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Stochastyczna analiza nośności granicznej

Przewłócki J.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

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2003

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z. 97

137-144

PL

Praca dotyczy modelowania stochastycznego ośrodka gruntowego metodami nośności granicznej. Zaproponowano probabilistyczne modyfikacje metod oszacowań i charakterystyk, które zastosowano do oceny nośności granicznej ławy fundamentowej posadowionej na idealnie spoistym podłożu. W pierwszym przypadku, wyznaczono dystrybuanty nośności granicznej stanowiące probabilistyczne, górne i dolne oszacowania. Metodę charakterystyk powiązano ze stochastyczną metodą różnic skończonych, a przyjęcie spójności w postaci pola losowego pozwoliło na uwzględnienie w analizie przestrzennej zmienności ośrodka gruntowego.

EN

The paper deals with a stochastic modeling of soil medium using limit analysis methods. Modifications of theorems of limit analysis and the method of characteristics are proposed. They are applied to a problem of bearing capacity of a strip footing based on the ideally cohesive subsoil. The distribution functions of the bearing capacity are considered as the probabilistic upper and the lower bounds. In the case of the method of characteristics, the stochastic finite difference method has been adopted. The influence of the spatial variability of cohesion on the standard deviation of the ultimate collapse load has been determined.

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Stochastic FEM analysis of strip foundation

Przewłócki J., Górski J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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1999

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Vol. 3, No 2

171-186

EN

The paper affords a stochastic description of a random soil medium subjected to an external loading. The strip foundation on a soil layer in the 3-D and the 2-D strain states is analysed. It is assumed that the soil medium is statistically homogeneous and its mechanical behaviour governed by the linear elasticity theor y. It is also assumed that elastic parameters can be modelled as the multidimens ional random fields. Stochastic 2-D and 3-D finite element methods (SFEM), based on the Monte Carlo technique were used. The influence of elements supports atta ched along vertical planes on standard deviations of displacements and stresses is discussed. Local averages of random field of elastic parameters are introduce d. The convergence of applied in SFEM simulation algorithm was tested. The analy sis performed enables determination of the standard deviations of components of the stress tensor and the displacement vector for the 3-D state, based on the so lution for the 2-D plane strain state.

3

Mass minimization of dynamically loaded machine foundations using different subsoil models

Sienkiewicz Z., Wilczyński B.

Engineering Transactions

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1999

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Vol. 47, iss. 2

183-201

EN

The effect of variation of the shear wave velocity profile of a layered soil a minimal mass of a rigid machine fountation under behaviour constraints on vibration and normal stress compact amplitudes and side constraints is numerically studied. The nonlinear programming problem has been solved by an iterative application of a sequential linear programming. The dynamic response of the machine foundation to unbalanced forces is evaluated including the dynamic soil-block interaction. The mixed-boundary value problem of elastodynamics was formulated as the system of Fredholm integral equations of the first kind with the Green's functions for a half-space as kernels and concact tractions as unknowns. The solution of the integral equations was accomplished numerically by a Boundary Element Method. In addition, the effect of embedment of the block into the soil was included by means of a local dynamic boundary used to simulate the backfill. Numerical results illustrate the sensitivity of the optimum design with respect to variations in problem preassigned parameters.

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2-D and 3-D analysis of stochastic, elastic soil medium

Przewłócki J., Górski J.

Engineering Transactions

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1999

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Vol. 47, iss. 2

173-181

EN

The paper presents a stochastic description of a three-dimensional soil medium and its modelling under strain conditions. The main aim of the paper of the paper is to work out a computational model enabling incorporation of three-dimensional variability of soil properties into the plane strain state analysis. It is assumed that the soil medium is statitically homogeneous and its mechanical behaviours is governed by the linear elasticity theory. It is also assumed that elastic parameters can be modelled as the multidimensional random fields. The strip foundation on a soil layer in the 3-D and the 2-D strain states is analysed. Stochastic 2-D and 3-D finite element methods, based on the Monte Carlo technique, were used. The analysis performed enables determination of the standard deviatios of components of the stress tensor and the displacement vector for the 3-D state, based on the solution for the 2-D plane strain state. Transfer functions between both states are determined.