WESTERGAARD SOLUTIONS RECONSIDERED

Abstract

The pioneering analytical work of Harold Malcom (1888-1950) has been at the heart of slab-on-grade pavement design since the 1920s. Every code of practice published since then makes reference to the Westergaard solutions. These solutions are only available for three particular loading conditions (interior, edge, and corner) and assume a slab of infinite or semi-infinite dimensions. Since their first appearance, beginning in the early 1920s, equations have often been misquoted or misapplied in subsequent publications. To remedy this situation, a reexamination of these solutions using the finite element method is described in this paper. A number of interesting results are presented: (a) Several equations ascribed to in the literature are erroneous, usually as a result of a series of typographical errors or misapplications, or both. The correct form of these equations and their limitations have now been conclusively established. (b) Westergaard's original equation for edge stress is incorrect. The long-ignored equation given in his 1948 paper should be used instead. (c) Improved expressions for maximum corner loading responses have been developed. (d) Slab size requirements for the development of responses have also been established.