Modified pseudo-dynamic analysis of slope considering logarithmic spiral failure surface with numerical solution

ABSTRACT

A methodology for the analysis of soil slope made up of c-ϕ soil using a modified pseudo-dynamic approach is tried to develop here. In this study, the slope is divided into a number of vertical slices and the failure surface of the slope is assumed to be logarithmic spiral. The suggested modified pseudo-dynamic approach satisfies the zero-stress boundary condition at the free ground surface and considers the damping properties of the materials. Results of the present analysis are presented in tabular form. The effects of the variation of different parameters like horizontal and vertical seismic acceleration, slope angle, soil friction angle, damping ratio, frequency ratio, cohesion and surcharge on the FOS are shown graphically. Consequently, required reinforcement strength is evaluated to ensure the safety of the slope under seismic loading conditions. The results obtained from the present method are compared with the results of the available literature and also a numerical validation of the model is given using PLAXIS 2D.

KEYWORDS:

• Logarithmic spiral rupture surface
• limit equilibrium approach
• modified pseudo-dynamic method
• damping
• numerical analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data, models, and code generated or used during the study appear in the submitted article.

List of symbols

a (z,t) = Acceleration at depth z, time t

Q_h, Q_v = Horizontal and Vertical inertia forces due to seismic acceleration

b₁ = Width of iˊ^th slice

b₂ = Width of jˊ^th slice

c = Cohesion of the soil

ϕ = Angle of internal friction of the soil

N = Normal force

T = Tangential force

Α = Angle of the base of the vertical slice with horizontal

iˊ, jˊ= Number of the vertical slice at different zones

r_o = Initial radius of logarithmic spiral arc

r = Final radius of logarithmic spiral arc

H = Height of the slope

W_iˊ, W_jˊ = Weight of iˊ^th and jˊ^th slices

G = Acceleration due to gravity

G= Shear modulus of the soil

Ω = Angular frequency of base shaking

k_h, k_v = Intensity of horizontal and vertical seismic acceleration respectively

q = Surcharge loading

t = Any time during vibration (seconds)

T = Time Period (seconds)

V_s = Shear wave velocity

V_p = Primary wave velocity

Β = Slope angle with horizontal

Γ = Unit weight of the soil

FOS = Factor of safety

η = Wave length of the vertically propagating shear wave, Tv_s

λ = Wave length of the vertically propagating primary wave, Tv_p

ρ = Density of soil

$\nu$ = Poisson’s ratio

K = Coefficient of reinforcement to maintain the stability

PGA = Peak ground acceleration

D = Damping ratio

τ = Shear resistance

η_s = soil viscosity

ω_sH/v_s = Normalized frequency of S-wave

ω_pH/v_p = Normalized frequency of P-wave

T_r = Reinforcement force

Additional information

Notes on contributors

Suman Hazari

Suman Hazari, Ph.D., Department of Civil Engineering, National Institute of Technology Agartala, Tripura, India.

Sima Ghosh

Sima Ghosh, Associate Professor, Department of Civil Engineering, National Institute of Technology Agartala, Tripura, India.

Richi Prasad Sharma

Richi Prasad Sharma, Professor, Department of Civil Engineering, National Institute of Technology Agartala, Tripura, India.