:4
-m              7          14.952        0.0669                                  0.0207                              0.0207 8      -

18.873 0.0530 0.02703 0.02703 9 22.013 0.0454 0.0279 0.0279 Vertical ', 10 22.293 0.0448 0.0213 0.0213 11 26.015 0.03844 0.0207 0.0207 12 26.749 0.03738 0.0202 0.0002 ~ 13 30.226 0.0331 0.0249 0.0249 Vertical 14 31.037 0.0322 0.0200 0.0200 15 34.511 0.0289 0.0206 0.0206 -'l E2II: y M Computed according to BV1 TSAR, Appendix B, page B.1-4. J m J 2253 154 i c J [ h M i i J 1 of 1 mai-imiim--in-mu----u---mm-um -s n men ii

M 1 M T I N 7 9, U _ g N M DO OI 5 0 T R HAT 0 A TT O - 4 OES 

 . I  G N

0, g SO RL MR E AF YW I P m M A FG RO D R ON O I TY P O _ 1 NTSE T A 9, OAI L 

                                                                    - SR HLA I

I W L L I C. 0 7I E EV R P S O _ EAOIMR RP E W _ UM G ETV A O H YE 8 I 7 

                                      -               0          'FCTBB W                                   -

S 

                                  -                   5 D
                                  -                   6 N                                             ,

W 0 O 

                                  --                       C E

S D W - 2 5 R O I 0 E 

                                          -                P
                                          -                          LG L
                                           -                         E Dl N E      D OP O MM A M

_ 9 3 DD D E E Or TN T HO H I G T lG s_ l EA E I WD Wu D A R Du 

                        ,\g
                              \                        6 O

HG Hi Ou 2 TN Tx }i l il 07 EI EA 

                              /                                      M D U       uu W                         0
                                -                                    YL Y7 RC R0 O N OO I

T T SG SG 

                                /;                     3 1

O IH N IHNi I E P Er M M Mu IA I A 

                                                                                           ;\       t

_ TD TD W _ D 0 0 N . 0 0 0 0 E - W 5 4 3 0$SI4bdoN 2 1 O G E L NNW _Cui W W

M I 1 T I N 7 U 1, - t N M DO OI T 5 0 T H A 0 A TT O . 4 S E S I G l l 0 1 R MRE A i l P M YW A F RO D O OP R N TY O SE lA T _ 1 9 2 O I HL L L L 

                                             -        0                 - S               A
                                            -                         7I              EV I

C R S O 

                                           -                          E A             MR
                                          -                           R P             I E
                                         -                            U G M TVA M                                         -

8 I O YE 7, 0 FC BB M - 

                                     '                     S
                                    ~                 5 D
                                   ~

6 N: . h i . ): 

                                   -                  0 O
                                  '                        C
                                  /

E S D 2 OI 5 R 

                                           -          0 E
                                           -               P
                                           -                             L G L M                                                                         E Dl N E   D
                                        +              9 OP O MM DD A

D M 3 E E p 0 TN T HO G l TI EA E WID W H G I M \ 6 DA O R DU HG HI OM M g\ 2 l! kN X i  : - i 0 EI EA MD U MM M u- YL Y7 R C R0 ON T I OO T SG SG I 3 H lN IN HI 

                                                -      1, EP       E P i

l 

                                                 -     0 i               M     MM       M
                                                  -                      I A      I A
                                                  -                      TD TD M                                                  _

0 0 D - N 0 D J 0 0 0 0. 0 E - 5 4 3 2 1 0 G - M o t $9 FtEJa.dW 

                      < h                          ,g           n.

t* M m

4 ., 

                                                      .. N. 7
                                                                   #   ,s
                                                                                                   ,.                 x c..

_. y w ss 1 t h t? N I 

 .                                                                                                                                                               j                              .

1,- t 1, . i 3 

                                                                                                                                                                              . . .  ,c.
                                                                                                                                                                                              ?

1 o! Mmi 1l m. m. 2: 4 O !. H 2253 157 RB . f C H '-: 

      +<

M 1? E'.-f 

      -l     .,4 11
)
   .-                                                                                                                                                            i. '

q p-e 

                                                                                                                                                                   \ -

11 I 

                                                                                                                                                                   , , ' .s                 .

I 3 1 k i 3 

                                                                                                                                                                                     .:?.

{ 

                                                                                                                                                                                                ?

c * 

                                                                                                                                                                                      ,w.
            ,                                                                                                                                                       .')                           A*

s V v-( 

                                                    ~                           ~                                                    ' '
                                                                                                       ;                                             . 33 eg

BEAVER VALLEY POWER STATION, UNIT 1 j 8.0 INVESTIGATION OF THE EFFECTS OF EARTHQUAKES SMALLER THAN THE DBE Because the soil shear , moduli used in the generation of ARS are functions of i strain, the ARS ate not direct linear functions cf maximum ground acceleration. Therefore, it is theoretically possible that at some 2 j frequencies the ARS for some smaller earthquake exceed those of the DBE. For the purpose of this study, an average strain compatible shear modulus for j a range of peak horizontal ground accelerations from 0.01 g to 0.125 g was i determined using SHAKE. The analyses were conducted for the free field 

     !  profile using the Taft and El Centro accelerograms                      and Gmax values. The average                shear  modulus   corresponding    to each peak horizontal ground

[ s.eceleration was determined by first averaging the shear moduli from the last 1 iteration of SHAKE for the two accelerograms, then calculating the average 1 value over the full depth of soil below the containment fcundation elevation. The variation in average shear modulus versus peak horizontal ground acceleration is given in Figure 8-1. The ARS generated for a range of soil moduli provide a basis for estimating the ARS for earthquakes smaller than the DBE. For example, the DBE shear moduli for the first iteration of SHAKE are actually consistent with a smaller earthquake. The maximum ground acceleration consistent with those moduli, j 2253 158 8-1

1 BIAVER VALLEY POWER STATION, UNIT 1 4 divided by 0.125 g yields a ratio which can be applied to the ARS resulting 

}

from analysis using the first iteration SMAKE moduli for the DBE. j

The. resulting family of ARS at the operating ficar are enveloped by the DBE spectrum, demonstrating that the effects of the DBE are not exceeded by those of smaller earthquakes (Figure 8-2). Therefore, it can be concluded that the stresses in piping due to the DBE are not exceeded by those due to smaller I earthquakes.

l 2253 159 i m 4 - 8 i _a l: 8-2 l =.i 3

i 5787i j 5000 - em vm k* 

  -         1 m-o U3                 .

58 eo rm s i W4 cy 

             <-  4000          -

km 4 i 3000 ' ' ' ' O .02 .04 .06 .08 .I O .12 HOR I ZO N TA L ACCELERATION, g's 2253 160 1 2 

)                                                   FIGURE 8-1 VARIATION OF SHEAR MODULUS
,                                                   WITH GROUND ACCELERATION j                                                    BEAVER VALLEY POWER STATION-UNIT I i                                                                                          i

1 5 2.0 i 1.8 1.6 l.4 O jb Z il i.2 i e H f1 , lu I g i.O _ j1 

-        a                                             1            6        I I

in o , g ii 1 O 0'8 vN 

         <                                       B'i p s
                                                                  '    qM.              N.y A
                                                        .n. s, b,
--           O.,                                                              ,

y.- r s. e4 i j I-i/ \ L 

                                                                                                                       \

04 y 

-;                                           i i

vs ^~-ss---~x s ysx n_, s.A.% .. > s d?k.~$,jl% ^.e... 

                                                          ..                       ..1. . . . . . . . . . . . . . . .
                                                                                                                                                   ^ ' '       -
                                                                                                                                                                 ^~.
  ,i                                 ...-

O.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 PERIOD-SECONDS 

      !,            LEGEND
~
                        ---- 0. 09 5 G
o. izs G 2253 161 r
  • O.060G
                       .... . . . . . . . . . ~ O. O l G               .

3 J 

~

FIGURE 8-2 SEISMIC AN ALYSIS OF CONTAINMENT s HORIZONTAL SSE HORIZONTAL RESPONSE SPECTRUM 3 AT OPERATING FLOOR BEAVER VALLEY POWER STATION-UNIT I a

2253 162 a e E 5

BEAVER VALLEY POWER STATION, UNIT 1 

  -s j

9.0 CONCLUSION

S 4 d Based upon the data and studies in this report, the following conclusions can be drawn about the effects of soil-structure interaction (SSI) analysis on 

  ]

_i amplified responso spectra (ARS) at the Beaver Valley Power Station site. -l s 9.1 USE OP SOIL-STRUCTURE INTERACTION i The principles and the methodology of SSI used to develop ARS are applicable to the Beaver Valley site and can be used with confidence to conservatively 

=

predict the seismic forces on piping systems, a 

 )           9.2    SOIL PROPERTIES The soil investigations made at the site to provide information for the licensing and design of Unit 1 are summarized in Section 2 of this report.

The data from these investigations provide an adequate basis for the 

  ;          development of strain compatible soil properties for use in the SSI analysis.

Soil shear moduli values derived from in situ measurements at the Beaver Valley site are consistent with those obtained from empirical relationships. 

 ]                                                                               2253 163 i                                                   9-1 a

a 

 =

w

BEAVER VALLEY PC'JER STATION, UNIT 1 e i 

      ;      The use of low strain shear moduli Gmax values for soil is not appropriate in developing ARS because earthquake-induced soil strain levels are approximately J           2 orders of magnitude higher than low strain levels.

The use of lov strain shear moduli values equal to 150 percent of the Gmax to e j serve as a basis for developing a range of values in the strain compatible '_- free-field soil profile is excessive. A more meaningful range would be a 4 variation of the iterated strain compatible soil shear moduli values by j 150 percent of the mean value. J 9.3 GROUND RESPONSE 

  =

Licensed ground response spectra and an enveloping artificial time history as input motion at the ground surface in the free field are appropriate for use in the SSI-ARS analysis. 9.4 AMPLITIED RESPONSE ANALYSIS 

  =

The use of the multi-step analysis procedure described in Section 4 of this = report provides an approach that includes conservatisms in stating the magnitude of .the amplified acceleration values and allows development of the _, analysis in a series of logical steps convenient for an engineering evaluation of results. 2253 164 

   =

9-2 a

BEAVER VALLEY POWER STATION, UNIT 1 = 

  =

9.5 COMPARISON OF RESULTS 

       ;    Tha results of comparing the different methodologies and the FSAR earthquake with the Regulatory Guide 1.60 earthquake, and the effect of varying soil

~ parameters lead to the following conclusions:

1. Comparison of ARS shown in Figures 5-1 through 5-3, calculated using the three-step analysis (REFUND / FRIDAY) and the one-step analysis
   ;                            (PLAXLY)        show good agreement at all building levels with respect to 2
  • frequencies at which peaks occur. The magnitudes of amplif'ri j acceleration agree reasonably well at lower levels in the structure.

j At higher levels, the REFUND / FRIDAY results generally exceed the 1 j PLAXLY results. At some frequencies, the ARS calculated for the base mat by REFUND / FRIDAY have amplitudes' less than those obtained from PLAXLY. Since the spectral amplitudes involved are small fractions of 1.0 g, there would be no serious consequences in using these spectra in pipe stress analysis. Nevertheless, it is concluded that = base mat spectra vill not be used in pipe stress analyses.

2. Comparisons of ARS shown in Figures 5-4 thru 5-6 made from Regulatory Guides 1.60 ground response spectra and 1.61 damping values and ARS
     =

calculated on the basis of the FSAR committed ground response spectra 2253 165 4 9-3 

     }

BEAVER VALLEY POWER STATION, UNIT 1 and damping values indicate geod agreement in amplitude and q frequencies of the peaks.

3. A comparison of ARS for soil parameter variations in Figures 5-7 through 5-15 using low strain shear modulus (Gmax), first iteration SHAKE, and last iteration SHAKE soil properties shows little variation in amplitude and frequency of peaks.

4 Comparisons of ARS for soil parameter variations in Figures 5-16 

     ]

J through 5-24 using strain compatible soil properties from the last 1 j iteration of SHAKE based upon (a) the low strain shear modulus (Gmax) g input to SHAKE, (b) Gmax plus 50 percent input to SHAKE, and (c) Gmax J minus 50 percent input to SHAKE show some variation in amplitude and i 

 ]i         frequency of the maximum response, i

h j 5. Changes in the shear modulus of the soil change the frequencies at i 

 ,          which the amplification function has                                          its peaks. This  shift in i

) frequency is evident in the general shapes of the response spectra i: for different values of G. The exact frequencies of the specific individual peaks are influenced by the frequency content of the artificial earthquake, so that each individual peak appears in all spectra. However, the essential phenomenon displayed is a shift in 2253 166 i 

       ~

9-4 .~ I I 

       !                                           BEAVER VALLEY POWER STATION, UNIT 1

_i frequency of the amplification function, causing different pre-existing peaks to be selected for amplification.

6. The results show that ARS are not sensitive to torsion in the e

structure.

7. Spectra calculated using the three-step method, the PSAR earthquake, i
 -                    and the strain compatible free-field soil properties are an adequate basis for analysis of piping systems when peak broadened 225 percent.

b Additional conservatism was directed by the NRC in the period range =l from .4 see to .55 see where amplitudes will be increased by W P 20 percent in accordance with their position confirmed in a letter d dated May 25, 1979. 9.6 APPLICATION OF SEISMIC INPUT TO PIPE STRESS ANALYSIS m The application of seismic input to pipe stress analysis as defined in J Section 6 of this report is conservative and serves as an adequate basis for 

=;           reevaluation of the designated piping systems.

b 2253 167 M 9-5 

                          ==

m-----i-m- e ni i

l BEAVER VALLEY PO*JER STATION, UNIT 1 1 5 9.7 SOIL-STRUCTURE INTERACTION ANALYSIS _= n j The effects of radiation damping due to soil-structure interaction analysis, q as shown in Section 7 of this report, generally decreases the amplified i acceleration valves, as discussed in Appendix B of the FSAR. 9.8 EFTECTS OF GROUND ACCELERATION ON ARS 4 

       ;         the ARS resulting from the DBE are not exceeded by those of smaller earthquakes. Therefore, the inertial pipe stresses due to the DBE are an adequate basis for qualificatier. of piping.

_- 9.9 COMPUTER PROGRAM VERITICATION

  • The computer programs used to generate the SSI ARS have been qualified by (1) comparison of results to those obtained from similar programs which are recogni:ed and videly used; or (2) cemparison of program results to those 1 obtained by hand calculations or analytic J. results published in technical
"                               These comparisons literature.                                               are shorn for the SHAKE, PLAXLY, REFUND, KINACT, and TRIDAY programs in Section 10 of this                                        report. Reasonable d               agreement is demonstrated for these computer programs.

F i 2253 168 I 

=
     -!                                                                         9-6

_a 

               .i . . . -

2253 169 5i 5l' S _ _ . . . . . . d 

                                                                . - - .           -~                 e i

] 

}                                            3EAVER VALLEY POWL1 STATION, UNIT 1 10.1 SHAKE 3
  ;       SHAKE is a public domain computer program developed at the University of California and described by Schnabel, Lysmer, and Seed. Stone & Webster has

] made a few changes in the program, principally the addition of plotter J capability and improvement of some of the output, but the pr.ogram in use for this work is essentially that described by Schnabel, et al. The program solves the problem of vertically propagating shear waves in a layered medium. The values of shear modulus and damping for a particular layer depend on the average shear strain induced in thtt layer by the earthquake. The program iterates to obtain values of modulus and damping that are compatible with the strains and with curves of modulus and damping versus strain. Although the program is well known and videly used, Stone & Webster has checked the results computed by the program against those developed 4 independently by Roesset'2' and has also checked that the calculations of modulus and da= ping are internally consistent. For example, Figure 10.1-1 shows the ' comparison of the amplification functions from SHAKE and Roesset's analysis for the first iteration on the seil profile in Figure 10.1-2. 2253 170 l r 10.1-1

BEAVER VALLEY POWER STATION, UNIT 1 REFERENCES

1. Schnabel, P.B.; Lysmer, J.; and Seed, H.B. SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites, Earthquake Engineering Center, Report No. EERC 72-12, University of California, Berkeley, California, December 1972.
2. Roesset, J.M., Tundamentals of Soil Amplification. In: Seismic Design for Nuclear Power Plants, R.J. Hansen, ed. , M.I.T. Press, Cambridge, Mass.,

1970, pp 183-244. 2253 171 O b 10.1-2

E i 1 3 1 0 7 \ o6 e - 5 I ) g5 , z l o4 N \ -- 23 I t 

~

E, f g ' y-ROESSET (1970) 

         $  '*0  'g'            \       gef R-G '
         *1                                 N;wr DL              i a~o
 ]                                                                         ,

I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 FREQUENCY IN CPS O NUMERICAL OUTPUT-SHAKE RUN M72532OI 2253 172 i = _ FIGURE 10.1-1 AMPLIFICATION FUNCTION OF SOIL

BEAVER VALLEY POWER STATION - UNIT 1
=-

2 LAYER i n 2 3 ]' SOIL I(TYPE 2-SAND) 4 in 7=0.125 KCF, Ko=0.5 5 @ Vs=75Cf/SEC, S=lO% 6 9 7 8 9 . 10 o 11 12 ~ SOIL 2 (TYPE 2-SAND) 9 1 7= 0.125 KCF, Ko =0.5 13 @ 3 Vs= 750'/SEC, S = 10% 14 ~ 15 g o l 16 SOIL 3 7=0.140 KCF, V =1,000,000'/SEC, S=0% = 2253 173 m FIGURE 10.1-2 ^ SOILS PROFILE BEAVER VALLEY POWER STATION - UNIT 1 

                                                -ii i
_r s
   ~

3EAVER VALLEY POWER STATION, UNIT 1 s 10.2 PLAKLY 

           ~'

PLAXLY is an isoparametric, plane-strain, finite element computer program used"~ ~ ~~~' in seismic soil-structure analysis. The equations of motion are solved in the j frequency domain. A primary element in the PLAXLY solution is the consistent transmitting 

  =

boundary modeling the layered far-field. This boundary avoids the unrealistic _; reflections associated with more simplistic " free" or "rolle r" -late ral- - -- -- boundary conditions. j ' N The principal limitations upon the program and its application are the following: 7 i J

1. Geometry and material properties must be such that they_can be_

1 y satisfactorily modeled in two dimensions. _l 2. Properties of the layered far-field cannot change horizontally. A 3. Base rock is assumed to be infinitely stiff. j 4 Material properties are isotropic linearly elastic. 4 * = 2253 174 

   -3

- 10.2-1 i e d 5

3EAVER VAUEY PO'JER STATION, UNIT 1 Tor purposes of comparison, the results of PLAXLY and those of a similar program in the public domain, TLUSH (CDC Version 2.2), are shown in 

                                                           ~

Tigure 10.2-1. The PLAXLY flow diagram is shown in Tigure 10.2-2. 2253 175 10.2-2

i Ja L O.7 - PLAXLY 

                                                                                                  ---- FLUSH 0.6  -
                                                        .          A

_ O.5 - 

                                                       ' '['      /'               EQUIPMENT DAMPLNG = 3*/.

S

  • I v' 1 z i "

90.4 - 

                                                  /                       's\

a: A s a w 02 - 

                                      /       s                                                        ,g a                             t
       !    N
  • N O.2 -
0.1 -

a 

                                   ,    ,         ,                          ,     ,                        e o
                                                              ,       ,                                 i         i 0.8  0.9
       ~

O O.1 0.2 0.3 0.4 0.5 0.6 0.7 1.0 PERIOD (SECONDS) 1 j _ r 2253 176 2 b FIGURE 10.2-1 i COMPARISON OF ARS BY PLAXLY AND FLUSH AT OPERATING FLOOR BEAVER VALLEY POWER STATION - UNIT 1 3

5 READ SOIL AND STRUCTURE PROPERTIES AND NODAL COORDINAT ES i r NONSEISMIC MODE 

                                         /

3 SEISMIC s r j READ INPUT EARTHQUAKE 1 r l COMPUTE FOURIER TRANSFORM i ( PRIMARY NONLINEARITY  : YES COMPUTE 1-D AMPLIFICATION 

       ,                 (DECONVOLUTION)

COMPUTE 1-D SHEAR STRAIN 

                                       , r                                                   3 r
       ,                                                                     2253 177 i

4 i. 3 FIGURE 10.2-2 (SH.10F 3) 

                                       'PLAXLY' FLOW DIAGRAM BEAVER VALLEY POWER STATION - UNIT 1

                                                                                       - . ~ ~ _             .       .._m ,

I A a i J __ NO STRAIN ERROR GT. TOLERANCE 1 YES 

                                                                                                ' r j                                       1r DETERMINE NEW SHEAR                                 CALCUL ATE AND ASSEMBLE MODULUS, DAMPlNG FOR                                ELEMENT STIFFNESS, MASS

] _ _ EACH SOIL LAYER 

                                                                                                 , r i

j - COMPLETE DYNAMIC BOUNDARY - MATRIX AND BOUNDARY FORCES ? NEXT FREOUENCY 

    "                                             GENER ATE LINEAR BEAM ELEMENTS' STlFFNESS i   r FORMULATE LOAD VECTORS r   FROM LEFT AND/OR RIGHT

_ BOUNDARY FORCES NEXT FREOUENCY , ADD TRANSMITTING BOUNgARIES _ AND/OR BEAM ELEMENTS STIFF ~ NESS TO GLOB AL STIFFNESS - - - - - - - - r 2253 178 J FIGURE 10.2-2 (SH. 2 0F 3) 

                                                                       'PLAXLY' FLOW DIAGRAM i                                                               BEAVER VALLEY POWER STATION - UNIT 1 d

A--- ...

e - EN ir 1 MODIFY FOR SPECIFIED DISPLACEMENTS = NEXT 

                  , FREQUENCY
                                                                                                                                       ~

DETERMINE TRANSFER FUNCTIONS (COMPLEX FREQUENCY RESPONSE) 

 ,                                                                          CYCLE COMPLETE SECONDARY N NLINEARITY g                                                                        YES 1   r
 }

ASSEMBLE NEW COMPUTE PRINCIPAL SHEAR t GLOBAL STIFF- STRAIN IN EACH ELEMENT j NESS MATRIX , 

                                                                         ?                                                            - . _ - . . .
   !                                                                                                            NO
   '_                                               STRAIN ERROR GT. TOLERANCE                                       r
                                                                                                                                       ~~~

g YES i r 1r ] DETERMINE NEW SOIL CALCULATE REACTION FORCES, PROPERTIES FOR NODAL TRANSFER FUNCTIONS j EACH ELEMENT FOR BEAM CLEMENTS 

 ~~l i

4 STORE INFORMATION ON TAPE  : j i COMPUTE DESIRED OUTPUT ], (PRINT / PLOT / PUNCH) i v END 1 2253 179 4 i FIGURE 10.2-2 (SH. 3 0F 3) 

                                                                            'PLAXLY' FLOW DIAGRAM BEAVER VALLEY POWER STATION - UNIT 1 4
   ?

A

3EAVER VALLEY p0WER STATION, UNIT 1 N 10.3 RETUND AND EMBED 1 The computer program RETUND is used for computation of the dynamic stiffness functions (impedance functions) of a rigid, massless, rectangular plate velded to the surface of a viscoelastle, layered stratum. The subgrade stiffness 

]

matrix is evaluated for all six degrees of freedom for the range of l frequencies specified by the user. Embedment effects are applied subsequently J __. by the program EMBED. 

 --1 a

The program reads the topology and material properties, assembles the subgrade _ flexibility matrix, and determines the foundation impedances by inversion. 

       =

The subgrade flexibility matrix is determined with discrete solutions, to the J problems of Cerruti and Boussinesq. A cylindrical column of linear elements li is joined to a consistent transmitting boundary, and the flexibility coefficients found by applying unit horizontal and vertical loads at the axis. The rectangular plate is discretized into a number of nodal points, and the global flexibility matrix found using the technique just described. The 7 __ foundation stiffnesses are then det' ermined solving a set of linear equations 

                                                                                                      ~~~~

which result from imposing unit rigid body translations and rotations to the 

 -!    E plate.                                                         ,
    =

i Since RETUND is restricted to surface-founded plates, the effects of embedment are included by adjusting the RETUlTD results with the program EMBED. The s J 2253 180 10.3-1 _i . j

_i 1 BEAVER VALLEY POWER STATION, UNIT 1 e theoretical bases of these programs and their application to the solution methodology are described in Section 4.2. Ths results of RETUND compara very well . vi' h published results. The

comparisons shown in Figures 10.3-2 through 10.3-7 are based upon " Impedance Functions for a Rigid Foundation on a Layered Medium", J.E. Luco, Nuclear Engineering and Design, Vol 2, 1974 of the various solutions presented by Luco, the following was selected for comparison (see rigure 10.3-1):

i j Laver 1 Laver 2 

   =
,             Shear wave velocity                     1                                                   1.25            -

i . 

"             Specific veight                         1                                                   1.1764
]             Poisson's ratio                         0.25                                                0.25 J

The comparisons shown are of the coefficients k and c from which the vertical, translational, and rocking impedances can be expressed: l j - 

       ,                                K: K.  [k + iae el i

E n in which as is a dimensions 1ess measure of frequency and K is a zero-1 frequency stiffness. 2253 181 1D.3-2 i = 4

BEAVER VALLEY POWER STATION, UNIT 1

  • The minor differences shown between the RETUND result and Luco's analysis can be attributed to the use of an " equivalent" rectangular plate in the RETUND analysis (Luco's is circular) and differences in boundary conditions at the footing (rough vs. smooth).

The RETUND and EMBED flow diagrams are shown in Figure 10.3-8. 2253 182 10.3-3

a ] i i I 

  =

UNIT RADIUS 

              ~
                                       ///////////////I H5 Es D$

e  ; 9 . n i J I J 2253 183 j i FIGURE 10.3-1 LUC 0'S TWO-LAYER PROBLEM j BEAVER VALLEY POWER STATION - UNIT 1 1

_ ~ _ . . . _ . . . . _ . . . .. . kr LUC 0 _ 

                                                                                                         --- REFUND 1.0
                                                                's O.8        -        s                               f g                _ _ _ _ _

s / \ N A 

                                                                                            /             \

0.6 - 

                                                                                          /                \
                                                                                         #                   N%
                                                                            \           /

g - 0.4 - N / f s 0.2 - 0 ' ' ' ' ' ' ' '  ; O 1 2 3 4 5 6 7 8 g 2253 184 FIGURE 10.3-2 ROCKING STIFFNESS COMPARISON - REAL PART BEAVER VALLEY POWER STATION - UNIT 1

Ce gyco 

                                                                                - - - -       REFUND 1D   ~

0.8 - 0.6 

                ,                    CA   =

0.2 - 

    - - - - - -                         0      ' '       '          '         '          '      '

2253 185 FIGURE 10.3-3 ROCKING STIFFNESS COMPARISON - IMAGINARY PART BEAVER VALLEY POWER STATION - UNIT 1

=. .- d J k 

      }
kg N i

i LUCO 7 j 1.6 - 1 

                                                                                                                       ---- REFUND
                                                                                                           \

l 1A - 1 l I ~ l \ s u ~ I \ ^ R 

                                                                         \

I \ 

   -=                  1.0                                           /    \                        g              \

s / \ g 

                                                                   /        \

C.8 - . t I t I _j \ l 0.6 - * \ I

\ l
                                                                                   \          l 0.4     -
                                                                                    \        l                                           -

1 M -

' ' ' ' ' ' ' '  ?
    ~~

O O 1 2 3 4 5 6 7 8 g,

, 2253 186 M

E _= l FIGURE 10.3-4 J HORIZONTAL STIFFNESS COMPARIS0N -

REAL PART BEAVER VALLEY POWER STATION - UNIT 1

? J 

      -u                                                                               . - -

           - - ~

C,d k Luco 

                                                                 - ~ ~~ REFUND 1.0  -

o3 - 0.6 ,/ O.4 i 

                  "     I I

F ' ' ' ' ' ' ' ' E O O 1 2 3 4 5 6 7 8 g, 2253 187 FIGURE 10.3-5 HORIZONTAL STIFFNESS COMPARISON - IMAGINARY PART BEAVER VALLEY POWER STATION - UNIT 1

i k, 4 LUCO 1.6 ~ ~ ~~~ REFUND 1.4 - 12 = ,s' \ 

                                                                           \

1.0 s . 0.8 - 0.6 - 

                                            \
                                              \
                                                             /

on \ 5 

         - - - - -~
                                                \         g                                     _ . - . . - . .   - - - . -

0.2 - 

                                                    \
                                                    ,\s ,      ,   ,    ,    ,       _

O 1 2 3 5 6 7 8 co 2253 188 FIGURE 10.3-6 VERTICAL STIFFNESS COMPARISON - REAL PART BEAVER VALLEY POWER STATION - UNIT 1

l 

   . _. . C,                                               LUC 0
                                                     ---- REFUND 1S   -

G8 - s',*~s %s 0.6 - 

                               /                    \

h / O.4 ,3 (/~ l o.2 

                 )

o f O 1 2 3 4 5 6 7 8 c, 2253 189 FIGURE 10.3-7 VERTICAL STIFFNESS COMPARISON - IMAGINARY PART BEAVER VALLEY POWER STATION - UNIT 1

READ FOUNDATION GEOMETRY AND INITIALIZE ARRAYS TOPOL 1 READ SOIL PROPERTIES AND ASSEMBLE ELEMENT STIFFNESS MATRICES : INSOIL ir DEFINE DYNAMIC STORAGE PARAMETERS 1r READ FREQUENCY INTERVALS l ' SOLVE OUADRATIC EIGENVALUE - 

    ' -'                                   PROBLEM WAVE
                                                           'r 5

COMPUTE TRANSMITTING BOUNDARY STIFFNESS MATRIX BOUMA 3r 

                                        ' SOLVE CERRUTI AND BOUSSINESO PROBLEMS s SOLVER y   '

COMPUTE MODAL PARTICIPATION ITERATE OVER FACTORS BACK FREQUENCIES I i r COMPACT EIGENVECTORS (ONLY THE DISPLACEMENTS - - - - AT THE FREE SURFACE ARE NEEDED): PRESS 3r COMPUTE FLEX 1BILITY M ATRIX REFUND ir COMPUTE STIFFNESS _ FUNCTIONS ZAPATA 8r OUTPUT (PRINT / PUNCH) 

    .                                                        I                                    2253 190 t

FIGURE 10.3-8 (SH.10F 2) 

                                                                   ' REFUND' I'.ND ' EMBED' FLOW DIAGRAMS BEAVER VALLEY POWER STATION - UNIT 1

l j - 3 1 - i - 

                                                                            +
    )
  • EMBED' u . _ .

u 

 $                                                     READ FOUNDATION GEOMETRY                                     _

READ REFUND OUTPUT _. _ _ STIFFNESSES e 1 u _ -i CALCULATE EMBEDMENT _' CORRECTION FACTORS 37 ADJUST STIFFNESSES _ . . 

    \

c - u OUTPUT (PRINT / PUNCH) '.i v i_ END i L_ FIGURE 10.3-8 (SH. 2 of 2) - 

  ~
                                                                           ' REFUND' AND ' EMBED' FLOW DIAGRAMS BEAVER VALLEY POWER STATION - UNIT 1 j
                                                                                                                                    =

i 

                                              - - _ _ . . .        . . . .                                                                 l

 -[                                                      BEAVER VALLEY POWER STATION, UNIT 1 d

10.4 KINACT i

i. _ _ _ _ _ . -

KINACT is a computer program used in the three-step solution of soil-structure _ interaction problems. Briefly, the program modifies the specified ~ translational time history at the surface to translational and rotational time histories at the base of a rigid, massless foundation. i The theoretical basis for the program is derived from.vava propagation theory , _ _ . _ _ 4 = and parametric studies of finite element solutions, described in more detail in Section 4.1.3. Comparisons of the spectra of translational and rotational ~ ~ ~~ 3 ) motion predicted by KINACT and by PLAXLY ars shown in Figures 10.4-1 and ---- } 10.4-2. ---- i As the figures indicate, KINACT slightly underestimates the translational part ... - of the motion, but significantly overstates the rotational part. This condition results from the dependence of the two variables Uandt) 1 - - Us) 

                            $=C(Us E 2253 192

? w 10.4-1 i E 

                                                                                --miumi---si --i

e.= BEAVER VALLEY P0b'ER STATION, UNIT 1 where h: surface translational acceleration h = translational acceleration of rigid 3 massless foundation C = constant E : embedment This self-compensating feature of the formulation is insurance against an unconservative result. The KINACT flow diagram is shown in Figure 10.4-3. 2253 193

y. e.,o4 .

O e gh A 10.4-2

A KINACT 

                                                                          ==

PLAXLY O.2 - 

                                  ,4 e

1 a a 

                                      ' r \'5   s
                           !\                       \.~
    .5             y)                                            \ /'~       K     ,s t-         AJ j O.1   - /

d 8 0 ' O O.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1D PERIOD (SECONDS) 2253 194 s FIGURE 10.4-1 TRANSLATIONAL RESPONSE SPECTRA AT BASE OF RIGID, MASSLESS FOUNDATION BEAVER VALLEY POWER STATION - UNIT 1

A l KINACT 

                                                                               --      PLAXLY 1.2   -

n 

                       'o 1.0     -

0.s - - z 

                     . 0.s    -
                        <c                   so
                            ^
                                       ,        V 0.2     -
                                     /                   g
                                                                   ~'~
                                           '    '   '     '          '     ' " ~ ~
            ' ~ ~ ~~

0 ' - 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 

                                                                                                              -~  '  --

PERIOD (SECONDS) 2253 195 FIGURE 10.4-2 ROTATIONAL RESPONSE SPECTRUM AT BASE OF RIGID, MASSLESS FOUNDATION BEAVER VALLEY POWER STATION - UNIT 1 4Y

a s-m READ IN SOIL PROPERTIES IN EACH LAYER l mr l COMPUTE SCIL FREQUENCY i ir a _-; RE AD EARTHOUAKE TIME HISTORY AND SCALE FACTOR 

   ?

a . 1 r SCALE EARTHOUAKE

i _

1 r COMPUTE FOURIER TRANSFORM OF EARTHOUAKE i r COMPUTE ROTATIONAL FOURIER SPECTRUM _t e

  • i r COMPUTE TRANSLATIONAL
                   ,,             FOURIER SPECTRUM                             , . , _ ._

ir BACKWARD TRA;<SFORM 

   =

COMPUTE ROTATIONAL AND TRANSFORM TIME HISTORIES- 

                                                'f 3

PUNCH OUTPUT TIME HISTORIES s l E,, 2253 196 5 FIGURE 10.4-3 

                                            'KINACT' FLOW DIAGRAM BEAVER VALLEY POWER STATION - UNIT 1
=-

EEAVER VALLEY POWER STATION, UNIT 1 10.5 TRIDAY The computer program TRIDAY is used for dynamic analysis of structures subjected to seismic loads, accounting for soil-structure interaction by means of frequency-dependent complex soil springs. - The structure is idealized as a set of lumped masses connected by springs or _ _ , linear members, and attached to a common support, the mat. The latter is supported by s of,1 springs or imp, dances, which may or may not be frequency-dependent. Alternatively, the mat may rest on a rigid subgrade. The 

                                                                                                      -~~~~~ ~

structure may be three-dimensional, but cannot be interconnected; each structure has to be simply connected. Fourier transform techniques are used to determine time histories; cutoff frequency is prescribed interna 11.y to 

                                                                                                       ~~ "

15 Hz. The theoretical basis and implementation of the program is described in Sectica 4.1.4 A comparison of TRIDAY vith a public domain program, STARDYNZ, for the seismic response of a fixed base, multi-mass, cantilever model is shown in Figure 10.5-1. The model is shown in Figure 10.5-2. e .ee= m 2253 197 10.5-1 

                                                                                         ..m &-   p

                                                                                       ^

r Jk 14.0 - FRIDAY 12.0 - ----- STAROYNE a _ 10.0 - e ' z , 9 a.0 - 5 6.0 - 

 .J U

W i 

                                      \

4.0 - 2.0 - 

                                                                                         =

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 PERIOD (SECONDS) 2253 198 FIGURE 10.5-1 COMPARIS0N OF ' FRIDAY' AND 

                                                 'STARDYNE'-ARS AT THE ROOF BEAVER VALLEY POWER STATION - UNIT 1

m EL 60' 1 1 

   ~ ~

EL 4a' 2 2 EL 36' 3 3 EL 24' 4 4 EL 12' 5 y0 5 . L0 / ///s ///// 2253 199 FIGURE 10.5-2 

                                                    'STARDYNE' MODEL BEAVER VALLEY POWER STATION - UNIT 1

       --- ~ _

INPUT PARAMETERS  : 3 r . __ _ INPUT SUBGRADE STIFFNESSES 3r READ SUPPORT MOTION i r COMPUTER FOURIER TRANSFORMS OF INPUT ACCELEROGRAMS 

                                                , r READ STRUCTURAL GEOMETRY                                ..

AND PRDPERTIES , 3r LOOPING OVER STRUCTURES GENERATE STIFFNESS MATRIX OF* STRUCTURES 9 r READ OUTPUT REQUESTS i r 

                            ~

FORWARD PASS ON STIFFNESS MATRIX lN ALL STRUCTURES.- 3 , ADD SOIL MATRIX = 2253 200 FIGURE 10.5-3 (SH.10F 2) 

                                              ' FRIDAY' FLOW DIAGRAM BEAVER VALLEY POWER STATION - UNIT 1

+ bN )k p 9 IMPOSE BOUNDARY CONDITIONS - LOOP OVER - FREQUENCIES , , BACK SU85TITUTION - IN ALL STRUCTURES LOOP OVER 3 r PROBLEMS COMPUTE AND STORE TRANSFER FUNCTIONS OF REQUESTED OUTPUT 

  ~

COMPUTE TIME HISTORIES FOR OUTPUT REQUESTS OUTPUT REQUESTS 3r PRINT, PLOT OR PUNCH' 9 END n -- 2253 201 _ FIGURE 10.5-3 (SH. 2 0F 2) 

                                                      ' FRIDAY' FLOW DIAGRAM BEAVER VALLEY POWER STATION - UNIT 1 s                          --um. i

_em W = = w as % , ,, er -=W eW* OW g m* es.- a .w. O e .,e - e APPENDIX 10.6 IN SITU SEISMIC VELOCITT MEASUREMENTS - - - - e e 2253 202 9 e- P-

L WESTON GEOPHYSICAL ENGINEERS, INC. Post ONice Box 550

  • Westboro, Massachusetts 01581 e (617) 366-9191 r

l p September 6, 1977 , ( Stone & Webster Engineering Corporation 245 Summer Street Boston, Massachusetts 02107 

           -            Gentlemen:

In accordance with your Contract No. 2BVC-52035, 

           ~

dated June 6, 1977, a seismic cross-hole study was conducted in the vicinity of the Beaver Valley Power Station, Unit 2. Fieldwork was conducted during the period of June 9 to June 22, 1977. _- Preliminary data have been previously submitted; this is a formal presentation of our findings. Very truly yours, WESTON GEOPHYSICAL ENGINEERS, INC. 

            -                                                                                 /   W}t,
          ,                                                                        Vincent J. Murphy VJM:df 2253 203 h

tumm he

IN-SITU SEISMIC VELOCITY MEASUREMENTS i I BEAVER VALLEY POWER STATION UNIT NO. 2

  • t DUQUESNE LIGHT COMPANY 6

t 

                                                                                    )

u-WESTON GEOPHYSICAL ENGINEERS, INC. 2253 204 M* h=

IN-SITU SEISMIC VELOCITY MEASUREMENTS BEAVER VALLEY POWER STATION UNIT NO. 2 INTRODUCTION AND PURPOSE 

 .            A seismic cross-hole study was conducted in the vicinity

_r of the Beaver Valley Power Station, Unit 2, of the Duquesne l Light Company between June 9 and June 22, 1977. The pQrpose of the study was to measure the in-situ compressional ("P") i and shear ("S") wave velocity values for a layer of granular l material which was densified by Franki Pressure Injected Footing (PIF) compaction piles. The in-situ "P" and "S" wave velocity values measured in this study were used to calculate the elastic moduli values for those materials en' countered within the seismic cross-hole array. The field effort at the site was expedited by Mr. J. W. Williams, the Superintendent of Construction for the construction division of Stone & Webster Engineering Corporation. Survey .- ! requirements were outlined and the project was coordinated by Mr. D. Campbell, the Lead Geotechnical Engineer for the d geotechnical division of Stone & Webster at the Boston office. Weston Geophysical's project geophysicist for this study is V. J. Murphy, and the assistant project geophysicist is R. P. Allen. L 2253 205 

   % m

1 

 '       LOCATION
 !             The area of investigation (Sheet 1) is on a high-level
  ~'

terrace on the south bank of the Ohio River (former elevation 735 feet) approximately 25 miles northwest of Pittsburgh. f ( Sheet 1 is a section of the Hookstown, Pennsylvania and j- Midland, Pennsylvania, United States Geological Survey topographic quadrangle maps (1:24,000). The seven boreholes i~ used for the in-situ velocity measurements are shown on Sheet 2, which was prepared from a map provided by Stone & r Webster. ] IN-SITU VELOCITY MEASUREENTS - CROSS-HOLE PROCEDURE m r 

     !         Cross-hole velocity measurements are made using geophones containing three orthogonal elements (one vertical and two horizontal).              Recordings are obtained using a 12- to 16-

_ channel seismograph that contained a two-millisecond timing a system. Seismic energy is generated with the energy source in one hole and detected in the geophone holes with the seismic source and the geophones at the same elevation ~ levels. The energy source (s) for this survey included both small explosive charges and an air gun. The "P" wave and "S" wave velocity data were obtained i

u at 5-foot intervals within the. densified zone and at 10-foot y intervals above and below the zone.

lL 2253 206 

-l

~~ w

A 

 ;              RESULTS Generalized results of the survey are presented in
          ,     Table 1, which also lists the results of a previous Weston survey (in this general vicinity) reported to Stone &

Webster in 1968. Table 2 lists the specific velocity values measured at each elevation for the present survey and the corresponding elastic moduli values. The various combinations of shothole and recording (detector) holes that were used I are also noted on Table 2. j- The densified zone occurs generally between Elevations 670 and 640. It is interesting to note that complete saturation, 

        !~      as evidenced by seismic velocities of about 5,000 ft/see or
                                                                                                                ~

j greater, does not occur above Elevation 652, although the 

 ~i water table elevation has been observed by geotechnical
  }[            personnel in the field at Elevation 667.                                    This apparent discrepancy can be explained by the possible injection of i       small amounts of air into the surrounding sediments during the densification process, (a minute percentage of air in an i       otherwise fully saturated layer can lower the seismic velocity value significantly).

2~ No anomalous conditions, other than that mentioned l' j above, were observed during the cross-hole study. it r 

      !L                                                                                         2253 207 1:

8' 

 =u
I
   -s I-

f TABLE I GENERALIZED "P"- AND"S"-WAVE VELOCITY VALUES , 1968 SURVEY AND PRESENT SURVEY

  • 1968 SURVEY PRESENT SURVEY
                    'P" WAVE                "S" WAVE                       'P' WAVE            'S" WAVE VELOCITY                 VELOCITY                      VELOCITY             VELOCITY

( FT/SEC) (FT/SEC) (FT./SEC) (FT/SEC.) gg, 7,g._ -E L.74 O' APPROX. GROUND SURFACE 

 ~                                                                                                                    '

150G 900-(SOkt lOOO) (SOME 600) 720*- - 720' APPROX. GROUND SURFACE 2000 900-1200-l 700*- - 700' NO SEtSMIC MEASUREMENTS g (NOTE TAKEN ABOVE EL.685 IN 

                                                                                     \     PRESENT SURVEY 2000-                   1050t 2000-2500                     700-8007 680'-                                                            f          T       ?          ?-    -

680' I 2400-2500 1000 i i APPROX. WATER TABLE _, _ 660'- 6000 GOC - 660' r 5000 1000-1200 I i- I APPROX. WATELTABL E _ 6000 1300-i 640'- - 640' 6300-6500 1500-1800 L. 620'- / / - 620' -1 12,000 6000- 12,000 4400-5800? i 600'- - 600' I 2253 208 _

  • CF TEXT t CF TEXT FOR DISCUSSION OF THE WATER TABLE ELEVATION FOR PRES 6NT SURVLY.

7 -__ . p__ . 7_ _ -7 *---) , y , - -- ) i l l l TABLE 2 ' 

                                              .               IN-SITU VEIDCITY MEASUREMENTS i

i apu mgu Have Wave Shear Young's Bulk - Velocity velocity Poisson's Modulus Modulus Modulus Elevation Density * (ft./sec.)i (ft./sec.)t Ratio (x 105 lbs./in.2) (x 105 lbs./in.2) (x 105 lbs./in.2) 685 123 2,000-2,500 700-800 .438 .149 .429 1.14 i 675 123 2,500 1,000 .405 .265 .746 1.31 670 123 2,400 1,000 .395 .265 .741 1.18 665 135.9 2,800 1,000-1,100 .418 .323 .917 1.87 660 135.9 3,000 1,000-1,100 .430 .323 .925 2.21 l 655 135.9 3,000 1,100-1,200 .414 .300 1.10 2.12 650 135.9 6,300-6,400 1,600-1,700 .464 .799 2.34 10.76 645 135.9 6,500 1,500 .472 .660 1.94 11.51 635 135'.9 6,400 1,800 .457 .950 2.77 10.75 625 155 12,000 4,400-5,000 .390 8.70. 24.19 36.57 t Note: There were five seismic arrays utilized during the cross-hole survey. They are listed below: Shot ilole Recording Holes i psy 1 2, 3, 4 and 5 j psj 1 3, 4, 7 and 6 LJ7 2 3, 4, 7 and 6 (f4 5 7, 4, 3 and 2 6 7, 4, 3 and 2 . N ' CC)*Provided by Stone & Webster Engineering Corporation. 

  'J3tWhere a range of velocity values is given, the average of that range was used in the moduli calculations.

I f I I

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lHOOKSTOWN QUADRANGLEfg3 /' M',, a (._Q, 'i 

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IN-SITU SEISMIC VELOCITY MEASUREMENTS (4-#*/ g ed s BEAVER VALLEY POWER STATION -UNIT NO. 2

l DUQUESNE LIGHT COMPANY
   'L                                                          "

for N) 

                 ) )

a v (%^ ' a' STONE & WEBSTER ENGINEERING CORPORATION o "7 'h'FT. . d WESTON GEOPHYSICAL ENGINEERS,INC. ,i .' - [ k if slet i of 2 2253 210

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2253 211 

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