Composite Tolerable Settlement and Horizontal Displacement Criteria for Reliability-Based Design of Foundations

The design of foundations should satisfy various serviceability performance requirements. A structural foundation may concurrently experience vertical displacement, horizontal displacement, and angular distortion. While the limiting value of a single displacement has been studied, the limiting values of multiple displacements when they occur simultaneously have not yet been well studied. The objectives of this paper are to determine the limiting tolerable displacements when multiple movement components occur and to propose a composite limiting tolerable displacement criterion involving both vertical and horizontal displacements. To determine the limiting tolerable displacements for foundations subject to movements in multiple directions, performance information of 280 bridges with either vertical displacement and/or horizontal displacement has been collected and evaluated. Limiting tolerable displacements are determined by using a fragility curve to represent the cumulative probability distribution. The limiting tolerable vertical displacement and horizontal displacement when they occur concurrently are found to be smaller than their respective limiting values when only one component occurs. Both the observed intolerable horizontal displacement and limiting horizontal displacement are smaller than the corresponding vertical displacements of the same category of bridges. A linear function between the limiting vertical and horizontal displacements is proposed. The sum of two dimensionless limiting displacement terms is equal to 1.0. The composite function is modified to allow for construction tolerances in both vertical and horizontal directions. The characteristic tolerable displacements for limit state design or the allowable displacements for conventional design in both vertical and horizontal directions can be obtained based on the composite function. INTRODUCTION Geotechnical limit state design methodologies were advanced substantially in the past two decades (e.g. Becker 1996; Phoon et al. 2003a, 2003b; Honjo 2011; Wang et al. 2011). In geotechnical design, several serviceability requirements have to be satisfied, including limits in the vertical displacement, horizontal displacement, and angular distortion or differential settlement of the structural foundation (e.g. Zhang & Ng 2005; Zhang & Phoon 2006; Paikowsky & Lu 2006). Most engineering design codes provide these limits without specifying whether multiple displacement components occur concurrently or not (e.g. AASHTO 1997; CEN 2001). The traditional limiting displacement surface involving three limiting displacement variables is shown in Figure 1. The three variables are assumed to be independent. The physical processes that cause serviceability problems are very complex. Different types of displacement may interact with each other. For example, the stresses in a structural element that lead to serviceability problems are functions of the displacement components (i.e., vertical