Relationship between p-multiplier and force ratio at pile head considering non-linear soil–pile interaction

The p-multiplier concept has been widely used to analyse the response of laterally loaded pile groups. Conventionally, the p-multiplier f_m is evaluated iteratively by trial and error comparisons of p–y curves and field measurements. However, these approaches could face numerical difficulties and often require subjective adjustment and therefore could result in non-unique solutions. This paper derives a power relationship between f_m and the force ratio at the pile head η_head, defined by the ratio of the lateral force acting at the head of a group pile to that of a single pile, where η_head equals f_m to the power of n. In the case of long piles, it was found that (a) n = 3/4 when the initial modulus of subgrade reaction k_ini and the ultimate soil resistance p_ult are constant with depth; and (b) n = 3/5 when both k_ini and p_ult increase linearly with depth. This analytical relationship can then be utilised to determine f_m from the test results of group piles and single piles, and quickly estimate the lateral bearing capacity of pile groups.