New pseudo-dynamic analysis of two-layered cohesive-friction soil slope and its numerical validation

doi:10.1007/s11709-020-0679-3

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (6) : 1492-1508 https://doi.org/10.1007/s11709-020-0679-3

RESEARCH ARTICLE

New pseudo-dynamic analysis of two-layered cohesive-friction soil slope and its numerical validation

Suman HAZARI, Sima GHOSH(

), Richi Prasad SHARMA

Department of Civil Engineering, National Institute of Technology, Agartala 799046, India

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Abstract

Natural slopes consist of non-homogeneous soil profiles with distinct characteristics from slopes made of homogeneous soil. In this study, the limit equilibrium modified pseudo-dynamic method is used to analyze the stability of two-layered c-φ soil slopes in which the failure surface is assumed to be a logarithmic spiral. The zero-stress boundary condition at the ground surface under the seismic loading condition is satisfied. New formulations derived from an analytical method are proposed for the predicting the seismic response in two-layered soil. A detailed parametric study was performed in which various parameters (seismic accelerations, damping, cohesion, and angle of internal friction) were varied. The results of the present method were compared with those in the available literature. The present analytical analysis was also verified against the finite element analysis results.

Keywords layered soil limit equilibrium method seismic analysis damping PLAXIS

Corresponding Author(s): Sima GHOSH

Just Accepted Date: 20 November 2020 Online First Date: 30 December 2020 Issue Date: 12 January 2021

Cite this article:

Suman HAZARI,Sima GHOSH,Richi Prasad SHARMA. New pseudo-dynamic analysis of two-layered cohesive-friction soil slope and its numerical validation[J]. Front. Struct. Civ. Eng., 2020, 14(6): 1492-1508.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0679-3
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I6/1492

Fig.1 Geometry of the log-spiral failure mechanism for a layered soil slope.

Fig.2 Forces acting on soil wedge and wave propagation at soil interface.

Tab.1 Factor of safety at dynamic condition at D₁/D₂= 0.5, c₁/c₂= 0.4, γ₁/γ₂= 1.0, and H₁/H₂= 0.6

Fig.3 Details of the optimization algorithm.

Fig.4 Variations of FOS for different values of D₁/D₂ ratio with ϕ₂/ϕ₁= 0.6, k_h= 0.1, k_v= k_h/2, c₁/c₂= 0.4, γ₁/γ₂= 1.0, and H₁/H₂_{= 0.6.}

Fig.5 Variations of FOS for different values of k_h with ϕ₂/ϕ₁= 0.6, D₁/D₂= 0.5, k_v= k_h/2, c₁/c₂= 0.4, γ₁/γ₂= 1.0, and H₁/H₂= 0.6.

Fig.6 Variations of FOS for different values of k_v with ϕ₂/ϕ₁= 0.6, D₁/D₂= 0.5, k_v= k_h/2, c₁/c₂= 0.4, γ₁/γ₂= 1.0, and H₁/H₂= 0.6.

Fig.7 Variations of FOS for different values of c₁/c₂ratio with ϕ₂/ϕ₁= 0.6, k_h= 0.1, k_v= k_h/2, D₁/D₂= 0.5, γ₁/γ₂= 1.0, and H₁/H₂= 0.6.

Fig.8 Variations of FOS for different values of ϕ₂/ϕ₁ratio with D₁/D₂= 0.5, k_h= 0.1, k_v= k_h/2, c₁/c₂= 0.4, γ₁/γ₂=1.0, and H₁/H₂= 0.6.

Fig.9 Variations of FOS for different values of γ₁/γ₂ratio with D₁/D₂= 0.5, k_h= 0.1, k_v= k_h/2, c₁/c₂= 0.4, ϕ₂/ϕ₁= 0.6, and H₁/H₂= 0.6.

Fig.10 Variations of FOS for different values of H₁/H₂ratio with D₁/D₂= 0.5, k_h= 0.1, k_v= k_h/2, c₁/c₂= 0.4, ϕ₂/ϕ₁= 0.6, and γ₁/γ₂= 1.0.

Fig.11 Plot of slope geometry with boundary and arrangement of mesh in the numerical study.

Fig.12 Sensitivity analysis results to decide the size of finite element mesh.

Tab.2 Input soil parameters for PLAXIS

Fig.13 Accelerogram for dynamic analysis in Plaxis as provided at the fixed end of slope model.

Fig.14 Acceleration vs time curves (at different depths A, B, C, …, E as shown in Fig. 11) due to application of dynamic loading (Fig. 13) at the fixed base of soil slope model.

Tab.3 Comparison of results between proposed analytical method and numerical analysis at ϕ₂/ϕ₁= 0.6, c₁/c₂= 0.4, γ₁/γ₂= 1.0, and H₁/H₂= 0.6

Fig.15 Pattern of failure surfaces at ϕ₂/ϕ₁= 0.6, β = 30°, D₁/D₂= 0.5, k_v= 0, c₁/c₂= 0.4, γ₁/γ₂= 1.0, and H₁/H₂= 0.6: (a) Analytical method (b) Numerical analysis.

Fig.16 Comparison of failure pattern with existing experimental study at ϕ = 11.3°, β = 39.4°, c₂ = 10.78 kN/m², γ₂ = 11.9 kN/m³, and H₁/H_{= 0 (z = any depth from the top, y = horizontal deformation).}

Tab.4 Comparison of FOS obtained in from the present analysis with other studies

Tab.5 Comparison of the results obtained by available solutions with the present study at k_v= 0 and c₁/c₂= 1

a(z,t): acceleration at depth z, time t

Q_h, Q_v: horizontal and vertical inertia forces due to seismic acceleration

c₁, c₂: cohesion of top and bottom soil layers, respectively

φf₁, φ₂: soil friction angle of the top and bottom soil layers, respectively

r_o: initial radius of log-spiral

r₁: final radius of log-spiral arc in the top layer

r₂: final radius of log-spiral arc in the bottom layer

H₁, H₂: heights of top and bottom layers respectively

g: acceleration due to gravity

G: shear modulus of soil

ΩW: angular frequency of base shaking

k_h, k_v: intensity of horizontal and vertical seismic acceleration

v_s: shear wave velocity

v_p: primary wave velocity

β: angle of slope with horizontal

γ₁, γ₂: unit weight of the top and bottom soil layers, respectively

FOS: factor of safety

ν

: Poisson’s ratio

D₁, D₂: damping ratio of top and bottom soil layers, respectively

η s

: soil viscosity

t: time during vibration (s)

T: time period (s)

A_I: amplitude of incident wave

A_t: amplitude of transmitted wave

A_r: amplitude of reflected wave

a_z: impedance ratio

m: mobilization factor

t/T: time ratio

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