## 1 Introduction  
In the course of highway construction, the integration of subgrade sections with culvert segments is a common occurrence. Nevertheless, the operational phase often witnesses the emergence of substantial differential settlements between the road and the culvert, resulting in abrupt alterations in vehicle behavior at the junction. This phenomenon aligns with the mechanism underlying the \"bridgehead bump\" phenomenon, and it has been elucidated that the primary driver behind the observed differential settlement lies in the substantial disparity in stiffness between the subgrade structure and the culvert structure [1, 2]. This sudden alteration in stiffness has the potential to induce rapid fluctuations in the dynamic response of traffic loads at the juncture, consequently giving rise to noteworthy differential deformation following prolonged interaction. Furthermore, once differential deformation takes root, it can further amplify the dynamic impact of traffic loads. Under the influence of multifrequency traffic load excitation, the differential deformation exhibits a progressive escalation [3]. In soft-soil regions, the management of differential deformation becomes more challenging due to the elevated water content and consolidation settlement characteristics inherent in the soft-soil foundation [4]. Currently, the primary strategy for managing settlement within the transition sections of highways situated in soft-soil regions revolves around reducing settlement through soil improvement or foundation treatment to establish a composite foundation. This approach can be broadly classified into the following three key aspects: (1) Subsoil treatment [5; 6; 7]. This entails the augmentation of the deformation modulus and bearing capacity of the unsaturated soft-soil foundation. It is achieved through various techniques, such as soft-foundation replacement, drainage consolidation, damping compaction, and composite-foundation treatment. (2) Subgrade-filling treatment [8; 9; 10; 11]. The management of subgrade filling involves the utilization of well-graded materials, such as sand, gravel, crushed stone, or lime soil, as fill, effectively diminishing the consolidation settlement experienced after construction. Employing lightweight filling materials to substitute the initial fill can reduce the embankment's self-weight. Furthermore, the incorporation of geocells and geogrids within the roadbed filling layer enhances its overall stability, thereby mitigating the differential settlement deformation within the transition section. (3) Road-surface treatment [12; 13; 14]: One approach involves the installation of an approach slab between distinct sections to distribute the settlement disparity over the slab's length. Alternatively, a transition paving technique may be employed during the pavement construction process. While the latter method is straightforward and facilitates easy repairs, it is noteworthy that the pavement may exhibit suboptimal grading during the initial stages of paving. When employed in combination, these methods have demonstrated their effectiveness in effectively managing differential settlement within transition sections located in soft-soil regions [15; 16]. Nevertheless, it is important to note that these methods are capable of mitigating the overall settlement, yet they do not provide a fundamental solution to the underlying issue of substantial stiffness disparities. In comparison to highways, railway engineering imposes more stringent demands on the control of roadbed deformation. The Technical Code for Ground Treatment of Railway Engineering (TB10106-2010) [17] prescribes that the utilization of a pile-net (raft) composite foundation, akin to the pile-supported subgrade, is restricted to addressing typical soft-foundation conditions. In cases of transition sections with deep soft foundations, the recommended foundation-treatment approach entails the implementation of a pile-plate structure.