Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability

Transcription

1 International Symposium Qualification of dynamic analyses of dams and their equipments and of probabilistic assessment seismic hazard in Europe 31th August 2nd September 2016 Saint-Malo Tatsuoka, F. Tokyo University of Science, Japan Session : 3 Stress-strain behaviour of compacted soils related to seismic earth-fill dam stability Saint-Malo Yannick LE GAL

2 SUMMARY-1 Several important features of the drained & saturated-undrained stress-strain properties of soil in monotonic & cyclic loadings related to the seismic stability of earth-fill dam Practical simplified seismic stability analysis needs appropriate balance among the methods chosen in the following items: 1) Criterion to evaluate of the stability: Global safety factor relative to a specified required minimum vs. Residual deformation relative to a specified allowable largest. 2) Design seismic load at a given site: Conventional design load vs. Likely largest load in the future 3) Stress strain properties of soil: Actual complicated behavior vs. Simplified model 4) Relevant consideration of the effects of other engineering factors: - compacted dry density; soil type; etc. 2

3 SUMMARY-2 Several important features of the drained & saturated-undrained stress-strain properties of soil in monotonic & cyclic loadings related to the seismic stability of earth-fill dam Practical simplified seismic stability analysis needs appropriate balance among the methods chosen in the following items: 1) Criterion to evaluate of the stability: Global safety factor relative to a specified required minimum vs. Residual deformation relative to a specified allowable largest. 2) Design seismic load at a given site: Conventional design load vs. Likely largest load in the future 3) Stress strain properties of soil: Main topic in this presentation Actual complicated behavior vs. Simplified model 4) Relevant consideration of the effects of other engineering factors: - compacted dry density; soil type; etc. 3

4 Stress strain properties of soil: (A) actual complicated behaviour vs. (B) simplified model (A) actual complicated behaviour a) Peak strength corresponding to actual compacted dry density b) Anisotropic stress strain properties as a function of δ c) Plane strain condition in many cases d) Strain-softening associated with shear banding with the thickness increasing with D 50 e) Progressive failure as a result of d) among others. σ 0 (A) (B) Peak strength only at a certain ε Strain-softening Residual strength Constant strength irrespective of ε ε Shear band σ 1 δ Plane strain conditions 4

5 Stress strain properties of soil: (A) actual complicated behaviour vs. (B) simplified model (B) simplified model (explained in this presentation) a) Design strength corresponding to conservatively (but not excessively) determined compacted dry density b) Isotropic stress strain properties c) Strength by triaxial compression test at δ= 90 o d) Strain-softening associated with shear banding with the thickness increasing D 50 to account for the effects of compaction & particle size e) No progressive failure in the limit equilibrium-based stability analysis σ 0 (A) (B) Peak strength only at a certain ε Constant strength irrespective of ε Shear band Strain-softening δ Residual strength σ 1 ε Plane strain conditions Good balance is required among simplifications a), b), c) and e) d) is to encourage good compaction Discussions on these topics a) - e)

6 Conservative determination of design soil shear strength under drained conditions- 1 The degree of compaction ρ d (in-situ) D c = (ρ d ) max (laboratory tests) 100 (%) Average of actual shear strength Dry density, ρ d (ρ d ) max ρ d (in-situ) in actual construction: average each measurement Zero air voids (S r = 100 %) Allowable lower bound of ρ d (e.g., D c = 90 %) in field compaction control w opt Water content, w Laboratory compaction curve by specified compaction energy level (CEL) Design shear strength - Often employed, but too conservative when well-compacted 6

7 Conservative determination of design soil shear strength under drained conditions- 2 Drained TC at σ 3 = 50 kpa φ peak = arcsin[(σ 1 - σ 3 )/[(σ 1 +σ 3 )] max Percentage passing by weight CBG1) Chiba gravel (1) CBG2) Chiba gravel (2) CCA) Crushed concrete aggregate CGR) Crushed gravel (for full-scale GRS integral bridge model) RGYY)Round gravel for rock-fill dam (Shin Yamamoto dam) RGSZ) Round gravel (Mt. Fuji Shizuoka Airport) NS) Narita sand IS-I) Inagi sand I IS-II) Inagi sand II IS-IV) Inagi sand IV TS) Toyoura sand YG) Yoshinogawa gravel (cut grading) DG) Dokigawa gravel (cut grading) NS, IS-I, IS -IV & IS-II TS DG CBG2 RGSZ CBG1 CGR CCA RGYY YG 1E-4 1E Particle diameter, d (mm) Design shear strength is often determined to correspond to the allowable lower bound of D c used in field compaction control conservative with better compacted soil Typical allowable lower bound Average of actual values 7

8 Conservative determination of design soil shear strength under drained conditions- 2 Drained TC at σ 3 = 50 kpa φ peak = arcsin[(σ 1 - σ 3 )/[(σ 1 +σ 3 )] max Percentage passing by weight CBG1) Chiba gravel (1) CBG2) Chiba gravel (2) CCA) Crushed concrete aggregate CGR) Crushed gravel (for full-scale GRS integral bridge model) RGYY)Round gravel for rock-fill dam (Shin Yamamoto dam) RGSZ) Round gravel (Mt. Fuji Shizuoka Airport) NS) Narita sand IS-I) Inagi sand I IS-II) Inagi sand II IS-IV) Inagi sand IV TS) Toyoura sand YG) Yoshinogawa gravel (cut grading) DG) Dokigawa gravel (cut grading) NS, IS-I, IS -IV & IS-II 0 The use of the design peak shear 1E-4 1E strength that Particle is diameter, slightly d (mm) lower than TS DG CBG2 RGSZ CBG1 YG RGYY the value that corresponds to the target of D c set equal to the anticipated average of actual values, together with the residual shear strength, is more realistic and can encourage better compaction (explained later) CCA CGR Typical allowable lower bound Average of actual values 8

9 Inherently anisotropic stress strain behaviour under drained conditions- 1 Drained PSC, saturated Toyoura sand σ 3 = 392 kpa, dense Pluviation through air σ 1 /σ 3 δ ( o ) e 4.9 Principal stress ratio, σ 1 /σ 3 σ 1 /σ 3 ε vol σ 3 = 392 kpa, loose δ ( o ) e 4.9 Volumetric strain, ε vol (%) ε vol Axial strain, ε 1 (%) 9

10 Inherently anisotropic stress strain behaviour under drained conditions- 2 Summary Drained PSC, saturated Toyoura sand σ 3 = 392 kpa, dense φ 0 (δ )/φ 0 (δ= 90 o )PSC Dense e 4.9 = (except a with 0.666) Average (D) Loose e 4.9 = except b (0.839) & c (0.836) Average (D) σ 3 (kpa) Average Principal stress ratio, σ 1 /σ 3 σ 1 /σ 3 σ 1 /σ 3 ε vol δ ( o ) e 4.9 σ 3 = 392 kpa, loose δ ( o ) e 4.9 Volumetric strain, ε vol (%) ε vol Average for loose specimens σ 1 σ 1 Angle, δ (in degree) Axial strain, ε 1 (%) 10

11 Inherently anisotropic stress strain behaviour under drained conditions- 3 A similar trend among different poorly-graded sands collected from different countries, with and without a minimum at δ= 20 o 30 o, where the shear band direction coincides with the bedding plane direction. φ0(δ )/φ0(δ= 90 o )PSC Drained PSC σ 3= 78.4 kpa OCR= σ σ 1 1 Angle, δ (in degree) Toyoura sand S.L.B. Silica Karlsruhe Monterey Ticino Hostun Glass beads σ 1 11

12 Inherently anisotropic stress strain behaviour under drained conditions- 4 Shear band σ 1 Percent passing by weight Hime Koushu Isomi Plane strain conditions A similar trend among different poorly-graded gravelly soils produced by vertical vibratory compaction δ φ 0 (δ )/φ 0 (δ= 90 o ) PSC Air-dried gravel (* vibro-compacted) (σ 3 =78.5 kpa) Drained PSC Drained TC Particle diameter (mm) Isomi* Hime Koushu* Koushu Isomi Drained TC Angle, δ (in degree) 12

13 Inherently anisotropic stress strain behaviour under drained conditions- 5 Shear band σ 1 Percent passing by weight Hime Koushu Isomi Plane strain conditions The TC strength (δ= 90 o ) is similar to, or smaller than, the average strength along a circular failure plane under plane strain conditions. δ φ 0 (δ )/φ 0 (δ= 90 o ) PSC Air-dried gravel (* vibro-compacted) (σ 3 =78.5 kpa) Drained PSC Drained TC Particle diameter (mm) Isomi* Hime Koushu* Koushu Isomi Drained TC Angle, δ (in degree) 13

14 Inherently anisotropic stress strain behaviour under drained conditions- 6 Shear band δ σ 1 Plane strain conditions φ 0 (δ )/φ 0 (δ= 90 o ) PSC Air-pluviated Toyoura sand Drained PSC Void ratio, e Inferred based on curve A σ 3 = 98 kpa: OCR= 1.0 Drained TC X e= (Oda et al., 1978) e 4.9 = 0.8 Tatsuoka et e 4.9 = 0.7 al. (1986a) Angle, δ (in degree) φ 0 ( o ) when e 4.9 = 0.7 φ 0 ( o ) when e 4.9 = The TC strength (δ= 90 o ) is noticeably smaller than the average strength along a circular failure plane under plane strain conditions. 14

15 Inherently anisotropic stress strain behaviour under drained conditions Air-pluviated Toyoura sand φ 0 (PSC, σ 3 = 49 kpa, δ=90 o ) φ 0 = arcsin[(σ 1 - σ 3 )/[(σ 1 +σ 3 )] max values in the direct shear test and the PSC test (δ= 40 o -50 o ) are nearly the same, because both tests are plane strain tests with similar anisotropy effects. Theoretical value φ 0 and φ ss (in degree) sinφ cos( ν ) φss = arctan 1 sin φ sin( ν ) 0 d max 0 d max φ 0 (PSC, δ=40 o -50 o ) φ 0 (TC, σ 3 = 49 kpa, δ=90 o ) φ 0 (TSS, σ a = 98 kpa; σ 3 = kpa) 35 σ ' t Stress condition in TSS test τ at σ ' 3 ε 2 = 0 τ at σ ' a σ ' 2 σ ' 1 ε = 0 n Measured φ ss =arctan(τ at /σ a ) (TSS, σ a = 98kPa) when τ at /σ a =max when σ 1 /σ 3 =max Void ratio, e (converted to the value measured at σ 3 = 4.9 kpa) 15

16 Inherently anisotropic stress strain behaviour under drained conditions Air-pluviated Toyoura sand φ 0 (PSC, σ 3 = 49 kpa, δ=90 o ) φ 0 = arcsin[(σ 1 - σ 3 )/[(σ 1 +σ 3 )] max values in the direct shear test and the TC test (δ= 90 o ) happen to be nearly the same due to cancelling out of the effects of anisotropy and (σ 2 - σ 3 )/(σ 1 - σ 3 ). Theoretical value φ 0 and φ ss (in degree) sinφ cos( ν ) φss = arctan 1 sin φ sin( ν ) 0 d max 0 d max φ 0 (PSC, δ=40 o -50 o ) φ 0 (TC, σ 3 = 49 kpa, δ=90 o ) φ 0 (TSS, σ a = 98 kpa; σ 3 = kpa) 35 σ ' t Stress condition in TSS test τ at σ ' 3 ε 2 = 0 τ at σ ' a σ ' 2 σ ' 1 ε = 0 n Measured φ ss =arctan(τ at /σ a ) (TSS, σ a = 98kPa) when τ at /σ a =max when σ 1 /σ 3 =max Void ratio, e (converted to the value measured at σ 3 = 4.9 kpa) 16

17 Inherently anisotropic stress strain behaviour under drained conditions- 9 In ordinary direct shear tests, φ 0 = arcsin[(σ 1 - σ 3 )/[(σ 1 +σ 3 )] max cannot be measured, but only φ ss = arctan(τ at /σ a ) max is measured. Theoretical value φ 0 and φ ss (in degree) sinφ cos( ν ) φss = arctan 1 sin φ sin( ν ) 0 d max 0 d max Air-pluviated Toyoura sand φ 0 (PSC, δ=40 o -50 o ) φ 0 (PSC, σ 3 = 49 kpa, δ=90 o ) φ 0 (TC, σ 3 = 49 kpa, δ=90 o ) φ 0 (TSS, σ a = 98 kpa; σ 3 = kpa) 35 σ ' t Stress condition in TSS test τ at σ ' 3 ε 2 = 0 τ at σ ' a σ ' 2 σ ' 1 ε = 0 n Measured φ ss =arctan(τ at /σ a ) (TSS, σ a = 98kPa) when τ at /σ a =max when σ 1 /σ 3 =max Void ratio, e (converted to the value measured at σ 3 = 4.9 kpa) 17

18 Inherently anisotropic stress strain behaviour under drained conditions- 10 φ ss = arctan(τ at /σ a ) max from the direct shear test is significantly lower than φ 0 from TC test (δ= 90 o ). The use of φ ss in the slope stability analysis is usually too conservative. Theoretical value φ 0 and φ ss (in degree) sinφ cos( ν ) φss = arctan 1 sin φ sin( ν ) 0 d max 0 d max Air-pluviated Toyoura sand φ 0 (PSC, δ=40 o -50 o ) φ 0 (PSC, σ 3 = 49 kpa, δ=90 o ) φ 0 (TC, σ 3 = 49 kpa, δ=90 o ) φ 0 (TSS, σ a = 98 kpa; σ 3 = kpa) 35 σ ' t Stress condition in TSS test τ at σ ' 3 ε 2 = 0 τ at σ ' a σ ' 2 σ ' 1 ε = 0 n Measured φ ss =arctan(τ at /σ a ) (TSS, σ a = 98kPa) when τ at /σ a =max when σ 1 /σ 3 =max Void ratio, e (converted to the value measured at σ 3 = 4.9 kpa) 18

19 Inherently anisotropic stress strain behaviour under drained conditions- 10 Shear band δ σ 1 φ 0 (δ )/φ 0 (δ= 90 o ) PSC TC strength (δ= 90 o ) Air-pluviated Toyoura sand Drained PSC Void ratio, e Inferred based on curve A e 4.9 = 0.8 e 4.9 = 0.7 σ 3 = 98 kpa: OCR= 1.0 Drained TC X e= (Oda et al., 1978) Tatsuoka et al. (1986a) Angle, δ (in degree) φ 0 ( o ) when e 4.9 = φ 0 ( o ) when e 4.9 = Plane strain conditions φ ss = arctan(τ at /σ a ) max from the direct shear test, much lower than the average strength along a circular failure plane under plane strain conditions. 19

20 Strain-softening associated with shear banding under drained plane strain conditions- 1 Uniform granular materials The stress is plotted against strain averaged for the whole specimen, not representative of the strain in the shear band. Particle diameter, D (mm) 20

21 Strain-softening associated with shear banding under drained plane strain conditions- 2 Uniform granular materials u s : shear displacement along a shear band (u s ) peak : values of u s at the peak stress (very small) Peak Particle diameter, D (mm) Larger D 50 u s 8 cm Residual 21

22 Strain-softening associated with shear banding under drained plane strain conditions- 3 Large PSC test Parcent passing in weight PSC tests on many poorly- & wellgraded gravelly soils Glass ballotini* Ottawa* Green rock/ CL Ticino* Hostun* Monterey* Karlsruhe* Toyoura* Wakasa* Chert /CH Chert /CL S.L.B.* Particle size (mm) Hime* Hasaki* Andesite 2 Andesite 1 Isomi* Andesite 2 (D 50 = 2.49 mm & U c = 4.1), at ε 1 = 4.25 %, σ 3 = 314 kpa 57cm 22

23 Parcent passing in weight Strain-softening associated with shear banding under drained plane strain conditions PSC tests on many poorly- & well-graded gravelly soils 0 Glass ballotini* Ottawa* Green rock/ CL Ticino* Hostun* Monterey* Karlsruhe* Toyoura* Wakasa* Chert /CH Chert /CL S.L.B.* Hime* Hasaki* Andesite 2 Andesite 1 Isomi* Particle size (mm) Shear stress level, R n Poorly graded granular materials (Yoshida and Tatsuoka 1997) Larger D 50 Test name toku1 toku2 toku3 toku4 NIU1 NIU2 NIU3 NIU4 NIU6 NIU7 NIU8 NIU9 an2-1 an2-2 an2-3 an u s *= u s -(u s ) peak (mm) (u s *) res Larger shear deformation of shear band for larger D 50 why? 23

24 (u s *) res increases with shear band thickness, t r, for a similar shear strain in the shear band Shear band thickness, t r (mm) Residual shear deformation, (u s * )res (mm) : Well-graded (Okuyama et al. 2003) Linear fitting: y = x R 2 = Non-linear fitting y=1.44*x (R 2 = 0.803) : Poorly graded (Yoshida and Tatsuoka 1997) Thickness of shear band, t r (mm) t r increases with D 50 Hostun sand 1:20 1: Particle size, D 50 (mm) 1:5 t r = c(d 50 ) 0.66 t r Poorly graded (Yoshida and Tatsuoka, 1997) An2 (well-graded) Chert (NIU: well-graded) Green rock (Tokuyama; well-graded) (Desrues and Viggiani, 2004) (u s *) res Strain-softening associated with shear banding under drained plane strain conditions- 5 At the start of residual state Residual shear displacement, (u s *) res So, (u s *) res increases with D 50 Yoshida & Tatsuoka (1997) Okuyama et al. (2003) Average Regression curve y = ax 0.66 R 2 =0.89 Slightly non-linear relation Particle mean diameter, D 50 (mm) 24

25 Strain-softening associated with shear banding under drained plane strain conditions Parcent passing in weight Poorly- & wellgraded gravelly soil Glass ballotini* Ottawa* Green rock/ CL Ticino* Hostun* Monterey* Karlsruhe* Toyoura* Wakasa* Chert /CH Chert /CL S.L.B.* Hime* Hasaki* Andesite 2 Andesite 1 Isomi* Particle size (mm) Shear stress level, R n Poorly graded sands & gravels (Yoshida and Tatsuoka 1997) Curves with symbols: Well graded gravels (Okuyama et al., 2003) (u s -u s.peak )/D (u s and D 50 in mm) Normalization as u s /(D 50 ) 0.66 : still a noticeable scatter, but no systematic effects of U c, σ 3, density, strain rate,.. Useful to infer the R n u s relation for a given D 50 to be used in the slip displacement analysis by the Newmark method. 25

26 Strain-softening associated with shear banding under drained plane strain conditions- 7 On the other hand, the friction angle decreases with an increase in the particle size in drained TC keeping the D max /specimen size constant! This trend is inconsistent with our intuition that the slope becomes more stable with an increase in the particle size. Angle of internal friction to the origin, φ 0 (in degree) Specimen size; 7.1 cm d x 17.8 cm h σ 3 = 46.4 kgf/cm cm d x 76 cm h Maximum particle size (inch) Crushed Basalt (U c = 10) σ 3 = 2.1 kgf/cm 2 σ 3 = 10.0 kgf/cm 2 σ 3 = 30.0 kgf/cm cm d x 228 cm h University of California, Berkeley (Marachi et al., 1969) 26

27 Strain-softening associated with shear banding under drained plane strain conditions- 8 On the other hand, the friction angle decreases with an increase in the particle size in drained TC keeping the D max /specimen size constant! This trend is inconsistent with our intuition that the slope becomes more stable with an increase in the particle size. Angle of internal friction to the origin, φ 0 (in degree) Pyramid dam material (U c = 8) σ 3 = 2.1 kgf/cm 2 σ 3 = 10.0 kgf/cm 2 σ 3 = 30.0 kgf/cm 2 σ 3 = 46.4 kgf/cm 2 Maximum particle size (inch) Angle of internal friction to the origin, φ 0 (in degree) Oroville dam material (U c = 40) σ 3 = 2.1 kgf/cm 2 σ 3 = 10.0 kgf/cm 2 σ 3 = 30.0 kgf/cm 2 σ 3 = 46.4 kgf/cm 2 Maximum particle size (inch) University of California, Berkeley (Marachi et al., 1969) 27

28 Strain-softening associated with shear banding under drained plane strain conditions- 9 On the other hand, the friction angle decreases with an increase in the particle size in drained TC keeping the D max /specimen size constant! This trend is inconsistent with our intuition that the slope becomes more stable with an increase in the particle size. One method to alleviate this contradiction in the seismic design, at least partly, is the evaluation of slip displacement by the Newmark method taking into account the effects of D 50 on the R n u s relation. Shear stress level, R n Poorly graded granular materials (Yoshida and Tatsuoka 1997) Larger D 50 Test name toku1 toku2 toku3 toku4 NIU1 NIU2 NIU3 NIU4 (u s *) res NIU6 NIU7 NIU8 NIU9 an2-1 an2-2 an2-3 an u s *= u s -(u s ) peak (mm) 28

29 Undrained stress- strain behaviour of saturated soil 1. Effects of dry density: - much larger than those on drained strength; and - become more significant by effects of preceding cyclic undrained loading. 2. Degradation of the undrained stress-strain properties and strength in the course of cyclic undrained loading: - more when more cyclically sheared undrained; and - how to model this trend for numerical analysis? Simplified model for simplified numerical analysis* vs. Full model for rigorous numerical analysis (* explained in this presentation) 29

30 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 1 Shear stress ratio, τvh/σ vc Torsional simple shear Toyoura sand Consolidated at σ vc = σ vc = 98 kpa Range of drained peak strength state for D r = 33.6 % % The figures indicate D r (%). Drained Undrained Effective stress ratio, σ v /σ vc 30

31 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 2 Torsional shear, Toyoura sand Isotropically consolidated to σ vc = σ vc = 98 kpa Shear stress ratio, τvh/σ vc Undrained Drained The figures indicate D r (%). Volumetric strain (%) Drained Expansion Shear strain, γ vh (%) Shear strain, γ vh (%) In drained tests, the peak strength is noticeably different with largely different volume changes for different dry densities (or different D r values)! 31

32 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 3 Torsional simple shear Toyoura sand Consolidated at σ v changes at a constant volume! Torsional simple shear Toyoura sand Consolidated at The figures indicate D r (%). Shear stress ratio, Undrained Drained The figures indicate D r (%). Shear Shear stress stress ratio, ratio, Range of drained peak strength state for D r = 33.6 % % Effective stress ratio, σ' / σ' Effective stress paths Drained Undrained v vc Shear strain, γ vh (%) In undrained tests, the effective stress path is largely different with largely different peak strengths for different densities! 32

33 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 4 Comparison among (A)drained strength in ML, (B) undrained strength in ML and (C) undrained CL strength of Toyoura sand A: drained peak stress ratio Shear strength, τvh/σ v Number of loading cycle, N c = 5 B: undrained peak stress ratio necessary to develop 15 % shear strain Toyoura sand; σ vc = σ vc = 98 kpa Shear stress, τ vh (kpa) Shear strain, γ vh (%) Excess pore water pressure, u (kpa) C: undrained cyclic loading strength necessary to develop 15 % double amplitude shear strain 10 seconds Undrained cyclic test Relative density, D r (%) 33

34 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 5 Shear strength, τvh/σ v A: drained peak stress ratio Number of loading cycle, N c = 5 B: undrained peak stress ratio necessary to develop 15 % shear strain Toyoura sand; σ vc = σ vc = 98 kpa C: undrained cyclic loading strength necessary to develop 15 % double amplitude shear strain 1) ML drained shear strength increases with D r, but the increase is not very large: e.g., only about 10 % when D r = 70 % 90 %. 2) In the stability analysis based on the drained shear strength, the benefit of compaction is large, but not as large as the one when based on undrained shear strength. Relative density, D r (%) 34

35 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 6 Shear strength, τvh/σ v A: drained peak stress ratio Number of loading cycle, N c = 5 B: undrained peak stress ratio necessary to develop 15 % shear strain Toyoura sand; σ vc = σ vc = 98 kpa C: undrained cyclic loading strength necessary to develop 15 % double amplitude shear strain 1) ML undrained shear strength significantly increases with D r : e.g., by a factor of three when D r = 40 % 60 %. 2) In the stability analysis based on the undrained shear strength, the benefit of compaction is significant. Relative density, D r (%) 35

36 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 7 Shear strength, τvh/σ v A: drained peak stress ratio Number of loading cycle, N c = 5 B: undrained peak stress ratio necessary to develop 15 % shear strain Toyoura sand; σ vc = σ vc = 98 kpa C: undrained cyclic loading strength necessary to develop 15 % double amplitude shear strain 1) Undrained cyclic shear strength increases with D r, significantly when D r becomes larger than a certain value: e.g., by a factor of three when D r = 70 % 90 %. 2) Significant benefits can be obtained by compaction to D r higher than a certain value. Relative density, D r (%) 36

37 Undrained stress- strain behaviour of saturated soil: 1. Effects of dry density - 8 Shear strength, τvh/σ v A: drained peak stress ratio Number of loading cycle, N c = 5 B: undrained peak stress ratio necessary to develop 15 % shear strain Toyoura sand; σ vc = σ vc = 98 kpa C: undrained cyclic loading strength necessary to develop 15 % double amplitude shear strain These undrained shear strengths, B & C, are necessary, but not sufficient, to evaluate the residual deformation by: a) slip displacement analysis by Newmark-D method; and b) residual deformation analysis by pseudo-static non-linear FEM. Relative density, D r (%) 37

38 Undrained stress- strain behaviour of saturated soil to evaluate the residual displacement/deformation-1 Residual displacement/deformation Allowable value 2. Slip displacement obtained by the Newmark method F s against Level 2 design seismic load 1.0 Perfect-plastic behavior without degradation during seismic loading is assumed 3. Total residual displacement/deformation: 1. Residual deformation not including slip displacement; plus 2. Slip displacement Estimated total ultimate residual displacement/deformation 1. Residual deformation obtained by pseudo-static non-linear FEM not including slip displacement Minimum safety factor by LE analysis, F s 38

39 Undrained stress- strain behaviour of saturated soil to evaluate the residual displacement/deformation - 2 τ w Apparent working shear stress, τ w Three consecutive zero-crossing points s Actualτ w (= soil shear strength, τ f ) e decreasing by cyclic undrained loading τ i 0 Pulse n Time Time history of apparent irregular working stress τ w obtained by total stress seismic response analysis not taking into account both strength degradation by undrained CL and slip failure Actual τ~γ behavior of soil Increments of slip displacement in all pulses where slip takes place (such as s e) are integrated to obtain the ultimate residual slip displacement τ 0 γ+ γ DA s τ initial e Undrained τ~γ relation Initial In pulse n Continuous degradation by undrained CL Shear strain, γ

40 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 1: Time histories of stress, strain and slip Laboratory stress-strain tests Seismic 地震動による荷重 load Seismic Damage 損傷ひずみ strain Damage strain Soil strength 土の強度 Slip すべり displacement 変位 (a) (b) (c) (d) Time 時間 Time 時間 Time 時間 Time 時間 Cyclic 繰返し stress amplitude 応力振幅 (e) Soil 土の強度 strength (f) Damage 損傷ひずみ strain= = 1% 2% 5%. 1%, 2%, 5% など 繰返し載荷回数 log(n c ) Damage 損傷ひずみ strain 通常のニューマーク法と同様の Calculation ニューマーク法の手順に従って of slip displacement 手順ですべり変位を計算 by the Newmark-D method 40

41 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 2: Typical example of cyclic undrained triaxial tests on isotropically consolidated specimens compacted to (D c ) 1Ec = 85 %; 90 % and 95 % Percent passing in weight 通過質量百分率 (%) 土粒子密度 : 2.67g/cm 3 Hokota sand D 50 = 0.20 mm U c = 17.0 F c = 13.6 % 平均粒径 : 0.204mm 均等係数 : 17.0 細粒分含有率 : 13.6% 粒径 (mm) Particle diameter, D (%) Cyclic 繰返し応力振幅比 stress ratio,, τ d /σ mi τ(d i /σ c ) mi 1Ec 緩詰め 85% 中詰め 90% 密詰め 95% 0.50 ε damage = 1%, 2%, 5%, 10% 緩詰め 85% 密詰め 95% 中詰め 90% Number 繰返し載荷回数 of loading, cycles, N N c 41

42 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 3: Time histories of stress, strain and slip Laboratory stress-strain tests Seismic 地震動による荷重 load Seismic Damage 損傷ひずみ strain Damage strain Soil strength 土の強度 Slip すべり displacement 変位 (a) (b) (c) (d) Time 時間 Time 時間 Time 時間 Time 時間 Cyclic 繰返し stress amplitude 応力振幅 (e) Soil 土の強度 strength (f) Damage 損傷ひずみ strain= = 1% 2% 5%. 1%, 2%, 5% など 繰返し載荷回数 log(n c ) Damage 損傷ひずみ strain 通常のニューマーク法と同様の Calculation ニューマーク法の手順に従って of slip displacement 手順ですべり変位を計算 by the Newmark-D method 42

43 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 4: S(t)=τ Definition cyc,i /σ init : shear of a pulse stress ratio Zero-crossing zero-crossing point 2τ cyc,i = τ max,i -τ min,i τ max,i τ (t) τ init τ min,i Buffer zone (i.e., zero-crossing is defined only by full crossing of this zone) 0 i Pulse cycle i t 43

44 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 5: SR Cumulative damage concept SR i Relationship between SR and N c necessary to develop a given damage strain* obtained by a series of uniform cyclic undrained tests Damage for damage strain* by pulse i: D i = (1/N i ) N i log(number of loading cyclic, N c ) SR i = τ cyc,i /σ 0 : cyclic stress ratio of pulse i τ cyc,i : shear Stress-strain stress behaviour amplitude; of compacted soilsand related to σ seismic 0 : initial earth-fill effective dam stability confining 2016 stress44

45 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 6: SR i SR Cumulative damage concept Relationship between SR and N c necessary to develop a given damage strain* obtained by a series of uniform cyclic undrained tests Damage for damage strain* by pulse i: D i = (1/N i ) N i log(number of loading cyclic, N c ) Total damage for damage strain* caused n by a series of irregular pulses until the end of pulse n: D = Di = If D becomes 1.0 at the end of pulse n, i it is assumed that this damage strain * takes place in pulse n. n = 1 i= 1 1 N i 45

46 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 7: SR SR i Cumulative damage concept Relationship between SR and N c necessary to develop a given damage strain* obtained by a series of uniform cyclic undrained tests Damage for damage strain* by pulse i: D i = (1/N i ) N i log(number of loading cyclic, N c ) Then, we can find the damage strain at the end of pulse n at which the n = i= 1 total damage D becomes N i 46

47 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 8: SR SR i Cumulative damage concept Relationship between SR and N c necessary to develop a given damage strain* obtained by a series of uniform cyclic undrained tests N i Damage for damage strain* by pulse i: D i = (1/N i ) log(number of loading cyclic, N c ) By this procedure, a given time history of irregular cyclic stresses causing a certain damage strain can be converted to uniform cyclic stresses with an arbitrary combination of SR & N c that develops the same damage strain. 47

48 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 9: τ w Consecutive zerocrossing points s e τ w (= soil shear strength, τ f ) decreasing by cyclic undrained loading τ i 0 Pulse n Uniform cyclic stresses equivalent to irregular working stresses before the start of pulse n obtained by the cumulative damage concept. Equivalent τ~γ behavior after have been subjected to equivalent uniform cyclic stresses obtained by the cumulative damage concept τ γ+ γ DA s e τ initial Undrained τ~γ relation τ f Initial In pulse n Time 0 Shear strain, γ

49 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 10: Time histories of stress, strain and slip Laboratory stress-strain tests Seismic 地震動による荷重 load Seismic Damage 損傷ひずみ strain Damage strain Soil strength 土の強度 Slip すべり displacement 変位 (a) (b) (c) (d) Time 時間 Time 時間 Time 時間 Time 時間 Cyclic 繰返し stress amplitude 応力振幅 (e) Soil 土の強度 strength (f) Damage 損傷ひずみ strain= = 1% 2% 5%. 1%, 2%, 5% など 繰返し載荷回数 log(n c ) Damage 損傷ひずみ strain 通常のニューマーク法と同様の Calculation ニューマーク法の手順に従って of slip displacement 手順ですべり変位を計算 by the Newmark-D method 49

50 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 11: Consolidation 両試験共通 圧密過程 ( 排水条件 ) 純単調載荷試験 単調載荷過程 ( 非排水条件 ) Undrained monotonic loading (ML) Undrained ML Deviator stress 主応力差 Undamaged 繰返し載荷の影響が無い強度 ( 初期非排水せん断強度 ) peak strength ( 非損傷強度 (σ a -σ r ) maxm ) 純単調載荷試験 Undrained ML 繰返し + 単調載荷試験 Damaged 繰返し載荷後に残存する強度 peak strength ( 損傷強度 (σ a -σ r ) maxd ) 繰返し載荷過程で生じた最大ひずみあるいはひずみ振幅 ( 損傷ひずみε D ) Strength drop due to damage strain by undrained CL 強度低下 End of undrained CL, where damage strain (DA) has taken place 繰返し + 単調載荷試験 繰返し載荷過程 ( 非排水条件 ) 繰返し + 単調載荷試験 単調載荷過程 ( 非排水条件 ) Undrained CL Undrained ML Time 50

51 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 12: Deviator 主応力差 stress Undrained shear strength after undrained CL, τ damage Initial undrained shear strength Deviator 主応力差 stress Strain 主応力差 Deviator stress Strain that has developed by undrained CL 61 Strain Strain 51

52 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 13: Typical example: loose Hokota sand 主応力差, q (kn/m 2 ) Deviator stress, q (kn/m 2 ) u Undrained CL 繰返し載荷 単調載荷 Undrained ML q maxs 強度低下 0 0 ρ d =1.44g/cm 3 (D c =85%), σ' -20 mi =100kN/m 2, τ d /σ mi =0.112, -60 N=23, ε damage =10%, (a) Initial 純単調載荷試験 undrained ML: q, u 軸ひずみ Axial strain,, ε a (%) ε a (%) q Strength drop due to undrained CL q maxd Excess 過剰間隙水圧 pore water pressure,, u (kn/m u 2 ) (kn/m 2 ) 52

53 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 14: Typical example: dense Hokota sand Deviator 主応力差 stress,, q q (kn/m 2 ) 2 ) ρ d =1.61g/cm 3 (D c =95%), σ' mi =100kN/m 2, τ d /σ mi =0.258, N=44, ε damage =10%, 純単調載荷試験 : q, u Initial undrained ML (b) u Undrained CL 繰返し載荷 q maxs 強度低下 Strength drop q Undrained ML 単調載荷 q maxd Excess 過剰間隙水圧比 pore water pressure,, u (kn/m u (kn/m 2 ) 2 ) Axial 軸ひずみ strain,, ε a (%) 53

54 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 15: Undrained shear strength after cyclic undrained loading becomes significantly smaller as sand becomes looser, due to: 1) lower initial undrained shear strength; 2) larger damage strain by undrained CL; and 3) a larger drop rate for the same damage strain. τ damage : undrained shear strength after undrained CL σ mi : initial mean effective stress 非排水繰返し載荷後に残存する強度, τ damage /σ mi 初期強度に対する比, τ damage /τ τ maxm damage /τ maxs τ damage /σ mi : 初期非排水せん断強度比 τ maxs /σ mi 緩詰め 中詰め 密詰め τ maxs : initial undrained shear strength 85 % 90 % 損傷ひずみ, ε damage (%) Damage strain, DA (%) 緩詰め 85 % 密詰め 中詰め 損傷ひずみ, ε damage (%) Damage strain, DA (%) (D c ) 1Ec = 95 % (D c ) 1Ec = 95 % 90 %

55 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 16: Undrained shear strength after cyclic undrained loading becomes significantly smaller as sand becomes looser, due to: 1) lower initial undrained shear strength; 2) larger damage strain by undrained CL; and 3) a larger drop rate for the same damage strain. Strength 各種せん強度比 ratio,, τ/σ τ/σ' mi 非排水試験 初期平均有効主応力 σ' mi = 100 kpa Undrained tests: σ mi = 100 kpa Drained 排水試験 tests: σ' mi = ピーク応力時平均有効主応力 σ σ' m at peak stress = σ mf mi : + 初期非排水 Initial undrained strength せん断強度, τ maxs /σ' mi Undrained 非排水繰返し載荷 (τ strength d /σ' mi = 0.19; after N=2) 後の残存強度 undrained CL* τ damage /σ' mi S r 供試体作成時飽和度 when compacted : 50 % : (S r ) opt = 71 % 排水せん断強度 Drained strength τ maxd /σ' mf 0.5, Cyclic 軸ひずみ両振幅が undrained N=3 strength 10% になる繰返し応力 for DA= 10 % N=10 振幅比 τ d /σ' mi * τ d /σ mi = 0.19; N c = 2 締固め度 (D c ) 1Ec (1Ec), (%) D c (%) 55

56 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 17: Undrained shear strength after cyclic undrained loading becomes significantly smaller as sand becomes looser, due to: 1) lower initial undrained shear strength; 2) larger damage strain by undrained CL; and 3) a larger drop rate for the 各種せん強度比, τ/σ' mi Strength ratio, τ/σ mi same damage strain. * τ d /σ mi = 0.19; N c = Initial undrained strength + τ maxs /σ' mi N=3 N=10, τ maxd /σ' mf, τ d /σ' mi Undrained strength τ damage /σ' mi after undrained CL* 締固め度 (D (1Ec), D c (%) c ) 1Ec (%) Drained strength Cyclic undrained strength for DA= 10 % 56

57 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 18: Time histories of stress, strain and slip Laboratory stress-strain tests Seismic 地震動による荷重 load Seismic Damage 損傷ひずみ strain Damage strain Soil strength 土の強度 Slip すべり displacement 変位 (a) (b) (c) (d) Time 時間 Time 時間 Time 時間 Time 時間 Cyclic 繰返し stress amplitude 応力振幅 (e) Soil 土の強度 strength (f) Damage 損傷ひずみ strain= = 1% 2% 5%. 1%, 2%, 5% など 繰返し載荷回数 log(n c ) Damage 損傷ひずみ strain 通常のニューマーク法と同様の Calculation ニューマーク法の手順に従って of slip displacement 手順ですべり変位を計算 by the Newmark-D method 57

58 Different soil models for different Newmark methods Working 作用せん断応力 stress, τ w, τ w Soil shear せん断強度 strength,, τ f τ f 0 τ i Slip displacement すべり変位 δ δ* Damage 非排水繰返し載荷 strain by による undrained DA* CL Drained 排水繰返し載荷 Initial 初期非排水せん断強度 undrained strength, (τ f )(τ 0 f ) 0 Undrained 非排水繰返し載荷 These values of δ & damage strain これら are * は different τ f の低下の設 among different soil 定法によって異なる models 時間 Time, t t 時間, t Time, t Peak drained strength, S 法 ( ひずみ軟化を考慮 ) ピークせん断強度 τ p Newmark-S (with strain-softening: τ τ f =τ p τ r ) p Newmark-O O 法 :τ f = 残留強度 (τ τ r ( 固定 ) f = drained residual strength τ r, fixed) D 法 (τ f は非排水繰返し載荷により低下 )(τ D ) Large effects of compaction No effects of compaction Newmark-D (with degradation by undrained CL Newmark-SD (with degradation by undrained CL & strain-softening) 0 SD 法 (τ f はひずみ軟化と非排水繰返し載荷により低下 )(τ SD ) Time, 時間 t t Significant effects of compaction

59 Undrained stress- strain behaviour of saturated soil - Undrained strength during cyclic undrained loading for slip displacement analysis by Newmark-D method - 20: Time histories of stress, strain and slip Laboratory stress-strain tests Seismic 地震動による荷重 load Seismic Damage 損傷ひずみ strain Damage strain Soil strength 土の強度 Slip すべり displacement 変位 (a) (b) (c) (d) Time 時間 Time 時間 Time 時間 Time 時間 Cyclic 繰返し stress amplitude 応力振幅 (e) Soil 土の強度 strength (f) Damage 損傷ひずみ strain= = 1% 2% 5%. 1%, 2%, 5% など 繰返し載荷回数 log(n c ) Damage 損傷ひずみ strain 通常のニューマーク法と同様の Calculation ニューマーク法の手順に従って of slip displacement 手順ですべり変位を計算 by the Newmark-D method 59

60 Yield seismic coefficient Newmark-O Newmark-D Yield seismic coefficient Time Time Contour of soil shear strength Contour of soil shear strength Slip displacement, δ=r θ Slip displacement, δ=r θ Time Time

61 Slip displacement by Newmark- D analysis of old Fujinuma dam, which collapsed by the 2011 Great East Japan Earthquake Reservoir Sediment Slide 3 Slide 1 Settlement Slide 2 Downstream Slide 4 Masonry wall (m)... Acc [m/s 2 ] θ [rad/s 2 ] θ [rad/s] δ=r θ [m] yield acceleration Circular slide 2 Start of slip: 63.39sec Elapsed time [sec] δ max =5.350 m Very large ultimate slip displacement: -Slip continues after the moment of peak acceleration (t= s) due to continuing deterioration in the undrained shear strength. Damage strain contour

62 Undrained stress- strain behaviour of saturated soil - Undrained stress strain relation in the course of cyclic undrained loading modelled for residual deformation analysis by pseudo-static non-linear FEM - 1 : Cyclic undrained torsional simple shear test on dense Toyoura sand applying seismic random stresses at a constant shear strain rate p o Axial load, W Torque, T p i γ vh ε v =0 σ r σ v ε h =0 τ vh α h σ h σ 1 V Shear stress ratio, τ vh /σ mc Shear strain, γ vh (%) Excess pore water pressure ratio, u /σ mc (a) [τ vh /σ mc ] max = 0.8 (b) (c) σ rc = 66 kpa σ mc = 98 kpa Horizontal bedding plane r Effective vertical stress ratio, σ v /σ mc (d) 1968 Tokachi-oki E.Q. main shock Hachinohe (NS) Elapsed time (hours) 62

63 (c) Shear stress, τ vh (x98 kpa) 1/ Air-pluviated Toyoura sand (e= Cyclic undrained simple shear Shear stress, τ vh (x98 kpa) Effective vertical stress, σ v (x 98 kpa) / Shear strain, γ vh (%) Complicated τ vh γ vh relation! Title

64 (c) Shear stress, τ vh (x98 kpa) 1/ Air-pluviated Toyoura sand (e= Cyclic undrained simple shear Shear stress, τ vh (x98 kpa) Effective vertical stress, σ v (x 98 kpa) / Shear strain, γ vh (%) Complicated τ vh γ vh relation, but smooth strain-hardening hysteretic τ vh /σ v γ vh relation: - Yielding starts when τ vh /σ v exceeds the previous maximum value in each direction. Shear stress ratio, τ vh /σ v Up to point A Up to point A Shear strain, γ vh (%) Title

65 Undrained stress- strain behaviour of saturated soil - Undrained stress strain relation in the course of cyclic undrained loading modelled for residual deformation analysis by pseudo-static non-linear FEM - 1 : Cyclic undrained torsional simple shear test on loose Toyoura sand applying seismic random stresses at a constant shear strain rate p o Axial load, W Torque, T p i γ vh ε v =0 σ r σ v ε h =0 τ vh α h σ h σ 1 V Shear stress ratio, τ vh /σ mc Shear strain, γ vh (%) Excess pore water pressure ratio, u /σ mc (a) (b) (c) b a 1 d 1 c e d 1 c σ rc = 66 kpa f 0.4 h f g i [τ vh /σ mc ] max = 0.4 g h i g i j h f σ mc = 98 kpa j j Horizontal bedding plane r Effective vertical stress ratio, σ v /σ mc (d) c d 1 f g 1968 Tokachi-oki E.Q. main shock Hachinohe (NS) h i j Elapsed time (hours) 65

66 Shear stress, τ vh (x98 kpa) (a) j i g h f f f e d 2 d 1 Air-pluviated Toyoura sand (e= 0.778) Cyclic undrained simple shear a 2 a Effective vertical stress, σ v (x 98 kpa) c b 2 b 1 Shear stress, τ vh (x98 kpa) i (c) A o g b 1, b 2 d 1, d 2 c a 1, a Shear strain, γ vh (%) e y1 f f f F y2 h j Complicated τ vh γ vh relation! 66

67 Shear stress, τ vh (x98 kpa) (a) j i g h f f f e d 2 d 1 Air-pluviated Toyoura sand (e= 0.778) Cyclic undrained simple shear a 2 a Effective vertical stress, σ v (x 98 kpa) Complicated τ vh γ vh relation, but smooth strain-hardening hysteretic τ vh /σ v γ vh relation: - Yielding starts when τ vh /σ v exceeds the previous maximum value in each direction. - The γ vh value at the peakτ vh /σ v state after having passed the yielding point (e.g. point h) can be determined only by the peakτ vh /σ v value and the ML stress strain relation starting from the origin (i.e., o y1 F h), not referring to previous cyclic loading histories. c b 2 b 1 Shear stress, τ vh (x98 kpa) i (c) g d 1, d 2 c a 1, a Shear strain, γ vh (%) Shear stress ratio, τ vh /σ v A o b 1, b 2 g o e b c y1 f d e f f Shear strain, γ vh (%) F f' y2 f f h F 67 j h

68 Shear stress, τ vh (x98 kpa) (a) j i g h f f f e d 2 d 1 Air-pluviated Toyoura sand (e= 0.778) Cyclic undrained simple shear a 2 a Effective vertical stress, σ v (x 98 kpa) c b 2 b 1 Shear stress, τ vh (x98 kpa) i (c) A o g b 1, b 2 d 1, d 2 c a 1, a Shear strain, γ vh (%) e y1 f f f F y2 h j The γ vh value at the peakτ vh /σ v state after having passed the yielding point (e.g. point h) obtained by following the reloading τ vh γ vh relation (e.g. f y2 F h) is the same as the value obtained by following the monotonic loading τ vh γ vh relation starting from the origin (e.g. o y1 F h) while not referring to previous cyclic loading histories. Shear stress ratio, τ vh /σ v g o b c d e Shear strain, γ vh (%) f' f f F h 68

69 Shear stress, τ vh (x98 kpa) (a) j i g h f f f e d 2 d 1 Air-pluviated Toyoura sand (e= 0.778) Cyclic undrained simple shear a 2 a Effective vertical stress, σ v (x 98 kpa) c The time history of the γ vh value at the peak τ vh /σ v states after having passed the yielding point (e.g. the values at points f, h & j) can be obtained by following respective ML stress-strain relations starting from the origin, o, that have degraded by respective preceding cyclic undrained loading histories. In a slope in which initial shear stresses are acting, most of the respective peak γ vh value remains as the residual value upon unloading. b 2 b 1 Shear stress, τ vh (x98 kpa) i (c) g d 1, d 2 c a 1, a Shear strain, γ vh (%) Shear stress ratio, τ vh /σ v A o b 1, b 2 g o e b c y1 f d e f f Shear strain, γ vh (%) F f' y2 f f h F 69 j h

70 Shear stress, τ vh (x98 kpa) (a) j i g h f f f e d 2 d 1 Air-pluviated Toyoura sand (e= 0.778) Cyclic undrained simple shear a 2 a Effective vertical stress, σ v (x 98 kpa) The time history of the residual deformation of a slope may be obtained by a series of pseudostatic non-linear FEM analyses incorporating gravity and seismic loads while using respective ML stress strain relations starting from the origin. Approximatedly, the maximum value of this deformation can be considered as the ultimate residual deformation caused by a given seismic loading history. c b 2 b 1 Shear stress, τ vh (x98 kpa) i (c) g d 1, d 2 c a 1, a Shear strain, γ vh (%) Shear stress ratio, τ vh /σ v A o b 1, b 2 g o e b c y1 f d e f f Shear strain, γ vh (%) F f' y2 f f h F 70 j h

71 A series of pseudo-static FEM analysis of old Fujinuma dam, which collapsed by the 2011 Great East Japan Earthquake Reservoir Slide 1 Settlement Downstream Acceleration [gal] Naganuma motion record (FKSH08) deconvoluted to Vs=450m/s rock bed and to FEM model base FEM base input motion max= gal (t=97.01s) Sediment Slide 3 Slide 2 Slide 4 Masonry wall dt=0.01s data: (m) The largest deformation (at t= s): -not by the peak acceleration (t= s), but later after the stress-strain relation has deteriorated more. Settlement at dam crest [m] Settlement at dam crest Independent analyses Elapsed time [sec] max=0.564m (t=100.14sec.) Elapsed time [sec.]

72 A series of pseudo-static FEM analysis of old Fujinuma dam, which collapsed by the 2011 Great East Japan Earthquake Reservoir Slide 1 Settlement Downstream Acceleration [gal] Naganuma motion record (FKSH08) deconvoluted to Vs=450m/s rock bed and to FEM model base FEM base input motion max= gal (t=97.01s) Sediment Slide 3 Slide 2 Slide 4 Masonry wall dt=0.01s data: (m) The largest deformation (at t= s): -not by the peak acceleration (t= s), but later after the stress-strain relation has deteriorated more. -This largest deformation is considered as the ultimate residual deformation. Settlement at dam crest [m] Settlement at dam crest Elapsed time [sec] Elapsed time [sec.] max=0.564m (t=100.14sec.)

73 Several important features of the drained & saturated-undrained stress-strain properties of soil in monotonic & cyclic loadings related to the seismic stability of earth-fill dam Practical simplified seismic stability analysis needs appropriate balance among the methods chosen in the following items: 1) Criterion to evaluate of the stability: Global safety factor relative to a specified required minimum vs. Residual deformation relative to a specified allowable largest. 2) Design seismic load at a given site: Conventional design load vs. Likely largest load in the future 3) Stress strain properties of soil: Actual complicated behavior vs. Simplified model 4) Relevant consideration of the effects of other engineering factors: - compacted dry density; soil type; etc. 73

74 Design seismic load at a given site: Conventional design load: - specified in many old seismic design codes - defined as Level 1 design seismic load in new seismic design codes (introduced after the 1995 Great Kobe E.-Q.) Likely largest seismic load during the lifetime of a given structure: - defined as Level 2 design seismic motion in new seismic design codes (introduced after the 1995 Great Kobe E.-Q.) 74

75 Japanese Society for Civil Engineers (1996) : Level 1 design seismic motion: It is a seismic motion with a high likelihood of occurring during the design lifetime of the concerned structure. It is required that, in principle, all new structures have sufficient seismic resistance to ensure "no damage" when subjected to this seismic motion. Level 2 design seismic motion: It is the strongest seismic motion thought likely to occur at the location of the concerned structure during its lifetime. It is required that the structure should not collapse, although damage that renders it unusable is acceptable if its functionality can be rapidly restored. The relationship among the design seismic load, design shear strength of soil and stability analysis method (i.e., global Fs vs. residual deformation) is complicated due to historical reasons. 75

76 Actual behavior during severe earthquakes Well-compacted fill A: Examples: high rock fill dams modern highway embankments modern railway embankments earth-fill dams Poorly-compacted fill B: Examples: old soil structures before introduction of modern design and construction codes and methods residential embankments Shear strength of fill, τ f Stable Collapse A (stable) B(collapsed) F s =Strength/Load= 1 Level 1 Level 2 Performance during severe E.Q. Working stress, τ w

77 Typical conventional seismic design of soil structure Design seismic load (τ w ) d : k h = 0.15 (Level 1 seismic coefficient) Design shear strength (τ f ) d *: Drained shear strength when D c by Standard Proctor (1Ec) is equal to the required minimum value (e.g., 90 %) Required min. F s by limit equilibrium stability analysis = 1.2, for example Shear strength of fill, τ f Well-compacted fill A: The use of k h =0.15 as Level 2 seismic load is on the unsafe side. However, the use of (τ f ) d * as the drained/ undrained strength of well-compacted fill is on the safe side. These two factors may be balanced. Conventional design of fill A: 1)Under-estimate of seismic load 2)Under-estimate of soil shear strength Stable A B Collapse A (stable) B(collapsed) F s =Strength/Load= 1 Level 1 Level 2 Performance during severe E.Q. Working stress, τ w

78 Typical conventional seismic design of soil structure Design seismic load (τ w ) d : k h = 0.15 (Level 1 seismic coefficient) Design shear strength (τ f ) d *: Drained shear strength when D c by Standard Proctor (1Ec) is equal to the required minimum value (e.g., 90 %) Required min. F s by limit equilibrium stability analysis = 1.2, for example Well-compacted fill A: The use of k h =0.15 as Level 2 seismic load is on the unsafe side. However, the use of (τ f ) d * as the drained/ undrained strength of well-compacted fill is on the safe side. These two factors may be balanced. If only k h is increased: i.e., if only (τ w ) d is increased Under-estimate of stability by losing balance (i.e., collapse despite actual stable performance against level) 2. Solution: 1) use of level 2 design seismic load; and 2) use of realistic high soil strength (τ f ) d corresponding to actual D c (> 90 %) (using undrained strength when relevant) Shear strength of fill, τ f Stable Realistic seismic design: 1) Use of level 2 seismic load 2) Use of realistic high soil strength Conventional design of fill A: 1)Under-estimate of seismic load 2)Under-estimate of soil shear strength A B Collapse A (stable) A B(collapsed) F s =Strength/Load= 1 Level 1 Level 2 Performance during severe E.Q. Working stress, τ w

79 Typical conventional seismic design of soil structure Design seismic load (τ w ) d : k h = 0.15 (Level 1 seismic coefficient) Design shear strength (τ f ) d *: Drained shear strength when D c by Standard Proctor (1Ec) is equal to the required minimum value (e.g., 90 %) Required min. F s by limit equilibrium stability analysis = 1.2, for example Poorly-compacted fill B: The use of k h =0.15 as Level 2 seismic load is on the unsafe side. Besides, the use of (τ f ) d * as undrained strength of saturated poorly-compacted fill subjected to seismic load is on the unsafe side. These two factors are not balanced. Only an increase in k h is not sufficient, but use of realistic low (τ w ) d is necessary to duly evaluate the stability against level 2 seismic load. Solution: 1) use of level 2 design seismic load and; 2) use of realistic soil strength that is much lower than the conventional value (τ f ) d * if saturated/undrained during seismic loading Shear strength of fill, τ f Stable Realistic seismic design: 1) Use of level 2 seismic load 2) Use of realistic low soil strength Conventional design of fill B: 1)Under-estimate of seismic load 2)Over-estimate of soil shear strength A B Collapse A (stable) B(collapsed) B F s =Strength/Load= 1 Level 1 Level 2 Performance during severe E.Q. Working stress, τ w

80 CONCLUDING REMARKS - 1 Several important factors that influence the drained &saturatedundrained stress-strain properties of soil when subjected to monotonic & cyclic loading histories related to the seismic stability analysis of soil structures, including earth-fill dams, were discussed. The following are the main conclusions: 1) Compacted soils exhibit significant strain-softening associated with shear banding, resulting in progressive failure in a slope. 2) As the thickness of shear band increases with D 50, the rate of strain-softening becomes slower with D 50,so the failure tends to become less progressive, making the slope more stable. 3) Although the effect of dry density on the drained peak shear strength is large, the effect on the undrained shear strength is much more significant. 80

81 CONCLUDING REMARKS - 2 4) The drained strength of compacted soil exhibits strong inherent anisotropy in plane strain compression. 5) The strength obtained by different stress-strain tests (i.e., triaxial and plane strain compression and direct shear) could be largely different due to the effects of different angles between the σ 1 direction and the bedding plane direction; different ratios of σ 2 to σ 1 & σ 3 ; and different definition of friction angle. 81

82 CONCLUDING REMARKS - 3 6) For the limit equilibrium-based stability analysis of a slope under plane strain conditions, a practical simplified method that assumes the followings, yet takes into account the effects of compacted dry density and particle size, can be proposed: a) Isotropic stress-strain properties exhibiting strain-softening of which the rate decreases with an increase in D 50. b) Use of the peak & residual strengths determined by the conventional TC tests at δ= 90 o,. c) Use of the peak strength corresponding to somehow conservatively determined compacted dry density (i.e., slightly lower than the value that corresponds to the anticipated average of the actual values of D c ). d) Progressive failure is not taken into account. 82

83 CONCLUDING REMARKS - 4 7) Under undrained monotonic loading conditions, loose & dense saturated soils exhibit the shear strength that is significantly lower and higher than the respective drained shear strengths. 8) The undrained shear strength decreases by preceding cyclic undrained loading. The effects of dry density on the damaged undrained shear strength are significant due to the following trends with an increase in the dry density: a) the increase in the initial undrained shear strength; b) the decrease in the damage strain by preceding cyclic undrained loading; and c) the decrease in the degradation rate by damage strain. 83

84 CONCLUDING REMARKS - 5 9) For simplified stability analysesof a slope having saturated zones by slip deformation by the Newmark method ad residual deformation by the pseudo-static non-linear FEM, the characteristic feature of undrained stress strain properties described above can be modelled in a unified framework from the same results of a set of monotonic and cyclic loading lundrained stress strain tests of saturated soil.. 84

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