Geotechnical probabilistic analysis by collocation-based stochastic response surface method: An Excel add-in implementation

Abstract

A general probabilistic method called collocation-based stochastic response surface method (CSRSM) was previously developed. It involves the propagation of input uncertainties through a computation model to arrive at a random output vector. It is assumed that the unknown random output can be expanded using a polynomial chaos basis with corresponding unknown coefficients. The unknown coefficients are evaluated using a collocation method because it has the important practical advantage of allowing existing deterministic numerical codes to be used as 'black boxes'. The roots of the Hermite polynomial provide efficient collocation points to evaluate the coefficients in the stochastic response surface. An Excel add-in is developed to produce the basis functions (multi-dimensional Hermite polynomials) without resorting to symbolic algebra practitioners. This is a major practical advantage that would bring realistic probabilistic analyses within reach of the practitioners. Full Excel implementation details are illustrated using a simple slope problem involving six input random variables. A second problem (sum of exponential random variables) is studied to examine CSRSM over a wider range of conditions. It also provides further validation because the solution is available in closed-form. The results show the ease and successful implementation of the proposed Excel-based CSRSM. However, the add-in is unable to handle correlated input parameters thus far. Future development work is needed.