----------------------------------------------------------------Rigid block limit analysis provides a simple method for computing rigorous upper bound solutions on the stability of geotechnical problems. The method requires the topology of a collapse mechanism to be defined a priori, from which an expression for stability is derived. For complex mechanisms optimizing these expressions using multivariate search algorithms requires enormous computational effort, and the initial feasible solution needed for local optimisation algorithms are difficult to obtain. This paper describes a method for successively subdividing blocks within a collapse mechanism, incrdsing its complexity gradually and allowing simple univariate optimization algorithms to be used. The performance of this technique is demonstrated by computing the bearing capacity factor for a strip footing on weightless fissured clay and the undrained stability of a circular tur;Jnel. The techniques developed in this paper are shown to provide a robust method for solving rigid block problems with demanding material behaviour and complex geometry. Rigid block limit analysis (RBLA) provides a simple method for directly computing rigorous upper-bound solutions on the stability of geotechnical problems. The method requires the topology of a collapse mechanism to be defined a priori which is then used in conjunction with the upper bound theorem of plasticity to formulate an expression for the stability of the mechanism. This expression is optimized to determine the geometry of the mechanism with the smallest collapse load. As the method is based upon the upper bound theorem of plasticity the resulting solution provides a rigorous upper bound to the true collapse load. A comprehensive summary of solutions to familiar problems is provided by Chen (1975). For simple collapse mechanisms the stability expressions have only a few variables and global optimisation methods such as grid searches can be used efficiently to find the smallest collapse load without any prior knowledge of a feasible solution. However, when mechanisms become larger, the stability expressions involve many unknown variables and global search algorithms require enormous computational effort. In such cases local search methods such as the Hooke-Jeeves method, can be used to efficiently obtain the minimum collapse load but these methods require a feasible solution within the vicinity of the global solution as a starting point. This paper describes a method for successively subdividing blocks within a collapse mechanism to gradually increase the complexity of the mechanism. Starting with a relatively simple mechanism allows global search methods to find the optimal solution efficiently. The rigid block splitting technique then forms a more complex mechanism by subdividing one or more of the rigid blocks in the mechanism. An initial feasible solution for the new mechanism is obtained via interpolation of the optimised geometry of the previous mechanism. This feasible solution permits the new mechanism to be optimized using local search algorithms. The subdivision of rigid blocks and optimisation of the resulting mechanism can then be repeated to obtain progressively more complex collapse mechanisms. The performance of this technique is demonstrated by computing the bearing capacity of a rigid strip footing sitting on a fissured soil and the undrained stability of a circular tunnel. The techniques developed in this paper are shown to provide a robust method for accurately and efficiently using rigid block methods to predict the stability of geotechnical structures. 1 RIGID BLOCK LIMIT ANALYSIS Stability analysis of a geotechnical problem using RBLA requires a collapse mechanism composed of sliding rigid blocks separated by velocity discontinuities to be defined in advance. The motion ofblocks within the mechanism must be kinematically admissible, satisfYing the velocity boundary conditions, compatibility, and an associated flow rule. The collapse load is then calculated by forming an expression equating the rate of energy dissipation between rigid blocks to the rate of work done by external loads and body forces as some virtual displacement occurs. The upper bound theorem of plasticity (Drucker, 1953) guarantees a solution computed by the rigid block method is an upper bound to the true solution. By defining the geometry of a mechanism in terms of an appropriate set of variables and optimizing the IACMAG 2011 Melbourne, Australia, 9-11 May 2011 I. 1 ComputatiJ --~~----------~s I resulting energy expressio for that specific mechanis · anisms are optimized efi '• and Hooke-] eeves optimis 1 methods seek the minim1 . . 1 I by evaluatmg 1t at regu ar i domain. The grid point [ value is chosen as the 1 carri~d ou~ usin~ eith~r ai muluple dimens10ns s1m · minimum. Alternatively, ~ be employed in which the 1 tion is performed one di 1 local minimum. To locat 1 process is repeated for : solution converges. Ho ' search requires an initial' fined making it less pract~ putational effort is requi: grid search. i The Hooke-] eeves met i cal optimization techniq: gion immediate to an ini, the direction of steepest d.: shifts the initial point d : mum and repeats the pr 1 Hooke-Jeeves methods is: of a'grid, and so it provid 1 minimum of stability fun: Large mechanisms imp' bound solutions but are~ timize. When using a hig possible layouts fail to sa. ary conditions and compa true for frictional soils w ~ block arrangements inco ' addition to this, complex [ dimensionality stability fi : iate grid searches imprac : algorithms may effectivel~ sions but seem excessive · rigid block limit analysis.~ use of simple grid searc. rithms to optimize stabili11 variables. :1 2 RIGID BLOCK SPLI I i The basis of the rigid bloc successive rigid block an' using increasingly complex! through subdivision of on mechanism. The key to apj formulation of an expressi of the mechanism so as to bers ofblocks. This can be1 an iterative definition of th