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An iterative algorithm for random upper bound kinematical analysis

Marcin Chwała
Marcin Chwała
   | 10. Nov. 2021
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Article Category: Original Study
Online veröffentlicht: 10. Nov. 2021
Seitenbereich: 13 - 25
Eingereicht: 29. Mai 2021
Akzeptiert: 27. Sept. 2021
DOI: https://doi.org/10.2478/sgem-2021-0027
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© 2022 Marcin Chwała, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

The three algorithms discussed in the study. Path ‘A’ is the base iterative algorithm, which is described in detail in the text, the path ‘B’ differs only from ‘A’ in Step 3 (see the description in the text), and the path ‘C’ is dedicated to a constant covariance matrix. Both ‘A’, ‘B’, and ‘C’ are repeated N times in the Monte Carlo framework.
The three algorithms discussed in the study. Path ‘A’ is the base iterative algorithm, which is described in detail in the text, the path ‘B’ differs only from ‘A’ in Step 3 (see the description in the text), and the path ‘C’ is dedicated to a constant covariance matrix. Both ‘A’, ‘B’, and ‘C’ are repeated N times in the Monte Carlo framework.

Figure 2

Failure geometry for two-layered soil for the probabilistic case. The indicated points and lengths are used to determine the failure geometry.
Failure geometry for two-layered soil for the probabilistic case. The indicated points and lengths are used to determine the failure geometry.

Figure 3

Eight randomly selected results among 200 Monte Carlo realizations for the case of θh=2 m, θv=1 m, and a=2 m.
Eight randomly selected results among 200 Monte Carlo realizations for the case of θh=2 m, θv=1 m, and a=2 m.

Figure 4

Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviations as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for two-layered soil, vertical scale of fluctuation θv=0.5 m,, foundation width b=1 m and averaging lengths a=2 m and a=8 m.
Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviations as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for two-layered soil, vertical scale of fluctuation θv=0.5 m,, foundation width b=1 m and averaging lengths a=2 m and a=8 m.

Figure 5

Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviations as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for two-layered soil, vertical scale of fluctuation θv=1 m,, foundation width b=1 m and averaging lengths a=2 m and a=8 m.
Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviations as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for two-layered soil, vertical scale of fluctuation θv=1 m,, foundation width b=1 m and averaging lengths a=2 m and a=8 m.

Figure 6

Three-dimensional failure geometry of the rough foundation base for the probabilistic case. The indicated angles and lengths are used to determine the failure geometry.
Three-dimensional failure geometry of the rough foundation base for the probabilistic case. The indicated angles and lengths are used to determine the failure geometry.

Figure 7

Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviations as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for a square foundation of size 1 m × 1 m.
Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviations as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for a square foundation of size 1 m × 1 m.

Figure 8

Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviation as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for a rectangular foundation of size 1 m × 4 m.
Bearing capacity mean values as a function of covariance matrix iteration number (a). Bearing capacity standard deviation as a function of covariance matrix iteration number (b). Case k=0 is for the constant covariance matrix. Results for a rectangular foundation of size 1 m × 4 m.

Figure 9

Bearing capacity mean values (a), standard deviations (b), and coefficient of variations (c) as a function of coefficient of variation of undrained shear strength. Two-layered soil considered with homogenous top layer (all parameters not mentioned here are the same as for earlier analyses).
Bearing capacity mean values (a), standard deviations (b), and coefficient of variations (c) as a function of coefficient of variation of undrained shear strength. Two-layered soil considered with homogenous top layer (all parameters not mentioned here are the same as for earlier analyses).

Figure 10

Stabilisation of bearing capacity mean values (a) and standard deviations (b) for the iterative approache for k=6.
Stabilisation of bearing capacity mean values (a) and standard deviations (b) for the iterative approache for k=6.
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