An analytical approach for estimating the bearing capacity of slopes under loading on the upper surface

Document Type : Research Paper


1 School of Mining Engineering, College of Engineering, University of Tehran, Iran

2 Thurber Engineering Ltd., Vancouver, British Columbia, Canada


Bearing capacity plays a significant role in evaluating the safety of the foundations rest on the slope. Many solutions have been proposed to assess the ultimate bearing capacity of foundation adjacent to the slope, however, the available analytical and empirical methods are associated with some shortcomings in view of slope material properties and geometry. Also, numerical methods suffer from the rigorous computational effort, and the accuracy of the outcome depends on the mesh and boundary effect. Therefore, a new analysis is employed in this research work that is able to consider all the effective parameters on the evaluation of ultimate bearing capacity. The results are compared with the existing numerical one in the literature and show good agreements. Also, in order to facilitate the use of the proposed method a Mathematica package code has been proposed to help the researcher to evaluate the bearing capacity of a shallow foundation rests on the slope.


[1] Terzaghi K. Theoretical soil mechanics, Wiley, New York. 1943.
[2] Meyerhof G. The ultimate bearing capacity of foundations on slopes.  Proc, 4th Int Conf on Soil Mechanics and Foundation Engineering1957. p. 384-6.
[3] Meyerhof GG. Some recent research on the bearing capacity of foundations. Canadian Geotechnical Journal. 1963;1(1):16-26.
[4] Georgiadis K. Undrained bearing capacity of strip footings on slopes. Journal of geotechnical and geoenvironmental engineering. 2010;136(5):677-85.
[5] Hansen B. A general formula for bearing capacity. Danish Geotechnical Institute, Bulletin. 1961;11(38-46.
[6] Vesic AS. Bearing capacity of shallow foundations. Foundation engineering handbook. 1975.
[7] Bowles L. Foundation analysis and design: McGraw-hill, 1996.
[8] Kusakabe O, Kimura T, Yamaguchi H. Bearing capacity of slopes under strip loads on the top surfaces. Soils and foundations. 1981;21(4):29-40.
[9] Leshchinsky B. Bearing capacity of footings placed adjacent to c′-ϕ′ slopes. Journal of geotechnical and geoenvironmental engineering. 2015;141(6):04015022.
[10] Zhou H, Zheng G, Yin X, Jia R, Yang X. The bearing capacity and failure mechanism of a vertically loaded strip footing placed on the top of slopes. Computers and Geotechnics. 2018;94(12-21.
[11] Xie H, Wang Q, Wu J, Chen Y. Analytical model for methane migration through fractured unsaturated landfill cover soil. Eng Geol. 2019;255(69-79.
[12] Haghgouei H, Kargar AR, Amini M, Khosravi MH. Semi-analytical solution for evaluating the bearing capacity of a footing adjacent to a slope. International Journal of Geomechanics. 2020 (In Press).
[13] Haghgouei H, Kargar AR, Amini M, Esmaeili K. An analytical solution for analysis of toppling-slumping failure in rock slopes. Eng Geol. 2020;265(105396.
[14] Haghgouei H, Kargar A, Khosravi MH, Amini M. Semi-Analytical Study of Settlement of Two Interfering Foundations Placed on a Slope. Journal of Mining and Environment. 2021;12(2):457-70.
[15] Sadd MH. Elasticity: theory, applications, and numerics: Academic Press, 2009.
[16] Filon LNG. III.—On a Quadrature Formula for Trigonometric Integrals. Proceedings of the Royal Society of Edinburgh. 1930;49(38-47.
[17] Goodman L, Brown C. Dead load stresses and the instability of slopes. Journal of the Soil Mechanics and Foundations Division. 1963;89(3):103-36.
[18] de Souza Neto EA, Peric D, Owen DR. Computational methods for plasticity: theory and applications: John Wiley & Sons, 2011.
[19] Dai Z-H, You T, Xu X, Zhu Q-C. Removal of Singularities in Hoek-Brown Criterion and Its Numerical Implementation and Applications. International Journal of Geomechanics. 2018;18(10):04018127.
[20] Krahn J. The 2001 RM Hardy Lecture: The limits of limit equilibrium analyses. Canadian Geotechnical Journal. 2003;40(3):643-60.
[21] Stianson JR, Chan D, Fredlund D. Comparing slope stability analysis based on linear elastic or elastoplastic stresses using dynamic programming techniques.  Proc, 57th Canadian Geotechnical Conf2004. p. 23-30.