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Nov 04, 2024

Predictive model for the instability of flexible formwork concrete wall in secondary mining of non-pillar coal mining | Scientific Reports

Scientific Reports volume 14, Article number: 21684 (2024) Cite this article 340 Accesses Metrics details The secondary mining movement in non-pillar coal extraction causes significant overrun damage

Scientific Reports volume 14, Article number: 21684 (2024) Cite this article

340 Accesses

Metrics details

The secondary mining movement in non-pillar coal extraction causes significant overrun damage to flexible formwork concrete walls, leading to extensive deformation of roadway roof and bottom plates. This adversely affects working face efficiency and safety. The engineering context focuses on the non-pillar gob-side retaining walls in the 1315 working face of Zhaozhuang Coal Mine and the 23107 working face of Xiegou Coal Mine. Through on-site investigation, numerical simulation, theoretical analysis, and testing, we explore the stress migration law and destabilizing mechanism of the flexible formwork concrete wall influenced by the secondary mining movement of the coal-free pillar along the hollow wall. The research results showed that: (1) During the mining back process, the concrete wall formed with flexible formwork may experience stress concentration, leading to excessive damage and compromising mining safety. (2) Developing a predictive stress model for the concrete wall with flexible formwork is essential. If the stress surpasses the ultimate compressive strength during mining back, reinforcement becomes necessary.3) The length of damage overrun in the flexible formwork concrete wall exhibits two distinct stages as the distance back to mining increases. The first stage shows nearly linear growth, while the second stage indicates a decreasing growth rate, ultimately stabilizing. The application of Z6 concrete reinforcing agent effectively strengthens the flexible formwork concrete wall.

Coal, holding a predominant position in energy consumption, plays a pivotal role in China, the globe’s leading coal producer and consumer. However, the challenges faced by the traditional stay-on-sector pillar mining method in terms of increasing coal extraction rate, reducing resource waste, and alleviating mining challenges have become increasingly evident1,2. Therefore, increasing the efficiency of coal mining, reducing resource waste3,4,5,6, and safeguarding the safety of workers, minimising the impact on the environment have become urgent needs in the field of coal mining7,8,9. Non-pillar mining technology has attracted attention because of its ability to significantly increase coal production and reduce resource waste10,11,12,13. However, this technique is often accompanied by roadway deformation14,15,16. Because the roadway needs to go through three stages of digging, mining in the current face (primary mining), mining in the next face (secondary mining), and after the current face has been mined, the roadway is affected by the collapse of the roof slab at the rear, which will cause serious and continuous deformation, resulting in the preserved roadway being deformed even more easily during mining in the next face. During this period, most of the coal gang anchors fail, resulting in the roadway shrinkage of both gangs generally more than 1.5 m, the bottom bulge more than 1.5 m, and the roof plate broken and sinking. Especially in the presence of soft coal zones or tectonic zones, the deformation becomes more pronounced, posing a threat to both roadway stability and ventilation efficiency17,18. To solve this problem, along-the-air retaining walls are being widely used as effective technological tool19,20,21,22. In this technique, flexible concrete formwork walls are installed instead of the original coal pillars to maintain the stability of the roadway and simultaneously achieve efficient coal mining23,24,25. Nonetheless, the primary design challenge for along-the-air retaining walls stems from the intricate subsurface environment. Factors such as elevated subsurface pressures, intricate geological conditions, and the existence of groundwater may impact the stability of the flexible-moulded concrete wall, consequently influencing roadway stability and safety26,27,28. Therefore, predicting when and where a retaining wall along the air space may become unstable under the influence of secondary mining is of far-reaching theoretical and practical significance for optimising the design and improving the safety and mining efficiency of coal mines.

Numerous scholars worldwide have conducted relevant research and exploration along an empty wall29,30. Hai et al.31 studied the perimeter rock stability control technology of the perimeter rock along an empty wall and verified its perimeter rock stress evolution and deformation characteristics during coal mining through numerical simulation. Shuai32 examined the evolution pattern of perimeter rock stress around the roadway, the plastic zone distribution, and the deformation characteristics throughout the mining phase. An in-depth exploration was carried out on the construction process of the perimeter rock along an empty wall. They also discussed the construction process and the steps involved in it. Jun et al.33 investigated the evolution traits of the structure in the peripheral rock along the open roadway. They proposed comprehensive methods to secure the stability of the remaining roadway, including reinforcement through inorganic grouting, enhancing the roof and gang structure, and optimizing high-resistance support within the roadway. Sheng et al.34 investigated the formation mechanism and bearing characteristics of asymmetrically anchored deep-beam bearing structure. Jun et al.35 explored the partial stress and plastic zone distribution and evolution in the surrounding rock of the open channel during mining. They unveiled the mechanism of asymmetric deformation and destruction. Chang et al.36 examined the adaptability of concrete walls formed with flexible formwork in the open channel. This investigation encompassed aspects such as structural form, destructive process, intrinsic relationship, and bearing capacity. Additionally, they outlined the design process for a block-type open channel. Peng et al.37 explored the stress and deformation distribution features in the surrounding rock, flexible formwork wall, and coal pillars of the open channel during the mining stage. They put forward suitable measures for support. Xiao et al.38 examined the mechanism leading to cracking and damage in the flexible formwork body along the hollow stay lane. They conducted an analysis of the exothermic characteristics of the filling material through a hydration heat measurement test and simulated the temperature field evolution of the lane-adjacent wall using ANSYS software. Qing et al.39 explored the motion patterns of the overlying rock in the quarry and the features of the lane-supporting structure adjacent to the lane. They established a simplified elasticity mechanics model for calculating the support reaction force and analyzed how the width and elasticity modulus of the filling body impact the width and elastic modulus of the support reaction force. Wang et al.40 regarding the determination of the width of the ribbed concrete roadway along shallowly buried coal seams, research findings indicate that choosing a ribbed wall width greater than 1.5 m effectively reduces stress concentration in both the ribbed wall and surrounding rock, ensuring the stability of the ribbed wall during mining operations. Yang et al.41 during excavation phases, minimal roof deformation and symmetric stress distribution are observed, whereas during secondary extraction stages, roof displacements are pronounced. The research underscores the importance of studying roof deformation throughout the entire mining cycle. Shan et al.42 regarding the bottom heave deformation monitoring along the goaf of the Zhongxing Mine, research indicates that bottom heave deformation primarily occurs during excavation and excavation stabilization stages, first mining advance stage, post-first mining stage, and second mining advance stage. Among these, the post-first mining and second mining advance stages are the main periods of bottom heave deformation, accounting for over 90% of the total deformation. Bottom heave deformation during the second mining period far exceeds that during the first mining period. Excessive bottom heave deformation can lead to instability and failure of side support in the roadway. Wu et al.32 research has found that significant stress concentration occurs in the front and side solid coal walls ahead of the working face, with plastic zone width and failure depth increasing with mining progress. Deformation in the roadway decreases progressively from behind the working face, highlighting the significant protective role of backfill support systems, ensuring sufficient time for the flexible wall structure to achieve the expected strength.

Existing research has conducted in-depth studies on the stability control, structural evolution characteristics, stress and deformation behavior, as well as construction processes and design of flexible concrete walls. However, there is still a lack of predictive research on when and where flexible concrete walls might become unstable under the impact of secondary mining. Therefore, this study uses the 1315 working face of Zhaozhuang Coal Mine and the 23,107 working face of Xiegou Coal Mine in Shanxi as engineering backgrounds. By employing field surveys, numerical simulations, theoretical analysis, and on-site experiments, the study investigates the stress migration patterns and instability mechanisms of flexible concrete walls under secondary mining impacts, and develops a stress prediction model for these walls. The research results not only achieve prediction of the advanced failure of flexible concrete walls but also propose reinforcement methods based on the stress prediction model, providing significant theoretical support for pillarless mining in Chinese coal mines.

Through the Shanxi Zhaozhuang and Xiegou coal mines, buried depth of 700 and 300 m, respectively, the thickness of the coal seam for the 5 and 7 m non-coal pillars along the wall of the face mining process on-site measurement and analysis found that if the soft formwork concrete wall occurs in the pre-stabilisation of the damage to the roadway top and bottom plates, it will cause a relatively large amount of deformation, which ensures the stability of the soft formwork concrete wall to ensure the necessary conditions for the safety of the production face. Examining the destructive process and mechanical mechanisms of flexible formwork concrete walls, we utilized the engineering context of non-coal pillars along the empty wall working face in Shanxi Zhaozhuang coal mine 1315 and Xiegou coal mine 23,107. The top and bottom slab’s physical and mechanical parameters for the rock layer are provided in Tables 1 and 2.

The numerical simulation software FLAC3D was selected for this study. Numerical models were established based on the Zhaozhuang Coal Mine and Xiegou Coal Mine in Shanxi, considering variations in coal seam depth and flexible concrete wall dimensions, and adjusting coal seam thickness based on the engineering background. The model dimensions were x (width) × y (thickness) × z (height), set at 220 m × 400 m × 100 m. This size was chosen based on the actual geological conditions of the mining area to effectively reflect the stress distribution and deformation characteristics of the working face and surrounding rock. To improve calculation accuracy, the overall grid size was set to 5 m, with a finer grid of 1 m around the coal seam to more precisely capture the stress and deformation details near the coal seam. A schematic of the model is shown in Fig. 1.

During the model calculation, the bottom was fixed to simulate the solidity of the actual strata, the sides were constrained to limit normal displacement, and the top was replaced with a surface force to reflect the pressure exerted by the overlying rock layers on the coal seam. Initial stress values were assigned based on geostress measurement results, with gravitational acceleration g = 9.81 m/s² considered. The Mohr-Coulomb constitutive model was used to simulate the mechanical behavior of the coal-rock mass, as it can reasonably replicate the failure process of the surrounding rock under stress conditions. The support strength for the roadway bolts (cables) was replaced with an equivalent support strength of 0.5 MPa to simplify the complexity of the support system in the simulation while maintaining its load-bearing capacity.

To mitigate boundary effects on the simulation results, a 50 m-wide boundary coal pillar was established around the model. The extraction length of the model was set to 300 m based on the actual mining length of the working face. The physical and mechanical parameters are shown in Tables 1 and 2.

The experiment was conducted in four steps to reflect the construction sequence and stress variation patterns in real engineering. The first step involved excavating Transportation Lane 1 and Return Air Lane 1 after initial stress equilibrium to simulate the stress release in the surrounding rock due to initial excavation. The second step involved mining Working Face 1 and constructing the flexible concrete wall adjacent to Working Face 1 in Transportation Lane 1 to simulate concurrent operations in actual construction. The third step involved excavating Transportation Lane 2 after the completion of mining and wall construction in Working Face 1, to simulate the impact of lane extension on the overall stress field. The fourth step involved mining Working Face 2, analyzing the stress changes and stability of the flexible concrete wall during the second mining process. The mining and excavation steps were set to 3 m, with each run consisting of 10,000 time steps to ensure convergence and accuracy of the simulation results. During the mining of Working Face 2, measurement points were set every 1 m along the centerline of the flexible concrete wall to monitor vertical stress changes. A schematic of the working face and flexible concrete wall is shown in Fig. 2.

Numerical model diagram.

The schematic diagram of working face and the flexible formwork concrete wall.

This study involved creating 18 models to vary both the coal seam depth and the dimensions of the flexible formwork concrete wall. The depth was specified as 300 and 700 m, while the height of the concrete wall was varied at 1, 3, and 5 m. Additionally, the width of the flexible formwork concrete wall was set at 1, 1.5, and 2 m. Refer to Table 3 for details on the specific numerical simulation test schemes.

During back mining of working face 2, in every 20 m of mining, the data were recorded once: (1) The stress values were extracted at each measurement point on the line of measurement. (2) The yield state of the flexible mould concrete wall was recorded. (3) Maps depicting the stress and displacement clouds of the rock surrounding the roadway were recorded.

(1) To analyse the scenario with a burial depth of 300 m, Scheme 7 was selected, considering the heightened risk of plastic damage with increased height and reduced thickness of the flexible formwork concrete wall. Figures 3 and 4, ,5 and 6 illustrate the stress distribution cloud diagram, longitudinal displacement diagram of the surrounding rock, and distribution diagram of the damaged unit in Scheme 7, respectively. Given the numerous excavation steps, analysis focused on four representative stages.

Vertical stress cloud diagram. (a) Mining Distance 20 m, (b) Mining Distance 100 m, (c) Mining Distance 200 m, (d) Mining Distance 280 m.

Stress profile of flexible concrete wall.

Longitudinal displacement diagram of roadway surrounding rock. (a) Mining Distance 20 m, (b) Mining Distance 100 m, (c) Mining Distance 200 m, (d) Mining Distance 280 m.

Distribution of damage units. (a) Mining Distance 20 m, (b) Mining Distance 100 m, (c) Mining Distance 200 m, (d) Mining Distance 280 m.

As depicted in Fig. 3, stress concentration manifests in the flexible concrete wall ahead of the working face during the initial mining stages. Moving farther from the working face, the impact of stress concentration diminishes, and the stress distribution gradually stabilizes. Throughout the mining process, there is a progressive increase in the degree of stress concentration, resulting in a trapezoidal stress distribution. This phenomenon originates from the stress redistribution mechanism during the mining process, which forms a clear stress concentration area.

As can be seen from Fig. 4, with the advancement of mining, the stress exceeded 12 MPa at some stages, and the rise of stress was mainly related to the stress redistribution of the surrounding rock during the advancement of the working face as well as the mining disturbance of the working face. With the increase of mining distance, the original stress balance of the surrounding rock was gradually destroyed, leading to the concentration of stress in the local area to the flexible concrete wall. When the mining distance is 20 m and 100 m, the surrounding rock near the roadway still has a strong supporting capacity, and the stress on the flexible concrete wall is relatively small. The stress curve shows a relatively gentle upward trend, indicating that flexible concrete wall has not yet been affected by the significant concentration of stress in the surrounding rock. When the mining distance is 200 m and 280 m, with the depth of the working face, the stress in the surrounding rock is concentrated to the unmined area and the flexible concrete wall, resulting in a significant increase in stress. At the location where the measurement point is more than the mining distance from the open cut eye, the stress on the flexible concrete wall shows a decreasing phenomenon. The decrease is fast at the beginning and then gradually flattens out, indicating that the stress concentration on the flexible concrete wall is not obvious at the unmined location. The overall change of the curve is directly related to the stress concentration and mining disturbance caused by the face mining. With the increase of mining distance, the stress of the surrounding rock is gradually redistributed due to mining disturbance, and the stress on the flexible concrete wall changes accordingly.

As depicted in Fig. 5, throughout the entire mining back process, the top plate of the final roadway experienced a maximum displacement of 138 mm, while the bottom plate reached 67 mm. This deformation falls within acceptable limits, indicating a reasonable pressure distribution and stable stress field distribution under this particular scheme.

Illustrated in Fig. 6, plastic deformation in the flexible formwork concrete wall occurs at the rear of the working face during the initial mining stages. However, this plastic deformation has no impact on the flexible formwork concrete wall in front of the working face, mitigating the risk of accidents. Around the 280 m mining distance, the portion of the flexible formwork concrete wall within 1–3 m in contact with the top and bottom plates experiences advanced plastic damage but doesn’t result in extensive plastic deformation. This deformation is attributed to the increased stress concentration with the deepening of coal mining. Consequently, the flexible formwork concrete wall in front of the working face undergoes stress surpassing its compression strength, leading to plastic deformation. This phenomenon validates the previously mentioned stress concentration.

(2) A scheme with a buried depth of 700 m was analysed. The stress concentration phenomenon of this scheme is similar to that of Scheme 7; only the concentration degree is greater and the stress is greater. Hence, a dedicated analysis was not conducted, and only the plastic deformation and longitudinal displacement diagrams were scrutinized in depth. Due to the extensive array of scenarios and excavation steps, representative scenarios and mining stages were chosen for analysis. Figures 7 and 8, and 9 depict the distribution of damage units in the flexible formwork concrete wall and the longitudinal rock displacement diagram of the surrounding roadway in schemes 12, 14, and 16, respectively.

Scheme 12 distribution of damage units of flexible formwork concrete wall and longitudinal displacement diagram of roadway surrounding rock. (a) Mining 100 m damage unit distribution, (b) Mining 200 m damage unit distribution, (c) Mining 280 m damage unit distribution, (d) Mining 280 m displacement diagram.

Scheme 14 distribution of failure elements of flexible formwork concrete wall and longitudinal displacement diagram of roadway surrounding rock. (a) Mining 180 m damage unit distribution, (b) Mining 180 m displacement diagram, (c) Mining 220 m damage unit distribution, (d) Mining 220 m displacement diagram, (e) Mining 260 m damage unit distribution, (f) Mining 260 m displacement diagram.

As evident in Fig. 7, throughout the entire mining process in Scheme 12, the flexible formwork concrete wall did not exhibit advanced plastic damage. The ultimate displacement of the top plate of the roadway reached 150 mm, and the displacement of the bottom plate was 77.6 mm, both falling within acceptable limits. This suggests a rational pressure distribution, a stable stress field distribution, and low stress concentration within the flexible formwork concrete wall.

As depicted in Fig. 8, within Scheme 14, as the mining distance increases, there is a growing occurrence of overrun damage in front of the flexible formwork concrete wall. Notably, at a mining distance of 260 m, a substantial area experiences extensive over-advanced damage approximately 1–15 m in front of the flexible formwork concrete wall. The displacement of the top plate of the roadway reaches 609 mm, and the bottom plate displacement is as high as 250 mm. The escalating degree of stress concentration in the flexible formwork concrete wall leads to its destruction, significantly impacting the normal operation of the transportation and ventilation systems.

As depicted in Fig. 9, within Scheme 16, even at a mining distance of only 100 m, a limited occurrence of over-advanced damage begins to emerge approximately 1–8 m in front of the flexible formwork concrete wall. During this phase, the displacement of the top plate of the roadway reaches 213 mm, and the bottom plate displacement is 115 mm. This indicates that the stress concentration in this scheme is excessively high, leading to over-advanced damage at the early stages of the mining process. By the time the mining distance reaches 180 m, overrun damage extends to approximately 1–12 m in front of the flexible formwork concrete wall. The displacement of the top plate of the roadway is 650 mm, and the bottom plate displacement is 216 mm, causing notable deformation that significantly impacts the transportation and ventilation system. When the mining distance reaches 240 m, a considerable range of overrun damage emerges in front of the flexible formwork concrete wall. At this point, the displacement of the top plate of the roadway is 1050 mm, and the bottom plate displacement reaches 650 mm, signifying a high degree of stress concentration that surpasses the bearing capacity of the flexible formwork concrete wall. This triggers an extensive overrun damage, rendering the working face unsafe for mining. Hence, measures such as top and bottom plate treatment are imperative.

Scheme 16 distribution of failure elements of flexible formwork concrete wall and displacement diagram of longitudinal rock around roadway. (a) Mining 100 m damage unit distribution, (b) Mining 100 m displacement diagram, (c) Mining 180 m damage unit distribution, (d) Mining 180 m displacement diagram, (e) Mining 240 m damage unit distribution, (f) Mining 240 m displacement diagram.

In the mining process, the stable condition of the flexible formwork concrete wall involves the redistribution of roof stress post-coal seam extraction. To maintain elastic equilibrium, the maximum principal stress after redistribution must not exceed the elastic limit of the flexible formwork concrete wall. Plastic deformation occurs when the stress surpasses the wall’s elastic limit.

In the coal mining industry, understanding the stability of the rock strata in the working face and its dynamic patterns is crucial for ensuring safe and secure mine production. Owing to the complex geological conditions of the mine, the force state and rupture development of the rock layer have a high degree of uncertainty; therefore, it is important to realise safe and efficient mining by analysing and fitting the existing measured data, establishing a prediction model, and quantitatively analysing the stability of the rock layer in the mine. Based on this, a prediction model for the instability of a flexible formwork concrete wall was established using the stress change data of the flexible formwork concrete wall in the numerical simulation.

Flexible formwork concrete wall instability prediction models have been proposed, including statistical regression, mechanics, and pattern recognition models. In recent years, as a research hotspot for pattern recognition methods, the support vector machine (SVM) method has received considerable attention43,44.

The support vector machine (SVM) stands out as a relatively recent approach in pattern recognition. Its fundamental concept involves nonlinearly mapping data to a high-dimensional kernel space. The key strategy is to maximize the boundary, constructing an optimal classification hyperplane with a low VC dimension in this kernel space. In contrast, traditional statistical pattern recognition methods rely on theoretical guarantees for their performance when the sample tends to infinity, essentially functioning as asymptotic theories. In comparison, SVM is a small-sample learning method with a robust theoretical foundation. The main feature is that it introduces structural risk minimisation instead of empirical risk minimisation, which can effectively avoid the problems of over-learning, dimensionality catastrophe, and local minima that exist in classical learning methods, has a good generalisation ability, and has been successfully applied in various classification and regression problems43.

Support vector machines: For a nonlinear classification problem, the training set is given\(\:T=\left\{\left({x}_{1},{y}_{1}\right),\cdots\:,\left({x}_{l},{y}_{l}\right)\right\}{\left({R}^{n}\times\:Y\right)}^{l}\), where,\(\:{x}_{i}\in\:{R}^{n},{y}_{i}\in\:Y=\left\{1,-1\right\},\)\(\:i=1,\cdots\:,l\), introduce a kernel function \(\:K({x}_{i},{x}_{j})\) and a penalty parameter \(\:C>0\), construct and solve a convex.

Quadratic programming problem:

S.T.: \(\:{\sum\:}_{i=1}^{l}{\alpha\:}_{i}{y}_{i}=0\), \(\:0\le\:{\alpha\:}_{i}\le\:C\), where \(\:i=1,\cdot\:\cdot\:\cdot\:,l\)。

Solving Eq. (1) yields the value of the Lagrangian coefficient as \(\:{\alpha\:}^{*}={\left({\alpha\:}_{1}^{*},\cdots\:,{\alpha\:}_{l}^{*}\right)}^{T}\);

The decision function is constructed as:

where: \(\:{b}^{*}={y}_{j}-{\sum\:}_{i=1}^{l}{y}_{i}{\alpha\:}_{i}^{*}K({x}_{i},{x}_{j}),\forall\:j\in\:\left\{j\right|{\alpha\:}_{j}^{*}>0\}\)。

From the decision function expression (2), it can be noted that not all of the training samples contribute, but only part of the training samples corresponding to the components \(\alpha _{i}^{*}\) of the solution \({\alpha ^*}\)of the quadratic programming problem described above are nonzero, that is, only the training samples corresponding to the support vectors contribute to the decision function.

Flexible formwork concrete wall instability is a typical nonlinear complex problem that is suitable for the use of support vector machines to construct a complex functional relationship between multiple variables and the final stress. Therefore, in this study, the support vector machine is used to predict the stress data of the flexible formwork concrete wall. First, the data of each variable affecting the stress of the flexible concrete wall are normalised. Then, the training and test sample sets are established. The prediction model is trained with the training sample set, and the test sample set is used to validate the prediction model obtained from the training.

The steps of the algorithm for the implementation of support vector machine in predicting the instability of flexible formwork concrete walls are as follows:

Normalisation of the data series of various factors influencing the instability of flexible formwork concrete walls.

To avoid the input variables in the variable order of magnitude difference being too large to affect the training, the support vector machine training data samples were normalised.

Let \(\:{x}_{max}\:\)and \(\:{x}_{min}\) represent the maximum and minimum values of the data series of various factors affecting the instability of the flexible formwork concrete wall in the set of training samples, respectively; \(\:{x}_{i}\) represents the actual data, and\(\:\:\:{\stackrel{-}{x}}_{i}\:\)is the normalised data.

The training data are converted to the interval [0,1]. Finally, (4) can be used to convert it into data in the normal range.

Initialize the parameters of the support vector machine.

The kernel function is the core of the support vector machine, which directly determines the performance of the support vector machine. In this study, we adopt the most classical Gaussian radial basis kernel function, and optimise the penalty parameter C and the parameter \(\:{\upgamma\:}\) of the kernel function by using cross-validation method.

According to the learning samples, the objective function is established.

Given the sample \(\:({\text{X}}_{\text{i}},{\text{y}}_{\text{i}})\), where, \(\:{\text{X}}_{\text{i}}=({\text{x}}_{\text{i}}^{1},{\text{x}}_{\text{i}}^{2},{\text{x}}_{\text{i}}^{3},{\text{x}}_{\text{i}}^{4},{\text{x}}_{\text{i}}^{5})\), \(\:{\text{x}}_{\text{i}}^{1}\) is the buried depth, \(\:{\text{x}}_{\text{i}}^{2}\) is the thickness of the coal seam, \(\:{\text{x}}_{\text{i}}^{3}\) is the thickness of the wall, \(\:{\text{x}}_{\text{i}}^{4}\) is the mining distance of the working face, \(\:{\text{x}}_{\text{i}}^{5}\)is the distance of xx, \(\:{\text{y}}_{\text{i}}\) is the stress, an objective function is established.

where \({\alpha _i}\)is the Lagrange multiplier corresponding to the ith sample.

Determine the prediction function equation.

Solving the objective function yields a unique optimal solution \({\alpha ^*}\), which can be determined using the prediction function Eq.

Where \(\:{b}^{*}={y}_{j}-{\sum\:}_{i=1}^{l}{y}_{i}{\alpha\:}_{i}^{*}K({x}_{i},{x}_{j}),\forall\:j\in\:\left\{j\right|{\alpha\:}_{j}^{*}>0\}\)。

This was performed using a known small amount of learning sample data to obtain an implied mapping function relationship between the various factors involved in the instability of a flexible formwork concrete wall and the final stresses.

According to the obtained prediction function relation equation, the theoretically predicted stress value of the flexible formwork concrete wall can be calculated by predicting the new input data series of the flexible formwork concrete wall instability.

Using the numerical simulation results in the previous section for analysis, the changing parameters include: depth of burial, height and width of the flexible formwork concrete wall, retrieval distance (one data record for every 20 m of retrieval), and location of the measurement point (one measurement point for every 1 m of the centre of the flexible mould concrete wall constitutes a line of measurement), and the stress at the point of measurement varies with the above parameters.

A total of 15,660 data sets were collected for the simulation, 90% of which were randomly used as training samples to train the support vector and prediction models, and the remaining 10% were used as validation and test samples for the training results. Leveraging the MATLAB 2022b software platform, the svm function is invoked. The Gaussian radial basis kernel function is chosen, and the penalty parameter C and kernel function parameter γ are determined through the 5-fold cross-validation method.

To verify the superiority of the SVM model, the example analysis in this study also uses a BP neural network and random forest regression for comparison. The BP neural network’s hidden layer was configured with 10 nodes, utilizing the tansig transfer function. The learning rate was set at 0.01, with the minimum error for the training target established as 0.00001. The training iterations were set to 1000. In the random forest regression algorithm, 100 decision trees were specified, and the minimum number of leaves was set to five.

To comprehensively assess the accuracy of the various prediction algorithms, four error evaluation metrics were used: mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). To avoid a loss of generality, all error statistics were averaged after running the program five times. The prediction result errors for the test samples after training using the training samples are listed in Table 4, and the comparison curves between the predicted and true values are shown in Fig. 10.

Comparison of predicted and true values of various predictive modelling algorithms.

Table 4 illustrates that the SVM-based prediction model exhibits error index values of MSE (0.9990), RMSE (0.9995), MAE (0.6845), and MAPE (0.0375). Notably, the MSE and MAE values, being closer to zero, indicate superior model performance. Comparatively, these error indicator values for the SVM-based model are smaller than those of the BP neural network and random forest regression models. Additionally, as depicted in Fig. 8, the predicted values from the SVM-based model closely align with the actual values, emphasizing the effectiveness and superiority of the SVM-based prediction model over the BP neural network and random forest regression models.

The predictive model is capable of estimating stress values at any central point of the flexible formwork concrete wall, considering various burial depths, heights, and widths, along with different advancing distances of the working face during air-retaining wall mining. If the predicted stress value is below the ultimate compressive strength of the flexible formwork concrete wall during face mining, the working face can proceed safely. However, if the stress value partially exceeds the ultimate compressive strength, it may result in significant deformation of the top and bottom plates, compromising mining safety. Therefore, it becomes essential to implement reinforcement treatment for the flexible formwork concrete wall before commencing mining operations.

To substantiate the industrial applicability of the prediction model, practical tests were carried out on the working faces 23,107 and 23,111 within the Xiegou Coal Industry. In this context, the 13,151 and 13,152 tape chute lanes serve as the air intake, load train, and coal transportation lanes, while the 13,153 air intake chute lanes function as the air intake and auxiliary transportation lanes. In the process of mining back to the working face, in the 13,151 roadway and 23,107 working face connecting position using C30 concrete masonry soft formwork concrete wall to protect the alley, soft formwork concrete wall with the width of 0.7 m, 5 m high. The end mining of 23,107 working face began in early October 2022, and 23,111 working face was mined after the removal of the support at the end of December 2022.

In the mining area of the 23,111 working face, the coal seam thickness for mining No. 3 coal from the Shanxi Group in the Lower Permian System ranges from 4.50 to 5.30 m, with an average of 5 m. The average burial depth is 400 m, and the working face spans a length of 350 m. The coal seam exhibits a slight inclination angle ranging from 0° to 8°, with an average inclination of 3°~4°. The coal seam thickness remains relatively constant with a discernible pattern of change. The entire area is suitable for mining, as it lacks gangue content; the structure is simple, the coal type is single, and the change in coal quality is very small. Regarding the characteristics of the coal seam, the black coal core was lumpy and short columnar, glassy lustre, strip structure, and step fractures.

The working face, flexible formwork concrete wall parameters, and mining distance data were input into the prediction model to predict the stress values at ten measurement points in the flexible mould concrete wall 30 m in front of this position at a certain mining distance during the mining process of the working face. Because of the low probability of instability of the flexible formwork concrete wall in the first 100 m of face mining, to reduce the number of computer calculations, it is predicted from the mining distance of 100 m. Input data corresponding to the prediction point’s location are utilized for the support vector machine prediction model, aiming to predict the stress level of the flexible formwork concrete wall. The x- and y-axis data are represented by the mining distance and prediction point’s position (measured from the open cut’s eye), respectively. The stress value is assigned to the z-axis data, forming a three-dimensional representation where the stress values are graphically depicted. For the z-axis data, the three-dimensional surface of the stress value of the predicted point is plotted, as shown in Fig. 10. When the stress value of the flexible formwork concrete wall greater than 30 MPa, it can be noted that the flexible formwork concrete wall will be plastically damaged and destabilized at this time. From this derives the length of overrun damage, part of the data are detailed in Table 5.

Stress Surface Diagram of Predicted Points.

As it can be observed from Fig. 11; Table 5 the longer mining distance the greater the length of overrun damage. The maximum value of the length of overrun damage is about 24 m.

Using the Origin software, with the retrieval distance as x and flexible formwork concrete wall super-damage length as y, the curve of the retrieval distance and super-damage length of the flexible mould concrete wall is constructed, as shown in Fig. 11.

Overrun damage length curve of flexible formwork concrete wall.

By fitting the regular curve, Eq. (7) is obtained, and the error of the calculated fitting data is less than 5%. It can be concluded that the overrun damage length of the flexible moulded concrete wall increased as a logarithmic function of the retrieval distance.

where x is the mining distance (m), and y is the advanced damage length of the flexible formwork concrete wall (m).

Examining Fig. 12 reveals an escalating trend in the damage strength of the flexible formwork concrete wall with increasing mining distance. Field measurements indicate that the curve depicting the damage length of the flexible formwork concrete wall can be categorized into two phases. In the initial phase, spanning a mining distance of 280 ~ 295 m, the damage length (denoted as y) exhibits nearly linear growth in tandem with the mining distance. Subsequently, in the second phase (covering a mining distance of 295 ~ 320 m), the growth rate of the curve gradually diminishes and achieves relative stability around 320 m. Ensuring the safety of workface mining becomes challenging when the flexible formwork concrete wall sustains damage. The length of reinforcement fluctuates with variations in the mining distance. Hence, establishing an appropriate range for reinforcing the flexible formwork concrete wall is crucial for effectively preserving the overall stability of the hollow area. At a mining distance of 280 ~ 310 m, the distance of the overreaching reinforcement can be calculated according to Eq. (7); after the mining distance reaches 320 m, the length of overreaching damage of the flexible mould concrete wall basically attains stability; every 1000 m of the working face can be reinforced according to a fixed distance, with a certain safety coefficient, and the curve of the length of overreaching damage of the flexible mould concrete wall determined by Eq. (7) is expected to be optimised. This is expected to optimise the coordination between the reinforcement process and workface mining, thereby improving the efficiency of workface mining.

It can be observed from Eq. (7), when the distance of back mining reaches 277.85 m, y is positive, indicating that the flexible formwork concrete wall begins to appear over the front damage phenomenon at this time. Then, mining back to the flexible mould concrete wall needs to be strengthened in advance. Equation (7) was used to calculate the specific reinforcement length and the corresponding range of the field of flexible formwork concrete wall reinforcement. Table 6 shows only part of the data owing to excessive data.

When the mining distance reaches 335 m, the length of the over-reinforcement is 29.3 m, and the reinforcement distance increases insignificantly after this point.

The Z6 concrete reinforcing agent is applied to the cleaned concrete surface and the application is repeated until the base layer does not infiltrate the permeable surface. The reinforced flexible formwork concrete wall was sampled and the unreinforced flexible formwork concrete wall was sampled, followed by a control test. The compressive strength of the samples was tested using RMT-150B electro-hydraulic servo-controlled rock mechanics testing system, as shown in Fig. 13.

Sample test of flexible formwork concrete wall. (a) pre-test, (b) post-test, (c) concrete compressive strength graph, (d) reinforced concrete compressive strength graph.

As can be seen from Fig. 13 the ultimate compressive strength of normal C30 concrete is about 30 MPa, while the ultimate compressive strength of reinforced concrete increases by 26%. It reaches to be 38 MPa, which shows the increase in the ultimate compressive strength of reinforced concrete. The peak ultimate compressive strength of normal C30 concrete corresponds to a displacement of about 3 mm, while the peak ultimate compressive strength of reinforced concrete corresponds to a smaller displacement of about 2 mm. This indicates that the reinforced concrete undergoes less deformation and has better stiffness when subjected to the same stress. In addition, plain concrete fails more rapidly after the stress peaks, is less ductile, and deforms more, while reinforced concrete is more stable under larger loads, deforms less, and fails slowly. Overall, the performance of reinforced concrete is superior in terms of curve performance, especially in terms of load carrying capacity and ductility.

From the prediction, it can be noted that the flexible formwork concrete wall at (from the distance of the cutting eye, the same below) 278 m began to exhibit the damage phenomenon in advance; therefore, the flexible formwork concrete wall 280 ~ 350 m range has an arrangement of a stress gauge (the total number is 8) at every 10 m. The stress on the flexible formwork concrete wall was documented at intervals of 1 m as the working face progressed. Within the recorded data range, the working face advanced 30 m beyond the stress meter position. The advancement ceased after the working face traversed the stress meter position (measured from the distance to the open-off cut, the same below). Through an analysis of the stress meter data, it becomes possible to ascertain the variation in stress experienced by the flexible formwork concrete wall as the working face advances. Furthermore, this analysis facilitates an assessment of the alignment between the prediction model and the results obtained from the industrial test.

The stress curve of measuring point with the mining distance of working face.

Illustrated in Fig. 14, the stress at each measuring point increases as the mining progresses towards the face. The maximum stress value recorded is 37.49 MPa, which is below the reinforced flexible formwork concrete wall’s ultimate compressive strength of 38 MPa. The field test validates the program’s capability to ensure the secure mining of the coal seam, confirming the prediction model’s effectiveness.

During the operation of the main haulage roadway at Xiegou Coal Industry, on average, maintenance is required once, with an average cost of 2 400 RMB per meter for roadway repairs. The cost for using Z6 concrete reinforcement technology is 300 RMB per meter. In 2023, the adoption of the new scheme ensured the safe production of the mine, preventing downtime caused by roadway instability and damage, which would have resulted in a shutdown estimated at 10 days, with a cumulative impact on coal production of 28,000 tons. The indirect economic benefit of the new scheme is 28 000 tons × 850 RMB/ton = 238 million RMB. The roadway project involves 1240 meters, generating a direct economic benefit of 1240 meters × (2400 − 300) RMB/m = 2.604 million RMB. This results in a total additional profit of 26.404 million RMB.”

(1) Using the forecast model, calculations revealed that the flexible formwork concrete wall would experience yielding and damage during secondary mining, and the corresponding damage range was determined. To enhance the flexible formwork concrete wall’s strength, the Z6 concrete reinforcing agent was selected, resulting in a 26% boost in the ultimate compressive strength to 38 MPa after reinforcement.

(2)The maximum reading from the stress meter is 37.49 MPa, which is below the ultimate compressive strength of the reinforced flexible formwork concrete wall. On-site testing confirms its safe production, and the industrial test outcomes align with the prediction model’s calculations, validating the scientific and effective nature of the prediction model method. This predictive model serves as a reference for coal pillar mining without coal pillars under comparable engineering conditions.

(1) In the process of secondary mining, stress is redistributed. There is a distinct zone of stress concentration observed in the flexible formwork concrete wall located in front of the working face. The degree of stress concentration gradually increases with deeper mining. Simultaneously, the flexible formwork concrete wall at the back of the working face undergoes plastic deformation, yet this deformation does not affect the flexible formwork concrete wall in front of it during the initial mining stages, ensuring the absence of accidents.

(2) Excessive stress concentration in the flexible formwork concrete wall results in over-advanced damage to the wall in front of the working face, impacting the transportation and ventilation systems. Deeper coal seams, narrower wall width, and higher wall height intensify the stress concentration, leading to extensive overrun damage to the flexible formwork concrete wall. This, in turn, causes deformation in the top and bottom slabs of the roadway, rendering the working face unable to safely execute back mining.

(3) The SVM-based prediction model, trained with simulated data, demonstrated effectiveness with error index values of 0.9990, 0.9995, 0.6845, and 0.0375 for MSE, RMSE, MAE, and MAPE, respectively. This model has the capability to forecast stress values at various positions along the flexible formwork concrete wall, considering different burial depths, heights, and widths. Additionally, it accounts for varying advancing distances of the working face during secondary mining along the air-retaining wall. This predictive capability aids in guiding the working face for a safe back mining process.

(4) The overrun damage strength of the flexible formwork concrete wall increased with the advancing mining distance. The data indicate a two-stage pattern for the pre-damage length curve: an initial stage characterized by nearly linear growth, followed by a second stage where the growth rate decreases and approaches stabilization.

(5) Based on the prediction model calculations, the utilization of the Z6 concrete reinforcing agent enhances the ultimate compressive strength of the flexible formwork concrete wall by 26%, reaching 38 MPa. On-site testing confirms its suitability for safe production, and the industrial test results align with the prediction model calculations, validating the scientific and practical utility of the prediction model method.

While this study significantly improved the compressive strength of flexible formwork concrete wall using Z6 concrete enhancer, there are some potential limitations that need to be acknowledged and discussed. Firstly, the data for this study were sourced from specific addresses in Zhaozhuang Coal Mine and Xiegou Coal Mine. Although these data cover a wide range of geological characteristics, their applicability in other geological environments still needs further validation.

To further enhance the outcomes of this study, future research could explore several directions. Firstly, comparing the effects of different types and brands of concrete enhancers on the performance of flexible formwork concrete wall could expand the range of enhancer options and optimize design solutions. Secondly, conducting broader field validations under different geological conditions would help assess the applicability and effectiveness of enhancers in diverse geological environments.

The data sets used and analyzed during the current study are available from the corresponding author upon reasonable request.

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This research is supported by the Fundamental Research Program of Shanxi Province (grant no. 202203021222088).

College of Mining Engineering, Taiyuan University of Technology, Taiyuan, 030024, China

Yanhui Zhu, Peilin Gong, Guang Wen & Kang Yi

School of Mines, China University of Mining & Technology, Xuzhou, 221116, China

Ye Tian

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Yanhui ZHU did the conceptualixation and formal analysis, wrote the main manuscript, and prepared all the Figures.Ye TIAN provided software, edited the manuscript, and performed the data curation.Peilin GONG provided the investigation, performed methodology.Guang WEN performed project administration and resource.Kang YI performed supervision & validation, and provided funding.

Correspondence to Peilin Gong.

The authors declare no competing interests.

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Zhu, Y., Tian, Y., Gong, P. et al. Predictive model for the instability of flexible formwork concrete wall in secondary mining of non-pillar coal mining. Sci Rep 14, 21684 (2024). https://doi.org/10.1038/s41598-024-72883-1

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Received: 24 July 2024

Accepted: 11 September 2024

Published: 17 September 2024

DOI: https://doi.org/10.1038/s41598-024-72883-1

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