Liquefaction-induced damage, in the aftermath of an earthquake, is a major source of failure for foundations and earthworks. Understanding soil behaviour and its response both for pre- and post-liquefaction scenarios is an area of active research. The main aim of the research presented in this thesis is to describe the post-liquefaction behaviour of sand using a state-dependent approach instead of the conventional approach based on relative density as the governing parameter. To fulfil this aim, the author has carried out soil element tests, conducted and gathered information from real field case studies, and has modelled soil using a numerical modelling approach. The soil element tests consist of a series of monotonic and multi-stage triaxial tests carried out on Redhill 110 sand (this particular sand was chosen because of its high susceptibility to liquefaction and used in previous liquefaction studies) to investigate its post-cyclic behaviour. The results are utilised to propose a state-dependent procedure to evaluate the post-liquefaction behaviour of the sand. These findings are subsequently used to develop a set of instability curves for the assessment of post-cyclic deformation of liquefied sloping grounds. These curves define the level of strain that the liquefied soil has to mobilise before regaining strength and stiffness and developing the characteristic strain-hardening behaviour observed in the element tests. Another series of triaxial tests is conducted on Kumamoto sand. The aim of these tests is to investigate the post-liquefaction response of a naturally deposited soil. The results are utilised to describe the post-liquefaction behaviour for the soil using a state-dependent approach. To validate the proposed instability curves, a case study which focuses on the failure of the Lower San Fernando Dam observed after the 1971 earthquake is conducted. The results show that the proposed post-liquefaction instability curves can be used for the preliminary stability assessment of sloping grounds in liquefiable soils in which a static shear stress component is present after the end of the ground shaking. The author also conducted another case study based on a field investigation carried out in the area affected by liquefaction phenomenon after the 2016 Kumamoto Earthquake sequence. The main finding from this investigation is the limited structural failure in the Kumamoto Port area despite clear liquefaction manifestations. The strain-hardening behaviour for liquefied soil observed in the element tests provides a reasonable explanation for the unexpected finding from the field survey. A numerical model is also built to study the site response analysis for Kumamoto Port to provide further insight into the limited effects caused by liquefaction. Finally, to investigate the capability of existing constitutive models to capture the post-cyclic deformation of the sloping ground and compare the results with the proposed instability curves, the thesis presents the results of a two-dimensional slope modelled using the Manzari-Dafalias constitutive model. The results show that the numerical model is capable of predicting the post-liquefaction deformation of sloping ground if considering the aftershocks in the analysis.