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Design Curves for Estimation of Amplification Factor in the Slope Topography Considering Nonlinear Behavior of Soil

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Abstract

Both surface and in-depth topography have significant effects on the earthquake records and inflicted damages. Despite various studies, the effects of topography have not yet been addressed comprehensively by the current construction codes. The effect of slope topography was investigated in this study considering the real (elastoplastic) behavior of the materials and the effects of the increase in stiffness with the depth on the ground surface response using numerical analysis. Such parameters as input motion frequency, slope height and angle, and the material type were evaluated. The finite-element software tool MIDAS GTS NX was used for modeling. The study results were presented as the acceleration amplification factor, which is the ratio of the maximum two-dimensional ground acceleration to the maximum one-dimensional ground acceleration. The results showed that the seismic analysis of slope topography had a significant effect on the surface amplification factor near the crest and toe of the slope. According to the evaluated parameters, the areas affected by topography on the ground types dense and medium dense reach the x/H = 1.5 and x/H = 0.67 of the crest, respectively. In this condition, the amplification factor of acceleration for the ground types dense and medium dense will be in 1–3.5 and 1.5–3 ranges, respectively.

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Abbreviations

f :

Dominant frequency

G o :

Initial shear modulus

γ 0.7 :

Threshold shear strain

ξ :

Damping ratio

E D :

Dissipated energy

E S :

Maximum strain energy

\(G_{0}^{\text{ref}}\) :

Reference initial shear modulus at the reference pressure (pref) of 100 kPa

c′ and φ′ :

Soil strength parameters

\(\sigma_{3}^{'}\) :

Minimum principal effective stress

\(E_{\text{ur}}^{\text{ref}}\) :

Loading–unloading stiffness

\(E_{50}^{\text{ref}}\) :

Secant stiffness in the drained triaxial test

\(E_{\text{oed}}^{\text{ref}}\) :

Tangent stiffness for the initial oedometer loading

V s :

Shear wave velocity

[C], [M], and [K]:

Matrices of damping, mass, and stiffness

αR and βR :

Coefficients proportional to mass and stiffness

ωi and ωj :

Natural frequencies of two vibration modes

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Authors and Affiliations

  1. Department of Civil Engineering, Kharazmi University, Mofatteh Avenue, P.O. Box 15719-14911, Tehran, Iran

    Mohammad Javad Shabani & Ali Ghanbari

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  1. Mohammad Javad Shabani
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  2. Ali Ghanbari
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Correspondence to Mohammad Javad Shabani.

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Shabani, M.J., Ghanbari, A. Design Curves for Estimation of Amplification Factor in the Slope Topography Considering Nonlinear Behavior of Soil. Indian Geotech J 50, 907–924 (2020). https://doi.org/10.1007/s40098-020-00443-1

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  • DOI: https://doi.org/10.1007/s40098-020-00443-1

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