# Stability Analysis of Soil Flow Protector and Design Method for Estimating Optimal Length
## 1 Introduction  
Structures such as abutments and box culverts, which serve as connections between roads and bridges or between two roads, are typically supported by pile foundations on rigid ground. Although they generally experience limited amounts of ground settlement, cavities are created due to water movement and internal soil erosion, and also cause by consolidation, drying shrinkage, and poor compaction as time passes (Figure 0(a)). In addition, the inflow of groundwater and soil from the surrounding ground at the point where the cavities occur can cause rapid settlement. [PERSON] [1] reported that ground erosion due to water penetration underneath a structure can be attributed to cavity formation. [PERSON] et al. [2] confirmed that cavities can develop below a structure due to the lack of compaction and settlement of the backfill. [PERSON] et al. [3] noted that surcharges on compressive ground can cause cavities to develop. Moreover, the occurrence of differential settlement (Figure 0(b)) in the soil causes faults relative to the surrounding ground; this displaces the underground water and soil, thus developing a cavity, which causes rapid ground settlement or ground failure [4, 5, 6]. The stress relaxation area of the surrounding ground expands continuously, inducing faster settlement [7]. However, it is difficult to provide a clear solution to these problems because the ground conditions, cavity shape, and ground abnormalities have a complex correlation [8]. The most frequently used measure to address these problems is the overlay method. However, in reinforced ground, the continuously overlaid pavement load causes the continuous settlement of the adjoining ground and reduces the usability of public roads owing to ongoing construction, which incurs additional economic and social costs. Therefore, there is no clear solution to the problems caused by ground settlement. In addition, the currently used measures are highly inefficient in terms of economic feasibility, constructability, and usability. Therefore, it is necessary to explore construction methods that can prevent ground settlement due to cavity development below structures. Based on this necessity, engineers have developed a soil flow protector (SFP) that can be easily installed beside a structure to reduce or prevent the various problems due to the development of cavities underneath structures supported by pile foundations. By installing the SFP beside the structure, as shown in Figure 2a, soil inflow is blocked from the adjacent ground into the cavity, thus ensuring stability. When ground settlement occurs, the SFP moves downward to the same extent. Even after the cavity develops, the soil in the adjacent ground continues to block the soil inflow into the cavity, which prevents the sudden settlement of the adjacent ground [9]. In other words, preventing the rapid settlement of the ground improves the stability of the structure, thus aiding sustainable urban development. Figure 1: Example of a problem due to the difference in the settlement between a structure supported by a soil foundation and the lateral ground [9]: (**a**) cavity development; (**b**) failure of the approach slab pavement. Figure 2: Principle of a soil flow protector (SFP) used to solve problems related to cavity development [9]: (**a**) with SFP; (**b**) without SFP. According to [PERSON] et al. [8], studies on cavity and surface settlement adopt the following techniques: empirical data utilization, calculations through analytical methods, and simulation techniques using numerical models. Among these, the empirical methods include field tests for full-size models and scaled models. In the former case, it is advantageous to predict future settlement through physical behavior; however, experimenting under different conditions is difficult because of time and cost constraints. In contrast, the latter case avoids these constraints, and it allows the analysis of settlement mechanisms under different conditions.