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Stress-weighted spatial averaging of random fields in geotechnical risk assessment Cover

Stress-weighted spatial averaging of random fields in geotechnical risk assessment

Studia Geotechnica et Mechanica
Volume 43 (2021): Issue 4 (December 2021)
By: Włodzimierz Brząkała  
Open Access
|Dec 2021

Figures & Tables

Figure 1

(a) Prototype defined by two random variables tan(φi), i = 1, 2. (b) Variance reduction factors γa(w1), depending on the dimensionless weight coefficient w1.
(a) Prototype defined by two random variables tan(φi), i = 1, 2. (b) Variance reduction factors γa(w1), depending on the dimensionless weight coefficient w1.

Figure 2

The dimensionless variance reduction factors γsa(S) depending on the correlation parameter d (m) and the stress parameter S (m).
The dimensionless variance reduction factors γsa(S) depending on the correlation parameter d (m) and the stress parameter S (m).

Figure 3

The dimensionless variance reduction factors γsa(e) depending on the correlation parameter d = dh (m) and the load eccentricities eB = eL = e (m).
The dimensionless variance reduction factors γsa(e) depending on the correlation parameter d = dh (m) and the load eccentricities eB = eL = e (m).

Figure 4

The effective depth zmax under considered foundation and the dimensionless variance reduction factor γsa(β) depending on the correlation parameter d = dv (m) and the footing shape ratio β.
The effective depth zmax under considered foundation and the dimensionless variance reduction factor γsa(β) depending on the correlation parameter d = dv (m) and the footing shape ratio β.

Figure 5

The dimensionless variance reduction factors γsa(β) and γga(β) for the correlation parameters dv = d = 1.5 m (solid lines) and dv = d = 0.5 m (dashed lines).
The dimensionless variance reduction factors γsa(β) and γga(β) for the correlation parameters dv = d = 1.5 m (solid lines) and dv = d = 0.5 m (dashed lines).

Figure 6

Simplified wedge stability for 2x2 random variables tan(φi), ci, i = 1, 2.
Simplified wedge stability for 2x2 random variables tan(φi), ci, i = 1, 2.

Auto- and crosscorrelation coefficients used in numerical calculations_

ρijtan(φ1)tan(φ2)c1c2
tan(φ1)1+0.10−0.30−0.06
tan(φ2)+0.101−0.06−0.30
c1−0.30−0.061+0.10
c2−0.06−0.30+0.101

Auto- and cross-covariances used in numerical calculations_

Cov{Xi;Xj}tan(φ1) (−)tan(φ2) (−)c1 (kPa)c2 (kPa)
tan(φ1) (−)0.0156250.0015625−0.15−0.03
tan(φ2) (−)0.00156250.015625−0.03−0.15
c1(kPa)−0.15−0.03161.6
c2(kPa)−0.03−0.151.616
DOI: https://doi.org/10.2478/sgem-2021-0039 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
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Language: English
Page range: 465 - 478
Submitted on: Jul 28, 2021
Accepted on: Nov 22, 2021
Published on: Dec 22, 2021
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
spatial variability,
effective soil parameters,
variance reduction,
the Vanmarcke averaging,
safety factor
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

© 2021 Włodzimierz Brząkała, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

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