Finite element and evolutionary polynomial regression analyses of the effect of a cavity on the bearing capacity factor Nc of strip footing

Calculating the undrained bearing capacity for strip footing resting on a soil with a cavity is very challenging due to the unavailability of closed form solutions that consider the effect of the cavity, as these solutions have been derived assuming perfect ground conditions. This paper, therefore, aims to address this gap in knowledge by studying the effect of the cavity on the undrained bearing capacity factor N-c. The two-dimensional finite element analysis was used to study the effect of the cavity on the footing, where it is noted that the presence of the cavity significantly reduces the bearing capacity factor, N-c and changes the failure mechanism of the footing. The percentage decrease of the N-c ranges between 3 and 79% based on the cavity size and location, where the percentage decrease reduces as the cavity depth or horizontal distance from the center of the footing increases. Importantly, a new mathematical model has been developed to implicate the effect of the presence of the cavity in the routine calculations of the N-c. The model has been developed using multi-objective evolutionary polynomial regression analysis. The model scored a mean, mean absolute error, and coefficient of determination of 1.00, 0.17, and 0.91, respectively, for training data, and 1.00, 0.18, and 0.92, respectively, for testing data. Thus, the model requires knowing the cavity diameter, cavity depth, and cavity horizontal distance with respect to the footing. Hence, it could be easily utilized by designers with confidence to consider the cavity effect in undrained bearing capacity problems.