On the Stability of Dilatant Hardening for Saturated Rock Masses

Fissured rock masses tend to dilate as they are deformed inelastically toward failure. When the rock is fluid saturated and the time scale does not allow drainage, suctions are induced in the pore fluid, and by the effective stress principle the rock is dilatantly hardened over the resistance that it would show to a cor­ responding increment of drained deformation. This paper considers a compressed layer of saturated rock deformed in shear. Inelastic stress-strain relations are formulated, and these relations illustrate dilatant hardening when the layer is sheared without drainage at its boundaries. Parameters governing the ~lope of the hardened stress-strain curve are identified; these parameters predict a rising slope even when that pre­ sumed for homogeneous deformation under drained conditions is' unstably falling. However, it is shown that the amount of dilatant strengthening that can actually be realized is limited by an instability. In par­ ticular, when the corresponding drained stress-strain curve has become unstable, small nonuniformities in the deformation field are shown to grow by local diffusive fluxes of pore fluid, and this is taken as the in­ ception of localized shearing in a fault zone. Fissured rock masses are observed to dilate as they are de­ formed inelastically toward failure under confining pressure [e:g. , Brace e¥ al., 1966]. This arises from frictional sliding on microcracks, which props them open at asperities and initiates further local tensile fissuring at their tips. The phenomenon in groundwater-saturated rock has received in­ tensive recent interest [Nur, 1972; Scholz lit ai. , 1973; Whit­ comb et al., 1973] due to its possible associath~n with seismical­ ly observable precursors to shallow-focus earthquakes. When rock is saturated and the time scale of deformation is too short for diffusional drainage, the tendency to dilate will induce suc­ tion in the pore fluid. This suction augments the effective nor­ mal stress on fissure surfaces and hence dilatantly hardens the rock against continuing deformation. The phenomenon was first discussed for granular materials by Reynolds and is well known in the soil mechanics literature. It has been studied in connection with seismic sources by Frank [1965] and observed by Brace and Martin [1968] in triaxial tests of saturated rock. Indeed, the possibility arises that rock in shallow-focus fault regions is stabilized by its pore fluid against rapid failure dur­ ing the premonitory period, when large-scale dilatancy seems to be taking place. Hence the processes and the extent of dilatant strengthen­ ing of saturated rock are of great interest, as are also the con­ ditions for its terminal loss of stability to localized de­ formation in a narrow fault zone. Frank [1965] has addressed the instability conditions for a special model of dilatant gran­ ular material. The present paper focuses attention on a com­ pressed layer of saturated rock that is sheared toward failure. Dilatant inelastic constitutive relations are formulated that in­ corporate the Terzaghi-Biot effective stress principle and Dar­ cy diffusion in the layer. In this way the parameters governing dilatant hardening are established, and conditions are derived for its loss of stability.