The softening hyperelastic model based on the strain energy limitation is of clear concepts and simple forms to describe the failure of materials. In this study, a linear and a nonlinear softening hyperelastic model are proposed to characterize the deformation and the failure in granular materials by introducing a softening function into the shear part of the strain energy. A method to determine material parameters introduced in the models is suggested. Based on the proposed models the numerical examples focus on bearing capacity and strain localization of granular materials. Compared with Volokh softening hyperelasticity and classical Mohr-Coulomb plasticity, our proposed models are able to capture the typical characters of granular materials such as the strain softening and the critical state. In addition, the issue of mesh dependency of the proposed models is investigated.

An analytical solution of the fully coupled system of equations governing the plane strain deformation of a poroelastic medium with anisotropic permeability and compressible fluid and solid constituents is obtained. This solution is used to study the consolidation of a poroelastic clay layer with free permeable surface resting on a rough-rigid permeable or impermeable base. The stresses and the pore pressure are taken as the basic state variables. Displacements are obtained by integrating the coupled constitutive relations. The case of normal surface loading is discussed in detail. The solution is obtained in the Laplace-Fourier domain. Two integrations are required to obtain the solution in the space-time domain which are evaluated numerically for normal strip loading. Consolidation of the clay layer and diffusion of pore pressure is studied for both the bases. It is found that the time settlement is accelerated by the permeability of the base. Initially, the pore pressure is not affected by the permeability of the base, but has a significant effect, as we move towards the bottom of the layer. Also, anisotropy in permeability and compressibilities of constituents of the poroelastic medium have a significant effect on the consolidation of the clay layer.

It is generally accepted that material heterogeneity has a great influence on the deformation, strength, damage and failure modes of rock. This paper presents numerical simulation on rock failure process based on the characterization of rock heterogeneity by using a digital image processing (DIP) technique. The actual heterogeneity of rock at mesoscopic scale (characterized as minerals) is retrieved by using a vectorization transformation method based on the digital image of rock surface, and it is imported into a well-established numerical code Rock Failure Process Analysis (RFPA), in order to examine the effect of rock heterogeneity on the rock failure process. In this regard, the numerical model of rock could be built based on the actual characterization of the heterogeneity of rock at the meso-scale. Then, the images of granite are taken as an example to illustrate the implementation of DIP technique in simulating the rock failure process. Three numerical examples are presented to demonstrate the impact of actual rock heterogeneity due to spatial distribution of constituent mineral grains (e.g., feldspar, quartz and mica) on the macro-scale mechanical response, and the associated rock failure mechanism at the meso-scale level is clarified. The numerical results indicate that the shape and distribution of constituent mineral grains have a pronounced impact on stress distribution and concentration, which may further control the failure process of granite. The proposed method provides an efficient tool for studying the mechanical behaviors of heterogeneous rock and rock-like materials whose failure processes are strongly influenced by material heterogeneity.

Shale gas formations exhibit strong mechanical and strength anisotropies. Thus, it is necessary to study the effect of anisotropy on the hydraulic fracture initiation pressure. The calculation model for the in-situ stress of the bedding formation is improved according to the effective stress theory. An analytical model of the stresses around wellbore in shale gas reservoirs, in consideration of stratum dip direction, dip angle, and in-situ stress azimuth, has been built. Besides, this work established a calculation model for the stress around the perforation holes. In combination with the tensile failure criterion, a prediction model for the hydraulic fracture initiation pressure in the shale gas reservoirs is put forward. The error between the prediction result and the measured value for the shale gas reservoir in the southern Sichuan Province is only 3.5%. Specifically, effects of factors including elasticity modulus, Poisson's ratio, in-situ stress ratio, tensile strength, perforation angle (the angle between perforation direction and the maximum principal stress) of anisotropic formations on hydraulic fracture initiation pressure have been investigated. The perforation angle has the largest effect on the fracture initiation pressure, followed by the in-situ stress ratio, ratio of tensile strength to pore pressure, and the anisotropy ratio of elasticity moduli as the last. The effect of the anisotropy ratio of the Poisson's ratio on the fracture initiation pressure can be ignored. This study provides a reference for the hydraulic fracturing design in shale gas wells.

Construction of a new cavern close to an existing cavern will result in a modification of the state of stresses in a zone around the existing cavern as interaction between the twin caverns takes place. Extensive plane strain finite difference analyses were carried out to examine the deformations induced by excavation of underground twin caverns. From the numerical results, a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) has been used to relate the maximum key point displacement and the percent strain to various parameters including the rock quality, the cavern geometry and the in situ stress. Probabilistic assessments on the serviceability limit state of twin caverns can be performed using the First-order reliability spreadsheet method (FORM) based on the built MARS model. Parametric studies indicate that the probability of failure $P_f$ increases as the coefficient of variation of Q increases, and $P_f$ decreases with the widening of the pillar.

In this study, a CPT-based p-y analysis method was proposed for the displacement analysis of laterally loaded piles. Key consideration was the continuous soil profiling capability of CPT and cone resistance profiles that do not require artificial assumption or simplification for input parameter selection. The focus is on the application into offshore mono-piles embedded in clays. The correlations of p-y function components to the effective cone resistance were proposed, which can fully utilize CPT measurements. A case example was selected from the literature and used to validate the proposed method. Various parametric studies were performed to examine the effectiveness of the proposed method and investigate the effect of property profile and its depth resolution on the p-y analysis. It was found that the calculation could be largely misleading if wrongly interpreted sub-layer condition or inappropriate resolution of input soil profile was involved in the analyses. It was also found that there is a significant influence depth that dominates overall load response of pile. The soil profile and properties within this depth range affect most significantly calculated load responses, confirming that the soil profile within this depth range should be identified in more detail.