Evaluation of water inrush from underlying aquifers by using a modified water-inrush coefficient model and water-inrush index model: a case study in Feicheng coalfield, China

Abstract

Water inrush from underlying aquifers seriously threatens mining of Permo-Carboniferous coal seams in many North China coalfields. To evaluate the risk of water inrush from underlying aquifers, a modified water-inrush coefficient method—using the water inrush coefficient (T) and geological structure index (G)—and a water-inrush index model (WII model) were proposed. The T_G model improved the traditional water-inrush coefficient method by quantifying the degree of geological structure development, considering three main controlling factors: G, aquifer water pressure (P) and aquitard thickness (M). The WII model was constructed to assess the risk of floor water inrush by the entropy weight method, which integrated six factors: G, P, M, the depth at which ground pressure creates a broken-rock zone (C_p), aquifer water yield property (Y), and percentage of brittle rock within the aquitard (B). Results from the engineering practice data analysis validated the T_G and WII models as operational tools to evaluate the risk of water inrush from an underlying aquifer. The comparative analysis of the predictions by these two models shows that the prediction accuracy of the WII model is 13% higher than that of the T_G model, and approximately 21% of the two model predictions are not in agreement. A more reasonable prediction was obtained with application of the T_G and WII models to Feicheng coalfield in Shandong Province to evaluate water inrush risk from the underlying aquifer, and the prediction offers guidance on different preventive measures against water hazards in the underlying Ordovician limestone in the different zones.

Résumé

L’émergence d’eau issue des aquifères sous-jacents menace sérieusement l’exploitation des veines de charbon du Permo-Carbonifère dans de nombreux bassins houillers en Chine du Nord. Pour évaluer le risque d’émergence d’eau issue des aquifères sous-jacents, une méthode modifiée de coefficient d’émergence d’eau—utilisant le coefficient d’émergence (T) et l’indice de structure géologiques (G)—et un modèle d’indice d’émergence d’eau (modèle WII) sont proposées. Le modèle T_G a amélioré la méthode traditionnelle du coefficient d’afflux d’eaux souterraines en quantifiant le degré de développement de la structure géologique, compte tenu de trois principaux facteurs de contrôle: G, la pression de l’eau dans l’aquifère (P) et l’épaisseur de l’aquitard (M). Le modèle WII a été élaboré pour évaluer le risque d’afflux d’eaux souterraines au niveau du sol à l’aide de la méthode de pondération de l’entropie, qui intègre six facteurs: G, P, M, la profondeur à laquelle la pression du sous-sol crée une zone de fragilité de la roche (C_p), le coefficient d’emmagasinement de l’aquifère (Y), et le pourcentage de roche fragilisée au sein de l’aquitard (B). Les résultats de l’analyse des données des pratiques d’ingénierie ont validé les modèles T_G et WII en tant qu’outils opérationnels pour évaluer le risque d’afflux d’eaux souterraines issues d’un aquifère sous-jacent. L’analyse comparative des prévisions de ces deux modèles montre que la précision des prévisions du modèle WII est 13% supérieure à celle du modèle T_G, et environ 21% des prévisions des deux modèles ne sont pas concordantes. Une prévision plus réaliste a été obtenue en appliquant les modèles T-G et WII sur le bassin houiller de Feicheng dans la province de Shandong pour évaluer le risque d’afflux d’eaux souterraines issues de l’aquifère sous-jacent, et la prévision offre des conseils sur les différentes mesures à mettre en œuvre pour se prémunir des dangers d’émergence d’eaux souterraines issues des calcaires sous-jacents de l’Ordovicien dans différentes zones.

Resumen

La filtración de agua de los acuíferos subyacentes amenaza seriamente la explotación minera de los yacimientos de carbón de Permo-Carboníferos en muchos de aquellos situados en el norte de China. Para evaluar el riesgo de filtración de agua desde los acuíferos subyacentes, se propuso un método modificado de coeficiente de filtración—utilizando el coeficiente de filtración (T) y el índice de estructura geológica (G)—y un modelo de índice de filtración (modelo WII). El modelo T_G mejoró el método tradicional del coeficiente de filtración cuantificando el grado de desarrollo de la estructura geológica, considerando tres factores principales de control: G, la presión del agua del acuífero (P) y el espesor del acuífero (M). El modelo WII se construyó para evaluar el riesgo de filtración desde el piso mediante el método del peso de la entropía, que integró seis factores: G, P, M, la profundidad a la que la presión del terreno crea una zona de roca rota (C_p), propiedad de rendimiento de agua del acuífero (Y), y porcentaje de roca quebradiza dentro del acuífero (B). Los resultados del análisis de datos de la práctica de ingeniería validaron los modelos T_G y WII como herramientas operativas para evaluar el riesgo de la filtración desde un acuífero subyacente. El análisis comparativo de las predicciones de estos dos modelos muestra que la precisión de la predicción del modelo WII es un 13% mayor que la del modelo T_G, y aproximadamente el 21% de las dos predicciones del modelo no están de acuerdo. Se obtuvo una predicción más razonable con la aplicación de los modelos T_G y WII al yacimiento de carbón Feicheng en la provincia de Shandong para evaluar el riesgo de filtración de agua desde acuífero subyacente, y la predicción ofrece orientación sobre diferentes medidas preventivas contra los peligros del agua en la caliza ordovícica subyacente en las diferentes zonas.

摘要

在中国很多华北型煤田,煤层底板含水层突水问题严重威胁石炭-二叠系煤层的开采。本文提出了一种改进的突水系数法(融合突水系数T与构造复杂指数G)与突水危险性指数法(WII模型)来评价煤层底板含水层突水危险性。T_G模型通过定量化构造发育复杂程度改进了传统的突水系数法,考虑了G,含水层水压(P)和隔水层厚度(M)三个主控因素。采用熵权法建立了WII模型,该模型融合了G,P,M,底板破坏深度(C_p),含水层富水性(Y)和脆性岩比率(B)六个主控因素。工程实践数据分析结果验证表明,T_G和WII模型是煤层底板含水层突水危险性评价的一种有效方法。综合分析表明,WII模型的预测精度比T_G模型高13%,并且有近21%的样本预测结果是不同的。将T_G和WII模型综合应用于山东省肥城煤田底板含水层突水危险性评价,得到了较为合理的预测结果,为不同区域的奥陶系灰岩含水层的水害防治措施提供了依据。

Resumo

A afluência a partir de aquíferos subjacentes é uma ameaça séria em minerações de carvão do Permo-Carbonífero no norte da China. A fim de avaliar o risco de afluência de aquíferos subjacentes, foram propostos um método modificado de coeficiente de afluência—usando o coeficiente de afluência (T) e o índice de estrutura geológica (G)—e um modelo de índice de afluência (modelo WII). O modelo T_G aperfeiçoou o método tradicional de coeficiente de afluência através da quantificação do grau de desenvolvimento de estruturas geológicas, considerando três fatores principais de controle: G, pressão da água do aquífero (P) e espessura do aquitardo (M). O modelo WII foi elaborado para estimar o risco de afluência a partir do piso através do método de peso de entropia, que integrou seis parâmetros: G, P, M, a profundidade na qual a pressão no piso cria uma zona de ruptura na rocha (C_p), rendimento do aquífero (Y), e porcentagem de rocha fraturada no aquitardo (B). Os resultados da análise de dados da prática de engenharia validaram os modelos T_G e WII como ferramentas operacionais para avaliar o risco de afluência de aquífero subjacente. A análise comparativa das previsões desses dois modelos mostra que a precisão do modelo WII é 13% maior em relação ao modelo T_G, e aproximadamente 21% das previsões dos dois modelos não estão em concordância. Uma previsão mais razoável foi obtida a partir da aplicação dos modelos T_G e WII para a jazida de carvão de Feicheng na Província de Shandong para avaliar o risco de afluência a partir do aquífero subjacente, e a previsão oferece orientação sobre medidas distintas de prevenção contra perigos hídricos no calcário Ordoviciano subjacente em zonas diferentes.

Introduction

The primary North China coalfields are the Permo-Carboniferous coalfields distributed mainly in the Shanxi, Shandong, Henan, Hebei, Anhui, and Shaanxi Provinces. These coal seams are typically exploited via underground mining but at the risk of water inrush from underlying confined aquifers (Sun et al. 2015), especially those in Ordovician limestone. More than 200 water inrushes from Ordovician limestone have occurred in North China coalfields over the past 40 years, resulting in economic losses of more than 30 billion yuan and 1,300 deaths (Qiu et al. 2017a; Shi et al. 2015). Water problems in deep mining become increasingly serious as the mining depth increases (Gu et al. 2010); therefore, evaluating the water inrush risk from underlying aquifers is important to help control mine water hazards, and several evaluation methods have been developed over the past decades (Li et al. 2018; Wu et al. 2007). Among them, the water-inrush coefficient method has been widely used and plays an active role in assessing the risk of water inrush from underlying aquifers. However, due to the qualitative description of the degree of geological structure development and the few controlling factors considered, applications of the method are limited. Another important method is the analytic hierarchy process (AHP) vulnerability index method proposed by Wu and Zhou (2008), which integrates multiple factors and has many potential advantages for assessing the probability of water inrush; however, the weights of the factors used in this method were assigned based on expert opinions, and included subjective judgments that vary for different individuals (Chang et al. 2007; Saaty 1980). Several mathematical methods have been introduced to assess the risk of water inrush, including the gray relational analysis, support vector machine (SVM), artificial neural network (ANN), random forest (RF), and unascertained measure theory, and these methods have enhanced the assessment of water inrush risk (Qiu et al. 2017b; Shi et al. 2017; Wang et al. 2012; Wu et al. 2008, 2017; Zhao et al. 2018); however, these methods have limitations for practical application. As an example, the gray relational analysis needs more water inrush cases to calculate the relative importance of each major controlling factor based on the geometric distance between the factors and the maximum water yield, but the maximum water yield does not well represent the risk of water inrush; the SVM model is limited because of its complex mathematical functions; the ANN model and RF can experience over learning, and their prediction processes are not well suited for field specialists because predicting a new case necessitates additional modeling and prediction; and in the unascertained measure theory (UMT), the constant weights of the factors are assigned based on subjective expert opinions.

In this study, a modified water-inrush coefficient method (T_G model) and a water-inrush index model (WII model) were proposed for comprehensive evaluation of the risk of water inrush from underlying aquifers into coal seams. The T_G model was developed by a comprehensive analysis of the water inrush coefficient (T) and geological structure index (G) based on water inrush cases, to improve the conventional water-inrush coefficient method that provides a fundamental basis for a water-inrush risk assessment. Meanwhile, the water-inrush index model (WII model), integrating multiple factors influencing water inrush, was established by the entropy weight method (EWM), which objectively assigns weights based on information given by an attribute database of factors, providing a more detailed scientific basis for water-inrush risk assessment. Data analysis of engineering practices was applied to verify the accuracy of the prediction results. A more reasonable prediction was accomplished by comprehensive application of these two model predictions to develop a zoning map of the water inrush risk, providing a more detailed scientific basis for safe production and control of water inrush.

Study area

The Feicheng coalfield is located in Feicheng City, Shandong Province in northern China, covering an area of approximately 120 km² that includes seven coal mines: Chazhuang, Guozhuang, Baizhuang, Taoyang, Dafeng, Caozhuang, and Yangzhuang mines from west to east. The coalfield region has a semiarid climate and warm temperatures. The average annual precipitation is approximately 662 mm, and the average annual evaporation is 442 mm. The overall geological structure of the coalfield is a monocline dipping to the north, accompanied by small folds. The dip angle is mainly 5–10°, but locally can be more than 20°. The faults are well developed with the main striking NE, NNE, NW, and ENE (Fig. 1).

Fig. 1

Location of the study area in Shandong Province, China, and the geological structure of the Feicheng coalfield

According to outcrop observations and drilling data, the strata in the Feicheng coalfield are of the Ordovician system (O), Carboniferous system (C), Permian system (P), Paleogene system (E), and Quaternary system (Q), from oldest to youngest. The coal-bearing strata in the Feicheng coalfield originated during the Permo-Carboniferous period. These strata include five primary mineable seams: No. 3₁ in the Shanxi Formation (F) and Nos. 7, 8, 9, and 10₂ coal seams in Taiyuan F (from top to bottom). Coal seams Nos. 8, 9, and 10₂ are threatened by underlying limestone aquifers, especially the fifth limestone aquifer of Taiyuan F and the Ordovician karst limestone aquifer. During mining of the No. 8 coal seam, 29 water inrushes from the fifth limestone aquifer and one extra-large-scale, two large-scale, and one medium-scale water inrushes from the Ordovician limestone aquifer occurred. The Ordovician limestone aquifers have abundant water with a large thickness of approximately 800 m and a high hydraulic pressure exerted by the upper confining bed. With increasing mining depth, the hydrogeological conditions become more complicated, and safe extraction of the No. 8 coal seam is increasingly threatened by the underlying Ordovician limestone aquifer.

Methodology

Modified water-inrush coefficient model

Water inrush coefficient

The water-inrush coefficient method was put forward for assessing the risk of water inrush from underlying aquifers in the 1960s and is stipulated in the “Regulations for Coal Mine Water Prevention and Control, China” (Ministry of Coal Industry 2009) which was modified several times. According to the latest Coal Mine Water Control Rules (Ministry of Coal Industry 2018), the water inrush coefficient is expressed as Eq. (1).

$$ T=\frac{P}{M} $$

(1)

where T is the water inrush coefficient, indicating the bearing pressure of the unit aquitard thickness (MPa/m); P is the aquifer water pressure sustained by the coal seam floor (MPa), which was calculated according to the elevation difference between the aquifer water level and the Ordovician limestone top in this study; and M is the aquitard thickness (m) which is defined as the distance between coal floor and aquifer floor, and the data of M was acquired from the geo-exploration. The data of P and M were processed using the SURFER software and interpolated with the Kriging function interpolation technique to create a contour map, respectively. The study area was divided into 500 m × 500 m grids by using longitudinal and latitudinal lines, and the values of P and M in each grid unit were obtained by interpolation of the established contour maps—Table S1 of the electronic supplementary material (ESM). Finally, the water inrush coefficient was computed using Eq. (1) in each grid unit, and the contour map of the water inrush coefficient was constructed using the Kriging function interpolation technique (Fig. 2).

Fig. 2

Contour map of the water inrush coefficient (T)

The Coal Mine Water Control Rules (Ministry of Coal Industry 2018) gives the critical value of water inrush. Water inrushes tend not to occur if T < 0.06 MPa/m in simple structural areas and T < 0.10 MPa/m in complex structural areas. The water-inrush coefficient method is simple and practical; therefore, it is widely applied and has an active role in assessing the risk of water inrush from underlying aquifers in China. However, the qualitatively described simple and complex structural areas are difficult to distinguish, resulting in subjective judgments that vary for different individuals; therefore, a modified water-inrush coefficient model should be proposed based on T and geological structure development degree.

Geological structure development degree

First, the degree of geological structure development, which has a significant influence on water inrush, was quantified. In the Feicheng coalfield, the faults associated with folds are well developed (Fig. 1), revealed by 3D-seismic exploration, geo-exploration, and roadway and workface extractions. Fault throw and strike length can reflect fault intensity, which is very closely related to water inrush (Qiu et al. 2017b). Faults with large fault throws and long lengths decrease the performance of an aquitard in preventing floor water inrush. Faults can also decrease the distance between coal seams and aquifers and even cause coal seams to connect with aquifers. The fault intensity index (I_FI) is defined as (Xu et al. 1991):

$$ {I}_{\mathrm{FI}}=\frac{\sum \limits_i^n{l}_i{h}_i}{S} $$

(2)

where I_FI is the fault intensity index, h_i is the ith fault throw (m), l_i is the ith fault’s strike length (m), S is the area with a grid unit size of 500 m × 500 m (m²), and i = 1, 2, …, n, where n is the total number of faults in each grid unit. The values of the fault throw and strike length of each fault were determined according to the map of the geological structure of the Feicheng coalfield (Fig. 1), which was drawn based on 3D-seismic exploration, geo-exploration, and roadway and workface extractions data, and then the I_FI value was obtained for each grid unit. The contour map of the fault intensity index was established by SURFER software using the Kriging function interpolation technique, as shown in Fig. 3.

Fig. 3

Contour map of the fault intensity index (I_FI)

The other important fault factor is the density of the fault intersections and endpoints (D_FIE), which reflects the extent of coal floor strata fracturing (Wu et al. 2011). Rock is more crushed and fractures are more developed at the intersections and endpoints of faults where ground stress tends to concentrate. The density of fault intersections and endpoints is the sum of all the intersections and endpoints of all faults divided by the grid unit area and is calculated by Eq. (3) (Wu et al. 2011):

$$ {D}_{\mathrm{FIE}}=\frac{n}{S} $$

(3)

where D_FIE is the density of fault intersections and endpoints (/m²), n is the total number of fault intersections and endpoints of all faults in each grid unit, and S is the area of the grid unit (m²). The number of fault intersections and endpoints in each 500 m × 500 m grid unit was counted according to the map of the geological structure of the Feicheng coalfield (Fig. 1), and the D_FIE value was obtained for each grid unit. The contour map of the density of fault intersections and endpoints was established by SURFER software and shown in Fig. 4.

Fig. 4

Contour map of the density of fault intersections and endpoints (D_FIE)

The density of the fold-axis length (D_FAL) is the main factor describing the fold distribution. Along the length of the fold axis, fractures are well developed which are destructive to the integrity and continuity of the coal floor strata. Even small folds can create water-inrush risk zones. D_FAL is calculated by the following equation (Qiu 2016).

$$ {D}_{\mathrm{FAL}}=\frac{\sum \limits_t^r{L}_t^2}{S} $$

(4)

where L_t is the tth fold’s axis length in a grid (m); S is the area with a grid unit size 500 m × 500 m (m²); and t = 1, 2, …, r, where r is the total number of folds in each grid unit. The length of each fold axis was counted to calculate D_FAL for each 500 m × 500 m grid unit, and the contour map of the fold-axis length density was established by SURFER software, as shown in Fig. 5.

Fig. 5

Contour map of the fold-axis length density (D_FAL)

After collecting each factor, the data should be normalized by relativization to make the data comparable and statistically significant because the different dimensions of the factors could unduly influence the evaluation results (Ma 2003), as shown in (Wu et al. 2011):

$$ {A}_i=a+\frac{\left(b-a\right)\times \left({x}_i-\min \left({x}_i\right)\right)}{\max \left({x}_i\right)-\min \left({x}_i\right)} $$

(5)

where A_i is the normalized data; a and b are the lower and upper limits of normalization, respectively (a = 0.1, and b = 0.9); x_i is the original data before normalization; and min(x_i) and max(x_i) are the minimum and maximum values.

Finally, a geological structure index (G) was established to quantify the degree of geological structure development based on normalized I_FI, D_FIE and D_FAL values. Based on practical experience, the field specialists (Jinwei Ma, Xiujun Zhang) and professors (Yongkui Shi, Jiuchuan Wei) working with the mines in the coalfield assigned weights of P₁ = 0.5, P₂ = 0.2, and P₃ = 0.3 to I_FI, D_FIE and D_FAL, respectively. The geological structure index (G) was calculated as:

$$ {\displaystyle \begin{array}{c}G={P}_1\cdot {I_{\mathrm{FI}}}^{\prime }+{P}_2\cdot {D_{\mathrm{FI}\mathrm{E}}}^{\prime }+{P}_3\cdot {D_{\mathrm{FAL}}}^{\prime}\\ {}=0.5{I_{\mathrm{FI}}}^{\prime }+0.2{D_{\mathrm{FI}\mathrm{E}}}^{\prime }+0.3{D_{\mathrm{FAL}}}^{\prime}\end{array}} $$

(6)

where G is the geological structure index; I_FI′, D_FIE′ and D_FAL′ are normalized values of the fault intensity index, quantity of fault intersections and endpoints, and fold-axis density, respectively, and P₁, P₂, and P₃ are the weights of the aforementioned factors.

Based on the geological structure index model, the value of the geological structure index in each 500 m × 500 m grid unit was obtained by using Eq. (6), and the contour map of the geological structure index was established by SURFER software, as shown in Fig. 6. The geological structure index is 0.087–0.666 in the study area, indicating large changes in the degree of geological structure development. A larger geological structure index value indicates a more complicated geological structure development degree.

Fig. 6

Contour map of the geological structure index (G)

To distinguish the simple and complex structural areas, the values of the geological structure index at 33 water inrush points were gathered (Fig. 6) and a histogram of the water-inrush point distribution is shown in Fig. 7. The geological structure index values of all water inrush points are greater than 0.137, indicating that the geological structure is the main factor controlling water inrush in the region where G ≥ 0.137. Therefore, G = 0.137 was taken as the partition threshold, and the structure development degree was divided into two distinct zones (Fig. 6):

• 1. Simple structural areas: G < 0.137, in only small parts of the study area, mainly distributed in the southern area and a small part of the western area

• 2. Complex structural areas: G ≥ 0.137, in two-thirds of the study area mainly distributed in the northern, eastern, and western areas of the study area

Fig. 7

Histogram of the distribution of water inrush points

T_G evaluation model

According to the Coal Mine Water Control Rules (Ministry of Coal Industry 2018), the modified water-inrush coefficient model for the risk evaluation of water inrush was established by comprehensive analysis of T and G and called the T_G evaluation model, or simply “T_G”, as shown in the following:

$$ T\_G=\left\{0.06\le \begin{array}{c}T<0.06\kern0.5em \left(\mathrm{safe}\right)\kern1em \\ {}T<0.10,\mathrm{and}\ \left\{\begin{array}{c}G<0.137\ \left(\mathrm{safe}\right)\kern1.5em \\ {}G\ge 0.137\kern0.5em \left(\mathrm{dangerous}\right)\end{array}\right.\\ {}T\ge 0.10\ \left(\mathrm{dangerous}\right)\end{array}\right. $$

(7)

As shown in Eq. (7), the water-inrush risk evaluation rules based on the T_G evaluation model are as follows: (1) the risk of water inrush is classified as safe when one of the following occurs: T < 0.06 MPa/m or 0.06 ≤ T < 0.10 MPa/m and G < 0.137; and (2) the risk of water inrush is classified as dangerous when one of the following occurs: T ≥ 0.10 MPa/m or 0.06 ≤ T < 0.10 MPa/m and G ≥ 0.137.

Water-inrush index model

Factors

The modified water-inrush coefficient model considers three main factors: aquifer water pressure (P), aquitard thickness (M), geological structure index (G). The aquifer water yield property (Y), mechanical strength of an aquitard denoted by the percentage of brittle rock within the aquitard (B), and the depth at which a zone of broken rock forms under the pressure associated with mining—hereafter, the ‘depth of broken rock created by ground pressure’ (C_p)—were neglected. Therefore, a water-inrush index model that integrates six factors, including P, M, C_p, G, Y, and B, was then proposed to improve the prediction results based on the entropy weight method.

• 1. Aquifer water pressure (P). Water inrush from an underlying aquifer results from pressure constantly acting on the upper confining bed of the aquifer below (Wu et al. 2011). As aquifer water pressure increases, coalmines are at a higher risk of water inrush. The data source of the aquifer water pressure is the same as that for the P in Eq. (1), and includes the same calculation method.

• 2. Aquitard thickness (M). Aquitards act as geologic barriers and can prevent water in an underlying aquifer from flowing into mines. One of the factors indicating the water-resistant ability of an aquitard is aquitard thickness. A thicker aquitard provides better protection. The data source of the aquitard thickness is the same as that of the M in Eq. (1).

• 3. Depth of broken rock created by ground pressure (C_p). During mining, the ground pressure caused by mining inevitably damages the surrounding floor rock. C_p is defined as the distance between the coal seam floor and the deepest boundary of the floor rock damaged by the ground pressure. A larger C_p results in a greater relative risk of water inrush. The C_p value can be calculated with reference to Pillar design and mining regulations under buildings, water, rails and major roadways (National Bureau of Coal Industry of China 2000), by using the following empirical formula:

  $$ {C}_{\mathrm{p}}=0.0085H+0.1665\alpha +0.1079L-4.3579 $$

  (8)

  where C_p indicates the depth of broken rock created by ground pressure (m); H indicates the mining depth (m), which was acquired from 3D-seismic exploration, geo-exploration, and roadway and workface constructions; α indicates the dip angle of the No. 8 coal seam (°), which was acquired from geo-exploration, and roadway and workface constructions; and L indicates the mining width of the mining face (m), which was acquired from actual mining width where the No. 8 coal seam was mined, and which was 105 m where the No. 8 coal seam has not been mined.

• 4. Geological structure index (G). The geological structure is the key to water inrush from the underlying aquifer. The geological structure index calculated by Eq. (6) was adopted for water inrush forecasting.

• 5. Aquifer water yield property (Y). The aquifer water yield property is a key factor in coal floor water inrush and indicates the productivity of an aquifer. The yield is directly reflected by the unit water inflow, which was obtained from pumping tests of hydrogeological boreholes.

• 6. Percentage of brittle rock within the aquitard (B). The percentage of brittle rock within the aquitard is another factor affecting the water-resistant ability of the aquitard, which was calculated by dividing brittle rock thickness by the aquitard thickness based on the geo-exploration data. Brittle rock tends to have a higher water-resisting ability than plastic rock (Li 2000; Meng et al. 2012); thus, the greater the percentage of brittle rock within the aquitard, the lower the probability of water bursts (Wu and Zhou 2008).

The data of P, M, C_p, G, Y, and B were processed using the SURFER software and interpolated with the Kriging function interpolation technique to create six thematic maps, shown in Fig. 8.

Fig. 8

Thematic map of the main water inrush factors: a aquifer water pressure, b aquitard thickness, c depth of broken rock created by ground pressure, d geological structure index, e aquifer water yield property, and f percentage of brittle rock within the aquitard

Data normalization and the database

The values of six main factors including P, M, C_p, G, Y, and B were collected in 479 grid units of 500 m × 500 m and four water inrush points by interpolation of the established thematic maps (Fig. 8). Then, normalization by relativization was carried out to make the data comparable and statistically significant using the following equation (Qiu et al. 2017b):

$$ {A}_i=\left\{\begin{array}{c}a+\frac{\left(b-a\right)\times \left({x}_i-\min \left({x}_i\right)\right)}{\max \left({x}_i\right)-\min \left({x}_i\right)},\mathrm{where}\ x\ \mathrm{is}\ \mathrm{a}\ \mathrm{positive}\ \mathrm{factor}\\ {}a+\frac{\left(b-a\right)\times \left(\max \left({x}_i\right)-{x}_i\right)}{\max \left({x}_i\right)-\min \left({x}_i\right)},\mathrm{where}\ x\ \mathrm{is}\ \mathrm{a}\ \mathrm{negative}\ \mathrm{factor}\end{array}\right. $$

(9)

In this paper, the positive factors are P, C_p, G, and Y, which indicate a higher risk when the factor value is larger, and the negative factors are M and B, which indicate a lower risk when the factor value is larger. After data normalization, an attribute database of the six normalized main factors (P′, M′, C_p′, G′, Y′, and B′) was established for constructing the evaluation model of water inrush index by EWM (Table S1 of the ESM).

Evaluation model of water inrush index by the entropy weight method (EWM)

The concept of entropy in information theory was proposed by Shannon (1948) and then widely employed in engineering fields. Entropy is a measure of the degree of uncertainty represented by a discrete probability distribution, which objectively weights factors based on the information given by the attribute database of the six main factors (Table S1 of the ESM) as a feasible scientific method. The greater the difference between factors, the smaller the entropy, indicating a larger weight factor. Four steps were followed to determine the objective weights of the six main factors (Wang et al. 2018):

• 1. Construction of the decision matrix (Wang et al. 2018).

  $$ R=\left(\begin{array}{ccc}{x}_{11}& \cdots & {x}_{1n}\\ {}\vdots & \ddots & \vdots \\ {}{x}_{m1}& \cdots & {x}_{mn}\end{array}\right) $$

  (10)

  where x_ij is the value of the ith evaluated-sample jth factor in Table S1 of the ESM; i = 1, 2, …, m; j = 1, 2, …, n; and m and n are the total number of evaluated samples and factors, respectively. In this paper, m = 483 and n = 6.

• 2. Calculation of the project outcomes, p_ij (Wang et al. 2018).

  $$ {p}_{ij}=\frac{x_{ij}}{\sum_{i=1}^m{x}_{ij}} $$

  (11)

• 3. Calculation of the entropy of the jth factor (Wu et al. 2015).

  $$ {E}_j=-\frac{1}{\ln m}{\sum}_{i=1}^m{p}_{ij}\ln {p}_{ij} $$

  (12)

• 4. Establishment of the entropy weight of the jth factor (Huang et al. 2017).

  $$ {\omega}_j=\frac{1-{E}_j}{\sum \limits_{j=1}^n\left(1-{E}_j\right)} $$

  (13)

In this study, a 483 × 6 decision matrix was established for the following calculations based on the attribute database of the six normalized main factors (P′, M′, C_p′, G′, Y′, and B′; Table S1 of the S1). Following the above steps, the entropy E and entropy weight ω of each factor were obtained as shown in Table 1. The weights of P, M, C_p, G, Y, and B were 0.169, 0.046, 0.177, 0.195, 0.293, and 0.120, respectively.

Table 1 The values of entropy E and entropy weight of each main factor of water inrush

The water inrush index (WII) can be defined as the comprehensive criterion of floor water-inrush risk of an evaluated sample. As for an evaluated sample, every main factor acts together and forms the comprehensive criterion. The water inrush index for each evaluated sample can be expressed as follows:

$$ \mathrm{WII}={\sum}_{j=1}^n{\omega}_j\cdot {f}_j\left(x,y\right) $$

(14)

where WII is the water inrush index; n is the number of main factors of water inrush considered, which is six in this paper; j = 1, 2, …, n indicates the sequence number of the main factors; and f_j (x, y) is the normalized value of the jth factor at the geographic location (x, y) of the evaluated sample. Based on the attribute database of the six normalized main factors and the weights listed in Table 1, the risk evaluation model for floor water inrush of the No. 8 coal seam in the Feicheng coalfield was ultimately established as follows:

$$ \mathrm{WII}={\sum}_{j=1}^n{\omega}_j\cdot {f}_j\left(x,y\right)=0.169P^{\prime }+0.046M^{\prime }+0.177{C}_{\mathrm{p}}^{\prime }+0.195G^{\prime }+0.293Y^{\prime }+0.120B^{\prime } $$

(15)

where P′, M′, C_p′, G′, Y′, and B′ are the normalized factors P, M, C_p, G, Y, and B, respectively.

The values of WII for areas where water inrush occurred and areas where safe mining was achieved were calculated to determine the partition threshold, and using this threshold, the risk of water inrush can be classified into two zones. The partition threshold is defined as follows:

$$ {T}_{\mathrm{s}-\mathrm{d}}={\left(\max \left({\mathrm{WII}}_{\mathrm{s}}\right)\cdot \min \left({\mathrm{WII}}_{\mathrm{d}}\right)\right)}^{1/2} $$

(16)

where T_s-d is the partition threshold that separate safe areas and dangerous areas; WII_s indicates the value of the water inrush index in the area where safe mining was achieved; and WII_d indicates the value of the water inrush index in the area where water inrush occurred. Thus, the water inrush risk from an underlying aquifer can be divided into two zones:

• Zone I in which WII < T_s-d, indicating a safe scenario

• Zone II in which WII ≥ T_s-d, indicating a dangerous scenario

Results and discussion

Results

The values of T and G were calculated for each 500 m × 500 m grid unit. Based on the T_G evaluation model, the risk-evaluation grade was realized. Meanwhile, a water-inrush risk zone map based on the T_G model was constructed by integrating the information storage layers of the water inrush coefficient (Fig. 2) and geological structure index (Fig. 6) into one layer (Fig. 9). As shown in Fig. 9, the study area was divided into two zones based on the T_G model: safe and dangerous. Among these, dangerous zones with high water inrush potential accounted for 65% of the total area, and these zones are located in the western and northern areas of the study area. Especially in the northwest part of the study area, water inrushes are most likely to occur with bigger values of T and G, because the water pressure is high and the degree of geological structure development is complicated. The safe zones are mainly located in the southern part and small southwestern part of the study area where the water pressure is low and the degree of geological structure development is simple.

Fig. 9

Water-inrush risk zone by the T_G model

The value of WII was obtained for each 500 m × 500 m grid unit based on the water-inrush index model. All grid unit data were then processed by using Surfer software. The WII contour model map was constructed by using the Kriging function interpolation technique, as shown in Fig. 10. The water inrush risk of the No. 8 coal seam from the underlying Ordovician limestone aquifer expressed by WII ranges from 0.164 to 0.587. The higher the WII value, the greater the probability of water inrush. To determine the partition threshold for the dangerous and safe zones, the values of WII were calculated for the four water inrush points and 70 safe mining units (Table 2). The minimum value of WII for the four water inrush points was 0.306, and the maximum value of WII for the four water inrush points was 0.305 (excluding two outliers in Nos. 58 and 155 in Table 2). Thus, the partition threshold was calculated based on Eq. (16) as T_s-d = 0.305, and the risk of water inrush in the No. 8 coal seam from the underlying aquifer was classified into two zones (Fig. 10):

• Zone I: WII < 0.305, safe zone with a small likelihood of water inrush, mainly located in the eastern, southern, and southwest parts of the study area.

• Zone II: WII ≥ 0.305, dangerous zone where water inrushes are most likely to occur, mainly in small parts of the western, northwestern, and northern areas of the study area. This risk zone occupies approximately 58% of the total area.

Fig. 10

Water-inrush risk zone by the WII model

Table 2 Comparison between the practical outcomes and the prediction results from the T_G and WII models

Validation of the predictions

Validation is crucial to verify results; therefore, to verify the accuracy of the prediction results based on the T_G and WII models proposed in this paper, validation tests were carried out by comparing the prediction results with practical results. A total of 74 test samples, including four water inrush points from the Ordovician limestone aquifer and 70 safe mining units, were collected to test the prediction results. The results predicted by these two methods and the practical results obtained for the 74 test samples are shown in Table 2.

Figure 11 shows the comparison between the prediction results from the T_G model and the practical outcomes for the 74 test samples. Among these 74 test samples, 11 samples were safe for mining but were classified as dangerous, and one sample with water inrush occurred but was classified as safe by the T_G model. Thus, the verification rate of the T_G model prediction was 84%.

Fig. 11

Comparison between the practice outcomes and prediction results by the T_G model

Figure 12 illustrates the comparison between the results predicted by the WII model and the practical outcomes for the 74 test samples. The predicted results for four water inrush points by the WII model were in agreement with the actual results. Only two samples that are safe in reality were predicted to be dangerous based on the WII model; thus, the verification rate of the WII model prediction was up to 97%, indicating that the predicted results align well with the actual results.

Fig. 12

Comparison between the practical outcomes and the prediction results from the WII model

Comparative analysis, and comprehensive application of the two methods

Based on the validation of the prediction results from these two methods, the accuracy of the methods is at least 84%. Both the T_G and WII models have satisfactory prediction abilities, but the prediction accuracy of the WII model is 13% higher than that of the T_G model. The zones of water inrush risk derived from the T_G and WII models were compared. For 79% of the assessment samples, the prediction results from the T_G and WII models were the same and were mainly distributed in the northern areas where T is greater than 0.1 MPa/m and the southern areas where T is smaller than 0.06 MPa/m (Figs. 9 and 10; whereas for 21% of the samples, the T_G model and WII model predictions are the opposite. Forty-two assessment samples were classified as safe by the WII model, but these samples were classified as dangerous by the T_G model in the areas where 0.06 ≤ T < 0.10 MPa/m (Fig. 9). In these areas, although the geological structure development degree is complex and the aquitard thickness is thin, the percentage of brittle rock within the aquitard is relatively high, indicating the strong mechanical strength of aquitards with complex geological structure development degree; thus, the aquifer water yield properties are poor (Fig. 8). By properly considering the influence of the mechanical strength of the aquitard and the water yield property, these 42 assessment samples were predicted to be safe from water inrush by the WII model, which was counter to the predictions from the T_G model. The remaining 61 assessment samples in areas where T < 0.06 MPa/m were classified as dangerous by the WII model, and safe by the T_G model (Fig. 9). The reasons for these results are that the water resistance of an aquitard with a thin thickness and low percentage of brittle rock is low and the water yield property is rich in these areas, but the water pressure and C_p values are small (Fig. 8).

Based on the validation, a risk assessment of coal floor water inrush based on the T_G model and WII model is satisfactory. However, according to the comparative analysis of the predictions from these two methods, approximately 21% of the predictions were not in agreement; therefore, more reasonable predictions can be achieved by combining the predictions from the T_G and WII models. The comprehensive application of the predictions from the T_G and WII models was proposed to evaluate the risk of water inrush from an underlying aquifer and used to divide the water inrush risk from an underlying aquifer into two zones and two subzones, as shown in Fig. 13.

• 1. Zone I: safe zone predicted by both the T_G and WII models, mainly distributed in the southeastern part and small parts of southwestern part in the study area.

• 2. Zone II: dangerous zone where at least one of the model predictions was dangerous and this zone was divided into two subzones:

  • a. Zone II-1: a relatively dangerous zone that is a transition zone between a safe zone and an extremely dangerous zone.

  • b. Zone II-2: extremely dangerous zone where predictions from both the T_G and WII models were dangerous; this zone type was mainly located in the northwestern part and small parts of the southwestern part in the study area.

Fig. 13

Water-inrush risk zones by comprehensive application of the predictions from the T_G and WII models

The water-inrush risk zone map (Fig. 13) created after comprehensive application of the predictions from the T_G and WII models offers guidance on preventive measures necessary in the study area. Different preventive measures against water hazards associated with the underlying Ordovician limestone are proposed for the different zones as follows:

• 1. Safe zones: Monitor and investigate. The changes in inflow and aquifer water level variations must be monitored. Second, investigations on geological structures in the Ordovician limestone aquifer should be carried out. However, exposure of water-conductive geologic structures should be avoided and impermeable coal pillars should be retained based on the Coal Mine Water Control Rules (Ministry of Coal Industry 2018).

• 2. Relatively dangerous zones: These zones must be monitored and investigated. Additionally, impermeable coal pillars should be retained, as in the safe zones, and abnormal observations should be reported in a timely manner. Second, the weak zone of the aquitard, the water properties of the Ordovician limestone aquifer, and the potential of water-conducting faults should be explored by drilling, geophysical exploration and other means. If indications are found, advanced grouting should be performed in water-rich areas, structural weak zones, and weak aquitards with thin thicknesses and low percentages of brittle rock.

• 3. Extremely dangerous zones: In addition to the conventional measures used in relatively dangerous zones, grouting should be used at the mining face, in conjunction with a drainage method. Pregrouting reinforcement of floor strata should be performed to strengthen and improve floor strata and the top of Ordovician limestone, to change the Ordovician top aquifer into a relatively water-resistant strata and to minimize the water inrush risk.

Conclusions

• 1. Water inrush from an underlying aquifer is a prominent problem threatening coal mine safety. It is essential but challenging to assess the risk of water inrush from an underlying aquifer. The T_G and WII models were comprehensively applied to refine the water-inrush risk zones in the No. 8 coal seam from the Ordovician limestone aquifer in Feicheng coalfield, China. The T_G model improved the traditional water-inrush coefficient method by quantifying the geological structure development degree, which considers three main controlling factors: P, M, and G. Based on the T_G model, the study area was divided into two zones: safe zones where T < 0.06 MPa/m or 0.06 ≤ T < 0.10 MPa/m and G < 0.137, which were mainly distributed in the southern part and small southwestern part of the study area, and dangerous zones where T ≥ 0.10 MPa/m or 0.06 ≤ T < 0.10 MPa/m and G ≥ 0.137, which were mainly located in the western and northern areas of the study area. Meanwhile, the WII model was constructed to assess the risk of floor water inrush by EWM, which integrated six factors, including P, M, C_p, G, Y, and B. The predicted water-inrush risk zones were divided into two zones: safe zones (WII < 0.305), mainly in the east, south, and southwest; and dangerous zones (WII ≥ 0.305), mainly in a small part of the western, northwestern, and northern parts of the study area.

• 2. Validation results from an analysis of the engineering practices showed that the risk assessment of a coal floor water inrush based on the T_G model and WII model is satisfactory. Based on the comparative analysis of predictions from these two models, the prediction accuracy of the WII model is 13% higher than that of the T_G model, and approximately 21% of the model predictions were not in agreement, which is partly because the T_G model neglects the influence of the aquifer water yield property, the depth of broken rock created by ground pressure and the percentage of brittle rock within the aquitard on water inrush, and also because the classification rules are different. Inevitably, the prediction quality of the methods should be further improved as more data are added.

• 3. A more reasonable prediction was finally accomplished by comprehensive application of the predictions from the T_G model and WII model to evaluate the risk of water inrush from an underlying aquifer. The comprehensive application of these two models allowed subdivision of the study area into two zones and two subzones, offering guidance on different preventive measures against water hazards in the underlying Ordovician limestone in the different zones.