Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory

doi:10.1007/s11709-021-0698-8

Front. Struct. Civ. Eng.

2021, Vol. 15

Issue (2) : 478-489 https://doi.org/10.1007/s11709-021-0698-8

RESEARCH ARTICLE

Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory

Rajarshi PRAMANIK(

), Dilip Kumar BAIDYA, Nirjhar DHANG

Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

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Abstract

The aim of this study is to investigate the applicability of reliability theory on surface square/rectangular footing against bearing capacity failure using fuzzy set theory in conjunction with the finite element method. Soil is modeled as a three-dimensional spatially varying medium, where its parameters (cohesion, friction angle, unit weight, etc.) are considered as fuzzy variables that maintain some membership functions. Soil is idealized as an elastic-perfectly plastic material obeying the Mohr–Coulomb failure criterion, where both associated and non-associated flow rules are considered in estimating the ultimate bearing capacity of the footing. The spatial variability of the soil is incorporated for both isotropic and anisotropic fields, which are determined by the values of scales of fluctuation in both the horizontal and vertical directions. A new parameter namely, limiting applied pressure at zero failure probability is proposed, and it indirectly predicts the failure probability of the footing. The effect of the coefficient of variation of the friction angle of the soil on the probability of failure is analyzed, and it is observed that the effect is significant. Furthermore, the effect of the scale of fluctuation on the probability of failure is investigated, and the necessity for considering spatial variability in the reliability analysis is well proven.

Keywords finite element method square footing reliability analysis fuzzy set theory coefficient of variation spatial variability

Corresponding Author(s): Rajarshi PRAMANIK

Just Accepted Date: 03 March 2021 Online First Date: 16 April 2021 Issue Date: 27 May 2021

Cite this article:

Rajarshi PRAMANIK,Dilip Kumar BAIDYA,Nirjhar DHANG. Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory[J]. Front. Struct. Civ. Eng., 2021, 15(2): 478-489.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-021-0698-8
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I2/478

Fig.1 Membership function of resulting fuzzy number and calculation of probability of failure.

Fig.2 Flow diagram of fuzzy reliability analysis.

Fig.3 Schematic diagram of footing position and boundary conditions.

Tab.1 Properties (elastic and shear strength) of soil

Tab.2 Comparison of shape factor (s_c) of square and rectangular footings (φ = 0)

Fig.4 Effect of shape of membership functions: (a) membership function of q_ult; (b) variation in P_f with different limiting applied pressures for various scales of fluctuation.

Fig.5 Membership function of final fuzzy number (ultimate bearing capacity): (a) COV of φ = 0.1; (b) COV of φ = 0.4.

Tab.3 Fuzzy variables and statistical parameters considered in analysis

Fig.6 Variation in P_f with different limiting applied pressures: (a) φ = 5°, CVO_?= 0.1; (b) φ = 5°, CVO_?= 0.4; (c) φ = 10°, CVO_?= 0.1; (d) φ = 10°, CVO_? = 0.4; (e) φ = 15°, CVO_? = 0.1; (f) φ = 15º, CVO_?= 0.4; (g) φ = 20°, CVO_?= 0.1; (h) φ = 20°, CVO_? = 0.4.

Fig.7 Effect of flow rule: (a) φ = 10°, CVO_? = 0.1; (b) φ = 10°, COV_?= 0.4; (c) φ = 20°, COV_? = 0.1; (d) φ = 20°, COV_?= 0.4.

Fig.8 P_f vs. q_lim for different ψ values.

Fig.9 Variation in q⁰_lim with varyingδ/B (isotropic case).

Fig.10 Effect of aspect ratio of footing on q⁰_lim value (for cohesive soil deposit only).

Fig.11 Variation in q⁰_lim with varying δ_x/B (anisotropic case).

Fig.12 Variation in influence factor for different scales of fluctuation.

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