Roof structure of shallow coal seam group mining in Western China

In order to realize roof control of shallow coal seam group mining in Western China, combining with engineering statistics, physical simulation and theoretical analysis, the roof weighting characteristics during lower coal seam mining were revealed, and the classification of shallow coal seam group was proposed. Based on this, mechanical models of roof structure were set up, and the calculation method of support resistance was determined. The results show that the roof weighting is closely related to the interburden thickness and the mining height of lower coal seam, considering the ratio of interburden thickness to the mining height, as well as the key stratum structure, the classification of shallow coal seam group was put forward. The first type is shallow coal seam group with no key stratum (SCSG-No), its roof pressure is mainly affected by caving roof of upper coal seam, and the interburden roof forms slanting pillar-beam structure. The second type is shallow coal seam group with single key stratum (SCSG-S), interburden roof represents step voussoir beam structure. The third type is shallow coal seam group with double key strata (SCSG-D), interburden roof can form double key strata structure, the lower key stratum forms slanting step voussoir beam structure, while the upper key stratum forms voussoir beam structure, besides, longwall face represents large—small periodic weighting. Through establishing the roof structure models, the calculation formulas of support resistance were determined, it can provide basis for roof control and promote safe mining in Western China.


Introduction
Shallow coal seams in Jurassic Coalfield are generally characterized by shallow depth (less than 300 m), small interburden (strata between upper and lower coal seam) thickness (less than 45 m), and 2-3 coal seams are mainly mined, consequently, it belongs to shallow coal seam group mining.
Recently, the upper coal seam in Jurassic Coalfield was already mined out, and mainly mines lower coal seam. During lower coal seam mining, roof weighting is complex, and supports damage caused by dynamic load is more frequent. In 2017, the number of people who died because of coal mine disasters is 357 in China, and 25% of those disasters are roof characteristics are revealed. As the mining height increases, the development height of caving zone increases, meanwhile, the key strata structures are also different, it can form "double key strata", "single key stratum" and "no key stratum" respectively. Therefore, interburden thickness and mining height can affect the key strata structure, and further affect the roof weighting characteristics.
Based on the analysis above, ratio of interburden thickness to the mining height is defined, written as G, which can be used as an index to obtain the classification of shallow coal seam group, based on G and the number of key strata, there are three cases during shallow coal seam group mining:  (1) Interburden with no key stratum. As shown in Fig 2, based on engineering experience, bulking coefficient of immediate roof is 1.3, according to classical theory, the thickness of immediate roof fillings full of goaf is 3.3 times of the mining height. It means that when G is less than 3.3, interburden usually shows as immediate roof and can not form key stratum. Due to the mining height of lower coal seam in Jurassic Coalfield usually is 3-7 m, consequently the interburden thickness that can not form key stratum is usually less than 10-22 m. As shown in Table 1, when G is less than 3.3, there is no key stratum in interburden, dynamic load coefficient is relatively smaller.
(2) Interburden with single key stratum. As shown in Fig 3, according to engineering statistics and physical simulation, periodic weighting interval of the key stratum is generally 8-12 m in Jurassic Coalfield, and the lumpiness (ratio of key stratum thickness to periodic weighting interval) of key stratum is about 1, consequently the thickness of key stratum is about  (3) Interburden with double key strata. As shown in Fig 4, If the thickness of immediate roof is calculated with 3.3 times of the mining height, in addition, both of the key strata thickness is 1-4 times of the mining height, it could be calculated that the interburden thickness with double key strata should be larger than 5.3-11.3 times of the mining height, G should be larger than 5.3-11.3 (As the mining height increases, G decreases). For instance, if the mining height is 3 m and G is 11.3, the interburden thickness with double key strata should be larger than 33.9 m, another instance, if the mining height is 7 m and G is 5.3, the interburden thickness with double key strata should be larger than 37 m, analysis above is also verified in Table 1.

Classification of shallow coal seam group
According to the engineering statistics and theoretical analysis above, based on the key strata in interburden and the index G, shallow coal seam group can be divided into three types below: (1) The first type is shallow coal seam group with no key stratum (SCSG-No). Interburden thickness is generally less than 3.3 times of the mining height, G is less than 3.3. Interburden shows as immediate roof, and it generally can not form key stratum, the dynamic load coefficient is small.
(2) The second type is shallow coal seam group with single key stratum (SCSG-S). Interburden thickness is 4.3-7.3 times of the mining height, and G is about 4.3-7.3. Roof shows as step voussoir beam structure, and the dynamic load coefficient is larger.
(3) The third type is shallow coal seam group with double key strata (SCSG-D). Interburden thickness is larger relatively, and it can form double key strata. Its thickness is   Fig 6. Physical simulation. In order to explore the roof structure of SCSG-No mining, and reveal the mechanism of roof weighting, physical simulation model was built with dimensions of 3 m long × 0.2 m wide × 1.2 m high. The major similarity coefficients were chosen as follows: geometric ratio α l is 1:100, bulk density ratio α γ is 1:1.5, strength ratio α R is 1:150. Considering the lithology and raw material property, during model set up, sand was used as the aggregates, gypsum and calcium carbonate were adopted as cementitious materials, mica powder was used to simulate tectonic fissure, and the physical simulation model is shown in Fig 7. The CL-YB-141 force test sensors were applied to monitor the support load during lower coal seam mining, in addition, digital camera was used to record the deformation and fracture of overburden. Firstly, the No. 2-2 upper seam was excavated, and then the LW22104 in No.

2-2 seam was mined.
Roof structure characteristics. According to the physical simulation, after upper coal seam mining, the caving roof mainly forms two zones (Fig 8), one is "free-caving zone" which the roof can not form articulated beam structure, another is "slanting pillar-beam zone". Voussoir beam is 2 times the length of slanting pillar-beam. During lower coal seam mining, interburden acts as immediate roof, roof caving characteristics are revealed. Caving roof can be divided into three zones, including free-caving zone, compaction zone and separation zone (Fig 9), compaction zone and separation zone are alternate periodically. The load constitution of support is shown in Fig 10, the characteristics of three zones are as follows: (1) Free-caving zone: Roof can not form key stratum and caves in time as the longwall face advances. The load of support is the weight of immediate roof and free-caving zone roof.
(2) Compaction zone: When mining under the voussoir beam blocks 2 and 4 (Fig 9), the upper voussoir beam block can transmit load to lower slanting pillar-beam. The load of support mainly is the weight of immediate roof, load of slanting pillar-beam and the transmitting load of voussoir beam, it results in large periodic weighting.
(3) Separation zone: When mining under the voussoir beam block 3 (Fig 9), there is interlayer separation between block 3 and lower slanting pillar-beam. The load of support is the weight of immediate roof and the load of slanting pillar-beam, it results in small periodic weighting.
Obviously, when mining under compaction zone, the load of support is the largest, and it is also verified by the physical simulation (Fig 11). Overall, taking consideration of the most dangerous situation of roof control, the support resistance should be calculated by compaction zone.    Experimental design. The physical simulation model was built with dimensions of 5 m long × 0.2 m wide × 1.03 m high. Geometric ratio α l is 1:200, and time ratio α t is 0.071. The raw materials of rock strata were consistent with experiment above-mentioned, as for red soil, it was found that sand and bentonite was the best aggregates, and silicone oil was the best cementitious material [27].
Firstly, the No. 1-2 seam was excavated, and then the lower No. 2-2 seam was mined. The force test sensor was applied to monitor the support load during mining, in addition, in order to obtain the transmitting load of upper goaf, the CL-YB-152 force test sensors with  dimensions of 0.2 m long × 0.025 m wide × 0.01 m high, were applied at the top of the interburden (Fig 13).
Roof structure characteristics. As the lower coal seam mining, firstly, immediate roof fractures and caves, then, the single key stratum fractures periodically and forms step voussoir beam, the key stratum mainly bears the transmitting load of upper goaf (Fig 14). Fig 15  shows the load of support with the longwall face advances, working resistance during periodic weighting is 9695.5-10592.7 kN, based on engineering practice of LWN1206, the maximum working resistance was 10794 kN, consequently physical simulation and engineering practice are basically consistent.

Physical simulation of SCSG-D
The No. 2-2 seam in Ningtiaota coal mine is 5 m thick on average, the No. 3-1 seam is 2.8 m thick, interburden thickness is 33.7 m and G is 12. therefore, it belongs to SCSG-D. The geometric ratio is 1:200.
As the longwall face advances, the lower key stratum fractures firstly, roof pressure is less intense (Fig 16), as the longwall face continues to advance, the double key strata fracture simultaneously, which results in intense roof pressure (Fig 17).

Roof structure model of SCSG-No mining
Mechanical model of roof structure. The support resistance should be determined in accordance with the most dangerous situation of roof structure. According to the analysis above, when mining under compaction zone, it results in large periodic weighting. Based on this, establishing roof model of SCSG-No mining as Fig 18. Where, ω 1 is the subsidence of voussoir beam, m; θ is the rotation angle of voussoir beam,˚; h is the thickness of voussoir beam, m; P 0 is the transmitting load of voussoir beam structure, kN; L 1 is the length of slanting pillar-beam, m; N 1 and N 2 are reaction force on slanting pillarbeam M and N respectively, kN; m 1 is the mining height of upper seam, m; K p is bulking coefficient; G is the weight of slanting pillar-beam, kN; α is caving angle of slanting pillar-beam,˚; q is uniform distributed reaction force of interburden on upper roof, kN/m.    Calculation method of support resistance. Putting the whole of slanting pillar-beam M and N as one object, according to SF X = 0, SM 0 = 0, SM F = 0, the formulas are listed below: Where, b is the width of support, m; ρ 1 g is the bulk density of slanting pillar-beam, kN/m 3 ; m 2 is the mining height of lower coal seam, m; Sh is the thickness of immediate roof, m.
The transmitting load of voussoir beam structure is: Where, P G is the weight of voussoir beam block, kN/m; ρg is the bulk density of voussoir beam, kN/m; The overlying strata form "load-off arch" above the voussoir beam, Q is the weight of "load-off arch", kN/m. According to the Protodyakonov theory [28], Q is: Where, ρ 1 g is the bulk density of strata in "load-off arch", kN/m 3 ; f is the Protodyakonov coefficient.
The rational support resistance P is made up with the weight of immediate roof W and transmitting load of slanting pillar-beam structure: Where, W is the weight of immediate roof, kN; l k is the roof-control distance of support, m; ρ 1 g is the bulk density of interburden, kN/m 3 .
Based on formulas (1)-(4), q can be determined as: Based on formulas (6)-(11), considering supporting efficiency μ = 0.9, the rational support resistance of SCSG-No mining is: Engineering practice. The LW12102 mines No.1-2 seam in Shigetai coal mine, its mining height is 2.8 m and dips 1-3˚. The LW101 mines No. 1-2 upper seam, mining height is 2 m, interburden thickness is 4.0 m and G is 2.2, therefore, it belongs to SCSG-No mining. The DBT8824/17/35 supports are adopted in LW12102 (Table 2)  with formula (12) and calculation parameters above, the rational support resistance is: According to mining practice of LW12102, the maximum working resistance of No.124 support was 8900 kN, the supports were applied successfully. Therefore, theoretical calculation is basically consistent with engineering practice results.

Roof structure model of SCSG-S mining
Mechanical model of roof structure. Based on the classification, interburden strata can form single key stratum, taking roof structure theory of typical shallow coal seam for reference [2], the single key stratum forms "step voussoir beam structure", and caving roof of upper coal seam is simplified as uniform distributed load. T he roof structure model with single key stratum is established and shown in Fig 19. Where, m 2 is the mining height of lower coal seam, m; Sh is the thickness of immediate roof, m; h is the thickness of key stratum, m; h 1 is the thickness of load strata, m; L 1 is the length of step voussoir beam block, m; R 1 is the sliding pressure of block M, kN; R 2 is the weight of load strata and block M, kN; q is the uniform distributed load, kN/m; θ 1 is rotation angle of block M,˚; ω 1 is the subsidence of block M, m.
Calculation method of support resistance. The rational support resistance P is made up with the weight of immediate roof W and the sliding pressure of step voussoir beam According to step voussoir beam theory [2]: Where, W is the weight of immediate roof, kN; ρ 1 g is the bulk density of immediate roof, kN/m 3 ; P 0 is the load of block M and its overlying strata, kN; i is lumpiness of step voussoir beam block M; θ 1max is the maximum rotation angle of block M,˚. P 0 is made up with two parts, one is the weight of block M and load strata R 2 , and another is the weight of caving roof of upper coal seam R 3 , formula (11) can provide reference for the determination of q.
Where, ρg is the bulk density of step voussoir beam block, kN/m 3 ; ρ 1 g is the bulk density of load strata, kN/m 3 .
Based on formulas (13)- (18), the reasonable support resistance is:  (19) and calculation parameters above, the rational support resistance is: According to the engineering practice of LW21305, during periodic weighting, working resistance was 10887 kN on average, and the largest working resistance was 11160 kN, the supports were applied successfully. Based on theoretical calculation, the rational support resistance is 10987.8 kN, therefore, it is basically consistent with engineering practice results.

Roof structure model of SCSG-D mining
Mechanical model of roof structure. According to physical simulation, lower key stratum fractures firstly and forms "slanting step voussoir beam structure", roof represents small periodic weighting, then, the double key strata fracture simultaneously, and the upper key stratum forms "voussoir beam structure", roof represents large periodic weighting. Considering the most dangerous situation, the support resistance should be determined by large periodic weighting, its roof structure model is established, shown as Fig 20. Where, P 0 is the weight of voussoir beam block M 1 and its overlying strata, kN; ω 2 is the subsidence of voussoir beam block M 1 , m; L 2 is the length of voussoir beam block M 1 , m; R 3 is the sliding pressure of voussoir beam M 1 , kN; ω 1 is the subsidence of block M, m; R 2 is the weight of block M and lower load strata, kN; θ is the rotation angle of block M,˚; R 1 is the sliding pressure of block M, kN; L 1 is the length of slanting step voussoir beam block M, m; α is the caving angle,˚; h 2 is the thickness of upper key stratum, m; h is the thickness of lower key stratum, m; h 3 is the thickness of upper load strata, m; h 1 is the thickness of lower load strata, m; Sh is the thickness of immediate roof, m; m 2 is the mining height of lower seam, m.
Calculation method of support resistance. The rational support resistance P is made up with the weight of immediate roof W and the sliding pressure of slanting step voussoir beam structure R 1 . The upper key stratum, mainly affecting the support resistance through transmitting its load to the lower key stratum structure. Based on this, the support resistance is: According to slanting step voussoir beam theory, R 1 is determined by the formula below: sin a cosða À yÞ þ L 1 2 cos y h sin a sinða À yÞ À o 1 À 0:5a Where, W is the weighting of immediate roof, kN; ρ 1 g is the bulk density of immediate roof, kN/m 3 ; a is the height of squeezing face, m; φ is the friction angle,˚; P 1 is the load of slanting step voussoir beam block M, kN. https://doi.org/10.1371/journal.pone.0255047.g020 P 1 is made up with two parts, one is the weight of slanting step voussoir beam block M and lower load strata R 2 , and another is transmitting load R 3 by voussoir beam block M 1 .
R 2 and R 3 are determined by the following formulas [29]: Where, φ is the friction angle,˚; ρg is the bulk density of lower key stratum, kN/m 3 ; ρ 1 g is the bulk density of lower load strata, kN/m 3 . P 0 is determined by the following formula [30]: Where, ρg is the bulk density of upper key stratum, kN/m 3 ; K G is load transmitting coefficient; ρ 1 g is the bulk density of upper load strata and caving roof, kN/m 3 .
According to the previous studies [2], ω 1 � ω 2 = m 2 −(K p −1)∑h, K p = 1.3, θ and a can be ignored due to the little effect on calculation results. Based on formulas (20)- (26), the rational support resistance of large periodic weighting is:  (27) and calculation parameters above, the rational support resistance is: According to engineering practice of LWN1200, during large periodic weighting, the working resistance was 13872 kN, the roof pressure was intense with rib spalling, the supports (Working resistance is 12000 kN) could not satisfy the roof support demand, the rational support resistance by theoretical calculation is 13810kN, therefore, it is also consistent with engineering practice results.

Conclusions
During shallow coal seam group mining in Western China, the roof weighting is mainly affected by key stratum structure of interburden, and the key stratum structure is closely related to interburden thickness and mining height of lower coal seam. The ratio of interburden thickness to the mining height is defined as a comprehensive index to divide shallow coal seam group, written as G.
Based on the key strata in interburden and the index G, shallow coal seam group can be divided into three types. The first type is SCSG-No, interburden can not form key stratum structure and shows as immediate roof, G is less than 3.3, and roof forms slanting pillar-beam structure. The second type is SCSG-S, G is about 4.3-7.3, interburden can form single key stratum. The third type is SCSG-D, G is about 5.3-11.3, interburden forms double key strata, the lower key stratum forms slanting step voussoir beam structure, and the upper key stratum forms voussoir beam structure.
SCSG-No, roof weighting is mainly affected by caving roof structure of upper coal seam, when mining under compaction zone, the load of support is the largest. SCSG-S, interburden roof represents step voussoir beam structure. SCSG-D, longwall face has large and small periodic weighting, when the double key strata fracture simultaneously, the roof is the most dangerous. Through establishing the roof structure models, the calculation formulas of support resistance are put forward, and they are verified by engineering practice.