Elastic-viscoplastic instantaneous response around circular and non-circular cavities performed in rock salt

摘要

Underground cavities of cross sectional shapes circular, or non-circular are often used in mining and civil engineering. The elasto-viscoplastic constitutive equations became in last decades important tools of phenomenological description of the main physical phenomena encountered at geomaterials, like yield, failure, dilatancy, or compressibility of the volume. In the study of stress behaviour around underground cavities we could distinguish two time periods : the first one, in which the cavity is excavated, followed by the time interval in which the cavity is exploited. The first time period is usually much shorter than the second one. Thus, in the constitutive model we could emphasize two tipes of mechanical behaviour : one related to instantaneous elastic response of the rock mass, corresponding to the first period of time, resp. a creep deformation of the material that lasts over a long period of tune. In the present paper we study the elastic-viscoplastic instantaneous response around one isolated square-like cavity, followed by the problem of the interaction between two circular nearby cavities. Within the elastic domain an interesting alternative to numerical approaches, like finite elements, is the combined use of complex potentials and conformal mappings, leading to explicite or semi-explicite solutions. Using the complete analysis of elastic stress distribution, we study the instantaneous viscoplastic behaviour around such cavities. Among others, the location of yield and failure domains, as well as dilatant and contractant characteristics are studied, based on recent researches by Prof. Cristescu. The examples given in our paper has been computed using the code MATHEMATICA for a rock salt, the numerical results showing quantitatively the effect of geometric and mechanical parameters on stress concentration and on location of instantaneous viscoplastic surfaces.