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Non-local yield limit degradation

Presented is a new type of a non-local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit. The key idea, which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation, is to apply the non-local concept only to those parameters which cause the degradation while keeping the definition of the strains local. Compared to the previously advanced fully non-local continuum formulation, the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions. The new formulation exhibits no zero-energy periodic modes, imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient. Two-dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy. The formulation is applied to tunnel excavation in a soil stabilized by cement grouting, with the objective of preventing cave-in (burst) of the tunnel sides due to compression softening.