1. Seismic Analysis of Some Geotechnical Problems – Pseudo-dynamic Approach Seismic Analysis of Some Geotechnical Problems – Pseudo-dynamic Approach Dr. Priyanka Ghosh Assistant Professor Dept. of Civil Engineering Indian Institute of Technology, Kanpur INDIA

2. Organisation

3.  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

4. Introduction to Pseudo-dynamic Approach and Upper Bound Limit Analysis

5. Pseudo-dynamic Approach Pseudo-static ApproachPseudo-dynamic Approach The dynamic loading induced by earthquake is considered as time independent, which ultimately assumes that the magnitude and phase of acceleration is uniform throughout the soil mass The time and phase difference due to finite primary and shear wave velocity can be considered Generally does not consider the amplification of vibration which takes place towards the ground surface Considers the amplification of excitation

6. For a Sinusoidal Base Shaking, the Acceleration at any Depth z below the Ground Surface and Time t

7. Mass of the Shaded Element m(z) and Total Weight of the Failure Wedge W Total Horizontal Seismic Inertia Force Q h (t) Where,  wavelength of the shear wave = TV s

8. Total Vertical Seismic Inertia Force Q v (t) Where,  wavelength of the primary wave = TV p

9. Upper Bound Limit Analysis Theorem: If a compatible mechanism of plastic deformation,, is assumed, which satisfies the condition = 0 on the displacement boundary S u ; then the loads T i, F i 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.

10. Equation = displacement rate = plastic strain rate compatible with displacement rate = stress tensor associated with plastic strain rate T i = external force on the surface S F i = body forces in a body of volume V

11. Seismic Bearing Capacity of Strip Footing using Upper Bound Limit Analysis Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.

12. Footing PuPu PuPu B C D   Q h1 Q v1 W1W1 U1U1    U 21 U2U2 Q h2 Q v2 W2W2 z z dz z V s, V p a h =  h g a h = f a  h g (a) A b  U2U2 U 21 U1U1 (b) Collapse mechanism and velocity hodograph Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.

13. Variation of N  E with  h and  v for different values of  with H/ = 0.3, H/  = 0.16 for (a) f a = 1.0, (b) f a = 1.2 Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.

14. Effect of soil amplification on N  E for different values of  h with  = 30 o,  v = 0.5  h, H/ = 0.3, H/  = 0.16 NENE hh f a = 1.0 f a = 1.2 f a = 1.4 f a = 1.6 f a = 1.8 f a = 2.0 Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.

15. Comparison of N  E with f a = 1.0,  v = 0.0, H/ = 0.3 and H/  = 0.16 for (a)  = 30 o, (b)  = 40 o Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.

16. 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.

17. Failure mechanism and associated forces Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.

18. Variation of f  E with  h for different values of f a,  and  v with  = 20 o, H/ = 0.3 and H/  = 0.16 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.

19. Fig. 5. Effect of soil amplification on f  E for different values of  h with  = 30 o,  v = 0.5  h,  = 3.0, H/ = 0.3 and H/  = 0.16. f a = 1.0 (upper most) 1.2 1.4 1.6 1.8 2.0 (lower most) fEfE hh Effect of soil amplification on f  E for different values of  h with  = 30 o,  v = 0.5  h,  = 3.0, H/ = 0.3 and H/  = 0.16 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.

20.  v /  h = 0.00 (upper most) 0.25 0.50 0.75 1.00 (lower most) fEfE hh Fig. 6. Effect of  v on f  E for different values of  h with  = 30 o, f a = 1.4,  = 3.0, H/ = 0.3 and H/  = 0.16. Effect of  v on f  E for different values of  h with  = 30 o, f a = 1.4,  = 3.0, H/ = 0.3 and H/  = 0.16 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.

21. Geometry of the failure patterns for different values of  with f a = 1.4,  = 3.0,  v = 0.5  h, H/ = 0.3 and H/  = 0.16 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.

22. hh fEfE Present analysisKumar (2001)Choudhury & Subba Rao (2004) 30 o 0.01.577 1.071 0.11.5711.5661.057 0.21.5531.5441.028 0.31.5201.4990.986 40 o 0.01.839 1.543 0.11.8351.8321.457 0.21.8211.8151.386 0.31.7981.7861.286 50 o 0.02.192 1.986 0.12.1892.1871.828 0.22.1792.1741.657 0.32.1632.1551.514 Comparison of f  E for f a = 1.0,  v = 0.0,  = 3.0, H/  = 0.3 and H/  = 0.16 Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.

23. Seismic Active Earth Pressure Behind Non-vertical Retaining Wall using Limit Equilibrium Method Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

24. Failure mechanism and associated forces Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

25. hh hh hh K ae  = 10 o 5 o 0 o -5 o -10 o (lower most)  = 10 o 5 o 0 o -5 o -10 o (lower most)  = 10 o 5 o 0 o -5 o -10 o (lower most)  = 0.0  = 0.5   =  Fig. 2. Variation of active pressure coefficient K ae with  h for  = 30 o,  v = 0.5  h, H/ = 0.3 and H/  = 0.16 (a) f a = 1.0, (b) f a = 1.4. hh hh hh K ae  = 10 o 5 o 0 o -5 o -10 o (lower most)  = 10 o 5 o 0 o -5 o -10 o (lower most)  = 10 o 5 o 0 o -5 o -10 o (lower most)  = 0.0  = 0.5   =  (a) (b) Variation of K ae with  h for  = 30 o,  v = 0.5  h, H/ = 0.3 and H/  = 0.16 (a) f a = 1.0, (b) f a = 1.4 Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

26. p ae /  H z/H Fig. 3. Normalized seismic active earth pressure distribution for different values of f a (  = 30 o,  = 0.5 ,  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16). f a = 1.0 f a = 1.4 f a = 1.2 f a = 1.6 f a = 1.8 Normalized seismic active earth pressure distribution for different values of f a (  = 30 o,  = 0.5 ,  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

27.  = 20 o p ae /  H z/H Fig. 4. Normalized seismic active earth pressure distribution for different values of  (  = 0.5 ,  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16, f a = 1.4).  = 30 o  = 40 o  = 50 o Normalized seismic active earth pressure distribution for different values of  (  = 0.5 ,  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16, f a = 1.4) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

28.  = 0 o p ae /  H z/H Fig. 5. Normalized seismic active earth pressure distribution for different values of  (  = 30 o,  = 0.5 ,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16, f a = 1.4)  = 5 o  = 10 o  = 15 o  = -15 o  = -10 o  = -5 o Normalized seismic active earth pressure distribution for different values of  (  = 30 o,  = 0.5 ,  h = 0.2,  v = 0.5  h, H/  = 0.3, H/  = 0.16, f a = 1.4) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

29.  = 0 p ae /  H z/H Fig. 6. Normalized seismic active earth pressure distribution for different values of  and  (  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16, f a = 1.4)  = 20 o  = 30 o  = 0.5   =  Normalized seismic active earth pressure distribution for different values of  and  (  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16, f a = 1.4) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

30. Geometry of the failure patterns for different values of  h with f a = 1.4,  = 10 o,  = 0.5 ,  v = 0.5  h, H/ = 0.3 and H/  = 0.16 Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

31. Comparison of K ae for  v = 0.5  h, H/ = 0.3, H/  = 0.16 and f a = 1.0 Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

32. Seismic Active Earth Pressure on Walls with Bilinear Backface using Limit Equilibrium Method Computers and Geotechnics (Elsevier Pub.), (In press).

33. Failure mechanism and associated forces

34. Variation of active pressure coefficients K ae1 and K ae2 with  h for  = 30˚, H 1 /H = 1/3,  v = 0.5  h, f a = 1.4, H/TV s = 0.3 and H/TV p = 0.16: (a) θ 2 =100˚ (b) θ 1 = 75˚ θ 1 = 90  (upper most) 75  60  45  δ 1 = δ 2 = 0.5  θ 1 = 90  (upper most) 75  60  45  δ 1 = δ 2 =  θ 1 = 90  (upper most) 75  60  45  δ 1 = δ 2 = 0 θ 2 = 120  (upper most) 110  100  90  δ 1 = δ 2 = 0 δ 1 = δ 2 = 0.5  θ 2 = 120  (upper most) 110  100  90  δ 1 = δ 2 =  θ 2 = 120  (upper most) 110  100  90  Computers and Geotechnics (Elsevier Pub.), (In press).

35. Variation of K ae1 and K ae2 for different combinations of  1 and  2 with  = 30˚,  1 =  2 = 0.5 , H 1 /H = 1/3,  v = 0.5  h, f a = 1.4, H/TV s = 0.3 and H/TV p = 0.16 (a) K ae1 (b) K ae2 Computers and Geotechnics (Elsevier Pub.), (In press).

36. Normalized p ae distribution for different f a (  = 30˚,  1 =  2 = 0.5 , θ 1 = 75˚, θ 2 = 100˚, H 1 /H =1/3,  h = 0.2,  v = 0.5  h, H/TV s = 0.3 and H/TV p = 0.16)

37. Computers and Geotechnics (Elsevier Pub.), (In press). Normalized p ae distribution for different  (  1 =  2 = 0.5 , θ 1 = 75˚, θ 2 = 100˚, H 1 /H =1/3, f a = 1.4,  h = 0.2,  v = 0.5  h, H/TV s = 0.3 and H/TV p = 0.16)

38. Computers and Geotechnics (Elsevier Pub.), (In press). Normalized p ae distribution for different θ 1 and θ 2 (  = 30 o,  1 =  2 = 0.5 , H 1 /H =1/3, f a = 1.4,  h = 0.2,  v = 0.5a h, H/TV s = 0.3 and H/TV p = 0.16)

39. Computers and Geotechnics (Elsevier Pub.), (In press).  = 20°  = 30° Normalized p ae distribution for different wall friction and  (θ 1 = 75˚, θ 2 = 100˚, H 1 /H =1/3, f a = 1.4,  h = 0.2,  v = 0.5  h, H/TV s = 0.3 and H/TV p = 0.16)

40. Computers and Geotechnics (Elsevier Pub.), (In press). hh Present analysis Greco [8] H/TV s = 0.3H/TV s = 0.4H/TV s = 0.5 H/TV p = 0.16H/TV p = 0.21H/TV p = 0.27 K ae1 K ae2 K ae1 K ae2 K ae1 K ae2 K ae1 K ae2 0.00.1470.2600.1470.2600.1470.2600.1470.260 0.10.2010.3180.1990.3120.1960.3050.2040.307 0.20.2660.3850.2620.3710.2560.3540.2730.355 0.30.3440.4620.3370.4370.3280.4090.3530.403 0.40.4350.5510.4260.5140.4160.4710.4470.453 0.50.5440.6550.5350.6010.5240.5380.5560.504 Comparison of K ae1 and K ae2 for H 1 /H = 1/2,  = 36˚,  1 =  2 = 18˚, θ 1 = 75˚, θ 2 = 105˚,  v = 0.5  h and f a =1.0

41. 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.

42. Failure mechanism and associated forces Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

43. Variation of passive pressure coefficient K pe with  h for  = 30 o,  v = 0.5  h, H/ = 0.3 and H/  = 0.16 hh hh hh K pe  = -10 o -5 o 0 o 5 o 10 o (lower most)  = -10 o -5 o 0 o 5 o 10 o (lower most)  = -10 o -5 o 0 o 5 o 10 o (lower most)  = 0.0  = 0.5  =  Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

44. Normalized p pe distribution for different values of  (  = 0.5 ,  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16)  = 20 o p pe /  H z/H  = 30 o  = 40 o  = 50 o Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

45.  = 0 o p pe /  H z/H  = 5 o  = 10 o  = 15 o  = -5 o  = -10 o  = -15 o Normalized p pe distribution for different values of  (  = 30 o,  = 0.5 ,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16) Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

46.  = 0 p pe /  H z/H  = 0.25   =   = 0.5   = 0.75  Normalized p pe distribution for different values of  (  = 30 o,  = 10 o,  h = 0.2,  v = 0.5  h, H/ = 0.3, H/  = 0.16) Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

47. Comparison of K pe for  = 0.5  = 0 o,  v = 0.0, H/ = 0.3 and H/  = 0.16 hh K pe Present analysis Chang (1981) Soubra (2000)Lancellotta (2007) 25 o 0.03.553.45 3.43 3.10 0.13.262.89 3.15 2.86 0.22.962.74 2.85 2.62 0.32.632.38 2.50 2.26 30 o 0.04.984.64 4.69 4.29 0.14.604.29 4.35 3.93 0.24.213.93 3.99 3.57 0.33.803.45 3.59 3.21 35 o 0.07.366.67 5.71 0.16.846.19 6.24 5.48 0.26.315.71 5.78 5.00 0.35.765.24 5.29 4.52 40 o 0.011.7710.00 9.99 8.33 0.111.009.29 9.40 7.86 0.210.218.57 8.79 7.26 0.39.418.10 8.15 6.67 Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

48. hh K pe Present analysis Mononobe- Okabe method Caquot and Kerisel (1948) Zhu and Qian (2000) 20 o 0 0.01.84 1.741.83 0.11.661.64-- 0.21.451.40-- 0.5  0.02.27 -2.26 0.12.001.96-- 0.21.701.62--  0.02.86 2.572.66 0.12.472.42-- 0.22.041.93-- 30 o 0 0.02.54 2.332.51 0.22.072.02-- 0.41.531.35-- 0.5  0.03.80 -3.73 0.22.962.85-- 0.42.001.70--  0.06.45 4.985.20 0.24.794.58-- 0.42.962.43-- Comparison of K pe for  = 0.5  = 10 o,  v = 0.5  h, H/ = 0.3 and H/  = 0.16 Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

49. Conclusions

50.  The magnitude of N  E 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 , a significant increase in N  E was observed at lower value of  h Strip Footing Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.

51.  The values of f  E were found to decrease extensively with increase in both  h and  v, 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  h Horizontal Strip Anchor Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.

52.  In presence of , the active earth pressure first decreases with increase in  up to z/H = 0.3 and then increases significantly at higher depth with increase in  for a particular value of   The seismic active earth pressure distribution was found to be non-linear behind the wall in pseudo- dynamic 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 Active Pressure on Cantilever Wall Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.

53.  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  h and the wall inclinations θ 1 and θ 2, 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 Wall with Bilinear Backface Computers and Geotechnics (Elsevier Pub.), (In press).

54.  It was found that the magnitude of seismic passive earth pressure decreases with the increase in the values of wall inclination , horizontal and vertical earthquake acceleration coefficients  In presence of , the passive earth pressure increases with the increase in  for a particular value of   The present analysis adopted the Coulomb failure mechanism, which generally overestimates the passive pressure coefficient K pe 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 Passive Pressure on Cantilever Wall Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.

55. "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.