Analysis of pile behaviour using constrained optimisation - Chan, Chin Loong (2008)
Although pile load tests provide the most accurate information about load-deformation behaviour of piles, they are usually time-consuming and expensive. Therefore, it would be useful to formulate analytical models based on past data, coupled with essential but minimal pile load tests, to predict pile behaviour. There are already in existence several computer programs that are able to accomplish this using the finite element or finite difference methods. The objective of this project is to conduct such deterministic analyses via commercially available spreadsheet software. All analyses in this research were performed using the widely used Microsoft Excel equipped with an optimisation tool (Solver) and a programming environment(Visual Basic for Applications, VBA). The deterministic numerical procedure is based on constrained optimisation in spreadsheet with minimum amount of programming. Soil resistance are modelled using springs, whose force-displacement relationships are characterised by either ‘t-z’or‘p-y’curves. Several case studies are presented, in which the numerical solutions are compared with experimental data and, where available, with solutions of other software. One particular advantage of the spreadsheet approach in the analysis of laterally loaded piles is the modelling of nonlinear pile flexural rigidity (EPIP), coupled with the use of nonlinear ‘p-y’curves. The deterministic study is then extended to stochastic or reliability analysis on the same spreadsheet platform, taking into consideration uncertainties in soil and pile properties as well as applied loading. The measure of reliability is the Hasofer-Lind (1974) β index, computed based on the alternative perspective of an expanding ellipsoid in the original space of the variables (Low and Tang, 1997). From the β index, one can easily deduce the probability of failure corresponding to a specified limit state. Comparisons are made with simulations (Monte Carlo/Latin Hypcrcube) and the point-estimate method. The ellipsoid optimisation approach provides a relatively easy investigation of multiple modes of failure. By incorporating spatial variability concepts, one can also account for spatial autocorrelation of soil properties. The reliability analysis is then switched to perform reliability-based design, in which the pile length and diameters can be selected to achieve a certain stipulated degree of reliability in one or more limit states.