## Relationship Between the Normalized Undrained Shear Strength at Initial Yield and at Critical State for Overconsolidated Fine-Grained Soils Under Triaxial Test Condition

We can develop a relationship between the normalized undrained shear strength at initial yield and at the critical state for overconsolidated fi ne-grained soils. We know from and that under a certain initial stress state and effective stress path, a soil can exhibit a peak shear stress and then strain-soften to the critical state. CSM allows us to establish what initial soil states will cause a fi ne-grained soil to show a peak undrained shear strength. Let us denote the ratio of the normalized undrained shear strength at initial yield to the normalized shear strength at the critical state as aycs. From , we obtain

plot of Equation for L in the range 0.75 to 0.85. When aycs . 1, the normalized yield undrained shear strength is greater than the normalized critical state undrained shear strength. This occurs over a limited range of Ro. For L 5 0.8, the range is 2 , Ro , 4. Since for each soil type there is a limiting value of Ro at which rupture would occur, then there is a cutoff value Ro 5 Rt for each value of critical state friction angle. Figure is applicable to f9cs 5 208. The practical signifi cance of aycs is to estimate the undrained shear strength at initial yield from knowing the undrained shear strength at the critical state and vice versa. Knowing the initial yield stress allows you to use an elastic analysis to analyze your geosystem.

Recall from Figure that Hvorslev found that peak shear stresses when normalized to the equivalent effective stress for overconsolidated fi ne-grained soils lie along the line TF. The slope of this line (TF) is

where nt is the slope of the tension line and tc is the intersection of the HV surface with the tension line given by Equation . Recall that in the triaxial compression test, nt . The initial deviatoric stress on the HV surface, qyH, is then

whereand the subscript yH denotes the limiting stress state on reaching the HV surface. The normalized undrained shear strength of the soil on reaching the HV surface is

plot of Equation . For Ro , 2, stable yielding would occur. For each value of critical state friction angle, there is a critical Ro 5 Rt at which the soil would rupture (tension

Variation of theoretical normalized undrained

shear strength on the Hvorslev’s surface for isotropically consolidated

fi ne-grained soils.

limit), as discussed previously. The end point of the curve for each critical state friction angle in Figure indicates the tension limit. The practical signifi cance of Equation is that it is an expression to calculate the limiting stresses (incipient instability) for heavily overconsolidated fi ne-grained soils.