Seismic Analysis of Some Geotechnical Problems – Pseudo-dynamic Approach Dr. Priyanka Ghosh Assistant Professor Dept. of Civil Engineering Indian Institute of Technology, Kanpur INDIA Organisation Introduction to Pseudo-dynamic Approach and Upper Bound Limit Analysis Seismic Bearing Capacity of Strip Footing using Upper Bound Limit Analysis Seismic Vertical Uplift Capacity of Horizontal Strip Anchors using Upper Bound Limit Analysis Seismic Active Earth Pressure Behind Non-vertical Retaining Wall using Limit Equilibrium Method Seismic Active Earth Pressure on Walls with Bilinear Backface using Limit Equilibrium Method Seismic Passive Earth Pressure Behind Non-vertical Retaining Wall using Limit Equilibrium Method Conclusions Introduction to Pseudo-dynamic Approach and Upper Bound Limit Analysis Pseudo-dynamic Approach Pseudo-static Approach Pseudo-dynamic Approach The dynamic loading The time and phase induced by earthquake is difference due to finite considered as time primary and shear wave independent, which velocity can be considered ultimately assumes that the magnitude and phase of acceleration is uniform throughout the soil mass Generally does not consider Considers the amplification of the amplification of excitation vibration which takes place towards the ground surface For a Sinusoidal Base Shaking, the Acceleration at any Depth z below the Ground Surface and Time t Mass of the Shaded Element m(z) and Total Weight of the Failure Wedge W Total Horizontal Seismic Inertia Force Qh(t) Where, l = wavelength of the shear wave = TVs Total Vertical Seismic Inertia Force Qv(t) Where, h = wavelength of the primary wave = TVp Upper Bound Limit Analysis Theorem: If a compatible mechanism of plastic deformation v p* , ij p* , is i assumed, which satisfies the condition v p* = i 0 on the displacement boundary Su; then the loads Ti, Fi determined by equating the rate at which the external forces do work to the rate of internal dissipation of energy will be either higher or equal to the actual limit load. Equation p* p* p* ij dV Ti v i dS Fi v i dV p* ij V S V v displacement rate pij* = plastic strain rate compatible with p* = i displacement rate = stress tensor associated with plastic strain p* ij rate Ti = external force on the surface S Fi = body forces in a body of volume V Seismic Bearing Capacity of Strip Footing using Upper Bound Limit Analysis Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123. b Pu xPu A Footing a B b Qv1 Qv2 U21 Qh1 z Qh2 f W1 f ah = faahg D f W2 z U1 U2 z dz dz C Vs, Vp ah = ahg (a) U2 U21 (a b) U1 (b) Collapse mechanism and velocity hodograph Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123. Variation of NE with ah and av for different values of f with H/l = 0.3, H/h = 0.16 for (a) fa = 1.0, (b) fa = 1.2 Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123. 40 fafa= = 1.01.0 fafa= = 1.21.2 faf= = 1.41.4 a faf= = 1.61.6 a 30 faf= = 1.81.8 a faf= = 2.02.0 a NE 20 10 0 0 0.1 0.2 ah 0.3 Effect of soil amplification on NE for different values of ah with f = 30o, av = 0.5ah, H/l = 0.3, H/h = 0.16 Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123. 0.4 Comparison of NE with fa = 1.0, av = 0.0, H/l = 0.3 and H/h = 0.16 for (a) f = 30o, (b) f = 40o Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123. Seismic Vertical Uplift Capacity of Horizontal Strip Anchors using Upper Bound Limit Analysis Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. Failure mechanism and associated forces Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. Variation of fE with ah for different values of fa, and av with f = 20o, H/l = 0.3 and H/h = 0.16 Pu f E = 2 b H = b Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. 10 fa = 1.0 (upper most) 1.2 1.4 1.6 1.8 2.0 (lower most) 9 fE 8 7 6 5 0.0 0.1 0.2 0.3 0.4 ah Effect of soil amplification on f for different values of a with f = 30o, av = 0.5ah, = 3.0, H/l = 0.3 and H/h = 0.16 Fig. 5. Effect of soil amplification on fE for different values of E ah with f = 30o, av = 0.5ah, = 3.0, H/l = 0.3 andh H/h = 0.16. Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. 10 av/ah = 0.00 (upper most) 0.25 0.50 0.75 1.00 (lower most) 9 fE 8 7 6 5 0 0.1 0.2 ah 0.3 0.4 o, f= 0.16. Fig. of 6. Effect av onf fE for different values of ah values with f = 30o, fof 3.0, H/lf= 0.3 and H/h Effect av ofon different ah =with = 30 a = 1.4, E for a = 1.4, = 3.0, H/l = 0.3 and H/h = 0.16 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. Geometry of the failure patterns for different values of f with fa = 1.4, = 3.0, av = 0.5ah, H/l = 0.3 and H/h = 0.16 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. Comparison of fE for fa = 1.0, av = 0.0, = 3.0, H/l = 0.3 and H/h = 0.16 f 30o 40o 50o ah fE Present analysis Kumar (2001) Choudhury & Subba Rao (2004) 0.0 1.577 1.577 1.071 0.1 1.571 1.566 1.057 0.2 1.553 1.544 1.028 0.3 1.520 1.499 0.986 0.0 1.839 1.839 1.543 0.1 1.835 1.832 1.457 0.2 1.821 1.815 1.386 0.3 1.798 1.786 1.286 0.0 2.192 2.192 1.986 0.1 2.189 2.187 1.828 0.2 2.179 2.174 1.657 0.3 2.163 2.155 1.514 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. Seismic Active Earth Pressure Behind Non-vertical Retaining Wall using Limit Equilibrium Method Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. Failure mechanism and associated forces Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. 0.8 0.8 q = 10o 5o 0o -5o -10o (lower most) 0.7 0.6 Kae 1.0 q = 10o 5o 0o -5o -10o (lower most) 0.7 0.6 Kae 0.8 0.7 Kae 0.6 0.5 0.5 0.5 0.4 0.4 q = 10o 5o 0o -5o -10o (lower most) 0.9 0.4 0.3 0.3 d = 0.0 0.2 0.0 0.1 0.2 ah 0.3 d = 0.5f 0.2 0.0 0.4 0.1 0.2 ah 0.3 0.3 d=f 0.2 0.0 0.4 0.1 0.2 ah 0.3 0.4 (a) 0.8 1.0 q = 10o 5o 0o -5o -10o (lower most) 0.7 0.6 Kae 1.4 q = 10o 5o 0o -5o -10o (lower most) 0.8 1.0 Kae Kae 0.6 0.5 q = 10o 5o 0o -5o -10o (lower most) 1.2 0.8 0.6 0.4 0.4 0.4 0.3 d = 0.0 0.2 0.0 0.1 0.2 ah 0.3 0.4 d = 0.5f 0.2 0.0 0.1 0.2 ah 0.3 0.4 d=f 0.2 0.0 0.1 0.2 ah 0.3 (b) Variation of Kofaeactive withpressure ah for f = 30Koae, with av =ah0.5a =0.5a 0.3h, and H/h 0.16 (a)(a)fafa == 1.0, 1.0, fa = 1.4 o, a = Fig. 2. Variation coefficient for f =h,30H/l H/l = 0.3 and=H/h = 0.16 (b)(b) fa = 1.4. v Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. 0.4 0.0 fa = 1.0 fa=1.0 0.1 fa = 1.2 fa=1.2 fa = 1.4 fa=1.4 0.2 fa = 1.6 fa=1.6 fa = 1.8 1.8 fa 0.3 0.4 z/H 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 pae/H Fig. 3. Normalized seismic activepressure earth pressure distribution for different values fa Normalized seismic active earth distribution forofdifferent values of fa o o (f = 30 , d = 0.5f, q = 10 , ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16). (f = 30o, d = 0.5f, q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. 0.0 f = 20o phi=20 f = 30o phi=30 0.1 f = 40o phi=40 f = 50o phi=50 0.2 0.3 0.4 z/H 0.5 0.6 0.7 0.8 0.9 1.0 0 0.1 0.2 0.3 0.4 pae/H 0.5 0.6 0.7 0.8 Normalized seismic active earth pressure distribution for different values of f Fig. 4. Normalized seismic active earth pressure distribution for different values of f (d = 0.5f, q = 10o,(da= h0.5f, = q0.2, ah v= 0.2, = 0.5a H/l = H/h 0.3, H/h = 10o, a av = 0.5a = 0.3, = 0.16, fa = = 1.4).0.16, fa = 1.4) hh,, H/l Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. 0.0 q = -15o theta=-15 0.1 q = -10o theta=-10 q = -5o theta=-5 0.2 q = 0o theta=0 theta=5 q = 5o 0.3 q = 10o theta=10 theta=15 q = 15o 0.4 z/H 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 pae/H Fig. 5. Normalized seismic earth pressure distribution for different of q Normalized seismic active earthactive pressure distribution forvalues different values of q o, d = 0.5f, a = 0.2, a = 0.5a , H/l = 0.3, H/h = 0.16, f = 1.4) (f = 30 a (f = 30o, d = 0.5f, ah = 0.2,h av = v0.5ahh , H/l = 0.3, H/h = 0.16, fa = 1.4) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. 0.0 d = 0 del=0 phi=20, f = 20o f = 30o 0.1 d = 0.5f phi=20, del=0.5phi phi=20, d = f del=phi 0.2 phi=30, del=0 0.3 phi=30, del=0.5phi phi=30, del=phi 0.4 z/H 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 pae/H Fig. 6.seismic Normalized seismic active earth pressure distribution for different values of f and for d Normalized active earth pressure distribution different o (q = 10 , ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16, fa = 1.4) values of f and d (q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16, fa = 1.4) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. Geometry of the failure patterns for different values of ah with fa = 1.4, q = 10o, d = 0.5f, av = 0.5ah, H/l = 0.3 and H/h = 0.16 Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. Comparison of Kae for av = 0.5ah, H/l = 0.3, H/h = 0.16 and fa = 1.0 Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. Seismic Active Earth Pressure on Walls with Bilinear Backface using Limit Equilibrium Method Computers and Geotechnics (Elsevier Pub.), (In press). Kae1 = 2Pae1 ( t ) H12 K ae 2 = 2 Pae 2 ( t ) H2 Failure mechanism and associated forces Computers and Geotechnics (Elsevier Pub.), (In press). θ1 = 90 (upper most) 75 0.8 60 45 0.6 0.2 0.4 δ1 = δ2 = 0 0.2 ah 0.3 0.4 0.1 0.2 ah 0.3 0.4 Kae2 0.4 δ1 = δ2 = 0 0.8 0.2 ah 0.3 0.4 0.1 0.2 ah 0.3 0.4 1.2 0.8 0.4 0.2 0.0 δ1 = δ2 = f 2.4 θ = 120 (upper most) 2 110 2.0 100 90 1.6 θ2 = 120 (upper most) 110 1.2 100 1.0 90 0.6 0.1 0.0 0.0 1.4 0.6 0.2 0.0 0.2 δ1 = δ2 = 0.5f Kae2 0.1 0.0 0.0 0.6 0.4 0.2 θ2 = 120 (upper most) 110 1.0 100 90 0.8 Kae2 θ1 = 90 (upper most) 75 1.0 60 45 0.8 θ1 = 90 (upper most) 75 0.8 60 45 0.6 Kae1 0.4 0.0 0.0 1.2 1.0 Kae1 Kae1 1.0 δ1 = δ2 = 0.5f 0.1 0.2 ah 0.3 0.4 0.4 0.0 0.0 δ1 = δ2 = f 0.1 0.2 ah 0.3 0.4 Variation of active pressure coefficients Kae1 and Kae2 with ah for f = 30˚, H1/H = 1/3, av = 0.5ah, = 1.4, H/TVs = 0.3 and H/TVp = 0.16: (a) θ2 =100˚ (b) θ1 = 75˚ Computers and Geotechnics (Elsevier Pub.), (In press). fa Variation of Kae1 and Kae2 for different combinations of q1 and q2 with f = 30˚, d1 = d2 = 0.5f, H1/H = 1/3, av = 0.5ah, fa = 1.4, H/TVs = 0.3 and H/TVp = 0.16 (a) Kae1 (b) Kae2 Computers and Geotechnics (Elsevier Pub.), (In press). 0.0 fa = 1.0 0.1 fa = 1.2 0.2 fa = 1.4 fa = 1.6 0.3 fa = 1.8 z/H 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 pae /H Normalized pae distribution for different fa (f = 30˚, d1 = d2 = 0.5f, θ1 = 75˚, θ2 = 100˚, H1/H =1/3, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16) Computers and Geotechnics (Elsevier Pub.), (In press). 0.0 f = 20 f = 30 f = 40 f = 50 0.1 0.2 0.3 z/H 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 pae /H Normalized pae distribution for different f (d1 = d2 = 0.5f, θ1 = 75˚, θ2 = 100˚, H1/H =1/3, fa = 1.4, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16) Computers and Geotechnics (Elsevier Pub.), (In press). 0.0 0.1 q1 = 60, q2 = 90 q1 = 70, q2 = 100 0.2 q = 80, q = 110 1 0.3 2 q1 = 90, q2 = 120 z/H 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 pae /H 0.6 0.7 0.8 0.9 Normalized pae distribution for different θ1 and θ2 (f = 30o, d1 = d2 = 0.5f, H1/H =1/3, fa = 1.4, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16) Computers and Geotechnics (Elsevier Pub.), (In press). 0.0 f = 20° f = 30° 0.1 d1 = d2 = 0 d = d = 0.5f 1 0.2 2 d1 = d2 = f 0.3 z/H 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 pae /H 0.8 Normalized pae distribution for different wall friction and f (θ1 = 75˚, θ2 = 100˚, H1/H =1/3, fa = 1.4, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16) Computers and Geotechnics (Elsevier Pub.), (In press). Comparison of Kae1 and Kae2 for H1/H = 1/2, f = 36˚, d1 = d2 = 18˚, θ1 = 75˚, θ2 = 105˚, av = 0.5ah and fa =1.0 Present analysis H/TVs = 0.3 H/TVs = 0.4 H/TVs = 0.5 H/TVp = 0.16 H/TVp = 0.21 H/TVp = 0.27 Kae1 Kae2 Kae1 Kae2 Kae1 Kae2 Kae1 Kae2 0.0 0.147 0.260 0.147 0.260 0.147 0.260 0.147 0.260 0.1 0.201 0.318 0.199 0.312 0.196 0.305 0.204 0.307 0.2 0.266 0.385 0.262 0.371 0.256 0.354 0.273 0.355 0.3 0.344 0.462 0.337 0.437 0.328 0.409 0.353 0.403 0.4 0.435 0.551 0.426 0.514 0.416 0.471 0.447 0.453 0.5 0.544 0.655 0.535 0.601 0.524 0.538 0.556 0.504 ah Computers and Geotechnics (Elsevier Pub.), (In press). Greco [8] Seismic Passive Earth Pressure Behind Non-vertical Retaining Wall using Limit Equilibrium Method Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. Failure mechanism and associated forces Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. 4.0 8.0 q = -10o -5o 0o 5o 10o (lower most) 3.5 3.0 q = -10o -5o 0o 5o 10o (lower most) 7.0 6.0 Kpe Kpe 25.0 5.0 15.0 Kpe 4.0 2.5 q = -10o -5o 0o 5o 10o (lower most) 20.0 10.0 3.0 2.0 5.0 2.0 d = 0.0 1.5 d = 0.5f d=f 1.0 0.0 0.1 0.2 ah 0.3 0.4 0.0 0.0 0.1 0.2 ah 0.3 0.4 0.0 0.1 0.2 ah Variation of passive pressure coefficient Kpe with ah for f = 30o, av = 0.5ah, H/l = 0.3 and H/h = 0.16 Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. 0.3 0.4 0.0 phi=20 f = 20o 0.1 phi=30 f = 30o phi=40 f = 40o 0.2 phi=50 f = 50o 0.3 0.4 z/H 0.5 0.6 0.7 0.8 0.9 1.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 ppe/H Normalized ppe distribution for different values of f (d = 0.5f, q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16) Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. 16.0 0.0 q = -15o theta=-15 q = -10o theta=-10 0.1 theta=-5 q = -5o q = 0o theta=0 0.2 q = 5o theta=5 0.3 theta=10 q = 10o theta=15 q = 15o 0.4 z/H 0.5 0.6 0.7 0.8 0.9 1.0 0.0 1.0 2.0 3.0 4.0 ppe/H 5.0 6.0 7.0 Normalized ppe distribution for different values of q (f = 30o, d = 0.5f, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16) Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. 8.0 0.0 d=0 del=0 0.1 del=0.25phi d = 0.25f del=0.5phi d = 0.5f 0.2 d = 0.75f del=0.75phi d=f del=phi 0.3 0.4 z/H 0.5 0.6 0.7 0.8 0.9 1.0 0.0 1.0 2.0 3.0 4.0 ppe/H Normalized ppe distribution for different values of d (f = 30o, q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16) Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. 5.0 Comparison of Kpe for d = 0.5f, q = 0o, av = 0.0, H/l = 0.3 and H/h = 0.16 f 25o 30o 35o 40o ah Kpe Present analysis Chang (1981) Soubra (2000) Lancellotta (2007) 0.0 3.55 3.45 3.43 3.10 0.1 3.26 2.89 3.15 2.86 0.2 2.96 2.74 2.85 2.62 0.3 2.63 2.38 2.50 2.26 0.0 4.98 4.64 4.69 4.29 0.1 4.60 4.29 4.35 3.93 0.2 4.21 3.93 3.99 3.57 0.3 3.80 3.45 3.59 3.21 0.0 7.36 6.67 6.67 5.71 0.1 6.84 6.19 6.24 5.48 0.2 6.31 5.71 5.78 5.00 0.3 5.76 5.24 5.29 4.52 0.0 11.77 10.00 9.99 8.33 0.1 11.00 9.29 9.40 7.86 0.2 10.21 8.57 8.79 7.26 0.3 9.41 8.10 8.15 6.67 Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. Comparison of Kpe for d = 0.5f, q = 10o, av = 0.5ah, H/l = 0.3 and H/h = 0.16 f d 0 20o 0.5f f 0 30o 0.5f f ah Kpe Present analysis MononobeOkabe method Caquot and Kerisel (1948) Zhu and Qian (2000) 0.0 1.84 1.84 1.74 1.83 0.1 1.66 1.64 - - 0.2 1.45 1.40 - - 0.0 2.27 2.27 - 2.26 0.1 2.00 1.96 - - 0.2 1.70 1.62 - - 0.0 2.86 2.86 2.57 2.66 0.1 2.47 2.42 - - 0.2 2.04 1.93 - - 0.0 2.54 2.54 2.33 2.51 0.2 2.07 2.02 - - 0.4 1.53 1.35 - - 0.0 3.80 3.80 - 3.73 0.2 2.96 2.85 - - 0.4 2.00 1.70 - - 0.0 6.45 6.45 4.98 5.20 0.2 4.79 4.58 - - 0.4 2.96 2.43 - - Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. Conclusions Strip Footing The magnitude of NE decreases with increase in soil amplification, shear and primary wave velocities, which can not be predicted by the existing pseudo- static approach In the upper-bound solution, for higher values of f, a significant increase in NE was observed at lower value of ah Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123. Horizontal Strip Anchor The values of fE were found to decrease extensively with increase in both ah and av, and soil amplification In presence of horizontal and vertical earthquake acceleration, the present values were found to be the highest In presence of amplification of vibration, no significant difference between present values and the existing pseudo-static values was found except for higher values of embedment ratio and ah Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351. Active Pressure on Cantilever Wall In presence of q, the active earth pressure first decreases with increase in d up to z/H = 0.3 and then increases significantly at higher depth with increase in d for a particular value of f The seismic active earth pressure distribution was found to be non-linear behind the wall in pseudodynamic analysis The non-linearity of active earth pressure distribution increases with the increase in seismicity, which causes the point of application of total active thrust to be shifted Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123. Wall with Bilinear Backface It was found that the magnitude of seismic active earth pressures for upper and lower parts of the wall increases with an increase in the horizontal earthquake acceleration coefficient ah and the wall inclinations θ1 and θ2, respectively Unlike the pseudo-static analysis, the seismic active earth pressure distribution was found to be nonlinear behind the wall in pseudo-dynamic analysis and the nonlinearity of seismic active earth pressure distribution increases with an increase in seismicity, which causes the point of application of the total active thrust to be shifted Computers and Geotechnics (Elsevier Pub.), (In press). Passive Pressure on Cantilever Wall It was found that the magnitude of seismic passive earth pressure decreases with the increase in the values of wall inclination q, horizontal and vertical earthquake acceleration coefficients In presence of q, the passive earth pressure increases with the increase in d for a particular value of f The present analysis adopted the Coulomb failure mechanism, which generally overestimates the passive pressure coefficient Kpe in case of a rough retaining wall and the error generated by the Coulomb theory increases as the wall inclination increases in the inward direction Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703. "The concern for man and his destiny must be the chief interest of all technical efforts. Never forget this among your equations and diagrams“ -Albert Einstein.