Constitutive Modelling of the Cyclic Response of Unsaturated Soils: A Discussion of the State-of-Art

Site response analysis (SRA) is an important aspect of seismic design that considers the impact of local site conditions on the ground response during earthquakes and plays a key role in the design of structures that interact or are made with soil. Although previous studies have demonstrated that factors such as the degree of saturation influence the site response, incorporating partial saturation into analysis has not been widely practiced. Numerical analysis tools exist; however, they are often unable to directly assess the influence of partial saturation, especially under seismic conditions. This is often caused by the missing implementation of constitutive models and finite elements able to account for partial saturation of soils under cyclic conditions. For this reason, a review of the most common constitutive models developed with a view to describing unsaturated soil behaviour subjected to cyclic loads is presented, followed by a critical discussion on their applicability to finite element frameworks, with the aim of providing a wide panorama of the available constitutive platforms suitable for implementation in numerical codes. Therefore, we present and discuss the mechanical and hydraulic properties of the constitutive models that can be applied to the analysis of boundary value problems, and specifically for SRA, focusing on partially saturated soils under cyclic loading conditions. It was observed that many constitutive model frameworks for cyclic loadings are based on the bounding surface or two-surface theories, and some of them are coupled with hydraulic behaviour through the Soil Water Retention Curve (SWRC) or its variations. Two main approaches were identified based on the mechanical features, while regarding the hydraulic behaviour, the main distinction lies in the selected SWRC. Furthermore, certain constitutive models have been implemented in finite element software for numerical analysis of geotechnical earthquake engineering problems.