Abstract
In this study, the impact of differential settlement in coal mining subsidence areas on the structural safety and operational performance of photovoltaic (PV) support structures was evaluated. Three-dimensional finite element models of fixed, horizontal single-axis tracking and flexible PV support structures were developed in ANSYS. Linear-gradient settlement was selected to represent ground inclination. The load-transfer paths, critical locations, and deformation adaptability of the three support types were compared. The results indicate that for fixed PV support structures, additional internal forces are mainly concentrated in the constrained columns. Mechanical response is strongly affected by both the support–settlement-gradient angle and the foundation constraint layout. The controlling critical inclination ranges from 17.5‰ to 19.2‰. Most load cases are governed by the column-top horizontal displacement limit. For horizontal single-axis tracking PV support structures, the strength-controlled and displacement-controlled critical inclinations are 31.8‰ and 17.5‰, respectively. However, the allowable height difference of the drive system limits the operation-controlled critical inclination to only 2.8‰. For flexible PV support structures, the prestressed steel strands are not the strength-controlled members within the analyzed range. In contrast, the Q235 end columns yield first. At this critical state, the controlling critical inclination is 18.3‰, and the column-top displacements remain within the code-specified limits. Fixed and flexible PV support structures exhibit comparable adaptability to the investigated inclination. In contrast, the horizontal single-axis tracking PV support structure is much more sensitive to foundation levelness and inter-column height differences. These findings provide a case-specific reference for comparing the deformation adaptability of the three investigated PV support systems under the prescribed linear-gradient settlement condition.
Highlights
The deformation resistance of three typical PV support structures was systematically compared and discussed under identical ground settlement conditions.
A critical inclination-based evaluation framework was established by integrating structural serviceability criteria, operational constraints, and deformation limits.
The control mechanisms for deformation and stress response in PV support structures were determined, providing design recommendations for the distribution of different types of PV supports in coal mining areas.
1 Introduction
The global transition toward low-carbon energy and the growing demand for intensive land use have encouraged the integration of coal-mining-subsidence remediation with photovoltaic power-plant construction (). This approach reuses degraded land without occupying large areas of new construction land and provides an engineering pathway for ecological restoration, new energy development, and industrial transformation in mining areas (; ; ; ). Coal mining subsidence areas possess the practical foundation for developing ground-mounted PV power plants (). However, compared to conventionally leveled sites, these areas exhibit distinct residual effects from mining operations and characteristics of ongoing deformation. PV support structures are numerous, widely distributed, and directly subjected to foundation deformation and environmental loads. Therefore, the effects of uneven surface deformation on the structural performance of PV support structures require systematic investigation.
Surface deformation in coal mining subsidence areas is essentially the result of overburden movement caused by underground mining disturbances being transmitted to the surface. Figure 1 illustrates that this typically manifests as the combined effect of multiple deformation components, including settlement, inclination, curvature, and horizontal tensile or compressive deformation (; ). Relevant studies indicate that surface movement in coal mining subsidence areas exhibits distinct spatial variability and temporal evolution characteristics (; ). During the post-mining phase, residual subsidence and delayed subsidence may persist for an extended period. Particularly in abandoned goafs and areas subject to long-term mining-induced effects, the surface does not necessarily stabilize immediately upon the completion of mining operations (; ; ). Furthermore, fault structures may lead to asymmetric development of subsidence basins and to localized concentrations of deformation (). Accordingly, the ground conditions beneath PV support structures in coal-mining subsidence areas should not be treated as simple, uniform settlement. They are better described as non-uniform deformation with spatial variability, continuous evolution, and multifactor control.
FIGURE 1
From the perspective of mining subsidence theory and the soil-foundation-structure interaction, ground deformation is transmitted to the superstructure through foundation constraints and support displacements. Similar deformation transfer and failure evolution mechanisms have been reported in mining support systems, where rock mass properties and reinforcement interactions influence load redistribution and structural stability (; ; ; ; ). This causes additional deformation, additional internal forces, and localized damage. systematically summarized the mechanisms, prediction methods, and engineering impacts of mining-induced subsidence. Their work established a theoretical foundation for evaluating its effects on engineering structures. Previous studies have proposed evaluation methods based on angular deformation, horizontal strain, and structural stiffness to assess structural damage caused by differential settlement (; ; ). These studies indicate that structural damage is closely related to differential settlement and structural stiffness, and that the transmission of free-field ground deformation to the superstructure through the foundation is jointly influenced by structural stiffness, foundation type, and boundary conditions (; ; ; ). Studies on excavation- and tunnel-induced ground deformation have shown that interaction between the superstructure and the foundation can alter the settlement profile and the internal force distribution within structural members (; ). Although these studies primarily focused on buildings and adjacent tunnel projects, A useful transmission mechanism has been revealed: ground surface deformation, foundation constraint, and structural response. This mechanism helps explain the mechanical response of PV support structures in coal mining subsidence areas under non-uniform ground deformation.
Under non-uniform ground deformation, structural response is affected by support settlement patterns, structural stiffness, and boundary constraints. Therefore, structural safety cannot be assessed solely from the maximum settlement value. Existing research indicates that different types of structures exhibit clear differences in their ability to adapt to differential settlement (; ). Taking spatial trusses as an example, support settlement leads to the redistribution of internal forces in members and the generation of additional bending moments at joints (). pointed out that the damage risk of engineering structures under non-uniform ground deformation requires a comprehensive evaluation. Both ground deformation characteristics and structural deformation capacity should be considered in this evaluation. For PV support structures in coal mining subsidence areas, non-uniform ground deformation is one of the key factors affecting structural safety performance and service adaptability.
Regarding the structural mechanical performance of PV support structures, existing research has primarily focused on fixed or ground-mounted PV arrays, horizontal single-axis tracking PV support structures, and flexible or cable-supported PV support structures. Previous studies on fixed PV support structures have mainly focused on structural design and wind-induced responses (; ; ). With the advancement of tracking technology, research on horizontal single-axis tracking PV support structures has increasingly focused on the effects of tracking error, irradiance mismatch, and operational conditions on structural forces (; ; ). In recent years, flexible PV support structures have garnered widespread attention due to their long spans and low steel consumption. Related research has primarily focused on wind-induced responses, structural design, and dynamic characteristic analysis (; ; ; ; ; ). Furthermore, as connection nodes play a crucial role in the transmission of structural forces, their mechanical properties and stress redistribution patterns have also received some attention (; ). However, existing research mainly addresses wind loads, self-weight, operational loads, and conventional foundation conditions. The structural response of PV support structures to uneven ground deformation in coal mining subsidence areas has received relatively limited attention.
The existing studies provide useful references for evaluating structural response under non-uniform foundation deformation and for improving the deformation resistance of PV support structures. However, most available research on PV support structures has focused on wind loads, self-weight, operational loads, or conventional foundation conditions. However, comparative investigations of fixed, horizontal single-axis tracking and flexible PV support structures under the same settlement-induced deformation have remained limited, particularly for coal mining subsidence areas. In particular, the differences in load-transfer mechanisms, critical members, serviceability limits, and operational constraints among these support types have not been systematically clarified. To address this gap, this study selected inclination induced by linear-gradient settlement as a representative deformation condition in coal mining subsidence areas. Three-dimensional finite element models of fixed, horizontal single-axis tracking and flexible PV support structures were established using ANSYS. Strength-controlled, displacement-controlled, and operation-controlled critical inclination limits were used to evaluate by considering member yielding, column-top horizontal displacement limits, and tracking-system operational requirements. The mechanical responses of the three support types were comparatively investigated. The results are intended to provide a comparative reference for the selection and deformation-resistant design of the investigated PV support structures.
2 Finite element modeling of PV support structures
2.1 Three typical types of PV support structures
This study is based on a national-scale PV project located in the Ordos coal-mining subsidence area. The project utilizes areas designated for future coal mining to construct a photovoltaic power plant. In response to the complex geological conditions, Shanghai Electric adopted solutions including fixed, flexible, and horizontal single-axis tracking PV support structures to effectively address the challenges of typical non-uniform subsidence in coal mining subsidence areas.
2.1.1 Fixed PV support structures
Fixed PV support structures feature a simple design, fewer components, and lower construction and O&M costs, offering good economic efficiency and reliability as shown in Figure 2. This makes them widely used in large-scale ground-mounted photovoltaic power plants. Their main advantages include high overall stiffness, clear load-bearing paths, and ease of installation and maintenance, making them well-suited for large-scale centralized construction. However, because the inclination angle of the modules is fixed and cannot be adjusted according to changes in the sun’s altitude angle, solar energy utilization efficiency is relatively low.
FIGURE 2
2.1.2 Horizontal single-axis tracking PV support structures
Figure 3 illustrates that single-axis tracking PV support structures track the sun’s movement around a horizontal axis, allowing the modules to maintain an optimal angle of incidence throughout the day. This improves power generation efficiency. Compared to fixed PV support structures, they offer higher solar utilization efficiency and are particularly suitable for regions with abundant solar radiation. However, the addition of drive systems, control systems, and transmission mechanisms increases structural complexity and construction costs. They also require higher installation precision and stricter operational and maintenance management, while the risk of equipment failure and subsequent maintenance costs also rise accordingly.
FIGURE 3
2.1.3 Flexible PV support structures
Figure 4 shows that flexible PV support structures typically use a load-bearing structure composed of prestressed steel strands, spatial trusses, and steel columns. They achieve long-span support for photovoltaic modules by leveraging the high tensile efficiency of the cable structure. Compared to traditional fixed PV support structures, they feature large spans, light structural weight, fewer foundation points, and strong site adaptability, offering promising application prospects in complex terrain and under special site conditions. Since flexible PV support structures belong to a low-stiffness structural system, their deformation compatibility and internal-force distribution characteristics are strongly affected by applied loads and boundary conditions. This makes them relatively sensitive to external disturbances such as wind loads and support displacements.
FIGURE 4
2.2 Element types and material constitutive models
Three-dimensional finite element models of fixed, horizontal single-axis tracking, and flexible PV support structures were established using the ANSYS platform to investigate the structural mechanical response and deformation resistance under uneven ground deformation in coal mining subsidence areas. For element selection, truss members such as purlins, diagonal beams, and columns were modeled with the BEAM188 beam element to capture coupled axial and bending effects. Prestressed steel strands were modeled with the LINK180 tension-only element to represent their tensile behavior and geometric nonlinearity. Concrete foundations were discretized with three-dimensional solid elements to represent foundation constraints and local stress transfer.
An ideal elastic-plastic constitutive model was adopted, and strength was assessed using the von Mises yield criterion. Table 1 lists the material parameters and yield strengths of each member. An initial tensile force of 80 kN was applied to the prestressed steel strands using the initial strain method to simulate the actual tension state during construction of the flexible PV support structure and its initial loading conditions, thereby ensuring a reasonable initial stress state for the model. The load from the photovoltaic modules was applied to the steel strands and the PV support structure as an equivalent uniformly distributed mass. This accounted for the effect of module self-weight on the internal-force distribution of the overall structure and improved computational efficiency. Connections between structural members were represented by ideal nodal compatibility.
TABLE 1
| Support structure | Main component | Material | Yield strength σs (MPa) | Section size (mm) |
|---|---|---|---|---|
| Fixed PV support structure | Front and rear columns | Q355 | 355 | Ø68 × 2 |
| Inclined beams and diagonal tie rods | S350 | 350 | C80 × 40 × 15 × 2 | |
| Purlins | S450 | 450 | C70 × 50 × 15 × 1.8 | |
| Diagonal braces | Q235 | 235 | C60 × 45 × 2 | |
| Horizontal single-axis tracking PV support structure | Main axis | Q500 | 500 | ST140 × 3.0 |
| Purlins | S420 | 420 | C30 × 80 × 79 × 1.5 | |
| Columns | Q345 | 345 | H200 × 100 × 4.3 × 5.2 | |
| Flexible PV support structure | Prestressed steel strands | Grade 1860 steel strand | 1860 | Ø15.2 |
| End columns | Q235 | 235 | Ø 152 × 4 | |
| Middle columns | Q355 | 355 | Ø 180 × 4 |
Material parameters of main components of PV support structures.
2.3 Boundary conditions and loading procedure
To quantitatively evaluate the deformation resistance of different PV support structures, this study used “critical inclination” as a key performance indicator. According to GB 51101-2016, Basic Technical Specifications for Solar Power Station Support structures (), inclination is defined as the ratio of the difference in uneven settlement Δ between two points to the horizontal distance L between adjacent columns, i.e., Δ/L. Surface deformation in coal mining subsidence areas stems from the structural failure of overlying rock in underground goafs and the redistribution of mining-induced stresses. It typically manifests as a subsidence basin centered on the goaf, with ground surface settlement exhibiting a gradient distribution characterized by greater settlement at the center and lesser settlement at the edges. This pattern is accompanied by the coupled development of horizontal displacement and inclination, forming a pronounced non-uniform deformation field. Linear-gradient settlement was selected because it represents the dominant component of differential ground inclination affecting PV support structures while allowing direct comparison among different structural systems. In the numerical simulation, differential settlement was modeled by controlling the vertical displacement of each column. It was assumed that the ground surface inclined uniformly along the dip direction, and gradient settlement displacements were applied to each column according to a linear relationship.
The finite element analysis used a two-step loading method. In Step 1, the structure’s self-weight was applied, and the column bases were fully constrained to obtain the initial stress state. In Step 2, vertical displacements were applied to each column along the longitudinal axis of the support to simulate ground surface settlement. As shown in Figure 5, for linear uniform settlement conditions, the settlement values were increased linearly in sequence according to the column spacing to simulate uniform-inclination settlement. Under each scenario, inclination was incrementally increased up to 45‰ until yielding occurred. This value was selected to cover relatively severe inclination conditions and to ensure that the principal strength or deformation control state of each PV support structure could be identified. By extracting the corresponding critical inclination values, a quantitative comparison of the deformation resistance capabilities of fixed, horizontal single-axis tracking, and flexible PV support structures was conducted.
FIGURE 5
Due to the asymmetric nature of fixed PV support structures, there are clear differences in settlement displacement and additional internal-force distribution among the columns under different settlement-gradient orientation conditions. Thus, the influence of settlement-gradient orientation on structural behavior should be analyzed. To this end, four support-settlement-gradient angles, θ = 0°, 30°, 68°, and 90° (where θ is the angle between the support plane and the settlement gradient) were set. Additionally, two boundary conditions, fixed front columns (FC) and fixed rear columns (RC), were considered to reflect the impact of different foundation constraints on the structural response. Figure 6 indicates that different support-settlement-gradient angles lead to clear differences in the uneven settlement displacements experienced by each column and in the resulting distribution of internal forces.
FIGURE 6
3 Deformation resistance of three typical PV support structures under inclination
To comprehensively evaluate the resistance of PV support structures to inclination deformation, two types of indicators are defined: strength-controlled critical inclination and displacement-controlled critical inclination:
Strength-controlled critical inclination: The inclination value corresponding to the point at which the maximum equivalent stress of the first member in the structure reaches the material’s yield strength;
Displacement-controlled critical inclination: The inclination value corresponding to the point at which the horizontal displacement at the top of any column in the structure first reaches the limit specified in the code.
Because deformation resistance may be governed by either strength or displacement, this study uses the smaller of the two critical inclination values as the controlling critical inclination. This value is then used to evaluate the support structure’s resistance to inclination under different conditions.
3.1 Deformation resistance of the fixed PV support structure
3.1.1 Strength characteristics
3.1.1.1 Overall strength response under inclination loading
Figure 7 presents the relationship between the maximum equivalent stress of a fixed PV support structure and increasing inclination. When the inclination is small, the maximum equivalent stress increases linearly with inclination, and the structure as a whole remains in the elastic stress stage. As the inclination continues to increase, the maximum equivalent stress gradually approaches 355 MPa, at which point the stress-inclination curve reaches an inflection point, and the rate of increase subsequently becomes zero. This change corresponds to local members transitioning from the elastic stage to the plastic deformation stage, and the overall structural stiffness begins to decrease. Based on the criterion that the first member reaches yield, the inclination value corresponding to this inflection point can be taken as the strength-controlled critical inclination for the fixed PV support structure.
FIGURE 7
The strength-controlled critical inclination differs under different support-settlement-gradient angles, as Figure 8. When the rear column is fixed, this value first increases and then decreases as the angle increases. When the front column is fixed, it gradually decreases as the angle increases. The critical inclination for strength control under the rear-column-fixed condition is approximately 36% higher than that under the front-column-fixed condition. When the settlement gradient direction changes, the distribution ratio of foundation differential displacement between the longitudinal and transverse members of the support changes, ultimately affecting the inclination value corresponding to the yield state.
FIGURE 8
3.1.1.2 Stress distribution patterns in the support structure
The equivalent inclination serves as the prescribed displacement input at the foundation end. Due to foundation constraints, the fixed columns first generate additional bending moments and axial forces, which are then transmitted to the upper part of the support through crossbeams, diagonal braces, and connecting members. Figure 9 shows the stress distribution and bending-moment response of the fixed columns under different fixing methods when the angle between the support structure and the settlement gradient is 90°. In terms of stress distribution, high-stress zones are primarily located at the base of the fixed column and at its connection points with the diagonal braces. When the rear column is fixed, stress concentrations are mainly located in the rear column and adjacent connection areas. When the front column is fixed, the high-stress zones shift to the vicinity of the front column.
FIGURE 9
As the position of the fixed end changes, Figure 10 indicates that the foundation displacement constraint is redistributed between the front and rear columns, and the zone of concentrated additional bending moments shifts accordingly. For both fixing methods, the columns directly constrained by the foundation serve as the primary load-bearing members for the additional internal forces. The bending moments in the fixed columns are distributed non-uniformly along the height, with peak values primarily occurring in the middle and lower sections of the columns. As the inclination increases, the additional bending moments in this region continue to rise. The location of the bending-moment peaks largely coincides with the stress-concentration zones. Consequently, the middle and lower sections of the fixed columns become the primary load-bearing areas of the fixed PV support structure.
FIGURE 10
3.1.1.3 Strength response of key columns under inclination
To further identify the strength-limiting members, the variation in equivalent stress of each column with inclination was analyzed, as shown in Figure 11. The stress in all columns increases with the rise in inclination, but the rate of stress increase in the fixed columns is considerably higher than that in the other columns, reaching the material’s yield strength when the inclination reaches 25.48‰. After the fixed columns yield, their stress increase slows down, while the stress in the other columns continues to rise, resulting in a certain degree of internal-force redistribution within the structure. Combining Figures 8, 9, it is evident that the fixed columns not only bear higher additional bending moments but also reach the yield state first. Differences in the strength-controlled critical inclination under various support-settlement-gradient angle combinations primarily stem from the additional bending effects of the fixed columns and changes in the reaction forces at the joints. When evaluating the inclination resistance of the structure, the yield of the fixed columns serves as the basis for determining the strength-controlled critical inclination.
FIGURE 11
3.1.2 Displacement characteristics
Strength analysis indicates that the yield of the fixed column determines the structure’s load-bearing limit. However, for the structure, excessive deformation can also affect normal operation; displacement evaluation is also necessary. The Design Standards for Photovoltaic Power Stations () specify that the horizontal displacement at the top of a fixed support column is limited to 1/60 of the column height. The front column of this support structure is 1,581 mm tall, with a corresponding displacement limit of 26.35 mm. The rear column is 3,369 mm tall, with a corresponding displacement limit of 56.15 mm. Based on the above requirements, the column-top horizontal displacement was analyzed for different support-settlement-gradient angle conditions, with the results shown in Table 2. The results indicate that, under the condition where the rear column is fixed, the critical inclination corresponding to displacement for each angle is less than the critical inclination based on strength. The structure reaches its deformation limit before material yield, and its control state is determined by displacement. The corresponding critical inclination range is 17.5‰–19.2‰. Under the condition where the front column is fixed, the control mechanisms vary depending on the angle: the conditions at θ = 30° and 68° are displacement-controlled, while the condition at θ = 90° is strength-controlled.
TABLE 2
| Boundary condition | Angle,θ(°) | Strength-controlled critical inclination (‰) | Column-top horizontal displacement (mm) | Displacement-controlled critical inclination (‰) |
|---|---|---|---|---|
| Rear column fixed | 0 | 25.5 | 77.7 | 18.6 |
| 30 | 34.2 | 110.0 | 18.1 | |
| 68 | 32.3 | 103.4 | 19.2 | |
| 90 | 30.2 | 97.2 | 17.5 | |
| Front column fixed | 0 | 25.5 | 77.7 | 18.6 |
| 30 | 21.6 | 30.0 | 18.7 | |
| 68 | 19.2 | 26.4 | 19.1 | |
| 90 | 17.6 | 23.0 | 19.8 |
Critical inclination of fixed support under different angles.
In most cases, the displacement limit is reached before the strength limit, indicating that the structure is more sensitive to deformation. To balance safety and normal service performance, the smaller of the strength-controlled critical inclination and the displacement-controlled critical inclination is adopted as the structural controlling critical inclination. The calculation results show that this range is 17.5‰–19.2‰, indicating that the structure’s resistance to inclination is primarily controlled by deformation.
3.2 Deformation resistance of the horizontal single-axis tracking PV support structure
3.2.1 Strength characteristics
3.2.1.1 Overall strength response under inclination loading
Figure 12 presents the variation in the maximum equivalent stress of the horizontal single-axis tracking PV support structure as the inclination increases. When the inclination is small, the stress-inclination relationship remains essentially linear, and the structure operates entirely within the elastic range. When the inclination reaches 31.8‰, the maximum equivalent stress increases to 356 MPa, exceeding the column’s yield strength of 345 MPa. Subsequently, the curve inflects and gradually flattens as local members begin to undergo plastic deformation. The strength-controlled critical inclination of the horizontal single-axis tracking PV support structure is 31.8‰. Compared to fixed PV support structures, the load transfer system of the structure includes an additional main axis and a tracking drive system. The additional internal forces caused by inclination act not only on the columns but are also transmitted to the main axis and drive system through the column-main-axis connection nodes. The overall maximum stress curve can only determine the inclination value at which the structure initially enters the yield state. The specific strength control point must be determined by combining stress distribution and bending-moment response analyses.
FIGURE 12
3.2.1.2 Characteristics of load transfer under inclination
Figure 13 presents the stress distribution and bending-moment response of a horizontal single-axis tracking PV support structure under a 31.8‰ inclination condition. High-stress zones are primarily concentrated in the columns and their connection points with the main axis, with Column 7 exhibiting the highest stress levels. Stress concentrations near the main axis mainly occur in the connection areas of Columns 6 and 2. The load-transfer process corresponding to this distribution can be described in three stages. Differential foundation displacement first acts on the column system, then is transmitted through the connection nodes to the main axis, and finally causes additional stress concentrations near the local connection areas of the main axis.
FIGURE 13
The bending-moment distribution indicates that the bending moment at the base of Column 7 reaches its peak, as shown in Figure 14. This makes it the most unfavorable location for bending under this operating condition. Compared to other columns, Column 7 is subjected to both a large bending moment at its base and additional constraints at the connection node, making it more sensitive to inclination inputs.
FIGURE 14
3.2.1.3 Strength response of key columns under inclination loading
Figure 15 shows the variation in equivalent stress in each column as a function of inclination. The stress in all columns increases with increasing inclination, but Column 7 exhibits the highest rate of stress increase and is the first to reach its yield strength at an inclination of 31.8‰. At this point, the remaining columns are still in the elastic stage. As the inclination continues to increase, the stresses in the other members continue to rise. Following the local yielding of Column No. 7, internal-force redistribution occurs within the structure. The stress growth rate, yield time, and peak bending moment at the base of Column No. 7 correspond with one another. The yielding at the base of Column No. 7 is the primary indicator that the horizontal single-axis tracking PV support structure has reached the critical state of strength control.
FIGURE 15
3.2.2 Displacement characteristics
In addition to meeting structural safety requirements, the horizontal single-axis tracking PV support structure must also ensure the normal operation of the drive system. According to installation technical requirements, the allowable longitudinal error of the support is ±14 mm. This parameter reflects the control requirements for the flatness of the main axis. If the allowable height difference is taken as the full range of ±14 mm, i.e., 28 mm between adjacent supports, the corresponding operation-controlled inclination is approximately 2.8‰. According to the Standard for Design of Photovoltaic Power Stations (), the limit for column-top horizontal displacement is 1/80 of the column height. The column height in this support structure is 2,208 mm, corresponding to an allowable displacement of 27.6 mm. Calculations indicate that when the inclination reaches the strength critical value of 31.8‰, the displacement at the top of Column No. 7 is 50.4 mm, which exceeds the code limit. The corresponding critical inclination for displacement is approximately 17.5‰. A comparison of the different control conditions indicates that the operation-controlled inclination (2.8‰) is much lower than the displacement-controlled value (17.5‰) and the strength-controlled value (31.8‰). The actual deformation resistance of a horizontal single-axis tracking PV support structure is therefore limited by the operational requirements of the drive system, and its controlling critical inclination is 2.8‰.
3.3 Deformation resistance of the flexible PV support structure
3.3.1 Strength characteristics
3.3.1.1 Overall strength response under inclination
Figure 16 indicates that the maximum equivalent stress of the flexible PV support structure continues to increase as the inclination increases. When the inclination reaches 38.3‰, the maximum equivalent stress is 627 MPa. The primary load-bearing system of the flexible PV support structure consists of prestressed steel strands, with a standard tensile strength of 1860 MPa. Notably, since the steel strands are primarily subjected to axial tension, their strength evaluation cannot simply apply the equivalent stress yield criteria used for ordinary steel members. Furthermore, the standard tensile strength cannot be directly adopted as the design allowable stress. Based on the calculation results, the steel strands do not exhibit strength-limiting behavior prior to other members within the scope of the analysis. Thus, the strength-limiting locations of the flexible PV support structure cannot be determined solely based on the maximum stress in the steel strands. The stress development processes of the columns, beams, and end PV support structures must also be examined. To identify the limiting members, the analysis was conducted in conjunction with the structural stress distribution and load-transfer characteristics under critical conditions.
FIGURE 16
3.3.1.2 Characteristics of load transfer under inclined loads
The columns of the flexible PV support structure are numbered sequentially from No. 1 to No. 4. Columns No. 1 and No. 4 are end columns. In each end-column group, the shorter columns are designated as Column No. 1a and Column No. 4a, respectively, whereas the longer columns are designated as Column No. 1b and Column No. 4b. Columns No. 2 and No. 3 are middle columns.
In Figure 17, the stress distribution of the flexible PV support structure under an 18.3‰ inclination condition exhibits distinct non-uniform characteristics. The beam members and prestressed steel strands bear greater tensile forces, while the stress levels in the concrete foundation are relatively low. Compared to fixed and horizontal single-axis tracking PV support structures, the flexible PV support structure can transmit and adjust additional loads to a certain extent through its upper tensioning system.
FIGURE 17
Stress in the columns is primarily concentrated at the column bases, which remain the most vulnerable areas to bending in the PV support structure, as Figure 18. In terms of bending moment distribution, the column bases are the primary areas subjected to bending. The overall stress level in the central columns is slightly higher than that in the end columns, posing a certain risk of plastic deformation. However, the central columns are made of Q355 steel, which has a relatively high strength reserve. The end columns are made of Q235 steel and are located at a critical position for transmitting strand tension to the foundation. In addition to bearing the additional bending moments caused by inclination, they must also withstand the local confinement effect during the load transfer process of the tensioning system. The analysis combines the stress variations of different columns with their changes under increasing inclination.
FIGURE 18
3.3.1.3 Strength response of key columns under inclination
Figure 19 presents the variation in equivalent stress for different columns as inclination increases. The stress in each column exhibits elastoplastic behavior characterized by an initially approximately linear increase followed by entry into a yield plateau. Among them, Columns 1a, 1b, 4a, and 4b reach the yield state first, corresponding to a strength-controlled critical inclination of 18.3‰. The central columns Nos. 2 and 3 reach yield at a considerably higher inclination value of 38.3‰. As the inclination increases, the end columns consistently enter the yield stage earlier than the central columns. Based on the criterion that the first member to reach yield determines the limit, the critical inclination controlling the overall strength of the flexible PV support structure is set at 18.3‰. The end columns yield first mainly for two reasons. First, they are made of Q235 steel, which has a lower yield strength than the middle columns. Second, the end regions carry additional internal forces generated as steel-strand tension is transmitted to the foundation, making the column bases more prone to bending concentration under inclination. Thus, the strength control of the flexible PV support structure is not primarily triggered by the steel strands but is mainly governed by the yield of the end columns.
FIGURE 19
3.3.2 Displacement characteristics
According to the Design Standards for Photovoltaic Power Stations (), the horizontal displacement at the top of steel support columns in flexible PV support structures is limited to 1/80 of the column height for deformation resistance evaluation. The corresponding displacement limits range from 33.60 to 43.39 mm for the different column heights. Analysis of the total horizontal displacement at the top node of each column indicates that, at the critical inclination of 18.3‰, all column-top displacements remain below the specified limits. End column b has the largest displacement, 29.20 mm, compared with a limit of 43.39 mm. End column a displaces 12.03 mm, and the central column displaces 18.00 mm; none exceed their limits. Throughout the entire loading process, the column-top horizontal displacement consistently satisfies the code requirements. Displacement is not a controlling factor in the deformation resistance of the flexible PV support structure. The critical inclination remains 18.3‰, and the end columns are the key members determining the structural strength limit.
4 Discussion of deformation resistance and engineering applicability of the three PV support structures
The analysis results indicate that fixed, horizontal single-axis tracking and flexible PV support structures exhibit different mechanical responses under inclination in coal mining subsidence areas. Table 3 summarizes the significant differences among the three support types in deformation adaptability and controlling factors, which arise from their different structural designs and operational requirements.
TABLE 3
| Support structure | Critical inclination (‰) | Governing criterion | Governing component |
|---|---|---|---|
| Fixed PV support structure | 17.5–19.2 | Displacement-controlled | Fixed column |
| Horizontal single-axis tracking PV support structure | 2.8 | Operation-controlled | Drive system |
| Flexible PV support structure | 18.3 | Strength-controlled | End column |
Comparison of resistance to ground inclination among three types of PV support structures.
Fixed PV support structures behave as a relatively rigid structural system under ground inclination. The system has a limited capacity to coordinate overall structural deformation. Consequently, inclination-induced forces cannot be effectively redistributed throughout the structure and are carried primarily by the constrained columns. The governing response therefore depends strongly on the foundation constraint layout and the support–settlement-gradient angle rather than on the strength of individual members. Serviceability rather than member strength governs the deformation resistance of fixed PV support structures. In coal mining subsidence areas, design priority should be given to controlling differential foundation settlement and column-top horizontal displacement rather than merely satisfying strength requirements.
Unlike fixed PV support structures, horizontal single-axis tracking systems are governed by both structural response and tracking-system operation. Inclination not only induces additional internal forces and structural deformation in the columns but also alters the height difference between adjacent columns and the flatness of the main shaft, thereby affecting synchronized drive-system operation and tracking accuracy. Consequently, although structural members still possess a certain safety margin, operational functionality typically becomes the limiting factor before structural failure occurs. The suitability of horizontal single-axis tracking PV support structures depends not only on structural safety but also on foundation-construction accuracy, long-term ground deformation, and operational maintenance.
Prestressed steel strands redistribute settlement-induced loads throughout the structural system. Unlike fixed PV support structures, the prestressed tensioning system provides an effective load-redistribution mechanism that accommodates differential foundation deformation and redistributes inclination-induced additional internal forces throughout the structural system. Consequently, the combined effects of cable tension and additional bending moments become concentrated in the end anchorage regions, making the end columns the governing members. The strong deformation adaptability of flexible PV support structures primarily stems from the load redistribution effect of the tensioning system, whereas their structural performance depends largely on the reliability of the end anchorage system. Engineering design should emphasize strengthening the end columns, column-foot joints, and anchorage foundations while reasonably controlling prestress loss.
A comprehensive comparison reveals that the responses of the three PV support structures to inclination reflect different structural design philosophies. The three support types exhibit distinct design philosophies. Fixed systems achieve stability through higher stiffness, flexible systems through load redistribution, and horizontal single-axis tracking systems through active tracking. These differences determine their sensitivity to ground deformation and their engineering applicability. Therefore, suitability assessments in coal mining subsidence areas should not be based solely on member strength. They should comprehensively consider structural safety, serviceability, and equipment operation while selecting appropriate support types and foundation-treatment schemes based on predicted ground-deformation characteristics. In areas with small ground slope and controllable long-term deformation, horizontal single-axis tracking PV support structures may be prioritized to improve power-generation efficiency. In areas where sustained differential settlement or significant ground slope is expected, fixed and flexible PV support structures offer better engineering adaptability. Flexible PV support structures provide better deformation adaptability because of load redistribution through the prestressed tensioning system.
5 Conclusion
Three-dimensional finite element models of fixed, horizontal single-axis tracking and flexible PV support structures were established. Uniform inclination induced by linear-gradient settlement was adopted as the representative deformation condition. The critical inclination of each support type was evaluated using the applicable strength, serviceability, and operational criteria. The main conclusions are as follows:
Due to differences in structural systems, constraint conditions, and operational requirements, the control mechanisms vary significantly. Fixed PV support structures are generally governed by serviceability displacement. Horizontal single-axis tracking PV support structures are controlled by the operational functionality of the drive system. Flexible PV support structures are controlled by the strength of the end columns.
For fixed PV support structures, the controlling critical inclination under most conditions ranges from 17.5‰ to 19.2‰, and the column-top horizontal displacement typically reaches its limit before member yielding occurs. For horizontal single-axis tracking PV support structures, the members still retain a safety margin in terms of strength and displacement, but the operation-controlled critical inclination is limited to 2.8‰ by the requirements of the drive system. For flexible PV support structures, the controlling critical inclination is 18.3‰. Since the steel strands do not reach yield within the analyzed range, the end columns serve as the controlling members.
There are significant differences in the resistance to inclination among the three types of PV support structures. Both Fixed and flexible PV support structures exhibit good deformation resistance. Among them, flexible PV support structures can coordinate structural stresses through a prestressed tensioning system, which gives them better deformation adaptability. In contrast, horizontal single-axis tracking PV support structures are more sensitive to foundation levelness and inter-column height differences, and the engineering applicability is constrained primarily by actual requirements.
In practice, ground settlement data can be obtained from prediction or monitoring, and the local inclination can be compared with structure-specific limits to guide structural selection and foundation design. The proposed evaluation method provides a quantitative approach for different limit states, but the critical thresholds should be recalculated for different PV support structures due to variations in structural and boundary conditions.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
YC: Writing – original draft, Investigation, Software. KZ: Conceptualization, Writing – review and editing. YL: Writing – review and editing, Data curation. FL: Writing – review and editing, Methodology. WD: Writing – review and editing, Formal Analysis. QG: Supervision, Writing – review and editing. LS: Writing – review and editing, Validation. LK: Funding acquisition, Writing – review and editing. YS: Resources, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Science and Technology Project of Power Construction Corporation of China, Ltd. (Project No. DJ-ZDXM-2023-12).
Conflict of interest
Authors YL and WD were employed by POWERCHINA Shanghai Electric Power Engineering Co., Ltd. Authors FL and LS were employed by Shanghai Clean Tunnel Engineering Technology Co., Ltd. Authors FL and LK were employed by China Energy Engineering Group Anhui No.2 Electric Power Construction Engineering Co., Ltd. Author YS was employed by Cambrian Deep Earth Technology (Suzhou) Co., Ltd.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The authors declare that this study received funding from China Power Construction Corporation Limited. The funder provided relevant technical materials and participated in reviewing parts of the manuscript for technical accuracy.
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Summary
Keywords
coal mining subsidence area, critical inclination, deformation resistance, ground surface settlement, numerical simulation, PV support structure
Citation
Chen Y, Zhang K, Li Y, Li F, Dai W, Gu Q, Shen L, Ke L and Shen Y (2026) Analysis of resistance to uneven deformation of typical photovoltaic support in coal mining subsidence area. Front. Mater. 13:1931864. doi: 10.3389/fmats.2026.1931864
Received
08 July 2026
Revised
07 August 2026
Accepted
10 August 2026
Published
11 September 2026
Volume
13 - 2026
Edited by
Hao Shi, Anhui University of Science and Technology, China
Updates
Copyright
© 2026 Chen, Zhang, Li, Li, Dai, Gu, Shen, Ke and Shen.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Kai Zhang, kzhang@cumt.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.