where ........................................................(6.7)

Rearranging the above equations for χ_f ,

........................(6.8)

Similarly, the following equation can be used for obtaining χ_f from the extended direct shear test data

...............................................................(6.9)

A relationship between effective stress parameter and degree of saturation can be established if the matric suction at failure can be used to obtain the degree of saturation from SWCC data. Based on the experimental data, it is found that the observed trend between χ_f and the degree of saturation follows

Question – 6.1 A series of shear tests and water retention tests are conducted on unsaturated silty soil using modified direct shear set-up. The results are tabulated in the following table. Determine the shear strength parameters using Bishop's formulation and obtain a relation between the effective stress parameter and the degree of saturation.

Solution : The cohesion intercept and friction angle under saturated condition can be obtained from the first two tests given in the table. The calculated values are c'=30.7 kPa and φ' = 41.3°. These values can be substituted in the Eq. 6.9 for obtaining effective stress parameter under different matric suction as tabulated in the following table. z