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Development of limiting soil slope profile under seismic condition using slip line theory

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Abstract

This study embraces the formation of the limiting geometry of finite slopes under the static and seismic conditions within the slip line theory framework coupled with the modified pseudo-dynamic approach. The proposed methodology is expected to achieve a global factor of safety of 1.0 for the obtained slope profile. While analysing the stability of slopes using the limit analysis or the limit equilibrium method, the cognition of the slope geometry and the nature of the slip surface need to be known in advance. Such limitations are ruled out in the present analysis with the aid of the slip line method. Further, by employing the modified pseudo-dynamic approach, the dynamic properties of soil, such as damping ratio and frequency effect, are effectively considered in this stability analysis. The consideration of the slip line theory permits to achieve an adaptive failure mechanism in the analysis. The impact of a set of parameters characterizing the input motion and the dynamic soil properties on the behaviour of a slope explains the relevance of the present modified pseudo-dynamic approach compared to the conventional pseudo-static and the original pseudo-dynamic approaches. The proposed solution serves as a measure of the seismic slope stability in accordance with the geomorphological process generally encountered in nature. Compared with the available literature, the present results propose safe, economical, and efficient design guidelines for finite slopes and intimate the need for preventive measures to enhance the stability of existing slopes.

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Abbreviations

a h(x, t):

Horizontal earthquake acceleration in the soil deposit at depth x and time t

a v(x, t):

Vertical earthquake acceleration in the soil deposit at depth x and time t

c :

Cohesion of soil

D :

Damping ratio of soil

f a :

Amplification factor for seismic waves

g :

Acceleration due to gravity

G :

Shear modulus of soil

h :

Height of slope

k h :

Horizontal seismic acceleration coefficient

k v :

Vertical seismic acceleration coefficient

N :

Numbers of data points along the slope profile

q :

Uniformly distributed surcharge

t :

Time

T :

Period of lateral shaking

u h0 :

Horizontal displacement amplitude at the base

u v0 :

Vertical displacement amplitude at the base

V p :

Velocity of primary wave

V s :

Velocity of shear wave

x, y :

Axes in two-dimensional Cartesian co-ordinate system

x i :

Ordinate of the ith data point along the slope profile

y ci :

Abscissa of the ith data point along the derived limiting slope profile corresponding to the ordinate xi

y li :

Abscissa of the ith data point along the known linear slope profile corresponding to the ordinate xi

X :

Body force per unit volume in the x direction

Y :

Body force per unit volume in the y direction

α h :

normalized horizontal earthquake acceleration = ah(x, t)/g

α v :

normalized horizontal earthquake acceleration = av(x, t)/g

β :

Magnitude of θ along the limiting slope profile (OA) but at the slope crest (O)

γ :

Unit weight of soil

γ s :

Shear strain

θ :

Angle made by σ1 in a counter-clockwise sense with the positive x-axis

θ g :

Magnitude of θ along the top surface of the slope (OG)

θ s :

Magnitude of θ along the limiting slope profile (OA)

λ :

First Lamé constant

ν 1, ν s :

Viscosities of soil

ρ :

Density of soil

σ :

Distance on the Mohr-stress diagram, between the centre of the Mohr circle and the point where the Coulomb’s linear failure envelope joins with the σ-axis

σ 1 :

Major principal stress

σ g :

Magnitude of σ along the top surface of the slope (OG)

σ s :

Magnitude of σ along the limiting slope profile (OA)

σ x :

Normal stress on the x plane

σ y :

Normal stress on the y plane

τ :

Shear stress

τ xy :

Shear stress in the xy plane

χ :

Inclination of a linear slope with the horizontal

ω :

Angular frequency of seismic wave = 2π/T

ϕ :

Angle of the internal friction of soil

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology, Kanpur, Kanpur, 208 016, India

    Shibsankar Nandi & Priyanka Ghosh

  2. Department of Civil Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, 641 112, India

    G. Santhoshkumar

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  1. Shibsankar Nandi
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  2. G. Santhoshkumar
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  3. Priyanka Ghosh
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Correspondence to Priyanka Ghosh.

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Nandi, S., Santhoshkumar, G. & Ghosh, P. Development of limiting soil slope profile under seismic condition using slip line theory. Acta Geotech. 16, 3517–3531 (2021). https://doi.org/10.1007/s11440-021-01251-4

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