RELATIONSHIPS FROM CSM THAT ARE OF PRACTICAL SIGNIFICANCE
this section, we will explore some relationships of practical interest by manipulating the various equations we have derived using CSM. One way of building relationships is to use dimensionless quantities. We learned from CSM that the initial state of the soil strongly infl uences its behavior. So, we will normalize (make dimensionless) stress parameters such as p9y, qp (5 qy), and tf by dividing them by the initial mean effective stress, p9o. We will also use f9cs, wherever possible, as the base for relationships because it is a fundamental soil property. Only compression will be considered, but the relationships will be cast in terms of a generic M value. You can replace M by Me in the derived relationships for soil extension consideration. CSM parameters will be used to build the relationships and then be converted to soil parameters familiar to practicing engineers where necessary. Some of the benefi ts of these relationships are:
1. They impart further insights into the mechanical behavior of soils.
2. They allow us to use a few well-established soil parameters obtained from simple soil tests such as one-dimensional consolidation and triaxial tests to predict soil strength for various field conditions.
3. They provide us with guidance as to what condition (drained or undrained) would likely be critical in analyzing the safety of geosystems.
4. They allow us to convert the shear strength from axisymmetric tests (triaxial) to plane strain tests (direct simple shear).
5. They guide us to the kind of analysis (elastic or elastoplastic) that may be appropriate for geosystems design.
6. They help us to estimate under what conditions a soil would likely exhibit a peak shear stress.
7. They defi ne limits to provide guidance on when a soil will behave in a ductile manner or show discontinuous response.
Relationship Between Normalized Yield (peak) Shear Stress and Critical State Shear Stress Under Triaxial Drained Condition:
Normalizing (making dimensionless) Equation by dividing both sides of it by p'o , we get
Similarly, Equation becomes
For the standard triaxial CD test, no 5 3 and Equation can be written as
Similarly, Equation become
We defi ne a ratio, apcs, to relate the normalized initial yield shear stress to the normalized shear stress at the critical state for triaxial drained test. Thus,
For triaxial compression, M is given by Equation and by substitution in Equation we get