## 1 Introduction  
Piled embankments, as an economically effective ground improvement technique, are widely utilized in constructing highways and railways in areas with soft soils [1, 2]. The piles in a piled embankment system typically penetrate through the soft soil stratum and are embedded in a stronger underlying bedrock for load-bearing purposes [3, 4, 5, 6, 7]. However, a floating piled embankment is a more cost-effective choice in regions with thicker soft soil. The foundation bearing capacity of the soil stratum at the pile tip is a primary factor distinguishing different pile types [8, 9, 10]. In previous studies [11, 12], floating piles have been classified as flexible or rigid based on the soil stratum where the pile tip is situated. Still, an accurate determination of the critical value for the foundation capacity of rigid floating piles has not been established. Rigid floating piles are embedded in moderately stiff soil, and research [11] has found that they provide a good balance between cost effectiveness and load-bearing capacity, effectively improving the performance of the supported embankment above. However, there is currently no uniform design guideline specifically for rigid floating piled embankments. Both French [13] and German [14] standards consider that the design methods for end-bearing piles are not applicable to floating piles. [PERSON] [15] and [PERSON] et al. [16] have proposed further research on the design of embankments supported by floating piles. [PERSON] et al. [17], as well as [PERSON] et al. [18], conducted field tests to monitor settlement and earth pressure during filling and the post-construction placement stages of embankment supported by floating piles. Model experiments conducted by [PERSON] et al. [19] and full-scale tests conducted by [PERSON] et al. [20] demonstrated that the pile cap of floating piles significantly improves the differential settlement of embankments and the evolution characteristics of the stress. [PERSON] [21] proposed a design method for embankments supported by floating piles. However, the studies mentioned above did not differentiate the bearing capacity of the soil stratum where the pile tips are located. Despite some comparative studies between floating piles and end-bearing piles (e.g., [PERSON] et al. [22]; [PERSON] et al. [23]; [PERSON] et al. [24]; [PERSON] et al. [25]; [PERSON] et al. [26]), the load-bearing mechanism of embankments supported by rigid floating piles still requires further investigation. The soil arching effect is a crucial component of the load transfer mechanism in piled embankments. It was initially confirmed through [PERSON]'s [27] trapdoor test. Various soil arching calculation models have been developed as a result of the continuous development of science and computational technology. [PERSON] et al. [28] categorized the theory models of soil arching into three types: the equal settling plane model presented by [PERSON] [27], the limit equilibrium model presented by [PERSON] and [PERSON] [29], and the wedge and pyramid model described by [PERSON] [30] and [PERSON] [31]. Additionally, the theoretical model of soil arching with morphological changes, presented by [PERSON] [32; 33; 34], has also gained increasing attention. However, most of these models focus on end-bearing piles, and few researchers have considered soil arching in embankments supported by floating piles. The conditions under which it occurs remain unclear. Previous studies [11] have qualitatively analyzed the soil arching of rigid floating piles based on engineering cases but have not investigated the influential factors. In this paper, the differentiation of pile types based on the foundation bearing capacity of the soil stratum at the pile tip has been innovatively proposed. This study aims to quantitatively determine the critical value of the foundation load-bearing capacity that distinguishes between rigid and flexible floating piles using three-dimensional finite element methods.