The role of rock joint frictional strength in the containment of fracture propagation

The fracturing phenomenon within the reservoir environment is a complex process that is controlled by several factors and may occur either naturally or by artificial drivers. Even when deliberately induced, the fracturing behaviour is greatly influenced by the subsurface architecture and existing features. The presence of discontinuities such as joints, artificial and naturally occurring faults and interfaces between rock layers and microfractures plays an important role in the fracturing process and has been known to significantly alter the course of fracture growth. In this paper, an important property (joint friction) that governs the shear behaviour of discontinuities is considered. The applied numerical procedure entails the implementation of the discrete element method to enable a more dynamic monitoring of the fracturing process, where the joint frictional property is considered in isolation. Whereas fracture propagation is constrained by joints of low frictional resistance, in non-frictional joints, the unrestricted sliding of the joint plane increases the tendency for reinitiation and proliferation of fractures at other locations. The ability of a frictional joint to suppress fracture growth decreases as the frictional resistance increases; however, this phenomenon exacerbates the influence of other factors including in situ stresses and overburden conditions. The effect of the joint frictional property is not limited to the strength of rock formations; it also impacts on fracturing processes, which could be particularly evident in jointed rock masses or formations with prominent faults and/or discontinuities

On cross-constraints method and physical contact laws

One of the crucial problems arising during iterative solution of contact problems is related to the unstable behaviour of the contact elements. Standard formulations do not permit oscillation of the solution path from one side to the other of the constraint limits. If a recursive change of state occurs the solution may not be reached. This fact is mainly due to the discontinuity which takes place moving from the status of gap closed to the status of gap open. A new method has recently been proposed to overcome such limitations. It permits the solution to take place on both sides of the constraint limit. Change of contact status in this case is smooth, hence a more stable solution path can be obtained. The basic formulation of the cross-constraints method adopts analytical functions to represent the non-linear behaviour of the contact. Both traditional penalty and barrier methods can be obtained as limit case of the proposed technique. In this paper we extend the method by replacing the analytical functions with constitutive laws based on micro- scopic characterisation of contact surfaces. The formulation permits problems where high precision and physical insight are required, to be dealt with. Many high-tech problems can be analysed by using the proposed method; the present work is a preliminary step for the thermomechanical analysis of cable in conduit superconductors

On augmented lagrangian algorithms for thermomechanical contact problems with friction

The detailed discretization of contact zones with contact stiffness based on real physical characteristics of contact surfaces can produce stiffness terms which induce ill-conditioning of the global stiffness matrix. Moreover the consistent treatment of frictional behaviour generates non-symmetric tangent stiffness matrices due to the non-associativity of the slip phase. Other non-symmetries are due to the coupling terms and to the dependencies on various parameters that can be involved. To overcome these difficulties almost consistent techniques based on two-step algorithms have been proposed in the past. Here an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase

A fast error check for structural analysis using the virtual force principle

An fast and effective error check for the FE stresses, based on the unit load theorem is proposed. The relative stress error is estimated by the relative error between displacements obtained by the unit load theorem and by the FE method. Analytical examples and numerical applications are presented