On California bearing ratio calculation: application of nonlinear regression approach with the wood function approximation

When constructing the paved roads or railway tracks, the California Bearing Ratio (CBR) is one of important measures, evaluating, in particular, the subgrade strength. In addition, it can also be used for a determination of the subgrade reaction of the soil, if the correlation is considered. CBR is calculated from the standard-measured load-penetration curve, which is, however, of empirical nature. Thus, in this study, we introduce a nonlinear-regression-based concept in modeling the experimental load-penetration profile with the Wood function. Such an approach provides to analytically perform all the steps strictly following the CBR measurement standard, including rigorous determination of the uncertainty of the CBR estimate. Furthermore, we present an algorithm for finding the inflection point and point of intersection which both play eminent roles on correcting the load-penetration curve, especially in the case of the presence of irregularities connected with the nature of the subgrade soil and testing procedures. The mathematical model, constructed herewithin, provides possibility for the software solution in the calculation of CBR without the participation of an experimenter. We believe that the results achieved here could stimulate further studies devoted to relating the parameters of the Wood function with those of the tested soil including soil density, plasticity index, and soil permeability.