# Research on the Influence Mechanism of Foam Slurry Wall Formation
## 5 Verification of Numerical Simulation Validity  
To verify the validity of the numerical simulation results, laboratory permeability tests on foam slurry were conducted under different conditions [19]. The base slurry materials mainly included bentonite, carboxymethyl cellulose (CMC), anhydrous Na\({}_{2}\)CO\({}_{3}\), NaOH, and cationic gel, with a plant-based foam agent. Using a self-designed experimental device, the slurry permeability under various mixing ratios (pure slurry; with 20%, 50%, and 90% foam; and 1.5% sand, among other combinations) was observed under different infiltration pressures (50 kPa, 100 kPa, 150 kPa, and 200 kPa), as shown in Figure 11.  
Due to limitations in experimental conditions and workload, it was not feasible to experimentally verify all the working conditions covered in the numerical simulations. Therefore, several representative cases were selected for preliminary experimental validation, focusing on key parameters such as foam concentration, swelling ratio, and infiltration pressure. The experimental results were then compared with the corresponding numerical simulation results for analysis.  
The flow-time curves for the slurry are shown in Figure 12a. It can be observed that compared to pure slurry, the infiltration rate significantly decreases when foam is added to the slurry, and the total infiltration rate is lowest when the foam concentration is 20%. This is consistent with the previous numerical simulation results, indicating that adding an appropriate foam concentration to the slurry is beneficial for mud cake formation.  
The flow-time curves for the slurry before and after adding sand are shown in Figure 12a,b. A comparison shows that when sand is added to the same foam slurry, the  
Figure 11: Schematic diagram of experimental setup.  
Figure 12: Flow-time process curves of slurry under different conditions. (**a**) Without sand addition. (**b**) After sand addition.  
infiltration rate of the slurry significantly decreases. This aligns with the previous numerical simulation finding that an increased swelling ratio helps accelerate mud cake formation.  
The foam flow-pressure relationship curves under different infiltration pressures are shown in Figure 13. It can be seen that within a certain range, the infiltration pressure has a noticeable impact on the flow rate. As the infiltration pressure increases, the flow rate also increases but gradually stabilizes. This is consistent with the conclusion from the numerical simulation that the effect of pressure gradient on the final membrane formation is relatively limited.  
Due to constraints in experimental conditions and workload, it was not feasible to experimentally validate every numerical simulation scenario. Instead, representative parameters (such as foam concentration, bentonite swelling ratio, and infiltration pressure) were selected for the preliminary experimental validation of the model. Given the inherent differences between the idealized numerical model and practical laboratory conditions, an exact quantitative agreement between simulation and experiment was not expected; accordingly, some discrepancies in absolute values were observed. Nevertheless, the experiments confirmed that the qualitative trends predicted by the simulations were accurate, particularly with respect to infiltration behavior and mud film formation. This agreement in overall trends--despite minor differences in magnitude--demonstrates that the numerical model reliably captures the essential mechanisms and accurately predicts the qualitative influence of key factors, thereby fulfilling the study's aim of validating trend predictions rather than achieving perfect numerical correspondence.  
In conclusion, the experimental results are consistent with the patterns revealed by the previous numerical simulation results, providing a preliminary verification of the reliability of the numerical simulation outcomes.