Simplified analytical "m-θ" curves for predicting nonlinear lateral pile response

The relationship between the distributed moment acting on a pile segment due to vertical shear tractions at the pile-soil interface and the corresponding pile rotation (known as an “m-θ” curve) is important when determining the response of offshore monopiles with low slenderness ratios. Two simplified approaches to derive nonlinear “m-θ” curves (for clay under undrained conditions) are considered. Firstly, the vertical shear tractions can be derived in closed-form using known “t-z” curves (power-law and quadratic forms are considered) and integrating with respect to the pile circumference. Secondly, similarity in shape between an “m-θ” and a “t-z” curve is investigated which would enable a linear-transformation between the abscissas of the two normalised curves. This paper derives analytical linear-transformation factors using power-law and quadratic “t-z” curves and compares these with solutions available for a linear-elastic soil material. Finally, the effect of slip at the pile-soil interface on the “m-θ” curve is considered.