The utility of reliability based design (RBD) methodology, such as the load and resistance factor design (LRFD) approach, is being increasingly recognized for the design of drilled shafts. The LRFD approach of drilled shaft design has the following advantages: (1) foundation design is easier and more efficient when the structure is designed using the LRFD method, as the load combinations need not be redefined, and (2) reliability may be rationally incorporated into the design process. In this paper, we develop a probabilistic mathematical model for drilled shaft load-displacement behavior. The soil-drilled shaft interaction is considered explicitly in the model development along the lines of the "t-z" approach. However, to ensure model simplicity, we consider the shaft-soil interface to be homogeneous and ideally elasto-plastic. Consequently, closed form expressions are derived for drilled shaft load-displacement behavior. These expressions are given in terms of the shear modulus of shaft-soil interface sub-grade reaction K, the ultimate shaft-soil interface shear strength τ u, and the modulus of tip soil sub-grade reaction, K t. The derived expressions are used along with the Monte Carlo simulation method to study the probabilistic character of the drilled shaft axial load-displacement behavior. The results are also used to develop probability and load capacity curves that may be utilized to determine resistance factors useful for design evaluation at the service limit state.
