The use of response surface methodology for reliability estimation of composite engineering structures

The study presents a probabilistic stability analysis of a Baltic cliff in Jastrzębia Góra, Poland. Progressive slope erosion is a threat to adjacent buildings, so safety assessment of the slope is essential. The cliff shows a compound, multi-layered geological structure, which makes the analysis of its reliability a complex multivariate problem. A simple, straightforward computational procedure was proposed, incorporating the Response Surface Method (RSM) linked with the standard Monte Carlo (MC) simulation method and the Point Estimate Method (PEM). PEM samples make it possible to analyse the sensitivity of the cliff’s stability to variation in subsoil parameters and to reduce the number of random variables of the problem. The proposed methods were tested in two cases: a high failure probability (undrained state) and a moderate failure probability (drained case). The so-called combined Response Surface Method (CRSM) proposed here may be successfully applied in geotechnical computations characterized by dispersion and uncertainty of soil data as well as a relatively high damage probability.

This work conducts a probabilistic inquiry on how the variability of the parameter defining soil deformability affects the settlement of the foundation located on the soil. The analysis addresses the random foundation model to relevantly estimate the probability of allowable deflection exceedance. The constitutive model parameter is based either on a single random variable or a random field. The computations incorporate direct Monte Carlo sampling and the variance reduction techniques, i.e. Stratified Sampling and Latin Hypercube Sampling. The work focuses on soil parameter modelling by random fields defined by various correlation functions. One of the analytical means is the application of a non-homogeneous function capable of reflecting the soil strata. The probabilistic methods proposed in the paper are tested on a standard example of a foundation strip featuring load eccentricity. It is proved that the modelling mode of the soil—a single variable or a random field—substantially affects the results, i.e. foundation settlements. It was detected that incorporating random fields in soil analysis allows for a valid reliability assessment of a foundation in respect to Serviceability Limit State. The relevantly adjusted correlation functions of random fields allow for a realistic subsoil analysis even in the case of a limited in situ measurement database.

This paper delivers a probabilistic attempt to prove that the selection of a random three-dimensional finite element (FE) model of a subsoil affects the computed settlements. Parametric analysis of a random soil block is conducted, assuming a variable subsoil Young’s modulus in particular finite elements. The modulus is represented by a random field or different-sized sets of random variables; in both cases, the same truncated Gaussian model is assumed. Mean values and standard deviations of random soil settlement are estimated by a Monte Carlo simulation procedure. With regard to the adopted FE model, the estimated settlement mean values do not vary significantly, but standard deviations do strongly. Similarities also appear in the diagrams of random field correlation length versus settlement standard deviation and the diagrams displaying a total number of model random variables versus settlement standard deviation. Thus, relevant single random variable models represent the random field approach well with regard to settlement parameter estimation. This remark is verified upon a settlement analysis of a three-dimensional FE model of a hypothetical strip foundation. Following the preliminary model observations, various probabilistic geotechnical analyses may be supported, e.g., continuous footing design, slope stability analysis, and foundation reliability assessment.