Expanded Reliability-Based Design Approach for Drilled Shafts

This paper develops a more general reliability-based design approach for drilled shafts that formulates the design process as an expanded reliability problem in which Monte Carlo simulations (MCS) are used in the design. Basic design parameters, such as the shaft diameter $\left(B\right)$ and depth $\left(D\right)$ , are formulated as discrete uniform random variables. Then the design process becomes one in which failure probabilities are developed for various combinations of $B$ and $D$ [i.e., conditional probability $p\left(\text{Failure}\mid B,D\right)$ ] and are compared with a target probability of failure $p_T$ . Equations are derived for this expanded reliability-based design $\left({\text{RBD}}^{\text{E}}\right)$ approach, and criteria are established for the minimum number of MCS samples to ensure a desired level of accuracy. Its usefulness is illustrated using a drilled shaft design example. This ${\text{RBD}}^{\text{E}}$ approach has the following advantages: (1) it gives results that agree well with current RBD designs, but it improves the resolutions of the designs; (2) it offers design engineers insight into how the expected design performance level changes as $B$ and $D$ change; (3) it gives design engineers the ability to adjust $p_T$ , without additional calculation effort, to accommodate specific needs of a particular project; and (4) it is transparent and “visible” to design engineers who are given the flexibility to include uncertainties deemed appropriate. Finally, the effects of uncertainties in the at-rest horizontal soil stress coefficient $\left(K_0\right)$ and allowable displacement $\left(y_a\right)$ are illustrated using this approach.