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Critical State Model (Advance Soil Mechanics)
- 1. CRITICAL STATE MODEL By- Pankaj Drolia
- 2. Central Idea The central idea in the CSM is that all soils will fail on a unique failure surface in (pโ, q, e) space The framework of CSM ties the concept of one dimensional consolidation behaviour and shear stress vs normal stress behaviour
- 3. Why CSM?
- 4. Basics
- 7. Preconsolidation ratio (Ro) is the ratio by which the current mean effective stress in the soil was exceeded in the past (Ro = pโc /pโo , where pโc is the preconsolidation mean effective stress, or, simply, preconsolidation stress, and pโo is the current mean effective stress). The overconsolidation ratio using stress invariants, called preconsolidation ratio
- 8. Soil Yielding โ Yield Surface is a surface which separates stress states that produce elastic responses from stress states that produce plastic responses. โ Yield surface is assumed to be elliptical with the initial major axis as preconsolidation stress. โ All combinations of q and pโ that are within the yield surface will cause the soil to respond elastically. โ Any tendency of โ a stress combination to move outside the current yield surface is accompanied by an expansion of the current yield surface, such that during plastic loading the stress point (pโ, q) lies on the expanded yield surface and not outside and the soil to behave elastoplastically .
- 9. โ Expansion of Yield surface implies strain hardening materials such as loose sands and normally and lightly overconsolidated clays. โ The initial yield surface can contact also which simulates strain softening materials such as dense sands and heavily overconsolidated clays. โ The CSL intersects at the crest of yield surface. โ Soil must yield before it fails.
- 10. Behaviour of normally consolidated and lightly overconsolidated soil under drained condition
- 14. Behavior of Normally Consolidated and Lightly Overconsolidated Soils Under Undrained Condition
- 18. Behavior of Heavily Overconsolidated Soils Under Drained and Undrained Condition
- 22. Critical State Boundary The CSL serves as a boundary separating normally consolidated and lightly overconsolidated soils from heavily overconsolidated soils
- 23. Volume Changes and Excess Porewater Pressures Drained Tests Undrained Tests Compression +ve excess porewater pressure Expansion -ve excess porewater ressure
- 24. Elements of Critical State Model
- 25. Yield Surface Equation for the yield surface ellipse is given by:-
- 26. Failure Line in (pโ , e) space eฮ is the void ratio on the critical state line when pโ = 1 kPa
- 27. Failure Stress from CSM
- 28. Drained Triaxial Test n0 is the slope of ESP The slope of ESP for CD triaxial test is 3
- 32. Modified CSM
- 33. โ Experimental data from shear box tests on heavily overconsolidated clays presented by Hvorslev (1937) reveal that the locus of peak shear strength is approximately a straight line. In considering heavily overconsolidated fine-grained soils, we will replace that portion of the initial elliptical yield surface on the left side of the critical state line by the straight line found by Hvorslev. This line defines limiting stress states โ Then there is a yield surface labeled as RSW (after Roscoe, Schofield, and Wroth, 1958). โ There is also a line which delineate limiting tensile stress states.
- 35. Region 1 :- Impossible state as uncemented soil cannot sustain tension Region 2 :- Soil will behave elastically but as it approaches HV surface discontinuity starts occurring and shear band started to form and especially within shear bands the permeability increases and may cause the structure to fail because of seepage Region 3 :- Desirable behaviour as soil will behave in a ductile manner
- 37. The response of the soil after the HV surface is reached depends on how the stresses are redistributed with the soil mass. Four possible responses are (1) a strain-hardening type of response and then failure on the CSL, (2) a strain-softening type of response followed by a strain-hardening type of response and then failure on the CSL, (3) a strain-softening response and failure by tension, and (4) a strain-hardening response followed by a strain- softening type of response and failure by tension It is desirable to design geotechnical systems such that the soil will behave in a ductile manner under anticipated loadings
- 39. Relationship Between Normalized Yield (peak) Shear Stress and Critical State Shear Stress Under Triaxial Drained Condition ฮฑpcs < 1 :- strain hardening ฮฑpcs > 1 :- strain softening
- 40. Relationship Between the Normalized Undrained Shear Strength at Initial Yield and at Critical State for Overconsolidated Fine-Grained Soils Under Triaxial Test Condition
- 41. Relationship Between Direct Simple Shear Tests and Triaxial Tests Direct simple shear apparatus are not as readily available compared with triaxial apparatus
- 42. Relationship for the Application of Drained and Undrained Conditions in the Analysis of Geosystems ฮฑSL < 1 :- Undrained Condition is critical ฮฑSL > 1 :- Drained Condition is critical
- 43. Compressibility Indices (l and Cc) and Plasticity Index
- 44. Thank You !