Whitney stratification, equisingular family and the aureole of quasi-ordinary singularity

A Whitney stratification is constructed for a quasi-ordinary singularity. Using this stratification equisingular family of quasi-ordinary singularities is studied. It is shown that the characteristic monomials determine and are determined by differential equisingularity. For a quasi-ordinary singularity $(V,0)$ the aureole, a (finite) family of subcones of the tangent cone C\sb{V,0} dual to the limits of tangent spaces to V\sp{o} at 0, is computed. It is seen that the aureole is determined by the characteristic monomials

A direction-dependent shear strength criterion for rock joints with two new roughness parameters

The surface morphology of a rock joint is closely related to its mechanical properties. To reasonably characterize a rock surface, two new roughness parameters were proposed in this paper. One is related to the average slope angle of asperities that contribute to the shear strength, and the other reflects the frictional behavior of asperities that is defined as the maximum possible contact area in the shear direction. Taking the standard joint roughness coefficient profiles as example, these two roughness parameters can be applied to describe the directional characteristics of shear strength. Based on their relationships with initial dilation angles, the proposed roughness parameters were incorporated into a peak shear strength criterion. It is shown that the predicted peak shear strength is consistent with experimental data, and there is a power–law relationship. The application range of new roughness parameters was determined, which may facilitate a measurement process