# Experimental Study of Erosion Prevention Model by Bio-Cement Sand
## 3 Results and Analysis
### Results and Analysis of Sink Scour Model  
Water scours the surface of the sandbox, inducing localized shear stress. When this shear stress exceeds a critical threshold, scour occurs, resulting in particle displacement. Any minor initial breach constitutes a vulnerable point where shear stress is elevated relative to its surroundings, facilitating rapid progression into a substantial gap. A water tank experiment was performed on surface samples of the sand model post MICP spray treatment. A constant pressure variable frequency pump was utilized to control water volume, with flow velocity being systematically increased. The mass of load and suspended material collected at varying flow rates was recorded, allowing for the calculation of the relationship between erosion rate and shear stress in the microbial cemented sand model subjected to washing within the water tank, as depicted in Figures 9 and 10. The relationship between erosion amount and shear stress is predominantly influenced by gravitational forces and the adhesive interactions among sand particles. The erosion shear stress of unconsolidated sand particles attains a critical threshold under the influence of water flow, which subsequently leads to an increase in the erosion rate as bed shear stress escalates: initially, this rate exhibits a gradual rise with increasing shear stress; however, at advanced stages, the acceleration becomes pronounced, ultimately conforming to a power function model. Moreover, due to the reinforcement effect of microbial grouting that enhances particle adhesion, water flow must first surmount this inter-particle adhesion to mobilize sand particles, resulting in erosion and degradation of surfaces reinforced by microbial grouting. Figure 8: The relationship between penetration resistance and cementation depth and calcium carbonate. Figure 9: The process of sediment load and suspended load collection over a certain period of time. The correlation between the erosion rate and shear stress of the unconsolidated sand bed surface is \(E=0.09582\tau^{3.0742}\); similarly, the correlation for the sand bed surface subjected to three cycles of reinforcement is \(E=0.00304\tau^{5.20591}\); while for six cycles of reinforcement, it is \(E=2.89\times 10^{-7}\tau^{10.28219}\). Notably, as the degree of reinforcement increases, the undetermined constant \(a\) decreases and \(n\) increases. This study demonstrates that an erosion of 1.0 mm on the sediment surface over a period of 15 min can be interpreted as achieving the initial state; specifically, when \(E=0.0001\) cm/s, the sediment reaches its critical initiation condition, defined by a critical shear stress denoted as \(\tau_{c}\). This critical shear stress was calculated by substituting the erosion rate E = 0.0001 cm/s into relevant equations, and the threshold for sand mobilization was subsequently derived using Formula (3). According to experimental findings, both the computed critical shear stress and corresponding initiation flow rates are summarized in Table 2.  
Flume tests were performed on samples from the surface of sand models treated with MICP spray application. Following adjustments to flow velocity, it was established that the critical initiation velocities for unreinforced samples, those reinforced three times, and those reinforced six times were determined to be 0.182 m/s, 0.435 m/s, and 0.886 m/s, respectively, indicating a pronounced increase in starting velocity with enhanced reinforcement levels. The flow erosion dynamics of the microbial spraying reinforced sand slope model are depicted in Figure 11, where stages I, II, III and IV, V, VI delineate the evolution of flow erosion grooves on the sand surface at various time intervals following three and six rounds of reinforcement, respectively. The results from three applications of microbial slurry reveal that during the initial phase of erosion at a defined flow rate, a small flushing channel along with several impact pits (e.g., I) formed on the surface of the sand box.