#Static equilibrium 3d problems cracked
Finally, a case study is adapted from an existing cracked hydraulic structure to evaluate its sliding stability using the QSE-FEM and 3D-LEM approaches. Three benchmark examples, of increasing complexities, are presented to verify the performance of the proposed methodology.
It is useful in preliminary sliding analyses to estimate the critical friction coefficient inducing sliding and the corresponding direction D. As part of the proposed methodology, a complementary simple tool, 3D-LEM, has been developed as a 3D extension of the classical limit equilibrium method (LEM).
In addition to the ratio of kinetic to internal strain energy, a new criterion is proposed to identify sliding initiation based on absolute displacements of a control point. However, in QSE-FEM, the determination of the incipient failure motion is challenging. QSE-FEM is known for its efficiency in solving highly nonlinear problems compared to implicit FEM. A methodology to assess a sliding safety factor ( SSF) and a sliding direction D for any structure with an a priori known 3D discrete crack surface geometry using the quasi-static explicit nonlinear finite elements method (QSE-FEM) is presented herein in the context of the strength reduction approach. It is important to consider the 3D particularities of the cracked surfaces in the nonlinear sliding safety evaluation of these structures. Several hydraulic concrete structures suffer from severe tridimensional (3D) discrete cracking, producing an assembly of concrete blocks resting one on top of the other.
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