Two-Dimensional Continuum Model for Jointed Media with Orthogonal Sets of Joints

This investigation involves the development of a two-dimensional continuum model for the description of jointed media. Specific application of the model developed here is for the potential geological disposal of radioactive waste in the layered sequence of fractured volcanic tuffs under Yucca Mountain, Nevada. This is currently being considered by the Nevada Nuclear Waste Storage Investigations Project, administered by the Nevada Operations Office of the U. S. Department of Energy. The work is a direct extension of the previous constitutive model by Thomas (1982) based on the work of Morland (1974). The main feature of Thomas's model includes two parts: a continuum approximation based on average discontinuous displacements across jointing planes within a representative elementary volume, and a material constitutive description based on linear elastic matrix material behavior and nonlinear normal and shear joint behavior between jointing planes. The mathematical descriptions by Morland based on strain partitioning among matrix material and joint sets allow multiple joint sets to be included in the model. However, the initial effort by Thomas to implement Morland's mathematical model included only a single set of joints. To make the material model reflect more realistically the field characteristics, the current work extended Thomas's model to include orthogonal sets of joints. The nonlinear elastic normal joint behavior is retained in the present model. Joint shear response was treated as linear elastic in the shear stress versus shear displacement relationship prior to attaining the stress level governed by the Coulomb friction criterion. Beyond this critical stress value, a horizontal line is assumed in the work of Thomas for the shear stress versus slip displacement relationship such that the shear stress remains constant while the slip displacement increases. Motivated by experimental observation, the current work generalized the shear response to allow a line with finite slope to govern the slip behavior beyond the critical stress level. The inclusion of an orthogonal joint set led to a fourth order algebraic equation for the calculation of stress increments as compared with a second order equation obtained by Thomas. The nonlinear elastic normal joint behavior provides criteria which allow the selection of the root that yields result consistent with the loading condition of the problem. The addition of one more set of joints provides the potential to more completely study the interaction of various parameters representing the characteristics of jointed media behavior. Material responses to various loading conditions based on the present constitutive model have been obtained. These results and their comparisons to single joint set results are presented. Formulation of the Continuum Model The inclusion of an orthogonal joint set led to a fourth order algebraic equation for the calculation of stress increments as compared with a second order equation obtained by Thomas. The nonlinear elastic normal joint behavior provides criteria which allow the selection of the root that yields result consistent with the loading condition of the problem. The addition of one more set of joints provides the potential to more completely study the interaction of various parameters representing the characteristics of jointed media behavior. Material responses to various loading conditions based on the present constitutive model have been obtained. These results and their comparisons to single joint set results are presented. Let us focus our attention on the set with normal n first. Let the jump dilation displacement and jump slip dasplacement associated with the [ ]