# A Dynamic Numerical Simulation on the Grouting Timing in Retained Rib of Pillarless Mining
## 4 Plastic Zone and Grouting Diffusing Range Development
The expansion of the plastic zone in the coal rib behind the working face shows the same stage characteristics as the deformation of the retained roadway, which can be divided into 0-40 m mining-affected severe section, 40-80 m mining-affected moderate section and out by 80 m mining-affected stable section behind the working face. The depth of the plastic zone in the severely mining-affected section increased sharply, from 6.0 m depth near the working face to 10 m depth at 30 m behind the working face. After the main roof breaking, rotating, and subsiding, the stress concentration occurred in the retained rib, which caused the shallow part of the coal rib to be crushed and squeezed out. At the same time, the weakening and failure of the bolting supporting structure also occurred. At this point, the surrounding rock-supporting load-bearing structure was already in a post-peak failure state. The roadway surrounding rock needed supplementary support in time to avoid a slow and continuous plastic flow in the future. In the severe mining affected section, the depth of the plastic zone increased from 6.0 m near the working face to 10 m at 30 m behind the working face. During the fracture, rotation and subsidence of the main roof, stress increased and intensified at the retained coal rib, resulting in the crushing and extrusion of the shallow part of the coal rib. This process was accompanied by the weakening and failure of the anchor support structure. At this time, the surrounding rock-support load-bearing structure was in a post-peak failure state. The surrounding rock of the roadway needed timely supplementary support to prevent slow and continuous flow deformation in the future. In the mining-affected stable section, the plastic zone in the retained coal rib basically no longer expanded and remained at 12 m. However, it is worth noting that the retained coal rib deformation reached 750 mm at this time, and the roadway will quickly enter a state of rheological instability if timely and effective supplementary support is not installed. The roadway surrounding rock is a low-strength, layered rock mass, embedded with many original joints. Under the influence of mining stress [43], many cracks tend to develop in the shallow part of surrounding rock. Grouting in roadway surrounding rocks is generally conducted under a low pressure, which is often maintained at 2 MPa. During low-pressure grouting, the slurry spreads mainly along the cracks in the rock, and the development of the cracks determines the surrounding rock permeability. According to studies by [PERSON] [44], a shear plastic strain reaching 0.007 is used as the criterion for the breaking state of the surrounding rock, and the zone where \(\varepsilon^{ps}>0.007\) is taken as the range to initiate the slurry injection. Figure 6 shows the ranges that can be grouted at different positions before and behind the working face, which is shown in the color green in the figure. A comparison of the slurry diffusion range, the mining affecting stage behind working face and the retained coal rib deformation reveals that the three elements are closely interrelated, as shown in Figure 7. Before the working face, the deformation of the roadway outside the mining-affected zone is small, and the depth of the plastic zone in the surrounding rock is only about 1 m. The surrounding rock remains intact with the limited shear plastic strain in the plastic zone and a small grouting diffusing range. Under the influence of severe mining-induced stress, the integrity of the surrounding rock was damaged before and after the work, and a large number of cracks were generated and gradually expand in the surrounding rock. The roadway deformation increased rapidly. In addition, the shear flow characteristics are observed in the damaged surrounding rock. In the simulation, the rapidly increasing amount of shear plastic strain in the surrounding rock gradually increased the grouting diffusing range.