Instability analysis about saturated rocks is carried out to understand the initiation and evolution of rock landslides and rock-falling. The spatial development of a single shear band in saturated rocks for anti-plane shear deformation is mainly investigated here. It is shown that if the angle between the proportional loading path and the direction of the localization ∆θ = π/2, then the deformation is stable. This corresponds to the case of neutral loading. The case ∆θ > π/2 corresponds to elastic unloading. ∆θ < π/2 corresponds to loading and the instability develops the fastest when ∆θ is equal to zero. Positive solutions for α require that the rate of pore pressure softening exceed the rate of strain hardening.
Shear band is often observed in saturated rocks and is the main reason that causes the failure of foundations, the emergence of landslide etc (Kebeasy, 2008). Such as during the earthquake occurred in Wenchuan, Sichuan province, China at 14:28 on May 12, 2008 (Beijing time), many rock landslides are excited. For rock landslides, the initiation and evolution of cracks in rocks which may cause the lose of the strength is the key problem. The development of shear band in rock determines the evolution of cracks. Thus to study the initiation and evolution of shear band in rocks is very important for understanding the initiation of rock landslides. Shear bands is closely dependent on the material characteristics and the local strain (Rice, 1975). For an example, when the pore pressure softening overcomes the strain hardening (Sulem, 2006; Lu 2000), localization shear may form.
The issue of the inception of localized shearing in rocks subjected to undrained deformation has been the object of both theoretical as well as experimental research. Theoretical contributions are related mainly to stability and bifurcation analysis of diffused and localized failure models (Rice, 1975). Typically, the stability problem is formulated by considering small perturbations in field variables (e.g. displacement and pore pressure). Classical continuum approach leads, in this case, to the ordinary diffusion equation for the perturbation in pore pressure (Rice, 1975). The results indicated that the uniform response is often followed by the onset of a diffused, nonhomogeneous deformation model, after which distinct shear bands form. However, this problem is often discussed under inertia-free undrained conditions (Rice, 1975; Pietruszczak et al 1993). Anti-shear is a commonly load bear by Rocks in the condition of earthquake, wind load etc.. Nevertheless, study on the failure under this type of load is few.
In viewpoint of above, we will investigate the spatial development of a single shear band for anti-plane shear deformation in this paper so as to obtain a comprehensive and precise picture of the instability phenomenon by using of the method of Douglas &Chen [1985].
Consider anti-plane shear deformation, for which the motion is governed by
(Equation in full paper)
(Equation in full paper)
Substitution of the equation above into the controlling equations (3) and (12) gives the first order.
