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

Sternik Krzysztof

Studia Geotechnica et Mechanica

2023

Vol. 45, nr s1

253--261

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.

Numerical Modeling of Water Flow in Expansive Soils with Simplified Description of Soil Deformation

Michalski S., Szymkiewicz A.

Archives of Hydro-Engineering and Environmental Mechanics

2018

Vol. 65, nr 4

301--313

In this paper we describe a numerical model of transient water flow in unsaturated expansive soils and the resulting soil volume change. The unsaturated flow equation is solved in a 2D domain using a finite-volume method and an explicit time discretization scheme. Strains in the soil mass are calculated by two simplified approaches, assuming that the strain state is either 1D (in the vertical direction only) or 2D with equal strains in horizontal and vertical directions. The model is applied to two cases described in the literature, in which the strains were computed from the solution of the stress equilibrium equation. It is shown that the simplified methods give results which are reasonably close to the more complex approach based on the equilibrium equations. The proposed model can be used to predict time-varying soil shrinkage and swelling caused by natural and anthropogenic factors.