The Mohr Failure Envelope
Over the last 40 to 50 years laboratory experiments have been conducted in order to quantify the conditions under which a wide range of materials might fail. Figure 23 is an illustration of a typical triaxial stress experiment. During the experiment, confining pressure and temperature are commonly held constant while s1 is progressively increased until failure occurs or some other critical experimental threshold is reached. Mohr circles can be used to "map" the values of normal and shear stresses at failure (Davis and Reynolds, 1984), failure being the loss of cohesion of a material when the differential stress (s1-s3) exceeds some critical value that varies with different types of Earth materials.
Figure 21. Triaxial stress test apparatus.
Triaxial stress test data used to plot the Mohr circles include the angle of the plane from the maximum principal stress on which the rock sample failed. Normal and shear stresses on that plane at the instant of failure can be calculated and plotted as a point on the Mohr circle. A best-fit line connecting the failure values of normal and shear stress for several Mohr circles is termed the Mohr failure envelope (Figure 23). The Mohr failure envelope is the locus of all shear and normal stresses at failure for a given rock material. The Mohr failure envelope delineates stable and unstable states of stress for a given rock material.