# Stress and Settlement of Footings in Sand

*by*Bengt H. Fellenius, (M.ASCE), Univ of Ottawa, Ottawa, Canada,

Ameir Altaee, Univ of Ottawa, Ottawa, Canada,

**Document Type:**Proceeding Paper

**Part of:**Vertical and Horizontal Deformations of Foundations and Embankments

**Abstract:**In current engineering practice, the magnitude of the settlement of a footing in sand, as compared to the settlement of a different size footing in the same sand, is considered to be a non-linear function of the footing width. Further, the settlement is considered to be proportional to the density of the sand. Results of finite element analysis of settlement for footings of three sizes placed in two different sand types show that the settlement in sand is a direct function of neither footing size nor soil density. Instead, the settlement should be related to the steady state line of the sand and to the upsilon distance of the sand, that is, the initial void ratio distance to the steady state line at equal mean stress and at homologous points. This requirement imposes scaling-rules for model tests and it limits the range of application of a small scale test to a prototype behavior. Moreover, it imposes boundaries on the geometric scale, because a model test can not realistically be carried out in a sand that is looser than the maximum void ratio, and it is meaningless if performed in a sand close to the minimum void ratio, because it would then not be representative for any prototype.

**Subject Headings:**Soil settlement | Sandy soils | Soil analysis | Foundation settlement | Soil stress | Model tests | Footings | Void ratio

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