Influence of adjacent undercutting line positions on surrounding rock stability in block caving

Abstract

In the block caving mining method, deformation and collapse can occur in roadways due to vertical stress concentration in front of the undercutting line. Therefore to better understand this behavior, we establish a mechanical model of two neighboring solidly-supported and two neighboring simply-supported stepped bottom space structures based on the theory of elastic plates. From this we derive an approximate analytical formula of the bending deflection function and an expression of the stress distribution using the Rayleigh-Ritz method. This mechanical model is applied to control the stability of perimeter rock near the undercutting advancement line in the Pulang Copper Mine in China, and optimize the positional relationship between adjacent undercutting advancement lines. The results indicate that both a larger misalignment between adjacent advancing lines and a closer spacing of the undercutting roadways significantly reduce the stability of the surrounding rock. The results of this study provide theoretical support and methodology for undercutting planning in block caving.

Introduction

Block caving is an efficient, large-scale, and low-cost mining method^1,2. Its advantages are comparable with that of open pit mining, and the undercutting technique is the core of the block caving method. As such, undercutting lines have been studied extensively^3–7. Rojas et al.⁸ found that facilities below the undercutting advancing line need to be monitored and repaired significantly before leaving ore to be extracted, and determined that it was undercutting that causes damage to the extraction structure; they found that the application of undercutting advancement can partially avoid this phenomenon⁹. This phenomenon can also be avoided to an extent by using advance undercutting. Castro et al.¹⁰ used a laboratory physical model to study the change of vertical stress in extraction structures under three kinds of ore release scenarios, demonstrating that the vertical stress is mainly affected by the ore release area and the distance to the ore release advancing line. Ding¹¹ monitored the stress and strain of an extraction structure during undercutting processes in the Copper Ore Valley Mine as part of block caving, revealing that the stress state of the extraction structure was mainly affected by the undercutting advancing line. The stress concentration in the extraction structure spanned the range of −30~20 m from the undercutting advancing line, and the peak of stress concentration was located in the first 10 m of the undercutting advancing line. Also, Cao¹² analyzed the stress concentration in front of the undercutting line in the Pulang Copper Mine during block caving, and concluded that the vertical stress concentration mainly manifests in front of the undercutting line, as shown in Fig. 1.

Fig. 1.

Schematic of the vertical stress distribution in front of the undercutting advancing line.

While previous studies have well documented the stress concentration ahead of a single undercutting advancing line, there is a notable lack of research addressing the mechanical interactions and stress superposition effects caused by the misalignment between adjacent advancing lines. In the process of block caving, the advancement speed of the undercutting branch roadway is often inconsistent, and this can lead to problems^13,14. For example, in China’s Pulang Copper Mine, when the horizontal gap between the adjacent undercutting branch roadway advancing line exceeded 8.0 m, the deformation of the roadway near the adjacent undercutting branch roadway advancing line increased, there was collapsing, and frequent secondary patching of the hole was required, as shown in Fig. 2. This negatively affects the execution of the undercutting plan, and also has an impact on the stability of the extraction structure. Therefore, it is vital to study the positional relationship between neighboring undercutting advancing lines (i.e., the horizontal spacing of undercutting branch alleys and horizontal gaps of undercutting advancing lines) to maintain the stability of undercutting roadways.

Fig. 2.

Engineering issues of the 3736 m undercutting roadways in the Pulang Copper Mine, Yunnan Province, China.

Mechanical modeling theory of drag bottom horizontal space structures

Spatial structure characteristics

The collapse of ore rock is not only affected by pressure arches, but also by self-gravity stress and the surrounding environment¹⁵. The formation of the mining airspace between adjacent undercutting advancing lines will cause the vertical stress concentrations to superimpose on each other at the convex corners, in a process called superimposed vertical stress concentration, as shown in Fig. 3.

Fig. 3.

Diagram of superimposed vertical stress concentration.

Since the progress of neighboring undercutting advancing lines in block caving is inconsistent, a step-shaped undercutting structure will be formed, as shown in Fig. 4. In the establishment of the corresponding mechanical model, the neighboring collapse side is regarded as the simply-supported boundary, and the mineral rock is regarded as the solidly-supported boundary, which can be equated to the isotropic uniform elastic plate of the surrounding rock that may collapse.

Fig. 4.

Schematic of the step-shaped undercutting structure.

According to existing research results on thick plate decomposition, when there is a weak interlayer in the thick plate, the thick plate will be delaminated under transverse shear, and the delaminated plate is then referred to as a “key thin layer,” as shown in Fig. 5. In addition, according to the theoretical deduction of Wang¹⁶, the thick magma rock will also be damaged by shear from the center plane, which will lead to layering of the thick plate. Block caving undercutting performed to induce the disintegration of the block is generally not greater than diameter 1.0 m, and is layered off, assuming the thickness of the disintegration of the center face of the key plate layer, and that the ratio of the length of either side of the rectangular rock plate and the thickness of the key thin plate layer is about 5 to 100, thus meeting the basic assumptions of elastic thin plate conditions. At the same time, the rock body applicable to the block caving is generally more broken, and can be disintegrated under the effect of small deflection bending; this is also in line with the assumptions of elastic thin plate theory.

Fig. 5.

Shear delamination motion model of the thick plate.

In this study, the key thin plate layer at the undercutting boundary step is regarded as a rectangular elastic thin plate. Small deflection theory for an elastic thin plate is used to solve for the deflection, stress, and energy of the induced avalanche enclosure under the boundary conditions of solid support on two adjacent sides and simple support on two adjacent sides. Accordingly, we also analyze the changes in stress and energy of the enclosure under the undercutting induced avalanche conditions.

Construction of the mechanical model

In the process of applying the theory of an elastic thin plate, it is necessary to make a few assumptions. Using Kirchhoff theory, we will consider a uniform, continuous material which is isotropic and linearly elastic to model small deflections. On the basis of ignoring the shear strain, the thin plate bending deformation occurs in a direction perpendicular to the normal length of the thin plate, after the mid-plane is unchanged and is still perpendicular to the elastic surface. The deflection at each point of the thin plate bending is the same as the deflection of the center surface. Compared with the other two directions of positive stress, the plane parallel to the center surface of the thin plate is negligible. Finally, the deflection of the center surface of the thin plate is very small, and the expansion and contraction displacement is considered to be zero.

The right-angle coordinate system’s XOY plane coincides with the midplane of the plate, and the thin plate face is subjected to a vertically homogeneous load q. In this notation, a is the length of the working face advancement, b is the length of the working face, and h is thickness of the plate (Fig. 6).

Fig. 6.

Mechanical model of the elastic thin plate.

According to the theory of elastic thin plates and elastic mechanics^17–20, we can calculate the stress, strain, and energy components of the bending deformation of thin plates as follows.

1. Stress component

1

Where:

σ_x, σ_y: Normal stress components in the x and y directions, respectively [MPa].

τ_xy: In-plane shear stress [MPa].

w: Bending deflection of the plate [m].

µ: Poisson’s ratio of the plate material.

E: Modulus of elasticity (Young’s modulus) of the plate material [GPa].

z: Vertical coordinate through the plate’s thickness, measured from the neutral surface [m].

• (2)Strain component

2

Where:

ε_x,ε_y: Normal strain components in the x and y directions, respectively.

γ_xy: Engineering shear strain component.

• (3)Bending control theory

3

Where:

D: Bending rigidity (or Flexural rigidity) of the plate [N·m].

∇⁴: Biharmonic operator.

q: Distributed transverse load on the plate [MPa].

The flexural rigidity D is defined as:

4

• (4)Bending deformation energy of thin plates with small deflection.

The key thin plate layer undergoes bending deformation under its own weight and overlying rock loads. During deformation, the internal bending moments and torques perform work, which is stored as strain energy within the rock layer. The contributions from bending and torsion can be superposed to obtain the total bending deformation energy:

5

Where U_w is the elastic bending deformation energy [J].

Boundary conditions

With the advancement of undercutting, the exposed area of the adjacent undercutting space (of the mining airspace) increases, forming a rectangular rock plate with one side unchanged and one side expanding with the increase of the adjacent undercutting advancement line. For this reason, a corresponding mechanical model is constructed, where the rock body in the inner side of the airspace area is regarded as a solid support side, and the side of the airspace area is regarded as a simple support²¹. In this way, the working face at the corner of the undercutting support lane can be regarded as a rectangular rock plate. In this paper, we study the stress concentration degree and energy accumulation law of the rectangular rock slab under the condition that the long side continuously changes during undercutting (Fig. 7).

Fig. 7.

Mechanical model of the step-shaped drawdown.

The boundary conditions of the elastic thin plate with two neighboring edges being solidly supported and two neighboring edges being simply supported are:

6

A deflection function satisfying these boundary conditions is established using a double trigonometric series. To simplify the calculation, the deflection function is approximated by retaining the first term of the series:

7

Where A are the amplitude coefficients [m⁻¹].

The deflection function Eq. (7) of the elastic thin plate is substituted into the bending deformation energy equation (Eq. (5)) to obtain the bending deformation energy of an elastic thin plate that is fixedly-supported on both sides and simply-supported on both sides:

8

Using the Rayleigh-Ritz method, the total potential energy for the bending of a thin plate with small deflection (in the absence of external forces) is:

9

where I is the total potential energy [J].

According to the principle of minimum potential energy, a necessary condition for minimizing the total potential energy is that the first order variation of the total potential energy is zero, i.e.:

10

From Eqs. (9) and (10), we can derive the following:

11

In summary, the deflection of the elastic thin plate is given by:

12

The deflection function in Eq. (12) can be substituted into the thin plate bending deformation energy equation (Eq. (8)) to obtain the thin plate bending deformation energy equation as:

13

And if we let , then we obtain:

14

Solving this equation, the points of maximum deflection of an elastic sheet before bending and fracturing can be found as ,.

From the relationship between bending deflection and stress for an elastic plate, the expression for stress distribution before bending breakage can be obtained as:

15

The point of maximum perturbation in the x-direction is selected (i.e., ,):

16

where σ_tx is the tensile strength of the rock [MPa].

Since the strength of the rock is characterized by σ_t<σ_τ<σ_c, the breakage is mainly tensile damage under the combined effects of self-weight and vertical loading, so the stress concentration factor k_x can be expressed as:

17

Where k_x is the stress concentration factor in the x-direction.

Boundary stress concentration and accumulation law

From Eq. (17), it can be seen that the stress concentration coefficient k of the step structure is related to the undercutting roadways spacing a, gap b, and the thickness h of the key thin plate layer. The relationship between these factors and stress concentration is analyzed below.

In order to study the relationship between undercutting roadways spacing a, adjacent undercutting advancing line difference b, and the degree of stress concentration, the degree of stress concentration in the x-direction is calculated as an example. We assume that the spacing of the adjacent undercutting roadway is 15 m, 30 m, 45 m, 60 m, 75 m, and the differences of the advancing lines of the adjacent undercutting roadway gaps are 1 m, 5 m, 8 m, 10 m, 15 m, respectively. Also, we assume the thickness of the elastic sheet layer reflects the degree of fragmentation of the rock body. The relationship between the key thin plate thicknesses of 0.1 m and 0.5 m and the degree of stress concentration is shown in Fig. 8.

Fig. 8.

Vertical stress concentration with relationship between undercutting lane spacing. (a) a = 30 m, h = 0.1 m, (b) a = 30 m, h = 0.5 m.

As shown in Fig. 8, the stress concentration coefficient of the step structure for the increase of the gap between the advancing lines of adjacent undercutting roadways is a power function of the distance between the adjacent undercutting roadways. The vertical concentration of the stress coefficient grows faster, and when the stress reaches the tensile strength of the rock body, the surrounding rock will be deformed unstably and broken. Figure 8(a) illustrates that, assuming the thickness of the key thin plate layer is 0.1 m, when the spacing of adjacent undercutting branch roadways is 30 m, and the gaps between the advancing lines of adjacent undercutting branch roadways are 1 m, 5 m, 8 m, 10 m, and 15 m, the corresponding stress concentration coefficients are 7.8 × 10^− 4, 0.47, 2.94, 6.85, and 29.32 respectively. A Comparison with Fig. 8(b), assuming that the thickness of the key thin plate layer is 0.5 m, the corresponding stress concentration coefficients are 3.1 × 10^− 4, 0.02, 0.12, 0.27, and 1.17. It can be seen that the stress concentration coefficients are correlated with the thickness of the key thin plate layer, and the thickness of the plate layer reflects the degree of fragmentation of the rock body. In block caving, when undercutting to the rock body takes place in a more broken area, the gap between adjacent undercutting advancing lines should be reduced appropriately. This is done to reduce the stress concentration in the undercutting level, which indicates that avalanches of weak and surrounding rock rock from block caving are not only caused by pressure arches, but also by the environment of the surrounding rock on the edge of the undercutting.

Methods

Based on the aforementioned theoretical analysis, this paper employs a Rhinoceros-FLAC3D coupled approach to establish a numerical simulation model.

Model construction

A Rhinoceros-FLAC3D coupled simulation model^22–24 was established according to the design parameters of the copper mine in Pulang, and the model structure is shown in Fig. 9. The model has a strike length of 500 m, a vertical strike length of 500 m, a height of 217 m, and a total of 1,302,620 units. A total of 4 production roadways, 6 undercutting roadways, 49 drawbells, and 49 draw point drifts are placed at the mine exit level. The dimensions of the model were determined based on the engineering reality and the principle of minimizing boundary effects in numerical simulation. To ensure that the model boundaries did not influence the stress field in the area of interest, the distance from the model boundaries to any excavation was set to be greater than 3 times the equivalent size of the roadway, complying with Saint-Venant’s principle and thereby guaranteeing the accuracy of the computational results.

Fig. 9.

Model structure and name.

Strength criteria

The mechanical model for the Mohr-Coulomb shear yield damage in FLAC3D was chosen as ^25,26:

18

19

The mechanical model for the tensile yield damage is:

20

Where:

φ: angle of internal friction [°].

c: cohesive strength [MPa].

σ₁: maximum principal stress [MPa].

σ₃: minimum principal stress [MPa].

σ_t: tensile strength [MPa].

Note that in FLAC3D software calculations, negative values represent compressive stresses and positive values represent tensile stresses.

Rock mechanical parameters

The first mining area of the Pulang Copper Mine is primarily composed of quartz monzonite porphyry, diorite porphyrite, marble, and hornfels. The physical and mechanical parameters of these rocks mainly include: density, uniaxial compressive strength (σ_c), uniaxial tensile strength (σₜ), elastic modulus (E), Poisson’s ratio (ν), cohesion (c), and internal friction angle (φ). The average values of the rock mechanical parameters measured from laboratory tests are detailed in Table 1.

Table 1.

Average values of measured rock mechanical Parameters¹³.

Rock Type	p (g/cm3)	σ c (MPa)	σ t (MPa)	E (GPa)	ν	c (MPa)	φ (°)
Quartz Monzonite Porphyry	2.70	128.0	7.1	54.6	0.27	22.1	47.3
Dacite Porphyry	2.76	185.7	12.3	58.7	0.25	22.7	41.2
Marble	2.66	126.4	8.7	47.2	0.26	27.2	44.5
Hornfels	2.77	192.5	14.7	57.3	0.17	32.5	40.0

As the quartz monzonite porphyry is the most predominant and representative rock type in the mining area, it was selected for further analysis. This study focuses on the rock mass behavior derived from its properties. The Hoek−Brown strength criterion was employed to reduce and invert the laboratory-measured parameters of this rock (from Table 1), resulting in the representative rock mass mechanical parameters presented in Table 2.

Table 2.

Rock mass mechanic Parameters¹³.

Rock Type	E (GPa)	ν	p(g/cm 3)	c (MPa)	φ (°)	σ t (MPa)
Quartz Monzonite Porphyry	4.5	0.25	2.70	0.88	27.8	1.06

Ground stress field application

In-situ stress measurements at the Pulang Copper Mine indicate a geostress field dominated by horizontal tectonic stress. Accordingly, in the established three-dimensional model, the maximum principal stress was applied horizontally in the y-direction, perpendicular to the ore body strike, while the intermediate principal stress was aligned with the strike direction (x-direction). At the 3720 `undercutting level, which has an average mining depth of 300 m, the maximum, intermediate, and minimum principal stresses are 17.09 MPa, 11.85 MPa, and 8.16 MPa, respectively. The minimum principal stress corresponds to the vertical self-gravity stress. The measured ratios of horizontal to vertical stress (i.e., lateral pressure coefficients) in the mining area are 2.09 and 1.45, respectively, which is consistent with the distribution characteristics of lateral pressure coefficients derived from regional geostress measurements in mainland China.

Simulation procedure and program design

First excavate the production roadway and the undercut roadway, in the undercutting collapse, the specific simulation steps are as follows:

• I: Import the model, constrain the model boundaries, apply the initial geostress, and form the initial stress equilibrium. At this time the ore rock is in the original rock’s stress state.

• II: The excavation of the production roadway and the undercutting roadway, as shown in Fig. 10(a), creates the initial avalanche environment.

• III: Undercutting is performed from the middle to the two ends of the advance. Each color in Fig. 10(b) represents an undercutting group of the unit. The first excavation step is at the ② position to form the initial chipping, and then at position ③, with the forward undercutting state continuing on until finishing at the ⑤ position of the simultaneous excavation.

Fig. 10.

Model excavation sequence.

It should be noted that the numerical simulation results were somewhat disturbed by the excavation of the poly-mining channel, causing the transfer of vertical stresses in front of the drawdown advancement line. For this reason, this numerical simulation does not involve excavation of the poly-mining channel, which is the location shown in Fig. 10(c).

Results and validation

Analysis of the results

Following the numerical simulation, the slices at the positions shown in Fig. 11 are selected for analysis, and Fig. 12 shows a cloud view of the sliced simulation results after undercutting position ①.

Fig. 11.

FLAC3D model slice location.

Fig. 12.

Sliced cloud image after undercut position ①. (a) x-axis displacement map, (b) y-axis displacement map, (c) plastic zone distribution map, (d) z-axis vertical stress distribution cloud diagram.

As shown in Fig. 12(a), undercutting at position ① causes the sidewalls on the x-axis to converge towards the model center, with displacement increasing progressively from the exterior. This displacement field is symmetric in magnitude and direction. Similarly, Fig. 12(b) shows that undercutting induces a convergent displacement in the y-axis bottom rock, which also increases from the outside inward and exhibits symmetry. Figure 12(c) reveals plastic damage zones extending approximately 10 m from the outer edges of both the bottoming and drawdown spaces. Furthermore, significant vertical stress concentration is observed at the outer edge of the drawdown space in Fig. 12(d), with a maximum value of about 16 MPa located approximately 10 m ahead of the advancement line. These results demonstrate that undercutting induces vertical stress concentration and drives convergent displacement of the surrounding rock towards the model center.

As shown in Fig. 13(a), the convergent displacement of the x-axis sidewalls towards the model center remained nearly constant after undercutting position ②. Figure 13(b) shows that the surrounding rock near the undercutting line exhibited increased y-axis displacement towards the model center, with a symmetric distribution in magnitude and direction. Figure 13(c) indicates that undercut position ② expanded the plastic damage zone on the sidewalls of the adjacent undercutting roadway, thereby compromising its stability. Furthermore, Fig. 13(d) reveals that the increased gap between adjacent undercutting advancing lines led to a rise in vertical stress concentration at the convex corner of the undercutting structure, suggesting the generation of superimposed vertical stress.

Fig. 13.

Simulation results at the undercut position ② cloud map. (a) x-axis displacement map, (b) y-axis displacement map, (c) plastic zone distribution map, (d) z-axis vertical stress distribution cloud diagram.

Numerical simulations show that the larger the gap between adjacent undercutting advance lines, the greater the superposition of vertically concentrated stresses occurring at the convex corners of the drawdown structure. This affects the stability of surrounding rock in the vicinity of the neighboring undercutting roadways.

On-site validation

The initial support of the undercutting roadway in the Pulang Copper Mine adopted plain spraying concrete or wet spraying steel fiber concrete support, and locally adopted anchor net spraying support. According to our on-site research, the stress concentration of the undercutting roadway occurs in the range of 0ཞ30 m in front of the undercutting advancing line, which is manifested in the deformation and damage at the brow line, and the occurrence of local undercutting roadway collapses. Figure 14 shows the completed undercutting advancement map. From this map it can be seen that West of the undercutting roadway, along the roadway advancement, has more irregular patterns, while East of the undercutting roadway along the advancement line, a regular step structure is formed. The collapsed roadway is located to the West of the undercutting roadway (along the adjacent undercutting advancing line) with a large gap in the area (Table 3).

Fig. 14.

Schematic diagram of the location of the collapse of the undercutting level.

Table 3.

Statistics on the location of 3736 m horizontal ground pressure manifestation in the Pulang copper Mine.

3736 Horizontal locations	Distance between adjacent undercut advance lines/m	Ground pressure display location
S1N West along	14	Partial collapse of the roadway (0–12 m)
S7S/S7N East coast	20.1	Severe brow line deformation (0–30 m)
S2N West edge	10.2	Partial collapse of the roadway (0 to 8.0 m)
S4N West edge	29.2	Severe tunnel collapse (0–30 m)
S5S West	12	Partial collapse of the roadway (0–6.1 m)

Discussion

Based on the known characteristics of vertically concentrated stress in front of undercutting advancing lines in block caving²⁷, we constructed an elastic thin plate mechanical model with simple supports on two sides and fixed supports on the other two sides according to the spatial structural characteristics of the caving area. Theoretical analysis establishes a clear correlation: both increased misalignment distance between adjacent undercutting advancing lines and reduced spacing of undercutting roadways contribute to higher vertical stress concentration ahead of the advancing line. While prior research by Castro et al.¹⁰ and Ding¹¹ has firmly established the stress concentration ahead of a single undercutting advancing line, our study extends this understanding to the practical scenario of multiple, misaligned advances. We demonstrate that the interaction between adjacent lines creates a synergistic effect—superimposed vertical stress concentration—which intensifies with increasing misalignment distance and manifests most severely at the convex corners of the step-shaped structure. This fundamental mechanism explains the limitations of traditional single-line models in capturing complex stress redistribution patterns observed in actual mining practice. Our quantitative analysis provides substantial evidence for this phenomenon. When the misalignment distance increases from 5 m to 15 m, the vertical stress concentration factor shows a 3–5 times enhancement, offering a mechanical explanation for the field-observed preferential failure at convex corners in the Pulang Copper Mine. Furthermore, reduced undercutting roadway spacing from 30 m to 15 m leads to an approximately 2.8 times increase in the maximum bending moment of the equivalent thin plate, demonstrating the significant control of roadway spacing on surrounding rock stability. These findings have direct practical implications. We recommend controlling the misalignment between adjacent advancing lines within 8 m while maintaining roadway spacing at no less than 25 m for optimal stability conditions. More importantly, our research reveals the cascading effects of surrounding rock instability—frequent secondary deep-hole drilling not only disrupts mining schedule execution but also induces permanent damage to the underlying extraction structure through stress transfer mechanisms.

Although previous studies have confirmed through numerical simulations and field monitoring that the advancing undercutting method benefits rock mass stability^10,28, the influence mechanism of spatial relationships between adjacent advancing lines remained unexplored. Our study addresses this gap by revealing that adjacent undercutting lines form a thick plate structure with specific boundary conditions, generating significant superimposed vertical stress effects. It should be noted that in simplifying the thick plate structure to an elastic thin plate model, we made assumptions based on engineering experience due to challenges in precisely quantifying the equivalent thickness. Therefore, while this research successfully reveals macroscopic trends in how spatial relationships affect surrounding rock stability, precise quantitative evaluation requires further verification through additional field measurement data and refined modeling approaches.

Conclusions

1. The results demonstrate that increased misalignment between adjacent advancing lines and reduced undercutting roadways spacing intensify stress concentration in the surrounding rock. Once the induced stress exceeds the rock’s tensile strength, it triggers fracturing and deformation, thereby significantly compromising the stability at the edges of adjacent undercut branches.

2. The induced stress of undercutting increases with increasing length of undercutting, and the narrower the spacing of undercutting supporting roadways, the faster the induced stress grows. When the induced stress reaches the tensile strength of the rock body, the surrounding rock will be broken, deformed, and destabilized, and with the continuous advancement of the undercutting, the induced stress will be transferred to the deeper part of the rock body; this will cause persistent avalanches.

3. Failure Mechanism and Energy Transfer: Instability initiates as tensile failure at the high-stress, high-energy concentration zone near the advancement line. Furthermore, the bending deformation energy stored in the rock plate increases with the advance lag, and this energy drives the subsequent failure process, influencing the stability of the entire undercutting level.

Author contributions

Yong Cao participated in the whole process of work; Xinzhu Hua, revised and checked this paper; Heng Zhang provided technical guidance and experimental support. All authors have read and agreed to the published version of the manuscript.

Funding

1. Yunnan Province Key Research and Development Program Projects, China(52227901), Supporter : Hua Xinzhu; 2. Anhui Postdoctoral Scientific Research Program Foundation, China (2024C972), Supporter : Cao Yong.

Data availability

The data used to support the findings of this study are available from the corresponding author and first author upon request.

Declarations

Competing interests

The authors declare no competing interests.