The Discontinuous Deformation Analysis (DDA) is a numerical model for the statics and dynamics of discontinuous block systems. In this paper, a three-dimensional (3D) version of DDA is briefly described and extended to allow the consideration of thermal loading. The thermal loading submatrices required for 3D DDA are derived. The extended 3D DDA is then applied to analyze the thermal-mechanical behavior of a block of fractured rock in an in situ thermal test known as the Large Block Test (LBT). The deformations of multi-point borehole extensometers (MPBXs) are calculated using 3D DDA forward analysis. The computed and measured MPBX anchor point deformations are compared in terms of their variations with time as well as their magnitudes. It can be seen that the shapes of the plots of the computed MPBX deformations with time are consistent with those of the measure ones. However, the magnitudes of the computed anchor point deformations are generally smaller than the measured ones, which may be due to accumulated round-off errors. The results show that the extended 3D DDA method can be applied to analyze coupled thermal-mechanical behavior of discontinuous rocks, with potential applications in the design of underground storage caverns and nuclear waste repositories.
1. INTRODUCTION
Coupled thermal-mechanical behavior of fractured rocks is an important consideration in the design of civil engineering works, such as slopes, underground storage caverns, and nuclear waste repositories. A numerical method useful in such a consideration is the three-dimensional Discontinuous Deformation Analysis (3D DDA). The original DDA developed by Shi [1] is a twodimensional (2D) numerical model for the statics and dynamics of discontinuous block systems. With many people contributing to its development and application, 2D DDA is well developed in terms of both theory and computer coding [2-6]. However, the highly directional nature of jointed rock mass behaviour makes the application of 2D DDA to many practical problems inappropriate. While various researchers are working on 3D DDA, only some preliminary work on this subject has been published [7-9].
In this paper, 3D DDA is briefly described and extended to allow the consideration of thermal loading. The thermal loading submatrices required for 3D DDA are derived. As a validation study, the extended 3D DDA is then applied to analyze the thermal-mechanical behavior of a block of fractured rock in an in situ thermal test known as the Large Block Test (LBT). The results of a 3D DDA analysis are reported and the computed and measured deformations compared.
2. BASIC PRINCIPLES OF 3D DDA
2.1. Displacement and Deformation of a RockBlock
In DDA, time steps are used to drive the computation. Large displacement and large deformation result from the accumulation of small displacements and small deformations within the individual time steps. Given that each time step satisfies the condition of infinitesimal displacement and deformation and assuming that each block has uniform stress and strain, the displacement and deformation of a block are determined by 12 independent deformation variables:
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