Numerical modelling of jointed rock masses by distinct element method for two- and three-dimensional problems

Abstract: The mechanical behaviour of a jointed rock mass is strongly, and sometimes dramatically, affected by the behaviour of the discontinuities present in jointed rock mass. In many cases, preferential failures are dominated or defined by the natural discontinuities present in the neighborhood of engineering engineering works. Closed form solutions rarely exist in general problems and numerical methods must therefore be used. The constitutive models for discontinuities, therefore, play an essential part in the successful application of any numerical techniques. In this thesis, two new constitutive models, one twodimensional and one three-dimensional, for the mechanical behaviour of rock discontinuities are developed according to the experimental results obtained from shear tests under cyclic shear sequences. Fifty concrete replicas of natural rock joints are made and tested in different shear directions under different constant normal stresses. The results obtained confirm that the anisotropy in both the angle of friction and shear stiffness are significant properties of rough joints which have been ignored in the past time. In addition, the shear stiffness and friction angle depend on the normal stress. Based on these results, the behaviour of rock joints under two or three-dimensional loading conditions and undergoing cyclic shear sequences was generalized. This generalized behaviour forms the physical background for the development of the new constitutive models. The two-dimensional constitutive model for rock joints is a generalization of Plesha's original model. The theory of non-associated plasticity was used to formulate the model in which both pre- and post-peak shear stress regions are considered, by using empirical laws for workhardening and work-softening. The most basic aspects of the rock discontinuities, for example, the appearance of peak and residual shear stresses during shearing, the increase in the magnitudes of both shear, and normal stresses under constant normal displacement condition, nonlinear dilatancy during shearing under constant normal stress condition, surface roughness degradation and the dependence of stiffness parameters on the normal displacement and normal stress are reflected in the model. The second law of thermodynamics is used to restrict the values of some of the model parameters so that entropy production of the system is non-negative. The three-dimensional model is formulated in the same manner as its two-dimensional counterpart with special interest in the anisotropic nature of both the angle of friction and shear stiffness. Empirical laws for work - hardening, surface degradation, stiffness changes due to normal stress and normal displacement, are all considered. The path dependence of the shear stress components in the shear plane is highlighted. An asperity ellipse and a shear stiffness ellipse are constructed to represent the anisotropy in the friction angle and shear stiffness. The second law of thermodynamics is also used to restrict some model parameters to secure a non-negative entropy production of the system during shearing. The newly developed constitutive models are validated against well known test results published in the literature and the test results obtained by the author's own test results. The predictions from the models concurs well with the test results. The models are implemented into existing distinct element method programs, UDEC and 3DEC, respectively. Three examples of application of the new joint models are presented. The first is a simulation for plate movements in the Earth's crust to investigate the mechanisms of intraplate earthquakes with the new two-dimensional constitutive model. The second is an equilibrium analysis of three-dimensional rock slope with anisotropic friction angle and the third one is a study on sensitivity of stability of underground mining stopes on the anisotropy of friction angle. The new three-dimensional constitutive model is used in the last two examples and a large computational model is used in the third example to test the performance of the new model under complex geometrical and mechanical loading conditions. It is concluded in this thesis that the behaviour of rock joints under cyclic shear tests is more complex than that under monotonic shear tests and contraction becomes important. Under three-dimensional loading conditions, the anisotropy in friction and stiffness properties of rock discontinuities should be considered. The path dependence in the shear plane is significant feature which has not been studied adequately in previous time. In order to deepen our understanding of the mechanical behaviour of rock joints under three-dimensional loading conditions, a truly threedimensional test machine is needed. Recommendations for future research are provided at the end of the thesis.