American Society of Civil Engineers

Three-Dimensional Probabilistic Foundation Settlement

by Gordon A. Fenton, M.ASCE, (Professor, Dept. of Engineering Mathematics, Dalhousie Univ., Halifax, NS, B3J 2X4 Canada. E-mail: and D. V. Griffiths, F.ASCE, (Professor, Division of Engineering, Colorado School of Mines, Golden, CO 80401-1887. E-mail:

Journal of Geotechnical and Geoenvironmental Engineering, Vol. 131, No. 2, February 2005, pp. 232-239, (doi:

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Document type: Journal Paper
Abstract: By modeling soil as a three-dimensional spatially random medium, the reliability of shallow foundations against serviceability limit state failure, in the form of excessive settlement and/or differential settlement, can be estimated. The soil’s elastic modulus, E, is represented as a lognormally distributed random field with an isotropic correlation structure. The settlements of individual and pairs of square footings placed on the surface of the soil are computed using the finite element method. A probabilistic model for total and differential settlement is presented and compared to results obtained using Monte Carlo simulation. The distributions of total and differential settlement are found to be closely predicted using the distributions of geometric averages of the underlying soil elastic modulus field.

ASCE Subject Headings:
Foundation settlement
Shallow foundations
Finite element method