1. The MSV of surface subsidence basin

To express the influence induced by underground mining to the surface with different mining area sizes, subsidence velocity is considered as an index to measure the severity of mining influence. The relationship between the maximum subsidence velocity on the major section of the surface subsidence basin and the advancing position of the working face is depicted in Figure 4.

**Figure 4.** Maximum subsidence velocity (MSV) curve of the surface survey line.

Based on the Knothe time function of the surface dynamic subsidence, the MSV(*V*max) function formula is obtained by curve fitting:

$$V\_{\text{max}} = 50.40(1 - e^{-0.0028d})\tag{1}$$

In Equation (1), *d* is the mining distance of the working face, m.

It can be seen from Figure 4 that with the advancement in the working face, the goaf area increases, and the influence of underground mining on the surface intensifies. As a result, the MSV on the major section of the surface trend gradually increases. When the mining distance of the working face reaches 663.8 m, the *V*max (MSV) of surface survey station S9 increases from 0 to 45.43 mm/d. However, when the mining distance exceeds 400 m (i.e., 1.4 times the mining depth), it reaches supercritical mining in the strike direction, and the increase amplitude of the MSV station gradually decreases, reaching a stable value of 50.40 mm/d.

#### 2. Variation of LDMSV

On the surface subsidence velocity curve, the position of the MSV always lags behind the working face by a certain distance. This phenomenon is called the lag phenomenon of MSV. Knowing the LDMSV of the surface is useful in identifying the area where the surface moves violently during the working face mining process and the time when the maximum subsidence velocity occurs, which is significant as a guide for the protection of surface buildings. It is well known that when the working face starts mining from the open-off cut, each station on the surface undergoes a process from subcritical mining to supercritical mining, and LDMSV will be a dynamic process. Therefore, studying the variation of LDMSV can dynamically determine the area with the most violent surface movement in the mining process.

To describe the variation of LDMSV on the strike major section of the surface subsidence basin during the mining process, the nonlinear functional relationship between the LDMSV(*L*) and the mining distance is obtained by curve fitting:

$$L = 95.60(1 - e^{-0.11d})\tag{2}$$

Figure 5 illustrates the relationship between the LDMSV and the mining distance as an exponential function. The LDMSV significantly increases with the mining distance before the latter is advanced to 400 m. When the working face reaches supercritical mining, the LDMSV gradually flattens, increases to a certain extent, and then essentially does not increase, maintaining stability at 95.50 m; namely, the lag angle of MSV is 71.47◦. It shows that in the mining process in this coal mine, the proportion of mudstone and sandstone in the overlying strata is large, and the overlying strata structure is weak. As the goaf area increases, the strata movement is quickly transmitted to the surface, resulting in a large lag angle for the MSV on the surface.

**Figure 5.** Dynamic curve of lag distance of maximum subsidence velocity (LDMSV).
