ML20028B556

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Seismic Capacities of Masonry Walls at Big Rock Point Nuclear Generating Plant
ML20028B556
Person / Time
Site: Big Rock Point File:Consumers Energy icon.png
Issue date: 08/31/1982
From: Banon H, Wesley D
STRUCTURAL MECHANICS ASSOCIATES
To:
Shared Package
ML20028B550 List:
References
TASK-03-06, TASK-3-6, TASK-RR IEB-80-11, SMA-13703.02, NUDOCS 8212030025
Download: ML20028B556 (62)
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Text

.

SMA 13703.02 SEISMIC CAPACITIES OF MASONRY WALLS AT THE BIG ROCK POINT NUCLEAR GENERATING PLANT I

i by D. A. Wesley H. Banon s

+

'i

, 6 prepared for i

i CONSUMERS POWER COMPANY Jackson, Michigan I

'l Augus t,1982

'(

8212030025 821124 g

PDR ADOCK 05000155 0

PDR g g STRUCTURAL mECHRnlCS 4

1

"""""" A S S OCI A T ES W

A Caht coep 5160 Birch Street, Newport Beach, Calif. 92660 (714) 833 7552

TABLE OF CONTENTS

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Section Title Page L I S T O F T AB L ES...................

ii LIST OF FIGURES iii 1

INTRODUCTION....................

1-1 2

DESCRIPTION OF BLOCK WALLS.............

2-1 f

3 SEISMIC INPUT MOTIONS 3-1 4

ANALYTICAL MODELS FOR TRANSVERSE RESPONSE

!I 0 F W ALLS......................

4-1 f

4.1 Single Block Model 4-1

'i 4.2 Two Block Vertical Model 4-4 f

4.3 Two Block Horizontal Model 4-6 i

5 ANALYTICAL RESULTS.................

5-1 1

t 5.1 Transverse Loads 5-1 1

5.2 Sensi tivi ty Studies..............

5-3 i

5.3 In-Plane Loads 5-5 i

j 6

CONCLUSIONS AND RECOMMENDATIONS 6-1 1

REFERENCES.....................

R-1 i '

l 1

i i

i t

f

LIST OF TABLES Table Title Pm

[

2-1 Big Rock Point Block Wall Construction........

2-3 5-1 Factors of Safety for BRP Walls Against Site g

p Specific Earthquake 5-7 5-2 Allowable Stresses in Reinforced Masonry.......

5-9 5-3 Allowable Stresses in Unreinforced Masonry......

5-11 1

lt 1

i e

5 i

o a

f ri i

i

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l ii I'

LIST OF FIGURES Figure Title h

2-1 Big Rock Point Block Wall Configurations......

2-4 2-2 Big Rock Point Block Wall Configurations......

2-5 2-3 Big Rock Point Block Wall Configurations......

2-6 i

2-4 Big Rock Point Block Wall Configurations......

2-7 t

2-5 D' Appolonia Model of Service and Turbine Buildings

( f rom Re fe re n ce 3).................

2-8 2-6 Plan View of Masonry Walls.............

2-9 i

3-1 Response Tine Histories at Elevations 593' i

(Node 153) and 616' (Node 353) for Column Line Location F-3..............

3-2 l

3-3 Response Time Histories at Elevations 593' (Node 146) and 616' (Node 346) for Column Line Location E 6 3-3 I

I 4-1 Response Mechanism of Walls Unsupported at the Top 4-8 l

4-2 Analytical Model for Walls Unsupported at the Top 4-8 4-3 Force-Deflection Representation 4-9 4-4 Response Mechanism for Walls Supported

?

Top and Bottom...................

4-10 t

4-5 Analytical Model for Walls Supported i

Top a nd B ot tom...................

4-10 l

4-6 Two-Block Vertical Model Response Components....

4-11 1r

'{

4-7 Failure Mechanism for a Tall Wall Supported at all Edges....................

4-12 i

4-8 Forces Developed During Arching 4-12 I) 4-9 Force-Displacement Relationship for the Two Block Horizontal Failure Model.........

4-13 i

iii

LIST OF FIGURES i

Figure Title Page h

5-1 Top Displacement of Wall M100.13 Subjected L

to SSE Base Input Motion, Scale Factor 5 1.0....

5-13 5-2 Top Displacement of Wall M100.13 Subjected to SSE Base Input Motion, Scale Factor = 1.10 5-14 5-3 Top Displacement of Wall M100.13 Subjected g

j to SSE Base Input Motion, Scale Factor = 1.20 5-15 5-4 Mid-Height Displacement of Wall M100.2 Subjected to SSE Top and Bottom SSE Input Motions, Scale Factor = 1.0.................

5-16 i

5-5 Mid-Height Displacement of Wall M100.2 Subjected j

to SSE Top and Bottom Input Motions, Scale Factor = 10.0 5-17 j

5-6 Mid-Height Displacement of Wall M100.2 Subjected to SSE Top and Bottom Input Motions, Scale Factor = 12.0 5-18 i

5-7 Mid-Height Displacement of Walls M100.4 and M100.5 Subjected to SSE Top and Bottom Input Motions, 1

Scale Factor = 1.0.................

5-19 5-8 Mid-Height Displacement of Walls M100.4 and M100.5 Subjected to SSE Top and Bottom Input Motions, Scalc Factor = 4.0.................

5-20 5-9 Mid-Height Displacement of Walls M100.4 and M100.5

. t Subjected to SSE Top and Bottom Input Motions, ll Scale Factor = 4.5.................

5-21 5-10 Mid-Height Displacement of Wall M100.6 Subjected e

l to SSE Top and Bottom Input Motions.

Scale Factor = 1.0.................

5-22 I

5-11 Mid-Height Displacement of Wall M100.6 Subjected li to SSE Top and Bottom Input Motions, Scale Factor = 2.8.................

5-23

>f I

5-12 Mid-Height Displacement of Wall M100.6 Subjected to SSE Top and Bottom Input Motions, Scale Factor = 3.5.................

5 !

iv f

U LIST OF FIGURES

(

l Figure Title Page Mid-Height Displacement of Wall M100.19 Subjected 5-13 to SSE Top and Bottom Input Motions, Scale Factor = 1.0.................

5-25 a

5-14 Mid-Height Displacement of Wall M100.19 Subjected to SSE Top and Bottom Input Motions, t

S cale Factor = 4.0.................

5-26

I' 5-15 Mid-Height Displacement of Wall M100.19 Subjected to Top and Bottom Input Motions,

- i Scale Factor = 4.5.................

5-27 I

l i

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1.

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1.

INTRODUCTION i

Historically, unreinforced masonry walls have been considered as vulnerable to seismic damage. Concern for block wall seismic capacity in nuclear power plants has recently been addressed by the USNRC in IE Bulletin 80-11 dated May 8, 1980.

In response to this bulletin, the a

ability of the Big Rock Point Nuclear Generating Plant block walls to l

withstand the original design basis seismic criteria was subsequently documented (Reference 1). As part of the Systematic Evaluation Program j

(SEP), the capacities of the critical block walls to withstand the seismic excitation described by the site specific response spectrum for i

the Big Rock Point site have been developed and are presented in this I

report.

I t

The concrete block walls identified as important to safety in the Big Rock Point plant are similar in construction to most masonry walls

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constructed in nuclear power plants in the same time period. The walls are non-load bearing and, with two exceptions, are connected at both too

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and bottom to the primary reinforced concrete structure. Most Bia Rock Point block walls were constructed without vertical reinforcing steel.

i Depending on the configuration, varying amounts of horizontal reinforcing steel are included in all but one wall.

I t

Masonry walls with this type of construction are sometimes regarded as brittle and subject to collapse at low levels of seismic

)

excitation.

In fact, failures of masonry walls with varying levels of workmanship constitute one of the principal measures of level of excitation described in the Modified Mercalli and other seismic intensity scales. However, a review of such intensity scales j

indicates that ordinary masonry walls have a high probability of k

surviving moderate levels of earthquakes. This is further supported by a number of test and analytical programs.

3 1-1 P

,,-w,

, - - - = -

\\

The site specific ground response spectra for Big Rock Point (Reference 2) are anchored to a 0.104g peak ground acceleration. The s

critical block walls in the Big Rock Point facility are located at low L

elevations within the structure, so that given the low expected levels of excitation at the site, the walls may be expected to survive an L

earthquake described by the site specific response spectra without the need for expensive modification and retrofit. The purpose of this report is to present the results of analyses conducted to establish the seismic j

capacities of the critical concrete block walls for Big Rock Point in their current conditions.

The evaluation conducted included both in-plane and out-of-plane seismic loads. Amplification through the turbine building complex struc-ture was considered including relative displacements between attachment locations at the tops and bottoms of the walls.

4

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1-2 i'

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2.

DESCRIPTION OF BLOCK WALLS Originally, 24 masonry wall segments were identified to be within the scope of NRC IE Bulletin 80-11 (Reference 1). A masonry wall segment was defined as a unifom, straight run of wall between supports or terminal points. However, it has been determined that only 19 walls need I.

be considered under the auspices of the SEP seismic reevaluation effort.

These walls are identified by M100.1 through M100.19 in Reference 1, and this notation is retained in the current SEP evaluation described in this report.

Schematic representations of these walls are shown in Figures 2-1 h

through 2-4 and a description of the walls appears in Table 2-1.

(

These walls are located in the service and turbine buildings between Elevations 593' and 616'.

Elevation 593' is the base slab of the structure.

Except for wall M100.2 which is a 4 wythe, 32 inch thick wall, L

all the walls are single wythe with thickness of either 6 or 8 inches.

The walls are located in the vicinity of Column Lines F-3 to E-5.

An isometric sketch of the overall structure (from Reference 3) showing the column line locations is shown in Figure 2-5, and a plan sketch of column lines including the block wall locations is shown in Figure 2-6.

[

The Big Rock Point walls which were part of the original construction conform to ASTM C90 Grade A standards (masonry strength q

fy=1350 psi,andmortarstrengthm,=1800 psi). Walls M100.6 through M100-13 which surround the Uninterruptible Power Supply (UPS) battery roomconformtoASTMC129 standards (fy=490 psi,m,=750 psi). Only y

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wall M100.9 contains vertical steel reinforcement. However, horizontal steel reinforcement in varying amounts is included in all the walls with f_

the one exception of wall M100.3.

Except for walls M100.18 and M100.19 which are core-filled, the rest of the walls are all hollow-core.

I l

2-1 t

l

a Tne Big Rock Point block walls were not designed to act as load ctrrying walls.

In some cases, some light equipment is attached to the walls. The extra equipment weights were included in the evaluations discussed in this report.

l I

1 2-2

. ~...

TABLE 2-1 BIG ROCK POINT BLOCK WALL CONSTRUCTION

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Wall Description M100.1 8" Single-w.ne, hollow-core M100.2 32" 4-wythe, hollow-core M100.3 8" Single-wythe, hollow-core M100.4 8" Single-wythe, hollow-core M100.5 8" Single-wythe, hollow-core M100.6 6" Single-wythe, hollow-core M100.7 6" Single-wythe, hollow-core M100.8 6" Single-wythe, hollow-ccre M100.9 6" Single-wythe, hollow-core M100.10 6" Single-wythe, hollow-core M100.11 6" Single-wythe, hollow-core M100.12 6" Single-wythe, hollow-core M100.13 6" Single-wythe, hollow-core M100.14 8" Single-wythe, hollow-core M100.15 8" Single-wythe, hollow-core M100.16 8" Single-wythe, hollow-core M100.17 8" Single-wythe, hollow-core M100.18 8" Single-wythe, core-filled M100.19 8" Single-wythe, core-filled O

I 1

2-3

I 1

20'-7" 3'-4" 15'-3" 7'-2" 6'-0" 20'-10" 24'-0" Wall M100.1 Wall M100.2 9'-4" h

9'-4" vc

.,,.c 12 51 3'-4" yParti tion s

9'-10" 9'-10" 7 '- 3l" T

4 9'-4" 2 -8" 21'-0" l

Wall M100.3 Walls M100.4 + M100.5 i

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y ri0uac 2 1.

e10 a0cx e01ur e<0cx w4<< <0,,r10uan110ms 2-4

C 1

i 4'-0" 4'-0" 11'-2" 11'-2" 11'-2" 7'-4" 7'-4*

4'-0 "

8*-2" 7'-3" 12'-2" Wall M100.6 Wall M100.7 Wall M100.8 4'-0" 4'-4" 11'-2" 11'-2" 11'-2" 7'-4" 7 '- 4" 4'-0" 12'-2" 8'-4" 7'-0" Wall M100.9 Wall M100.10 Wall M100.11 5

1 D

FIGURE 2-2.

BIG ROCK POINT BLOCK WALL CONFIGURATIONS 2-5

l i

1/2" gap 1/2" gap 11'-2" 11'-2" 11'-8" __

10'-0" 33'-7" Wall M100.12 Wall M100.13 1

24'-1" 8'-10" w

.v:

8'-8" 10'-0" 7'-2" 3'-4" 7'-4" 14'-0" Wall M100,14 Wall M100.15 I

FIGURE 2-3.

BIG ROCK POINT BLOCK WALL CONFIGUPATIONS 2-6 i

i 1

1

~

11'-2" 11 2"

16'-6" 4'_ga Wall M100.16 Wall M100.17 20'-8" ll, O

Dowels h

20'-8" kh

^^

22'-0" 9

11'-2" n

v 10'-6" h

c 5'

l.*l 21'-8" 14'-3" Wall M100.18 Wall M100 l9 f

I FIGURE 2-4.

BIG ROCK P0lf4T BLOCK WALL C0flFIGURATIONS 2-7

amman m

w w

e '

y,,,0

'l*

" &( v 'y

= =

m s."..,e,

/

., ~

/

9. \\ f f

'['

Yk N p

$ $jd f

s N

N /

0

~

/'/ m.. -

N s- -,, N, # 1h s

.D i

EXTERNAL SCHEMATIC FIGURE 2-5.

D'APPOLONIA MODEL OF SERVICE AND TURBINE BUILDINGS (FROM REFERENCE 3)

COLUMN LINES e

1 l

2 0

z D i J

=

=z 7

h 19 e

u e.

18 16 14 3

4 5

10 l

'l6 8,

9, 15 11 g

12

. 13 n

FIGURE 2-6.

PLAN VIEW 0F MASONRY WALLS l

3.

SEISMIC INPUT MOTIONS 1

As part of the SEP, a seismic analysis of the Big Rock Point structures to withstand seismic excitation was conducted (Reference 3).

Included in the analysis was the turbine building complex where the block walls of concern are located. The turbine building complex consists of the turbine building, service building, and liquid radwaste vault. The turbine building complex was modeled analytically using substructuring techniques together with beam, truss, and plate finite elements.

Soil-structure interaction was included as appropriate.

The SEP seismic analysis of the structure was originally conducted using response spectrum analysis techniques (Reference 3).

Subsequently, time history input motions to the block walls were developed using the same analytical model (Reference 4). An artificial earthquake time history with a peak acceleration of 0.104g and 12 second duration was generated to envelop the 7% damped site specific ground response spectrum for the Big Rock Point site.

Response time histories were developed from the turbine building complex analytical model to provide input to the block walls. Locations at column lines F-3 and E-5 were selected. The time histories were generated at Elevations 593' and 616' in order to account for the amplification in tha turbine building complex structure as well as the phasing and relative motion between the tops and bottoms of the block walls.

Figures 3-1 and 3-2 show the three components of motion at the two elevations for locations F-3 and E-5, respectively.

l1 3-1

bemess emme assen w

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DIRECTION X DIRECTION Y DIRECTION Z

( Nor t h-Soutti)

(Esot weet)

( Vertitell

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9 9

9 a'

E ll a

e Y

!\\? f hfl!

i bW

'l ff e

4.

4.

,.;,,,g

,.4,,g g,,y

....e-.

..... nn..

c...

sa-.

rmas=

=.. m

.e em nr.. am pa.

nam.

NODE POINT 153 Y

N I

8

?

q s

e f

a.

h

I j illi jli t

i a

11' j

k 'lkI fM I

{ lY s

' lg Ii' h

i 3

t...,.,..,

'..- :- c;;.-:-

t.

,c.,

..............m....

NODE POINT 353 l

FIGURE 3-1.

RESPONSE TIME HISTORIES AT ELEVATIONS 593' (N0DE 153) AND 616' (N0DE 353) FOR COLUMN LINE LOCATION F-3

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h

'm I

asumuse humed DIRECTION X DIRECTION Y DIRECTION Z I

( Nor th-Soum)

(East West )

(Vertleel)

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e e

q a

'a f,fldfh i/

fi,}l! qfhef II If I

a k ;i)ffWye

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..c..............

NODE POINT 146

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e.

w a'

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II h. h

$.$r MW hh I klbYW t-i af 1

.r l

r s'

.s-53,,,,

...::,-.::- t t.;

'..-.- r; g

..,.,3,,,,

NODE POINT 346 FIGURE 3-2:

RESPONSE TIME HISTORIES AT ELEVATIONS 593' (N0DE 146) AND 616' (NODE 346) FOR COLUMN LINE LOCATION E-5

4.

ANALYTICAL MODELS FOR TRANSVERSE RESPONSE OF WALLS For masonry walls of the configuration and construction found in Big Rock Point, transverse (or out-of-plane) seismic response is normally more critical than in-plane response. The dynamic models which were developed to analyze the transverse response of the BRP block walls are described in this section. The first model described is for vibrations of a rigid block subjected to dynamic base excitation. This model is appropriate for walls without top support and where arching from top to bottom does not occur such as walls M100.12 and M100.13. The second model is an extension of the first model where vibrations of two blocks, one on top of another one, is modeled. This model is appropriate for the majority of the walls with adequate top support since for walls of this configuration, cracking at approximately mid-height will occur at high seismic input levels. Once cracking has occurred in these two types of walls, rigid block models are considered applicable since there is no vertical reinforcing steel through the cracks which would form a plastic hinge. Finally, a model based on behavior of inelastic beams is developed for some of the walls which did not fit into the precedino two models. These final models are appropriate where plastic hinges form along a vertical crack such that the horizontal reinforcino steel becomes effective.

4.1 SINGLE BLOCK MODEL This model may be used to calculate seismic capacity of a long wall which is not attached at the top. Figure 4-1 shows the postulated failure mechanism under base excitations. Once the lateral displacement becomes large enough that the P-aeffects become controlling, the wall may be expected to experience essentially a vertical, in-place collapse. The boundary condition at the base may be initially either fixed or simolv

=

supported. However, the moment needed to develop cracks at the base for a fixed support condition is small and may be neglected. A conservative method of analyzing the wall is to isolate a vertical slice of the wall 4-1 l

l

and then analyze that slice as a freestanding block on a rigid base.

The approach presented here is based on Housner's original work and its extensions (Reftirences 5, 6, 7) on behavior of inverted pendulum 1

structures during earthquakes.

A rigid block on a rigid foundation will start oscillating about its two centers of rotation (points 0 and O' in Figure 4-2) when the moment of the inertia loads about the center of rotation is greater than the restoring moment of the weight about the same point. The assumotion made is that the coefficieat of friction is large enough so that no sliding will occur betwern the block and the base. This assumption is subsequently verified efc the levels of instability predicted by the rocking model. For r. rotated block as shown in Figure 4-2, the equation of motion may be written as l s = -MRX Cos(a-e) - MR( g+9) Sin (a-0)

(4-1) o g

where I is the mass moment of inertia about point 0, M is the mass, o

X is the base acceleration in X direction, and Y is the base g

g acceleration in y direction. Angles a and e and distance R are defined in Figure 4-2.

For small angles a and e, Equation 4-1 may be linearized as follows I 'e' + MRig + MR(V +g)(a-0) = o (4-2) o g

The above equation describes forced vibration of a block and may be rearranged to read l s + F = -WR5 /g (4-3) o g

1 1

4-2

(.

where F =Fo + Ke (4,4)

-WR(1+Y /g)

K

=

g (4-5)

Fo = WR(1+V /g) a = Wb(1+V /g) g g

(4-6)

Equation 4-4 is graphically shown in Figure 4-3(a).

It may be noted that before the driving force on the right hand side of Equation 4-3 exceeds F, the system has infinite stiffness. Once the block starts rotating o

about one edge, it has a negative stiffness which is depicted in Figure

{

4-3(a) and also appears as K in Equation 4-5.

The solution technique used in the present study is to introduce a very stiff system, as shown in Figure 4-3(b), to model the initial vibrations of the block. Once the resisting force F is exceeded, o

the block would start rotating about one of the two edges. Although the problem is nonlinear in this case, it could be solved as a linear system with a correction force which becomes effective when lel > 0*.

A damoing value of 10 percent critical was assumed for the impact region, which was f

taken to be 0* 1 lel 1 ne* with n=6.

The Nigam-Jennings integratio'n method (reference 8) was used to solve the equation of motion.

In order to find the capacity of each wall, the input motion was scaled up until the instability point was reached.

It may be seen in Figure 4-3(b) that wall displacements are relatively small before the restoring force F is exceeded. Once F is exceeded, a softening in o

o the system is observed, i.e., the wall starts to rotate about its edges and its top displacements become much larger.

If the inout motion is increased further, a point is reached where the dynamic inertia loads cannot bring the wall back to its original position and the wall starts l

drif ting to one side. This is the point of instability for each wall.

Failure in actual walls seldom results from rigid body rotation of the entire wall through a 90-degree arc until impact with the ground occurs.

Instead, the P-aeffects become significant sometime after the point of instability is reached, and the mode of failure is normally in-place, vertical collapse.

i 4-3

Also from kinematics, e2 = (-X +X ) /L2 + (L + L ) 63 /L2 (4-9) t b i

2 where Xt and y.b are the top and bottom horizontal displacements respectively. Using the last two equatione, one could eliminate Ht and 62 in Equation 4-7 to write 3=-E(Cg+C/L)

C + C (1+8) 5+

C + Cu(1+s) ei + C b

2 2 i

2 1

3

+(C /L ) E + (Cu/L )(X -X )

(4-10) 2 2 t

2 t b where e = L /L2 (4-11) i Ci = 1o3 - slo 2 + 0.5M Li (L +L )

(4-12) 2 i 2 C2 = slo 2 - 0.5M L L (4-13) 2 i 2 3 = (-0.5M L -0.5M L )(g+V )

(4-14)

C i i 2 i g

Cu = (-0.5M L )(g+Vg)

(4-15) 2 i 3 = (0.5M l a+1.5M L a)(g+Vg)

(4-16)

C ii 2 l (4~17)

C6 = 0.5M Li i + 0.5M L21 It is evident from Equation 4-10 that the forcing function on the right hand side depends on accelerations and displacements at the top and bottom. Again, as in the single block model, one may write the equation of motion in terms of a restoring moment and a stiffness term as follows I;s + F = -X (Cc+C /L ) + (C /L ) E + (Cu/L )(X -Xb)

(4-18) b 2 2 2 2 t

2 t

l 4-5

where F

Fo + Ke

=

(4,gg)

C3 + Cg(1+8)

K

=

(4-20)

Fo = C3 (4-21)

^

I$ = C3 + C (1+8) 2 W 22)

Therefore, the two block vartical model results in a similar type of equation of motion as in the single block model (Equation 4-3).

The solution strategy for the two block model was the same as the one described for the single block model except that both upper and lower displacements as well as accelerations were required as input to the

model, i

4.3 TWO BLOCK HORIZONTAL MODEL Analytical models for the conservative seismic response of relatively long block walls under seismic excitation were presented in l

sections 4-1 and 4-2.

For walls where the vertical span significantly exceeds the horizontal length, the plastic hinge will appear as a vertical hinge so that a horizontal slice of the wall provides a more realistic analytical model. The walls which did not fit into the previous models were modeled as horizontal slices or beams which were allowed to develop inelastic hinges. The failure criteria defined for these walls was based on the maximum relative displacement of a wall with respect to its supports, i.e., failure was assumed to occur when the maximum relative displacement of a wall exceeded one half of its thickness.

Figure 4-7 shows a rectangular wall which is assumed to develoo a vertical crack in the middle under dynamic loads. For the purpose of analysis, a horizontal slice of the wall may be isolated and modeled as two beams connected in the middle (Section A-A in Figure 4-7). Once a vertical crack is formed in the middle, only the horizontal reinforcing j

steel in the wall can carry the inertia loads.

Thus, displacements of j

the wall are controlled by yielding in the horizontal steel.

4-6 i

t W

---r

,,,.y--,.me.-~r

.-----,---,--a

,--~--e....-,-.n--

--n------..,w-,,,nn--

n-

l Figure 4-7 also shows a vertical cross view (B-B) of a wall under the assumed cracking condition.

It is realized in Figure 4-7 that g

the lower section of the wall becomes unstable when relative displacement 5

of the wall equals half of its thickness. Although this criteria is conservative for dynamic loads, it was retained as the failure criteria for this type of analysis.

The computer program DRAIN-2D (Reference 9) was used to carry out the inelastic dynamic analysis. Concentrated masses equal to half the mass were located at a distance t /4 from each support where lh is the h

distance between two horizontal supports. This is in accordance with recomnendations in Reference 10.

The effect of arching on transverse load caoacity of a wall was accounted for by introducing rotational springs at its two ends. This is schematically shown in Figure 4-8.

A one inch contact area is assumed when the wall has rotated about its edge. This is in accordance with the recomnendations in Reference 11. Arching was only considered for the walls which were supported by concrete walls or columns at both ends.

t Figure 4-9 shows a typical force-displacement relationship for a block wall which develops a vertical crack in the middle. For many walls which were in this category, the load which causes initial cracking in the wall was calculated to be higher than the load which causes vielding in the horizontal steel. Although the load may drop after the initial cracking capacity is exceeded, dynamic ultimate capacity of the wall, which is based on the peak disolacement failure criteria, could be much higher than its cracking capacity.

For the present study, the cracking stage was conservatively neglected, i.e., only the horizontal steel was assumed to be acting to resist the inertia loads. On the other hand for block wall M100.3, which did not have sufficient horizontal steel, onlv cracking capacity is reported.

I 4-7

1 ra Section A-A FIGURE 4-1.

RESPONSE MECHANISM 0F WALLS UNSUPPORTED AT THE TOP b

3 l

ME e

t 9

Af M(Y +g) o e

v O

O' I

I 0'

+{

(a)

(b)

FIGURE 4-2.

ANALYTICAL MODEL FOR WALLS UNSUPPORTED AT THE TOP 4-8

F p

Fcorr

]

F p

a

,,h i

K i

1

-0*

0

\\'

\\

l e*

I I

l J

-F

_p o

g (a)

(b)

-m FIGURE 4-3.

FORCE-DEFLECTION REPRESENTATION 1

4-9

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/

i f

X Secdon A-A A

FIGURE 4-4.

RESPONSE MECHANISM FOR WALLS SUPPORTED TOP AND BOTTOM 02 L2 L 2 e

1 R2

)e2 bl e

Li R

O at i

l-03 (a)

(b)

I FIGURE 4-5.

ANALYTICAL MODEL FOR t1 ALLS SUPPORTED TOP AND BOTIOM 4-10

\\

vg n

i i

- t 1

M R 5 -M R 5 c2(5 -5 )

i2 1 222 I

2 1

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2 i 1

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i i g

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i g

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s X

=H o

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i

'I FIGURE 4-6.

TWO-BLOCK VERTICAL MODEL 1

RESPONSE C0tiPCNENTS 3

4-11

A A

see Figure 4-8 7

l k

L~

h Section A-A b

N LB Section B-B 4

l FIGURE 4-7.

FAILURE MECHANISM FOR A TALL WALL SUPPORTED AT ALL EDGES (2b2-b) K 0Cose M

=

y W(2b-1)ek 2

(2b -b) K s 2b M

=

y a=1"b 2

(2b -b)K K

=

y e

AE M

y V

L r

h e

=

FIGURE 4-8.

FORCES DEVELOPED DURING ARCHING 4-12

8 O

1 1

1 j

Force Cracking Ultimate K

N Yielding of Steel Displacement 9

1 1

FIGURE 4-9.

FORCE-DISPLACEMENT RELATIONSHIP TOR THE TWO BLOCK HORIZONTAL FAILURE MODEL 4-13

5.

ANALYTICAL RESULTS Analytical results for the Big Rock Point block walls subjected to seismic excitation were developed for both in-plane and out-of-plane (or transverse) response. The results are presented in terms of factors of safety to withstand the site specific Safe Shutdown Earthquake (SSE).

Since the SEP is based on an assessment of the overall seismic safety of the plant, strict compliance with current codes and licensing criteria is not required. Rather, an assessment of the general level of safety is desired. Consequently, loads resulting from the Operating Basis Earthquake (0BE) were not developed in this analysis, nor are comparisons presented with allowable stresses from current design codes which normally contain significant margins of conservatism.

t 5.1 TRANSVERSE LOADS Analytical models which were developed to calculate the Big Rock 4

Point wall capacities under transverse loads were described in Section 4.

Only walls M100.12 and M100.13, which are walls with a gap at the top, were analyzed via the single block model. The two block vertical vibration model was used to analyze walls M100.2, M100.4, M100.5, M10014, M10015, M100.16, and M100.19. The remaining walls were analyzed using the two block horizontal model.

In a number of cases, the transverse 1

capacity of the wall was determined using both a vertical slice model and a horizontal slice model.

The transverse response of wall M100.13, which was analyzed l

using the single block model, is shown in Figure 5-1.

This is one of the two walls (M100.12 and M100.13) which is unsupported at the top and hence responds as an inverted pendulum rather than developing a mid-height or 6

mid-length crack and responding as predicted by one of the two block models. The long period displacement cycles shown in Figure 5-1 indicate that this wall rotates about the two edges when subjected to the given i

transverse base excitation.

Figure 5-2 shows the too disolacment of wall l

M100.13 when the input motion is scaled up by a scale factor equal 5-1 i

L

capacities of horizontal two block models are reported. This introduces some additional conservatism into the analytical results since the seismic input must be sufficient to cause cracking before the point of l

instability is reached.

The results of all transverte load analyses are sumarized in Table 5-1.

Factors of safety against failure for transverse response are shown for the walls identified as important for safety. Not every wall was modelled and analyzed since the configurations of a number of walls were so similar that this was judged unnecessary. Table 5-1 lists the type of analysis used to find the capacity of each wall, or if evaluated by similarity, the wall judged most similar and its capacity. As indicated, several walls were evaluated with both horizontal and vertical two block models.

Many of the walls in the Big Rock Point Plant are made up of two or more segments. These segments are defined in alphabetical order, and the method of analysis for each segment is listed separately. Walls M100.4 and M100.5 were modeled together as one long wall. Wall M100.3 does not have any steel reinforcement. Therefore, only the elastic f actor of safety based on code allowables is reported for this wall in Table 5-1.

Table 5-1 shows that wall M100.2, which is a 4-wythe 32" thick j

wall, has the highest capacity among all walls in the Big Rock Point plant. Walls M100.6 through M100.12 were analyzed by horizontal two block models, but their capacity from either the vertical one or two block model also appears in the table. Wall M100.17 is a olug wall and it was qualified by checking the code allowable stresses against shear failure.

E 5.2 SENSITIVITY STUDIES In addition to compating wall capacities using the seismic inout described in Section 3, several supplementary analyses were also carried out to find the sensitivity of the single block and two block vertical models to the input parameters.

5-3 1

In order to find the effect of different input motions on the response of a block wall, three different earthquake motions were input to wall M100,13. A single block wall was selected for this part of the I

sensitivity study since its response could be evaluated from a single earthquake record only rather than calculate the response at the top of l

the wall which is controlled by the overall structure response. However, the conclusions reached for a single block wall are also expected to be generally applicable to the two block failure mode walls. These earthquake motions were an artificial ea.hquake which was simulated to fit the NRC Regulatory Guide 1.60 response spectra, the 1952 Taft earthquake record, and Array No. 5 record in the 1979 El Centro earthquake. Seismic capacity of wall M100.13 for thase motions were found to be 0.12g, 0.15g, and 0.16g, respectively.

It may be observed that even an artificial earthquake whose response spectra envelop the broad band, mean plus one standard deviation spectra in R.G.1.60 does not produce failure in the wall at icwer input levels than the artificial earthquake used in this evaluation. For actual earthquakes, particularly those with shorter durations such as could logically be expected to affect the Big Rock Point site, significantly higher factors of safety than those presented in Table 5-1 are expected.

Several additional sensitivity analyses were also carried out for the two block vertical model. Since both vertical and horizontal motions are input to this model, the response of a wall could conceivably become sensitive to the phasing of the two motions. A study.of wall M100.6 using the two block vertical model showed that changino the phasing of the vertical input motion with the horizontal input motion, i.e., changing the signs of vertical accelerations does not influence the wall capacity. A sensitivity study for wall M100.2 showed that the model I

is neither sensitive to the value of its initial stiffness nor is it O

sensitive to the damping assumed for impact (Equation 4-18). The results for wall M100.6 also showed that when the location of failure surf ace was changed from the mid-height of the wall, its capacity to withstand transverse loads was increased. Therefore, all the walls which were analyzed via the two block model were conservatively assumed to fail at their mid-heights.

5-4

Y 5.3 IN-PLANE LOADS Since none of the walls in the Big Rock Point plant were intended to act as shear resisting elements, in-plane loads which are induced by seismic excitations are not expected to govern wall capacities. However, there are three potential modes of behavior under in-plane loads, namely shear, flexure, and sliding which were evaluated for the Big Rock Point walls as part of this evaluation. A discussion of

~

each mode of behavior and wall capacities based on allowable stresses is presented in this section.

In-plane shear in masonry block walls is similar to the shear behavior of deep reinforced concreta beams. Therefore, horizontal reinforcement in a wall is expected to act as shear reinforcement and contribute to the shear capacity of the wall.

Values of allowable shear l

stresses in reinforced and unreinforced masonry block walls as reconnended in Reference 12 appear in Tables 5-2 and 5-3.

The allowable stresses used here are for the severe environmental conditions. A minimum f actor of safety equal to 30 was calculated for in-olane shear when the Big Rock Point walls are subject to SSE (A = 0.104 )

p 9

accelerations.

Since with one exception, there is no vertical reinforcement in the Big Rock Point block walls, an elastic in-plane flexural capacity f

based on allowable tensile stress normal to the bed joints was calculated for each wall. Allowable tensile stresses also appear in Tables 5-2 and

(

5-3.

It was found that a minimum factor of safety of 2.5 against flexural failure is present for SSE loads.

In order to calculate the factor of safety against in-plane p

sliding, the friction coefficient for the walls was taken to be equal to 5.

0.8 (Reference 11).

It may be noted that this assumption is especially conservative for the walls which are recessed into the floor. Assuming

[

that the peak vertical acceleration acts upward, a uniform factor of safety equal to 7.6 against sliding was computed for the Big Rock Point block walls.

A m

5-5 lP e

f

\\

l F

j j

From the above paragraphs, it is apparent that a minimum factor of safety of 2.5 exists when the BRP walls are subjected to in-plane SSE

}

loads.

It must be kept in mind that even for extreme environmental conditions, the allowable stresses presented in Tables 5-2 and 5-3 have additional factors of safety associated with them. Therefore, the actual factors of safety for in-plane loads are expected to be higher than the values which are presented in this report.

1 i

l i

l i

I l

l' ll

'l l

lI I

if i

5-6

t L

TABLE 5-1 FACTORS OF SAFETY FOR BRP WALLS AGAINST SITE SPECIFIC EARTHQUAKE Factor 1

of Wall No.

Safety Type of Analysis M100.1 2.8 Horizontal Two Block Model M100.2 10.2 Vertical Two Block Model M100.3(a) 4.1 Horizontal Two Block Model M100.3(b) 4.1 Horizontal Two Block Model, Similar to M100.3(a)

M100.4(a)-

4.0 Vertical Two Block Model M100.5(a)

M100.4(b)-

4.0 Vertical Two Block Model, Similar to M100.4(a)

M100.5(b) andM100.5(a)

M100.6 7.8 Horizontal Two Block Model 2.8 Vertical Two Block Model M100.7 7.8 Horizontal Two Block Model, Similar to M100.6 2.8 Vertical Twc Block Model, Similar to M100.6 M100.8 2.6 Horizontal Two Block Model 2.8 Vertical Two Block Model M100.9 2.6 Horizontal Two Block Model, Similar to M100.8 2.8 Vertical Two Block Model, Similar to M100.8 M100.10 7.8 Horizontal Two Block Model, Similar to M100.6 2.8 Vertical Two Block, Similar to M100.6 l

M100.11 7.8 Horizontal Two Block Model, Similar to M100.6 2.8 Vertical Two block Model, Similar to M100.6 l

M100.12 2.6 Horizontal Two Block Model, Similar to M100.8 1.1 Vertical Single Block Model, Similar to M100.13 M100.13 1.1 Vertical Single Block Model l

M100.14(a) 4.0 Vertical Two Block Model, Similar to M100.4(a) and M100.5(a)

!l 5-7 i

(

TABLE 5-1(cont'd)

FACTORS _0F SAFETY FOR BRP WALLS i

AGAINST SITE SPECIFIC EARTH 0VAKE Factor of Wall No.

Safety Type of Analysis 1

M100.14(b) 4.0 Vertical Two Block Model, Similar to M100.4(a) andM100.5(a)

M100.15 4.0 Vertical Two Block Model, Similar to M100.4(a) and M100.5(a)

M100.16 4.0 Vertical Two Block Model, Similar to M100.4(a) and M100.5(a)

M100.17

" 1. 0 Static Analysis M100.18(a) 0.9 Horizontal Two Block Model M100.18(b) 4.0 Vertical Two Block Model, Similar to M100.19(a)

M100.18(c) 11.5 Horizontal Two Block Model M100.19(a) 4.0 Vertical Two Block Model M100.19(b) 4.0 Vertical Two Block Model, Similar to MMO.19(a) 1 1

5-8

TABLE 5-2 Allowable Stresses in Rainforced Mas:nry U**

Description Allowable Maximum Allowable Maximum (Psi)

(psi)

(psi)

(psi) 1 Compressive Axial (I) 0.22f' 1000 0.44f' 2000 Flexural 0.33f' 1200 0.85f; 3000 Bearing On full area 0.25f' 900 0.62f; 2250 On one-third area 0.375f"'

1200 0.95f"'

3000 or less Shear Flexural members (2) 1.1 8*

50 1.7ff*-

75 Shear Walls (3,4)

Masonry Takes Shear M/Vd 11 0.9/f' 34 1.54 56 M/Vd = 0 2.0 74 3.4 {

123 Reinforcement Takes Shear 75 2.5 4 125 M/Vd 11 1.5 (

M/Vd = 0 2.0 %

120 3.4K 180 Reinforcement Bond Plain Bars 60 80 Defonned Bars 140 186 I

Tension Grade 40 20,000 0.9F l

y i

Grade 60 24,000 0.9Fy Joint Wire

.5F or30,000 0.9F,

=

y Compression 0.4F 0.9F y

y 1

i 5-9

Notes to Table 5-2.

(1) These values should be multiplied by (1 - (h)3) if the wall has a significant vertical load.

1 (2) This stress should be evaluated using the effective area.

(3) Net bedded area shall be used with these stresses (4) For M/Vd values between 0 and 1 interpolate between the values given for 0 and 1.

l S = nomal environmental loads

    • U = severe environmental loads 1

em 1

1 5-10

TABLE 5-3.

Allowable Stresses in Unreinforced Masonry S*

LP*

1 Description A11cwable Maximum Allowable Maximum (psi)

(psi)

(psi)

(psi) 1 Compressive II)

Axial 0.22fy 1000 0.44fy 2000 Flexural 0.33fy 1200 0.85fy 3000 Bearing On full area 0.25fy 900 0.62fy 2250 On one-third area 0.375f"'

1200 0.95f"'

3000 or less Shear 1.7 %

75 Flexural members (2,3) j,)

50

)

1.5 %

56 Shear walls 0.9 34 Tension Normal to bed joints Hollow units

0. 5 /m, 25 0.83 (

42 Solid or grouted 1.0 %

40 1.67/iEI 67 g

Parallel to bed joints (4)

Hollow units 1.0 /m 50 1.67K 84 g

Solid or grouted 1.55 80 2.5 K 134 4.2 %

l Grout Core 2.5 Collar joints Shear 8

12 Tension 8

12 1

5-11

Notes to Table 5-3.

(1) These values should be multiplied by (1 - (h)3) if the wall has a significant vertical load.

(2) Use net beddad area with these stresses.

- (3) For stacked bond construction use two-thirds of the values specified.

(4) For stacked bond construction use two-thirds of the values specified 1

for tension nonnal to the bed joints in the head joints of stacked bond construction.

  • S = normal environmental loads
    • U = severe environmental loads l

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I 5-27

4 6.

CONCLUSIONS AND RECOMMENDATIONS An evaluation to determine the ability of concrete block walls in the vicinity of critical equipment at the Big Rock Point Nuclear Generating Plant to withstand seismic excitation was conducted, the seismic input to the walls was developed in accordance with the f

Systematic Evaluation Program (SEP) site specific response spectra for the Big Rock Point site. Time History inputs to the walls were determined from the response of the turbine building comolex subjected to an artificial earthquake whose response spectra envelop the site specific i

ground response spectra.

g Analyses were performed to determine the capacities of the wall i

segments to withstand both in-plane and transverse seismic loeds.

In-plane load capacities were determined by comparing the seismic f

stresses obtained from static analyses of the walls with code allowable values. Transverse load capacities were determined from time history analyses of nonlinear two-dimensional analytical models of the walls.

Separate inputs were used at the tops and bottoms of the walls to reflect the amplification through the turbine building complex.

Factors of safety based on the stability of the walls were determined for the transverse response and on code allowable stresses for the in-plane response. The minimum factor of safety for in-olane loads

'l considering shear, flexure, and sliding was calculated to be 2.5.

All the walls with the exception of M100.18 were shown to have a factor of safety of 1 or greater in the transverse direction. Walls M100.12 and M100.13 are ungrouted at the top. These walls have a factor of safety of i~

1.1 Although this is more than adequate to withstand the exoected I

maximum seismic input, the capacity of these walls could be increased t

considerably by the addition of restraints against transverse motion at i

the top. Wall M'.00.18 has a factor safety calculated at slightly less

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'l than 1 based on the conservature two-dimensional analyses used in this evaltation, and it is recomended that either the wall be strenathened by external bracing or that a more refined three-dimensional non-linear ana7ysis be conducted to assure its capacity. All other walls have a minimum f actor of safety against transverse instability of 2.6 or g'. tater, and require no modification.

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w REFERENCES 1.

" Big Rock Point 180-Day Response to NRC IE Bulletin 80-11 for Consumers Power Company Big Rock Point Nuclear Plant, Charlevoix, Michigan", Bechtel Power Corporation, Ann Arbor, Michigan, Oct.1980 2.

Crutchfield, D. M., " Site Specific Ground Response Soectra for SEP Plants Located in the Eastern United States", letter report to all SEP Owners (Except San Onofre) June 8,1981 3.

" Seismic Safety Margin Evaluation - Big Rock Point Nuclear Power Plant Facilities" D' Appolonia Engineers for Consumers Power Company,

,l Jackson Michigan, Project No.78-435, December 1980 4.

Eggenberger, A. J. (D' Appolonia Consulting Engineers) to R. B.

l Jenkins (Consumers Power Company), " Generation of Floor Time Histories, Turbine Building complex, Big Rock Point Nuclear Power i

Plant, Charlevoix, Michigan," letter report, March 5,1982 5.

Housner, G., "The Behavior of Inverted Pendulum Structures During Earthquakes," Bulletin of the Seismological Society of America, Vol.

53, No. 2, February 1963 8

6.

Yim, C. S., Chopra, A. K. and J. Penzien, " Rocking Response of Rigid 1985 a c 7.

" Structural Condition Documentation and Structural Capacitv

,5 Evaluation of the Babcock and Wilcox Facility at Lynchburgh, l

Pennsylvania for Earthquake and Flood," Engineering Decision t

Analysis, Palo Alto, California, May 1978 i

8.

Nigam, N. C. and P. C. Jennings, " Calculation of Response Spectra i

from Strong-Motion Earthquake Records," Bulletin of the Seismological Society of America, Vol. 59, No. 2, April 1969 9.

Kanaan, A. E., and G. H. Powell, " DRAIN-20, A General Purpose Computer Program for Dynamic Analysis of Inelastic Plane q

Structures," University of California, Berkeley, April 1973 j'

10. Lin, Chi-Wen, "How to Lump the Masses - A Guide to the Piping Seismic Analysis," ASME, Pressure Vessels and Pioing Conference with Nuclear Engineering and Materials Divisions, Miami Beach, Florida, 2

June 1974 g

11. "Recomended Guidelines for the Reassessment of Safety Related

[

Concrete Masonry Walls," prepared by Owners and Engineerino Firms Informal Group on Concrete Masonry Walls, October 6,1980

}

12.

" Building Code Requirements for Concrete Masonry Structures," ACI 531-79, American Concrete Institute, June 1979

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