Journal of Mountain Science

, Volume 15, Issue 7, pp 1559–1571 | Cite as

Analytical expressions for determining the stability of cohesionless soil slope under generalized seismic conditions

  • Sahoo Pragyan PradattaEmail author
  • Shukla Sanjay Kumar
  • Mohyeddin Alireza


In recent major earthquakes, the researchers have found the need for consideration of vertical seismic acceleration for the stability analysis of the man-made and natural slopes. However, in most past studies, the performance of slopes has been assessed by accounting only the horizontal seismic component of the ground motion, without giving due weightage to the effect of vertical component. In the present study, analytical expressions are derived to determine the factor of safety, yield seismic coefficient and consequently the seismic displacement of cohesionless soil slope under combined horizontal and vertical components of the ground motion. The derivation uses the Newmark’s sliding block approach, in which the soil slope with a planar failure surface within the framework of conventional pseudo-static analysis is assumed to follow the Mohr-Coulomb failure criterion. The effects of vertical seismic coefficient on the stability of cohesionless slope have been studied through a set of graphical presentations for a specific range of soil parameters. It is observed that overlooking the effect of the vertical component of the ground motion on factor of safety and the displacement while designing the slope may be detrimental, resulting in the slope failure. The general expressions presented in this paper may be highly useful in the field of earthquake geotechnical engineering practice for designing the cohesionless soil slopes under combined horizontal and vertical seismic loads.


Factor of safety Horizontal and vertical seismic coefficients Soil slopes Yield acceleration Sliding block displacement Seismic slope stability 



maximum amplitude of input acceleration (dimensionless)


base area of the sliding block (m2/m)


frequency of excitation (Hz)


driving force to induce sliding (N/m)


resisting force against sliding (N/m)


dynamic factor of safety (dimensionless)


factor of safety index (dimensionless)


acceleration due to gravity (=9.8) (m/s2)


angle of inclination of the slope (degrees)


horizontal seismic coefficient (dimensionless)


yield seismic coefficient (dimensionless)


vertical seismic coefficient (dimensionless)


shear strength on the failure plane (Pa)


time duration for excitation (s)


time interval until yield acceleration is attained (s)


weight of the sliding block (N/m)


sliding displacement of the system (m)


relative velocity of the sliding block (m/s)


relative block acceleration (m/s2)


angle of inclination of the failure plane of the slope with the horizontal (degrees)


angle of internal friction of the soil (degrees)


normal stress on the failure plane (Pa)


ratio of vertical seismic coefficient to horizontal seismic coefficient (=kv/kh) (dimensionless)


fundamental circular frequency of the sinusoidal motion (rad/sec).


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Copyright information

© Science Press, Institute of Mountain Hazards and Environment, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Discipline of Civil and Environmental Engineering, School of EngineeringEdith Cowan UniversityJoondalup, PerthAustralia
  2. 2.Fiji National UniversitySuva, Fiji, and Chitkara UniversityHimachal PradeshIndia

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