<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

An iterative algorithm for random upper bound kinematical analysis

Wroclaw University of Science and Technology

Department of Geotechnics and Hydrotechnics, Faculty of Civil Engineering

Studia Geotechnica et Mechanica

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"An iterative algorithm for random upper bound kinematical analysis"}

A new approach for stochastic upper bound kinematical analyses is described. The study proposes an iterative algorithm that uses the Vanmarcke spatial...

An iterative algorithm for random upper bound kinematical analysis

Article Category: Original Study

Published Online: Nov 10, 2021

Page range: 13 - 25

Received: May 29, 2021

Accepted: Sep 27, 2021

DOI: https://doi.org/10.2478/sgem-2021-0027

Keywords
random bearing capacity, shallow foundation, scale of fluctuation, iterative algorithm, upper bound, spatial variability

© 2022 Marcin Chwała, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

An iterative algorithm for random upper bound kinematical analysis

Article Category: Original Study

Published Online: Nov 10, 2021

Page range: 13 - 25

Received: May 29, 2021

Accepted: Sep 27, 2021

DOI: https://doi.org/10.2478/sgem-2021-0027

Keywordsrandom bearing capacity, shallow foundation, scale of fluctuation, iterative algorithm, upper bound, spatial variability

© 2022 Marcin Chwała, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
random bearing capacity, shallow foundation, scale of fluctuation, iterative algorithm, upper bound, spatial variability