PileBetaGR: An R-based integrative tool for predicting the geometric reliability index of piles using load-displacement curves

The PileBetaGR package is a web application designed to enable accessible and reproducible computation of the geometric reliability index for piles using site-specific load-displacement curves. The application compiles a series of functions for analyzing load-displacement data: (i) a power law regression is used to fit each load-displacement curve, yielding a set of regression parameters for the site; (ii) a normal copula model is established to fit the joint distribution of these regression variables, allowing a geometric reliability index to be computed; (iii) the critical environmental contour is determined based on the joint probability density function and the limit state function. The PileBetaGR enables users to construct three- and four-dimensional environmental contours by treating the dead and live load as random variables and to understand the roles various correlation coefficients, marginal distributions, and loading ratios play in the reliability index evaluation. A web application that facilitates the use of the package even for those with no background in R programming is offered via Shiny apps.