Study on the Impact of Spontaneous Combustion of Coal Gangue on Photovoltaic Pile Foundations and Surface Structures

Abstract

With economic growth, constructing photovoltaic power plants on gangue mountains holds significant potential for the development of renewable energy and the effective utilization of gangue mountains. However, it is crucial to account for the impact of the spontaneous combustion of coal gangue on surface structures and the mechanical performance of pile foundations. This study uses COMSOL Multiphysics software (version 6.2) to conduct a simulation by establishing a multiphysical coupling model of the temperature field, oxygen concentration field, and seepage velocity field, simulating the dynamic evolution of spontaneous combustion in gangue mountains. The reasonableness of the model was verified by comparison, and a mechanics module was added to explore the effects of pile foundations and ground surfaces at high temperatures. The results indicate that the spontaneous combustion of coal gangue initially generates high-temperature regions beneath the slope of the pile, which gradually expand outward. Due to thermal expansion, thermal stress and displacement occur in both the gangue mountain and pile foundations, potentially compromising the stability of the foundations and increasing the risk of structural failure. These findings can serve as valuable references for the construction of photovoltaic power plants and the effective utilization of gangue mountains.

1. Introduction

With the rapid development of China’s economy, energy demand has surged significantly, making China the world’s largest energy consumer. Over 80% of China’s energy consumption comes from fossil fuels, including coal, oil, and natural gas, resulting in massive greenhouse gas emissions. The rapid growth in energy consumption has also raised concerns about energy security, as China relies heavily on imports of oil and natural gas to meet domestic demand, exposing the energy supply to external risks.

During the 13th Five-Year Plan period, China’s energy structure underwent significant adjustments under the guidance of national energy policies, promoting the rapid development of renewable energy sources such as solar, hydro, wind, and geothermal energy. Photovoltaic (PV) energy, an emerging clean energy source, has shown tremendous potential and rapid growth due to its characteristics of being noise-free, pollution-free, and requiring minimal maintenance [1]. Despite this progress, the utilization rate of coal gangue in China remains low, with most gangue accumulating as industrial solid waste in piles known as gangue mountains. Coal gangue has become the largest industrial waste in terms of both annual discharge and cumulative storage, accounting for approximately 25% of the total industrial solid waste in China. Coal gangue production is estimated at 15% of raw coal production, and the annual accumulation rate is approximately 300 million tons, resulting in over 2000 large gangue mountains across the country [2,3]. Building photovoltaic power plants on coal gangue mountains can not only make full use of these abandoned resources [4] but also integrate gangue mountain remediation with economic benefits, thus fostering the development of renewable energy [5]. However, coal gangue contains residual coal and carbonaceous combustible materials, making it highly prone to spontaneous combustion when exposed to air for extended periods. Prolonged combustion of gangue mountains can lead to the formation of internal cavities, increasing the risk of collapse and landslides. Therefore, when constructing photovoltaic power plants, it is essential to fully consider the potential impacts of spontaneous combustion on pile foundations and adopt appropriate countermeasures.

The study of coal spontaneous combustion dates back several centuries, and significant progress has been made since the late 20th century. Researchers have proposed various theories regarding the mechanism of spontaneous combustion in coal gangue, including the coal–oxygen complex theory, pyrite oxidation theory, bacterial action theory, free radical theory, and volatile matter theory. Additionally, theories related to coal spontaneous combustion, such as the phenolic group theory, electrochemical theory, and hydrogen atom theory, also provide insights into the mechanism of gangue mountain combustion. Research on the spontaneous combustion of coal gangue primarily focuses on temperature and oxygen concentration variations [6] and the types and concentrations of gases released during combustion [7,8]. Studies have shown that the essential cause of coal gangue spontaneous combustion is the combustion of residual coal within the gangue [9]. Zhang et al. [10] used a simultaneous thermal analyzer to investigate the microstructure of coal and gangue, examining the thermal behavior during co-combustion of coal and gangue in different mass ratios. Their findings indicated a higher risk of spontaneous combustion when coal and gangue coexist. Deng et al. [11] established a low-temperature spontaneous combustion ignition experiment platform for coal and developed a theoretical system for coal spontaneous combustion. They proposed that the coal spontaneous combustion oxidation process generally involves three stages: physical adsorption, chemical adsorption, and chemical reaction. Deng et al. [12] conducted large-scale experiments using a 15-ton platform to study the temperature and oxygen consumption during coal spontaneous combustion, achieving results consistent with actual conditions. Most researchers have adopted field experiments and numerical simulations to analyze the temperature distribution inside gangue mountains. Ozdeniz A H et al. [13] monitored a 120-ton coal pile (5 m wide, 10 m long, and 3 m high) under normal atmospheric conditions, obtaining internal temperature data from 20 points across two layers and developing a time-temperature distribution model. Liu et al. [14] proposed a monitoring system based on LoRa wireless communication technology to monitor the internal temperature of long-term gangue mountains in real time. Zhou et al. [15] employed COMSOL to develop a multiphysical coupling model for seepage, heat transfer, and oxidation in coal gangue, studying the spatiotemporal evolution of temperature, seepage, oxygen concentration fields, and residual fuel levels. They also performed sensitivity analyses of key parameters and proposed a novel artificial thermal reservoir system for extracting energy from abandoned gangue mountains, providing new ideas for gangue disposal and thermal energy utilization. Li et al. [16] developed a semi-open storage model for gangue mountains and conducted systematic fire experiments to study the temperature distribution and spontaneous combustion dynamics, offering empirical data for deep-layer temperature distribution and combustion mechanisms. Zhu et al. [17] used COMSOL Multiphysics to conduct a numerical study of spontaneous combustion in temporary coal storage sites, analyzing five variables—wind speed, oxygen concentration, height, porosity, and slope—on spontaneous combustion. Based on extensive simulations, they developed a theoretical prediction model for combustion onset and location. Wu et al. [18] constructed various gangue mountain models typical of the Chengzhuang coal mine in Shanxi, continuously monitoring internal temperature and gas concentrations to explore the effects of different stacking methods on spontaneous combustion. This study identified CO and C₂H₄ as key indicator gases for early warning and monitoring of spontaneous combustion. Wang et al. [19] conducted numerical simulations to study the exothermic oxidation mechanism under different oxygen supply conditions, establishing a three-field coupling model for the heating process of coal gangue mountains using computational fluid dynamics (CFD) to analyze thermal behavior under external airflow conditions and clarify combustion risks. Liu et al. [20] used infrared thermal imaging to detect shallow fire zones and dense drilling methods to locate deep fire zones, then injected three-phase foam for cooling, providing a reference for fire detection and environmental protection in gangue piles. Zhao et al. [21] developed a wireless temperature monitoring system to monitor the internal temperature of coal gangue platforms, dividing them into low, medium, and high-temperature zones, and used finite element methods to simulate temperature evolution over 1 to 5 years. Bai et al. [22] applied the Achar differential method and the Coats–Redfern integral method to solve the kinetic parameters of coal gangue combustion, analyzing heat transfer processes in gangue piles using a heat pipe system based on coal spontaneous combustion conditions. Zhang et al. [23] identified high-risk zones in coal and coal gangue spontaneous combustion fires by studying heat release and transfer characteristics, establishing a combustion growth index to quantify combustion hazards.

In summary, existing studies mostly focus on the mechanism of spontaneous combustion, while the pile–surface coupling effect is still unclear. Given the importance of these effects for photovoltaic power plants built on abandoned coal gangue mountains, this study employs numerical simulations to establish a scaled-down model of coal gangue mountains. The model is based on the temperature field, and mechanical modules are incorporated to analyze the impact of coal gangue combustion on pile foundation mechanical performance and surface subsidence, providing valuable references for the construction of photovoltaic power plants and the remediation of coal gangue mountains.

2. Model Development

In this paper, the finite element method is used to simulate the dynamic evolution of spontaneous combustion of a coal gangue mountain. To investigate the internal temperature development trend of the gangue mountain, the temperature distribution law, and the impact of gangue spontaneous combustion on the pile foundation and the ground surface, a mine gangue spontaneous combustion model was established using COMSOL software. The air seepage velocity field, oxygen component transport field, and temperature field were considered to satisfy the partial differential equations and boundary conditions, and the spontaneous combustion of the gangue mountain was simulated.

2.1. Modeling Basis for the Temperature Field and Fundamental Assumptions

Gangue spontaneous combustion is a complex process driven by the mutual coupling of the temperature field, oxygen concentration field, and seepage field. Studies have shown that its nature is a chain reaction triggered by the imbalance between oxidative exothermic and heat transfer in the porous medium inside the gangue. In the initial stage of spontaneous combustion, oxygen diffuses through the pores and fissures of the gangue accumulation, and the combustible material undergoes physical adsorption and slow oxidation reaction, gradually releasing heat. When the rate of heat accumulation exceeds the environmental heat dissipation capacity, the system temperature breaks through the critical value and finally triggers spontaneous combustion.

The process contains the following multi-field mechanism: firstly, the external air infiltrates into the pore space of the gangue mountain under the action of pressure gradient, forming a non-uniform seepage field; secondly, the oxygen migrates with the seepage, forming a concentration gradient in the pore network, which determines the regional distribution of oxidative reaction; subsequently, the active substances such as pyrite and other active substances in the oxygen-rich region undergo exothermic reaction, increasing local temperature and the formation of the dynamic temperature field; The high-temperature environment feeds back to the system through two pathways: one is to accelerate the rate of oxidative reaction (following Arrhenius’ law), and the other is to generate thermal buoyancy to change the seepage pathway; at the same time, heat conduction and convective heat dissipation together regulate the system’s thermal equilibrium, whereas oxygen consumption inhibits the reaction intensity.

The evolution of gangue mountain spontaneous combustion is influenced by multiple factors, such as particle gradation, stacking structure, water content, sulfur content, and ventilation conditions, and its heat transfer process contains three basic forms: solid heat conduction, pore convection heat transfer, and thermal radiation. Due to the dynamic imbalance between oxidative exothermic reactions and heat dissipation, the spontaneous combustion process presents unsteady-state heat transfer characteristics. To simplify the modeling analysis, the following basic assumptions are proposed, according to reference [24]:

(1) The coal gangue is uniformly distributed and isotropic at any location within the gangue mountain, and the loose gangue body is treated as a porous medium.

(2) The influence of gravitational forces on airflow and frictional heating due to airflow within the gangue mountain is neglected.

(3) The gangue mountain is assumed to have constant physical properties, such as density and specific heat, which do not change with temperature, and the airflow velocity inside the gangue mountain is minimal.

(4) The heat dissipation from the gangue mountain to the surrounding environment is assumed to be proportional to the temperature difference, with a constant convective heat transfer coefficient. The ambient temperature is set at a constant 20 °C and does not vary with time.

2.2. Geometric Model Development

It is assumed that the gangue mountain is formed by natural deposition and stacking on flat ground, resulting in a trapezoidal shape with stepped layers. The gangue mountain contains residual coal and other combustible materials and is exposed to the environment without any obstructions or buildings around it. Over time, due to exposure to direct sunlight, strong winds, and rainfall, high-temperature regions gradually develop inside the gangue mountain, eventually triggering spontaneous combustion.

The irregular external shape of the gangue mountain is simplified into a right trapezoidal prism in COMSOL to facilitate modeling. The geometric model is scaled down for computational efficiency while maintaining the boundary effects relevant to the pile foundation. The geometric parameters are defined as follows: the base length is 15 m, the top length is 16 m, the slope length is 7.07 m, the height is 5 m, and the slope angle is 45°.

To account for boundary effects on the pile foundation, the pile foundation model is positioned at the center of the gangue mountain. The pile has a length of 2 m and a diameter of 0.2 m. The geometric models of the gangue mountain and pile foundation are shown in Figure 1. The finite element method discretizes the continuous solution domain into a combination of finite elements. The geometric model is meshed using tetrahedral elements, and finer mesh refinement is applied to critical areas, such as corners and slopes. The mesh comprises 87,928 tetrahedral elements, 16,273 prism elements, and 104,286 total elements, with 415 edge units and 20 vertex units. The minimum element quality is 0.1109, the average element quality is 0.6908, the mesh volume ratio is 1.009 × 10⁻⁴, and the mesh volume is 937.5 m³. The geometric shape functions are linear elements. For temporal discretization, considering the real-time conditions of spontaneous combustion in the gangue mountain, the simulation is set as a transient analysis. The solver is configured for transient calculations, with the time unit set to years, a total computation period of 5 years, a time step of 0.1 years, and a relative tolerance of 0.01.

2.3. Basic Equations for Model Calculations

The rate of oxidation reaction for spontaneous combustion of coal gangue [25] was calculated using the Arrhenius equation:

$$k=A\cdot e^{-{\displaystyle \frac{E_a}{RT}}}$$

(1)

where k is the reaction rate constant; A is the prefactor (also known as the frequency factor), which indicates the rate constant of the reaction when there is no activation energy barrier, s⁻¹; E_a is the activation energy, defined as the minimum energy required to convert a reactant molecule into an activated complex, J/mol; R is the molar gas constant, which has a value of 8.314 J/(mol∙K); and T is the absolute temperature, K.

According to reference [21], the model uses the outdoor ambient temperature of 20 °C as the initial value of the temperature field, a multi-year average wind speed value of 2 m/s as the initial wind speed, and an initial oxygen concentration of 9.375 mol/m³.

(1) Temperature field boundary conditions

The top and the windward side of the gangue mountain are in direct contact with air, and convective heat exchange with the external environment occurs; this is set as a convective heat transfer boundary condition. The convective heat transfer is:

$$-n(-\lambda \nabla T)=h(T_0-T)$$

(2)

where $\lambda$ is the thermal conductivity in W/(m∙K); T₀ is the atmospheric temperature and T is the solid temperature in K; n is the unit normal vector of the boundary; h is the convective heat transfer coefficient (in W/(m²·K)), reflecting the intensity of the heat transfer between the fluid and the solid surface; and $\nabla T$ is the gradient vector of the temperature (pointing in the direction of the temperature increase), which is physically the rate of change of the temperature in space.

(2) The air seepage velocity field. The windward side is set as the first type of boundary condition. The wind speed is set to v = 2 m/s. The top is the outlet with free gas flow, at a pressure of one atmosphere. The remaining boundaries are zero-flux boundaries: v = 0 m/s.

(3) The oxygen concentration transport field. Oxygen enters the interior of the gangue with the air flow. The windward side is set as the first type of boundary condition: c = 9.375 mol/m³. Oxygen flows freely at the top as the second type of boundary condition, and the rest of the boundary is a zero-flux boundary. The specific values of the physical parameters of the model are shown in

Table 1. Physical parameter settings.

Parameter Name	Parameter Symbol	Numerical Value (Units)
Initial wind speed	v0	2 m/s
Initial oxygen concentration	c0	9.375 mol/m3
Barometric pressure	Pa	1 atm
Indexing factor	A	180 L/s
Air diffusion coefficient	D	1.5 × 10−5 m2/s
Air density	ρg	1.43 kg/m3
Convection coefficient	h2	0.75 W/(m2∙K)
Activation energy	E	50,000 J/mol
Convection coefficient	h	0.75 W/(m2∙K)
Universal gas constant	R	8.314 J/(mol∙K)

.

From the perspective of heat source, oxygen mainly enters from the windward side of the slope, and the combustibles in the gangue undergo an oxidation reaction to release exothermic heat; analyzed from the perspective of heat dissipation, the internal heat is mainly dissipated by using heat conduction within the gangue as well as convective heat transfer on the surface. The oxygen consumption rate involved in the oxygen concentration field is closely related to the temperature value; the heat source term in the temperature field is expressed as a function of oxygen concentration and flow rate in the mathematical equation. Under the coupling of these three physical fields, the gangue auto-ignition process is advanced.

2.4. Model Comparison Validation

In this study, a physical model, boundary conditions, and parameter values were established based on reasonable assumptions, incorporating heat transfer, airflow, and the conservation equations for mass, momentum, and energy related to oxygen transport. By applying time discretization and spatial meshing, a three-dimensional multiphysics coupling model for spontaneous combustion in coal gangue mountains was constructed using the finite element method (FEM), followed by numerical simulation.

To validate the reliability of the numerical simulation, the development of coal gangue spontaneous combustion can be assessed by analyzing the temperature variation patterns of the model. Figure 2 compares the average temperature of the gangue mountain spontaneous combustion obtained through finite element simulation over 2–4 years with the data from reference [26], while Figure 3 shows the temperature distribution in the fifth year of combustion. The numerical simulation yields the following conclusions:

(1). In the initial stage, the coal gangue mountain heats up rapidly as a whole. Over time, as oxygen is consumed by the reaction and its concentration decreases, the rate of temperature rise gradually slows. When heat generation and dissipation reach equilibrium, the temperature stabilizes.

(2). During the spontaneous combustion process of the gangue mountain, due to favorable ventilation conditions along the slope surface, high-temperature zones initially emerge in areas adjacent to the lower slope region. As time progresses, these high-temperature areas gradually propagate inward.

Since the timing and conditions of spontaneous combustion vary across different gangue mountains in the field, the specific temperature values may not perfectly match the simulation. Therefore, when comparing and validating the model’s temperature field, we focus on the trends in temperature development. The average temperature field established in this study shows minimal deviation from reference [26], and the temperature variation pattern aligns with the observed trends of spontaneous combustion in field gangue mountains from reference [27]. This indicates that the numerical model accurately reflects real-world conditions. Thus, the developed model can be reliably used for simulating and predicting the temperature field of gangue mountain spontaneous combustion.

3. Effect of Gangue Spontaneous Combustion on the Gangue Surface

Coal gangue is a solid waste generated during coal mining, containing a certain amount of unburned coal, organic matter, and sulfides. When exposed to air, these components may undergo oxidation, leading to spontaneous combustion. The prolonged occurrence of this phenomenon alters the structural integrity of the gangue mountain, reducing its stability and increasing the risk of geological hazards. This study establishes a scaled-down coal gangue mountain model and employs numerical simulation to analyze the combustion evolution process and investigate the impact of spontaneous combustion on the gangue mountain’s surface.

Figure 4 shows the temperature map of spontaneous combustion in gangue mountain for 1–4 years simulated by the numerical model. As can be seen in Figure 4, with the increase in the burning degree of gangue mountain, its high-temperature region also gradually expands. The high-temperature region first appeared in the area below the slope; with growth over time, the high-temperature region will gradually spread to the surrounding area and ultimately cause the whole gangue mountain temperature to increase. If no timely measures are controlled, the spontaneous combustion of coal gangue can generate temperatures as high as several hundred degrees centigrade, seriously affecting the safety of the building structure and the stability of the slope.

Spontaneous combustion of coal gangue is the main driver of surface subsidence in gangue mountain. Duan et al. [28] pointed out that due to the long years of burning coal gangue, the internal temperature is very high, and the combustible materials are generally calcined into ashes, resulting in the formation of internal cavities of different sizes. In this way, there is constant gangue burnt to ashes, and the small cavities are interconnected due to combustion, gradually changing from small to large and forming an arch. The temperature inside the arch shell is high when encountering a large amount of rainfall; the rain meets the high-temperature gangue and instantly turns into water vapor. When the energy builds up to a certain extent, and the pressure is more than the gangue mountain surface can withstand, it may result in a geological disaster. As the coal gangue burns out, the voids formed internally become increasingly larger and more numerous, potentially leading to the development of arch-shaped structures within the gangue mountain. Therefore, spontaneous combustion of coal gangue hills may induce displacement within the structure, affecting their overall stability. To investigate the internal displacement caused by coal gangue combustion, four measurement points were selected vertically at 1 m intervals from top to bottom in high-temperature zones of the gangue hill. As shown in Figure 5, thermal expansion under rising temperatures drives outward displacement and lateral expansion of the hill. Meanwhile, temperature variations between combustion-affected and unaffected areas result in differential displacement magnitudes. This phenomenon may create elevation differences at the hilltop, potentially leading to uneven ground surface displacement.

Gangue mountain in the combustion process, due to the significant increase in the porosity and permeability of gangue [29], will lead to a decrease in the overall strength of the pile body. In addition, the generated gas generates pressure on the interior of the pile body under high-temperature conditions, which accelerates the destruction of the internal structure of the gangue mountain. At the same time, the volume contraction, pyrolysis reaction, and local collapse generated during the combustion process form cavities through the pyrolysis reaction and gradually propagate to the surface, which may ultimately lead to widespread subsidence. Figure 6 shows the displacement distribution on the slope crest of the coal gangue mountain. As illustrated in the figure, the displacement is not uniformly distributed. The regions closer to the heat source center exhibit larger displacements, while displacements gradually decrease with increasing distance from the heat source. The majority of displacements on the slope crest range between 1.8 mm and 3.4 mm. On the windward side, continuous oxygen influx leads to frequent oxidation reactions and higher heat exchange efficiency, resulting in a rapid temperature rise and, consequently, greater displacements in these areas. In the figure, although the displacement of the gangue mountain surface is within a certain range, if it is not controlled, the long-term accumulation may have an impact on the stability of the mountain and may even lead to geological disasters, such as landslides.

To investigate the variation of soil pressure around the pile under the influence of coal gangue self-heating, measurement points were selected at a distance of one pile diameter (200 mm) from the pile perimeter and depths of 540 mm, 840 mm, 1140 mm, and 1440 mm. The variation in soil pressure at these points due to the coal gangue combustion was analyzed. Figure 7 shows the temporal variation in soil pressure around the pile. As depicted in the figure, with the progression of time, the intensity of coal gangue self-heating increases, resulting in a rise in the temperature of both the gangue mountain and the pile foundation. Consequently, this causes an increase in the soil pressure surrounding the pile. Over the period from the first year to the fifth year, the soil pressure around the pile exhibits a continuous upward trend. Furthermore, the interaction between pile and soil thermal expansion increases soil pressure at the pile–soil interface compared to other areas, while the pressure decreases toward the central portion of the pile.

4. Mechanism of Gangue Spontaneous Combustion on Pile Foundation

Coal gangue self-heating is a complex physicochemical process influenced by multiple factors, including the intrinsic properties of coal gangue, the conditions for spontaneous combustion, and external environmental factors. The self-heating process can result in a significant temperature rise, leading to thermal expansion and pyrolysis of materials, which may compromise the stability of the pile foundation. The high temperatures generated during the self-heating process could induce chemical changes in pile materials, potentially reducing their load-bearing capacity. Moreover, the displacement variations of the gangue mountain during combustion may impact the stability of the pile foundation. Regions with larger displacements are likely to correspond to areas where self-heating is more severe or where the heat source is more concentrated, whereas regions with smaller displacements may indicate areas with lesser thermal impact or inadequate heat transfer.

4.1. Temperature Distribution

Figure 8 presents the temperature profile of the pile foundation within the gangue mountain, clearly illustrating the impact of coal gangue self-heating on the pile’s temperature distribution. The figure reveals that under prolonged self-heating, heat primarily propagates upward from the heat source located at the base of the coal gangue mountain. As a result, the bottom of the pile, being closer to the heat source, exhibits higher temperatures, with the temperature gradually decreasing from the bottom to the top of the pile. This forms a distinct thermal gradient, where the bottom region of the pile experiences the highest temperatures, while the upper region remains relatively cooler.

This temperature distribution aligns with the fundamental principle of heat conduction, whereby heat transfers from regions of higher temperature to those of lower temperature. Under the influence of coal gangue self-heating, elevated temperatures may degrade the mechanical properties of the pile material, thereby increasing the risk of structural failure.

Figure 9 illustrates the temperature variations at different positions along the pile shaft, specifically at the pile top, mid-shaft, and pile bottom, all aligned along the same vertical axis. The results indicate that the pile shaft experiences continuous temperature increases due to coal gangue self-heating, with the rate of temperature rise being higher in regions closer to the heat source. Owing to the sustained heat release from the gangue combustion process, areas nearer to the heat source are subjected to more pronounced thermal effects, resulting in elevated temperatures that reach up to 400 °C. In contrast, the pile top, situated outside the gangue mountain and directly exposed to ambient air, exhibits a slower rate of temperature increase due to enhanced convective heat dissipation, with temperatures remaining below 100 °C.

4.2. Thermal Stress Variation in the Pile Shaft

During the spontaneous combustion of coal gangue, the high temperatures generated induce thermal expansion, leading to the development of thermal stress within the pile. As the temperature rises, the internal thermal stress gradually increases (Alice et al. [30]). When the stress exceeds the material’s yield strength, plastic deformation or failure may occur. Due to the greater constraints imposed by the surrounding soil at the bottom, the pile ends experience higher compressive stress compared to the middle section. Additionally, the interaction between the pile and the surrounding soil influences the stress distribution. Differences in thermal conductivity between the soil and the pile material, as well as the thermal expansion coefficient, may cause stress concentration at the interface, resulting in maximum stress at the pile–soil contact surface. Figure 10 shows the stress distribution in the pile. Stress variations under thermal stress were studied at the pile–soil interface; 1/4, 1/2, and 3/4 of the pile length; and near the pile bottom. The thermal stress in the pile changes due to soil constraints during thermal expansion, and its trend aligns with the temperature variation. Higher thermal stresses are observed at the pile–soil interface and near the pile ends due to pile–soil interaction.

4.3. Displacement

According to the theory of thermal expansion, material displacement due to temperature changes could be described using the thermal expansion coefficient and temperature variation. In the case of coal gangue spontaneous combustion, the temperature gradient induced by the heat source generates thermal expansion within the pile foundation, resulting in displacement. The distribution and magnitude of this displacement are critical for assessing the stability and safety of the pile foundation. Figure 11 illustrates the displacement profile of the pile cross-section, with data collected at three specific points: the pile top, mid-pile, and pile base. Analysis of the figure indicates that displacement is largest in the pile top region, likely due to significant thermal expansion caused by high temperatures generated during the spontaneous combustion of coal gangue. As temperature increases, the thermal expansion effect intensifies, leading to increased displacement of the pile.

In contrast, the displacement near the base edge of the pile is relatively small. This can be attributed to the greater depth of this region, where stronger constraints limit thermal expansion effects. The maximum displacement of the pile shaft reaches approximately 3.5 mm.

4.4. Variation in Pile Shaft Strain

Figure 12 and

Table 2. Strains in pile body.

Time (Year)		Strains (×10−3)
	Top	Middle	Near Bottom
0	0	0	0
1	0.495	0.204	2.317
2	0.599	0.241	2.803
3	0.638	0.256	2.988
4	0.654	0.263	3.066
5	0.662	0.266	3.102

show the strain distribution in the pile foundation at three points: the pile top, mid-pile, and base. The pile’s thermal expansion is constrained by the surrounding soil, and the soil’s expansion is similarly influenced by the pile. This interaction causes localized strain increases. Additionally, due to the differing thermal expansion coefficients between pile foundation materials and surrounding soil under thermal loading, significant strain concentration occurs at both the pile tip and pile head.

The lower pile section is closer to the heat source from coal gangue combustion. As a result, the surrounding soil absorbs more heat, causing greater thermal expansion and higher strain. Over time, the cumulative thermal effects further increase the strain magnitude.

5. Conclusions

Coal gangue spontaneous combustion is a complex physicochemical process involving multi-field coupling of flow, oxygen concentration, and temperature fields. These fields interact through oxygen mass transfer, heat accumulation, and thermal buoyancy effects, collectively driving the combustion process. The three-dimensional multi-field coupling model of coal gangue spontaneous combustion established using the finite element method accurately simulates the dynamic evolution of the internal combustion process in the gangue pile. The temperature variation trend predicted by the model is consistent with actual field observations, verifying the model’s reliability. The main conclusions are as follows:

• The self-heating and oxidation of coal gangue result in continuous temperature increases. During the early stages of spontaneous combustion, due to better ventilation conditions along the slopes, high-temperature regions first appear beneath the slope surfaces. Initially, the gangue pile experiences a rapid temperature rise, followed by a slower and stabilized rate of increase. Over time, high-temperature zones gradually expand toward the interior.
• The high temperatures generated by spontaneous combustion cause thermal expansion of the pile materials, leading to thermal stress within the pile. The variation trend of thermal stress in the pile corresponds closely with the temperature evolution. Due to pile–soil interactions, thermal stress is highest at the pile–soil interface and near the pile tip. Over time, the accumulated thermal effects from spontaneous combustion result in increasing strain, with maximum pile displacement reaching approximately 3.5 mm. These changes may compromise the stability and load-bearing capacity of the pile, increasing the risk of structural failure.
• Spontaneous combustion increases the porosity and permeability of the gangue pile, reducing its overall strength. Simulation results indicate that the displacement is most significant at the top of the gangue pile, especially in high-temperature regions. If not properly controlled, long-term cumulative displacement could compromise slope stability and potentially lead to landslides and other geological hazards.

Based on the numerical model predictions, several engineering measures are proposed to mitigate the effects of spontaneous combustion on surface subsidence and pile foundation stability. These include implementing soil covering or structural modifications to reduce internal temperatures, enhancing the thermal resistance of pile foundation materials, and designing real-time monitoring systems to detect temperature changes and potential risks.

To reduce computational time and improve convergence, this study adopts simplified model conditions. Future research could incorporate environmental factors such as material heterogeneity in gangue piles, sulfur-driven reactions, and radiative heat transfer to better characterize coal gangue spontaneous combustion. Additionally, model refinement could focus on pile–soil interaction mechanisms and other critical aspects.