Joint Stiffness and Deformation Behaviour of Discontinuous Rock

Nassir, M. (University Of Calgary) | Settari, A. (University Of Calgary) | Wan, R. (University Of Calgary)


Some rock masses are characterized by joints, fractures and other plane of weakness which reduce the strength and deformation properties of rock structure. Under different loading conditions, joints with weaker normal and shear strength undergo a relatively higher strain than intact rock. Since permeability of jointed rock masses in fractured reservoirs is a strong function of joint aperture size, one may expect a major change in the permeability when subjected to confining load variation. Therefore, it is very important to establish the relation between the stress-strain of the jointed rock mass and the reservoir permeability. This relation is particularly important to model hydraulic fracturing and productivity decline in tight gas wells.

In this paper, a new relation is proposed to model pre-peak shear stiffness of the joint based on the conventional joint surface parameters and the confining load. Furthermore, constitutive matrices for evaluating deformation behavior of single joint and regularly jointed rock are presented as the results of an analytical study. Based on the concept of joint stiffness, an equivalent stiffness for regularly jointed rock masses was derived, assuming that the deformation of the jointed rock mass equals the sum of the deformation of the rock matrix and the joints. Finite element technique is used to numerically model the deformation behavior of the jointed rock under various loading conditions. The applicability of the constitutive model to represent jointed rock mass was confirmed from comparison of the numerical results with some of the existing experimental data. The model presented here will be the key element for integrated geomechanical modeling of tight gas wells, naturally fracture reservoirs, and other fracturing processes in stresssensitive reservoirs.


Mechanical behavior of the jointed rock in naturally fracture reservoirs or in rock bodies stimulated by hydraulic fracturing (i.e., an artificially fractured well in a tight gas reservoir) is highly influenced by the presence of joints. Since joints are the main flow conduit in jointed rocks and the joint permeability is a quadratic function of its aperture size, it is crucial to investigate the variations in a joint aperture size under different loading conditions.

Mechanical behavior of a joint is characterized by its normal-shear mechanical deformation and is defined in the form of a joint constitutive model. Here we will first review the literature related to rock joint normal and shear deformations. Different techniques by which the composite system of rock and joints (jointed rock) are mechanically modeled will be reviewed in the next section.

Normal deformation of a joint has been the subject of many studies in the early investigations on the jointed rock mechanical behavior. It was first formulated by Goodman (1976) and later by Swan (1980) in an empirical approach by Power law mathematical functions. Afterward, based on numerous experimental results, Bandis et al. (1983) proposed an empirical hyperbolic model for normal deformation of rock joint. This model is similar, in both formulation approach and functional form, to Goodman's model; however, each fits best their own experimental results.