Scale Effects of Shallow Foundation Bearing Capacity on Granular Material

Scale effects of shallow foundation bearing capacity on granular materials were investigated to further evaluate the trend of decreasing bearing capacity factor, $N_{\gamma }$ , with increasing footing width, $B$ , observed by other researchers. Model-scale square and circular footing tests ranging in width from 0.025 to $0.914\mathrm{m}$ were performed on two compacted sands at three relative densities. Results of the model-scale footing tests show that the bearing capacity factor, $N_{\gamma }$ , is dependent on the absolute width of the footing for both square and circular footings. Although this phenomenon is well known, the current study used a large range of footing sizes tested on well-graded sands to show that the previously reported modifications to the bearing capacity factor, $N_{\gamma }$ , using grain-size and reference footing width do not sufficiently account for the scale effect seen in the test results from this study. It also shows that behavior of most model-scale footing tests cannot be directly correlated to the behavior of full-scale tests because of differences in mean stresses experienced beneath footings of varying sizes. The relationship of the initial testing conditions (i.e., void ratio) of the sand beds and mean stress experienced beneath the footing (correlated to footing size) to the critical state line controls footing behavior and, therefore, model-scale tests must be performed at a lower density than a corresponding prototype footing in order to correctly predict behavior. Small footings were shown to have low mean stresses but high $N_{\gamma }$ values, which indicates high operative friction angles and may be related to the curvature of the Mohr–Coulomb failure envelope.