Measuring Curvature in Concrete Slabs and Connecting the Data to Slab Modeling Theory

Slab curling, warping, and load deflection basins are analyzed by quantifying slab curvature. Warping and curling curvature can cause the edges or midslab regions of slabs to lift off the foundation, with increases in slab-bending stress and deflections caused by loading. This paper provides an overview and comparison of methods for measuring slab curvature from curling and warping. Methods described include the end-slope, string-line, and straight-edge methods, best-fit polynomials, and shape functions. In addition, for multiple slabs, a rapid traveling profiler method is described: the profiler uses thousands of closely spaced data points and a generalized analysis of variation of curvature known as the road profile curvature index. To show key differences, the methods are compared by means of a test slab. The three primary ways of matching measured slab shape data to theoretical models are matching on the basis of the mean value theorem for integrals for continuous functions, matching on the basis of a best-fit or least squares error approach for the full slab length, or matching the difference in magnitude of the elevation between the ends and middle portions of the slabs. It is shown that fitting methods based on the mean value theorem for integrals are the most accurate and theoretically correct and will closely match the end of slab slope conditions near joints and overall average slab curvature simultaneously. On the basis of the mean value theorem for integrals, how to fit theoretical equations by Westergaard or any finite element method solution to the site average slab curvature measurement is described.