LEC-5 CL 601Characteristics of soil behavior.pptx

Constitutive modelling of Geomatrials;
Characteristics of soil behaviour;
Laboratory tests;
Plane stress problem;
Plain strain problem;
Stress and strain variables;
stress path;
Pre-consolidation;
Smooth cap model;
Critical state;
Stress dilatancy relationship;
Constitutive modelling;
M Tech geotechnical engineering;

1. Constitutive Modelling of Geomaterials Prof. Samirsinh P Parmar Mail: [email protected] Asst. Prof. Department of Civil Engineering, Faculty of Technology, Dharmasinh Desai University, Nadiad , Gujarat, INDIA Lecture: 5 : . Characteristics of S oil B ehaviour

2. 4. Characteristics of soil behavior

3. Laboratory tests: (special case) Plane strain

4. Laboratory tests: (special case) Plane stress

5. Laboratory tests: (special case )

6. Laboratory tests: Axisymmetric tests: drain triaxial, oedometric compression and undrained triaxial  1   a  2   r  3   r Check the sign convention

7. Stress and strain variables: The triaxial apparatus provides the possibility for confined uniaxial testing of soils or other materials and evidently provides two degrees of freedom in control of externally applied stress states. Few facts: Generally drained tests are carried for high permeable soils Undrained tests are carried out for low permeable soils Tests are done under fully saturated conditions (except unsaturated soil mechanics) Pore fluid is considered to be incompressible . Effective stress is assumed to be responsible for the deformation of any specimen  i  j   ij  u  ij This expression embodies the assumption of point contacts between the particles (and hence ‘zero’ area of contact), so that the pore water pressure acts over the whole area of any interface passing through particle contact points

8. Stress and strain variables: p  q  a  r  v  s Volumetric axial  a  radial  r  3 a r p   1     2    2  v   a  2  r  s  3   a   r  q    a    r   Work done per unit volume General stress space??  a   1  sin  m   3  2 q  3   q p   p   3  2     3        r  1  sin  m  6sin  m  3  sin  m  Triaxial Extension?? Avoid 2D representation of p-­‐q not correct from work done point of view  W  p   v  q  s   a   a  2  r   r Stress-­‐ratio and mobilized friction angle  m  ( compression ) Shear/ Deviatoric /Distortional

9. Stress path and invariants: triaxial compression Undrained stress path Extension and compression problem Predict the stress path of the staged embankment construction considering bottom layer is (a) high permeable: (b) low permeable  a  r  r  r  a p   I 1 3 q  3 J 2 p-­‐q plane (π plane)

10. Stress path and invariants: Significance of the third invariant J 3  J 2  1 . 5 c o s ( 3  )  3 3 2 Lode angle: θ  3  1  2 Hydrostatic axis, p’ TXC  2 TXC  1 TXC TXE TXE TXE  3 θ In case of axisymmetric loading conditions lode angle is zero as the stress path merged with principal axis Deviatoric plane

11. Stiffness: Isotropic elastic Material is called isotropic , if its mechanical properties are the same in all geometric directions. Constitutive relationships for these isotropic materials should be invariant to transformations of the coordinate system.   E  E  i j   1     1  2   i j  k k   1    i j Important property of the isotropic linear elastic model is that volumetric and deviatoric components of the stress-­‐strain behavior in this model are completely uncoupled 1  ij  s ij  3  kk  ij  ij  e ij   k k  i j 3 i j   K   i j k k 2 G e i j p  K  v q  3 G  s

12. Nonlinearity : secant and tangent stiffness   G t    G s   Tangent stiffness: incremental stress-­‐strain relation Secant stiffness: Average stiffness over a chosen range of strain Stiffness varies with the range of applied strain and requires special equipment for measurement Stiffness:

13. Stiffness: Nonlinearity : (pressure dependent) dq ⎫ ⎩ ⎭ ⎧ K  p   ⎬  ⎨ ⎩ ⎫ d  v e 3 G  ??  ⎬ ⎨ ⎭ ⎩ d  s ⎧ e ⎫ ⎬ ⎭ ⎧ d p  General representation ⎨ Example: the reversible swelling-­‐reloading stress-­‐strain curve can be approximated by a straight line.

14. Stiffness: Nonlinearity : (pressure dependency-­‐uncoupled) Model 1: (linear dependency on bulk modulus but constant shear modulus) r ⎛ p  ⎞ K t   p r ⎝ ⎜ p ⎠ ⎟ Model 3: (power law model) n Model 2: (linear dependency on both bulk modulus and shear) K t   p  G t  g s p  r ⎛ p  ⎞ G t  g s p r ⎝ ⎜ p ⎠ ⎟ n May lead to unrealistic Poisson’s ratio May violate energy conservation law within a closed loop stress path dq K t   p  ⎧ d p  ⎨ G t  G K  p   3 G ⎬  ⎨ ⎫ ⎧ ⎫ ⎩ ⎭ ⎩ ⎭ d  v e d  s e ⎧ ⎬ ⎨ ⎩ ⎫ ⎬ ⎭ dq ⎧ dp  ⎨ ⎩ ⎭ ⎫  K  p   3 G  p   ⎧ ⎬ ⎨ ⎩ d  v d  e s ⎫ ⎧ e ⎫ ⎬ ⎨ ⎬ ⎭ ⎩ ⎭

15. Nonlinearity : (pressure dependency) Duncan and Chan Model (1970) Tangential young modulus at u nloading-­‐ r eloading stage ur K : Modulus number n : exponent which govern the rate of change of E with cell pressure p a : Atmospheric pressure Hardin and Black Model (1969) G max  1230 OCR k  2 . 973  e  2 1  e  '   . 5 Empirical model for shear modulus (in psi ) determine d fro m th e wav e propagation velocities and from small amplitude cyclic simple shear test. Stiffness :

16. Stiffness: Nonlinearity : (coupled pressure and deviatoric stress dependent) Both bulk and shear modulus are the functions of both first stress invariant and second deviatoric stress invariant K  K  p  ,q  G  G  p  ,q  Lade and Nelson (1987) Nonlinear Elastic model M: Modulus number *, not true bulk or shear modulus Should not be singular

17. Stiffness: Nonlinearity : (Lade and Nelson, 1987 )

18. Stiffness: Hypoelastic Elas tic Hyperelastic

19. Stiffness: Anisotropy

20. Stiffness: Polarized shear wave velocity is measured using bender elements G ij   V ij 2 Anisotropy Microscopic analysis of particle fabric Orientation of soil particle and layout of the center of particles (geometric fabric). Orientation and activation of the inter-­‐particle contact and contact force (Kinetic fabric) Macroscopic analysis at continuum level Static test using sensitive stress-­‐strain measuring devise Dynamic test using piezoceramic bender elements Gault clay (Wood, 2004) Roesler , (1979) model Zero Strain Moduli (Elastic)

21. Stiffness: Cross anisotropy a special kind of anisotropy, which follows the axial symmetry with respect to any vertical axis. Normal Shear an anisotropic constitutive law cannot be expressed via stress and strain tensor invariants . (An exception is made when the formulation includes mixed invariants with the fabric tensor, reflecting material anisotropy) p  K  v q  3 G  s If z is the axial direction in triaxial then K = ? G = ? Stress path dependency and coupling!!!

22. Stiffness: Cross anisotropy

23. Stiffness: Anisotropy Graham and Houlsby (1983) model where E h and E v horizontal and vertical drained stiffnesses Stiffness anisotropy deduced from slope of effective stress path for undrained unload/ reload cycle within drained test

24. Numerical problems (a)

25. (b) For the following strain energy function deduce the stiffness in p’-­‐q space and find the stability condition for that Numerical problems

26. 6. Characteristics of soil behavior (II)

27. Preconsolidation OCR = p c / p

28. Preconsolidation Elastic response Hardening rule Yield envelope

29. Double hardening model / cap model

30. Smooth cap model

31. Direct shear experiment on sand http://www.tonygraham.co.uk/house_repair/wattle_daub/WD-­‐ 4_1_2.html

32. Critical state  p    q   v    s   s   s q f p f q p c s   f  cs   cs  M

33. Critical state “These are asymptotic states in which shearing of the soil can continue without further change in effective stress or density. The exact nature of the fabric of the soil at a critical state is not clear. It is certainly intended that any initial interparticle bonding should have been broken down so that the particles are all individually free to move and rotate.” – M.Wood Vesic and Clough, 1968

34. Critical state

35. Critical state Bishop and Henkel (1957)

36. Loose and dense sand behavior Work fully dissipated due to friction

37. Stress dilatancy relationship Analogy

38. Disclaimer The purpose of publishing this “ PPT” is fully academic. Publisher does not want any credit or copyright on it. You can download it , modify it, print it, distribute it for academic purpose. Knowledge increases by distributing it, hence please do not involve yourself in “ Knowledge Blockade” nuisance in academic industry. Before thinking of copyright just think @ the things we use in routine which we are using freely, without copyright. Man may die- does not knowledge. Jurisdiction is limited to Godhra , Panchmahals , Gujarat, India.

39. Any Questions ? Thank You