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.
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
Qh, Qv = Horizontal and Vertical inertia forces due to seismic acceleration
b1 = Width of iˊth slice
b2 = Width of jˊth 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
ro = Initial radius of logarithmic spiral arc
r = Final radius of logarithmic spiral arc
H = Height of the slope
Wiˊ, Wjˊ = Weight of iˊth and jˊth slices
G = Acceleration due to gravity
G= Shear modulus of the soil
Ω = Angular frequency of base shaking
kh, kv = Intensity of horizontal and vertical seismic acceleration respectively
q = Surcharge loading
t = Any time during vibration (seconds)
T = Time Period (seconds)
Vs = Shear wave velocity
Vp = 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, Tvs
λ = Wave length of the vertically propagating primary wave, Tvp
ρ = Density of soil
= Poisson’s ratio
K = Coefficient of reinforcement to maintain the stability
PGA = Peak ground acceleration
D = Damping ratio
τ = Shear resistance
ηs = soil viscosity
ωsH/vs = Normalized frequency of S-wave
ωpH/vp = Normalized frequency of P-wave
Tr = 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.