Cavern Response to Earthquake Shaking With and Without Dilation

INTRODUCTION The Northwestern University Rigid Block Model (NURBM) has been extended to explicitly model dilatant behavior of rock joints. By incorporating dilatancy, the resistance to shear displacement and slip, which previously was limited to simple Coulomb friction, along edge-to- edge contacts is now provided by contact roughness as well as frictional resistance. The explicit formulation is based on concepts presented by Plesha (1985) in which a plasticity-based phenomenological approach was used to model dilatant joint behavior. This approach has been modified to allow for joint closure upon reversal of shear deformation. After presenting a brief description of the new joint constitutive relationship, model behavior will be illustrated with two examples. The first involves a simple two-block model to simulate a cyclic direct shear test of a single joint. The second example involves simulation of a large cavern in a moderately jointed rock mass subjected to cyclic excitation. It will be shown that in- creasing joint roughness increases cavern stability by interlocking of adjacent blocks. JOINT CONSTITUTIVE RELATIONSHIP Within NURBM adjacent two-dimensional rigid blocks interact along their common edge-to-edge contact with contact forces transmitted at the contact midpoint. The contact constitutive relationship was originally restricted to a Coulomb friction yield criterion with no tensile stresses permitted along the smooth contact surfaces. The local coordinate system for any contact is described as shown in Figure 1 with the elastic stresses and displacements related by the linear- elastic constitutive law: [ ] The contact microstructure has been modeled as Patton-type saw-tooth surfaces such as shown in Figure 2. Sliding can be active along the right asperity with angle aR and length lR or along the left asperity with angle a and length lL. In general, aR and aL will difkr as will lR and lL but for purposes of this paper it has been assumed that these angles and lengths are identical. By a simple transformation, the microscopic asperity stresses can be expressed in terms of the macroscopic contact stresses [ ] If Coulomb friction is assumed along the asperity surfaces, the plastic slip condition will be [ ] where µ is the friction coefficient with the convention that compressive stress is negative. When F is negative, the behavior is elastic and when F is zero, slip can ensure. When plastic slipping does occur, it is assumed that the relative tangential and normal displacements between the two contacting rigid blocks are additively composed of recoverable elastic parts and nonrecoverale plastic parts, [ ]