Keywords: discrete element method, rigid blocks, bearing capacity, shallow foundation, slope, Winkler spring.

In last decades, extensive studies have been made for two dimensional problems of strip footing which rests on a horizontal or inclined slope surface and different methods of analysis are introduced. It seems that theoretical approaches have reached a certain satisfactory level for 2D problems with ordinary loading and soil characteristics but three dimensional problems of bearing capacity still faces many unsolved difficulties. Common practice to evaluate the 3D bearing capacity is therefore to introduce experimental and empirical shape factors into the ordinary 2D equations for strip footing developed by earlier researchers such as Terzaghi & Peck [1], Meyerhof [2], Hansen [3], Vesic [4], and etc.

Different methods of computation can be used to incorporate 3D effect of shallow foundation bearing capacity problem. Calculations based on Limit Equilibrium, generally do not satisfy all equilibrium conditions; therefore, additional assumptions are required with respect to interslice forces and stresses. Finite Element Method or Finite Difference Method, require information about the initial stress state existing in the soil, a correct constitutive model and correct parameters for the constitutive model. These requirements increase the complexity of analysis and probability of uncertainly in the results.

Discrete Element Method (DEM) can be used for numerical analysis of different geotechnical problems such as slope stability, bearing capacity of shallow foundations, pressure distribution on retaining wall and relative displacement of rock masses.

In this research, an effort is made to use the method to determine three dimensional bearing capacity of foundations near or on a slope. The soil mass is modeled as several discrete blocks connected with Winkler springs. The equations employed in this method completely satisfy the equilibrium conditions of forces and moments, with the assumed elasto-plastic behavior for the springs. The geometry of the failure mechanism of soil mass under the foundation is determined by six independent angles, which are determined by trial and error to minimize the ultimate bearing load. A computer program based on the DEM (BCAP^3D - 3 Dimensional Bearing Capacity Analysis Program) is developed. Several examples are analyzed and the results presented in this paper.

1

Terzaghi K., Peck R.B. "Soils Mechanics in Engineering Practice", J.Wiley, New York. 1967.

2

Meyerhof G.G. "Some Recent Research on the Bearing Capacity of Foundations", Canadian Geotechnical Journal, Vol. 1, No.1, 16-26, 1964. doi:10.1139/t63-003

3

Hansen J.B. "A Revised and Extended Formula for Bearing Capacity", Danish Geotechnical Institute Bulletin, No.28, Denmark, 1970.

4

Vesic A.S. "Analysis of Ultimate Loads of Shallow Foundations", Journal of Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol.99, No.SM1, pp. 45-73, 1973.

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