Two-dimensional Discontinuous Deformation Analysis Research Articles

Numerical analysis of discontinuous rock masses using three-dimensional discontinuous deformation analysis (3D DDA)

Numerical analysis methods are considered very important in the field of geotechnical engineering, particularly in the area of disaster prevention. Discontinuous Deformation Analysis (DDA) is a type of discontinuous numerical analysis method that is frequently used in this topic. Since most geotechnical engineering problems are three-dimensional, Two-Dimensional Discontinuous Deformation Analysis (2D DDA) computations have exhibited limited accuracy. In order to simulate three-dimensional block behavior more accurately, the Three-Dimensional Discontinuous Deformation Analysis (3D DDA) theory for blocks with general shape was developed. This paper describes the basic principles of 3D DDA, and goes a step further by developing a new 3D DDA method. This new 3D DDA method proposed by authors is applied to an actual example site. In order to demonstrate the capability of this new method in the numerical analysis of discontinuous rock masses, the simulation results were compared and examined with the actual monitoring of the displacement behavior proceeding that led to the failure at the field site. The results show the applicability of 3D DDA in determining the deformation and failure mechanisms of rock masses.

The stability of a laminated Voussoir beam: Back analysis of a historic roof collapse using DDA

The stability of a horizontally bedded and vertically jointed roof, referred to here as a laminated Voussoir beam, is studied using careful documentation of a historic roof collapse, which occurred in an ancient underground water storage reservoir dated back to ca. 1000 B.C. The roof of the opening failed immediately after the excavation leaving a dome shaped loosened zone, with a span of 7 m and height of 2.5 m, consisting of horizontal beds and vertical joints with mean spacing of 50 and 25 cm, respectively. The ancient engineers erected a massive pillar at the center of the dome in order to passively support the failed roof and the opening remained in service for several hundred years following the failure. Analysis of the roof using iterative Voussoir beam procedure [Beer, G. and Meek, J. L., Design curves for roofs and hanging walls in bedded rock based on Voussoir beam and plate solutions. Trans. Inst. Min. Metall. , 1982, 91 , A18–22.] shows that the roof was more sensitive to failure by shear along the abutments rather than by crushing at hinge zones and that the required friction angle ( φ req. ) for stability would have been 36°. The available friction angle is estimated between 38.6° and 46.4° and, therefore, the result of the iterative solution is considered unconservatively wrong. Results of DDA [Shi, G. -H. and Goodman, R. E., Two-dimensional discontinuous deformation analysis . Int. J. Numer. Anal. Methods Geomech. , 1989, 13 , 359–380; Shi, G. -H., Block System Modeling by Discontinuous Deformation Analysis . Computational Mechanics Publications, Southampton, 1993, pp. 209.] however indicate that φ req. must have been greater than 60°, a shear strength which was not available at the time of construction, thus the immediate failure. Using DDA we further demonstrate that φ req. is related to joint spacing (or block length) in a parabolic function: with increasing joint spacing φ req. decreases to a minimum value and than increases with further increase in joint spacing. This result is attributed to the interaction of two competing forces: one is the stabilizing axial thrust which increases with increasing moment arm in individual blocks (a function of joint spacing or block length), the other is the destabilizing vertical load which increases with increasing weight of overlying blocks.

Effects of joint attributes on tunnel stability

Abstract A parametric study was carried out using the two-dimensional Discontinuous Deformation Analysis (DDA) to study the effects of joint attributes on tunnel stability. Cases were analyzed with different combinations of tunnel depth, joint orientation, joint spacing, and joint friction angle. The DDA results for 22 cases presented shed light on the effects of joint attributes on tunnel stability. DDA results show that for relatively shallow tunnels, blocks may slide on joints dipping at an angle steeper than its friction angle. Furthermore, different joint orientations may result in different block sizes and shapes even though all the joint sets have the same spacing. As a result, joint spacing may not be an adequate measure of block size. A rock block volumebased parameter may be more appropriate than joint spacing as a measure of the effects of block size on tunnel stability. In addition, DDA results show that if the intact rock is hard and the tunnel is not extremely deep, deeper tunnels are in general more stable than shallower ones due to better confinement at depth. However, higher stresses at depth may cause local failures that may not occur at shallower depths.

Generalization of two-dimensional discontinuous deformation analysis for forward modelling : Shi, G H; Goodman, R E Int J Num Anal Meth GeomechV13, N4, July–Aug 1989, P359–380

Generalization of two-dimensional discontinuous deformation analysis for forward modelling : Shi, G H; Goodman, R E Int J Num Anal Meth GeomechV13, N4, July–Aug 1989, P359–380