Finite element evaluation of ultimate capacity of strip footing: assessment using various constitutive models and sensitivity analysis

Abstract

Finite element method can be used for computing bearing capacity of shallow foundation with irregular geometry resting on variable subsoil. It is necessary to quantify the parameters affecting the ultimate capacity of footing. This paper presents the results of finite element (FE) analysis of the ultimate failure load of a rough base rigid strip footing resting on c-ϕ soil. The soil is assumed as linear elastic perfectly plastic with Mohr–Coulomb failure criterion and non-associative flow rule. Sensitivity analysis is carried out to examine the ultimate capacity of strip footing considering the strength parameters (c′, ϕ′, and ψ), width of strip footing (B), unit weight of soil (γ), surcharge (q) at the base level of footing, and the deformation parameters (E and ν) as the variables. The study also examines the effect of different material models on the ultimate capacity of the strip footing. The material models considered are Mohr–Coulomb (MC) model, Hardening Soil (HS) model, Hardening Soil model with small-strain stiffness (HSsmall), and Soft Soil (SS) mode-l. It is found from the results of FE analysis that the ultimate load of the strip footing is dependent on the strength parameters, width of footing, unit weight of soil, and surcharge at the base level of the footing. The ultimate capacity is independent of the deformation parameters and will remain almost same corresponding to the material models like MC, HS, HSsmall, and SS. The FE results are compared with the analytical solutions of Terzaghi and Meyerhof. Based on the study, a few suggestions are given in regard to the FE analysis of geotechnical stability problems to obtain the quick results.

Appendix 1

Mohr–Coulomb model In Mohr–Coulomb (MC) model, the yield function consists of principal stresses and strength parameters of the soil, c′ and ϕ′ [2]. In the principal stress space, the Mohr–Coulomb failure envelope represents a straight line at the intersection with an octahedral plane. It is shown to provide a good fit to the experimental data in triaxial compression and extension. The Mohr–Coulomb material model can be used most conveniently in the numerical simulation. The defining parameters are: the unit weight of soil, strength parameters (c′, ϕ′, and ψ), deformation parameters (E and ν), and K₀ is coefficient of earth pressure at rest which is by default taken as 1 – sin (ϕ′).

Hardening Soil model The Hardening Soil (HS) model is an advanced soil model which is an isotropic hardening double surface plasticity model, in which the stiffness is described based on three input stiffness. They are the triaxial loading stiffness (E₅₀), the triaxial unloading stiffness (E_ur), and the oedometer loading stiffness (E_oed), which account for the stress dependency of the stiffness values. The HS model [23] gives more realistic displacement patterns for the working load conditions, especially in the case of an excavation. The input parameters of HS model are: the unit weight of soil (γ), soil cohesion (c′), friction and dilatancy angles of soil (ϕ′ and ψ), triaxial loading stiffness (E₅₀), triaxial unloading stiffness (E_ur), oedometer loading stiffness (E_oed), Poisson’s ratio (ν), power for stress level dependency of stiffness (m), $K_{0}^{\text{nc}}$ for normal consolidation, and failure ratio (R_f).

Hardening Soil model with small-strain stiffness The Hardening Soil model with small-strain stiffness is a modification of the Hardening Soil model that accounts for the increased stiffness of the soil at small strains. This model is most apparent in working load conditions and gives more reliable displacements than the HS model. It has the same defining parameters of HS model with two additional parameters, i.e., small-strain shear modulus (G₀) and the shear strain level (γ_0.7) at which the shear modulus has reduced to about 70% of the G₀.

Soft Soil model The Soft Soil (SS) model is a Cam-clay type model especially meant for the primary compression of near normally consolidated clay type soils, which is better in capturing the compression of very soft soils. The input parameters of SS model are: the unit weight of soil (γ), soil cohesion (c′), friction and dilatancy angles of soil (ϕ′ and ψ), modified compression index (λ*), modified swelling index (κ*), Poisson’s ratio (ν), and $K_{0}^{\text{nc}}$ for normal consolidation.