Similarity-Based Nonlinear Settlement Predictions of Circular Surface Footings on Clay

In 1951, Skempton introduced the concept of similarity to obtain predictions of non-linear settlement of rigid circular footings on deep clay deposits under undrained conditions. This approach is based on the premise that the pressure-settlement curve of the footing and a stress-strain curve from a characteristic point in the soil can be linearly scaled to collapse into a single “master” curve. The method has been extended to predict deflections of axially and laterally loaded piles and is widely used in the offshore industry. Despite the theoretical and practical appeal of the method as well as its wide application in a range of geotechnical problems, limited investigation and validation exists in the literature. In this work, (1) existing “classical” similarity methods are reviewed, including a Boussinesq solution for elastic soil and the Mobilisable Strength Design (MSD) method by Bolton and coworkers. (2) The similarity factors derived from these methods are compared with those obtained from a novel non-linear cone model solution. (3) The resulting expressions are evaluated against rigorous numerical analyses undertaken by the authors in FLAC. These are based on two different non-linear constitutive models calibrated against triaxial tests from three clay deposits. Two alternative families of similarity methods are also compared with classical similarity. (4) Firstly, a “two-part” similarity technique (based on separate scaling factors for elastic and plastic strains) and (5) secondly, a “stiffness” similarity approach introduced by Atkinson (based on secant stiffness degradation). Finally, (6) three field test results are evaluated as case studies to demonstrate the applicability of the method in real-life problems. It is concluded that similarity approaches offer a rational yet approximate tool for non-linear settlement analysis of footings.