Second-Order Work Criterion in the Stability Analysis of an Earth Dam Subjected to Seepage

Failure may take different forms: reaching the Mohr–Coulomb limit stress condition is accompanied by yielding, strain localisation may occur in shear, compaction or dilatant bands, arbitrary large strain and loss of strength may be accompanied by a field of chaotic displacements of soil particles. Failure is also related to material instability. It takes place when there is a loss of uniqueness of constitutive relationships. It has been found that instability domains exist strictly inside the Mohr–Coulomb failure surface. Material instability can be detected by local Hill's criterion, that is the second-order work at a point. Results of a coupled hydro-mechanical finite element analysis of an ‘earth dam – subgrade’ system at changing hydraulic boundary conditions have been presented in the article. Normalised values of the second-order work and factor of safety values by the shear strength reduction procedure for corresponding stages of the analysis were calculated. It has been shown that the value of the safety factor corresponds to the values of the second-order work. The analysis results show that a decrease in the value of the safety factor is accompanied by a decrease in the value of the second-order work until negative values occur at some points.