Seismic Earth Pressures under Restrained Condition

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1 Seismic Earth Pressures under Restrained Condition Fred Yi, PhD, PE Chief Engineer C.H.J., Incorporated

2 Table of Contents Introduction Review of Previous Studies Purpose of This Study Pseudostatic Numerical Simulation FEM Modeling Sample Results Seismic Earth Pressures of Restrained Walls Pseudostatic Seismic Coefficient, k h Static Design vs. Seismic Design Conclusions & Recommendations

3 Introduction Seismic Earth Pressure (SEP) a classic but unresolved problem Studies since 1920 (Okabe, 1926, Mononobe & Matsuo, 1929) Seismic earth pressure for non-yielding wall (Wood, 1973) Seismically Induced Earth Pressures for LRFD Seismic Design of Retaining Structures - Transportation Research Board s 4 years & $850k project since 2010

4 TRB Research Project

5 Introduction The fact Lew, M., Sitar, N. and Al Atik, L. (2010). Seismic Earth Pressures: Fact or Fiction. Proceedings of the Earth Retention Conference 3, Geo-Institute of ASCE, Bellevue, WA.

6 Introduction Main unresolved problems Existing SEP formula may be too conservative SEP distributions normal triangular, inverted triangular, parabolic Seismic vs. pseudostatic confusion in pseudostatic seismic coefficient, k h

7 REVIEW OF PREVIOUS STUDIES

8 Review of Previous Studies Cantilever Wall (Flexible / Yielding) Okabe (1924), Mononobe & Matsuo (1929) Seed & Whitman (1970) Restrained Wall (Stiff / Non-yielding) Wood (1973) Ostadan (1998, 2004) Most recent Atik & Sitar (2007, 2008, 2010) Maleki & Mahjoubi (2010)

9 Mononobe-Okabe (M-O) Method Okabe (1926), Mononobe & Matsuo (1929)

10 Seed & Whitman (1970) or Φ 35⁰ Φ=38⁰ Seed & Whitman (1970) k h M-O K Φ=30º AE Ka+3/4k h M-O K Φ=33º AE Ka+3/4k h M-O K Φ=35º AE Ka+3/4k h M-O K Φ=38º AE Ka+3/4k h by Fred Yi, 2/16/2011

11 Wood (1973)

12 Ostadan (1998, 2004)

13 Atik & Sitar (2007, 2008, 2010)

14 Atik & Sitar (2007, 2008, 2010)

15 Maleki & Mahjoubi (2010)

16 Purpose of This Study This study intends to solve Effects of soil strength parameters Effects of base conditions Relationship between k H and PGA A simple equation for engineers

17 PSEUDOSTATIC NUMERICAL SIMULATION

18 Pseudostatic Simulation by FEM Soil property Elastoplastic Mohr-Coulomb failure criteria (c=0, Φ) Boundary conditions Rigid base model Wall movement = 0 & deflection = 0 Non-rigid base model Wall movement & deflection = 0 Wall movement 0, deflection = 0

19 FEM model Rigid base, Restrained Rigid Wall Fixed in X 5H Fixed in X Gravity H k H Fixed in XY Changed to Fixed in Y

20 FEM model Non-Rigid base, Restrained Rigid Wall Fixed in X Fixed in X Fixed in X 5H H Gravity k H Fixed in XY Changed to Fixed in Y

21 FEM model Non-Rigid base, Rigid Wall No rotation Fixed in X 5H Fixed in X H Gravity k H Fixed in XY Changed to Fixed in Y

22 FEM Results Rigid base, Restrained Rigid Wall Lateral Stress (psf) Passive EP At-rest EP Lateral Stress (psf)

23 FEM Results Non-Rigid base, Restrained Rigid Wall Lateral Stress (psf) Passive EP At-rest EP Lateral Stress (psf)

24 FEM Results Non-Rigid base, Rigid Wall Lateral Stress (psf) Passive EP At-rest EP Lateral Stress (psf)

25 FEM Results Non-Rigid base, Rigid Wall Lateral Stress (psf) Lateral Displacement (ft)

26 Seismic Earth Pressure Rigid base, Restrained Rigid Wall 0.7 Rigid Base P 0E /γh φ=30⁰ φ=33⁰ φ=35⁰ φ=38⁰ Seismic Coefficient, k H

27 Seismic Earth Pressure Non-Rigid base, Restrained Rigid Wall 0.7 Non-Rigid Base, Restrained Wall P 0E /γh φ=30⁰ φ=33⁰ φ=35⁰ φ=38⁰ Seismic Coefficient, k H

28 Seismic Earth Pressure Non-Rigid base, Rigid Wall 0.7 Non-Rigid Base, Rigid Wall P 0E /γh φ=30⁰ φ=33⁰ φ=35⁰ φ=38⁰ Seismic Coefficient, k H

29 Seismic Earth Pressure Rigid base, Restrained rigid wall Non-Rigid base, Restrained rigid wall Non-Rigid base, Rigid wall Wood (1973) 0.5 P 0E /γh Pseudostatic Seismic Coefficient, k H

30 Seismic Earth Pressures of Rigid Walls Rigid base, Restrained Rigid Wall Non-Rigid base, Restrained Rigid Wall Non-Rigid base, Rigid Wall

31 Distribution of Seismic Earth Pressure Rigid base, Restrained rigid wall Non-Rigid base, Restrained rigid wall Non-Rigid base, Rigid wall z/h kh=0.1 kh=0.2 kh=0.3 kh=0.4 kh=0.5 z/h kh=0.1 kh=0.2 kh=0.3 kh=0.4 kh=0.5 z/h kh=0.1 kh=0.2 kh=0.3 kh=0.4 kh= ( P 0E )/(P 0 ) H /1.02k H ( P 0E )/(P 0 ) H /1.17k H ( P 0E )/(P 0 ) H /1.15k H

32 Thrust Point of Seismic Earth Pressure Thrust Point, z/h Rigid base, Restrained rigid wall Non-Rigid base, Restrained rigid wall Non-Rigid base, Rigid wall Pseudostatic Seismic Coefficient, k H

33 PSEUDOSTATIC SEISMIC COEFFICIENT, k h

34 Seismic Coefficient (k H ) Confusion: k H =PGA Seed & Whitman (1970) FEMA 450 (k H =S DS /2.5) HCHRP Report 611 FHWA-NHI k H =PGA/2 ASSHTO LRFD Bridge Design Specification, 2010 Kramer (1996), k H =(1/3 ~ ½) PGA What should it be?

35 What should k h be? The magic number of 0.65 Idriss & Boulanger (2008), Soil Liquefaction During Earthquakes, EERI MNO-12

36 Data by Atik & Sitar (2008) 0.31 k h = 0.46PGA k h = 0.47PGA k h PGA K ae k H Atik & Sitar (2008), Experimental and Analytical Study of the Seismic Performance of Retaining Structures, University of California, Berkeley

37 Examination of an earthquake record Acceleration records Acceleration (m/s 2 ) Velocity time history Velocity (m/s) Displacement time history Distance (m) Time (sec) El Centro Earthquake Record (N-S) Time (sec) El Centro Earthquake Record (N-S) Time (sec) El Centro Earthquake Record (N-S)

38 Earthquake record, cyclic and pseudostatic Irregular time history of earthquake records Acceleration (m/s 2 ) Cyclic loading in laboratory testing Acceleration (m/s 2 ) Time (sec) Pseudostatic seismic coefficient Equivalent k H (m/s 2) Time (sec) El Centro Earthquake Record (N-S) Time (sec)

39 Considering Energy Conservation: t=0~5 s Original acceleration record Acceleration (m/s 2 ) Equivalent Harmonic cyclic wave Acceleration (m/s 2 ) Equivalent Pseudostatic load Equivalent k H (m/s 2) PGA=3.42m/s 2 Time (sec) El Centro Earthquake Record Amp=1.27m/s 2, T=0.556sec Time (sec) Time (sec) k H =0.81m/s 2

Equivalent cyclic wave Amp & Pseudostatic k H 4 0.4 3.5 0.35 Harmonic Pseudostatic 3 PGA 0.3 Acceleration (m/s 2) 2.5 2 1.

40 Equivalent cyclic wave Amp & Pseudostatic k H Harmonic Pseudostatic 3 PGA 0.3 Acceleration (m/s 2) Harmonic Pseudostatic Normalized Amplitude (*/PGA) Time (sec) Time (sec) El Centro Earthquake Record (N-S)

41 Examination of an earthquake record Acceleration records Acceleration (m/s 2 ) Distance (m) Velocity time history Velocity (m/s) Time (sec) Time (sec) Kobe Earthquake (1995), Type Displacement time history Time (sec) Kobe Earthquake (1995), Type111 Kobe Earthquake (1995), Type111

Equivalent cyclic wave Amp & Pseudostatic k H 3.5 0.6 3 0.5 Harmonic PGA Pseudostatic Acceleration (m/s 2) 2.5 2 1.

42 Equivalent cyclic wave Amp & Pseudostatic k H Harmonic PGA Pseudostatic Acceleration (m/s 2) Harmonic Pseudostatic Normalized Amplitude (/PGA) Time (sec) Time (sec) Kobe Earthquake (1995), Type111

43 Suggested k H PGA relationship Essential Structures Other Structures

44 STATIC DESIGN VS. SEISMIC DESIGN

45 Static Design vs. Seismic Design Factor of safety for static design Factor of safety for seismic design Therefore, a statically designed structure can withstand a seismic load of

46 Upper Bound of PGA covered by static design PGA upper bound (g) Essential Structures (Rigid Base) Others (Rigid Base) Essential Structures (Rigid Base) Others (NonRigid Base, restrained) Essential Structures (Rigid Base) Others (NonRigid Base, rigid wall) Frictional angular, φ (⁰)

47 CONCLUSIONS AND RECOMMENDATIONS

48 Conclusions The increment of SEP of rigid walls is independent of internal frictional angle of the backfill soils The ratio of the increment of SEP of rigid walls to γh 2 depends only on k h and base conditions The increment can be expressed as 1.02 & 1.17 Thrust point is lower than the middle point of the wall and can be conservatively taken as 0.45H K h is significantly lower than PGA and can be conservatively taken as β for essential structures

49 Recommendations Seismic Earth Pressures under Restrained Condition Type of Structures Rigid Base Non-Rigid Base Essential Structures Other Structures Thrust point=0.45h

50 THANK YOU!

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