A rock burst prevention and control parameter design method based on risk grading
Patent Information
- Application Number
- CN202610985794.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-03
- Publication Date
- 2026-09-25
AI Technical Summary
参数与具体位置的应力状态、煤体强度、地质构造没有定量对应关系,应力高的地段可能卸压不足,应力低的地段又过度施工
[0040]本发明的关键技术手段与有益技术效果:本发明卸压与支护参数设计由经验选取变为定量计算。孔径、间距、深度和支护参数与各分区的应力、强度、埋深、地质条件一一对应,并经六项验算保证卸压充分、卸压圈搭接、支护承载要求。按等级差异化施工使防控资源向高风险区集中,在同等安全水平下减少中低风险区的无效投入。
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Figure CN122818474A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of rockburst prevention and control technology, and relates to a quantitative design method for pressure relief boreholes and roadway support parameters. Specifically, it involves dividing the prevention and control area into zones based on geological and stress similarity, assessing the risk level based on stress level, and designing pressure relief and support parameters differently for different zones and risk levels. Background Technology
[0002] In rockburst prevention and control projects, pressure relief drilling and tunnel support are the most important local control measures, and the selection of their parameters directly determines the control effect and project investment. Current parameter determination methods have the following problems.
[0003] First, there's the reliance on empirical values. On-site, parameters are generally selected based on standard ranges and past experience. For example, large-diameter stress-relief boreholes are typically selected with diameters of 75–153 mm, spacing of 1–3 m, and depths of 15–30 m, with support methods copied from adjacent roadways. However, these parameters lack a quantitative correlation with the specific location's stress state, coal strength, and geological structure. Areas with high stress may experience insufficient stress relief, while areas with low stress may suffer from over-construction.
[0004] Second, analytical calculation methods consider only one factor. Existing technologies calculate the parameters of pressure relief boreholes based on simplified elasticity formulas, but the borehole diameter, spacing, and depth are determined independently and are not coordinated with each other. There is no correction for geological conditions, and after calculating the parameters, there is no verification process for whether the pressure relief is sufficient or whether the pressure relief ring overlaps.
[0005] Third, numerical simulation methods are inefficient. Using software like FLAC3D to calculate and analyze prevention and control plans requires 1 to 3 days to model and solve a single plan, and parameter optimization can only be done manually with two or three sets of trial calculations, making point-by-point optimization impossible.
[0006] Fourth, there is a lack of uniformity in prevention and control. A single set of parameters is often applied across the same mining area, without differentiation based on regional risk levels. While monitoring and early warning technologies can provide hazard alerts, these alerts don't translate into specific engineering parameters; where and how much reinforcement is needed remains subjective. The result is insufficient prevention and control in high-risk areas and wasted materials and time in low-risk areas.
[0007] In summary, the existing technology has three shortcomings: First, the control parameters are determined by experience, and there is a lack of a multi-factor quantitative design method that considers comprehensive stress, coal strength, burial depth and geological conditions; second, there is a lack of zoning and risk classification mechanisms, and it is impossible to allocate control resources according to risk differences; third, the parameter design lacks verification and iterative adjustment, and the design quality depends on personal experience. Summary of the Invention
[0008] To address the aforementioned technical problems, this invention proposes a risk-based design method for rockburst control parameters. The method divides the control area into spatially continuous zones based on geological and stress similarity and assesses their risk levels. For each zone, the diameter, spacing, depth, support density, and support strength of the pressure relief boreholes are quantitatively calculated according to its stress state, coal strength, burial depth, and geological conditions. Verification rules and iterative adjustments ensure that the design results meet requirements such as sufficient pressure relief, overlapping pressure relief rings, and support bearing capacity. Specifically, the method includes the following steps:
[0009] S1: Obtain stress distribution data within the rockburst prevention and control area;
[0010] S2: Calculate the similarity of each region within the control range and cluster them into zones, grouping regions with similar geological conditions, stress states, and spatial adjacencies into the same zone;
[0011] S3: Assess the risk level of each zone based on the stress ratio;
[0012] S4: Calculate the diameter, spacing, depth, support density, and support strength of the pressure relief boreholes for each zone based on its stress state, coal strength, burial depth, and geological conditions.
[0013] S5: Verify the pressure relief and support parameters of each zone through pressure relief adequacy calculation, pressure relief ring overlap calculation, depth coverage calculation, support bearing capacity calculation, construction feasibility calculation, and economic calculation.
[0014] Preferably, in step S1, the stress distribution data includes at least the maximum stress σ. max And the corresponding stress concentration factor.
[0015] Preferably, in step S2, the clustering and partitioning method includes S21: determining the comprehensive similarity between any two regions i and j within the control range:
[0016]
[0017] In the formula, F is the stress and strength eigenvector, including stress concentration factor, coal strength, and mining depth; d ij c is the spatial distance between the centers of region i and region j. g The geological relevance is expressed using the following formula:
[0018]
[0019] Δth, Δdip, and Δha represent the differences in coal seam thickness, dip angle, and hardness between regions i and j, respectively; σ f σ s σ t σ d σ hThese are the standard deviations of the stress eigenvector, the standard deviation of the spatial distance between the centers of the regions, the standard deviation of the coal seam thickness, the standard deviation of the coal seam dip angle, and the standard deviation of the coal seam hardness, respectively.
[0020] Preferably, in step S2, the clustering partitioning method further includes S22: performing clustering partitioning using an improved K-means algorithm.
[0021] by As a distance metric; the initial cluster centers are selected based on the local extrema of the stress distribution; after each iteration, the spatial connectivity of each cluster is checked, and unconnected clusters are split or isolated units are merged into adjacent clusters to ensure that each partition is spatially connected and can be constructed piece by piece in engineering.
[0022] Preferably, in step S3, the ratio of the predicted maximum stress to the critical bearing stress in each zone is used. As an indicator, R r A value ≥0.9 indicates a Level I high risk, while a value ≤0.7 indicates a high risk. r <0.9 indicates a Level II medium risk, R r <0.7 indicates Level III low risk; among which, σ a The critical bearing stress of the coal body. k is the confining pressure bearing capacity enhancement factor, σ c It represents the uniaxial compressive strength of the coal body.
[0023] Preferably, in step S3, the safety factor s under each risk level is determined. f Safety factor s for Level I risk zone f Take 1.6; Safety factor s for Level II risk area f Take 1.5 as the safety factor s for Level III risk areas. f Let's set it to 1.4.
[0024] Preferably, in step S4, the diameter D of the pressure relief borehole is calculated using the following formula. o
[0025]
[0026] In the formula, D b K is the reference diameter. s K is the stress concentration factor for the zone. r σ serves as the benchmark for stress concentration factor; r H serves as the benchmark for the uniaxial compressive strength of coal. d H represents the coal seam mining depth. r α is the benchmark for coal seam mining depth; α, β, and γ are fitting indices. The geological correction factor is calculated using the formula. Calculate Δhar, Δst, and Δwa, respectively, the normalized deviations of hardness ratio, structural complexity, and moisture content relative to standard conditions. , , This is the corresponding correction factor.
[0027] Preferably, in step S4, the spacing S of the pressure relief boreholes is calculated using the following formula. o
[0028]
[0029] In the formula, S b k is the reference spacing for pressure relief drilling. d f is the stress distribution density coefficient; i This is the correction factor for the interaction between adjacent holes.
[0030] Preferably, in step S4, the pressure relief borehole depth H is calculated using the following formula. o
[0031]
[0032] In the formula, H b L is the reference depth for pressure relief drilling. s L represents the influence length of the stress concentration zone along the drilling direction. r To affect the length reference value; G n For the normalized stress gradient, ρ g p is the stress gradient correction factor. f This represents the formation penetration coefficient.
[0033] Preferably, in step S4, the support density ρ is calculated using the following formula. s
[0034]
[0035] In the formula, ρ b The base support density; σ is the proportionality coefficient, n is the exponential coefficient; p The expected stress after depressurization using pressure-relief drilling. ;t f This is the material aging compensation coefficient. κ t The annual attenuation rate of support resistance, t s The service life of the tunnel design.
[0036] Preferably, in step S4, the support strength P is calculated using the following formula. s
[0037]
[0038] In the formula, P b As the benchmark support strength, The support resistance stress sensitivity index; l d denoted as the load distribution factor, and co as the component compatibility coefficient.
[0039] Preferably, in step S5, if any verification rule is not met, adjustments are made and the process returns to step S4 for recalculation until all rules are passed.
[0040] Key technical means and beneficial effects of this invention: The design of pressure relief and support parameters in this invention changes from empirical selection to quantitative calculation. The aperture, spacing, depth, and support parameters correspond one-to-one with the stress, strength, burial depth, and geological conditions of each zone, and six verification calculations ensure sufficient pressure relief, overlapping of pressure relief rings, and support bearing requirements. Differentiated construction according to risk level concentrates prevention and control resources in high-risk areas, reducing ineffective investment in medium- and low-risk areas under the same safety level. Attached Figure Description
[0041] Figure 1 A flowchart illustrating the parameter design method for rockburst prevention and control based on risk classification. Detailed Implementation
[0042] The specific embodiments of the present invention will now be described in conjunction with the accompanying drawings.
[0043] like Figure 1 As shown, the risk-based rockburst control parameter design method proposed in this invention is particularly applicable under the following conditions: mining depth 200–1200 m, coal seam thickness 1.5–8.0 m, coal seam dip angle 0–25°, coal strength 5–45 MPa, structural complexity index 0.1–0.9, gas content 0–20 m³ / t, and moisture content 0–15%. Specifically, it includes the following steps:
[0044] S1: Obtain stress distribution data within the rockburst prevention and control area.
[0045] The stress distribution data can be obtained from borehole stress measurements and microseismic activity inversion, or from numerical simulation calculations; the stress distribution data at least includes the maximum stress σ at each location within the control range. max (Generally the maximum vertical stress) and the corresponding stress concentration factor (maximum stress σ) max (Ratio to the original rock stress γH).
[0046] S2: Calculate the similarity of each area within the prevention and control scope and perform clustering and partitioning.
[0047] The purpose of zoning is to group areas with similar geological conditions, stress states, and spatial proximity into the same zoning, so that control parameters can be designed uniformly according to zoning and construction can be organized according to zoning.
[0048] The comprehensive similarity between any two regions i and j within the control area is calculated using the following formula:
[0049]
[0050] In the formula, F is the stress eigenvector, which generally includes the stress concentration factor, coal strength, and mining depth. Each component of the stress eigenvector F is first normalized to min-max and then the Euclidean distance is calculated; d ij Let be the spatial distance between the centers of region i and region j.
[0051] c g The geological relevance is expressed using the following formula:
[0052]
[0053] Δth, Δdip, and Δha represent the difference in coal seam thickness, dip angle, and hardness between regions i and j, respectively. The stress eigenvector F is related to the geological correlation c. g Orthogonal partitioning and non-overlapping inclusion are used to measure stress state similarity and geological occurrence similarity, respectively; σ f σ s σ t σ d σ h These are the standard deviations of the stress eigenvector, the standard deviation of the spatial distance between the centers of different regions, the standard deviation of the coal seam thickness, the standard deviation of the coal seam dip angle, and the standard deviation of the coal seam hardness. These are all standard deviations of statistical data. The data source for the standard deviations is to select N regions within the entire mine area and statistically analyze the standard deviations of the corresponding indicators based on these regions.
[0054] Clustering partitioning is performed using a constrained improved K-means algorithm: As a distance metric (the higher the similarity, the smaller the distance); the initial cluster centers are selected based on the local extreme points of the stress distribution to avoid random initialization leading to unstable partitions; after each iteration, the spatial connectivity of each cluster is checked, and unconnected clusters are split or isolated units are merged into adjacent clusters to ensure that each partition is spatially connected and can be constructed piece by piece in engineering; the number of clusters K is determined within the range of 3 to 8 based on the contour coefficient and engineering experience.
[0055] S3: Assess the risk level of each zone based on stress ratio.
[0056] The ratio of predicted maximum stress to critical bearing stress in each zone For the indicator: R r ≥0.9 is Level I (high risk), 0.7≤R r <0.9 indicates Level II (medium risk), R r A value <0.7 indicates Level III (low risk). σ a The critical bearing stress of the coal body is the vertical stress γH in the deep original rock, which often approaches or even exceeds the uniaxial compressive strength σ of the coal body.c Directly using the uniaxial compressive strength σ of the coal body c Using this as a benchmark would cause widespread exceedances in deep regions, resulting in a loss of distinguishability. Furthermore, the bearing capacity of coal under triaxial stress is far higher than its uniaxial compressive strength; therefore, we take... k is the confining pressure bearing capacity enhancement coefficient, which is determined by regression analysis of triaxial compression tests on coal seams, and is generally taken as 2.5 to 3.5.
[0057] Determine the safety factor s for each risk level. f Safety factor s for Level I risk zone f Take 1.6; Safety factor s for Level II risk area f Take 1.5 as the safety factor s for Level III risk areas. f Let's set it to 1.4.
[0058] S4: Determine the depressurization and support parameters for each zone.
[0059] S41: Determine the diameter D of the pressure relief borehole. o
[0060]
[0061] In the formula, D b The reference diameter is 100mm (95-153mm is commonly used in engineering); K s K is the stress concentration factor for the zone. r As the benchmark for stress concentration factor, it is taken as 2.0; σ c σ is the uniaxial compressive strength of the coal. r The benchmark for uniaxial compressive strength of coal seams is 15 MPa (for impact-prone coal seams, it is mostly between 10 and 30 MPa); H d H represents the coal seam mining depth. r The benchmark for coal seam mining depth is 600m (rockbursts mostly occur at depths greater than 400m). α, β, and γ are fitting indices: the more severe the stress concentration, the stronger the uniaxial compressive strength of the coal body, the more energy stored, and the greater the burial depth, the higher the foundation stress and the greater the required stress relief strength. Therefore, they are all taken as positive values, with initial empirical values of α=0.43, β=0.28, and γ=0.35.
[0062] The geological correction factor is calculated using the formula. Calculate, where Δhar, Δst, and Δwa are the normalized deviations of hardness ratio, structural complexity, and moisture content relative to standard conditions (taken as 0 under standard conditions, where η is zero). g =1), correction factor is taken as =0.15、 =0.22、 =−0.08 (Water content softens the coal body, which is beneficial for pressure relief, therefore...) (Take the negative); the optimized borehole diameter is limited to the range of 75-200mm, and rounded according to the specifications of the drill bit on site.
[0063] S42: Determine the spacing of the pressure relief boreholes S o
[0064]
[0065] In the formula, S b The baseline spacing for pressure relief boreholes is 3m; the larger the borehole diameter, the larger the pressure relief ring per hole, and the spacing of the pressure relief boreholes can be increased accordingly, therefore, we take 3m. Positive correlation; k d The stress distribution density factor is 0.6–0.8 for high stress concentration areas and 1.0 for general areas; f i The correction factor for the interaction between adjacent holes is 0.9 to 1.1; the spacing between pressure-relief boreholes, S. o Limited to 1-6m.
[0066] S43: Determine the pressure relief borehole depth H o
[0067]
[0068] In the formula, H b The reference depth for pressure relief drilling is set at 20m; L s L represents the influence length of the stress concentration zone along the drilling direction (the distance from the coal face to where the stress has essentially returned to the original rock level, measured from the predicted stress profile). r To avoid affecting the baseline length value, 20m is taken. G n For the normalized stress gradient (the ratio of the stress gradient to the typical value, 0 to 1), ρ g This is the stress gradient correction factor, ranging from 0.1 to 0.3. The steeper the gradient, the deeper the stress relief borehole needs to be to exceed the peak value; p f The formation penetration coefficient is taken as 0.9 to 1.1; the pressure relief borehole depth H o Limited to 10-50m.
[0069] S44: Determine the support density ρ s
[0070]
[0071] In the formula, ρ b As a baseline support density, 1.2 units / m² is used. is a proportionality coefficient used to control the initial sensitivity of support density to the overload ratio (the ratio of the target stress of the support to the standard stress of the coal and rock). For every unit increase in the overload ratio, the initial increment is 0.80, meaning the density responds approximately at 80% of the ratio. n is an exponential coefficient controlling the nonlinearity of the response; n>1 makes the curve concave upwards, resulting in a gradual increase when the overload is small, and a more dramatic increase when the overload is large, consistent with the physical law that support demand accelerates under high stress. In this embodiment, =0.80, n=1.15; σ p The expected stress after depressurization using pressure-relief drilling. . t f Material aging compensation factor: Factors such as anchor bolt / cable preload loss and aging of individual support seals cause a decrease in support resistance over service time. This must be compensated for in advance during design. κ t The annual attenuation rate of support resistance (0.05–0.10 / year), t s The service life of the tunnel design is generally no more than 5 years; the longer the service life, the greater the required initial density; support density ρ s The number of anchor bolts is limited to 0.8 to 2.5 per m², and anchor bolts, anchor cables, or single hydraulic props are generally used for support.
[0072] S44: Determine the support strength P s
[0073]
[0074] In the formula, P b The baseline support strength is taken as 800kN. The support resistance stress sensitivity index is set to 0.35 in this embodiment to avoid a marginally decreasing increase in support resistance with rising surrounding rock stress, and to prevent the support strength from blindly increasing under high stress. This ensures the stability of the shallow surrounding rock while effectively limiting the risk of equipment overload (such as seal bursting) and floor collapse. d Let P be the load distribution factor and co be the component compatibility coefficient, both ranging from 0.9 to 1.1. Support strength P s Limited to 500–1500 kN.
[0075] S5: Verify the depressurization and support parameters for each zone.
[0076] The depressurization and support parameters for each zone determined in step S4 must be checked sequentially according to the following six verification rules. If any verification rule is not met, adjustments must be made and the calculation must be repeated until all rules are met. The six verification rules include:
[0077] 1. Verification of pressure relief adequacy: Based on the pressure relief parameters determined in step S4, predict the maximum stress after pressure relief. ,Require If the requirements are not met, increase the diameter D of the pressure relief borehole. o Reduce the spacing between pressure relief boreholes (S) o Or increase the depth H of the pressure relief borehole o When the pressure relief drilling parameters have reached the interval boundary but still do not meet the requirements, auxiliary pressure relief methods such as coal seam water injection (softening the coal body and reducing the tendency to impact) and roof cutting are superimposed.
[0078] 2. Pressure relief ring overlap verification: It is required that the pressure relief rings of adjacent pressure relief boreholes overlap, i.e. ;at the same time S min Take 3 to 5 times D o To avoid cross-holes and collapsed holes, r re This indicates the effective pressure relief radius of a single orifice.
[0079] 3. Depth Coverage Verification: H o It is necessary to exceed the peak support pressure and retain a margin, that is L p The distance from the peak pressure of the advanced support to the coal face (5-25m), Δ ma For safety margin, it should be no less than 3m.
[0080] 4. Support bearing capacity verification: The support strength provided by the support shall not be less than the remaining load of the roof slab, with a margin allowed. q re The remaining load on the roof after depressurization, based on the depressurization parameters determined in step S4, can be calculated according to the expected caving zone height h. c Multiply by the estimated rock density to obtain the bearing capacity safety margin k. sa ≥1.5.
[0081] 5. Construction feasibility calculation: The pressure relief and support parameters must fall within the project range (D). o ∈[75,200]mm、S o ∈[1,6]m、H o ∈[10,50]m、ρ s ∈[0.8,2.5] units / m², P s ∈[500,1500]kN), and is compatible with the on-site drilling rig capacity and support installation space.
[0082] 6. Economic verification: Under the premise of meeting the above hard constraints, the cost of prevention and control per unit area shall not exceed the budget limit, and the solution with the lowest cost shall be selected from the feasible solutions.
[0083] This invention is not limited to the preferred embodiments described above. Anyone can derive other methods in various forms under the guidance of this invention. Any technical solution that is the same as or similar to this application falls within the protection scope of this invention.
Claims
1. A method for designing parameters for rockburst prevention and control based on risk classification, characterized in that, Includes the following steps: S1: Obtain stress distribution data within the rockburst prevention and control area; S2: Calculate the similarity of each region within the control range and cluster them into zones, grouping regions with similar geological conditions, stress states, and spatial adjacencies into the same zone; S3: Assess the risk level of each zone based on the stress ratio; S4: Calculate the diameter, spacing, depth, support density, and support strength of the pressure relief boreholes for each zone based on its stress state, coal strength, burial depth, and geological conditions. S5: Verify the pressure relief and support parameters of each zone through pressure relief adequacy calculation, pressure relief ring overlap calculation, depth coverage calculation, support bearing capacity calculation, construction feasibility calculation, and economic calculation.
2. The method for designing parameters for rockburst prevention and control based on risk classification according to claim 1, characterized in that, In step S1, the stress distribution data includes at least the maximum stress σ. max And the corresponding stress concentration factor.
3. The method for designing parameters for rockburst prevention and control based on risk classification according to claim 2, characterized in that, In step S2, the clustering and partitioning method includes S21: determining the comprehensive similarity between any two regions i and j within the control range: ; In the formula, F is the stress and strength eigenvector, including stress concentration factor, coal strength, and mining depth; d ij c is the spatial distance between the centers of region i and region j. g The geological relevance is expressed using the following formula: ; Δth, Δdip, and Δha represent the differences in coal seam thickness, dip angle, and hardness between regions i and j, respectively; σ f σ s σ t σ d σ h These are the standard deviations of the stress eigenvector, the standard deviation of the spatial distance between the centers of the regions, the standard deviation of the coal seam thickness, the standard deviation of the coal seam dip angle, and the standard deviation of the coal seam hardness, respectively.
4. The method for designing rockburst control parameters based on risk classification according to claim 3, characterized in that, In step S2, the clustering partitioning method also includes S22: using an improved K-means algorithm for clustering partitioning. by As a distance metric; the initial cluster centers are selected based on the local extrema of the stress distribution; after each iteration, the spatial connectivity of each cluster is checked, and unconnected clusters are split or isolated units are merged into adjacent clusters to ensure that each partition is spatially connected and can be constructed piece by piece in engineering.
5. The method for designing rockburst control parameters based on risk classification according to claim 4, characterized in that, In step S3, the ratio of the predicted maximum stress to the critical bearing stress in each zone is used. As an indicator, R r A value ≥0.9 indicates a Level I high risk, while a value ≤0.7 indicates a high risk. r <0.9 indicates a Level II medium risk, R r <0.7 indicates Level III low risk; among which, σ a The critical bearing stress of the coal body. k is the confining pressure bearing capacity enhancement factor, σ c Determine the uniaxial compressive strength of the coal seam; determine the safety factor s for each risk level. f Safety factor s for Level I risk zone f Take 1.6; Safety factor s for Level II risk area f Take 1.5 as the safety factor s for Level III risk areas. f Let's set it to 1.
4.
6. The method for designing rockburst control parameters based on risk classification according to claim 5, characterized in that, In step S4, the diameter D of the pressure relief borehole is calculated using the following formula. o ; In the formula, D b K is the reference diameter. s K is the stress concentration factor for the zone. r σ serves as the benchmark for stress concentration factor; r H serves as the benchmark for the uniaxial compressive strength of coal. d H represents the coal seam mining depth. r α is the benchmark for coal seam mining depth; α, β, and γ are fitting indices. The geological correction factor is calculated using the formula. Calculate Δhar, Δst, and Δwa, respectively, the normalized deviations of hardness ratio, structural complexity, and moisture content relative to standard conditions. , , This is the corresponding correction factor.
7. The method for designing rockburst control parameters based on risk classification according to claim 6, characterized in that, In step S4, the spacing S of the pressure relief boreholes is calculated using the following formula. o ; In the formula, S b k is the reference spacing for pressure relief drilling. d f is the stress distribution density coefficient; i This is the correction factor for the interaction between adjacent holes.
8. The method for designing parameters for rockburst prevention and control based on risk classification according to claim 7, characterized in that, In step S4, the depth H of the pressure relief borehole is calculated using the following formula. o ; In the formula, H b L is the reference depth for pressure relief drilling. s L represents the influence length of the stress concentration zone along the drilling direction. r To affect the length reference value; G n For the normalized stress gradient, ρ g p is the stress gradient correction factor. f This represents the formation penetration coefficient.
9. The method for designing parameters for rockburst prevention and control based on risk classification according to claim 8, characterized in that, In step S4, the support density ρ is calculated using the following formula. s ; In the formula, ρ b The base support density; σ is the proportionality coefficient, and n is the exponential coefficient; p The expected stress after depressurization using pressure-relief drilling. ;t f This is the material aging compensation coefficient. , The annual attenuation rate of support resistance, t s The service life of the tunnel design.
10. The method for designing rockburst control parameters based on risk classification according to claim 9, characterized in that, In step S4, the support strength P is calculated using the following formula. s ; In the formula, P b As the benchmark support strength, The support resistance stress sensitivity index; l d denoted as the load distribution factor, and co as the component compatibility coefficient.