ML19257C747

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

ML19257C747
Person / Time
Site:	Fort Saint Vrain
Issue date:	04/24/1979
From:	Anderson C, Bennett J, Dove R LOS ALAMOS NATIONAL LABORATORY
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ML19257C744	List: ML19257C743 ML19257C747
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REPORT TO NRC ON THE EFFECT GF INSTALLING CORE REGION CONSTRAINT DEVICES ON THE SEISM;., RESPONSE OF THE FORT ST. VRAIN CCRE R. C. Dove J. G. Bennett C. A. Anderson LE

._ =.sei=s=._

1835 004 8 00130 0 E65

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INTRODUCTION The Reactor and .1dvanced 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 fluctuation problem currently experienced at FSV under certain operating conditions.

The questions that we have addressed are how 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 low intensity levels of known and predicted earthquakes for the Fort St. Vrain region, and because of the relatively large values of coefficient of friction for graphite on graphite in a dry helium environment, the fuel regions will initially respond as top restrained cantilever columns excited at their base during a seismic event.

Since we desire to know the relative effect of RCD installation upon maximum dowel shear forces and maximum impact forces during a seismic event, we have examined the effects of imposing two types of end restraint on a cantilever column undergoing seismic excitation. To facilitate the analysis we have used an available bottom head reactor horizontal response spectra corrected to one that we believe to be appropriate for the core support plane at the Fort St. Vrain plant. We have also used the horizontal response spectra for the Fort St. Vrain plant reactor and turbine building floor slabs. This response spectra includes the FSV PCRV motion but not the core support plane.

We have determined the possible extreme values of the lowest natural frequency of the fuel columns by including in the analysis such effects as bending, shear effects, geometric stiffness effects caused by both the fuel column 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 the fuel

. e. , u = 16 s-I and e = 29 s~I) and the response spectra, and

_xam1ning the relative stiffening effect of changing the end conditions Kh

s n

on the cantilever column from free to one that is simply supported or clamped , the relative effect of the RCD on dowel shear forces can then be predicted. Table II gives this rv 3

SUMMARY

OF CONCLUSIONS With regard to the seismic response of the Fort St. Vrain core, the addition of the RCDs can be expected to decrease the maximum dowel shear forces as shom in column 3 of Table II. One exception is noted. This exception involves FSV being a very " soft" (low natural frequency) or a very "hard" (high natural frequency) system. In these cases maximum shear forces could increase. Based on general knowledge 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 surmary, the addition of '.he RCDs should serve to make the FSV core a more seismically safe structure.

TABLE I FUEL COLUMN NATURAL FREQUENCIES (1/s)

Graphite Material Modulus u) u H-327 2 "3 "4 "5 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, ej - bending only e2 - bending plus geometric stiffness due to weight e3 - bending plus geometric stiffness due to weight and end loads w4 - bending plus geometric stiffness and lateral pressure effects e5 - bending plus geometric stiffness plus lateral pressure effects plus shear correction

.1835 006~

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TABLE II EXPECTED CHANGE IN COLUMN MAXIMUM SHEAR FORCES Case Bounding natural Column maximum shear frequency (rad /s) force Case I W = 16 Sy 7

(Cantilever column - (Tg = 0.39 s) 1.e. g RCDs)

W = 29 S 7 y (Ty= 0.22 s)

Case II W = 6.4 x 16 Using Fig. 3 77 (RCDs produce = 102 577= 0.08 S g fixed condition (T77 = 0.06 s) Using Fig. 4 at top of column) Syy= 0.47 S7 U

yy

= 6.4 x 29 Using Fig. 3

= 185 Syy= 0.28 Sy (Tyy = 0.03 s) Using Fig. 4 577= 0.19 57 Case III W ggy = 4.4 x 16 Using Fig. 3 (RCDs produce = 70 Syyg=0.13 Sy pinned condition (Tyyy = 0.09 s) Using Fig. 4 at top of column) Syyy=0.58 57 u = 4.4 x 29 Using Fig. 3 777

= 127 S177=0.45 Sy (T777 = 0.05 s) Using Fig. 4 Syyy=0.99 Sy C . -

T f^

h APPENDIX METHOD OF ANALYSIS INTRODUCTION Since it was issumed 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 ti.a seismic loading on the individual core blocks.

A review of the FSAR reveals that for the FSV Nuclear Generating Station the Operating Basis Earthgake (0BE) 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 core support structure indicated that these ground accelerations result in accelerations at the core level of 0.19 g (0BE) and 0.26 g (SSE). At these relatively low acceleration levels the individual core blocks would not be expected to slip horizontally relative to each other until after an impact event. The reason for 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 friction between blocks (graphite on graphite), and previous research indicates that this coefficient is greater than 0.2 and probably greater than 0.3.* From this observation it follows tht 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 BOUNDING 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 ratio of the column shear forces in the new configuration as compared with the original

• Ref. 1 shows that the coefficient of kinetic friction of graphite on graphite is in excess of 0.3 in a dry, high temperature, helium envrionment. The static coefficient is known to be higher than the kinetic value.

~

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3; -

configuration. Let the original configuration be represented by a cantilever beam with a unit lateral load applied at the end for which the statical deflections give a good approximation to the first mode shape of the beam. Using simple beam theory, we can show that relationship between the maximum shear force, 5 7

, and maximum deflection, 2 7

, of the tip is

= 3EI S Z I 3 I*

L where EI is the bending stiffness of the bean (The term 3EI/L 3 is the corrnonly known spring stiffness for the cantilever). 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 S 7 II 3 II*

2L .

The bounciary 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, S

777

= 33 8 Z 777 L

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

II

II II

III 32 and 24 -

I I I I

\p6 B0 v.

b 's a w

)

where Z$ are the maximum relative displacecents. Furthermore, the ratios of the first mode natural frequencies for these cases are such that,*

g II = 6.4 and g III

= 4.4.

I I The question 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 harmonic. Figure 1 taken from Ref. 3 shows the response curves for a horizontally base excited single degree of freedom system. Referring to Fig. 1 we can see that if the original system (case I) is relatively flexible (i.e. w/wn" 1, where e is the forcing 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 forces developed. As an example, assume w/w n

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

1.56 "II From Fig.1, Z

7 X, where X is the input displacement and Zy ; = 1.48 X. Then S 1.48 II = 32 x whereupon S yy = 47 S y, a 1 z

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

• For example, see Ref. 2.

p 1836 010

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h)

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

"III , 4,4, assume we have

= 1 and h = 0.3 g"I 2- no n.o

,x 1.5-

.y hs 8i /N/ 7M - -

5 }";-

9

//////"'V f /

[h=1

$f / **> / /

5 // 5

/

E,

< .2 / V 5-

.3 .4 $ A.7 AbI 1.'5 2 '$ d 56789O FREcuENCY RATIO S = /..

Fig. 1. Steady-state response of a seismic system to harmonic base displacement (from Reference 3). ,

': : ~

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then

'n III

= 0.23.

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

II = 24 x whereupci. S777 = 0.45 Sy.

I Clearly the same a..u.. is 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 be reduced depends upon 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 Fcrt 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 acceleration values, a fuel region can be expected to respond as seven base excited columns restrained to move together at their top (Fig. 2).

We can describe the lowest mode response for this system in terms of the tip response Z(t) relative to the base excitation vg (t). Let the absolute displacement of a fuel column be v"(x,t). Let the displacement of a point on the column relative to the base be w(x,t) (see Fig. 2). We will assume the predominate response to be in the first mode, and write v a(x,t) = v + w(x,t) g and that w(x,t) =

Y (x) Z(t) where y(x) is an admissible shape function. By writing the kinetic and potential energy expressions for all effects that we may wish to include, and applying Hamilton's principle to the result we can develop an equation of motion of the form

' O, s

m eff Z(t) + k eff Z(t) = -m g vg (t) - peff(t) where m eff

= the effective mass k

eff

=

the effective stiffness p e ff

= the effective loading.

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

kb-k g -k a -k g +k eff sc REFERENCE AXIS X

.- s j-- i N 2(t) ~

d i_ _ _

,/

G

-v ' ' -

q 4~/ ..

vt w

L

. j - - - - - = -

./

'il 1

I l

I I

i-

'] ,' t "NN ##// /Vn'//,//'H H U g -* __

U9,__

J Fig. 2. Motion of a fuel region.

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N

/r J

where 2

EIo [ L y"(x) '"

k =

b 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 c, = N

[L y'(x) dx o

is an added geometric stiffness term accounting for the constant axial load (N) that occurs because of the keyed plenum blocks, RCDs, etc. The term 2

k g =[L q(x) y (x) dx o

is a stiffness effect because of the lateral pressure q(x) across a fuel column. The term k

sc

=

?"'(x) dr.

is a term that represents the shear stiffness of the column. The two te ms m

eff and mg given by L

m eff =f o a(x) y (x) 2 dx 1836 014

x m =

g m(x) Y(x) dx ,

represent an effective mass for the fuel column and a mass like term to convert the base motion to an eff ective 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 geometric shear correction factor A =

the cross sectional area 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 effects on the undamped natural frequency and bound the possible frequencies such that the method that has been described can be appl.ad.

TaUe I gives the result of carrying out the details of the analysis with Y(x) = l-cos (nX/2L), where eff 1 *eff ~

We have also included the irradiation effect on Young's modulus by taking the extreme values for H327 gra hite as given in Raf. 4. Table III shows 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 red /sec, and looking at the effects of the boundary conditions of cases Il and III, we can compare the idealized ratios of maximum shearing stress in the new configuration (with RCDs) to thn original configuration (without RCDs) d,uring an earthquake j"st as in the harmonic excitaticn examples provided that we use the response curves for an earthquake exciting function.

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s lY TABLE III PARAMETERS USED IN FSV COLUMN FREQUENCY CAL (.

2

• 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 response spectra for the FSV core support floor is not available.

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

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

The original (solid line) is fo; 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 period 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 concerned about the magnitudes in Fig. 3, and unless some very unusual " filtering" occurs leading to an extremely broad band peak response, the dotted spectra should he 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 installation of the RCDs with one exception. If the spectra is shif ted so f ar to the right that point "A" (Fig. 3), is at a period of 0.22 sec (w = 29 rad /s) or greater, then the maximum shear forces could increase by 28% provided that the original natural frequency of the fuel column (eg ) is as high as 29 rad /s and also that the RCDs result in a pinned end condition. Such conditicas are net deemed likely for this structure.

1835 016 e

s.

li )

We also note that if the true response spectra is shif ted to the lef t (Fig. 3) so that point "B" is at a period 'f 0.09 s or less, then the shear forces may also be increased by the installation of the RCDs.

Figure 4 shows the floor respoise spectra 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 (low pericd) would be filtered out of a response spectra that applied only to the core support structure, and would appear much as the dashed line. However, we can use Fig. 4 as it is to estimate the effect of the RCDs on the maximum shear stresses. These results are also shown in Table II, column 3.

1.0% DAMPING l .0 + 01 y "B" 6.0400 g

/ \

e /

/ \ \ 'N \

o zo.m g j j i / / \

< /

/ \

a: ___ ./ \

W N *A" .\

w 4.0-01 \

e \

2 0 \

LO-OI 6.O-02 0.00l 0. I 1.0 I b.

h)ERIOD (s)

Fhg.3. Reactor bottom head horizontal response spectra for operating basis earthquake.

I835 017

A FUEL ELEMENT IMPACT VELOCITIES AND FORCES Vibration studies7 ,8,9 on core like structures (stacked blocks) suggest that by far the largest forcer produced during a seismic event are the forces prodcced 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 block impacts. The vibration studies referred to above indicate that the larger the clearance between elements the larger the impact forces.

The proposed Ra3 will limit the accumulation of gaps br.; ween the fuel regions and tnerefore 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 region 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. 5 is a model of the FSV core with RCDs in place (case II). It we again assume an impulsive ground motion to the right the fuel region on the right (#7) will impact on the RCD .ter undergoing a relative motion of approximately 0.030 in. (0.150-0.120). The impact sequence will then propagate from right to left. .

The analysis which follows illustrates the difference in the magnitude of the impact forces involved in the two cases.

Assume that the relative displacement (Z) and the relative velocity (i) of the core regions are as shown in Fig. 7. These curves represent the relative response motion that would be produced by the seismic motion x(t) at the core base for. the case where no contact between core regions is allowed. Now assume that in Case I (Fig. S, no RCDs) this initial (before contact) relative motion is such that contact occurs at some point to the left of line a-a in Fig. 7, say at pt. #1; then the initial impact velocity is 1). With the RCDs present (case II) the initial contact will occur at pt. !2 with an impact velocity of Z .

2 Since forces are proportional to impact velocities, forces will be reduced.

1836 O!

T 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 caps 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 c,ystem" relative to the appropriate response spectra. Consequently the addition of the RCDs can be expected to decrease the impact velocities and thus the impact forces.

l

1. 5 -

/ 1 N E

5 '-

/ \ \

, , // \ N.'

\ //

3 \

/

z O

p I r

/

/

1

< / (

Hi /

/

d 0.2 j u

< 0.15 - ] #

O.10 -

0.02-

. i e i i i i O.02 0.03 0.04 .I 15 .2 .3 1.0 1.5 2.0 PERIOD (S)

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

1836 019

?!

c. 4.

OJ2H H l---O.12 r7-"r7e '

i ' t r - T s 7

D 'i 'il\ \ 'i s

'i s

'N ,

]

l ', i, I I

k4 1 2 3 4 5 6 7 X

BASE _ '

l _

I Fig. 5. Podel illustrating initial impact sequence without RCDs 9

x r r r ,_r, r rp_q, ti  !

', F4 i i pq I 2 3 4 5 6 7 pg X BASE _

T 1836 020 Fig. 6. Podel illustrating initial impact sequence with RCDs e

Z, a

RELATIVE DISPLACEMENT RELATIVE VELOCITY

. es z, e ,/ s

.: / s

. /Y 4 ;/'

42 \

\

Z2 Z2 & 2 s

'N , t

\ /

\ /

\ /

a \ /

N y/

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

cir Al .4 ' < , - ,

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s (9 )

REFERENCES

1. M. Stansfield, " Friction and Wear of Graphite in Dry Helium at 25, 400, and 8000C," Nuclear Apolications Vol. 6, April 1969, pp. 313-320.

2. W. F. Thomson, Vibration Theory and Apolications, Prentice Hall, Englewood Cliff s, NJ,1965.

3. R. C. Dove, P. H. Adams, Esperimental Stress Analysis and Motion Measurement, Charles E. Merrill Books, Inc., Columbus, Ohio, 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 Report.

6. Fort St. 'Vrain Nuclear Generating Station - PSCo Document, " Core Fluctuation Investigation Status and Safety Evaluatiun Report," A':g.

1978.

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

8. J. G. Bennett, "A Physically Based Analytical Mocel for Predicting HTGR Core Seismic Response," Proceedings of the Japan-US Seminar on HTGR Safety Technology, BNL-NUREG-50689 - Vol. I, pp. 126-135.

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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