Nonlinear Power-Type Failure Laws for Geomaterials: Synthesis from Triaxial Data, Properties, and Applications

Nonlinear power-type failure envelopes of the form τ=(a+bσ)n were examined in this paper. It is shown that equations for which 0<n<1/2 are legitimate failure envelopes provided that a is greater than some function of b, contrary to earlier assertions. The principal stress σ1-σ3 relations corresponding to these laws have been derived explicitly for the quadratic law (n=1/2) and implicitly for n=1/3,2/3,and 3/4. For other n values, a numerical algorithm for deducing the principal stress relations has been given. The procedure for evaluating the parameters a and b from triaxial test data for a specified n value is presented in detail, and it parallels Baker's earlier effort. Almost all previous studies on nonlinearity have concentrated on its effect on the factors of safety of slopes. This study provides a numerical method for evaluating the earth pressures on smooth retaining walls, under plane-strain conditions, for the case n≠1/2. When n=1/2, closed-form equations, which are nonexistent in the literature, were derived for both the earth pressures and the slip surfaces in two-dimensional plane-strain active and passive stress states. A new explicit formula is presented for the depth of tension cracks in plastic soils for n=1/2, whereas new implicit formulas are developed for n=1/3,2/3,and 3/4. The assumed value of this depth has a profound influence on the calculated factor of safety of a slope. Existing Rankine, Bell, and Coulomb formulas overestimate the passive resistance of geomaterial, and this study shows that the use of a nonlinear law predicts more realistic reduced values of passive resistance. Therefore, the factor of safety of 2 or more hitherto applied to passive resistance in the design of embedded walls can now be reduced to a lower value. A computer program was included for automatically determining the best n value that matches the triaxial test data together with the associated a and b and also for doing the rest of the calculations rapidly. As a consequence, a best-fit nonlinear power-type envelope can now be fitted effortlessly to the Hoek-Brown criterion.