# Axial and Lateral Efficiency of Tapered Pile Groups in Sand Using Mathematical and Three-Dimensional Numerical Analyses | Journal of Performance of Constructed Facilities | Vol 36, No 1 AbstractThis study presents a new mathematical equation for calculating the pile group efficiency in cohesionless soil under combined axial and lateral loading conditions, considering the tapering angle effect. Based on the mathematical definition of the pile group efficiency, analytical correlations are developed. The tapering effect is considered by developing a new geometry coefficient for efficiency associated with the shaft vertical bearing component of tapered piles. In addition, a simplified mathematical equation is developed for predicting the group interaction factor as a function of pile spacing, number of piles in the group, diameter of the cylindrical reference pile, tapering angle, and pile slenderness ratio. On the other hand, an array of three-dimensional numerical analyses is performed for modeling same-volume single bored piles and pile groups with various arrangements to capture the accuracy of the proposed mathematical equation. The hardening soil constitutive model is adopted for the modeling of piles in loose sand. Subsequently, the load-displacement diagrams of single piles, as well as pile groups, are obtained. The bearing capacities of straight-sided and tapered bored piles are then calculated and compared using a definite settlement criterion. By computing the various bearing-capacity components, group efficiencies can be attained from both numerical and mathematical analyses. The results indicate an acceptable agreement between both analyses. Finally, the developed equation can predict the pile group efficiency incorporating the tapering angle and other influencing parameters as a novel and simple relationship under simultaneous axial and lateral loading conditions.