VOLUME CHANGE PREDICTIONS

1. VOLUME CHANGE PREDICTIONS Unsaturated soil undergos volume change when the net normal stress or the matric suction variable changes in magnitude. Underconstant total stress, unsaturated soil will experience swelling and shrinking as a result of matric suction variations associated with environmental changes. In a collapsible soil, the collapse phenomenon occurs when the matric suction of the soil decreases.

2. Diagrammatic representation of Volume Change Theory An intermediate state volume with stress states Initial volume with stress states Final state volume with stress states

3. Volume change prediction Stress state for saturated and unsaturated soils

4. Volume change prediction Comparison of governing equations for saturated and unsaturated soils

5. 1. INTRODUCTION The effective stress (  - uw) has been proven to be an adequate variable to define the stress state of the saturated soil. There is a need to use a state variable approach in the understanding of the behavior of unsaturated soils.

6. 3. Suction component that produces the commonly observed changes in stress strain behavior in unsaturated soils are: Matric suction(ua-uw), and Net pressure term ( - ua ).

7. 4. Stress state Variables. Under triaxial conditions, The net mean stress p is then (1+23)/3 The deviator stress q is (1-3)/2, The suction is ua-uw

8. VOLUME CHANGE PREDICTIONS Matric suction is the suction exerted by the soil material (matrix) that induces water to flow in unsaturated soil. It is the positive equivalent of negative pore-water pressures.

9. Volume change constitutive equations      Constitutive relation for soil structure saturated soils

10. 1.3 Volume change constitutive equations ---Continued unsaturated soils

11. 1.3 Volume change constitutive equations ---Continued But the change in volumetric strain dεv is Summing the above relations

12. Volume change constitutive equation’s graphical representation

13. The relationships among the various volumetric coefficients –Cont.

14. Volume change constitutive equation • Compressibility form Saturated soil coefficient of Volume Change Unsaturated Soil

15. Volume change constitutive equations • Volumetric-Mass form Saturated soil, coefficient of compressibility Unsaturated soil

16. Swelling Volume Change The pre-consolidation pressure Pc refers to the maximum stress producing a volume decrease, that the soil has previously been subjected to in its past history. . The over-consolidation ratio, OCR, is defined as the ratio of Pc/ P’s,

17. Swelling Volume Change Total Heave Formulations e = Cs log PfCs from Rebound curve) P0 Po = (y – Ua) + (Ua-Uw)e

18. Swelling Volume Change Pf = y +y-Uw1 hi = ei *(hi) 1+eoi hi = Cs*hi log Pf 1+eoi Poi H= hi

19. One Dimensional Consolidation and Swelling Physical relations required for the formulation 1D US con eq Water phase Air phase ma1k coef. dueto net normal stress ma2 coef. Dueto matric suction

20. Water phase Partial Differential Equation This equation is the general form of partial differential equation for the water phase In saturated Conditions: mw1k=mw2=mv, kw=ks . This is Terzaghi form of the one dimensional consolidation equation for saturated soils.