2003 6
A Stu dy on Determ in ation of Con solidation Settlem en t in Soft Grou n d w ith th e Titled Load 2003 6
2003 6
Ab stract A Stu dy on Determ in ation of Con solidation Settlem en t in Soft Grou n d w ith th e Titled Load by park, chi-woo Dept. of Civil Engineering Graduate School of Engineering Changwon National University Changwon, Korea T his study determined con solidation settlem ent in soft ground with the tilted load by m eans of T erzaghi' s one- dimensional con solidation theory and FEM. It w as also compar ed with a m easure v alue. T he conclusion s ar e summ arized in the following. 1) T he con solidation settlem ent from T erzagh ' s one- dim en sion al con solidation theory differ con sider ably from the m easur e v al ue, but show ed alm ost similar t o that from FEM. 2) T er zaghi' s one- dimensional consolidation theory show ed v ari able con solidation settlem ent accordin g to m ethods t o obt ain p. 3) Con solidation settlem ent det ermined by FEM turned out t o b etter ev alu ate the field settlem ent th an T er zaghi' s one- dimen
sion al con solidation theory does.
. 1.1 1 1.2 3. 2.1 4 2.2 5 2.3 11. 3.1 12 3.1.1 Terzaghi 1 12 3.1.2 Barron 14 3.1.3 Yoshikuni & N akanodo 15 3.1.4 Hansbo 16 3.1.5 Onou e 16 3.1.6 Zeng-Xie 17 3.1.7 Lo 17 3.2 18 3.2.1 18 3.2.2 t 20 3.2.3 (Asaoka) 21 3.2.4 Monden 23
. 4.1 26 4.2 (PLAXIS) 29. 5.1 35 5.2 Terzaghi 38 5.3 46 5.4 52. 54
2.1 4 2.2 5 2.3 8 2.4 9 2.5 10 3.1 13 3.2 19 3.3 t / ( S t - S 0 )t 20 3.4 t / ( S t - S 0 ) 2 - t 21 3.5 (Asaoka) 23 3.6 U T v 25 4.1 Coulomb 30 4.2 Mohr 31 4.3 Mohr-Coulomb 32 4.4 c=0mohr-coulomb 33 5.1-36 5.2 1 38 5.3 39 5.4 ( 1) 42 5.5 ( 2) 43 5.6 Vrignon 44 5.7 47 5.8 48
2.1 (1) 5 2.2 (2) 6 2.3 (3) 7 2.4 11 5.1 35 5.2 Mohr-Coulomb 46 5.3 49 5.4 52
. 1.1.,.,., -,,, 2. T erzaghi.... - 1 -
,. - 2 -
1.2,..,,, 1 : 1.50,. - 3 -
. 2.1,,. 2.1-4 -
2.2 2.1 (1) - --- - - BH-1- - - BH-2-- - BH-1 STA.4+113 23m ( BH-2 STA.4+113 ) 2.2-5 -
2.2 (2) BH-1 BH-2 3.0m - - 5.3m - 7.0m 1.1m 1.2m 1.4m 1.0m - : - 6 -
2.3 (3) USCS SC 5.3m CL 7.0m 3.0m : 500mm : (),, ( ) - GP(S P) 1.11. 2m (GP) (SP) : 1050mm, 3050%, :, () - - D-2, S-2, F-4-5 (, ) 1,2641,318 kgf/ cm 2-7 -
, ( ) () () ( ) 2.3-8 -
2.4-9 -
2.5-10 -
2.3 BH-2 2.4. 2.4 (%) USCS (%) BH-2 74.07 2.705 47.5 19.3 ML 0.622-11 -
. 3.1 3.1.1 Terzagh i1.. 3.1(a).. (b). z z, z + z. h = h(z, t) h( z, t) h. h + h z z ------------------------------------------------------------------------- (3.1) v (z, t), - 12 -
v. (a) (b) 3.1 v + v z z --------------------------------------------------------------------------- (3.2) A t V w V w = ( v + v z z)a t - va t = v z za t ------------------------------ (3.3). t, v V s V s = ( v z)a = v t t za ------------------------------------------------- (3.4). V w V s. v t = v z -------------------------------------------------------------------------- (3.5) - 13 -
. i, - (h / z) z,. i = - h z z z = - h z = - 1 r w u e z ----------------------------------- (3.6) Darcy v = ki k v z = - z ( ki) = - k r w 2 u e z 2 ------------------------------------------ (3.7), m v v = m v v '. v. v v' = m t v t = m v ( v t - u e )---------------------------------------- (3.8) t (3.7)(3.8)(3.5) u e = t k r w m v 2 u e z 2 + v t ---------------------------------------------- (3.9). Terzaghi. 3.1.2 Barron Barron., 2. (Sm ear effect) (Well resistance) - 14 -
. Barron Terzaghi. u t = C v ( 2 u z 2 ) + C h ( 2 u r 2 + 1 r u ) ---------------------------------- (3.10) r, (3.11). u t = C h ( 2 u r 2 + 1 r u ) -------------------------------------------------- (3.11) r, u. (1) U r (3.12). U r = 1 - exp [ - 2 T r F ( n) ] ------------------------------------------------------ (3.12) F ( n) = n 2 n 2-1 ln ( n) - 3n 2-1 4n 2 ---------------------------------------------- (3.13) (Sm ear) (3.12), F ( n)(3.14). F ( n) = n 2 n 2-1 ln ( n s ) - 3n 2-1 4n 2 + k h k s n 2 - s 2 n 2 ln (s) ------------------ (3.14) 3.1.3 Yosh iku ni & Nak anodo Yoshikuni & N akanodo (Well resistance) ( U r )(3.15). U r = 1 - exp [ - 2 T r F ( n) + 0.8L ] = 1 - exp [ - 2 T r F ( n) + 2.6G ] ------- (3.15) - 15 -
, F ( n) = L = 32 2 n 2 n 2-1 ln ( n ) - 3n 2-1 4n 2 k h k w l d w = 32 2 G 3.1.4 Hansb o Hansbo. Barron, Hansbo Barron. (3.12) F ( n)(3.16). F ( n) = n 2 n 2-1 ( ln n s + k h k s ln (s) - 3 4 ) + s 2 n 2 ( 1 - s 2 1 4n 2 ) + k h 1 k s n 2-1 ( s4-1 n 2 - s 2-1) ------------------------------------ (3.16) 4 Hansbo. z (3.12) F ( n, s) (3.17). F ( n) = n 2 n 2-1 ( ln n s + k h k s ln (s) - 3 4 ) + s 2 n 2 ( 1 - s 2 1 4n 2 ) + k h 1 k s n 2-1 ( s4-1 n 2 - s 2-1) + z (2l - z) 4 k h q w ( 1-1 n 2 )---- (3.17) 3.1.5 Onou e Onou e, (Equivalent sp acing ratio : n' ) (3.18) - 16 -
. U r = 1 - exp [ - 2 T r F ( n) + 0.8L ] --------------------------------------------- (3.18) F ( n' ) = 2 n' n' 2-1 ln ( n' ) - 3n' 2-1 2 ------------------------------------------ (3.19) 4n', n' = n s - 1 = k h k s = 3.1.6 Zeng-Xie Zeng-Xie (3.20). U r = 1 - exp [ - 2 T r F ( n, s) + G ] --------------------------------------------- (3.20), G = k h k w ( l d w ) 2 F ( n) = n 2 n 2-1 ( ln n s + k h k s ln (s) - 3 4 ) + s 2 n 2 ( 1 - s 2 1 4n 2 ) + k h 1 k s n 2-1 ( s4-1 n 2 - s 2-1) 4 3.1.7 Lo LoZeng-XieHansbo t. Zeng-Xie (3.21). - 17 -
U r = 1 - exp [ - 2 T r F ( n, s) + 2.5G ] ------------------------------------------ (3.21) 3.2 1, Skempton-Bjerrum, Lambe., tmonden. 3.2.1 (Hyp erb olic) 3.2,.. S t = S 0 + t + t ----------------------------------------------------------- (3.22), S t : t S 0 : t :, : - 18 -
3.2 t S t - S 0 = + t ----------------------------------------------------------- (3.23). (3.23) 3.3 t / ( S t - S 0 )t, t S t. ( S f ) t =. S f = S 0 + 1 ----------------------------------------------------------------- (3.24) - 19 -
3.3 t ( S t - S 0 ) t 3.2.2 t Terazaghi. t. t = - (3.25). S t = S 0 + S d = S 0 + A K t 1 + K 2 t ---------------------------------------- (3.25), S t : S 0 : S d : t : A, K : - 20 -
K, A. (3.26). t ( S t - S 0 ) 2 = t A 2 + 1 A 2 K 2 -------------------------------------------- (3.26) t ( S t - S 0 ) 2 - t 1, 1 A 2 A 2 K 2. ( 3.4 ) 3.4 t ( S t - S 0 ) 2 - t A, K. (S f )(3.27). S f ( t = ) = S 0 + A -------------------------------------------------------- (3.27) 3.2.3 (Asaok a) Asaoka(1978)Mikasa(1963). Mikasa - 21 -
Terazaghi v. C v = 2 v Z 2 = v ------------------------------------------------------ (3.28) t (3.29). S + a 1 ds d 2 S d n S + a dt 2 dt 2 + + a n dt n + = b -------------- (3.29), Sa 1, a 2, a n, b. n S j = 0 + n i = 1 j + S j - 1 ----------------------------------------------------- (3.30) 1(3.31). S + a 1 ds dt = b, ( a 1 = 5 12 h 2 C v ) S j = 0 + i S j - 1 ------------------------------------------------------------- (3.31). S( t) = S f - ( S f - S 0 ) exp ( - t a 1 ) ---------------------------------------- (3.32) S t : t = S 0 : t = S j = S j - 1 = S j S j. S f = i 1-0 ----------------------------------------------------------------- (3.33) (3.34). - 22 -
S f = 0 1-1 - ( 0 1-1 - S 0 )( i) j --------------------------------------- (3.34), Asaoka.. 1) - t. t 30 100. t 1, 2 t, 3 t. ( 3.5 ) 2) S i - 1 S i S 1, S 2, S 3 ( S i - 1, S ). i S i - 1 = S 45. i 3) 45 3.5 (Asaoka) 3.2.4 Mon den U(%), U - 23 -
(3.35). U = 1 - m = 0 2 M 2 exp (M 2 T v ) ------------------------------------------- (3.35), M = (2m + 1)/ 2 m : U T v, T v 3.6. U = 0 U 40 % U = 40 %. T v U f ( u) (3.36). t/ H 2 = f ( u) C v ----------------------------------------------------------------- (3.36) 3.6 U, t/ H 2 U 40 %, C v Monden. S t S ct S 0 S c S 0 U( % ). - 24 -
3.6 U T v - 25 -
. 4.1 Biot... SunduhWilson (1969) Gurtin (1964) Hw ang Morgenstern (1971) Yokoo(1971) (Discontinuou s function). Gelerkin -. -.. - 26 -
- [ ] [ C E ] [ ] T { } + [ ] { } u = {f b } x 0 0 0 z y [ ] = 0 y 0 z 0 x 0 0 x x x 0 [ C E ] : {w} : { } = ( 1, 1, 1,0,0,0) T { } : {f b } : - - 1 w { } T {k} { }u + { } T {w} - t 1 Q u t = 0 w : - 27 -
{ } T = ( / X, / z, / z) [ k] : [ k] = k xx k xy k xz k yx k yy y yz k zx k zy k zz {v} = ( v x, v y, v z ) T {w} = ( w x, w y, w z ) T 1/ Q : - 28 -
4.2 ( PLAXIS ) PLAXISVerm eer(1993) (Finite Elem ent Method). Elastic, Mohr-Coulomb, Advanced Mohr-Coulomb, Cap, Cam-clay, Drucker-Prager Model,,,,. -Mohr-Coulomb. Mohr-CoulombCoulomb. Coulomb. Coulomb 4.1 Coulomb. f = c + n tan ( 4.1 ) 4.1 f, n, c,. Coulomb Coulomb - 29 -
Vince. c (chesion intercept), (angle of shearing resistance). 4.1 Coulomb Mohr, 4.2. = f( ) ( 4.2 ),, 1, 3 4.2Mohr P., Mohr P, = f( ) Mohr. - 30 -
4.2 Mohr Mohr-Coulomb Mohr = f( ) 4.3 Mohr-Coulomb. c 4.1. = c + tan ( 4.3 ) Mohr 4.3 1, 34.4. 1-3 = 2 ccos + ( 1 + 3 )sin ( 4.4 ) - 31 -
. = 4 + 2, = 34-2 ( 4.5 ) 4.3 Mohr-Coulomb Mohr-Coulomb 2, Mohr-Coulomb 3.(Smith & Griffith, 1982) f 1 = 1 2 2-3 + 1 2 ( 2 + 3 )sin - ccos 0 f 2 = 1 2 3-1 + 1 2 ( 3 + 1 )sin - ccos 0 (4.6) f 3 = 1 2 1-2 + 1 2 ( 1 + 2 )sin - ccos 0 4.4 6. 3. - 32 -
g 1 = 1 2 2-3 + 1 2 ( 2 + 3 )sin g 2 = 1 2 3-1 + 1 2 ( 3 + 1 )sin (4.7) g 3 = 1 2 1-2 + 1 2 ( 1 + 2 )sin 4.4 c=0mohr-coulomb.,. c > 0 Mohr-Coulomb. (tension cut-off). - 33 -
Hooke. G. Mohr-Coulomb 5. : G : : : c : - 34 -
. 5.1 ( ) ( ), 5.1. 5.1 (cm) (cm) 2000.9-0 10 4.3 4.3 11 3.1 7.4 2000.12 2.8 10.2 1 0.3 10.5 2 0.1 10.6 3 0.2 10.8 4 9.8 20.6 5 0.5 21.1 6 0.5 21.6 7 2.2 23.8 8 2.7 26.5 9 2.7 29.2-35 -
- 5.1. 5.1-5.1 5.1 1 29.2cm (Cv) (Tv). 1 60% 60% - 36 -
(U) (S). - (H) = 7.0m - (h) = 3.50m - (Cv) = 2.48510-4 cm 2 / sec - (t) = 1 - ( ) (S) = 29.2cm - (Tv) = C v t = h 2 (2.485 10-4 ) (365 24 60 60) 350 2 = 0.06397 - (U) (Tv) U = 0~60%, T v = 4 ( U 100 ) 2 (U) = T v 4 100 2 = 0.06397 4 100 2 = 28.54% (S) = 29.2 0.2854 = 102.3cm - 37 -
5.2 Terzaghi 1. p 0 A, H. p 1 S. 5.2 1 V = V 0 - V 1 = HA - (H - S)A = SA (5.1) V 0 V 1., V V., V= SA = V V0 - V V1 = V V (5.2) V 0 V 1.. V V = e V s (5.3) - 38 -
, e =, V S = V 0 1 + e 0 = A H 1 + e 0 (5.4) e V 0, (5.1), (5.2), (5.3), (5.4). V= S A = e V S = A H e S = H (5.5) 1 + e 0 1 + e 0 5.3 e-logp e. e = C C [ log (p 0 + p) - log p 0 ] (5.6) C C e-log p, (compression index). - 39 -
(5.6)(5.5). S = C c H p log 1 + e 0 ( 0 + p (5.7) p 0 ).,. S= [ C c H i 1 + e 0 log ( p 0( i) + p ( i) p 0( i) ) ] (5.8), ( 8.13) P 0 + P P C e-log p cb,. C s (smell index)., e = C s [ log (p 0 + p) - log p 0 ] (5.9) (5.5)(5.9). S = C s H p log 1 + e 0 ( 0 + p p 0 ) (5.10) P 0 + P > P c. - 40 -
S = C s H 1 + e 0 log ( p c p 0 ) + C s H p log 1 + e 0 ( 0 + p (5.11) p c ), e-log p e. (5.5) S. Terzaghi - (H) = 7.0m - ( C c ) = 0.622 - ( e 0 ) = 1.51 - ( p 0 ) (H) = 5.3m ( su b) = 0.8 t/ m 3 (H) =16.5m ( w) = 1.0 t/ m 3 p 0 = H = 5.30.8 + 16.51 = 20.74 t/ m 2-5.4, 5.5 (m). - 41 -
5.4 ( 1) p p 5.41) P e M e =(P e). 5.5 2) P 1 ( P 1-1 ) ( P 1-2 ) ( P 1-2 ) P 1-2 ( P 1-2 - 1 ) ( P 1-2 - 2 ). - 42 -
5.5 ( 2) - 1 ( A 1 ) = 90.88 m 2-2 ( A 2 ) = 50 m 2 - ( sub) = 0.9 t/ m 3 -( A ) = 12.5 m 2 1) p = P A + M e I = (A 1 + A 2 ) su b A + P e I P = (A 1 + A 2 ) su b = (90.88+50) 0.9 = 126.79 A = 12.5 1 = 12.5 m 2 I = 1 12.5 3 12 = 162.76 m 3 P5.6 Vrignon. - 43 -
5.6 Vrignon Vrignon, P 1 X 1 + P 2 X 2 + P 3 X 3 + P 4 X 4 + P 5 X 5 + P 6 X 6 + P 7 X 7 = P X 8.66 2.33 + 21.04 6.33 + 5.06 6.5 + 9 10 + 5.63 13.67 + 32.4 14 + 50 21.17 = 126.79 X X = 14.71m 5.6e 9.04m. p = P A + M e I = (A 1 + A 2 ) su b A + P e = I 126.79 12.5 + 126.79 9.04 162.76 = 17.18 t/ m 2-44 -
1) p, (S) = c c H p log 1 + e 0 ( 0 + p p 0 ) = 0.622 7 1 + 1.51 log ( 20.74 + 17. 18 20.74 ) = 46.5cm 2) P = A 1 su b cos 2 45 + A 2 su b = 133.23 t p = P A = 133.23 12.5 = 10.66 t/ m 2 2) p, (S) = c c H p log 1 + e 0 ( 0 + p p 0 ) = 0.622 7 1 + 1.51 log ( 20.74 + 10.66 20.74 ) = 31.2cm - 45 -
5.3 PLAXIS 5.2. 5.2 Mohr-Coulomb t ( t/ m 3 ) c ( t/ m 2 ) 1.8 0.350 28 0.5 0 1.9 0.350 30 1 0 1.750 0.350 0 1.8 0 2 0.250 40 0.3 0 PLAXIS 5.7 5.8, 5.3. 5.7 5.8. 5.3. PLAXIS.,. - 46 -
- 47 -
- 48 -
5.3 Step Uy[m] Step Uy [m] Step Uy[m ] 0 0.00E+00 33-1.25E-02 66-2.40E-01 1 0.00E+00 34-1.32E-02 67-2.72E-01 2 0.00E+00 35-1.40E-02 68-2.88E-01 3 0.00E+00 36-1.57E-02 69-3.19E-01 4 0.00E+00 37-1.67E-02 70-3.35E-01 5 0.00E+00 38-1.79E-02 71-3.67E-01 6 0.00E+00 39-1.93E-02 72-3.98E-01 7 0.00E+00 40-2.09E-02 73-4.13E-01 8 0.00E+00 41-2.26E-02 74-4.43E-01 9 0.00E+00 42-2.62E-02 75-4.55E-01 10 0.00E+00 43-2.81E-02 76-4.65E-01 11 0.00E+00 44-3.20E-02 77-1.64E-02 12 0.00E+00 45-3.98E-02 78-2.54E-02 13 0.00E+00 46-4.78E-02 79-3.18E-02 14-1.05E-03 47-5.57E-02 80-3.65E-02 15-1.07E-03 48-7.17E-02 81-3.93E-02 16-2.91E-03 49-7.96E-02 82-4.02E-02 17-3.81E-03 50-8.96E-02 83-4.20E-02 18-4.64E-03 51-1.03E-01 84-4.52E-02 19-5.48E-03 52-1.11E-01 85-4.61E-02 20-6.31E-03 53-1.15E-01 86-4.74E-02 21-6.75E-03 54-1.24E-01 87-4.76E-02 22-7.13E-03 55-1.28E-01 88-4.76E-02 23-7.49E-03 56-1.32E-01 89-4.76E-02 24-8.18E-03 57-1.40E-01 90-4.77E-02 25-8.53E-03 58-1.48E-01 91-4.80E-02 26-8.67E-03 59-1.65E+00 92-4.85E-02 27-8.91E-03 60-1.73E-01 93-4.96E-02 28-9.42E-03 61-1.81E-01 94-5.02E-02 29-9.79E-03 62-1.97E-01 95-5.13E-02 30-1.05E-02 63-2.01E-01 96-5.36E-02 31-1.10E-02 64-2.09E-01 97-5.80E-02 32-1.15E-02 65-2.25E-01 98-5.81E-02-49 -
Step Uy[m] Step Uy [m] Step Uy[m ] 99-5.80E-02 133-1.32E-01 167-2.53E-01 100-5.81E-02 134-1.33E-01 168-2.58E-01 101-5.81E-02 135-1.35E-01 169-2.63E-01 102-5.84E-02 136-1.36E-01 170-2.67E-01 103-5.93E-02 137-1.39E-01 171-2.76E-01 104-6.13E-02 138-1.39E-01 172-2.95E-01 105-6.33E-02 139-1.39E-01 173-3.13E-01 106-6.54E-02 140-1.39E-01 174-3.30E-01 107-6.97E-02 141-1.39E-01 175-3.48E-01 108-7.38E-02 142-1.39E-01 176-3.83E-01 109-7.78E-02 143-1.39E-01 177-4.17E-01 110-8.55E-02 144-1.39E-01 178-4.33E-01 111-9.28E-02 145-1.40E-01 179-4.41E-01 112-9.94E-02 146-1.40E-01 180-4.44E-01 113-1.02E-01 147-1.40E-01 181-4.50E-01 114-1.03E-01 148-1.41E-01 182-4.53E-01 115-1.03E-01 149-1.42E-01 183-4.56E-01 116-1.04E-01 150-1.44E-01 184-4.60E-01 117-1.06E-01 151-1.46E-01 185-4.65E-01 118-1.08E-01 152-1.48E-01 186-4.74E-01 119-1.12E-01 153-1.50E-01 187-4.92E-01 120-1.15E-01 154-1.55E-01 188-4.97E-01 121-1.19E-01 155-1.58E-01 189-5.02E-01 122-1.20E-01 156-1.61E-01 190-5.03E-01 123-1.20E-01 157-1.64E-01 191-5.04E-01 124-1.20E-01 158-1.68E-01 192-5.07E-01 125-1.20E-01 159-1.75E-01 193-5.12E-01 126-1.21E-01 160-1.81E-01 194-5.17E-01 127-1.22E-01 161-1.94E-01 195-5.22E-01 128-1.23E-01 162-2.07E-01 196-5.27E-01 129-1.25E-01 163-2.19E-01 197-5.33E-01 130-1.27E-01 164-2.25E-01 198-5.38E-01 131-1.28E-01 165-2.31E-01 199-5.49E-01 132-1.31E-01 166-2.42E-01 200-5.70E-01-50 -
Step Uy [m] Step Uy [m] 201-5.91E-01 225-9.54E-01 202-6.13E-01 226-9.54E-01 203-6.23E-01 227-9.54E-01 204-6.44E-01 228-9.54E-01 205-6.64E-01 229-9.55E-01 206-6.85E-01 230-9.55E-01 207-7.05E-01 231-9.56E-01 208-7.24E-01 232-9.57E-01 209-7.43E-01 233-9.57E-01 210-7.61E-01 234-9.59E-01 211-7.70E-01 235-9.60E-01 212-7.78E-01 236-9.62E-01 213-7.94E-01 237-9.63E-01 214-8.10E-01 238-9.64E-01 215-8.25E-01 239-9.66E-01 216-8.54E-01 240-9.69E-01 217-8.69E-01 241-9.71E-01 218-8.97E-01 242-9.75E-01 219-9.10E-01 243-9.79E-01 220-9.16E-01 244-9.85E-01 221-9.22E-01 245-9.92E-01 222-9.33E-01 246-9.98E-01 223-9.44E-01 247-1.00E+00 224-9.54E-01-51 -
5.4 5.4Terzaghi PLAXIS. 5.4 PLAXIS Mod el - Mohr-Coulomb Terzaghi (cm) 102.3 100 1 2 46.5 31.2 102.3cm. PLAXIS 100cm. Terzaghi PLAXIS. Terzaghi 1.. 2.. 3.. Terzaghi. - 52 -
Terzaghi p. Terzaghi.. - 53 -
. Terzaghi1 PLAXIS. 1 ) Terzaghi. PLAXIS. Terzaghi1. 2 ) Terzaghi1p. p p. 3 ) Terzaghi1. 4 ) 1data Terzaghi1-54 -
.. 5 ) 1. - 55 -
1.,,, 1998 2.,,,, 1999 3.,,, 2002. 4.,,, 1994. 5.,, 2001. 6.,, 1999. 7. Braja M. das..,, 2001. 8. Braja M. Das, "Princip les of Fou nd ation En gieering", PWS p ublishing Com p any, Boston, 1990 9. Braja M. Das, "Advance Soil Mech ancis", Mc Graw Hill, 1983 10. Gere & Tim oshenko.,.,, 1997.
11. Terzaghi, K., an d Peck,R, "Soil Mechanics in En gineering Pactice", John Wiley and Son s,inc,n ew York N.Y, 1948
.,,..,..,
,.. 2003 6