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Stochastic numerical approach to the bearing capacity of adjacent footings on spatially variable soils Cover

Stochastic numerical approach to the bearing capacity of adjacent footings on spatially variable soils

Studia Geotechnica et Mechanica
Volume 48 (2026): Issue 1 (March 2026)
By:   
Open Access
|May 2026
Figures & tables

Figures & Tables

Figure 1

The scheme of the impact of adjacent foundations on each other.

Figure 2

The adopted numerical model.

Figure 3

Node displacement results for a deterministic task with foundation spacing 0.9–8 m.

Figure 4

Analytical and numerical results for deterministic values of soil parameters for each approach: (a) ideal cohesive, (b) purely frictional, and (c) TBC.

Figure 5

Normalised analytical and numerical results for deterministic values of soil parameters for each approach: (a) ideal cohesive, (b) purely frictional, and (c) TBC.

Figure 6

Mean BC for probabilistic values of soil parameters for each approach: (a) ideal cohesive, (b) purely frictional, and (c) TBC.

Figure 7

BC COV for probabilistic values of soil parameters for each approach: (a) perfectly cohesive, (b) purely frictional, and (c) TBC.

Figure 8

Performance efficiency factor for all approaches (A1 – Approach 1 – perfectly cohesive; A2 – Approach 2 – purely frictional; A3 – Approach 3 – TBC).

Figure 9

Probability of failure. (a and b) Approach 1 – perfectly cohesive soil, (c and d) Approach 2 – purely frictional soil, and (e and f) Approach 3 – cohesive-frictional soil (TBC).

Soil parameters for non-cohesive approach_

Mean valueStandard deviationDistributionDistribution parameters
Cohesion (c)1 kPa—Deterministic
Friction angle ( ϕ \phi )35°—Bounded ϕ min = 25 ° {\phi }_{\min }\hspace{1em}=25^\circ
Unit weight ( γ \gamma )19 kN/m3 —Deterministic ϕ max = 45 ° {\phi }_{\max }\hspace{1em}=45^\circ

Soil parameters for a perfectly cohesive approach_

Mean valueStandard deviationDistribution
Cohesion (c)36.3 kPa19.6 kPaLognormal
Friction angle ( ϕ \phi )——Deterministic
Unit weight ( γ \gamma )——Deterministic

Analytical values of resistance for each design approach_

Analytical formulaBC value for B = 1 mBC value for B = 2 m
Approach 1 – perfectly cohesive soil q a = 5.12 c u {q}_{a}=5.12\hspace{0.25em}{c}_{u} 185.86 kPa185.86 kPa
Approach 2 – purely frictional soil q a = q N q + 0.5 B γ N γ {q}_{a}=q{N}_{q}+\hspace{0.25em}0.5B\gamma {N}_{\gamma } 1108.41 kPa1538.08 kPa
Approach 3 – cohesive-frictional soil q a = c N c + q N q + 0.5 B γ N γ {q}_{a}=c{N}_{c}+q{N}_{q}+0.5B\gamma {N}_{\gamma } 697.43 kPa734.77 kPa

Soil parameters for the cohesive-friction soil approach (TBC)_

Mean valueStandard deviationDistributionDistribution parameters
Cohesion (c)36.3 kPa19.6 kPaLognormal
Friction angle ( ϕ \phi )20° Bounded ϕ min = 5 ° {\phi }_{\min }=5^\circ
Unit weight ( γ (\gamma )19 kN/m3 —Deterministic ϕ max = 35 ° {\phi }_{\max }=35^\circ
DOI: https://doi.org/10.2478/sgem-2026-0005 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
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Language: English
Page range: 63 - 75
Submitted on: Apr 8, 2025
Accepted on: Mar 10, 2026
Published on: May 18, 2026
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Adjacent foundations,
RFEM,
Soil spatial variability,
Probability of failure,
Bearing capacity
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

© 2026 Joanna M. Pieczyńska-Kozłowska, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 48 (2026): Issue 1 (March 2026)
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