## 2 Lateral Load-Bearing Behavior of the Roadway-Side Support
### The Lateral Loading Characteristics of Gangue
#### 2.2.2 Study on the Lateral Compression Characteristics of Gangue  
Assuming the coal seam is nearly horizontal, the gangue in the gob area is affected by the dip angle and fills the gob accordingly. Based on the fundamental assumptions of [PERSON]'s earth pressure theory [30], the fallen gangue is divided into two regions: the compaction phase (gangue region A) and the stable consolidation phase (gangue region B). Under the influence of the critical layer, gangue region A is subjected to lateral confinement from adjacent gangue and overlying strata load, with a corresponding unit weight denoted as \(\gamma_{\mathbf{1}}\). In contrast, gangue region B is influenced by the self-weight of gangue region A, the overlying load, and the stress from the base plate in the vertical direction, with its unit \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Particle Size** & \begin{tabular}{c} **Grading** \\ **Total** \\ **Weight/kg** \\ \end{tabular} & **Proportion/\%** & \
\begin{tabular}{c} **Particle Size** \\ **Grade/mm** \\ \end{tabular} &
\begin{tabular}{c} **Grading** \\ **Total** \\ **Weight/kg** \\ \end{tabular} & **Proportion/\%** \\ \hline
0–5 & 47.988 & 15.48 & 20–25 & 79.67 & 25.7 \\
5–10 & 55.304 & 17.84 & 25–31.5 & 26.567 & 8.57 \\
10–16 & 32.581 & 10.51 & 31.5–40 & 13.516 & 4.36 \\
16–20 & 36.704 & 11.84 & 40–50 & 17.67 & 5.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The mass ratio of gangue in each particle size grade. Figure 6: Theoretical device and experimental results of gangue compression: (**a**) Gangue test device; (**b**) relationship between stress–strain curve and bulking coefficient. weight denoted as \(\mathbf{\gamma_{2}}\). Gangue region B is selected as the object of study. According to the theory of retaining walls, when the overlying load exceeds the internal shear strength of the compacted gangue pile, a sliding shear plane will form within the compacted gangue. The lateral resistance of the roadway-side support then acts on the gangue, resulting in the lateral pressure exerted on the support structure under the equilibrium state of the gangue. In line with typical engineering practices, the following is assumed [31]:  
1. In the compressed state, the fractured gangue is considered the primary object of study, and the inter-particle cohesion, \(\mathbf{c}\), is neglected. 2. The roadway-side support structure is made from grout material, which can be treated as a rigid barrier to support the gangue pile. After the grout material consolidates, it can be considered a homogeneous, non-cohesive body with no vertical friction between it and the gangue. 3. When the gangue in the gob and the surrounding rock reach the ultimate equilibrium state, a sliding failure surface exists within gangue zone B. This surface is an inclined plane passing through the heel of the wall, with a sliding wedge-shaped triangular body, ABC, forming. The triangular body is considered a rigid body. 4. The load, \(\mathbf{q}\), applied to the gangue wedge can be approximated as a linear distribution. 5. The soil pressure problem is treated as a two-dimensional problem, and calculations are performed using a unit wall length, \(l_{m}\). The basic model of the Coulomb soil pressure distribution is shown in Figure 7a. Figure 7b illustrates the force distribution of the wedge-shaped triangular body ABC within gangue zone B. When the gangue wedge reaches the ultimate equilibrium state, the force equilibrium of the system can be analyzed using the rigid equilibrium method in theoretical mechanics, allowing the calculation of the lateral pressure on the barrier (AB) in the gangue equilibrium state. In addition, \(\mathbf{P_{a}}\) is the lateral support resistance required to maintain the stability of the wedge-shaped body. \(\mathbf{\phi_{4}}\) is the angle between the load \(\mathbf{q_{B}}\) and the horizontal plane. \(\mathbf{\phi_{5}}\) is the angle between \(\mathbf{P_{a}}\) and the horizontal plane.