**1. Introduction**

The surface subsidence caused by underground mining is a spatiotemporal process. In the mining process, the impact of mining varies for various areas of the surface, and its influence is dominated by the relative position of the working face and the surface area. In production practice, it is nowhere near sufficient to solve the actual problems on site according to the final subsidence law [1,2]. It is often necessary to study the dynamic subsidence and master the variation of subsidence velocity of surface and overlying strata in order to judge the intensity and location of surface and overlying strata movement and deformation, as well as to protect and repair surface structures (houses, dams, roads, and railways, etc.) and structures in overlying strata (chambers, roadways, etc.) [3–5].

The dynamic movement of the surface and overlying strata caused by coal mining has been deeply studied in China and other countries. Considering the changes in stress-strain state of rock mass and coal mass around the goaf and the working face in the process of mining [6–10], there is a close relationship between surface movement and overlying strata movement. Shu [11,12] proposed a theoretical model of the relationship between sub-surface and surface subsidence movements, which can be used to predict sub-surface subsidence components at any point within the zone influenced by the extraction of a

**Citation:** Xu, G.; Li, D.; Zhang, Y.; Li, H. Overlying Strata Dynamic Movement Law and Prediction Method Caused by Longwall Coal-Mining: A Case Study. *Processes* **2023**, *11*, 428. https://doi.org/ 10.3390/pr11020428

Academic Editors: Feng Du and Aitao Zhou

Received: 2 January 2023 Revised: 25 January 2023 Accepted: 27 January 2023 Published: 31 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

<sup>1</sup> School of Mining Engineering, Guizhou University of Engineering Science, Bijie 551700, China

panel according to the subsidence components obtained from field measurements. Based on the subsidence data in the Southern Coalfield of the Sydney Coal Basin, the proposed prediction is examined. Amar [2] studied the behavior of dynamic active and residual subsidence for a few panels of Jharia coalfield, and found that the subsidence and slope were linearly related to time. Compressive and tensile strains showed a typical fluctuating characteristic behavior, and the rate of mining being a key and controlling parameter for the rate of subsidence and its inter-relationship was developed. The time effect is studied in the coalfield of Asturias, Northern Spain, with the aim of predicting subsidence phenomena and characterizing the trough in the different intermediate stages of the process of excavation and subsidence. In addition, the subsidence is predicted following the models of Knothe and Sroka–Schober and a new time function based on the normal distribution function [13].

According to the difference of surface subsidence velocity in the process of surface dynamic subsidence, Huang [14] divided the whole process of surface subsidence into three stages: Subsidence development, full subsidence, and subsidence attenuation. The development and variation laws of surface subsidence deformation in these three stages were respectively analyzed, and a new concept of "deformation velocity in surface subsidence" was also put forward. Chudek [15] analyzed the impact of overlying strata lithology on the time influence parameters of surface movement and determined the relationship between these parameters and mining depth according to a large amount of survey data. Knothe [16], a foreign scholar, introduced the time function into the prediction of dynamic surface subsidence. Numerous scholars have conducted extensive studies based on Knothe time function, and the findings have been able to accurately predict the entire process of surface subsidence. Scholars have worked to improve the Knothe time function in light of its drawbacks and defects, and they have provided the ideal distribution form of time function to make up for its shortcomings. Based on the static prediction model of probability integral, Zhang [17–19] discussed the prediction method of dynamic subsidence for the inclined main section using the "optimized segmented Knothe time function". The outcome showed that regardless of which direction the mining begins from or whether the prediction direction is uphill or downhill, the results of dynamic subsidence and deformation of the inclined major section are always consistent with the rules of the theory. Guo [20] analyzed the dynamic surface movement characteristics and parameters affected by fully mechanized mining under thick hydraulic collapse, based on the data from the monitoring station. The results indicate that the surface movement is intensive, the surface subsidence velocity is rapid, and the surface deformation and damages are serious in this mining area with thick loess. Deng [21] used the relationship between the maximum subsidence velocity and the relative position of the working face to calculate the prediction formula of the subsidence velocity at any point and time during the mining process. For monitoring the movement of overlying strata, vertical boreholes were drilled from the ground into the rock stratum, Wang [22] adopted the distributed optical fiber sensor monitoring technology and multipoint borehole extensometer methods to the movement data of the strata. Guo [23] conducted field monitoring of overburden displacement, stress, and water pressure changes at the longwall panel in Anhui, China. A three-dimensional annular-shaped overlying zone along the perimeter of the longwall panel is identified for optimal methane drainage during mining. The above researches mainly studied the process and stage of surface subsidence induced by underground longwall coal mining, and obtained the prediction model of surface dynamic subsidence. However, for the protection of surface and underground structures, the distribution characteristics and prediction of subsidence velocity are crucial. In the existing researches, the impact of mining extraction area on surface dynamic movement characteristics is not considered, which makes it impossible to effectively predict the whole process of the working face mining. Moreover, due to the difficulty of overlying the strata field monitoring experiment, the research on overlying strata movement is mainly a static movement, and the relationship between the dynamic movement of the ground surface and the dynamic movement of the overlying strata is not established. As a result, there are few research results on the dynamic movement law and prediction theory. This paper first examines the relationship of movement and deformation between surface and overlying strata, and then analyzes the variation characteristics of subsidence value and subsidence velocity at the maximum subsidence point along the survey line with different goaf areas. The dynamic relationship between the surface dynamic movement parameters (maximum subsidence velocity and lag distance of maximum subsidence velocity) and the advancing distance of the working face is analyzed. The numerical simulation model of the dynamic movement of overlying strata is established, and the rock mechanics and dynamic excavation parameters are determined. When comparing the subsidence and subsidence velocity curves of the surface survey line and monitoring the line of the numerical model, it is considered that the parameters of the numerical model are accurate and can provide appropriate data for analyzing the movement of overlying strata. The variation functions and lag distance of the maximum subsidence velocity at different cover depths of rock strata during the advancement of the working face are determined based on numerical simulation results. The subsidence velocity prediction function on the major section of the surface and overlying strata subsidence basin is obtained based on the distribution function of surface subsidence velocity with supercritical extraction on the major section and the dynamic subsidence prediction method of the major strike section.

In this paper, based on the surface survey data above the panel in Peigou Coal Mine, the variation characteristics of surface dynamic movement parameters, the maximum subsidence velocity (MSV), and the lag distance of maximum subsidence velocity (LDMSV) are obtained during different advancing distances of the working face. To explore the overlying strata movement law, a numerical simulation model is established, and variation functions of dynamic movement parameters for rock strata with different depths are obtained based on the results of the numerical simulation. The prediction model of subsidence velocity at any time and any position on the strike major section of the subsidence basin is established through the dynamic description of surface and overlying strata movement. The study's findings not only provide guidance for surface and overlying strata structures protection and treatment technologies, but also further enrich the body of knowledge regarding the dynamic movement of the surface and overlying strata.

#### **2. Relationship between Surface and Overlying Strata Movement and Deformation**

In the past, the overlying strata movement mainly focused on the strata pressure around the working face, the fluid migration of the overlying strata aquifer, the mininginduced fracture evolution, and relieved methane delivery. These factors form an important basis for addressing a number of safety and environmental issues, such as ground pressure accidents, water and gas disasters, surface subsidence, etc. [24]. Studies on surface subsidence focus on environmental, facility, life, and ecological impacts. However, there is a link between overlying strata and surface subsidence, and mining excavation will inevitably cause the movement of the overlying strata. Considering the key layer as the main body of rock strata movement research, mechanical methods are used to explain changes in the structural form, stress field, and mining-induced fracture field of rock strata. Therefore, there is a relatively unified understanding and complete mechanical description of ground pressure, mining subsidence, and water and gas migration in mining-induced rock strata [25].

The relationship between surface subsidence and rock strata movement was studied by similarity simulation and numerical simulation tests. Adhikary [26] established a practical hydrogeological model based on the large coal seam sub-critical longwall panel in Australia, and stated that the rock collapse and fracture zones are trapezoidal large structures similar to the "inverted funnel" arch. Zuo [27] used the mechanical model to explain the complex mechanical relationship between strata movement and surface subsidence based on the hyperbola-like shape of the broken boundary of strata movement. The boundary of surface subsidence and strata movement was unified as a whole, and an overall strata movement model that can describe the movement of overlying strata to

surface subsidence was established. The movement and deformation of overlying strata caused by coal mining are a mechanical phenomenon in rock mass. Due to the presence of rock mass and the complexity of mining boundary conditions, it is difficult to develop a complete mathematical model and its parameters in order to express the overlying strata damage and movement deformation caused by coal mining. According to the laws of strata subsidence and displacement at different buried levels [28,29], as shown in Figure 1, it is assumed that the subsidence curve of different strata considers the projection line of coal wall as the inflection point, and the relationship between overlying strata and surface movement and deformation lies in the following:


In summary, due to the complex mechanical behavior of the mining-induced rock mass, rock strata movement is closely related to the surface movement. The surface subsidence basin is the external manifestation of the rock strata movement, and the rock strata movement is the fundamental reason for the surface subsidence. Due to the complexity of the occurrence of the rock mass itself and the mechanical boundary condition, it is impossible to fix many in-situ monitoring points for the movement of boreholes in the overlying strata as the surface survey stations [30,31]. Therefore, based on the measured surface data, this paper establishes a numerical simulation model of overlying strata dynamic movement and studies its law. Combined with the aforementioned information, the dynamic movement prediction model of the surface and overlying strata is established.

**Figure 1.** Movement and deformation characteristics of the overlying strata.
