Jerzy Bauer

Reliability with respect to settlement limit-states of shallow foundations on linearly-deformable subsoil

Abstract A step by step procedure for applying the response surface and SORM methods in estimating the reliability index associated with exceeding a certain allowable settlement level by a shallow foundation is presented in this paper. Two random variables, the Young modulus and Poissons ratio, of lognormal and beta distribution respectively, in a single soil layer are taken into account. A linearly-deformable model of soil is assumed which is most frequently used in engineering practice when the serviceability limit state is considered. The main problem encountered in using the response surface methodology was the existence of false design points that prevented coordinate calculations of the real ones. Two procedures were employed. The first one consisted of widening the area covered by the response surface (polynomial of the second degree) with an additional “oedometric” term. Inserting the oedometric term improves the quality of the fitting and enables one to extend the range of approximation. The latter added a barrier to prevent the procedure from moving into the false design point region. Moreover, the paper presents the effect of random variation of the Young modulus E and Poissons ratio ν as well as their mutual correlation, on the reliability index associated with exceeding the assumed level of a shallow foundation settlement.

INFLUENCE OF VARYING SOIL PROPERTIES ON EVALUATION OF PILE RELIABILITY UNDER LATERAL LOADS

Abstract A three dimensional probabilistic approach to analyzing laterally loaded piles is presented. Two typical subsurface models are used in the analyses: the first one consists of layered linear elastic soil where each layer has a random modulus of elasticity; while the second model takes the form of linear elastic soil with a random modulus of elasticity that increases with depth. Efficient step by step procedures for the reliability computation involving pile displacements are proposed. The solution is based on three-dimensional modeling by the finite element method. A series of results has been obtained for various values of elastic parameters of the soil. Next by a non-linear regression procedure a response surface is obtained. To get the final response surface allowing for a reliability analysis, an iterative algorithm based on the so-called design point concept is applied. The failure criterion is defined as the pile head displacement exceeding displacement threshold. The two cases of piles subj...

Constitutive Equation of a Gas-Filled Two-Phase Medium

A set of equations governing the consolidation of a two-phase medium consisting of a porous elastic skeleton saturated with a highly compressible liquid (gas), is described. The homogenization method was utilized to deduce the equations. For the equivalent macroscopic medium, mass and momentum conservation equations and the flow equation of pore liquid are presented. Sample material constants were calculated using laboratory test results which were carried out at the Institute of Geotechnics, Technical University of Wroclaw.

Application of the response surface method

The response surface method can be applied to numerous fields of knowledge. In general, this method consists in approximation an unknown function by known function chosen appropriately. It can be successively utilised in reliability measures computations when the failure criterion does not depend on random variables explicitly. Within this study an application of the response surface method in dealing with random settlement in geotechnical engineering is discussed. In practical applications, an explicit closed form of settlement function U(X) is only rarely known. Most often, if program of the finite element method is available, we are able to determine the function values for assumed material properties, loads and geometrical constants of the FEM computation model. In order to obtain the limit state function in the form appropriate for reliability computations, one can model a closed form of U(X) by means of non-linear regression. To simplify the reliability computations, rather simple functions, e.g. polynomials of the second degree are in use. The approximation in the vicinity of a design point (known from preliminary FORM computations) is especially convenient in computing the probability of failure, because the neighbourhood of this point affects most strongly the value of a failure probability. In order to make computational algorithm more efficient the application of neural network with a hyperbolical activation function is suggested. If U(X) is a continuous function then the three-layered neural network with one hidden layered containing necessary number of neurones could give a satisfactory result. Neural networks allow approximation in cases of large variability intervals of independent variables preserving sufficient accuracy. Furthermore they make possible to overcome some numerical drawbacks of second order approximation known as “false branches problem”.

Model of gas-coal medium with a sorption phenomenon

Constitutive equations of a gas-coal two-phase medium with a local mass exchange due to a sorption-desorption phenomenon are presented. The equations have been deduced taking advantages of the theory of mixtures. Parameters of the constitutive equations have been calculated on the basis of results of laboratory tests published in recent papers. The governing set of equations of the theory is introduced and results of a sample calculation are presented.

Effect of partial mining of shaft protection pillar in terms of reliability index

ABSTRACT The work presents calculations of shaft support reliability index during partial extraction of protection pillar deposit and the related seismic phenomena. It has been assumed that the probability of failure caused by seismic phenomena depends on the velocity random variable of the shaft support vibrations. The random vibration velocity is a function of random variables of energy, shock distance and vibration frequency. Estimations of probability distributions for energy and frequency have been based on the actual measurement data from a mine. Failure probability has been estimated by means of methods based on so-called Hasofer-Lind reliability index β.