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This paper proposes a method of describing a global failure in geomechanics problems using the finite element method. When considering a quasi-static approach, a limit state cannot be described properly before a numerical divergence of the computation is reached. The main idea is to use a dynamic approach to catch the failure state of a quasi-static problem. However, the events that occur after the failure state are not taken into consideration, because after such a state, the response of a geostructure is not physically and mathematically unique. The second point developed in this paper is the definition of a proper safety factor, which can be useful for engineers. The second-order work criterion under local (homogeneous problems) and global (boundary value problems) forms is reviewed to determine the physical and mathematical interests of using it. Selected finite element simulations are presented. The best way of defining a safety factor using such numerical methods is proposed.

Definition of a safety factor using the finite element method in geomechanics, from a static to dynamic regime