The strength evaluation methods conventionally applied for rocks do not consider progressive failure. The authors explained these effects based on the non-linear strength behavior of the rock masses. The classical theory is applied in relation to the dilatancy of rock mass to describe this phenomenon. The strength of rock masses depend upon the strain history, expressing themselves as discontinuities at varied orientation of plane of weakness in diverse condition of joints containing numerous fill materials in closely packed joints at wide ranging confining pressures. There is a great multiplicity in the proposed relationships for the strength of jointed rocks. In the present study, the authors conceive the effect of increasing stresses as to induce permanent strains. This permanent strain appears as micro crack and fracture. A fully developed net work of permanent deformations forms joint. The joint may contain deposits of hydraulic and hydrothermal origin commonly known as gouge. The dilatancy may numerically captures varied engineering possibilities of joints in a rock mass. The joints grow as an effect of loading. The strength reduction of jointed rock with granular fill is expressed as Scr. The strength reduction factor [Scr] as a ratio of un-dilated to a fully dilated rock mass strength. An expression for strength reduction [Scr] due to dilatancy of gouge is obtained as Scr = exp (ξIr) where ξ=A/C The limiting values of coefficients of relative dilatancy index, (ξ=A/C) with variation of initial confining pressure ratio are obtained. The coefficient A takes a value of 3 for axi-symmetrical case and 5 for plane strain case. The values of coefficients of relative dilatancy index, when initial confining pressure is 10% of uniaxial compressive strength (pi/σci<<1) of intact rock of parent material loaded through a circular footing system, is 0 -0.6. However, the value of coefficients of relative dilatancy index, when initial confining pressure is 2 to 3 times that of uniaxial compressive strength (pi/σci>>1) loaded through a circular footing system, is -3. Similarly under plane strain conditions, the value of coefficients of relative dilatancy index, for low confinement (pi/σci<<1), is -1. The value of coefficients of relative dilatancy index, for high confining pressure (pi/σci>>1) in plane strain conditions is -3. This study provides a simple and integral solution for strength of jointed rocks, interpreted in relation to the commonly used soil, and rock parameters, used for a design of structure on rock masses. It has scope for prediction of an equivalent strength for tri-axial and plane strain conditions for unconfined and confined rock masses. Few novel observations presented here show that the extent of progressive failure of rock masses is a compressed function of material characteristics of the rocks, orientation and confinement of the elements.
The strength of jointed rock mass is important for the design of structures built on rocks such as towers, bridge piers, tunnels, deep seated nuclear and hazardous waste confinements and dams. The rock masses occur in nature with joints and varying amount of infill material commonly known as gouge.