Numerical Study on the Surface Movement Regularity of Deep Mining Underlying the Super-Thick and Weak Cementation Overburden: A Case Study in Western China

Abstract

While surface movement regularities have been sufficiently understood in the mining practices of eastern China, the case seems to be very different in western China where the super-thick and weak cementation (STWC) overburden exists. To better understand such knowledge, we compared geomining conditions and surface subsidence data for 16 coal mines and developed a carefully calibrated numerical model, with primary concern the relationship between subsidence rate and mining scale. We find that mining under the STWC overburden is characterized by the extremely small subsidence rate compared to the deep mining cases in eastern China, and the unusual subsidence phenomenon should be regional rather than an isolated case. We also find that the critical subsidence basin can be formed only when the goaf length and width both reach about 3.3 h (h is the average mining depth), which is far beyond the conventional understanding. We suggest that the large-scale mining under the STWC overburden carries enormous risks, which require great attention. The reported data, findings, and suggestions in this paper should be quite useful for coal mines with similar geomining conditions, and are also important for ecological protection and sustainable development of western China.

1. Introduction

Underground coal mining induces strata movement and in turn causes ground surface subsidence or cracking [1]. As a consequence, farmland, foundations, various buildings and infrastructure will be affected to varying degrees in terms of geomining conditions, which poses a huge challenge to the sustainable development of the coal industry [2,3]. The regularities behind surface movement are the keys to evaluating ground damage and are the basis of engineering design. Although such knowledge has been sufficiently understood in the mining practices of eastern China, the case seems to be completely different in western China, where exists the so-called super-thick and weak cementation (STWC) [4,5] rock strata. As China’s major coal producing areas are moving westward, the study on the surface movement regularity of the STWC overburden, as will be presented in this paper, is necessary and important.

The surface movement regularity can be characterized by many indicators, such as the subsidence rate, angle of draw, angle of critical deformation, and others. For different collieries using the same mining method in the adjacent or same mining area, the value of each indicator may be very close and therefore show certain regularity; in other cases, it may vary greatly. To guide engineering practice and as a summary of knowledge, the Chinese State Bureau of Coal Industry [6] published the book Regulations of coal pillar design and extraction for buildings, water bodies, railways, main shafts and roadways, where a large amount of surface movement data obtained from collieries in eastern China was listed. Also as a classic summary, some textbooks [7,8] provide general understandings on the surface movement regularity. For example, it is suggested that when both the length and width of goaf reach a size of (0.9–2.2) h in the USA or (1.2–1.4) h in China, where h is the average coal seam depth, surface subsidence reaches the maximum possible value, which will be further discussed in Section 4. Another widely used suggestion is that when the average mining depth is 30 times or more of the average mining thickness, there will be no fissures on the surface [7].

In recent years, researchers have made interesting discoveries and progress. Notably, Sroke [9], Dudek and Tajduś [10,11], and Vervoort [12,13] reported that, after some European coal mines are closed and under the influence of flooding, the surface may move upwards. Zhao and Konietzky [14] also studied this phenomenon in Germany by a large-scale FLAC3D model and believe that the surface uplift velocity in the area studied will reach 0.5–3.0 mm/year within the next few years. Xu [15] found that the boundary of subsidence basin under the influence of normal faults is beyond general understanding, and is larger on the side of the fault, showing an asymmetrical characteristic. Li [16] found that surface movement regularity of underground coal gasification is similar to that of strip mining and suggested that their subsidence prediction parameters are basically the same.

There have also been surface movement studies focusing on western China or on the STWC overburden. Specifically, in the Da-Liu-Ta (DLT) coal mine where the unconsolidated layers are thick, the rock layers are thin, and the mining depth is shallow, Liu [17,18] reported that various evident cracks were formed on the surface along with the mining process. In the Chen-Jia-Gou (CJG) coal mine where the average mining depth reaches 580 m, a deep mining case, Yu [19] suggested, through 3DEC simulation, that the critical subsidence basin will be formed when the goaf width reaches 0.96 h and the subsidence rate, defined as the ratio of the surface maximum subsidence to the thickness of coal seam, is 0.475. In the Xia-Gou (XG) coal mine, Yang [20] reported that after mining a 9.3-meter-thick panel, the ground surface only sank 79 mm. This peculiar subsidence phenomenon is also reported in our previous study [21] in the Ying-Pan-Hao (YPH) coal mine, and further, we [4,5] studied the mechanism and characteristics behind strata movement of the STWC overburden by physical modeling and numerical methods. However, due to data limitations, the previous numerical models were not sufficiently calibrated, and as a result, the conclusions reached may have been undermined.

In this study, we will have a more in-depth understanding of the surface movement regularity of the STWC overburden on the basis of a fully calibrated FLAC3D model. The mining and geological conditions as well as the characteristics of the YPH coal mine were explained in Section 2. The basic model setup, mesh size calibration, rock mass property calibration, and simulated mining schemes were described in Section 3. Calibration effects were firstly discussed by comparing the measured and computed subsidence values in Section 4, and this is followed by the further discussion on the relationship between subsidence rate and mining scale. Since there are no reported cases of large-scale mining corresponding to the critical mining condition under the STWC overburden, the new findings and suggestions presented in this paper will have important guidance and reference significance for safe and efficient coal mining and for ecological environment protection, in mining areas of western China.

2. Engineering Background and Characteristics

2.1. General Description and Geological Characteristic

Our attention is placed on the YPH coal mine, located in Wushen County, Erdos, western China (see Figure 1). The first and second mining panels of the mine, namely, 2201 and 2101, adopt the full-seam mechanized longwall mining method. Their geometric dimensions are partially illustrated in Figure 2, and the average coal thickness, average mining depth, and dip are 6.5 m, 730 m, and 1°, respectively. Two observation lines are arranged directly above the 2201 panel: the one along the panel (observation line C) has 81 monitoring points numbered from C1 to C80, and the other one across the panel (observation line B) has 72 monitoring points numbered from B10 to B81.

It should be mentioned that some of these monitoring points have been damaged or flooded, and in the end, the measurement data of 70 points is reliable and complete, which is further used for comparison in this study. The comprehensive borehole log and more details can be found in our previous studies [1,22,23].

The geological condition here has its own characteristics. Seen from the perspective of chronnostratigraphy, the coal seams formed belong to the Jurassic, while these in eastern China were formed mostly in the Carboniferous or Permian. Seen from the perspective of lithostratigraphy, the stratigraphic units are categorized into Zhi-Luo Formation, Yan-An Formation, An-Ding Formation, and Zhi-Dan Group from ancient to recent. Most importantly, the meanings of super-thick and weak cementation should be noted: (1) “super-thick” is expressed on the scale of rock masses, which implies that the rock mass structure here can be classified as “Intact or Massive”, mostly; and (2) “weak cementation” is expressed on the scale of rock specimens, which implies that the strength of intact rock is low, about 30 MPa on average (uniaxial compressive strength, UCS).

2.2. Surface Subsidence Characteristic

The surface subsidence in the YPH coal mine is very peculiar when we try to understand it from the perspective of subsidence rate, defined as the ratio of the surface maximum subsidence to the thickness of the coal seam. It is recorded to 0.06 after mining the two panels (the 2201 and 2101 panels) about 300 m apart. In

Table 1. Subsidence rate and mining conditions of coal mines in eastern China. The data come from the book Regulations of coal pillar design and extraction for buildings, water bodies, railways, main shafts and roadways [6]. Only the cases where the mining depth is greater than 500 m are listed.

Coal Mine Name	Abbr.	Panel Name	Average Mining Depth (m)	Panel Size (Length × Width)	Average UCS (MPa)	Subsidence Rate
Chang-Cui	CC	21132	620	942 m × 180 m	60	0.15
Heng-Da	HD	5333	825	2500 m × 200 m	30	0.66
Pan-San	PS	1731–3	516	896 m × 154 m	40.1	0.54
		1552–3	636	920 m × 160 m	60.4	0.77
Yao-Qiao	YQ	7005	756	1649 m × 159 m	40.2	0.21
Tang-Kou	TK	1301	1012	1303 m × 208 m	/	0.82
Nan-Zhi	NZ	3115	599	475 m × 120 m	45	0.54
Liang-Zhuang	LZ	5210–5211	568	1000 m × 270 m	40~50	0.63
Zhai-Zhen	ZZ	District 1	606	920 m × 440 m	40~50	0.58
Sun-Cun	SC	District 4	612	600 m × 500 m	40~50	0.6
WU-Tong-Zhuang	WTZ	182102	588	777 m × 155 m	40~60	0.4
		182101	610	1021 m × 176 m	40~60	0.61
Ma-Jia-Liang	MJL	14101	590	2849 m × 159 m	25	0.86
Xiang-Shan	XS	21306	589	1880 m × 220 m	37.8	0.8
Liang-Jia	LJ	2408	572	1260 m × 134 m	/	0.37

, we list the key geological and mining conditions and corresponding subsidence rates of different panels in various coal mines (see Figure 1 for locations) of eastern China, for comparison with this case. If we recall that the sizes of the 2201 and 2101 panels are 2600 m × 300 m and 2087 m × 300 m, the average mining depth is 730 m, and the average UCS is 30 MPa, then we can clearly see from Table 1 that the subsidence rate in the YPH coal mine is indeed very small from any angle. Consider the panels of the Heng-Da, Yao-Qiao, and Tang-Kou coal mines as examples, their coal seams are buried even deeper, the panel sizes are even smaller, and the average UCS is even larger, but on the contrary, the surface subsidence rate is significantly greater (0.66, 0.21, and 0.82 versus 0.06). As mentioned before, such phenomenon has also been observed in the Xia-Gou coal mine with a subsidence rate of 0.008 [20], plus the similar findings in the Ba-Yan-Gao-Le and Na-Lin-He coal mines, which support that the unusual subsidence should be regional rather than a special case.

Demonstrably, the surface subsidence is far from reaching the maximum possible after mining the two panels underlying the STWC overburden. The questions are subsequently raised as to when that happens and what is the relationship between mining scale and subsidence rate. In the following, these questions are answered via large-scale FLAC3D modeling, since there are no such large-scale mining practices yet, and the potential huge risk of rockburst limits such mining plans.

3. Method

The finite difference method referred to as FLAC3D is used for simulating the underground coal mining process because of its successful application in many cases [23,24] and merits in dealing with asymmetric 3D issues. The numerical simulation process is as follows.

3.1. Basic Model Setup

We present the established model in Figure 3, where we can see that it is a typical “layer-cake” model with a geometry of 5.5 km × 5.4 km × 0.76 km. The four lateral surfaces and the bottom surface are restricted to move along the x-, y-, and z-axes, and the top one represents the ground surface without any constraint. The Mohr–Coulomb model [25] was used for calculating the deformation of rock masses. Gravity, and the lateral stress coefficient at rest, k = μ/(1−μ), where μ is Poisson’s ratio, were used to apply the in situ stress. Different colors in Figure 3 indicate different strata of various lithologies, which were determined on the basis of the comprehensive borehole log (see Gong et al. [23] for details). In particular, we can see from Figure 3 that the most prominent rock strata are the red and orange ones, which represent the 300-m and 120-m-thick sandstone, respectively.

This is an optimized model on the basis of the previous one [23], created by merging those rock beds with a thickness of fewer than 5 m to adjacent rock beds. The purpose is to generate the computational grid more uniformly, which helps to improve the computational accuracy to some extent. Doing so is acceptable also because the strata movement simulation via FLAC3D is based on the concept of equivalent continuum. In other words, it is a further simplification of the model to form a new equivalent rock mass or a combined rock bed. However, note that it may not be acceptable in the discontinuous simulations because these thin rock layers may serve as the weak interfaces for large deformations. The mechanical properties of the combined rock bed are calculated using the previously proposed formula:

$${\overline{MP}}_i=\frac{{{\displaystyle \sum }}_{j=1}^{n}M{P}_{i,j}\times H_j}{{{\displaystyle \sum }}_{j=1}^n{H}_j}$$

(1)

where $n$ is the number of rock beds to be merged; $H_j$ represents the thickness of the $j$-th rock bed ($1\ll j\ll n$); $M{P}_{i,j}$ represents the $i$-th mechanical parameter of the $j$-th rock bed ($i=1,2,3,4,\mathrm{or}5$ indicates bulk modulus, shear modulus, friction angle, cohesion, and tensile strength, respectively); ${\overline{MP}}_i$ is the weighted average of the $i$-th mechanical parameter for the combined rock bed.

3.2. Mesh Size Calibration

Mesh size has a significant impact on the calculation result, which has been widely accepted [26,27,28,29,30]. Generally, the finer the grid, the more accurate results can be reflected, while on the other hand, the finer grid will also lead to longer calculation times that may last for several weeks depending on the differences in software, hardware, and model size. One has to find out the balance between modeling details and calculation time and to understand the modeling accuracy. Since our major attention is posed on surface subsidence, we can see from Figure 4 that, in our case, the maximum subsidence keeps increasing with the shrinking of grid size and finally stabilizes at a fixed value. Therefore, the meshing scheme of 25 m × 25 m is applied hereafter.

3.3. Rock Mass Property Calibration

Since rock mass is composed of intact rocks and discontinuities, it is necessary to understand the classification level of rock masses in the YPH coal mine and implement rock mass property calibration. In our case, we learned from the geological reports that 90% of the rock strata in the study area are classified as “Massive”, which suggests that the mechanical properties of rock specimens and rock masses should be relatively close according to the rock mass classification systems. Therefore, the initial rock mass properties are considered to be consistent with the results obtained from laboratory tests on rock specimens. Note also that this is very rare in the mining areas of eastern China, where “blocky” or “very blocky” rock masses are more common, and where the strength of rock masses is usually one-third or less of that of rock specimens.

Among various calibration methods, the orthogonal array testing method was chosen mainly because of its successful application in mining subsidence prediction via FLAC3D. In the following, we directly list the five levels (see

Table 2. The selected levels for the four mechanical parameters. E, μ, C, and $\varnothing$ represent elastic modulus, Poisson’s ratio, cohesion, and friction angle, respectively.

Level	Experimental Factor
	E (GPa)	μ	C (KPa)	$\varnothing$ (°)
I	4.34	0.267	5220	24.3
II	5.58	0.293	6850	26.6
III	6.81	0.318	8480	28.9
IV	8.05	0.344	10,100	31.2
V	9.29	0.370	11,700	33.5

) selected for each parameter and list the 25 schemes and the corresponding test results in

Table 3. The orthogonal array and the results of the tested schemes.

Scheme	E	μ	C	$\varnothing$	The Calculated Maximum Surface Subsidence (mm)
1	I	I	I	I	98.0
2	I	II	II	II	88.5
3	I	III	III	III	82.7
4	I	IV	IV	IV	78.0
5	I	V	V	V	72.3
6	II	I	III	II	74.3
7	II	II	IV	III	68.6
8	II	III	V	IV	64.5
9	II	IV	I	V	59.7
10	II	V	II	I	56.7
11	III	I	V	III	60.1
12	III	II	I	IV	56.1
13	III	III	II	V	52.4
14	III	IV	III	I	49.4
15	III	V	IV	II	46.3
16	IV	I	II	IV	51.1
17	IV	II	III	V	47.6
18	IV	III	IV	I	44.7
19	IV	IV	V	II	41.2
20	IV	V	I	III	39.0
21	V	I	IV	V	44.2
22	V	II	V	I	41.8
23	V	III	I	II	38.5
24	V	IV	II	III	35.7
25	V	V	III	IV	33.7

. The details of the analysis process can be found in the work by Xu, Kulatilake, Tian et al. [24].

In our previous word, the overestimation effect in FLAC3D was analyzed theoretically [23] and was later observed [1], which shows that the overlying strata are the closest to the equivalent continuum hypothesis in the early stage of mining, especially before the rock roof has collapsed in a large area, and that the surface subsidence is overestimated to varying degrees as the rock roof continues to collapse. Therefore, it may be the best choice to calibrate rock mass properties using the early-period data of the in-situ measurement. That explains the simulated mining scheme in the FLAC3D models corresponding to each scheme in Table 3, i.e., the 2201 panel was mined to 361 m.

We can see from Figure 5 that the measured maximum subsidence is 63.3 mm in the first-period measurement. Hence, we can easily find the best match in Table 3, i.e., scheme 8. In addition to the maximum subsidence, we can also see from Figure 5 that the predicted results of other monitoring points are very close to the measured ones, as well. If we consider this from the perspective of root mean square error (RMSE), the prediction error of the 70 points is only 4.0 mm. The detailed parameters of each rock stratum are shown in Figure 6.

3.4. Further Simulation Schemes

After calibration of mesh size and rock mass properties, a sound FLAC3D model seems to have been built, but we still want to further verify the robustness of the model, that is, establish to what extent it can predict the observations in the next few periods. As of now, we have mastered the field subsidence data of the first eight periods, so we designed a simulation scheme, as shown in Figure 7a. The numbers together with the color variation indicate the order and limits of excavation, which is consistent with the actual mining situation of the 2201 and 2101 panels.

Subsequently, we also designed the simulation scheme shown in Figure 7b to answer the questions raised in Section 2.2. As can be seen, the fictitious excavation range reaches 2500 m × 2400 m, including 8 panels, numbered from 2201 to 2208, each with a width of 300 m.

4. Results and Discussion

4.1. Analysis of Calibration Result

In Figure 8, we present the measured and predicted subsidence values at each monitoring point. The second, middle, and last periods are fully illustrated in order to gain direct visual understanding. The remaining periods are omitted because the subsidence change is not obvious and is hard to distinguish from the others, while their statistical results are fully shown in

Table 4. Summary of the calibration results. MSS represents maximum surface subsidence, and RMSE is short for root mean square error.

Period	Relative Error of MSS	RMSE of 70 Monitoring Points (mm)
1	1.4%	4.0
2	1.6%	5.0
3	8.1%	8.2
4	4.7%	9.8
5	6.7%	10.7
6	2.7%	14.5
7	2.9%	17.9
8	2.2%	17.5

.

We can see from Figure 8 that in general the variation trend of the predicted values basically follows the measured ones, but the followability is different in each period. Specifically, on observation line B, the difference between them becomes larger and larger as the number of periods grows, while on observation line C, the predicted values are quite close to the measured ones in all periods and can reflect the maximum subsidence. This is also observed from the statistical results in Table 4, where we can conclude that the calibrated model is quite accurate in predicting the maximum subsidence but is less accurate when considering all monitoring points. In addition, it should be noted that the subsidence values of monitoring points of C9 to C14 are negative, which is either a measurement error or due to the uplift effect under the influence of water [12].

Since our interests are focused more on the subsidence rate that is closely related to the maximum subsidence, the results drawn from the calibrated model in the following should be reasonable and reliable.

4.2. Relationship between Subsidence Rate and Mining Scale

According to the planned scheme in Figure 7b, we conduct the excavation simulation, record the peak subsidence, and present them in Figure 9 in the form of subsidence rate. We can see that, when mining the 2201 panel, the subsidence rate gradually increases and finally converges to 0.035 after the mining distance exceeds about 1300 m, while, when mining the 2202 panel, it does not seem to show signs of convergence and it seems that further mining is required. In the following three panels, 2203 to 2205, the advancing lengths when the peak subsidence rate was achieved are basically the same, about 2100 m, and the corresponding subsidence rates are 0.357, 0.502, and 0.59, respectively. During the mining process of the remaining panels, the subsidence rate fluctuates less and less and finally tends to settle around 0.7.

The relationships revealed above are quite inconceivable from a conventional cognitive perspective because the ratio of the goaf length and width to the average mining depth (h) reached 3.42 and 3.28, respectively, which is far beyond the size required to form the critical subsidence basin, whether it is compared to the experience of the United States (0.9–2.2 h) or China (1.2–1.4 h). However, this phenomenon is very likely to actually occur if large-scale mining is performed due to the following two reasons. First, since an extremely small subsidence rate has been widely observed when mining a single panel in multiple coal mines as we have discussed before, the unusual relationships revealed above should not be surprising either. Second, and most importantly, we learned from the BYGL coal mine that the subsidence rates after sequentially mining three adjoining panels are about 0.03, 0.29, and 0.37, respectively, which is basically consistent with our numerical results except for the case when mining the second panel (0.29 versus 0.194). However, also note that the advancing length in the BYGL coal mine is even greater, approximately 3500 m. If we recall that in our simulation corresponding to the 2202 panel, there is no sign of peak subsidence and the greater mining length may cause larger subsidence, then we can find that the larger advancing length probably accounts for the difference between 0.29 and 0.194. Collectively, this once again proves that the results revealed by the calibrated FLAC3D model should fall within a reasonable range.

To better understand the relationship between subsidence rate and mining scale, we calculated the variation velocity of the subsidence rate (VVSR) and present it in Figure 10. We can see that the maximum VVSR was recorded for the first four panels when mining a distance of 700 m to 900 m, and was recorded for the following three when mining a distance of around 300 m. For all panels, the VVSR basically increases first and then decreases. We can also observe that when mining the 2208 panel, the fluctuation of VVSR has been very small, which is the sign of the formation of a critical subsidence basin.

On the other hand, we should keep in mind that the whole model is based on the concept of equivalent continuum, that is, the predominant discontinuities such as a minor fault or a local flaw, which are hard to find but may actually exist somewhere in the overlying strata, are not reflected in our FLAC3D model. This will not be a big issue if the overlying rock strata are highly jointed, because their equivalent rock mass property, such as the elastic modulus, is quite small, which in turn results in the quick energy release and fast subsidence. Yet things are totally different in this case. The goaf size needed to form the critical subsidence basin is very large, and it seems that some kind of structure formed in the overlying rock that controlled the surface subsidence. We can deduct from Figure 9 that the energy is not fully released but is highly accumulated, which, on one hand, is beneficial for ground control only if the overlying strata are indeed intact everywhere, and on the other hand, carries huge risks if there happens to be a predominant discontinuity where the energy builds up. If the latter scenario holds, it may trigger earthquakes and provide an alternative explanation for the rockburst phenomenon in this area.

Another point worth discussing is the effect of water. In the YPH coal mine, water flows into the roadways and panels with the formation of overlying cracks, which is not reflected in the numerical simulation. We believe this will exacerbate the surface subsidence due to the influx of water and how much more the actual surface subsidence should be than predicted depends on the amount of water inflow, which merits further study.

5. Summary and Conclusions

Recall that the objective of this paper is to study the surface movement regularities under the super-thick and weak cementation (STWC) overburden with the primary concern on the subsidence rate. Specifically, we first analyzed the relationship between the geomining conditions and the measured subsidence data of a total of 16 coal mines in eastern and western China. We clarified and found the following points:

• “Super-thick” is expressed on the scale of rock masses, which implies that the rock mass structure can be classified as “Intact or Massive”, mostly, and “weak cementation” is expressed on the scale of rock specimens, which implies that the strength of intact rock is low.
• Mining under the STWC overburden is characterized by the extremely small subsidence rate compared to the deep mining cases in eastern China, and this phenomenon should be regional rather than an isolated case.

We then established the FLAC3D model on the basis of the Ying-Pan-Hao coal mine and corrected the rock mass properties and mesh size. The calibration result was analyzed by comparing the difference between the measured subsidence values and the computed ones, and we found that the calibrated model can well predict the maximum subsidence of the following seven periods of data. Based on this, we explored the relationship between surface subsidence rate and mining scale in the YPH coal mine and found the following:

• The critical subsidence basin can be formed only when the goaf length and width both reach about 3.3 h (h is the average mining depth), which is beyond the conventional understanding;
• For a single panel, only when the advancing distance is close to 1300 m does the surface subsidence reach the maximum possible;
• Large-scale mining under the STWC overburden suggests huge risks, which could lead to earthquakes.

The reported data, findings, and suggestions in this paper have important guidance and reference significance for other collieries when mining under the STWC overburden, as well as having important scientific value for the protection of ecological environment and the sustainable development of coal industries.