SEABROOK UPDATED FSAR

APPENDIX 2 0

GEOTECHNICAL REPORT DISCUSSION OF DERIVATION OF COEFFICIENTS OF SUBGRADE REACTION

The information contained i n this appendix was not revised, but has been ex t r ac t ed from t h e o r i g i n a l FSAR and i s provided for h i s t o r i c a l informat ion .

GEOTI3CLINICAL ISNGINElUtS I NC. I 1037 MAIN STREET. WINCHESTER. MASSACHUSETTS 01890 (617) 729-1625

I < ~ U C l L l ( 5

March 22, 1978 C H A H L t 5 c OSCOOD B * I I l L L T T W PAULDIMG. JR

Pro jec t 77386 F i l e No. 2 .0

Mr. John H e r r i n Publ ic Service Co. of New Hampshire 1000 Elm Street - 11th Floor

Manchester, NH 03105

Subjec t : Discussion of Der iva t ion of Coefficients of Subgrade Reaction

Dear Mr. Herrin:

I n t h e fol lowing we desc r ibe some techniques t h a t we have developed to convert the moduli obtained from triaxial tests to moduli of subgrade reaction for various loading conditions. We present this information to complement various telephone con- versations with D. Pate1 of UE&C.

Computation of Coefficients of Subgrade Reaction

The coefficient of subgrade reaction, k, , represents soil deformation, due t o pressure a c t i n g along a boundary sur face , as if the soil were composed of independent springs, each repre- senting a unit of area with a spring constant ks. The spring cons tant i s def ined a s a pressure d iv ided by a displacement. Such a representation is convenient for analytical purposes but neglects the influence of adjacent loaded surface areas on the displacement of any given po in t on t h e boundary su r f ace . ~ h u s , the coefficient of subgrade reaction is not a unique number for an elastic material but is a function of the size of the loaded area , t h e pressure d i s t r i b u t i o n , and the geometry of $hc material. For a s o i l , the modulus of subgrade reaction is also dependent on t h e method o r sequence of loading, i . e . , t h e s t r e s s pa th .

On the basis of the theory of elasticity, we have computed coefficients of subgrade reaction for the structural backfill and the sand cement for three geometries of loading using the modulus of elasticity and Poisson's ratio data obtained in the triaxial t e s t r e s u l t s . The geometries of loading studied are illustrated i n F igs . 1 through 9 and a r e a s fol lows:

Mr. John Herrin March 22, 1970

1. C i r cu l a r o r square f o o t i n g subjec ted t o v e r t i c a l load .

2 . Pressure inside a cylindrical cavity in the soil mass assuming a plane s t r a i n condi t ion . This is reyresen ta-. t i v e , f o r example, f o r t h e loading produced by thermal expansion of the c r o s s s e c t i o n of a bur ied p ipe .

3. Pressure inside a cylindrical cavity with simultaneous application of a vertical surcharge, p, and a horizon- tal pressure, k g . This loading is an approximate re- presentation of the placement of fill over a buried pipe, which deforms to produce an increased lateral s t r e s s around the pipe . A p lane s t r a i n condi t ion was assumed.

The modulus of elasticity and Poisson's ratio used in the compu- tations are strain dependent and were selected for the average strain in the region of the soil mass that contributes most to the displace- ments, namely, within a distance of one diameter from the pipe and one foo t ing width below t h e foo t ing base. These strains were correlated with t h e displacements which, i n t u rn , were expressed i n terms of footing settlement divided by footing- width, 6/B, or i n terms of the diameter strain of the pipe, Ed. In Figs. 1 through 9, t h e va lues of t h e c o e f f i c i e n t of subgrade r e a c t i o n a r e p l o t t e d a s a funct ion of (T/B or Ed and confining pressure. Confining pressure is to be taken as the effective overburden pressure computed at the elevations shown in t h e f i gu re s . An exception to the above procedure is that for the sur- charge type loading, a cons tant Poisson ' s r a t i o of 0.3 was used.

The elastic modulus E and Poisson's ratio v used as a basis for the coefficient of subgrade reaction computations were obtained from triaxial compression tests in which the minor principal stresses were kept constant and the major principal stress was increased monotoni- c a l l y u n t i l t h e specimen f a i l e d . Such a stress path would be sufficient t o determine E and v f o r an e l a s t i c m a t e r i a l . However, soil is not elastic and E and v are dependent on the stress path or stress history. In particular, higher values of E would be obtained for repeated or c y c l i c loading. For the static load conditions, we feel that the values of subgxade reaction presented are reasonable estimates for the in-situ loading condi t ions . As shown in the next section, the values compare wel l with values given i n publ i shed l i t e r a t u r e . We recommend, however, t h a t when these va lues a r e used, sensitivity analyses should be made to assure that the designs are safe for a range 25% above and below the given va lues .

Comparison With Published Coefficients of Subsrade Reaction

The coefficients of subgrade reaction obtained from the GEI tests were compared with da t a presented by K . Terzaghi in the paper entitled

M r . J o h n Herrin March 22, 1978

"Evaluation of Coeff ic ients o f Subqrade Reaction , " Geotechnique, vol. 5, 1955, pp. 297-326.

F o r s h a l l o w f o o t i n g s t h e v e r t i c a l c o e f f i c i e n t o f subgrade re- a c t i o n f o r a o n e square f o o t p l a t e , ksl, i s est imated by Terzaghi t o r a n g e b e t w e e n 300 a n d 1 , 0 0 0 t o n / c u f t f o r d e n s e s a n d s , i.e., a r a n g e f o r kS1 x B of 4,000 t o 14,000 p s i . T h e s e v a l u e s are i n t e n d e d fo r shallow foot ings , e -9- . a typical d e p t h o f embedment, Of, of 4 f t , and f o r a width, B, of one f o o t . Thus, t h e y are representative of c o n f i n i n g p r e s s u r e s e q u i v a l e n t t o a d e p t h o f 4 . 5 f t o r a b o u t 4 p s i .

The c o e f f i c i e n t o f h o r i z o n t a l subgrade r e a c t i o n i s g i v e n by T e r z a g h i f o r a 1 sq f t vert ical area a t a g i v e n d e p t h , a n d it is assumed t o be propor t ional t o the e f f e c t i v e s t r e s s a t t h a t depth. For example, f o r d e n s e s a n d s a t a c o n f i n i n g p r e s s u r e o f 10 p s i , a range of kSD of 7,000 t o 14,000 p s i is indicated .

The G E I data f o r s t r u c t u r a l b a c k f i l l , f o r s t r a i n s o f a b o u t 1%, Figs. 1, 2, 4 and 5, agree with Terzaghi ' s da ta . No s p e c i f i c i n f o r - m a t i o n o n s t r a i n l e v e l i s g i v e n by T e r z a g h i f o r h i s d a t a , b u t h e i n d i c a t e s t h a t t h e d a t a a r e a p p l i c a b l e t o a f a c t o r of s a f e t y a g a i n s t bearing capaci ty f a i l u r e t h a t i s l a r g e r than two. I t i s a l s o i m p l i c i t t h a t t h e f a c t o r of s a f e t y would not be much more than 2. Perhaps i t l i e s i n t h e range of 2 t o 4 . F o r s u c h f a c t o r s of s a f e t y , t h e r e s u l t s o f p l a t e l o a d tests o n s a n d s (1 s q f t p l a t e ) would i n d i c a t e t y p i c a l se t t lements of 0.1 i n . t o 0.3 i n . , wh ich would be e q u i v a l e n t t o a v e r t i c a l s t r a i n o n t h e o r d e r o f 1% i n t h e s o i l a d j a c e n t t o t h e plate. Thus, t h e data f o r the s t r u c t u r a l b a c k f i l l o b t a i n e d f r o m t h e t r i a x i a l tests c o r r e s p o n d t o c o e f f i c i e n t s of subgxade r e a c t i o n w i t h i n t h e range given by Terzaghi.

S incere ly yours,

GEOTECHNICAL ENGINEERS INC.

Pr inc ipa l

Steve J. Poulos P r i n c i p a l

GC/S J P : ms Encl . cc w/encl-: R. Pizzuti, YAEC

D. Rhoads, rJE&C A. D e s a i , UE&C D. P a t e l , UEbC

FIGURES

.- U) Q

m

m 6 = SETTLEMENT 2'

P k = - 6 6 5 = - 8

$ = EFFECTIVE VERTICAL STRESS AT DEPTH ( D ~ t 8/21

5 , psi .

Public Service Company of Subgrade Reaction New Hampshire Sand and Sand-Cement

I Backfill

Geotechnical Engineers Inc. Winchester, Massachusetts Project 77386

8

FOOTItu'rJ PRESSURE ON STRUCTURAL BACKFILL

9 0 % COMPACT ION

March 13, 3.978 Fig. 1

6 = SETTLEMENT

t = EFFECTIVE VERTICAL 5 S T R E S S AT DEPTH

(Df t 8 1 2 ) 4 . h A r

4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 0 0

q, , psi

2

Public Service Company of New Hampshire

Geotechnical Engineexs Inc. Winchester, M a s s a c h u s e t t

* .-

Subgrade Reaction Sand and Sand-Cement

Backfill ,

s Project, .77386

FOOTING PRESSURE ON STRUCTURAL BACKFILL

95% COMPACTION

March 13, 1978 Fig. 2

t

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L

m A!"

4 5 6 7 8 9 1 0 2 3 4 1 6 7 89100

6 = SETTLEMENT

k =P 6 6 & = - B

= EFFECTIVE VERTICAL STRESS AT DEPTH (Df + 8/2)

a, , psi

-

Public Service Company of New Hampshire

I

~eotechnical Engineers Inc . ,

Winchester, Massachusetts

Subgrade Reaction Sand and Sand-Cement

B a c k f i l l

Project 77386

FOOTING PRESSURE ON SAND-CEMENT

BACKFILL I

March 13, 1 9 7 8 F i g . 3

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L& DlSPiACEMENT U

n r*

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3

INTERNAL PRESSURE P I P E BURIED IN

STRUCTURAL BACKFILL .go% COMPACTION

March 13, 1978 Fig. 4

Public Service Company of New Hampshire

Geotechnical Engineers Inc . Winchester, Massachusetts

Subgrade Reaction Sand and Sand-Cement

Backf i l l

Project 77386

= EFFECTIVE VERTICAL STRESS AT DEPTH Z '

Sand and Sand-Cement PIPE BURIED IN

Winchester, Massachusetts

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, psi

SURCHARGE PRESSURE ON P I P E IN STRUCTURAL

. BACKFILL 90% COMPACTION

March 13, 1978 Fig. 7

Public Service Company of New Hampshire

I . . .

Geotechnical Engineers Inc. Winchester, Massachusetts

Subgrade Reaction Sand and Sand-Cement

B a c k f i l l ,

Project 77386

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SURCHARGE PRESSURE ON PIPE IN STRUCTURAL

BACKFILL ' 9 5 % COMPACT I O N

March 13, 1978 Fig. 8

Public Service Company of New Hampshire

Geotechnical' Engineers I n c . Winchester, Massachusetts

Subgrade Reaction Sand and Sand-Cement

Backfill

Project 77386

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