ML20151A371

Cask Drop Analysis Yankee Nuclear Power Station Spent Fuel Pool

ML20151A371
Person / Time
Site:	Yankee Rowe
Issue date:	03/31/1988
From:	James R, Rashid Y, Sullaway M ANATECH RESEARCH CORP.
To:
Shared Package
ML20151A373	List: ML20151A371 ML20151D295
References
ANA-88-0072, ANA-88-72, NUDOCS 8804060483
Download: ML20151A371 (31)

Text

'

, ' ANATECH liesearch Corp. P.o. nox 9165

-========:== 19 55 6350 ANA-88-0072

() CASK DROP ANALYSIS YANKEE NUCLEAR POWER STATION I SPENT FUEL POOL l

1 I

Prepared by I Y. R. Rashid M. F. Sullaway I

n I Reviewed by /[ '

+7 te Approved by Ol~ -

R. J. James R. S. Dunham I Manager, Structural Methods Vice President I

I Prepared for Yankee Atomic Electric Company Framingham, Massachusetts March 1988 Corpor.te Office: 10975 Torreyana Road, Suite 301, San Diego, CA 92121 p[

Telex: 188992 (ANATECil ULA) Fax: (619) 455-1094 8804060483 880331 [

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~ CONTENTS l

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1.0 INTRODUCTION

1 b 2.0 ANALYSIS APPROACH 3 2.1 Material Models 3

[ 2.2 Material Properties 2.3 Computational Model 4

5 r' 2.4 Analysis Procedure 5 2.5 Analysis Results 6

[ 3.0 DROP ORIENTATION 3.1 End-Drop Case (0 = 90')

18 18 7 3.2 Corner-Drop Case (0* < 0 < 90') 18 3.3 Side Drop Case (e = 0') 19

4.0 CONCLUSION

S 20

{

5.0 REFERENCES

21

[ APPENDIX A - CHARACTER!ZATION OF THE CASK DROP LOADING A-1 E

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E L

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E F

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1.0 INTRODUCTION

E I At the request of Yankee Atomic Electric Company, an analysis was performed to determine the consequences of a hypothetical cask drop into the spent fuel pool.

I This analysis evaluates the effects of a specific fully loaded 37-ton cask which does not contain spent fuel. The report presents the results of this evaluation I with a specific focus on the resistance of the pool floor to leakage. The evalu-ation of this extreme event is based upon realistic assumptions and as-built conditions.

The primary barrier against leakage in the spent fuel pool is the steel liner, with the reinforced concrete slab providing a secondary but not essential ba rri e r.

Reinforced concrete, which is low tensile-strength material, generally sustains microcracking due to shrinkage and service loads, it is not regarded as a reliable leak tight pressure boundary, particularly when it is subjected to severe loading.

I For this reason, steel liners are used in nuclear structures where leak tightness is a primary requirement. Thus, the question of leak tightness in the pr, at conte xt is more appropriately addressed through the structural integrity of the liner. Clearly, the liner derives its resistance to deformations and rupture from the reinforced concrete slab and its foundation. Therefore, all three elements, namely, foundation, sia and liner, must be properly modeled and analyzed.

I The response of the pool floor in general, and the liner in particular, to the cask drop loading is strongly dependent on the modeling of the cask itself. The simu-I lation of the energy exchange between the cask and the floor during impact has a direct bearing on the floor response. The usual rigid-cask assumption, which implies total energy transfer to the floor, and hence is highly conservative, does not provide the means for properly calculating the true safety margin of the liner against rupture. The present analysis is based on a realistic modeling of both the cask and the floor. Appropriately conservative assumptions are used where necessary, such as in material properties and in the characterization of the drop event.

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L The analysis was carried out for a 37-ton cask drop from a 38' height in the spent L fuel pool with a minimum water depth of 33' 9". Detailed results are presented for the floor slab and liner. Ample margin against liner rupture is demonstrated, c

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2.0 ANALYSIS APPROACH e

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- The analysis approach adopted in this investigation follows the method outlined in Ref. [1], which is a static simulation of a cask drop using the SAFE-CRACK consti-i tutive model [2] and the ABAQUS-EPGEN computer code [3]. A mathematical description of the constitutive model is included as an appendix to Ref. [1]. The analytical basis for a static simulation of impact loading is the assumption that the stresses in the cask and the floor are closely approximated by the average (or steady) deceleration. The large fluctuation of deceleration usually measured in cask drop tests is caused by high frequency vibtation of the cask about some mean deformation and does not produce significant stresses. In order to demonstrate this analytic-ally, stress analyses were performed for a cask impact test by Jones [4] who showed that the steady deceleration rather than the peak deceleration governed the stress I level; for example, although the peak deceleration varied by over 50%, the stresses varied by less than 10% from the steady deceleration stresses. This was an ex-tremely useful result since it enabled the use of equivalent static analyses for the evaluation of cask and target stresses rather than the more costly dynamic time-history analyses.

At the instant of impact, the impact energy is absorbed by both the pool floor and the cask during the steady deceleration of the cask. Our primary interest is to calculate the floor's participation in this energy exchange. This is done with the I aid of a finite element nonlinear computational procedure [1] that utilizes a detailed constitutive elastic-plastic-cracking model for the concrete and elastic-plastic model for the liner and reinforcement.

2.1 MATERIAL MODELS The concrete constitutive model employed in this analysis is described in detail in Ref. [1]. This model considers the cracking and the elastic-plastic behavior of concrete, including post-critical strain-sof tening and crushing. The stress-strain representation is shown in Figure 1. This curve is based on an experiment for which the measured ultimate strength and elastic modulus are 4650 psi and 3.35 x 3

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psi, respectively [5]. The shape of this curve is representative of concrete s%ress-strain curves in general and, therefore, was used in a normalized form to represent the concrete properties considered in the present analysis. The elastic modulus E and the ultimate stcength f' were adjusted for the present material, but c

the normalized shape of the curve was unchanged. The cracking strength f' was as-sumed to be 10% of the ultimate strength, as usually assumed in concrete structural analysis. The soil sublayer is treated as an elastic material (in compression) but tSith a small tensile strength. The steel liner and reinforcement are treated as elastic-plastic materials with strain hardening properties. The cask materials are i assumed to be elastic-perfectly plastic.

2.2 MATERIAL PROPERTIES The material properties used in the present analysis are listed below.

Concrete: Elastic Modulus (ACI formula) = 4.03 x 106p34 Poisson's Ratio = 0.17 Ultimate Strength (based on in-situ probe test) = 5000 psi I Tensile Strangth = 500 psi Soil: Elastic Modulus = 2.6 x 10 5psi i Poisson's Ratio = 0.45 Tensile Strength = 5 psi A285 Gr. C Steel - Elastic Modulus = 30 x 106 p34 l Cask:

Poisson's Ratio = 0.3 Yield Stress = 30,000 psi Lead - Elastic Modulus = 5.3 x 10 6p3j I Poisson's Ratio = 0.3 Yield Stress = 3000 psi Liner (SS-304): Elastic Modulus = 29 x 106 p34 Poisson's Ratio = 0.3 Yield Stress = 30,000 psi Ultimate Strength = 70,000 psi I Strain Hardening Modulus = 0.35 x losp34 Thickness = 0.25 in.

Reinforcement: Elastic Modulus = 30 x 10 6p34 Yield Stress = 40,000 psi Ultimate Strength = 70,000 psi I Strain Hardening Modulus = 30 x 103 psi Two Layers (top and bottom)

1. 10 at 9" in the longitudinal direction (N-5)

1. 11 at 6" in the transverse direction (E-W) 4

u 2.3 COMPUTATIONAL MODEL A finite element model of the cask and the target, which includes the steel liner, i the concrete floor, and the underlying soil half-space, is shown in Figure 2. A thin layer of contact elements is inserted between the cask and the target to permit the simulation of the variable contact stress between the cask and the target. The cask is represented by four layers of elements in the cylindrical wall and three layers in the end closures. The inner and outer layers represent the steel shells, and the middle layers represent the lead material. The cask contents are replaced by equivalent load applied to the inner surf ace of the bottom enclo-sure. A smeared weight density of 0.4083 lb/in3 , which is equal to the empty weight of the cask divided by the net volume of the solid material, is used for all I cask elements.

The liner is represented by a layer of elements attached to the concrete surface.

A fine grid is utilized in the vicinity of the cask corner for better accuracy.

l All elements in the grid are 8-node elements with quadratic shape functions and 2x2 integration points. This type of element provides superior accuracy for capturing the highly nonlinear behavior of the concrete and the liner in the local contact region.

I 2.4 ANALYSIS PROCEDURE The analysis was carried out in an incremental procedure in which the weight of the cask, multiplied by an incrementally increasing f actor, was applied step by step.

The equivalent drop height was calculated from an energy balance by equating the I energy absorbed by the floor and the cask to the potential energy of a f alling cask. This energy balance is expressed as follows (1) f o$) dcq = GWH Hence (2)

H = (1/WG)y f og dcq

where oj ) and og are the stresses and strains respectively calculated for the slab L and the cask, W is the weight of the cask, H is the drop height, and G is the g gravity multiplier. At each step in the analysis, H is calculated from Eq. 2.

[ Calculations of the drop height in the pool are given in the Appendix, which shows that due to drag effects of water a 38' drop height is equivalent to a 23' drop in air.

I 2.5 ANALYSIS RESULTS The results of the analysis are depicted in Figures 3 through 8. Figure 3 shows I the deformed shape of the slab, magnified by a f actor of 25, at the final step in the analysis. The cracking patterns are shown in Figure 4, which illustrates the I manner in which the concrete slab responds to the loading, in this figure, the vertical and horizontal cracks are due to direct tension resulting from either bending tensile stresses or tensile Poisson's effect (i .e. , splitting). The shear cracks, which are inclined, are seen to emanate f rom the footprint corner and extend nearly through the slab thickness. The maximum width of the ficxural cracks in the bottom of the slab is 0.1 inches. This is obtained by integrating the cracking strain over the element length.

The minimum principal (compressive) stress contours are shown in Figure 5. A small I gone beneath the cask corner enclosed by the 5000 psi contour line, which repre-sents the material's ultimate strength, indicates that concrete crushing is limited to a small volume. This local crushing acts as a relief mechanism for the liner strain but, because of its confinement, does not lead to the failure of the slab.

The slab f ailure mode for this type of loading is the formation of a shear cone extending through the slab, which does not occur in this analysis. Even though continuous cracking does not extend through the floor, one would not rely on partially cracked concrete es a fully effective leakage barrier. Leak tightness is assured more by the liner than the concrete slab; therefore, we must examine the I liner's response to determine the floor's leakage resistance.

The history of the force imparted to the floor is shown in Figure 6 as function of the drop height. The liner strain and stress as functions of drop height are shown

in Figures 7 and 8 respectively for the most highly strained point in the liner, i thich occurs at the top surface adjacent to the cask corner. As can be seen from Figure 7, the maximum strain in the liner is about 3%, which is a small fraction of I the material ductility limit of approximately 40%; furthermore, the strain rate of increase with drop height is bounded. This is due to the fact that concrete crushing locally beneath the cask corner relieves the siner from sharp deformations due to indentation. Also, the cask corner deformab'.lity contributes in a similar manner to maintaining low rate of liner strain buildup. Figure 8 shows that the liner stress remains below 40 ksi compared to the minimum ultimate strength of 70 I ksi.

A measure of the accuracy of the results is illustra?.ed in a plot of the effective (von Mises) stress versus the ef fective strain shown in Figure 9. This plot, which is the uniaxial representation of the two-dimensional (axisymmetric) stress-strain state in the liner, closely follows the material property stress-strain curve used in this analysis. As mentioned in Section 2.2 of the roport, the liner material is represented by a bilinear stress-strain curve with a 30 ksi yield stress and a 350 ksi strain hardening modulus. The stress-strain relationship in the plastic I regime can be shown to be as follows:

2 Et ~

2 Et E (}

1. e *7E-E t y"7E-Et 0 where e: Effective stress o:

y Yield stress c:

e Total effective strain E: Elastic modulus E:t Tangent (strain hardening) modulus (350 ksi in this analysis)

For a small Et (in comparison with E), the ratio Et /E can be neglected, and Eq. 3 can be approximated as follows:

7

a ,

o e " #y = 2/ 3 Et *e L

As can be seen f rom this equation, the average post-yield slope of the stress-L strain curve shown in Figure 9 is 2/3 Et = 233 ksi, which can be verified by inspection.

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3.0 DROP ORIENTATION I The analysis was performed for the end drop case (0 = 90 , where e is the angle between the cask centerline and the horizontzl axis). This is more critical than I the side drop (0 = 0 ) or corner drop. The explanation for this follows.

3.1 END-DROP CASE (0 = 90 )

The footprint area remains constant for this case. The footprint average stress l remains below the concrete ultimate compressive strength of 5000 psi, but the stress distribution over the footprint shows peaking near the periphery directly below the stiff cylindrical wall of the cask (see Figure 5). The stress is reduced towards the more flexible center. In this upright configuration, the stiffness of the cylindrical wall of the cask is maximum since it is derived mainly from the axial stiffness of the inner and outer steel cylindrical shells. Furthermore, the wall contains 70% of the cask weight which is positioned closest to the edge of the cask, and thus causes maximum damage.

I 3.2 CORNER-DROP CASE (0 < 0 < 90 )

This is an unstable ccnfiguration in the sense that it is virtually impossible for I the cask to remain in this orientation as it falls through the fluid. For it to remain in a corner drop position, both tha drag force and gravity force vectors I must be exactly co-linear, which is virtually impossible. If the drag force resultant vector is offset to one side of the cask's net gravity force vector, it acts as a restoring force and drives the cask towards the end-drop position. If it is offset to the other side of the gravity force vector, it will tip the cask over to a side drop position. Hence, a corner drop condition in water can be dismissed on physical grounds.

I Nevertheless, if such an event occurrcd, the impact velocity for this case would be smaller than either the end drop condition or the side drop condition because the I drag area, hence the drag force, is largest for the corner drop orientation.

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Although the drag coefficient for the horizontal cask is about half that for the L vertical cask, the drag area of the horizontal cask is about three and one-half times that of the vertical cask. Even if one ignores the reduction in impact velocity due to drag, the cask is more vulnerable to corner plastic deformations because the corner stiffness of the inclined cask is at least an order of magnitude smaller than the upright cask. Thus, in the corner-drop case the cask corner will plastically deform and absorb much of the impact energy. The fact that the impact area is much smaller than the end-drop case contributes further to the local plastic deformations of the cask.

I 3.3 SIDE DROP CASE (0 = 0 )

The side drop orientation produces a smaller impact velocity than the end-drop case because the drag force is larger. Although the initial impact area at the instant of impact is smaller 'han the end drop case, the footprint area increases very rapidly due to both ovalization of the cask and slab deformation. The more impor-tant factor, however, is the fact that in this case the liner deforms with much smaller curvature (by at least a factor of two) than in the end drop case and, hence, sustains much smaller strains.

On the basis of the above arguments, we can rank drop ccoditions as follows: end I drop with a severity factor of 10, corner drop with a severity factor of about 8, and finally side drop with a severity factor of about 5.

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4.0 CONCLUSION

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[ Based on the detailed analysis of the cask drop event described in this report, the primary leakage barrier, namely, the stainless steel liner, remains intact with a j factor of safety of two on stresses and at least ten on strains.

1 It should be stated further that the present analysis considers several conserva-tive elements. First, as shown in the Appendix, smaller drag force (hence larger drop height) is used; second, very small tensile strength is assumed for the sub-foundation; third, no credit is taken for the increased dynamic tensile strength of the concrete; and fourth, minimum properties are used for steel reinforcement, liner and concrete. A further reassuring factor is the fact that the Yankee Nuclear Power Station spent fuel pool rests directly on stiff grade which strongly resists punching shear failure of the floor, as is demonstrated by the present analysis.

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5.0 REFERENCES

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1. Y. R. Rashid, "The Effects of Target Hardness on the Structural Design of Concrete Storage Pads for Spent-Fuel Casks", EPRI Final Report NP-4830, ANATECH International Corp., October 1986.

[ 2. "SAFE-CRACK - Two-Dimensional Code for the Analysis of Concrete Structures",

ANATECH Report ANA-85-0034, July 1985.

3. H. D. Hibbitt, et al . , "ABAQUS-EPGEN Version 4-5, Vol . 1, User's Manual and Vol. 2, Theoretical Manual", EPRI Report NT-2709-CCM, 1982.

4. P. McConnell and J.W. Jones, "Pre-Drop Test Analyses of a Spent Fuel Cask",

EPRI Report NP-4785, October 1986.

5. ASCE Task Committee on Finite Element Analysis of Reinforced Concrete Struc-

{ tures, "State-of-the-Art Report on Finite Element Analysis of Reinforced Concrete", 1981.

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w APPENDIX A. CHARACTERIZATION OF THE CASK DROP LOADING The cask is assumed to drop from a height of 4'3" above the water surface of the spent fuel pool with a minimum water depth of 33'9" (administratively controlled).

The normal water depth is approximately 36 feet. The cask falls through three different stages: air, partial submergence, and full submergence. The final 9 I loading on the floor is calculated based on this history of the fall.

A1. FALLING THROUGH AIR A free fall of 4'3" results in a velocity of 16.544 ft/sec at the instant the cask bottom surface impacts the water surface. The impulse delivered to the cask by the water surface can be estimated from experimental data on cylinders and flat-bottomed structures falling into water at low velocities, with air trapped between the structure and the water providing a slight cushion during impact. The pressure is given by a function of the form 2

p = 1/2 p v 7 (3)

I where p is the mass density of water, v is the cask impact velocity, and F is a function of impacting surface cross section. The deceleration forces for various orientations and initial velocities have been calculated by Fischer, et al. [1], in their severe transportation accident study. For a rigid truck cask, the average deceleration forces are:

Unyielding Truck Cask Velocity Impact Orientation Angle, e (mph) 87* 45 0* (Side Drop) 30 17.7 g 0.9 g 12.6 g 60 70.8 g 3.6 g 50.4 g 90 159.3 g 8.5 g 119.0 g I 120 283.2 g 14.5 g 203.0 g i

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A.1

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For a drop of 4 feet onto the water surf ace, the initial velocity would be 16 ft/sec, or about 11 mph.

EPRI cylinder impact data [3] at initial velocities of 16.9 ft/sec gave peak pres-sures of about 12 psi for a rigid cylinder in the e = 0* (side drop) orientation, with an impulse of about 90 psi-millisecond during the 24 millisecond engulfment period. The peak deceleration was about 30 g, with an average deceleration of about 5 g. This is in reasonable agreement with the values of Fischer, et al.

Integrating the impulse ever the area of impact of a truck cask (say, 50 in. x 200 in. = 10,000 in )2 gives an impulse of 900 lb-sec. For c cask with a mass of 37 '

tons (191.5 lb-sec2 /in), the change in velocity is estimated to be only 4.6 in/sec (a very negligible decrease and therefore is ignored in the present analysis).

I A2. FALLING THROUGH WATER A more important contributor to the cask velocity are the buoyancy and drag forces exerted by the water on the falling cask that is accelerating due to gravity. The equation of motion is given by W-F -I B * (

D where W is the cask weight (37 tons), FD is the drag force, FB is the buoyancy force, and a is the acceleration downward toward the pool floor. The buoyancy force can be approximated by adjusting the gravity force to a lower equivalent density, and the drag force is given by FD = 1/2 p A W I where p is the mass density of water, v is the instantaneous cask velocity, and A is the cross-sectional area of the cask perpendicular to the direction of fall.

I The drag coef ficient of the cask, similar to most blunt bodies, is very nearly equal to unity and is essentially independent of Reynolds number [2].

A-2 j

u The cask has dimensions of D = 50.5" and L = 133.75" (Figure A-1), giving an r -1 z

footprint area of 2003 in and a volume of 267,896 in 3. The apparent density of the cask is 74,000/267,896 = 0.2762 lb/in 3

, while that of water is 0.0362 lb/in3 .

r l

Let V: Volume of cask (in3) y: Density of cask (lb/in 3) c Y: g Density of water (lb/in 3)

A: Footprint area of cask (in2 )

g: Gravity acceleration (in/sec2)

The drag force becomes F = Av 2 (4)

D The buoyancy force is (5)

FB'"YTw where a = 0 for unsubmerged or partially submerged cask and a = 1 for totally submerged cask.

I W=Vy c

(0)

I Substituting Eqs. 4, 5 and 6 into Eq. 2 gives i

v ,c . ; ) A v 2 .vy=1c a (7)

I Substituting for A = V/L where L is the length of the cask, we have A-3 b _

~ VY c 1 TY w

L g a+7L9 v - V( Yc - T}" W

(}

Equation 8 can be rewritten as I

h+ (0) v2 - g(1 - a B) = 0 (9) where S = gY c/Y and the cask acceleration, a, is replaced by dv/dt.

Equation 9 will be solved first for the partially submerged condition (a distance of 133.75", which is the length of the cask), and then for the fully submerged condition (until it impacts the floor). For simplicity, we make the conservative assumption that a = 0 during partial submergence (a is ac+,ually a function of the drop distance x). This gives I 2 for 133.75 > x > 0 (partially submerged) (10) h + 1 (0) v -g=0 and h+ (0)v -2 g(1 - s) = 0 for 271.25 > x > 133.75 (fully submerged) (11)

We first obtain a general solution for Eq. 11 and then modify it to obtain the solution for Eq. 10. Using simple substitution of variables and remembering that v = dx/dt, it can be shown that the closed form solution of Eq. 11 is:

28 1

~

v 2= [y 2 -

(1 - 8)) e I +h(1-8) (12)

I and the solution for Eq. 10 is 26 v

2, 2

[y - )eI +f (13)

w L

Using the following values for g, L and 8 L = 133.75 in.

g = 386.4 in 2/sec

,= q x, = 0.0362/0.2762 = 0.1311 Equation 13 becomes v 2, (y2 - 394,210.53) e-0.00196 x + 394,210.53 for 133.75 > x > 0 _ (14) b for which the following initial conditions apply vo = 16.544 x 12 = 198.528 in/sec At x = 133.75" (when the cask becomes fully submerged), Eq.14 gives y = 348.18 in/sec or 29 ft/sec (15) which is the initial velocity for Eq.12. After substitution for the cask para-b meters, Eq. 12 becomes v 2, (y -92342,529.53) e-0.00196 x + 342,529.53 for 271.25 < x > 0 (16)

Equation 16 gives b

v = 460.96 in/sec or 38.41 ft/sec (17) which is the impact velocity at the pool floor. This is compared to a 49.5 f t/sec impact velocity for a 38' drop in air. The equivalent drop height in air can be obtained by equating the potential and kinetic energies, namely, 2

WH = f f v

[

A-5 r -- _ _ _ _ _ _ _

d' .

from which L

2 38 H=f = g x. ,2

= 22.9 ft L

The above calculations show that a 38' cask drop in a pool with a minimum water depth of 33'9" is conservatively equivalent to a 23' drop in air. This value is used in the finite element analysis described in Section 2.

A3. REFERENCES

1. L.E. Fischer, et al., "Shipping Container Response to Severe Highway and Railway Accident Conditions -- Volume II: Appendices", NUREG/CR-4829, Vol.

II, Lawrence Livermore National Laboratory, January 1987.

2. K. Souter, N. Manale, and H. Krachman, "Water Impact Tests of Rigid and Flexible Cylinders", EPRI Final Report NP-798, Developmental Sciences, Inc.,

May 1978.

{

3. K. Souter and H. Krachman, "Two-Dimensional Water-Impact Tests of Flexible Cylinders", EPRI Final Report NP-1612, Developmental Sciences, Inc., November 1980.

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