Elastic settlement of arbitrarily shaped foundations embedded in half-space

Abstract

The settlement of foundations under working loads which induce relatively small strains in the soil is frequently estimated in practice on the basis of results from the theory of elasticity. Despite its shortcomings in modelling actual soil behaviour, elastic theory may be quite useful especially in predicting immediate settlements on saturated clayey deposits, provided that an appropriate value of undrained secant Young’s modulus has been experimentally determined. Most of the available elastic solutions refer to loads acting directly on the ground surface. To estimate the settlement of an embedded foundation without resorting to expensive numerical (mainly finite element and boundary element) techniques, engineers apply reduction factors to the settlement of the corresponding surface foundation. While most available reduction factors are purely empirical in nature, an approximate solution by Fox (1948) has been particularly popular for embedded flexible rectangular foundations. Fox’s solution has been reproduced in the form of a simple chart by Janbu, Bjerrum & Kjaernsli (1956). This chart is still widely used in geotechnical engineering, being recommended in several textbooks of soil mechanics and foundation engineering. Unfortunately, as Burland (1970) and Christian & Carrier (1978) have shown, Fox’s factors may grossly exaggerate the effect of embedment, when compared with the results of finite element analyses. This is hardly surprising: Fox’s results, based on Mindlin’s solution for a point load within a half-space, refer to a uniformly loaded area surrounded by (and bonded to) an elastic continuum, rather than to an embedded foundation. That is, Fox’s results implicitly assume that part of the carried load is transmitted to the ground through tension between the upper side of the foundation mat and the overlying soil. However, no (net) tension can usually develop between soil and foundation and, in most cases, the ‘overlying’ soil has been removed by excavation. The results of the studies by Burland and