Incorporating shear stress ratio and load cycle number in a simple permanent deformation model for unbound material

Abstract

A power model (ε = A. NB) to estimate permanent strain (ε) from single-stage repeated load triaxial (RLT) tests can simulate both shakedown and incremental collapse. When the exponent B < 1, the ε versus load cycle number (N) plot concaves downwards, resembling that of a material that shakes down. When B > 1, the same plot concaves upwards, mimicking that of a material that incrementally collapses. A power model that relates A and B to the shear stress ratio (SR = 1/factor of safety), a measure of how far the RLT specimen is away from static failure, is proposed. Use of SR as an independent variable in a PD model is advantageous because it embodies the geomaterial’s gradation, physical state, suction, stress level, shear strength and margin of safety against static failure. No other parameters bar N and SR are needed, enabling the number of independent variables and hence model complexity to be kept low. This model was applied to a virgin and a recycled concrete aggregate utilizing 2 independent variables (N and SR) with A and B both functions of SR. A rational procedure to estimate the mobilized shear stress is presented and a methodology to quantify SR that considers non-linearity of the Mohr-Coulomb failure envelope and cohesion due to suction in the unsaturated RLT specimens is proposed; such considerations have been absent in previous models. For the materials tested, A was found to decrease non-linearly with increasing SR while the relationship between B and SR is quite linear. The resulting model was able to simulate the RLT test data quite well with four fitting parameters. The fitting parameters can be easily derived using linear regression on a spreadsheet and were all statistically significant with a confidence level exceeding 95%. Once B is known, the shakedown limit can be estimated by setting B < 1. An appropriate margin of safety can be incorporated on the shakedown load to limit the permanent strain.