Expanded reliability-based design of piles in spatially variable soil using efficient Monte Carlo simulations

Inherent spatial variability is considered as a major source of uncertainties in soil properties, and it affects significantly the performance of geotechnical structures. However, research that considers, directly and explicitly, the inherent spatial variability in reliability-based design (RBD) of geotechnical structures is limited. This paper develops a RBD approach that integrates a Monte Carlo Simulation (MCS)-based RBD approach, namely the expanded RBD approach, with random field theory to model, both directly and explicitly, the inherent spatial variability of soil properties in RBD of drilled shafts. The proposed approach is implemented in a commonly-available spreadsheet environment to effectively remove the hurdle of reliability computational algorithms and to provide a user-friendly graphical user interface to practicing engineers. To improve the efficiency and resolution of MCS at small probability levels, the expanded RBD approach is enhanced with an advanced MCS method called “Subset Simulation”. Equations are derived for the integration of the expanded RBD approach and Subset Simulation. The proposed approach is illustrated through a drilled shaft design example, and is applied to explore the effects of inherent spatial variability (including the scale of fluctuation and correlation structure) and to evaluate systematically the equivalent variance technique that is commonly used to indirectly model inherent spatial variability in current RBD approaches. It is found that inherent spatial variability significantly affects the RBD of drilled shafts, and its effects are considered in RBD using the proposed approach in a direct and explicit manner. In addition, the results show that the indirect modeling of inherent spatial variability using the equivalent variance technique with the simplified form of variance reduction function in RBD might lead to relatively conservative designs in design practice.