Knowledge of the behavior of rock joints is essential in the design and construction of large structures like tunnels, underground power houses, dams and foundations. When a numerical solution technique, such as finite element method is employed to analyze an underground structure, it is required that the realistic behavior of rock joints be known for a meaningful analysis. Many investigators have worked on the refinement of the constitutive relationship for a jointed rock mass. In this investigation, an attempt was made to examine the direct shear behavior of rock joints and to formulate a representative Constitutive Law.
The failure theory for rock joints in its simplest form can be expressed As (mathematical equation) (available in full paper) Where F and N are shear and normal forces and µ is the coefficient of friction. Failure criteria most often used is Mohr - Couloumb's law (mathematical equation) (available in full paper) Where r and s are shear and normal stresses and So is the inherent shear strength of contact surface. However, normal and shear stress relations for peak and residual strengths of rock joints can be represented generally by Figure 1. Here the residual strength can be viewed as the strength of an uncemented discontinuity while the peak strength is the strength of the intact cemented joint. Friction is the controlling factor between the surface of joints and fracture planes. Maximum values for the coefficient of friction may be high as 75 to 80 degrees. However, residual values rarely deviate beyond the range of 25 to 30 degrees. For smooth surfaces, the coefficient of friction will range, generally between 0.4 and 0.8 but mostly be about 0.5 and 0.6 Relatively smooth surfaces fail by stick-slip. Rough surfaces slide by stick-slip at low normal stresses. The shear strength of a rock joint is sensitive to degree of surface roughness, compressive strength of the rock, degree of weathering, mineralogy, and the presence or absence of water. Irregular and poorly matching joint surfaces can cause stress distribution to be complex. The roughness of a joint is classified into first and second order roughness. First order roughness correspond to major undulations on the bedding plane. The small bumps and protrusions on the primary undulations are re- ferred as second order roughness. At low normal stresses, the second order projections control behavior and account for what is often called a slight cohesion. This will become less important as the normal stress increases and small asperities are sheared. The the primary or first order projections will come into play. The behavior of a joint where the discontinuity surface is not exactly parallel to the direction of the shear stress, Figure 2, can be expressed as (mathematical equation) (available in full paper) Where i = the slope of the inclined plane. In case of a rough rock joint, Figure 3, due to dilation, any horizontal (shear) displacement, must accompanied by a displacement in the vertical direction (normal). Con- traction is also possible and is the closing of the joint due to large normal stresses.