## 1 Introduction
The ASSI has been investigated by researchers through field monitoring, experimental tests, and theoretical analyses [31; 32; 33; 34; 35; 36; 37; 38; 39; 40]. The service performance monitoring of a buried approach slab (BAS) indicated that a strain concentration is localized at the end of the approach slab and further extends obliquely upward from the end of the approach slab to the road surface [31; 33]. Monitoring of the BAS in a jointless bridge revealed that when the temperature rises, the expansion of the girder pushes the BAS toward the connecting road, resulting in an increment in the compressive stress of the pavement; when the temperature drops, the contraction of the girder pulls the BAS away from the connecting road, resulting in a decrement in the stress of the pavement [34; 35]. Experimental tests demonstrated that the longitudinal strains of the soil near the distal end of the approach slab and the pavement above the distal end of the approach slab are inversely proportional to \(H\). With an increase in \(H\), the risk of cracking on the pavement decreases [36]. The friction-displacement curves of a GFAS with different sliding materials installed between the bottom surface of the approach slab and the soil beneath it were simplified as a bilinear mathematical model by [PERSON] et al. [33; 41]. A simplified calculation model of a deck-extension jointless bridge with bilinear springs was established to analyze the influence of the GFAS on the mechanical performance of the deck-extension jointless bridge. In summary, qualitative analyses on the influence of \(H\) on the strain distribution of embankment fill and the cracking of the pavement were conducted in existing studies. However, there is a lack of systematic analyses on the mechanism of the FAS in transferring and absorbing \(u_{\text{t}}\) by considering the mechanical performance of the approach slab and the deformation of the soil. Additionally, there is no quantitative analysis of the influence of \(H\) on the reduction of the settlement and cracking of the connecting road pavement. Moreover, the simplified calculation method on the flat approach slab-soil interaction (FASSI) is required. To address this gap in the literature, investigations on the FASSI with different embedded depths and slab lengths were carried out. The rest of the paper is organized as follows: Section 2 presents the design and fabrication of the experimental test on the FASSI and discusses the test results, including the force-displacement curve, sand deformation, and earth pressure; Section 3 establishes a finite element model of the FASSI using software of PLAXIS 2D CE V20, the accuracy of which is verified by experimental data; Section 4 conducts a parametric analysis to investigate the influence mechanism of different embedded depths and slab lengths on the FASSI; Section 5 proposes a simplified calculation formula for the force-displacement curve of the FASSI, the accuracy of which is verified by the results of experimental tests and finite element models. The research presented herein is of profound significance for the design and construction of BFASs in jointless bridges. Specifically, by delving deeply into the understanding of the mechanism of FASs in transferring and absorbing longitudinal displacement, especially by conducting quantitative analyses on the longitudinal displacement transfer mode (LDM) and vertical deformation distribution mode (VDM) of the sand, optimized designs that minimize the potential risk of pavement cracking can be obtained. These include the arrangement positions of geogrids in the sand and elastic materials at the end of the approach slab. Moreover, the simplified calculation formula for predicting the force-displacement curve of the FASSI can calculate spring stiffness for numerical models of jointless bridges, presenting a novel method for the design of FASs in jointless bridges.