1. Amit Prashant Associate Professor Dept. of Civil Engineering Indian Institute of Technology Gadhinagar, India 5th Tongji-UBC Symposium on Earthquake Engineering, May 4-8, 2015 Tongji University Shanghai, China

2. Introduction Failure modes in compression: Euler mode, bulging, barreling, surface instability, asymmetric shear banding and symmetric shear banding (Bigoni, 2012). Experimental observation of barreling and localization of deformation under triaxial compressive loading (Bigoni, 2012). 2 Plastic instabilities: precursor to failure during laboratory experiments (Vardoulakis, 1985; Bardet & Shiv, 1995; Iai & Bardet, 2001) Bulging Buckling Shear bands due to strain localization Liquefaction type solid-fluid instability

3. Introduction 3 Modes of plastic instability Depend on material properties, loading and boundary conditions. Any mode can trigger the other and subsequently leads to failure. Stability under liquefaction and post-liquefaction condition Solid-fluid diffused instability modes result into catastrophic failure of complex geotechnical structures in loose saturated sand. Undrained shear bands influence stability and post-liquefaction deformation of earth structure. Present study Theoretically examines instability behavior of saturated sand in biaxial test under both drained and undrained condition Possible instability modes with varying initial density, confining pressure, aspect ratio of sample and applied boundary conditions

4. Plane strain instability analysis 4 Bifurcation problem from a uniform stress-strain condition Captures evolution of intermediate principal stress 3D pressure-dependent non-associative constitutive model Flexible lateral boundary enables to capture the possibility of drained diffused modes Biaxial configuration simulated assuming both rigid and flexible lateral boundaries Large deformation formulation employed to predict onset of various drained and undrained instabilities

5. Drained instability & boundary conditions 5 (a) (b) Drained instability modes  Diffused instability: Antisymmetric and symmetric modes Sinusoidal type velocity perturbation  Localized instability: Perturbation in form of velocity jump across a sharp shear plane Geometry and boundary conditions with (a) flexible and (b) rigid lateral boundary

6. 6 Undrained instability & boundary conditions Undrained instability modes  Liquefaction or solid-fluid type diffused mode: Sinusoidal type velocity and pore pressure perturbation  Localized instability: Perturbation in form of velocity jump across a sharp shear plane Assumption of locally drained condition (a) (b)

7. Condition for instability onset 7 Initially homogeneous stress-strain field Onset of non-homogeneous stress-strain field due to strain localization Constitutive relation Perturbed velocity mode Condition for emergence of perturbed velocity field, i.e., characteristic equation Stress equilibrium equation Perturbed velocity mode Boundary condition Diffusion equation (undrained case)

8. Constitutive relation (Wood, 2004) 8 The stress ratio acts as a state variable: evolution depends on the accumulated plastic shear strain through a hyperbolic equation The peak value of stress ratio is a function of accumulated plastic volumetric strain and initial void ratio. Material parameters of Hostun RF sand for the analysis (Gajo & Wood, 1999 and Wood, 2004) Plastic potential and yield surface for the hardening plasticity model and definition of state variable .

9. 9 Drained instability response( G=G 0 /3 ) e 0 =0.65 e 0 =0.9

10. 8 th FMGM Berlin, September 12-16, 2011 10 Drained instability response( G=G 0 /6 ) e 0 =0.65 e 0 =0.9 σ c =-300 kPa

11. 8 th FMGM Berlin, September 12-16, 2011 11 Drained instability response ( G=G 0 /8 )

12. 12 Drained instability response( G=G 0 /6 ) e 0 =0.65e 0 =0.9

13. 8 th FMGM Berlin, September 12-16, 2011 13 Drained instability response (a) Shear strain and (b) band angle variation with confining pressure for void ratio 0.65 and 0.9 for the case G=G 0 /6. (a) (b)

14. 8 th FMGM Berlin, September 12-16, 2011 14 Undrained instability response e 0 =0.65

15. 8 th FMGM Berlin, September 12-16, 2011 15 Undrained instability response e 0 =0.85

16. 8 th FMGM Berlin, September 12-16, 2011 16 Undrained instability response σ' c =-100 kPa σ' c =400 kPa

17. 8 th FMGM Berlin, September 12-16, 2011 17 Undrained instability response Effect of initial effective confining pressure on (a) shear strain at localization and (b) band angle inclination for two void ratios. (a) (b)

18. Co-authors Mousumi Mukherjee Doctoral Research Scholar Dept. of civil Engineering Indian Institute of Technology Kanpur India Anurag Gupta Assistant Professor Dept. of Mechanical Engineering Indian Institute of Technology Kanpur India 18

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