Lattice models provide discontinuous approximations of the displacement field over the computational domain, which facilitates the modeling of fracture and other discontinuous phenomena. By discretizing the domain with two-node elements, however, ordinary lattice models cannot simulate the Poisson effect in a local (intra-element) sense, which is problematic for some types of analyses. Furthermore, such methods are limited in the range of Poisson ratio values that can be simulated. We present a new approach to remedy such known, yet underappreciated, shortcomings of lattice models. In this approach, the Poisson effect is modeled through the introduction of fictitious stresses into a regular lattice. Capabilities of the new approach are demonstrated through compressive test simulations of homogeneous and heterogeneous materials. The simulation results are compared with theory and those of continuum finite element models. The comparisons show good agreement for arbitrary Poisson ratios (including ν≥ 1/3) with respect to nodal displacement, intra-element stress, and nodal stress. This form of discrete method, supplemented by the proposed fictitious measures of stress, retains the simplicity of collections of two-node elements.

This paper presents a modeling approach for studying hydro-mechanical coupled processes, including fracture development, within geological formations. This is accomplished through the novel linking of two codes: TOUGH2, which is a widely used simulator of subsurface multiphase flow based on the finite volume method; and an implementation of the Rigid-Body-Spring Network (RBSN) method, which provides a discrete (lattice) representation of material elasticity and fracture development. The modeling approach is facilitated by a Voronoi-based discretization technique, capable of representing discrete fracture networks. The TOUGH-RBSN simulator is intended to predict fracture evolution, as well as mass transport through permeable media, under dynamically changing hydrologic and mechanical conditions. Numerical results are compared with those of two independent studies involving hydro-mechanical coupling: (1) numerical modeling of swelling stress development in bentonite; and (2) experimental study of desiccation cracking in a mining waste. The comparisons show good agreement with respect to moisture content, stress development with changes in pore pressure, and time to crack initiation. The observed relationship between material thickness and crack patterns (e.g., mean spacing of cracks) is captured by the proposed modeling approach. © 2013 Elsevier Ltd.