Integral bridges have been proposed as an attractive design concept that negate the requirements for expansion joints. However, owing to structural continuity, seasonal and diurnal thermal fluctuations have subjected the abutments to long-term cyclic interaction with approach backfills. This resulted in two notable geotechnical complications: ratcheting of lateral stresses and progressive soil deformation. To understand these phenomena, considerable research has been conducted using numerical methods. Here, either Winkler springs or simple constitutive relations, such as the Mohr-Coulomb model, are predominantly utilized. However, the former is based on monotonic displacement-dependent stiffness theories, and the latter is constrained by the limitations of the traditional yield surface plasticity. Hence, neither possesses the capability to simulate the hysteretic response, which is a characteristic of integral bridge approaches. Therefore, this study aims to present the advantages of using advanced constitutive relations to predict the long-term behavior of integral bridge approach backfills. First, using a lateral cyclic triaxial simulation, the significance of soil densification was highlighted by comparing the performance of the Mohr-Coulomb model with that of the bounding surface Dafalias-Manzari-2004 model. Subsequently, further comparisons were performed with the centrifuge model data of the integral abutment. At both the element and boundary value levels, the Mohr-Coulomb model could not capture the gradual accumulation of the lateral stresses. Conversely, the Dafalias-Manzari-2004 model can estimate the long-term passive pressure accumulation along the height of the abutment.