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

Abstract

The p-multiplier concept has been widely used to analyse the response of laterally loaded pile groups. Conventionally, the p-multiplier fm 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 fm and the force ratio at the pile head ηhead, defined by the ratio of the lateral force acting at the head of a group pile to that of a single pile, where ηhead equals fm 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 kini and the ultimate soil resistance pult are constant with depth; and (b) n = 3/5 when both kini and pult increase linearly with depth. This analytical relationship can then be utilised to determine fm from the test results of group piles and single piles, and quickly estimate the lateral bearing capacity of pile groups.