ML19260E191

Rept to NRC on Effect of Installing Core Region Constraint Devices on Seismic Response of Facility Core.

ML19260E191
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Site:	Fort Saint Vrain
Issue date:	04/24/1979
From:	Anderson C, Bennett J, Dove R LOS ALAMOS NATIONAL LABORATORY
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REPORT TO NRC ON THE EFFECT OF INSTALLING CORE REGION CONSTRAINT DEVICES ON 'HE SEISMIC RESPONSE OF THE FORT ST. VRAIN CCRE R. C. Dave J. G. Bennett C. A. 1.nderson h2

_=ser=

8002130 f

A 2

INTRODUCTION The Reactor and Advanced Heat Transfer Technology Group (Q-13) of the Los Alamos Scientific Laboratory (LASL), acting as consultants to the Nuclear Regulatory Comission, has examined the effects of the Public Service Company of Colorado's (PSC) proposal to install core region constraint devices (RCDs) onto the top plane of the Fort St. Vrain (FSV) core with regard to the seismic safety of the core. The devices are being considered for installation in an effort to solve a temperature fluctuatien problem currently experienced at FSV under certain operating conditions.

The questiens that we have addressed arc 5 the addition of the RCDs will affect the dowel shear forces and fuel element impact forces during a seismic event.

SUMMARY

OF ANALYSIS Because of the relatively lcw intensity levels of known and predicted earthquakes for the Fort St. Vrain region, and because of the relatively large values of ccefficient of friction for graphite on graphite in a dry helium environment, the fuel regicns will initially respond as top restrained cantilever columns excited at their base during a seismic event.

Since we desire to knew the relative effect of RCD installation upon maximum dowel shear fo. ces and maximum impact forces during a seismic event, we have examined the effects of imposing two types of end i astraint on a cantilever column undergoing seismic excitation. To facilitate the analysis we have used an available bottom head reactor horizontal r% pense spectra corrected to one that we believe to be appropriate for the core suppcrt plane at the Fort St. Vrain plant. We ha e also used the horizontal response spectra for the Fort St. Vrain plant reactor and turbine buildi:1g ficar slabs. This response spectra includes the FSV PCRV motion but not the core sucport plane.

• /e have detarmined the possible extreme values of the lowest natural frquency of the fuel columns by including in the analysis such effects as beiding, shear effects, geometric stiffness effects caused by both the fuel co'.umn weight and end loads, lateral pressure effects and irradiation material property changes. Table I shows the results of this analysis. By using the extreme bounding values of lowest natural frequency of tne fuel columns (i.e., u = 16 s-I and a = 29 s-I) and the response spectra, and by examining the relative stiffening effect of changing the end conditiens

on the cantilever column from free to one that is simply supported or clamped , the relative effect of the RCD cn dowel shear forces can then be predicted. Table II gives this result.

SUMMARY

OF CONCLUSIONS With regard to the seismic respense of the Fort St. Vrain core, the addition of the RCDs can be expected to decrease the maximum dowel shear forces as shown in column 3 of Table II. One exception is noted. This exception involves FSV being a very "sc' , (low natural frequency) or a very "hard" (high natural frequency) system. In these cases maximum shear forces could increase. Based en general kncwledge of large massive structures of the FSV type, these exceptions are not deemed credible. For motions produced when fuel block slippage occurs, the fuel element impact velocities and impact forces will also be decreased.

In su:mlary, the addition of the RCOs should serve to make the FSV core a mere seismically safe structure.

TABLE I FUEL COLUMN NATURAL FREQUENCIES (1/s)

Grapnite Material Modulus u z

0 2 "3 "4 "5 H-327 1.3 x 106 psi (unirradiated) 16.27 16.21 16.19 17.10 17.15 3.9 x 106 psi (irradiated) 28.19 28.15 28.14 28.68 28.93 where, w) - bending only u2 - banding plus gecmetric stiffness due to weight w3 - bending plus geometric stiffness due to weight and end leads u4 - bending plus geometric stiffness and lateral pressure effects u5 - bending plus geometric stiffness plus lateral pressure effects plus shear correction

.s TABLE II EXPECTED CW r IN COLUMN MAXIMUM SHEAR FORCES Case Bounding natural Column maximum shear frequency (rad /s) force Case I W = 16 Sy y

(Cantilever column - (Tg = 0.39 s) 1.e. no RCDs)

=

"y 29 S y

(T; - 0.22 s)

Case II '" g g = 6.4 x 16 Using Fig. 3 (RCDs produce = 102 577= 0.08 57 fixed conditicn (Tyy = 0.06 s) Using Fig. 4 at top of column) 577= 0.47 Sy "gi = 6.4 x 29 Using Fig. 3

= 185 Sgg= 0.28 Sy (Tyg = 0.03 s) Using Fig. 4 577= 0.19 Sg Case III "g;; = 4.4 x 16 Using Fig. 3 (RCDs produce = 70 S777=0.13 Sg pinned ccndition (Tygg = 0.09 s) Using Fig. 4 at top of column) S.7y=0.58 Sg u Using Fig. 3 ggy = 4.4 x 29

= 127 5777=0.45 Sy (Tyyy = 0.06 s) Using Fig. 4 5777=0.99 Sy

. N y

h APPENDIX METHOD OF ANALYSIS INTRODUCTION Since it was assumed in the Final Safety Analysis Report (FSAR) for the FSV reactor that the core was restrained during seismic events and the analysis used involved the application of an equivalent static load to this

" restrained" core it is not possible to extend this original analysis to determine how the addition of the RCDs will change the seismic loading on the individual core blocks.

A review of the FSAR reveals that for the FSV Nuclear Generating Station the Operating Basis Earthqake (CBE) is taken as 0.05 g horizontal and the Safe Shutdown Earthquake (SSE) is taken as 0.10 g horizontal. Further, dynamic analysis of the care support structure indicated that these ground acceleraticns result in acceleraticns at the core level of 0.19 g (OBE) and 0.26 g (SSE). At these relatively lcw acceleration levels the individual core biccks would not be expected to slip horizontally relative to each other until af ter an impact event. The reascn icr this is the fact that without some other driving force slippage does not occur until the base acceleration in "gs" is equal to or greater than the static coefficient of fricticn between blocks (graphite en graphite), ar.d previous research indicates that this coefficient is greater than 0.2 and probably greater than 0.3.* From this cbservation it folicws that during seismic excitation the stacked core blocks will respond first as a column rather than as individual blocks moving (slipping) relative to each other.

SIMPLIFIED BC'JNDING ANALYSIS Three cases will be considered to investigate the effect of adding the RCDs en the seismic response. Since we wish to examine the effect in terms of dowel shear forces, we need a method to estimate the ratic cf the column shear forces in the new configuration as compared with the original

• Ref. I snows that the coefficient of kinetic friction of graphite on graphite is in excess of 0.3 in a dry, high tempe-ature, helium anvrienment. The static coefficient is known to be higher than the kinetic value.

r confi guration. Let the original configuration be represented by a cantilever beam with a unit lateral load applied at the end for which the statical deflecticns give a good approximation to the first made shape of the beam. Using simple beam theory, we can show that relationship between the maximum shear force, 5 , and maximum deflection, Z y

, of the tip is 7

= 3EI S

g Z y.

3 L

where El is the bending stiffness of the bean (The termi 3EI/L 3 is the cortmonly kncwn spring stiffness for the cantileve;-). We define this approximation for the original configuration as case I.

With the addition of the RCDs, the fuel column will behave differently.

Under the proper conditions it can behave as a beam clamped at both ends. An appropriate mode shape to estimate maximum shear forces is a beam fixed at both ends and loaded in the center which we will define as case II. For case II, the relationship between the maximum shear forces and the maximum deflection can be shown to be

= 192EI 7 S

II 3 'II*

2L The boundary condition at the RCD end of the column can also be approximated as a pinned condition which we define as case III. In case III,

• I III III 1.

We can conclude that the relationship between maximum shear forces, S, developed in these cases are as follcws II =

I I =

II 32 and 24 I I I I

7) wnere Zg are the maximum relative displacements. Furthermore, the ratios of the first mode natural frequencies for these cases are such that,*

II III

= 6.4 and = 4.4.

I I The questien to be answered is, "How will the stiffening (an increase in the natural frequency), affect the shear forces (s) developed during a seismic event.

The approach that we will use in answering this question can best be illustrated by assuming that the exciting function (x) is harmenic. Figure 1 taken from Ref. 3 shows the response curves for a horizontally base excited single degree of freedcm system. Referring to Fig. I we can see that if the original system (case I) is relatively flexible (i.e. w/un" 1, where u is the for:ing frequency), then increasing the stiffness (as in case II) will decrease the ratio of u/en. Such a decrease will result in an increase in the shear fcrces developed. As an example, assume u/u n,

= 10 and h (the damping ratio) = 0.3. Then

" = 1.56 "n II From Fig. 1,

=

Zy X, where X is the input displacement and Zy7 = 1.48 X. Then S I*#8 whereupon S yy II = 32 x = 47 S y.

1 S)

This example illustrates that the increase in shearing force can be quite severe under the proper conditicns.

• Fcr example, see Ref. 2.

h)

On the other hand, if the original system (case I) is near resonance (w/ u n = 1) or already a " stiff" system (w/uj < 1) then increasing the stiffnksswilldecreasetheshearforcedeveloped. For example, using case III data for which u

II = 4.4, assume we have

= 1 and h = 0.3 g"I 2- 93 n.o 1 5- *-

'5 5 E-

/h\_

IU/VWM 5% . II////"'/ X V

/ =Z y

/ p ii / / f= /

.2

.e-

.b 4 b .6.h ab I I!S 2 $1 5 6 h 8 9C FREccENCY RATIO A = /..

Fig. 1. Steady-state response of a seismic system to har. nic base displacement (frcm Reference 3).

N then

= 0.23.

u"III From Fig.1 (extended) ZI = 1.6 X and ZIII = 0.03 X. Then 0

III = 24 x whereupon Syyy = 0.45 57 I

Clearly the same analysis can be carried out if we work with an earthquake shaking function instead of harmonic excitation, provided we have the response curves similar to Fig.1 in the form of a core support response spectra. In sumary, if we approach the problem by assuming that the effect of the RCDs is to stiffen the fuel region, then whether pin shear forces will ce reduced depends upcn the natural frequency of the original system and the frequency spectra of the driving function.

ESTIMATE OF FUEL COLUMN FREQUENCIES To apply this method to the Fort St. Vrain reactor core, we will describe the response of a core column in terms of a single degree of freedom or a single coordinate so that we can estimate the fuel column natural frequencies. Because of the relatively high friction between blocks and the relatively low known and predicted earthquake acceleraticn values, a fuel regicn can be expected to respond as seven base excited columns restrained to move together at their top (Fig. 2).

'de can describe the icwest mode respcnse for this system in terms of the tip respense Z(t) relative to the base excitation vg (t). Let the absolute displacement of a fuel column be 3v (x,t). Let the displacement of a point en the column relative to the base be w(x,t) (see Fig. 2). *We will assume the predominate response to be in the first mcde, and write v a(x,t) = v + w(x,t) g and that w(x,t) =

7 (x) Z(t) where f(x) is an admissible shape functicn. By writing the kinetic and pctantial energy expressiens for all effects that we may wish to include, and applying Hamilton's principle to the result we can develop an equatien of motien of the form

10 eff Z(t) + k eff Z(t) g vg (t) - pff(t) m =-m e

where m,ff = the effective mass k

eff

= the effective stiffness p,ff = the effective. loading.

In this analueis, we will include a number of different terms in the effective stiftnew so that we can assess their relative effects on the response. Thus, in the above equation k,ff =

kb-k g -k a -k p +k sc REFERENCE AXlS lX 1

.--' MM-A

!._ _ /

0 -' - '

,/

-v A-l w ..

U t

. j ---+

!/

.,t7 I

I

,I I

I l

"N //

1. //// /Vo //f/// U9

//

ug- _ _ _ .

Fig. 2. Motion of a fuel region.

y Il J

where 2

k 3

=

EIo[ L

• 7"(x) dx is the bending stiffness of the column, and k

g

=

[L o

W(x) y'(x) 2 dx is the geometric stiffness (W(x) is the axial load as a function of the length because of the weight of the column). The term 2

k a

= N

[L o

7'(x) dx is an added geometric stiffness term accounting for the ccnstant axial load (N) that occurs because of the keyed plenum blocks, RCDs, etc. The term k

g =[L o q(x)  ? (x) dx is a stiffness effect because of the lateral pressure q(x) across a fuel column. The term

=

k sc  ?'" (x) dx is a term that represents the shear stiffness of the column. The two terms m

eff and mg given by L

m eff m(x)  ?(x) dx

= [o

. w' m

g

=

m(x) ?(x) dx ,

represent an effective mass for the fuel column and a mass like term to convert the base motion to an effective force, respectively. In the above E = Young's modulus for graphite I = the cross sectional moment of inertia q(x) = the lateral pressure loading on the column a = the gecmetric shear correcticn f actor A = the cross sectional a..a of a fuel column G = the shear modulus of elasticity m(x) = the mass per unit column length.

By including all these terms separately, we can assess their relative eff ects en the undamped natural frequency and bcund the possible frequencies such that the method that has been described can be applied.

Table I gives the result of carrying out the details of the analysis with ?(x) = l-cos (nX/2L), where feff 3m,, -

e

'4e have also included the irradiation effect on Young's modulus by taking the extreme values for H327 graphite as given in Ref. 4. Table III shcws the other values of parameters used in carrying out the details of the analysis.

APPLICATION TO THE FSV CORE Using the bounding values of natural frequency as 16 rad /sec and 29 rad /sec, and lcoking at the effects of the boundary conditions of cases II and III, we can compare ...e ealized ratios of maximum shearing stress in the new configuration (ti'  ;) to the original configuratien (without RCDs) during an earthquake lust as in the har.uonic excita :n examples provided that we use the response curves for an earthquake exciting function.

s IE TABLE III PARAMETERS USED IN FSV COLUMN FREQUENCY CALCULATIONS 2

m eff = 1.526 lb-s /in.

k = 3394 lb/in k = 3.109 x 10-4 E lb/in k

a

= 0.6366 lb/in (with RCDs, 1.002 lb/in) k P

= -46.3 lb/in sc = 1.475 (E)2 k

The respense spectra for the FSV core support floor is not available.

However, two spectra are availab79 that should allow a satisfactory estimate of the relative effects of the installaticn of the RCDs.

The first response spectra that we have used is shown in Fig. 3 by the dashed lines. This respense spectra was obtained in the folicwing manner.

The criginal (solid line) is for the bottom head of the PCRV of a larger 5

plant as given in GASSAR-6 . This response spectra was shifted to the right (dotted line) so that the peak response occurs at a period of 0 5 see to correspond to the measured natural pericd of the FSV PCRV as reported in Ref. 6. Note that because we are only interested in the relative effect of the RCDs, we are not ccncerned about the magnitudes in Fig. 3, and unless some "ery unusual " filtering" occurs leading to an extremely broad band peak respense, the dotted spectra should be representative of the PCRV for the FSV plant. Table II, column 3 shows the results of the calculations using the dashed spectra of Fig. 3.

If the actual FSV core plane response spectra is shif ted even further to the right on Fig. 3, the fuel column shear stresses will continue to be reduced by the installaticn of the RCDs with one exception. If the spectra is shifted so f ar to the right that point "A" (Fig. 3), is at a period of 0.22 sec (w = 29 rad /s) er greater, then the maximum shear forces could increase by 2S% provided that the original natural frequency of the fuel column (e7) is as high as 29 rad /s and also that the RCDs result in a pinned end ccndition. Such cor.ditions are not deemed likely for this structure.

(Y ]

We also note that if the true response s;actra is sh ._ 60 the left (Fig. 3) so that point "B" is at a period of 0.09 s or less, then the shear forces may also be increased by tne installation of the RCDs.

Figure 4 shows the floor response pectra for the FSV reactor and turbine building floor slabs. The dotted line shows the previously discussed response spectra of Fig. 3 scaled down to 1.5 g. It is likely that much of the high frequency (lcw period) would be filtered out of a response spectra that applied only to the core support structure, and would appear mucn as the dashed line. Hcwever,- we can use Fig. 4 as it is to estimate the effect of the RCDs on thi maximum shear stresses. These results are also shewn in Table II, column 3.

1.0% oAMPWG 1.o+ C

• B*

6.o* OC g

/ \

/ \

-e zo.m / \ \

. j g i / \

to a / \

< / \

c: __ /

3 w 4.0-01 N 4- \

\

e \

\

2 0-01 Lo-Cl 6.0-C2 ,

6 \.

0.001 0.01 1.0 Io.

PERIOD (s)

Fig. 3. Reactor bottem head horizontal response spectra for operating basis earthquake.

-s g

FUEL ELEMENT IMPAC' VELOCITIES AND FCRCES Vibration studies7 'O'9 on core like structures (stacked blocks) suggest that by f ar the largest forces produced during a seismic event are the forces produced by impact of block against block. In the FSV reactor even though the initial response of the core may be column bending, impact between a core block column and the side wall may be expected to occur (assuming the relative displacement response is greater than the gap between a boundry column and the side wall) and once the first impact occurs it will be followed by numerous block to blocx impacts. The vibration studies referred to above indicate that the large; the clearance between elements the larger the impact forces.

The proposed RCD. dill limit the accumulaticn of gaps between the fuel regions and therefore may limit the intensity of impact forces. Fig. 5 is a model of the FSV core without RCDs (case I). If we assume an impulsive ground motion to the right, the fuel regicn on the left (#1) will impact the permanent reflector block af ter undergoing a relative displacement of approximately 0.12 in. The impact sequence will then propagate from left to right. Fig. 6 is a model of the FSV core with RCDs in place (case II). If we again assume an impulsive ground motion to ':.e right the fuel regicn on the right f17) will impact en the RCD af ter unde going a relative motion of approximately 0.030 in. (0.150-0.120). The impact sequence will then propagate frcm right to left. .

The analysis which folicws illustrates *he difference in the magnitude of the impact fcrces involved in the two cases.

Assume that the relative displacement (2) and the relative velocity (5) cf the core regicns are as shewn in Fic. 7. These curves represent the relative response motion that would be produced by the seismic motion x(t) at the core basa for the case where no contact between core regions is allcwed. New assume that in Case I (Fig. 5, no RCDs) this initial (before contact) relative motion is such that contact occurs at some point to the lef t of line a-a in Fig. 7, say at pt. #1; then the initial impact velocity is Ej . With the RCDs present (case II) the initial contact will occur at pt. #2 with an impact velocity of 1. Since forces are proportional to 2

impact veloc ties, forces will be reduced.

i

O gy If in case I (no RCDS) the first impact is< to the right of line a-a then the effect of adding RCDs (case II) may be to either increase or decrease the impact force. However, in general, for a system capable of large relative motion excursions without stops (a "sof t" system), constraint involving the smallest clearance gaps will result in the lowest impact forces. The computations previously referred to in this report for the natural frequency of the FSV fuel columns show that the FSV is a " soft system" relative to the appropriate response spectra. Consequently the additicn of the RCDs can be expected to decrease the impact velocities and thus the impact forces.

e i.s -

/ 1 x e / \

sx 5 , , // \ N. '

= \

/ // \

/

z O

p I V

/

i

\

< )

5

-.1

/

W O'2 /

0

< l l \

0.15 -

0.10 -

0.02-e i i ,

e o i i O.02 0.03 0.04 .I 1.5 .2 .3 1.0 1.5 2.0 PERIOD (S)

Fig. 4. Horizontal ficor response spectra, safe shutdown earthquake.

c. 4.

a } __

OJ2 ' H }--O.12 Q

I l' YCT'; lii g

1 . 'i I l

\ i ~T i

1 i

t I

1--$ '

\ \

r t s

' I i i 1

6 f4 1 2 3 4 5 6 7 /

X BASE I

w -

E Fig. 5. Model illustrating initial impact sequence without RCDs k

_r < , , e r-pu fl 1 i i i 1 g i 2 3 4 5 6 7  ; g X BASE _ -

+

1 Fig. 6. Model illustra ing initial impact sequence with RCDs

. g-Z,Z 0

RELATIVE DISPLACEMENT RELATIVE VELOCITY

. -s s

4 ,/

- /; , N Z2 . /_ / \

Z2 '

Z2 & d/2 ' \ ,

N / t

\ /

N /

0 \ '

N /

Z i = 0.120 in Z2 =0.030in Fig. 7. Illustration for effects of increased displacement constraint on impact velocities.

s

(? l REFERENCES

1. M. Stansfield, " Friction and Wear of Graphite in Dry Helium at 25, 400, and 800cc," Nuclear Acolications Vol. 6, April 1969, pp. 313-320.

2. W. F. Thomson, Vibration Theory and Acolications, Prentice Hall, Englewood Cliffs, NJ, 1965.

3. R. C. Dove, P. H. Adams, Experimental Stress Analysis and Motion Measurement, Charles E. Merrill Books, Inc., Columous, Onio, 1964.

4. R. J. Price, " Mechanical Properties of Graphite for High Temperature Gas Cooled Reactors: A Review," General Atomic Report #GA A13524 - UC77, Sept. 22, 1975.

5. GASSAR-6, General Atomic Standard Safety Analysis Repcrt.

6. Fort St. Vrain Nuclear Generating Station - PSCo Document, " Core Fluctuation Investigation Status and Safety Evaluation Report," Aug.

1978.

7. K. D. Lathrop, Ed., " Reactor Safety and Technology Quarterly Progress Report," July 1 - Sept. 30, 1976, LA-NCREG-6579-PR, pp. 13-19.

8. J. G. Bennett, "A Physically Based Analytical Model for Predicting HTER Core Seismic Response," Proceedings of the Japan-US Seminar en HTGR Safety Technology, BNL-NUREG-50689 - Vol. I, pp. 125-135.

9. Experimental Seismic Program for HTGR Safety as Reported in the Nuclear Reactor Safety Quarterly Progress Reports, Los Alamos Scientific Laboratory, NUREG/CR-0062 - LA-7278-PR, LA-NUREG-69-34-PR, NUREG/CR-0522 - LA-7567-PR,1978.

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