The semi-infinite concrete plate assumption. The influence of the side and of the radius of relative stiffness. Part I

The classical analysis of the stress state in concrete pavements bearing on the Winkler soil is based on several assumptions, the outstanding one being the semi-infinite length of thin plates. This study proposes to evaluate the conditions and the limits under which this assumption is sound. In particular it will be shown that no single value for the limit plate length exists for which the assumption holds good when exceeded, since influencing too are load position, the magnitude of the radius of relative stiffness, and, most especially, whether the study was carried out in terms of stresses or of strains. The study was conducted on a number of cement-concrete airport pavements consisting of square plates from 1.5 to 40.0 cm deep, one to ten meters on a side, bearing, as called for by thinplates theory, on beds of springs having reaction moduli k of from 1.19 to 30.00 daN/cm3. The load [load imprint??], supposed circular, is represented by a single wheel of the Boeing 447/400 main landing gear. Using combinations of the quantities in play 147 stiff superstructure schemes were readied, resolved using both the classical procedures of high-prestige authors (Westergaard, Pickett & Ray, Theller & Sutherland, Jeuffroy, Bradbury) and sophisticated FEM methods, the plates being so discretized and constrained as to approach as far as possible the conditions suggested by the researchers mentioned. The study’s formulation and analytic development provide useful indications for deeming the semi-infinite plate hypothesis sound and for making to Westergaard’s theory those inevitable corrections when plate geometric dimensions descend below particular values