Experimental Evaluation of Size Effects on the Coefficient of Subgrade Reaction for Sand under Various Conditions

The coefficient of subgrade reaction (k) is widely used in the analysis and design of substructures, but there is a need for a proper method to estimate it. The objective is to investigate the effect of the size on k value for sand under different conditions. The experimental methodology used a large-scale California bearing ratio (CBR) apparatus with a piston of varying diameter. The results are presented in terms of complete spectra of the secant and tangent coefficients (k_s and k_t) as functions of normalized penetration and pressure. Data was normalized by using appropriate scaling relations for various quantities, to eliminate the size effects. Normalization caused the curves of any quantity to fall within a narrow range. The scaling ratio for k is 1, but the variations of k with the piston diameter indicate some size effects. The spectrum of k_s versus the normalized penetration is the most appropriate one. Results of k_s and k_t obtained at the peak are the highest, and those at a penetration of 5.08 mm are the lowest. For soaked conditions, using a factor of safety equals 3, the average values for the allowable k_s are 147 and 19 MN/m³ for dense and loose conditions, respectively. The corresponding values for k_t are 229 and 35 MN/m³, respectively. For unsoaked conditions, the corresponding values are 103, 14, 159, and 13 MN/m³, respectively. These values are comparable with those reported in the literature.