A new indicator for estimating the degree of mining-induced land subsidence: the overburden’s average GSI value

Underground coal mining leads to land subsidence, which, in turn, results in damage to buildings and infrastructure, disturbs the original ecological environment, and hinders the sustainable development of coal mining cities. A reasonable estimation of land subsidence, on the other hand, is the foundation for building protection, land reclamation, and ecological environment reconstruction. However, when we applied the existing land subsidence estimation theory to the deep mining areas of the Ordos coalfield in western China, there was a significant deviation between the estimations and the measurements. To explain such unusual case, we propose using the overburden’s average GSI (Geological Strength Index) value instead of the compressive strength (UCS) of rock specimens for a better representation of the overburden’s overall properties. By using on-site subsidence monitoring results and historical data, we provided evidence which supports that the overburden’s average GSI value has a much greater impact on subsidence rates than the UCS. Subsequently, we investigated the relationship between three typical overburden’s GSI values and the subsidence rates via a calibrated numerical model, revealing the variation patterns of maximum surface subsidence when the overburden’s average GSI value is set at 30, 50, and 75, respectively. Finally, on the basis of the measured and simulated results, we discussed a non-conventional strip mining method for mining subsidence control in the deep mining areas of the Ordos coalfield in western China, and explained why it is possible and what are the significant advantages behind. The proposed methods, findings, and suggestions in this paper are therefore quite helpful for researchers and engineers who wish to estimate and control the mining-induced land subsidence, as well as for those who are particularly interested in the study of environment science related to land subsidence.

A new indicator for estimating the degree of mining-induced land subsidence: the overburden's average GSI value Yaqiang Gong 1,4* , Jianfeng Zha 2 , Qingbiao Guo 3 & Guangli Guo 2 Underground coal mining leads to land subsidence, which, in turn, results in damage to buildings and infrastructure, disturbs the original ecological environment, and hinders the sustainable development of coal mining cities.A reasonable estimation of land subsidence, on the other hand, is the foundation for building protection, land reclamation, and ecological environment reconstruction.However, when we applied the existing land subsidence estimation theory to the deep mining areas of the Ordos coalfield in western China, there was a significant deviation between the estimations and the measurements.To explain such unusual case, we propose using the overburden's average GSI (Geological Strength Index) value instead of the compressive strength (UCS) of rock specimens for a better representation of the overburden's overall properties.By using on-site subsidence monitoring results and historical data, we provided evidence which supports that the overburden's average GSI value has a much greater impact on subsidence rates than the UCS.Subsequently, we investigated the relationship between three typical overburden's GSI values and the subsidence rates via a calibrated numerical model, revealing the variation patterns of maximum surface subsidence when the overburden's average GSI value is set at 30, 50, and 75, respectively.Finally, on the basis of the measured and simulated results, we discussed a non-conventional strip mining method for mining subsidence control in the deep mining areas of the Ordos coalfield in western China, and explained why it is possible and what are the significant advantages behind.The proposed methods, findings, and suggestions in this paper are therefore quite helpful for researchers and engineers who wish to estimate and control the mining-induced land subsidence, as well as for those who are particularly interested in the study of environment science related to land subsidence.
Underground longwall coal mining alters the initial stress regime of overlying rock strata (overburden), leads to the collapse of highly jointed rock mass or the bending of intact layers, and eventually causes land subsidence (i.e., mining subsidence) around the world [1][2][3][4][5][6][7][8][9][10][11][12][13][14] , which poses a serious threat to surface buildings, infrastructure, farmland, and the ecological environment if the laws of surface subsidence are not thoroughly grasped.Pioneers have clearly pointed out that the degree of mining subsidence is closely related to influential factors such as rock stiffness, mining depth, the thickness ratio of loose layers to the bedrock, etc.While such knowledge appears to be sufficient for mining practices of eastern China, we have faced significant challenges when applying it to the mining areas of western China, and all clues point to a seldom-mentioned but important influencing factor -Rock Mass Classification 15 .As China's major coal producing areas are moving westward, the study on the relationship between mining subsidence and rock mass classification, as will be presented in this paper, is therefore necessary and significant.
The research on mining-induced land subsidence has a rather along history.In China, the classical textbook published in 1991, Coal Mining Subsidence 16 , had summarized the influencing factors of mining subsidence in general, including mechanical properties of the overlying strata, thickness of loose layers, dip angle of coal seams, ratio of mining thickness to mining depth, panel size, repeated mining, mining method, and roof control method.

Estimating mining subsidence via rock mass classification
The study of this paper stems from three coal mines, Yingpanhao (YPH), Nalinhe (NLH), and Bayangaole (BYGL), located in Wushen banner, Ordos, Inner Mogolia Province, China (see Fig. 1).The three coal mines belong to the deep part of the Ordos coalfield, and are developed in recent five years.For those new coal mines, it is often necessary to estimate the possible subsidence values by similarity analysis for engineering design before mastering the monitoring data.Therefore, we list the basic geomining conditions of the three coal mines in Table 1 together with additional 9 coal mines chosen from historical data in the classical book 46 to carry out the similarity analysis.
We can see that the panels 2201, 31101, and 311101 actually have quite similar geomining conditions.Specifically, they all adopted the longwall mining method with mining depth larger than 600 m, mining thickness larger than 5 m, panel size larger than 2500 m × 240 m, and most importantly the average uniaxial compression strength (UCS) of 30 MPa to 35 MPa.Based on this, if we first look at the panel 5333 of HD coal mine, which is closest to these three, it can be deduced that the subsidence rate of the panels 2201, 31101, and 311101, should be at least 0.7, because while their average UCS is almost the same, the mining depth of the three panels is shallower and the panel size is larger.If we then look at the panel 1552-3 of PS coal mine, it is reasonable to assume that the subsidence rate of the panels 2201, 31,101, and 311,101, should be at least 0.8, because while their mining depth is parallel, the UCS of the three panels is much smaller and the panel size is much larger.As such comparisons continue, one may finally find that it is almost not possible to obtain their real subsidence rates (i.e., 0.035, 0.093, and 0.033) based on current understanding, nor even come close to them.
The up to 24-fold difference between the measured (0.035, 0.093, and 0.033) and estimated (0.700 or 0.800) subsidence rates suggests that there must be an influencing factor that we have not clearly identified, and to the author's opinion the rock mass classification probably is it.This is because, as we have mentioned in the Introduction, the behavior of a rock mass is not solely determined by the properties of individual rocks, but by the way in which they are oriented, jointed, and interlocked with one another.For example, a rock mass composed of stronger individual rocks (high UCS rocks) may be unstable if the rocks are poorly-jointed or fractured, while a rock mass composed of relatively weak individual rocks (low UCS rocks) may still be stable if the rocks are well-jointed and interlocked.
Therefore, if we see the discrepancy from the perspective of GSI (Geological Strength Index 44,47 , one of the many rock mass classification systems) for example, it will be much easier to explain.Our theory is that, in the context of similar mining depth and mining scale, the core factor that determines the degree of land subsidence is the weighted average GSI value ( GSI ) of the overburden, and the larger the GSI value, the smaller the subsid- ence rate.In particular, GSI is calculated by where n is the total number of overlying rock strata, m i is the thickness of the i-th strata, and GSI i is the GSI value of the i-th strata, which can be estimated via the basic GSI chart (see Fig. 2).The application of Eq. 1 is data dependency, i.e., the GSI value can only be calculated when each stratum has a detailed geological description.1.
Table 1.Basic geomining conditions for the panels of the YPH, NLH, and BYGL coal mines.The data of the other 9 coal mines comes from the book 46 .The locations of the coal mines can be found in Fig. 1.However, it is well-known that in many cases, borehole logs are incomplete, leading to a rough estimate of the GSI value.But also note that, when there is a significant difference in the GSI values between two compared objects, a rough estimate can still reflect their divergence, at least avoiding the situation of estimating a 24-fold difference.Therefore, a rough estimate remains meaningful, and Eq. 1 can, at a minimum, be regarded as a theoretical approach for estimating the degree of mining-induced land subsidence in a more comprehensive manner.The proposed theory can be supported by borehole logs collected from coal mines in the eastern and western China, which are available on an online database 48 .Specifically, the eastern coal mines in the database are Tangkou (TK), Daizhuang, Dongtan, Xinhe, and Xuchang, located in the city of Jining, Shandong province; the western coal mines are YPH, NLH, and BYGL.It can be found through the eastern borehole logs that terms such as 'weathered' , 'well-developed or extensively developed fractures' , 'persistent bedding planes' , 'fragmented core' , or 'too fragmented to core' are frequently seen, and the strata thicknesses are generally no more than 10 m, with the majority having a thickness of less than 5 m.From the 'STRU CTU RE' (see Fig. 2) perspective, these characteristics should not exceed the 'Very Block' category in the basic GSI chart (see Fig. 2).When considering 'SURFACE CONDITIONS' , they are likely to align with, or not perform better than, the 'Fair' category.This is especially true when taking into account that some internal strata also exhibit signs of weathering.Collectively, this suggests that the overburden's GSI values for the eastern coal mines are likely not more than 50.Meanwhile, since the geological descriptions also document a small portion of relatively intact rock strata, the overburden is also unlikely to be classified as 'DISINTEGRATED' .Therefore, an overburden's GSI value of 30 to 50 should be a reasonable guess for the eastern coal mines.
On the other hand, it can also be found through the western borehole logs that the majority of strata are characterized as 'Massive' with only a small portion described as having 'horizontal bedding' or 'wavy bedding' .In addition, strata with a thickness exceeding 10 m are quite prevalent, and terms used in the eastern borehole logs (i.e., 'weathered' , 'well-developed or extensively developed fractures' , 'persistent bedding planes' , 'fragmented core' , or 'too fragmented to core') are seldom seen.Based on this and referring to the basic GSI chart (see Fig. 2), it seems that the overburden's GSI value in the western coal mines should not be lower than 60, and due to the pres- ence of some locally developed joints and fractures within the overburden, it is also unlikely to be higher than 90.
In summary, despite our relatively rough assessment of GSI values aforementioned, it is evident that the overburden's GSI value in the western coal mines are generally higher than those in the east, and the difference is significant.If we recall our proposed theory that the larger the GSI value, the smaller the subsidence rate, it becomes quite clear why the subsidence rates of YPH, NLH, and BYGL are significantly lower than those of the other coal mines listed in Table 1, despite their overburden's average UCS values are very close (i.e., because the overburden's GSI values of the coal mines in the deep mining area of the Ordos coalfield are a lot more higher).If we were to perform a similarity analysis via the proposed indicator in Table 1, we would probably not yield highly unrealistic subsidence rates such as 0.7 or 0.8 for the YPH, NLH, and BYGL coal mines.
However, knowing only the relative size of overburden's GSI value is not enough.To more conveniently estimate the degree of mining-induced land subsidence via GSI system, one may subsequently ask, what is the relationship between the overburden's typical GSI value and the corresponding subsidence rate?

Methods
In this section, we take the YPH coal mine as engineering background and use the FDM (finite difference method) based commercial software, FLAC3D (Fast Lagrangian Analysis of a Continua in 3 Dimensions), to answer the question posed in Section "Estimating mining subsidence via rock mass classification" due to its many successful applications [49][50][51] .

Fundamentals and model calibration
In our previous study 51 , also taking the YPH coal mine as engineering background, we used the earliest surface subsidence data together with the orthogonal experiment method to calibrate a FLAC3D model.The calibrated model successfully predicted surface subsidence corresponding to several subsequent mining operations, with a maximum subsidence error of less than 10% (see the reproduced Fig. 3).Moreover, the predictions of the calibrated model also match the measured outcomes from the BYGL coal mine, which had been mined earlier than the YPH coal mine (see Table 2).Collectively, the comparison between the measurements and predictions at least proved that the previously established FLAC3D model and the corresponding rock mass parameters are within a reasonable range.
).The remaining periods (3rd, 4th, 6th, and 7th periods) are omitted because the subsidence changes are not obvious and are difficult to distinguish from the others.Overburden's typical GSI values and the corresponding rock mass properties The determination of overburden's typical GSI value and the corresponding rock mass properties are based on the GSI system and the Hoek-Brown equations, which have been updated for many times.In a recent edition, Hoek and Brown 44,47 provided the basic GSI chart shown in Fig. 2, where we selected three typical GSI values (30, 50, and 75) to represent different types of overburden.Please note that, as emphasized in Fig. 2, there's no need to be excessively precise when determining GSI values, and a range of values is often more practical and realistic.Hence, GSI values of 30, 50, and 75 can actually represent rock masses with GSI values of 25 to 35 (very poor quality), 45 to 55 (average quality), and 70 to 80 (very good quality), respectively, which basically covers a variety of different geological conditions.Another reason for choosing these three typical GSI values is that Hoek 52 had conducted extensive research on different types of rock masses and directly provided the typical parameters for the three kinds of overburden (see Table 3).For the overburden with an average GSI value other than 30, 50, and 75, researchers who are interested in the study of mining subsidence and strata movement are suggested to use the Hoek-Brown Eqs. 44nd the empirical parameters 47 to obtain the detailed rock mass properties, so as to better and fully understand the laws under varying GSI values and varying geomining conditions.

Establishment of numerical models
We can see from Fig. 4a that the established FLAC3D model has dimensions of 5.5 km long, 5.4 km wide, and 760 m high, with the green layer for the Quaternary, the red layer for the three different types of overburden ( GSI value set at 30, 50, and 75, respectively), the silver layer for the coal seam 2-2, and the blue layer for the floor rocks.All layers obey the linear elastic pre-failure behavior and the perfect plastic post-failure behavior using the Mohr-Coulomb 49 failure criterion.The gridpoints on the four lateral surfaces are not allowed to move along the x-, y-, and z-axes, and the top is a free surface without any loads.Mesh size effect had been checked previously 51 , and it turns out that a density of 25 m × 25 m is accurate enough in this case.Statistically, the established model has a total of 3.13 million zones and 3.26 million gridpoints.
Figure 4c is a top view of the coal seam, showing the detailed mining process to be simulated, where the Arabic numerals and their corresponding colors represent the sequence and area of excavation.We can see that the simulated mining area contains a total of 8 panels, each of which is 300 m wide and 2,500 m long.Every Table 3.Three typical GSI classified rock masses (used for three different types of overburden) and their properties, provided by Hoek 52 .

Rock parameters Very good quality overburden Average quality overburden Very poor quality overburden
Geological strength index 75 50 30   Hoek-brown constant 25 12  8   Friction angle 46°33°24°C panel is excavated 12 times, for a total of 96 excavations, and the cumulative mining length is 20,000 m.In addition, the mining area is 1,500 m away from the model boundary, which is enough to reduce the boundary effect considering the average mining depth of 730 m.

Relationship between subsidence rate and overburden's typical GSI value
According to the aforementioned simulation scheme, we perform excavation operations in sequence, record the maximum surface subsidence value, and present it in the form of subsidence rate in Fig. 5.
We can first see that the relationship between subsidence rate and overburden's GSI value also relates to mining scale, and it can be very much different at varying stages.When mining the panel 2201, the maximum subsidence rate of Model 1 ( GSI = 75) is only 0.012.This is quite close to that observed in the deep mining areas of the Ordos coalfield (i.e., 0.035 for YPH, 0.093 for BYGL, and 0.033 for NLH), where the rock strata are classified as 'Massive' mostly.Although 0.012 still exhibits a several-fold difference compared to the measured values of 0.035, 0.093, and 0.033, it is evidently more reasonable compared to the results derived based on UCS, such as 0.7 or 0.8, at least placing 0.012 within the same order of magnitude as the measured values.In addition, note that the subsidence rate (0.012) of Model 1 is lower than that observed in all the three coal mines, which suggests that the GSI value of the YPH, BYGL, and NLH coal mines may not exceed 75.
We also see that, when mining the panel 2201, the maximum subsidence rate of Model 2 ( GSI = 50, average quality overburden) and Model 3 ( GSI = 30, very poor quality overburden) reached 0.33 and 0.72, respectively.A subsidence rate of 0.72 is quite common in the eastern mining areas (as can be seen in Table 1), while a subsidence rate of 0.33, although less common, is also recorded in the Table.Specifically, we can find that the subsidence rate (0.33) of Model 2 is similar to that of panel 7005 (0.21) and panel 2408 (0.37).The subsidence rate (0.72) of Model 3, on the other hand, is more similar to the cases of panels 5333 (0.66), 1552-3 (0.77), 1301 (0.82), 14101 (0.86), and 21306 (0.80).Based on this, we may say that the subsidence characteristics of Models 2 and 3 collectively covered the various subsidence phenomena encountered in the mining areas of eastern China, at least for the cases listed in Table 1.Therefore, it can be inferred that the overburden type in the eastern coal mining areas may belong to the very poor quality to average quality with an GSI value possibly ranging between 30 and 50.
When mining the panel 2202 and the subsequent ones, we can observe from Fig. 5 that the subsidence rate gradually increased and eventually tend to converge during the excavation process of each panel between 1300 and 1900 m.This is more clear in Table 4, where we can see that Model 3 basically reaches the critical mining state when the width-to-depth ratio approaches between 1.23 and 1.64, not far from the range of 1.2 to 1.4 given in the textbook 16 .It seems that the empirical width-to-depth ratio of 1.2 to 1.4 is likely derived under the condition of poor to very poor quality overburden (in terms of rock mass classification), and may no longer be appropriate for the overburden of average quality to very good quality.Regarding the later scenarios, it appears, based on the properties provided by Hoek and the modeling methodology, that the critical mining state should be achieved when the width-to-depth ratio reaches between 2.05 and 2.46 for the average quality overburden, and beyond 3.28 for the very good quality overburden.
At last, we can generally conclude from Fig. 5 and Table 4 that the larger the GSI value, the slower the vari- ation of surface subsidence rate, the larger the width-to-depth ratio as it reaches the critical mining state, and the smaller the final subsidence rate.Please also note that the above discussion is for the case of deep mining and the size of panels being 2500 m × 300 m.While this cannot cover all cases encountered in projects, it is quite

Discussion on rationality and irrationality of dividing overburden types based on rock stiffness
According to the modeling results in Section "Relationship between subsidence rate and overburden's typical value" and rock mechanics theories, Table 5 is used to elaborate on why it is unreasonable to estimate the subsidence rate based only on rock stiffness, and where the problem lies.
As listed in Table 5, each type of overburden can be composed of rocks with different stiffness.Specifically, the very good quality overburden can be composed of 'hard' rocks with UCS of 64.8 MPa.This is exactly the case provided by Hoek 52 and investigated as Model 1 in this paper.Also, the very good quality overburden can be composed of 'soft' or 'medium hard' rocks with UCS of around 30 MPa.This is the case in the deep mining areas of the Ordos coalfield, and such rock mass is named 'Super-Thick and Weak Cementation' (STWC) 51 overburden in our previous study.To demonstrate the impact of the two cases on subsidence rates, we added the subsidence variation curve under the condition of the STWC overburden (red dots) in Fig. 6.As can be seen, it is more close to Model 1 than the others, but the overall subsidence is larger, which probably due to their difference in UCS (64.8 MPa vs. 30 MPa).Therefore, based on the simulation results, it seems that the surface  subsidence rate variation curve is more significantly influenced by the type of overburden, or in other words, by the overburden's average GSI value.On the other hand, the very poor quality overburden can be composed of 'hard' rocks with UCS of 60.4 MPa, such as the case of the panel 1552-3 (in PS coal mine, with panel size of 920 m × 160 m and subsidence rate of 0.77) shown in Table 1.If we recall that the subsidence rate of Model 1 (very good quality overburden composed of 'hard' rocks with UCS of 64.8 MPa) is only 0.01 after mining a larger size (2500 m × 300 m), we can, once again, see that it is the type of overburden or the overburden's GSI value, rather than the UCS, that has a much greater impact on mining subsidence.
However, it is additionally important to note that estimating mining subsidence rate by comparing UCS under similar GSI value will still be meaningful.That's probably why the method of dividing overburden into 'hard' , 'medium-hard' , and 'soft' categories had successfully guided a large amount of engineering practices in the mining areas of eastern China (i.e., because the overburden's GSI value in the eastern coal mines are not signifi- cantly different, and under such conditions, the differences in UCS become evident, highlighting their impact on subsidence).But it is more important to stress that if there is an evident difference in the overburden's GSI value at two locations, using traditional indicator of UCS may lead to significant errors, as discussed in Section "Estimating mining subsidence via rock mass classification".
Discussion on the mechanism 'regional strata control' from the perspective of overburden's

GSI value
The relationship between overburden's typical GSI value, subsidence rate, and mining scale also holds a non- conventional strata control method through strip mining or backfill-strip mining, which we refer to as 'large-scale regional strata control' .This is further discussed in this section and can be schematically illustrated in Figs. 7, 8, 9.
Figure 7 schematically shows a general picture of land subsidence and flood after continuous mining 8 longwall panels.Each panel is of 300 m in width, and the total excavated length is 2400 m.Under such scale, and according to the relationship between subsidence rate and mining scale, we have known that the subsidence rate can be 0.99 when the overburden's GSI value is 30.Hence, if the coal thickness is 6.5 m, the original land surface will sink approximately 6.5 m to the new place indicated by the red line (see Fig. 7).A subsidence of 6.5 m is below the groundwater level in many regions of China such as the Yellow-Huaihe Plain (3.8 m in average), the Jingchu Plain (3.9 m), and the Changjiang River Delta Plain (2.5 m).Then, the subsidence basin will become a water-filled pit, greatly changing the original ecological environment.When the overburden's GSI value is 75, on the other hand, subsidence rate can also reach 0.61, which means that the maximum land subsidence is 3.9 m,  www.nature.com/scientificreports/discussed the relationship and applicability conditions between the traditional indicator and the newly proposed one, and finally discussed an unconventional strata control method from the perspective of overburden's average GSI value.The main conclusions of this paper are: (1) The overburden's average GSI value, as a newly proposed indicator for estimating the degree of mininginduced land subsidence, successfully explains the unusual extremely low subsidence rates observed in the YPH, BYGL, and NLH coal mines, which appears to be more comprehensive than the traditional indicator of UCS.(2) According to the borehole log database and the modeling results, the overburden's GSI value in the mining areas of eastern China probably falls within the range of 30 to 55, while that for the mining areas of the deep Ordos coalfield should be between 60 and 75.The much smaller land subsidence rate observed in the YPH, BYGL, and NLH coal mines is essentially because of their much higher overburden's GSI value.(3) When the overburden's GSI values in two locations are relatively close, it is reasonable to use the traditional indicator of UCS to estimate subsidence rates.However, when there is a significant difference in their overburden's GSI values in two locations, using the UCS still may lead to considerable errors.(4) The 'Massive or Intact' rock mass dominated overburden in the deep mining areas of the Ordos coalfield is very well-suited for using a non-conventional strip or backfill-strip mining method (large scale regional strata control) by taking full advantage of the overburden's high GSI value.

,Figure 1 .
Figure 1.Illustration of the relative position of the coal mines mentioned in Table1.

Figure 2 .
Figure 2. The basic GSI chart (modified after Hoek and Brown 44 ) used for estimation of GSI value.

Figure 3 .
Figure 3.Comparison of the measured and computed subsidence values for the 1st, 2nd, 5th, and 8th periods based on the previously calibrated FLAC3D model (reproduced after Gong et al.51 ).The remaining periods (3rd, 4th, 6th, and 7th periods) are omitted because the subsidence changes are not obvious and are difficult to distinguish from the others.

Figure 4 .
Figure 4. Illustration of the established FLAC3D model and schematic of the simulation scheme: (a) FLAC3D model; (b) coal seam; (c) mining sequence to be simulated.

Figure 5 .
Figure 5. Relationship between subsidence rate and mining scale.The top coordinate axis represents the excavation times, and the numbers are consistent with those in Fig. 4.

Figure 7 .
Figure 7. Schematic of land subsidence and flood after continuous longwall coal mining.

Figure 8 .
Figure 8. Schematic of land subsidence control mechanism behind strip mining or backfill-strip mining.

Table 2 .
Comparison between the measured subsidence rates from the BYGL coal mine and the predicted results via the calibrated FLAC3D model for the YPH coal mine.

Table 4 .
The final subsidence rate after total excavation of each panel.

Table 5 .
Relationship between overburden's typical GSI values and rock stiffness. Overburden'