T h e G ro u p E f f e c t o f L at e r a lly L o a d e d P i le s in C o h e s i v e S o i l 200 1 2
T h e G ro u p E f f e c t o f L at e r a lly L o a d e d P i le s in C o h e s i v e S o i l 200 1 2
200 1 2
LPILE P L U S, GROUP 4.0 for Windows (Reese, 1990).,,. 15mm, PC 47 50%, 46 50%, PC 38 40%, 38 39%.. 8 1. Prakash Saran (1967).
A b s tract T he group effect s b ased on allow able deflection of a pile head and pile cap in a group have been studied by the computed program, LPILE P L U S, GROUP 4.0 for Window s (Reese etc, 1990). Variou s parameters such as pile stiffness, fixity condition of pile heads, soil type and pile spacing are considered for behavioral study of piles. From the comparison of different fixity conditions (free/ fixed) of a single pile, it can be seen that the head fixity ratio(free/ fixed) for lateral load is shown to be 47 50% for PC pile, 46 50% for steel pipe pile and the head fixity ratio for the maximum moment is 38 40% for PC pile, 38 39% for steel pipe pile. T he influence of average undrained shear strength and pile rigidity on the ratio of lateral load and maximum moment are shown to be a single pile or group piles. when pile spacing is greater than 8 times (8D) of pile diameter, the group pile behaves as a single pile. From the comparison of the pile model test v alue of Prakash and Saran (1967), the group reduction factor from the model test accords to program computed within allow able deflection.
Abstract 1 1 1.1 1 1.2 2 1.3 2 2 4 2.1 4 2.1.1 4 2.1.2 p - y... 8 2.1.3...13 2.2 17 2.2.1 17 2.2.2 19 2.2.3 22 3 24 3.1 24
3.2 26 4 28 4.1 28 4.2 37 5 50 52
1 1.1,.,,,,.,....,,,,,..
1.2,,.,. Reese Matlock (1966) LPILE P L U S, GROUP 4.0 for Windows (Reese, 1990) PC. 1.3,,. Hrennikoff(1949) -, -
., Hrennikoff(1950)., Hrennikoff, Hrennikoff.(Reese, 1990) Reese Matlock (1960, 1966),. Parker Cox (1969) Reese Matlock. Reese(1970) 1977 O'neill Mindlin - -. poulos. Brown (1987). Peter (1996). Prakash Kumar (1996) k h m ax ( ).
2 2. 1 2.1.1 2,,. Hansen (1961) Broms (1964),. 2.1.3.,,. (Free head) (Fixed head), -. 2.1. Brinch Hansen (1961) 2.1 z (2.1). Q u M u 2.1 z r (2.2) (2.3).
p uz = p oz ' K p + c K c (2.1), p uz : z p oz ' : z c : K q, K c : ( 2.2) (2.2) 0 z r Q u. Q h = 0, Q u - 0 z r P uz d dz + L z r p uz d dz = 0 (2.2), Q u : d L z : : : Q u M u = Q u e 2.3. M = 0, Q u e - 0 z r P uz z d dz + L z r p uz z d dz = 0 (2.3) Broms Hansen. ( c = 0 ) ( =0)
. Fig. 2.1 Brinch han sen ' s m ethod for calculating ultimat e later al resistance Fig. 2.2 Brinch han sen ' s coefficient s of Kp and Kc 2.1
T R (2.4). T able. 2.1 Criteria for rigid pile and flexible pile Coefficient of subgr ade r eaction Criteria of pile Linearly incresing Constant Short rigid piles L / T 2 L / R <2 long flexible piles L / T 4 L / R 3.5 T = ( E I n h ) 1 5, R = ( E I k h ) 1 4 (2.4), T, R : k h = n h z : n h : E p : I : 2.2.3,,. ( H u ) ( M y ).(,, 1997)
2.4,,. 2.1.2 p - y y p. p- y, p- y. p- y, p- y. Reese (1983). Matlock (1970) p- y. 2.5 p u, 50% y 50.
deflection soil reaction bending moment (a) short rigid pile deflection soil r eaction bending m om ent (b ) long flexible piles Fig. 2.3 Soil r eaction s and bending moment s for free head piles under horizontal load in cohesiv e soil (Br om s, 1964)
deflection soil r eaction bending moment (a) short rigid pile deflection soil r eaction bending m om ent (b ) long flexible piles Fig. 2.4 Soil r eaction s and bending moment s for fix ed head piles under horizontal load in cohesiv e soil (Br om s, 1964)
50% 2.2 2.3. (2.5) (2.6) p u. p u y 50 (2.7) (2.8) y = 8 y 50 p. p- y p- y y = 8y 50 y = 16 y 50 (2.8) 1/ 3 1/ 4. p u = [3 + ' c u x + J d x ] c u d (2.5), ' : x c u d J : : x : : ( = 0.5, = 0.25) p u = 9 c u d (2.6) y 50 = 2.5 50 d (2.7)
, 50 : 50% p p u = 0.5 ( y y 50 ) 1 3 (2.8) Fig. 2.5 Criteria for load- deformation p- y curves for later ally loaded piles T able. 2.2 Values of 50 for clay s in clay Con sist ency of clay 50 soft 0.02 medium 0.01 stiff 0.005
T able 2.3 Values of 50 for stiff clay s Av erage undr ained shear strength (kpa) 50-100 0.007 100-200 0.005 300-400 0.004 50 2.1.3. (modulus of subgrade reaction approach ) (elastic approach). 2.6(a)., 2.6(a) Winkler..,.
.. Reess (1974) p- y. Reese (1974) 2.6(a ) (2.9). E p I p d 4 y dx 4 + p = 0 (2.9), E p I p : : 2 y : x p : p 2.6(b),(c) p = k h y (2.10), k h :
k h 2.4. T able. 2.4 Soil- modulus parameter k h for clay type (unit : kn / m 3 ) Clay type Avg. undrained shear strength cu (kpa) Static Cyclic soft 12 24 8140 - medium 24 48 27150 - stiff 48 96 136000 54300 k h x y (2.10). p y.,..,. Spiller Stoll(1964) Mindlin. Douglas Davis (1964) Mindlin. Poulos (1971) Spiller Stoll..(,, 1993)
F i g 2. 6 Behavior of later ally loaded pile : subgr ade r eaction approach. (a)winkler ' s idealization, (b ) Laterally loaded pile in soil, (c) Later ally loaded pile on spring s.
2.2.. Ge.. 2.7. Poulos Davis (1 980). Poulos (1971). Mindlin (1963). Poulos Davis (1980). 2.2.1. Fig 2.7 Pile- gr oup behavior
(Ov erlapping zones for individual piles). (1985) 8 (8D)... Poulos Davis (1980).
. 6D. 8. 2.2.2 Ge (2.11). Prakash Saran (1967), Oteo(1972) Ge Ge = ( Q u ) g n Q u (2.11)
, (Q u ) g : n Q u : :. Ge Spacing / diameter of pile (S/ D) Fig. 2.8 Lateral group efficiency from model tests (Prakash and saran, 1967) T able. 2.5 Gr oup efficiency Ge for cohesionless soils (Oteo, 1972) S/ D Ge 3 0.50 4 0.60 5 0.68 6 0.70
T able. 2.5 Group efficiency Ge for piles in cohesive soils (Pr akash and sar an, 1967) S/ D Ge 2 2 group 3 3 group Recommended 3 0.42 0.39 0.40 3.5 0.50 0.42 0.45 4.0 0.57 0.44 0.50 4.5 0.61 0.47 0.55 5.0 0.63 0.48 0.55 6.0 - - 0.65 8.0 - - 1.00 2.8 2.5 2.6. 2.8 Ge. Prakash Saran (1967) Ge. 2.6 S/ D 5 Ge S/ D 6 0.65 S/ D 8 Ge.
2.2.3. Prakash (1967) 6D 8D. 2.5D. Davisson (1970) n h 2.7. T able. 2.7 Group reduction factor for the coefficient of subgrade r eaction (Davisson, 1970) Pile spacing in the dir ection of loading Group reduction factor for n h 3D 0.25 4D 0.40 6D 0.70 8D 1.00 or k h n h
n h. k h Poulos (1971). Poulos.
3 3.1 PC., PC 40 60cm, 60 80cm.,, 3. 2. p- y LPILE P L U S, GROUP 4.0 for Window s (Reese, 1990)..3.1, 3.2, 3.1. 3 3. T able. 3.1 Phy sical pr operties of soil Con sistency of clay soft medium stiff cu (kpa) 18 36 72 ' ( kn / m 3 ) 15 16 17 k h ( kn / m 3 ) 8,140 27,150 136,000
T able. 3.2 Phy sical pr operties of pile Pile PC- pile Steel pipe pile L (m ) 13 20 D (m ) 0.4 0.5 0.6 0.6 0.7 0.8 A p (m 2 ) 0.0765 0.1159 0.1571 0.0149 0.0174 0.0199 I p (m 4 ) 0.00109 0.00262 0.00522 0.00065 0.00104 0.00156 E p (kn/ m 2 ) 2.65 10 7 2.06 10 8 (a) Free- head (b) Fix ed- head Fig. 3.1 Applied model of single pile 3.2
3.1 3.2 3.1., 15mm. 3.2 3D, 4D, 6D, 8D. Free head Fixed head Fig. 3.2 Applied model of group pile 3 3.
, 15mm,.
4 3, 15mm., 3 3,,. 4.1 ( 1997) 15mm 15mm 4.1 4.4., 4.1 4.4 4.1 4.2. 4.1 4.2-28 -
4.3. 4.1 4.3 PC 47 50%., 4.2, 4.3 PC 46 50%. 4.3, 4.4 4.3, PC, 38 40% 38 39%.. PC. Yan Byrne(1992) 50% 50%. Yan Byrne(1992) 50% 50% 10% 40%. - 29 -
(a ) P C pile D40 - Single (b ) P C pile D50 - Single (c ) P C pile D60 - Sin gle Fig. 4.1 Later al load with fixity condition for allow able deflection - 30 -
(a ) St eel pipe pile D60 - sin gle (b ) St eel pipe pile D70 - sin gle (c) St eel pipe pile D80 - sin gle Fig. 4.2 Later al load with fixity condition for allow able deflection - 3 1 -
(a ) P C pile D40 - Sin gle (b ) P C pile D50 - Sin gle (c) P C pile D60 - Single Fig. 4.3 Variation of bending moment with fixity condition for allowable deflection - 32 -
(a ) St eel pipe pile D60 - sin gle (b ) St eel pipe pile D70 - single (c) St eel pipe pile D80 - sin gle Fig. 4.4 Variation of bending moment with fixity condition for allowable deflection T able. 4.1 lateral load and maximum bending moment for allowable deflection of 15mm - 33 -
T ype of pile PC pile Head type Diameter (cm ) Soil Lateral load Mmax type (kn) (kn - m ) soft 35.4 47.6 D40 medium 89.6 96.5 stiff 115.6 103 Free soft 50.4 80.4 D50 medium 126.5 159.5 head stiff 163.9 174 Fixed head D60 D40 D50 D60 soft 65.7 121.3 medium 166.6 239.6 stiff 215 262.9 soft 73.3 123.9 medium 186 242.4 stiff 231.9 266.9 soft 103.2 207.7 medium 268.5 410.1 stiff 325.8 446.6 soft 136.3 315.8 medium 354.7 615.1 stiff 428.9 673.4.. T able. 4.2 Lateral load and maximum bending moment for allowable deflection of 15mm - 34 -
T ype of Head type Diameter (cm ) pile Steel pipe pile Free head Fixed head D60 D70 D80 D60 D70 D80 Soil Later al load Mmax type (kn) (kn - m ) soft 65 118.6 medium 164.4 233.4 stiff 212.8 258.6 soft 80 159.9 medium 197.9 307.6 stiff 259.1 341.5 soft 94.7 204.9 medium 232.5 391.8 stiff 308.4 440. soft 134.6 309.9 medium 349.9 602.8 stiff 424.1 659.1 soft 164 414.5 medium 428.9 809.2 stiff 516.1 880 soft 195.7 529.8 medium 506 1040.5 stiff 612.3 1128.1.. - 35 -
T able. 4.3 Lateral load and Mmax (Free/Fixed)ratio for allowable deflection of 15mm T ype of pile PC pile Steel pipe pile Diameter (cm ) D40 D50 D60 D60 D70 D80 Soil type Later al load free/ fix ed Mmax free/ fix ed soft 0.48 0.38 medium 0.48 0.4 Stiff 0.5 0.39 dsoft 0.49 0.39 medium 0.47 0.39 stiff 0.5 0.39 soft 0.48 0.38 medium 0.47 0.39 stiff 0.5 0.39 soft 0.48 0.38 medium 0.47 0.39 stiff 0.5 0.39 soft 0.49 0.39 medium 0.46 0.38 stiff 0.5 0.39 soft 0.48 0.39 medium 0.46 0.38 stiff 0.5 0.39-36 -
4.2 4.1 3D, 4D, 6D, 8D 15mm 4.4 4.5. 15mm 4.5 4.6. 4.5 4.6 3D 4.6 4.7. 4.5 4.6 46 50%, 35 40% 4. 5 4.8.,,. 4.6 4.7 (Group - 37 -
T able. 4.4 Lateral load and maximum bending moment for allowable deflection of 15mm T ype of pile PC pile Lateral load Mmax Diameter (cm ) Spacing Head type (kn) (kn - m ) 3D free 118.1 18.5 fix ed 246.5 50.3 4D free 144 22.8 fixed 311 61.2 D40 6D free 221.3 31.5 fix ed 462.3 80.5 8D free 309.5 48 fix ed 668.5 120.1 Single free 315.2 48.5 fix ed 680.8 123.8 3D free 164.4 31.6 fix ed 337.3 83.4 4D free 213.1 40.7 fix ed 441.2 108 D50 6D free 302.5 58.6 fix ed 644.5 145.4 8D free 449.1 79.8 fix ed 921.6 203.5 Single free 459.2 81.4 fix ed 942.3 207.7 3D free 219.6 46 fix ed 448.6 126.2 4D free 284.4 56.9 fix ed 573.2 160.9 D60 6D free 411.3 83.6 fix ed 847.3 220.8 8D free 606 117.5 fix ed 1221.1 309.1 Single free 618.3 121.1 fix ed 1246 315.4-38 -
T able. 4.5 Lateral load and maximum bending moment for allowable deflection of 15mm T ype of pile Steel pipe pile Lateral load Mmax Diameter (cm ) Spacing Head type (kn ) (kn - m ) 3D fr ee 232.1 48.6 fix ed 506.8 126.8 4D fr ee 281.4 60.3 fix ed 613.5 155.3 D60 6D fr ee 413.1 84.8 fix ed 933.7 222 8D fr ee 591 118.7 fix ed 1327.3 313 Single fr ee 598.7 121.1 fix ed 1333.8 317 3D fr ee 287.8 64.1 fix ed 582.5 171.2 4D fr ee 346.9 84.6 fix ed 733 236.7 D70 6D fr ee 509.2 119.3 fix ed 1062.1 325.4 8D fr ee 715.9 158.2 fix ed 1481 459.6 Single fr ee 738 162 fix ed 1495.9 464.2 3D fr ee 341.6 81 fix ed 694.3 221.5 4D fr ee 439.2 108.8 fix ed 914.7 291.2 D80 6D fr ee 663.6 156 fix ed 1362.3 425.1 8D fr ee 927.1 214.9 fix ed 1887.8 580.7 Single fr ee 975.9 231.5 fix ed 1946.2 598.7-39 -
(a) PC pile (spacing = 3D) (b) Steel pipe pile (spacing = 3D) Fig. 4.5 Comparison of lateral load for different fixity condition in pile spacing of 3D - 40 -
(a) PC pile (spacing = 3D) (b ) St eel pipe pile (spacing = 3D) Fig. 4.6 Comparison of bending moment for different fixity condition in pile spacing 3D - 4 1 -
(a) PC pile D40 (b) steel pipe pile D60 Fig. 4.7 Comparison of lateral load for different fixity condition with pile spacings - 42 -
(a) PC pile D40 (b) Steel pipe pile Fig. 4.8 Comparison of bending moment for different fixity condition with pile spacings T able. 4.6 Gr oup reduction factor and head fixity (Free/ Fix ed) ratio - 43 -
T ype of pile PC pile Diameter Spacing Head 3D 4D D40 6D 8D Single 3D 4D D50 6D 8D Single 3D 4D D60 6D 8D Single Later al load Mm ax type R F free/ fixed R F free/ fixed fr ee 0.37 0.38 0.48 fixed 0.36 0.41 0.37 fr ee 0.46 0.47 0.46 fixed 0.46 0.48 0.37 fr ee 0.70 0.65 0.48 fixed 0.68 0.65 0.39 fr ee 0.98 0.98 0.46 fixed 0.98 0.98 0.39 free fixed 0.46 0.39 fr ee 0.36 0.39 0.49 fixed 0.36 0.40 0.38 fr ee 0.46 0.50 0.48 fixed 0.47 0.52 0.38 fr ee 0.66 0.72 0.47 fixed 0.68 0.70 0.40 fr ee 0.98 0.98 0.49 fixed 0.98 0.98 0.39 free fixed 0.49 0.39 fr ee 0.36 0.38 0.49 fixed 0.36 0.40 0.36 fr ee 0.46 0.47 0.50 fixed 0.46 0.51 0.35 fr ee 0.67 0.85 0.49 fixed 0.68 0.80 0.35 fr ee 0.98 0.97 0.50 fixed 0.98 0.98 0.38 free fixed 0.50 0.38-44 -
T able. 4.7 Gr oup reduction factor and head fixity (Free/ Fix ed) ratio T ype of pile Steel pipe pile Diameter Spacing Head 3D 4D D60 6D 8D Single 3D 4D D70 6D 8D Single 3D 4D D80 6D 8D Single Lateral load Mmax type R F free/ fixed R F free/ fixed free 0.39 0.40 0.46 fixed 0.38 0.40 0.38 free 0.46 0.50 0.46 fixed 0.46 0.49 0.39 free 0.69 0.70 0.44 fixed 0.70 0.70 0.38 free 0.99 0.98 0.45 fixed 0.99 0.99 0.38 free fixed 0.45 0.38 free 0.39 0.40 0.49 fixed 0.39 0.49 0.37 free 0.47 0.52 0.47 fixed 0.49 0.51 0.36 free 0.69 0.74 0.48 fixed 0.73 0.70 0.37 free 0.97 0.98 0.48 fixed 0.99 0.99 0.34 free fixed 0.49 0.35 free 0.35 0.35 0.49 fixed 0.36 0.37 0.37 free 0.45 0.47 0.48 fixed 0.47 0.49 0.37 free 0.68 0.67 0.49 fixed 0.70 0.71 0.37 free 0.95 0.93 0.49 fixed 0.97 0.97 0.37 free fixed 0.50 0.39-45 -
4.6 4.7 (Group reduction factor ),,. 15mm,,. 2.27 Ge 15mm. 4.6 4.7 46 50% 36 40%. 2.5 Prakash Saran (1967) 4.8 4.9 4.10. 4.9 PC 4.10 (Gropu Reduction Factor ). 3D 4D Prakash Saran (1967) PC, 6D., 6D 6D 8D. - 46 -
T able 4.8 Comparison of group r eduction factor pr ogram solution w ith Prakash & Saran T ype of pile PC pile Steel pipe pile Diameter (cm ) Spacing D40 D50 D60 D60 D70 D80 Computed lateral load P rakash & S aran free F ix ed Recom en ded 3D 0.37 0.36 0.4 4D 0.46 0.46 0.5 6D 0.7 0.68 0.65 8D 0.98 0.98 1 3D 0.36 0.3.6 0.4 4D 0.46 0.47 0.5 6D 0.66 0.68 0.65 8D 0.98 0.98 1 3D 0.36 0.36 0.4 4D 0.46 0.46 0.5 6D 0.67 0.68 0.65 8D 0.98 0.98 1 3D 0.39 0.38 0.4 4D 0.46 0.46 0.5 6D 0.69 0.7 0.65 8D 0.99 0.99 1 3D 0.39 0.39 0.4 4D 0.47 0.49 0.5 6D 0.69 0.73 0.65 8D 0.97 0.99 1 3D 0.35 0.35 0.4 4D 0.45 0.47 0.5 6D 0.68 0.7 0.65 8D 0.95 0.97 1-47 -
(a ) P C pile D40 (b ) P C pile D50 (c ) P C pile D60 Fig. 4.9 Comparison of reduction factor for each PC pile - 48 -
(a ) St eel pipe pile D60 (b ) St eel pipe pile D70 (c) Steel pipe pile D80 Fig 4.10 Comparison of reduction factor for each steel pipe pile - 49 -
5.. 1. 15mm, PC 47 50%, 46 50%, PC 38 40%, 38 39%,. 2. PC 46 50%, 44 50% PC 35 39%, 34 38%. - 50 -
3.. - -. 4. Prakash Saran (1967) 4.8 4.9, 4.10 8 (8D). - 5 1 -
1.,,, (1997),,, 13, 5, pp. 59-74. 2. (1995),,, 15 pp. 1783-1794. 3. (1993), pp. 167-212. 4. (1997), pp. 171-188 5. Adam, M., and Lejay, J. E tude des p ieux sollicites horizontalem ent, Annales de Institut T echnique du Batiment et des T r av aux Publics, 280 1971, pp.125-156. 6. Brinch Han sen, J. "T he Ultimat e Resistance of Rigid Piles Against T ransver sal Forces", Danish Geotechnical I ns titute( Geoteknisk I ns titut) B ull. No. 12, Copenhagen, 1961, pp. 5-9. 7. Brom s, B., "T he Lat eral Resistance of Piles in Cohesiv e Soils", J ournal of the S oil M echanics and F oundations D ivision, ASCE, Vol. 90, No. SM2, Mar ch 1964a, pp. 27-63. 8. Br om s, B., "T he Later al Resist ance of Piles in Cohesionless Soils", J ournal of the S oil M echanics and F oundations D ivision, A SCE, Vol. 90, No. SM3, May 1964b, pp. 123-156. - 56 -
9. Brown, D. A., Reese, L. C., and O'Neill, M. W., "Behavior of a Lar ge Scale Pile Group Subject ed to Cyclic Lateral Loading", J ournal of Geotech. E ng ineering D ivis ion.,asce, 113(GT 11), 1987, pp. 1326-1343. 10. Canadian Geotechnical Society, F oundation E ng ineering M anual, 2nd ed ition, 1985, p.456. 11. Davisson, M. T.and. Gill M. L "Lat erally Loaded Piles in a Lay ered Sy stem", J ournal of the S oil M echanics and F oundations D ivision, A SCE, SM3, 1963, pp. 63-94. 12. Davisson, M. T. and Prakash, S., "A Review of Soil Pile Behavior", H ighway R es earch R ecord, No. 39, 1963, pp. 25-48. 13. Davis son, M. T., "Later al Load Capacity of Piles", H ig hway R esearch R ecord, Washington, DC, 1970, pp. 104-112. 14. Hetenyi, M., B eam s on E lastic F oundation, Univ. of Michigan Pr ess, Ann Arbor, Mich. 1946. 15. Matlock, H., and Reese, L. C., "Generalised Solutions for Laterally Loaded Piles", J ournal of the S oil M echanics and F oundations D ivision, ASCE, Vol.86, No. SM5, 1960. 16. Matlock, H. "Corr elation s for the Design of Later ally Loaded Piles in Soft Clay", P rep rint, 2d A nnual Offshore Technology Conf., Houston, T ex., Vol. 1, 1970 pp. 577-594. 17. McClelland, B. and F ocht, J. A., "Soil Modulu s for Later ally Loaded Piles", T rans. ASCE, Vol. 123, 1958, pp. 1049-1086. - 53 -
18. Mindlin, R. D. "F or ce at a Point in the Interior of a Semi- Infinite Solid", P hy sics, Vol. 7, pp. 195-202. 19. Morrison, C., and Reese, L. C., "A Lateral Load T est of a Full- Scale Pile Group in Sand", Geotechnical E ng ineering R ep ort GR 86-1, Geotech. Engrg. Center, Univ. of T exas at Austin, Austin, T ex. 1986. 20. O 'Neill, M. W., Ghazzaly, O. I., and Ha, H. B., "Analy sis of T hree- Dimensional Pile- Soil- Pile Interaction", P roc. 9th Offshore T echnology Conf. 2, 1977, pp. 245-256. 21. Oteo, C. S., "Displacement s of a Vertical Pile Gr oup Subjected to Lateral Loads", P roceeding s of 5th E urop ean Conf erence of S oil M echanics and F oundation E ng ineering, Madrid, Vol. 1, 1972, pp. 397-405. 22. Palmer, L. A. and T hompson, J. B., "T he Earth Pressure and Deflection Along the Embedded Length s of Piles Subjected to Lateral T hru st ", P roceed ing s S econd I nternational Conf erence on S oil M echanics and F oundation E ng ineering, Rotterdam, Holland, Vol. V, 1948, pp. 156-161. 23. Poulos, H. G., "Behavior of Laterally Loaded Piles : I- Single Piles", J ournal of the S oil M echanics and F oundations D ivision, A SCE, Vol. 97, No. SM5, May, 1971, pp. 711-731. 24. Poulos, H. G. "Behavior of Laterally Loaded Piles : Pile Gr oups",, J ournal of the. S oil M echanics and F oundation E ng ineering D ivision ASCE, Vol. 97, No. SM5, pp. 733-751. - 54 -
25. Poulos, H.G. and Davis, E.H. P ile F oundations A nalys is and D esig n, New York : John Wiley and Son s. 1980. 26. Pr akash, S., B ehavior of P ile Group s S ubj ected to Lateral L oads, Ph.D. T hesis, Univ er sity of Illinois, Urbana, 1962, p.397. 27. Pr akash, S. and Sar an D., "Behavior of Lat erally Loaded Piles in Cohesive Soils", P roceedings 3rd A s ian R eg ional Conf erence on S oil M echanics and F oundation E ng ineering, H aifa(israel), 1967, pp. 235-238. 28. Reese, L. C., and Matlock, H., "Non - dimensional Solutions for Laterally Loaded Piles w ith Soil Modulu s A s sumed Proportional t o Depth", P roceeding s 8th T exas Conf erence on S oil M echnics and F oundation E ng ineering, Austin, T X, 1956, pp. 1-41. 29. Reese, L. C. "Lat erally Loaded Piles : Program Documentation ", J ournal of Geotechnical E ng ineering D ivision, ASCE Vol. 103, No. GT 4, April, 1977, pp. 287-304. 30. Reese, L. C., O'Neill, M. W., and Smith, E., "Generalized Analy sis of Pile F oundation s", J ournal of the S oil M echanics and F oundations D ivision, ASCE, Vol. 96, No. SM 1, 1970, pp. 235-250. 31. Yan, L. and Byrne, P.M., "Lateral Pile Respon se to Monotonic Pile Head Loading", Canadian. Geotech., J.29, pp. 955-970. - 55 -
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