Geometric Reliability Analysis of Composite Foundations Comprising Cement–Fly Ash–Gravel Piles at Site-Specific Scale

Abstract

Evaluating the pressure-settlement response of a composite foundation at a specific site is important for supporting the safety of superstructures in the design process to determine the bearing performance of the foundation. The uncertainties in the power law regression parameters stem from a significant scattering of pressure-settlement curves when a series of static load tests are conducted for the composite foundations composed of cement–fly ash–gravel piles at a particular site. Thus, in this work, a probability density contour (PDC) of these regression parameters is constructed using a bivariate distribution, which offers great flexibility in fitting the marginal distributions and the dependency between the two regression parameters. Based on an intuitive evolutionary geometry of the PDCs in the original physical space of two dependent random variables, a reliability index is defined as a distance ratio of two PDCs, i.e., the dispersed PDC that just touches the limit state curve and the one standard deviation PDC. These bivariate PDCs are discretized with several segments that adapt to the different spreads of the asymmetric data. Reliability indices are calculated based on the geometric reliability analysis, which offers great transparency for engineers in evaluating the safety of the composite foundation at a site-specific level. By using this reliability technique, the effects of uncertain regression parameters are explicitly explored at six sites consisting of 280 static loading tests.

Solving the geometric reliability index for a case involving multivariate random variables in the original physical space

“…where 𝑃 ua is the allowable pressure. When the displacement is set to 𝑆 a =40 mm, the value of 𝑃 ua is calculated according to the power law function 6 :…”

“…The performance function or limit state equation used to evaluate the bearing resistance of composite foundation is defined as: $$$$\begin{equation}g = {P}_{{\mathrm{ua}}} - {P}_{{\mathrm{LD}}}\end{equation}$$$$where P ua is the allowable pressure. When the displacement is set to $${S}_{\mathrm{a}} = $$40 mm, the value of P ua is calculated according to the power law function 6 : $$$$\begin{equation}{P}_{{\mathrm{ua}}} = {p}_1S_{\mathrm{a}}^{{p}_{_2}}\end{equation}$$$$where p 1 and p 2 are the power law function regression parameters. After the curve‐fitting regression analysis, the parameters p 1 and p 2 of each curve are obtained.…”

“…Such a physical space is also denoted as "generalised space" as it holds a clear physical meaning for all variables. An interactive and visual solution of the reliability index under fewer random variables is achieved in several areas 5,6 using the R platform. 7,8 However, a solution in the case of multiple random variables needs to be further studied.…”