PRACTICAL IMPLICATIONS OF THE FAILURE CRITERIA
When we interpret soil failure using Coulomb, Mohr–Coulomb, Tresca, or Taylor failure criteria, we are using a particular mechanical model. For example, Coulomb’s failure criterion is based on a sliding block model. For this and the Mohr–Coulomb failure criterion, we assume that:
1. There is a slip plane upon which one part of the soil mass slides relative to the other. Each part of the soil above and below the slip plane is a rigid mass. However, soils generally do not fail on a slip plane. Rather, in dense soils, there are pockets or bands of soil that have reached critical state while other pockets are still dense. As the soil approaches peak shear stress and beyond, more dense pockets become loose as the soil strain-softens. At the critical state, the whole soil mass becomes loose and behaves like a viscous fl uid. Loose soils do not normally show slip planes or shear bands, and strain-harden to the critical state.
2. No deformation of the soil mass occurs prior to failure. In reality, signifi cant soil deformation (shear strains ~2%) is required to mobilize the peak shear stress and much more (shear strains >10%) for the critical state shear stress.
3. Failure occurs according to Coulomb by impending, frictional sliding along a slip plane, and according to Mohr–Coulomb when the maximum stress obliquity on a plane is mobilized.
The Coulomb and Mohr–Coulomb failure criteria are based on limiting stress. Stresses within the soil must either be on the slip plane or be below it. Taylor failure criterion considers not only the forces acting on the soil mass, but also the deformation that occurs from these forces. That is, failure is a combination of the forces and the resulting deformation. Tresca’s criterion, originally proposed as a yield criterion in solid mechanics, has been adopted in soil mechanics as a failure (limiting stress) criterion. It is not the same as the Mohr–Coulomb failure criterion.
With the exception of Taylor’s criterion, none of the failure criteria provide information on the shear strains required to initiate failure. Strains (shear and volumetric) are important in the evaluation of shear strength and deformation of soils for design of safe foundations, slopes, and other geotechnical systems.
Also, these criteria do not consider the initial state (e.g., the initial stresses, overconsolidation ratio, and initial void ratio) of the soil. In reality, failure is infl uenced by the initial state of the soil. , we will develop a simple model in which we will consider the initial state and strains at which soil failure occurs. A summary of the key differences among the four soil failure criteria. We are going to defi ne three regions of soil states, as illustrated in Figure , and consider practical implications of soils in these regions.
Region I. Impossible soil states. A soil cannot have soil states above the boundary AEFB.
Region II. Impending instability (risky design). Soil states within the region AEFA are characteristic of dilating soils that show peak shear strength and are
Interpretation of soil states.
Region III. Stable soil states (safe design). One of your aims as a geotechnical engineer is to design geotechnical systems on the basis that if the failure state were to occur, the soil would not collapse suddenly but would continuously deform under constant load. This is called ductility. Soil states that are below the failure line or failure envelope AB (Figure 10.16a) or 0-1-3 (Figure ) would lead to safe design. Soil states on AB are failure (critical) states When designing geotechnical systems, geotechnical engineers must consider both drained and undrained conditions to determine which of these conditions is critical.
The decision on what shear strength parameters to use depends on whether you are considering the short-term (undrained) or the long-term (drained) condition. In the case of analyses for drained condition, called effective stress analyses (ESA), the shear strength parameters are f9p and f9cs. The value of f9cs is constant for a soil regardless of its initial condition and the magnitude of the normal effective stress. But the value of f9p depends on the normal effective stress. In the case of fi ne-grained soils, the shear strength parameter for short-term loading is su. To successfully use su in design, the initial condition, especially the initial vertical effective stress and the overconsolidation ratio, must be known.