Stability analysis of blocky system structures based on discontinuity layout optimization technique

Computing the collapse loads and identifying the associated mechanism of block assemblage structures is an important task in practical engineering. The discontinuity layout optimization (DLO) is proposed entirely based on velocity discontinuities with rigorous plasticity theory, which the optimization uses to determine the critical arrangement of the discontinuities from a large set of potential discontinuities. In DLO procedure, the initial problem is discretized using the nodes distributed across the body under consideration. The potential discontinuity lines or slip lines along which jumps in rate of displacement are created by linking each node to every other node. Compatibility can be straightforwardly checked at each node by a simple linear equation involving movement variables. Finally an objective function may be defined based on the total energy dissipated due to translation along all discontinuities, a linear function of the velocity variables. In order to improve the performance of the classical ground structure approach, the adaptive member refinement (adaptive nodal connection procedure) considers both deletion and addition of members in the iterative process. Although the solution will be influenced somewhat by the starting position of the nodes, when fine nodal refinement is used, the exact positions of individual nodes will have relatively little influence on the solution generated. The procedure is applied to the problems from the literature and also to new benchmark problems including masonry walls and jointed rock slopes so as to illustrate potentialities of the method. The results show that the proposed adaptive member refinement algorithm can deal with the stability analysis of practical blocky structures and avoid oscillating between two different solutions at successive iterations with the results that the optimization efficiency is improved significantly.