Reliability-based design of spread foundations by Monte Carlo simulations

In this paper a general reliability-based design (RBD) approach for spread foundations is developed that addresses, explicitly and simultaneously, the ultimate limit state (ULS), serviceability limit state (SLS), reliability and economic requirements. The design process is formulated as an expanded reliability problem that is evaluated by a single run of Monte Carlo simulations (MCS). Design parameters (i.e. foundation width B, length L and depth D) are artificially treated as discrete uniform random variables, and the design process is considered as a process of finding failure probabilities for designs with various combinations of B, L and D (i.e. conditional probability p(Failure|B,L,D)) and comparing them with target probability of failure p_T. Feasible designs are those with p(Failure|B,L,D) ≤ p_T, and the feasible design with the minimum construction cost is selected as the final design. Equations are derived for this expanded reliability-based design (RBD^E) approach and criteria are established for the minimum number of MCS samples to ensure a desired level of accuracy. The RBD^E approach with MCS is illustrated through a design example of a square spread foundation with a fixed depth that has been used for the evaluation of Eurocode 7. The results are consistent with those from previous reliability analysis reported in the literature. In addition, the RBD^E approach with MCS offers design engineers insights into how the expected performance level of spread foundations changes as B, L and D change, and it allows design engineers to adjust p_T, without additional computational efforts, to cater for the needs of particular projects. It also provides design engineers with flexibility in modelling the uncertainties and selecting proper deterministic ULS and SLS calculation models.