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Extended Mohr-Coulomb Criterion - Lesson Summary

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Extended M-C Criterion – Concepts

Researchers conducted a Null-Type test to evaluate whether the independent stress state variables that were used by Bishop are valid or not. The null type test is based on the manipulation of a different combination of stress state variables. It did confirm the validity of Bishop’s effective stress equation for unsaturated soils. After the Bishop’s effective stress equation for unsaturated soils was confirmed to be valid, Fredlund and Morgenstern came up with a new form of Modified Column Failure Criterion for unsaturated soils. In 1978, Fredlund Morgenstern and Widger proposed the Extended Mohr-Coulomb Criterion. The graphical representation of the stress state of the unsaturated soils can be very well defined using the form of Mohr-Coulomb Criterion, given by Fredlund and Widger
Extended Mohr-Coulomb Criterion – Triaxial Test Data
The strength parameters of the Modified Mohr-Coulomb Criterion and Extended Mohr-Coulomb Criterion are different. To estimate the strength parameters of Modified Mohr-Coulomb Criterion and Extended Mohr-Coulomb Criterion, the Suction Control Direct Shear Test data or Suction-Control Triaxial Test data is required. To estimate the strength parameters of Bishop’s Modified Mohr-Coulomb Criterion, at a fully saturated state, a minimum of 2 test data is required. At a fully saturated state, no test data is required to estimate the strength parameters of Extended Mohr-Coulomb Criterion.
Extended Mohr-Coulomb Criterion - Non-Linearity In 1988, Gan et al observed that shear stress versus matric suction data isn’t all linear. The angle of internal friction in the matric suction plane isn’t constant. This angle of internal friction was found to vary with matric suction. In the Extended Mohr-Coulomb envelop, the angle of friction in the matric suction plane becomes non-linear once the matric suction surpasses the air entry suction of the soil.
Fredlund, then, suggested three ways of handling the non-linearity in the angle of internal friction in the matric suction plane. The suggested ways are:
- Considering two linear zones
- Conservative approach
- Piecewise linear approach
In 1996, Vanapalli et al. came up with a new model for handling the non-linearity in the angle of internal friction in the matric suction plane.