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

Włodzimierz Brząkała

Włodzimierz Brząkała

Department of Geotechnics, Hydroengineering, Underground- and Water-Structures, Wroclaw University of Science and TechnologyWroclaw, Poland
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Brząkała, Włodzimierz
  
22. Dez. 2021
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Artikel-Kategorie: Original Study
Online veröffentlicht: 22. Dez. 2021
Seitenbereich: 465 - 478
Eingereicht: 28. Juli 2021
Akzeptiert: 22. Nov. 2021
DOI: https://doi.org/10.2478/sgem-2021-0039
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© 2021 Włodzimierz Brząkała, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

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_

ρij tan(φ1) tan(φ2) c1 c2
tan(φ1) 1 +0.10 −0.30 −0.06
tan(φ2) +0.10 1 −0.06 −0.30
c1 −0.30 −0.06 1 +0.10
c2 −0.06 −0.30 +0.10 1

Auto- and cross-covariances used in numerical calculations_

Cov{Xi;Xj} tan(φ1) (−) tan(φ2) (−) c1 (kPa) c2 (kPa)
tan(φ1) (−) 0.015625 0.0015625 −0.15 −0.03
tan(φ2) (−) 0.0015625 0.015625 −0.03 −0.15
c1(kPa) −0.15 −0.03 16 1.6
c2(kPa) −0.03 −0.15 1.6 16
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