Bulletin of Earthquake Engineering

, Volume 17, Issue 6, pp 2963–2987 | Cite as

V–H–M seismic capacity envelopes of strip foundations on slopes for capacity design of structure-foundation system

  • Dhiraj Raj
  • Yogendra SinghEmail author
  • Amir M. Kaynia
Original Research


The columns and the supporting foundations are invariably subjected to the interacting axial force, V, shear force, H and moment, M. It is quite common to consider the interaction of these forces in design of structural components, but the available standards and literature usually ignore the effect of interaction in case of foundations on slopes. Further, very little information is available about seismic capacity of foundations located on slopes. This article presents a numerical study on evaluation of the V–H–M capacity envelopes of strip foundations placed on top and face of slopes and subjected to earthquake action, with an objective of enabling a direct comparison with the capacity of the supported columns. Nonlinear 2D finite element limit analyses are performed for this purpose. Modified ‘Probe’ analyses are carried out for two representative c-ϕ soil slopes to develop the V–H–M capacity envelopes. The computed capacity envelopes are compared with their counterparts on flat ground. The characteristic features of the capacity envelopes are identified and explained considering the failure patterns under different combinations of V, H and M. A comparison of the capacity envelopes of counterpart foundations on flat ground and of columns is presented to highlight the relative hierarchy of strength of columns and foundations of a typical building on slope.


Capacity envelope Slope-foundation interaction Seismic loading Finite element limit analysis (FELA) Capacity design 



The research work presented here was supported by the Institute fellowship to the first author from the Ministry of Human Resource Development, Government of India. The authors are grateful to ‘Optum Computational Engineering’ (OptumCE) for providing free academic license of OptumG2 software to perform the present study. The authors would also like to thank the anonymous reviewers for their valuable comments and suggestions for improving the paper.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Earthquake EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of Structural EngineeringNTNUTrondheimNorway
  3. 3.Norwegian Geotechnical InstituteUllevaal StadionOsloNorway

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