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Reliability assessment of bearing capacity of layered soils using High Dimensional Model Representation (HDMR)

Suska M., Puła W.

Studia Geotechnica et Mechanica

2013

Vol. 35, nr 1

233--243

HDMR (High Dimensional Model Representation) is a relatively new method that is used to form response surface based on results obtained through laboratory experiments or through numerical calculations. So far the method has been used mainly in chemistry, although a few studies conducted in recent years show that it can be considered a useful tool in soil mechanics and foundation engineering. The subject matter of this paper is the application of HDMR method to reliability assessment of bearing capacity of layered soils. Madej’s method, widely recognized and used by Polish engineers, is applied to conduct the calculations. In the analysed case bearing capacity is not expressed by means of an explicit formula. To fit the approximate functions of bearing capacity, its values are calculated on a grid of points equally spread on ranges of variables. Finding the relation between input and output data is conducted by means of assessing each variable’s influence on response’s mean value within a given scope. Approximate functions have been used to calculate reliability indices by means of FORM, SORM and Monte Carlo methods.

Application of HDMR method to reliability assessment of a single pile subjected to lateral load

Bauer J., Kozubal J., Puła W., Wyjadłowski M.

Studia Geotechnica et Mechanica

2012

Vol. 34, nr 3

37--52

The paper presents an application of High Dimensional Model Representation (HDMR) to reliability assessment of a single pile subjected to lateral load. The purpose is to compare HDMR with some classical method based on response surface technique. First 3D numerical model of the problem for finite elements computations in the ABAQUS STANDARD program has been presented. The soil model is assumed to be linear elastic. However, contacts between the sidewall and the foundation of the pile and the soil are modelled as Coulomb one with friction and cohesion. Next the Response Surface Method is briefly reviewed in conjunction with reliability approach.Then the High Dimensional Model Representation approach is presented. In our approach the HDMR algorithm is based on polynomial of the second degree. Finally the numerical studies have been carried out. The first series of computations demonstrate the efficiency of HDMR in comparison to neural network approach. The second series allows comparison of reliability indices resulting from three different approaches, namely neural network response surface, first-order HDMR and second-order HDMR. It has been observed that for increasing values of the length of the pile reliability indices reach similar values regardless of the method response surface applied.