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1

An iterative algorithm for random upper bound kinematical analysis

Chwała Marcin

Studia Geotechnica et Mechanica

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2022

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Vol. 44, nr 1

13--25

EN

A new approach for stochastic upper bound kinematical analyses is described. The study proposes an iterative algorithm that uses the Vanmarcke spatial averaging and kinematical failure mechanisms. The iterative procedure ensures the consistency between failure geometry and covariance matrix, which influences the quality of the results. The proposed algorithm can be applied to bearing capacity evaluation or slope stability problems. The iterative algorithm is used in the study to analyse the three-dimensional undrained bearing capacity of shallow foundations and the bearing capacity of the foundation for two-layered soil, in both cases, the soil strength spatial variability is included. Moreover, the obtained results are compared with those provided by the algorithm, based on the constant covariance matrix. The study shows that both approaches provide similar results for a variety of foundation shapes and scale of fluctuation values. Therefore, the simplified algorithm can be used for purposes that require high computational efficiency and for practical applications. The achieved efficiency using a constant covariance matrix for one realisation of a three-dimensional bearing capacity problem that includes the soil strength spatial variability results in about 0.5 seconds for a standard notebook. The numerical example presented in the study indicates the importance of the iterative algorithm for further development of the failure mechanism application in probabilistic analyses. Moreover, because the iterative algorithm is based on the upper bound theorem, it could be utilised as a reference for other methods for spatially variable soil.

2

Bearing capacity of eccentrically loaded strip footing on spatially variable cohesive soil

Dobrzański Jędrzej, Kawa Marek

Studia Geotechnica et Mechanica

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2021

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Vol. 43, nr 4

425--437

EN

The study considers the bearing capacity of eccentrically loaded strip footing on spatially variable, purely cohesive soil. The problem is solved using the random finite element method. The anisotropic random field of cohesion is generated using the Fourier series method, and individual problems within performed Monte Carlo simulations (MCSs) are solved using the Abaqus finite element code. The analysis includes eight different variants of the fluctuation scales and six values of load eccentricity. For each of these 48 cases, 1000 MCSs are performed and the probabilistic characteristics of the obtained values are calculated. The results of the analysis indicate that the mean value of the bearing capacity decreases linearly with eccentricity, which is consistent with Meyerhof's theory. However, the decrease in standard deviation and increase in the coefficient of variation of the bearing capacity observed are non-linear, which is particularly evident for small eccentricities. For one chosen variant of fluctuation scales, a reliability analysis investigating the influence of eccentricity on reliability index is performed. The results of the analysis conducted show that the value of the reliability index can be significantly influenced even by small eccentricities. This indicates the need to consider at least random eccentricities in future studies regarding probabilistic modelling of foundation bearing capacity.

3

Reliability analysis of sheet pile wall in spatially variable soil including CPTu test results

Kawa M., Baginska I., Wyjadlowski M.

Archives of Civil and Mechanical Engineering

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2019

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Vol. 19, no. 2

598--613

EN

The paper deals with reliability analysis of cantilever sheet pile wall located in non-cohesive soil with random properties. Spatial variability of friction angle has been described using random fields theory. The influence of both vertical as well as horizontal scale of fluctuation on the mechanical response of sheet pile wall is investigated. Deflection of wall top as well as maximum bending moment in the sheet pile wall are tested. The point distribution of soil friction and its vertical fluctuation scale is estimated using quasi-continuous results of cone penetrometer tests (CPTu). The boundary value problem is solved using finite difference code FLAC. The Fourier series method (FSM) allowing for non-uniform meshes is used to generate random fields for individual realizations. By utilizing Monte Carlo Simulation (MCS) technique the probability distributions of the results for different values of vertical and horizontal scales of fluctuation are obtained and used for reliability analysis. The results of analysis show that in case of cantilever sheet pile wall it is very important to properly estimate value of vertical fluctuation scale for the reliability analysis. It is also illustrated that in the considered problem horizontal scale of fluctuation significantly influences probability of failure.

4

Technical note: Comparison between two methods for estimating the vertical scale of fluctuation for modeling random geotechnical problems

Pieczyńska-Kozłowska J.

Studia Geotechnica et Mechanica

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2015

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Vol. 37, nr 4

95--103

EN

The design process in geotechnical engineering requires the most accurate mapping of soil. The difficulty lies in the spatial variability of soil parameters, which has been a site of investigation of many researches for many years. This study analyses the soilmodeling problem by suggesting two effective methods of acquiring information for modeling that consists of variability from cone penetration test (CPT). The first method has been used in geotechnical engineering, but the second one has not been associated with geotechnics so far. Both methods are applied to a case study in which the parameters of changes are estimated. The knowledge of the variability of parameters allows in a long term more effective estimation, for example, bearing capacity probability of failure.