# Reinforcement Effect of a Concrete Mat to Prevent Ground Collapses Due to Buried Pipe Damage
## 4 Numerical Analysis  
### Finite Element Analysis (FEA)  
A two-dimensional finite element analysis (FEA) was performed using ABAQUS, which is useful for evaluating the soil-structure relationship and analyzing the stress reduction effect induced through the stress occurrence of the concrete mat for various load conditions. The FEA was verified using the results of the plate loading test for the non-reinforced ground. Using the verified model, the stress reduction effect was analyzed in a consideration of the density of the ground, the type of load, and the application conditions of the concrete mat. The engineering properties of the soil and concrete mat used in the analysis are shown in Table 3. First, the unit weight and internal friction angle of the sand were applied with the experimental research. The elastic modulus and Poisson's ratio of sand were obtained from the results of a study by [PERSON] [30]. [PERSON]'s research on the engineering properties of sand is one of the most frequently referenced studies in Korea. The elastic modulus, density, and Poisson's ratio of the concrete mat considering the concrete strength were obtained from previous studies [31; 32]. To verify the analysis model, modeling was conducted, in which a plate bearing test was taken into consideration, as shown in Figure 6. In order to develop a reasonable analysis model, the analysis of the stress change in the ground according to the load range, ground width, and depth was performed in the case of the non-reinforced ground. Here, 4 kPa of uniform load was applied, and the analysis was conducted, in which the concrete mat was buried at 0.1 m for verifying the analysis results of applying the concrete mat. The analysis results for the uniform load range, as well as the width and depth of the ground, are presented in Figure 7 for the condition where the concrete mat was not applied. As Figure 7a shows, when the uniform load range in the FEA was large (uniform load range = 0.3 m), the analysis and experimental results varied as the soil depth increased; however, the tendency of the underground stress was similar for both results. Based on these results, when the analysis was performed for the different soil widths and depths while fixing the pressure range at 0.3 m, no significant difference was \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Classification** & \multicolumn{2}{c}{**Soil (Sand)**} & **Concrete Mat** \\ \hline
**Material Model** & \multicolumn{2}{c}{**Elastic and Plastic (Mohr-Coulomb)**} & **Elastic** \\ \hline \multirow{3}{*}{Elastic modulus (kPa)} & \multicolumn{2}{c}{Density condition of sand} & \\ \cline{2-4}  & Loose & Medium & Dense & 27,800 \\ \cline{2-4}  & 785 & 1570 & 2945 & \\ \hline Unit weight (kN/m\({}^{3}\)) & & 16.2 & 24.5 \\ \hline Poisson’s ratio & & 0.25 & 0.2 \\ \hline Friction angle (\({}^{\circ}\)) & & 32.8 & - \\ \hline Cohesion (kPa) & & 0 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of the soil and concrete mat. observed. As the diameter of the loading plate was 0.3 m during the plate bearing test, the analysis results for applying the same pressure range were determined to be reasonable. Using the analysis model that was previously mentioned, an analysis was performed for when the concrete mat was installed at G.L. \(-\)0.1 m and G.L. \(-\)0.2 m. Figure 8 presents a comparison  
Figure 6: Finite element analysis (FEA) model produced for verification. Figure 7: Analysis results for model verification: (**a**) effect of the pressure range; (**b**) effect of the soil length; (**c**) effect of the soil depth. of the experimental and FEA results. First, as mentioned in Section 3.3, the stress reduction effect was approximately 28.5-30.9% at the depth directly below where the soil was reinforced with the concrete mat when 4 kPa of load was applied in the laboratory test.