Geological suitability evaluation method for development of underground space in coastal bedrock city

Abstract

The present application relates to the technical field of underground space development, and provides a coastal bedrock type city underground space development geological suitability evaluation method, comprising the following steps: analyzing key geological problems of land and sea underground space development, and extracting relevant geological factors; collecting and classifying basic geological data, constructing a geological suitability evaluation index system and dividing geological evaluation units; determining subjective and objective weights based on the analytic hierarchy process and entropy weight method, and obtaining optimal comprehensive weights through game theory combination weighting; modeling based on grey correlation analysis method, calculating evaluation unit suitability score and grading; integrating evaluation results to generate a land-sea integrated underground space development geological suitability zoning map. The present application optimizes the underground space development pattern, promotes the comprehensive utilization of land and marine resources, and effectively supports the safe, efficient and sustainable development and utilization of coastal city underground space.

Description

Technical Field

[0001] This invention relates to the field of urban underground space development technology, specifically to a method for evaluating the geological suitability of underground space development in coastal bedrock-type cities. Background Technology

[0002] With rapid socio-economic development, the demand for urban space and resources continues to grow. Developing and utilizing underground space has become an important way to alleviate urban problems, optimize urban structure, and expand the dimensions of urban development. However, current urban underground space development generally lacks systematic evaluation and planning guidance, leading to increasingly prominent problems such as arbitrary development layout and chaotic functions. Therefore, establishing a scientific and comprehensive suitability evaluation system for underground space development is an important foundation and prerequisite for achieving its safe, efficient, and sustainable utilization.

[0003] Compared with typical inland cities, coastal cities have a higher degree of underground space development, but they also face more complex challenges: on the one hand, coastal cities are located at the intersection of land and sea, with complex geological conditions, widespread distribution of special soil types, and frequent coastal engineering geology and environmental geology problems; on the other hand, various underground projects in coastal cities, especially cross-sea tunnels and submarine pipelines, are affected by seawater dynamics throughout their construction and operation cycles, significantly increasing the engineering difficulty.

[0004] Currently, suitability assessments for underground space in coastal cities are mostly limited to the land area, failing to fully consider the interaction between land and sea and the impact of the marine environment on underground space development. This land-sea separation assessment model is not conducive to the scientific site selection and overall planning of cross-sea projects, and also restricts the systematicness and synergy of the overall planning of urban underground space, hindering the development of underground space in coastal cities towards a three-dimensional and integrated direction.

[0005] Therefore, it is urgent to coordinate the development needs and potential conflicts of underground space in the land and sea systems, and to construct a new method for assessing the suitability of underground space in coastal cities that integrates land and sea, so as to support the planning of underground space development and utilization across the entire region and promote the sustainable development of coastal cities. Summary of the Invention

[0006] To address the problems existing in the background technology, this invention proposes a geological suitability evaluation method for underground space development in coastal bedrock cities. It establishes evaluation index systems for land and sea areas, conducts geological suitability evaluations for underground space development, optimizes the development pattern of underground space, promotes the comprehensive utilization of land and marine resources, and strongly supports the safe, efficient and sustainable development and utilization of underground space in coastal cities.

[0007] To achieve the above objectives, the present invention adopts the following solution:

[0008] A method for evaluating the geological suitability of underground space development in coastal bedrock cities includes the following steps:

[0009] Step 1: Conduct an analysis of the key geological problems faced by the development and construction of underground space in the land and sea areas of coastal bedrock cities, and obtain the geological factors affecting the development of underground space in the land and sea areas;

[0010] Step 2: Based on the geological factors, acquire and classify basic geological data of land and sea areas, establish a land-sea integrated evaluation index system for the geological suitability of underground space development, and divide it into several geological evaluation units.

[0011] Step 3: Based on the evaluation index system, the subjective weight of each specific evaluation index is determined by the analytic hierarchy process (AHP), and the objective weight of each specific evaluation index is determined by the entropy weight method.

[0012] Step 4: Based on the game theory combined weighting model, the subjective weights and the objective weights are combined and optimized to obtain the optimal comprehensive weights for each specific evaluation index.

[0013] Step 5: Based on the grey relational analysis method, construct a geological suitability evaluation model, input the optimal comprehensive weight into the evaluation model, calculate the geological suitability score of each geological evaluation unit, and classify the suitability level according to the score range;

[0014] Step 6: Based on the geological suitability score, integrate the evaluation results of various geological evaluation units in the land and sea areas, perform visualization processing, and generate a geological suitability zoning map for the integrated development of underground space in coastal bedrock cities according to the suitability level classification standard.

[0015] Optionally, in step 1, the analysis of key geological issues includes an analysis of the geological overview of coastal bedrock cities, an analysis of environmental geological issues affecting the development of underground space in coastal bedrock cities, and an analysis of the geological causes of accidents that are prone to occur during the construction of cross-sea underground engineering projects.

[0016] Optionally, the geological overview includes, but is not limited to, topography, engineering geology, hydrogeology, tectonic zoning, and seismic characteristics;

[0017] The environmental geological problems mentioned include, but are not limited to, soft soil, land subsidence, land collapse, sand liquefaction, seawater intrusion, storm surge, soil salinization, and coastal siltation.

[0018] Optionally, the basic geological data of the land and sea areas include, but are not limited to, digital elevation models (DEM), remote sensing image data, land and sea engineering geological drilling and hydrogeological drilling data, geological profile maps, geotechnical engineering investigation reports, single-beam bathymetry data, coastal erosion and sedimentation profile measurement data, seabed surface sample and seabed columnar sample data.

[0019] Optionally, in step 2, the evaluation index system is divided into a land evaluation index system and a marine evaluation index system; wherein, the land evaluation index system is constructed based on key indicators identified by natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions, and environmental geological problems; the marine evaluation index system is constructed based on key indicators identified by natural geographical conditions, geological conditions, and hydrodynamic conditions; at the same time, the coastal bedrock type urban area is divided into multiple geological evaluation units including land and marine sub-regions.

[0020] Optionally, in step 3, determining the subjective weights of each specific evaluation indicator using the analytic hierarchy process (AHP) specifically includes:

[0021] Step 3.a1: Construct hierarchical structure models of target layer, criterion layer, and indicator layer for the land evaluation index system and the marine evaluation index system respectively. Among them, the target layer of the land hierarchical structure model is the geological suitability for the development of underground space in the land area. The criterion layer includes natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions, and environmental geological issues. The indicator layer includes specific evaluation indicators belonging to the indicators of each criterion layer, including but not limited to landform type, slope, thickness of Quaternary strata, thickness of aquifer, rock and soil type, distance of active fault, seawater intrusion, and landslides.

[0022] The target layer of the marine hierarchical structure model is the geological suitability for development of marine underground space. The criteria layer includes natural geographical conditions, geological conditions and hydrodynamic conditions. The indicator layer includes specific evaluation indicators belonging to each criteria layer, including but not limited to water depth, slope, Quaternary sediment thickness, sediment type, distance from active faults, erosion and deposition, and ocean currents.

[0023] Step 3.a2, construct the judgment matrix:

[0024] The nine-scale method is used to compare the importance of each indicator in the criterion layer with that in the target layer in pairs, and to construct the criterion layer judgment matrix.

[0025] For each criterion-level indicator, the importance of each specific evaluation indicator in its corresponding indicator layer is compared pairwise using the nine-scale method, and a corresponding indicator-level judgment matrix is ​​constructed.

[0026] Step 3.a3: Calculate the eigenvectors of each judgment matrix to obtain the relative weights of the indicators it contains.

[0027] The sum-product method is used to calculate the maximum eigenvalue of each judgment matrix. λ max and the corresponding feature vectors ;

[0028] The sum-product method includes: normalizing the judgment matrix by column, then summing the normalized matrix by row to obtain a vector, and then normalizing the vector to obtain the eigenvector;

[0029] Step 3.a4, perform a consistency check on each judgment matrix:

[0030] Calculate the consistency index ,in, Given the matrix order; query the average random consistency index corresponding to the matrix order. RI Calculate the consistency ratio CR = CI / RI ;when CR When the value is less than 0.1, the judgment matrix is ​​considered to have passed the consistency test, confirming that the relative weights obtained in step 3.a3 are valid;

[0031] Step 3.a5, Determine the final subjective weights: Multiply the relative weight of each specific evaluation indicator relative to its criterion layer by the weight of that criterion layer indicator relative to the target layer, and synthesize the subjective weights of each specific evaluation indicator relative to the target layer, i.e., the subjective weights of each specific indicator in the land area. Subjective weights of various specific indicators in the sea area Based on the aforementioned subjective weights, the subjective weight vectors of specific evaluation indicators for land areas are obtained. Subjective weight vector of specific evaluation indicators for sea areas .

[0032] Optionally, the determination of the objective weights of each specific evaluation index using the entropy weight method specifically includes:

[0033] Step 3.b1: Construct the original evaluation matrix for the land evaluation index system. ,in x ki Indicates the first k The first geological evaluation unit i Specific evaluation index values. m The total number of geological evaluation units. l The total number of evaluation indicators;

[0034] Step 3.b2: Normalize the original data matrix to eliminate dimensions, obtaining a standardized matrix. :

[0035] For positive indicators, the formula is as follows: ,

[0036] For negative indicators, the formula is used: ,

[0037] in, and The firsti The maximum and minimum values ​​of each specific evaluation indicator across all geological evaluation units;

[0038] Step 3.b3, for the standardized matrix, calculate the first... k The first geological evaluation unit i The proportion of features under each indicator :

[0039] ,

[0040] Step 3.b4, calculate the... j Information entropy value of the indicator e i :

[0041] ,

[0042] in, Information entropy e i satisfy ,

[0043] Step 3.b5, ​​calculate the... j Coefficient of difference of the items d i :

[0044] ,

[0045] Step 3.b6: Determine the objective weights of each specific evaluation indicator. :

[0046] ,

[0047] Based on the aforementioned objective weights, the objective weight vector of specific evaluation indicators for land areas is obtained:

[0048] ;

[0049] Step 3.b7, following steps 3.b1-3.b6, obtain the objective weight vector of specific evaluation indicators for the sea area:

[0050] .

[0051] Optionally, in step 4, the subjective weights and the objective weights are combined and optimized based on a game theory-based combinatorial weighting model, specifically including:

[0052] Step 4.1: For the land evaluation index system, the subjective weight vector obtained by the analytic hierarchy process and the objective weight vector obtained by the entropy weight method are linearly combined.

[0053] Step 4.2: With the objective of minimizing the deviation between the combined weight vector and any weight vector obtained by the analytic hierarchy process or the entropy weight method, a game theory combinatorial weighting model is established. The optimal weight coefficients are obtained by solving the following system of linear equations. and :

[0054] ,

[0055] Step 4.3: Normalize the optimal weight coefficients according to the following formula:

[0056] ,

[0057] Step 4.4, the optimal combination weight vector obtained according to game theory is:

[0058] ;

[0059] Step 4.5: Following steps 4.1-4.4, obtain the optimal weight coefficients for each specific evaluation indicator of the sea area. and and the optimal combination weight vector of all indicators .

[0060] Optionally, in step 5, the construction of the geological suitability evaluation model based on grey relational analysis specifically includes: Step 5.1, for the land evaluation index system, constructing an original data matrix containing all geological evaluation units and specific evaluation indicators:

[0061] ;

[0062] in, Indicates the first m The geological evaluation unit in the first l The values ​​of each indicator; Step 5.2, determine the reference sequence composed of the optimal values ​​of each specific evaluation indicator of all geological evaluation units and the comparison sequence composed of the actual values, wherein the reference sequence is expressed as:

[0063] ,

[0064] The comparison sequence is represented as follows:

[0065] ;

[0066] in, This indicates that all geological evaluation units are in the first... l The optimal value for each indicator is determined by the following criteria: positive indicators are represented by their maximum value across all geological evaluation units, and negative indicators are represented by their minimum value across all geological evaluation units. Indicates the first kThe geological evaluation unit in the first l The values ​​of each index; Step 5.3, standardize the reference sequence and all comparison sequences to obtain a dimensionless reference sequence. and comparison sequences ;

[0067] in, For the reference sequence in the 1st l Dimensionless values ​​for each indicator For the first k The comparison sequence in the th ... l Dimensionless values ​​for each evaluation index; Step 5.4, calculate the correlation coefficients between the comparison sequences of each geological evaluation unit and the reference sequence for each index, the expression of which is:

[0068] ;

[0069] in:

[0070] For the reference sequence in the 1st i Dimensionless values ​​for each indicator For the first k The comparison sequence in the th ... i Dimensionless values ​​for each evaluation indicator i =1,2,…, l .

[0071] For the first k The comparison sequence in the th ... i The absolute difference between each geological suitability evaluation index and the reference sequence

[0072] The minimum difference between the two levels is the minimum value among all the absolute differences.

[0073] The maximum difference between the two levels is the maximum value among all the absolute differences.

[0074] The resolution coefficient has a value range of (0, 1).

[0075] Step 5.5: Use the combined weights to weight the correlation coefficients and calculate the correlation degree between each comparison sequence and the reference sequence. The correlation degree is the geological suitability score of the geological evaluation unit corresponding to the comparison sequence, and the expression for the correlation degree is:

[0076] ;in, For the first i The combined weights of each indicator;

[0077] Step 5.6: Following steps 5.1-5.5, obtain the correlation between the geological assessment units in various sea areas and their reference sequences. .

[0078] Optionally, the suitability level is divided according to the geological suitability score, specifically as follows: evaluation results with scores in the range of (0, 0.25) are classified as unsuitable; evaluation results with scores in the range of (0.25, 0.5) are classified as slightly unsuitable; evaluation results with scores in the range of (0.5, 0.75) are classified as slightly suitable; and evaluation results with scores in the range of (0.75, 1) are classified as suitable.

[0079] The beneficial effects of this invention are as follows: This method achieves a systematic and integrated assessment of the geological conditions of both the land and sea areas of coastal bedrock-type cities by constructing a land-sea integrated evaluation system for the geological suitability of underground space development. First, by comprehensively analyzing regional geological conditions, environmental geological issues, and risks associated with cross-sea engineering, key geological factors affecting development are accurately identified, and a comprehensive evaluation index system is established. Second, an innovative game-theoretic combined weighting model is adopted, organically integrating the subjective expert experience of the analytic hierarchy process (AHP) with the objective data-driven approach of the entropy weight method. This ensures that the weight allocation aligns with actual engineering judgments and fully reflects the internal laws of geological data, significantly improving the scientific rigor and credibility of the evaluation results. Furthermore, an evaluation model is constructed based on grey relational analysis, effectively handling multi-source geological information and uncertainties, and achieving precise quantification and classification of the geological suitability of each evaluation unit. Finally, a land-sea integrated geological suitability zoning map is generated using visualization technology, providing an intuitive and reliable decision-making basis for urban planning and engineering construction. This effectively overcomes the limitations of traditional land-sea separated evaluations and strongly supports the safe, efficient, and sustainable development and utilization of underground space in coastal cities. Attached Figure Description

[0080] Figure 1 This is a flowchart of the method of the present invention;

[0081] Figure 2 This is a schematic diagram of the system structure of the geological suitability evaluation index for underground space development in an embodiment of the present invention;

[0082] Figure 3 This is a geological suitability zoning map for integrated land and sea underground space development in an embodiment of the present invention. Detailed Implementation

[0083] To make the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the given embodiments are merely one implementation method and do not represent all embodiments.

[0084] Combination Figure 1 This invention provides a method for evaluating the geological suitability of underground space development in coastal bedrock cities, comprising the following steps:

[0085] Step 1: Conduct an analysis of the key geological problems faced by the development and construction of underground space in the land and sea areas of coastal bedrock cities, and obtain the geological factors affecting the development of underground space in the land and sea areas.

[0086] The key geological issues analysis includes an analysis of the geological overview of coastal bedrock cities, an analysis of environmental geological issues affecting the development of underground space in coastal bedrock cities, and an analysis of the geological causes of accidents prone to occur in cross-sea underground engineering construction. Specifically, the analysis of the geological overview of coastal bedrock cities systematically integrates and analyzes regional geological conditions such as topography, engineering geology, hydrogeology, and seismic characteristics of tectonic zones. The analysis of environmental geological issues affecting the development of underground space in coastal bedrock cities focuses on environmental geological issues prone to occur in coastal bedrock cities, such as soft soil, ground subsidence, ground collapse, sand liquefaction, seawater intrusion, storm surge, soil salinization, and coastal siltation. The analysis of the geological causes of accidents prone to occur in cross-sea underground engineering construction identifies common accidents in cross-sea underground engineering construction and analyzes their corresponding geological causes, providing a basis for the establishment of a subsequent evaluation index system, as shown in Table 1 below.

[0087] Table 1. Common Accidents and Geological Causes in Cross-Sea Underground Engineering Construction

[0088]

[0089] Step 2: Based on the aforementioned geological factors, acquire and integrate basic geological data for both land and sea areas, and establish a land-sea integrated evaluation index system for the geological suitability of underground space development, such as... Figure 2 .

[0090] The acquired land and sea basic geological data are geological factors that affect the development of underground space, including digital elevation models (DEM), remote sensing image data, land and sea engineering geological drilling and hydrogeological drilling data, geological profile maps, geotechnical engineering investigation reports, single-beam bathymetry data, coastal erosion and sedimentation profile measurement data, seabed surface sample and seabed columnar sample data, etc.

[0091] Furthermore, the aforementioned basic geological data for both land and sea areas are categorized to establish a geological suitability evaluation index system for underground space development, including both land and sea evaluation index systems. Using ArcMap software, the coastal bedrock-type urban area is divided into multiple geological evaluation units comprising both land and sea sub-regions. Specifically, the hierarchical vector graphics of each indicator for the evaluation area are imported, coordinate system one and boundary consistency calibration are completed, and the graphics are successively overlaid using the software's built-in overlay tool to generate a comprehensive vector map and divide the geological evaluation units. Its attribute table can fully contain all indicator values ​​for each evaluation unit.

[0092] The land evaluation index system is constructed based on key indicators for identifying natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions, and environmental geological problems; the marine evaluation index system is constructed based on key indicators for identifying natural geographical conditions, geological conditions, and hydrodynamic conditions.

[0093] Key indicators within the land area evaluation indicator system include:

[0094] From the perspective of natural geographical conditions, the differences in landform type and slope directly determine the suitability of underground space development. Plains and gentle slopes are easy to construct and layout, while hilly areas and areas with large slope changes are difficult to excavate, have complex layouts, and limited available land. Therefore, landform type and slope are selected as specific evaluation indicators under natural geographical conditions.

[0095] Specific indicators in basic geology and hydrogeology include the thickness of Quaternary strata and aquifer thickness: the stratigraphic characteristics of coastal bedrock cities often exhibit a binary structure of soft upper layers and hard lower layers, with the upper Quaternary strata generally being relatively loose and having poor engineering properties. Aquifer thickness reflects groundwater abundance; as development depth increases, the impact of groundwater becomes more severe, and the difficulty of its management increases exponentially. Improper groundwater control can easily lead to disasters such as sudden water inrushes and surges in underground engineering projects, seriously affecting their safety.

[0096] From an engineering geological perspective, rock and soil types and the distance to active faults are used as specific evaluation indicators. Rock and soil masses are fundamental to determining the engineering geological conditions of different regions. Various types of rock and soil masses differ in their formation conditions, mechanical properties, and strength, thus affecting the stability of building foundations to varying degrees. It is worth noting that due to long-term interaction between land and sea, soft soil and saline-alkali soil are often widely distributed in coastal areas, making them the least suitable soil types for development. Active faults have a crucial impact on the construction and operational safety of cross-sea projects. Fault fracture zones have high permeability, forming fault gouge in the fractured rock sections. Low rock strength can easily lead to tunnel water inrush accidents.

[0097] In terms of environmental geology, seawater intrusion is generally a prominent problem in coastal cities, with pollution levels typically reaching Cl-level concentrations.- It is measured by concentration. Seawater intrusion not only leads to soil salinization but also reduces the area of ​​usable land; the corrosive ions (Na+) contained in seawater... + Cl - SO4 2- Sulfates seeping into the ground can also corrode the foundation. They crystallize in concrete, and the growth of these crystals causes the concrete to expand and crack, exposing the reinforcing steel and significantly reducing the lifespan of the structure. Landslides and other geological disasters pose a significant threat to urban development, blocking or burying underground passage exits and being a major limiting factor for underground space development. Therefore, seawater intrusion and landslides are specific evaluation indicators for environmental geological problems.

[0098] Key indicators within the marine area evaluation indicator system include:

[0099] In terms of natural geographical conditions, water depth and slope are used as specific evaluation indicators: increased water depth leads to higher water pressure, increasing the cost and difficulty of submarine engineering construction; in addition, high water pressure can cause cracks in weak pressure-bearing areas, inducing more serious collapse accidents. Changes in seabed slope affect the difficulty of construction; areas with lower slopes are less difficult to construct, and the engineering route is relatively flat.

[0100] Specific evaluation indicators for geological conditions include the thickness of Quaternary sediments, sediment type, and distance from active faults. The thickness and sediment type of Quaternary sedimentary layers are crucial to construction safety. The typical soft-over-hard strata in coastal bedrock cities can easily cause abnormal wear of tunnel boring machine blades and lead to deviations in excavation posture. Weak sedimentary layers have poor self-stability after excavation and are prone to collapse accidents. At the same time, submarine faults are the most critical unstable factors in cross-sea projects. The surrounding rock in fault fracture zones is fractured and fissured, resulting in extremely high risks of collapse, water inrush, and mudslides during construction.

[0101] Among hydrodynamic conditions, scouring and deposition, as well as ocean currents, have a significant impact on cross-sea engineering projects. In areas with severe scouring and deposition, the soil is loose. During construction, submarine landslides or uneven settlement are prone to occur, increasing construction difficulty and risks. Furthermore, strong ocean currents erode the foundation structure, reducing the foundation's depth and weakening its bearing capacity and stability. Therefore, scouring and deposition, and ocean currents, are used as specific evaluation indicators.

[0102] Step 3: Based on the evaluation index system, the subjective weight of each specific evaluation index is determined by the analytic hierarchy process (AHP), and the objective weight of each specific evaluation index is determined by the entropy weight method.

[0103] The subjective weights are obtained using the analytic hierarchy process (AHP), which clearly reveals the logical relationships between evaluation indicators under both land and sea conditions, and enhances the scientific rigor and operability of the weight assignment process. This provides a reliable expert basis for the comprehensive evaluation of the geological suitability of underground space development in coastal bedrock cities. Specifically, the steps for determining the subjective weights include:

[0104] Step 3.a1: For both the land-based and marine evaluation index systems, construct hierarchical models consisting of a target layer, a criterion layer, and an indicator layer, as shown in Table 2. In the land-based hierarchical model, the target layer is the geological suitability for underground space development; the criterion layer includes natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions, and environmental geological issues; and the indicator layer includes specific evaluation indicators belonging to each criterion layer. Similarly, in the marine hierarchical model, the target layer is the geological suitability for underground space development; the criterion layer includes natural geographical conditions, geological conditions, and hydrodynamic conditions; and the indicator layer includes specific evaluation indicators belonging to each criterion layer.

[0105] Table 2 Hierarchical Structure

[0106]

[0107] Step 3.a2, construct the judgment matrix:

[0108] Based on the opinions of experienced experts in the field, the first step is to use the nine-scale method, as shown in Table 3, to compare the importance of each indicator in the criterion layer with that in the target layer, construct a criterion layer judgment matrix, and assign scores to their relative importance.

[0109] Table 3. Meaning of the Nine-Scale Method

[0110]

[0111] Then, for each criterion-level indicator, the importance of each specific evaluation indicator in its corresponding indicator layer is compared pairwise using the nine-scale method to construct the corresponding indicator-level judgment matrix. Table 4, taking the land area criterion-level indicators as an example, gives the judgment matrix for the land area criterion-level. A .

[0112] Table 4 Land Area Criterion Layer Judgment Matrix A

[0113]

[0114] Step 3.a3: Calculate the eigenvectors of each judgment matrix to obtain the relative weights of the indicators it contains.

[0115] The sum-product method is used to calculate the maximum eigenvalue of each judgment matrix. λ max and the corresponding feature vectors The obtained eigenvectors are the relative weights of the indicators contained in each of the judgment matrices.

[0116] The sum-product method includes:

[0117] (1) Normalize the judgment matrix column by column: ,

[0118] in Indicates the first i The first indicator is relative to the first j The normalized value of the importance of each indicator. u To determine the order of a matrix.

[0119] (2) Sum the normalized matrix row by row using the following formula:

[0120] .

[0121] (3) For vectors Normalization yields the eigenvectors:

[0122] ,in, .

[0123] (4) Find the largest eigenvalue of the judgment matrix:

[0124] ,

[0125] in, Representing vectors The i Each component.

[0126] The judgment matrix can be obtained through the above calculation process. A The corresponding weight vectors for each indicator in the criterion layer are as follows:

[0127] ,

[0128] in, , , and The weights are respectively the four indicators included in the terrestrial criterion layer: natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions, and environmental geological issues.

[0129] For the specific evaluation indicators under the four criteria layers of natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions, and environmental geological issues, the same steps are used to construct judgment matrices for each specific evaluation indicator under the index layer. The maximum eigenvalue and corresponding eigenvector of each matrix are then calculated using the sum-product method. This yields the weights corresponding to each specific evaluation indicator in each index layer, as follows:

[0130] The two specific evaluation indicators under the natural geographical conditions criterion layer correspond to a second-order judgment matrix, and their weight vectors are: ;

[0131] The two specific evaluation indicators under this criterion layer for basic geological and hydrogeological conditions correspond to a second-order judgment matrix, and their weight vectors are as follows: ;

[0132] The two specific evaluation indicators under this criterion layer for engineering geological conditions correspond to a second-order judgment matrix, and their weight vectors are as follows:

[0133] ;

[0134] The two specific evaluation indicators under the environmental geology problem criteria layer correspond to a second-order judgment matrix, and their weight vectors are as follows:

[0135] .

[0136] It should be noted that the above example analysis only uses the land-based hierarchical structure model. For the weight vector of the marine hierarchical structure model, the above judgment matrix construction method can be used directly for calculation.

[0137] Step 3.a4: To ensure the logical consistency of the expert's judgment, a consistency check needs to be performed on each of the above judgment matrices:

[0138] Calculate the consistency index ; Look up the average random consistency index corresponding to the matrix order in Table 5. RI Calculate the consistency ratio CR = CI / R I; when CR If the value is less than 0.1, the judgment matrix is ​​considered to have passed the consistency test, confirming the validity of the relative weights obtained in step 3.3.

[0139] Table 5 Average Random Consistency Index RI value

[0140]

[0141] Specifically, taking the land-based hierarchical structure model as an example, the consistency of the fourth-order judgment matrix, composed of natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions, and environmental geological issues, is first checked. After the consistency check, the consistency of the second-order matrices, composed of specific evaluation indicators under each criterion level, is checked separately, and the calculation process is the same. All judgment matrices must pass the consistency check.

[0142] Step 3.a5, Determine the final subjective weights: Multiply the relative weight of each specific evaluation indicator with the weight of that indicator relative to the target layer, and synthesize the subjective weights of each specific evaluation indicator relative to the target layer, i.e., the subjective weights of each specific indicator in the land area. Subjective weights of various specific indicators in the sea area The subjective weight vector of specific land area indicators can be expressed as: ,in l The total number of specific evaluation indicators for land areas; the subjective weight vector of specific indicators for sea areas can be represented as: ,in t This represents the total number of specific evaluation indicators for the sea area.

[0143] The raw data for various evaluation indicators (such as slope, soil and rock type, ocean currents, etc.) often exhibit varying degrees of dispersion. These data characteristics themselves carry important objective information and determine the geological suitability for regional underground space development. The entropy weight method, starting from the inherent differences in the data, scientifically identifies the degree to which each evaluation indicator affects geological suitability. Based on the inherent dispersion of the data, it objectively determines the indicator weights and quantifies the amount of information provided by the indicators through information entropy. This process does not rely on subjective judgment and is entirely driven by measured geological data, thus effectively avoiding interference from human preferences and ensuring the scientific and data-driven nature of the weight allocation. Specifically, the steps for determining the objective weights include:

[0144] Step 3.b1: Construct the original evaluation matrix for the land evaluation index system. ,in x ki Indicates the first k The first geological evaluation unit i Specific evaluation index values. m The total number of geological evaluation units. l This represents the total number of evaluation indicators.

[0145] Step 3.b2: Normalize the original data matrix to eliminate dimensions, obtaining a standardized matrix. :

[0146] For positive indicators, the formula is as follows: ,

[0147] For negative indicators, the formula is used: ,

[0148] in, and The first i The maximum and minimum values ​​of each specific evaluation indicator across all geological evaluation units;

[0149] Step 3.b3, for the standardized matrix, calculate the first...k The first geological evaluation unit i The proportion of features under each indicator :

[0150] ,

[0151] Step 3.b4, calculate the... j Information entropy value of the indicator e i :

[0152] ,

[0153] in, Information entropy e i satisfy ,

[0154] Step 3.b5, ​​calculate the... j Coefficient of difference of the items d i :

[0155] ,

[0156] Step 3.b6: Determine the objective weights of each specific evaluation indicator. :

[0157] ,

[0158] Based on the aforementioned objective weights, the objective weight vector of specific evaluation indicators for land areas is obtained:

[0159] ;

[0160] Step 3.b7, following steps 3.b1-3.b6, obtain the objective weight vector of specific evaluation indicators for the sea area:

[0161] .

[0162] Step 4: Based on a game theory-based combined weighting model, the subjective weights and objective weights are combined and optimized to obtain the optimal comprehensive weights for each evaluation index. This method systematically integrates experts' rich experience in judging geological suitability with the objective information reflected within the geological data, overcoming the subjective bias or objective one-sidedness that may result from a single weighting method. By constructing a coordination model, it seeks a "consensus" between subjective judgment and objective information, ensuring that the final comprehensive weights reflect both the experts' judgments on key geological factors and the information structure of the data itself.

[0163] Specifically, the optimization steps include:

[0164] Step 4.1: For the land evaluation index system, the subjective weight vector obtained by the analytic hierarchy process (AHP) and the objective weight vector obtained by the entropy weight method are linearly combined using the following formula:

[0165] ,

[0166] in, ω Represents the combined weight vector. ω k T For the weighted results of a single method, β k These are the weighting coefficients;

[0167] Step 4.2: With the objective of minimizing the deviation between the combined weight vector and any weight vector obtained by the analytic hierarchy process or the entropy weight method, a game theory combinatorial weighting model is established. The optimal weight coefficients are obtained by solving the following system of linear equations. and :

[0168] ,

[0169] Step 4.3: Normalize the optimal weight coefficients according to the following formula:

[0170] ,

[0171] Step 4.4, the optimal combination weight vector obtained according to game theory is:

[0172] ;

[0173] Step 4.5: Following steps 4.1-4.4, obtain the optimal weight coefficients for each specific evaluation indicator of the sea area. and and the optimal combination weight vector of all indicators .

[0174] Step 5: Based on grey relational analysis, construct a geological suitability evaluation model, input the optimal comprehensive weight into the evaluation model, calculate the geological suitability score of each evaluation unit, and classify the suitability level according to the score range.

[0175] The evaluation of geological suitability for underground space development is a complex multi-objective decision-making problem with multiple factors and incomplete results. This method quantifies the correlation between the geological index sequence of each evaluation unit and the ideal geological suitability conditions (reference sequence) to comprehensively measure its proximity to the optimal geological environment. This enables precise ranking and classification of suitability in different regions and can objectively reveal the nonlinear correlation between each specific evaluation index and the final suitability, providing a scientific basis for regional geological suitability.

[0176] Specifically, it includes the following steps:

[0177] Step 5.1: For the land evaluation index system, construct an original data matrix containing all geological evaluation units and specific evaluation indicators:

[0178] ;

[0179] in, Indicates the first m The geological evaluation unit in the first l Values ​​on each indicator;

[0180] Step 5.2: Determine a reference sequence consisting of the optimal values ​​of each specific evaluation index for all geological evaluation units and a comparison sequence consisting of the actual values. The reference sequence is expressed as follows:

[0181] ,

[0182] The comparison sequence is represented as follows:

[0183] ;

[0184] in, This indicates that all geological evaluation units are in the first... l The optimal value for each indicator is determined by the following criteria: positive indicators are represented by their maximum value across all geological evaluation units, and negative indicators are represented by their minimum value across all geological evaluation units. Indicates the first k The geological evaluation unit in the first l The values ​​of each index; Step 5.3, standardize the reference sequence and all comparison sequences to obtain a dimensionless reference sequence. and comparison sequences ;

[0185] in, For the reference sequence in the 1st l Dimensionless values ​​for each indicator For the first k The comparison sequence in the th ... l Dimensionless values ​​for each evaluation index; Step 5.4, calculate the correlation coefficients between the comparison sequences of each geological evaluation unit and the reference sequence for each index, the expression of which is:

[0186] ;

[0187] in:

[0188] For the reference sequence in the 1st i Dimensionless values ​​for each indicator For the firstk The comparison sequence in the th ... i Dimensionless values ​​for each evaluation indicator i =1,2,…, l。

[0189] For the first k The comparison sequence in the th ... i The absolute difference between each geological suitability evaluation index and the reference sequence

[0190] The minimum difference between the two levels is the minimum value among all the absolute differences.

[0191] The maximum difference between the two levels is the maximum value among all the absolute differences.

[0192] The resolution coefficient, with a value range of (0, 1), is typically set to... . The smaller the value, the greater the resolution.

[0193] Step 5.5: Use the combined weights to weight the correlation coefficients and calculate the correlation degree between each comparison sequence and the reference sequence. The correlation degree is the geological suitability score of the geological evaluation unit corresponding to the comparison sequence, and the expression for the correlation degree is:

[0194] ;

[0195] in, For the first i The combined weights of each indicator.

[0196] Furthermore, m The correlation between the comparative sequences and the reference sequences is ordered from largest to smallest. The larger the correlation, the more consistent the trend of the comparative sequence with the reference sequence, meaning that the geological suitability result of the geological evaluation unit is closer to the most ideal geological conditions in the evaluation area.

[0197] Step 5.6: Following steps 5.1-5.5, obtain the correlation between the geological assessment units in various sea areas and their reference sequences. The results obtained from grey relational analysis range from 0 to 1. Based on the calculated scores, the geological suitability evaluation results of this geological evaluation unit can be divided into four categories, specifically:

[0198] Evaluation results with scores in the range (0, 0.25) are classified as unsuitable; evaluation results with scores in the range (0.25, 0.5) are classified as slightly unsuitable; evaluation results with scores in the range (0.5, 0.75) are classified as slightly suitable; and evaluation results with scores in the range (0.75, 1) are classified as suitable.

[0199] Step 6: Based on the geological suitability score, integrate the evaluation results of various geological evaluation units in the land and sea areas, use ArcMap software for visualization processing, and generate a geological suitability zoning map for the integrated land-sea development of underground space in coastal bedrock cities according to the suitability level classification standard. This map will intuitively present the suitability levels of various geological units in the land and sea areas, clearly delineate development zones, and provide accurate and intuitive decision support for the integrated land-sea planning of underground space in coastal bedrock cities.

[0200] Specifically, the geological suitability score data of various geological assessment units in the land and sea areas are imported into ArcMap software and linked to the attribute table of the comprehensive vector map to form a "Geological Suitability Score" field. According to the aforementioned geological suitability classification criteria, the symbol system display of this field in the layer attributes is updated, thereby generating a visual map of the geological suitability zoning of the underground space in the land and sea areas of coastal bedrock-type cities in ArcMap software, such as... Figure 3 As shown.

[0201] This method constructs a land-sea integrated geological suitability evaluation system for underground space development, achieving a systematic and integrated assessment of the geological conditions of both the land and sea areas of coastal bedrock-type cities. First, by comprehensively analyzing regional geological conditions, environmental geological issues, and risks associated with cross-sea engineering, key geological factors influencing development are accurately identified, and a comprehensive evaluation index system is established. Second, an innovative game-theoretic combined weighting model is adopted, organically integrating the subjective expert experience of the analytic hierarchy process (AHP) with the objective data-driven approach of the entropy weight method. This ensures that the weight allocation aligns with actual engineering judgments while fully reflecting the internal patterns of geological data, significantly improving the scientific rigor and credibility of the evaluation results. Furthermore, an evaluation model is constructed based on grey relational analysis, effectively handling multi-source geological information and uncertainties, achieving precise quantification and classification of the geological suitability of each evaluation unit. Finally, a land-sea integrated suitability zoning map is generated using visualization technology, providing an intuitive and reliable decision-making basis for urban planning and engineering construction. This effectively overcomes the limitations of traditional land-sea separated evaluations and strongly supports the safe, efficient, and sustainable development and utilization of underground space in coastal cities.

[0202] The specific embodiments of the present invention have been described in detail above with reference to the figures, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A method for evaluating the geological suitability of the development of underground space in a coastal bedrock city, characterized by, Comprising the following steps: Step 1, carry out the key geological problem analysis of the land and sea space development and construction of the coastal bedrock city, obtain the geological factors affecting the land and sea space development; Step 2, based on the geological factors, obtain the land and sea basic geological data and classify them, establish the index system of geological suitability evaluation of land and sea unified underground space development and divide it into several geological evaluation units; Step 3, based on the evaluation index system, determine the subjective weight of each specific evaluation index by using the analytic hierarchy process, and determine the objective weight of each specific evaluation index by using the entropy weight method; Step 4, based on the game theory combination weighting model, the subjective weight and the objective weight are combined and optimized to obtain the optimal comprehensive weight of each specific evaluation index; wherein the combination optimization specifically includes: Step 4.1, for the land evaluation index system, linearly combine the subjective weight vector obtained by the analytic hierarchy process and the objective weight vector obtained by the entropy weight method; Step 4.2, a game theory combination weighting model is established to minimize the deviation between the combination weight vector and any weight vector obtained by the analytic hierarchy process or entropy weight method, and the optimal weight coefficient is obtained by solving the following linear equations and : ， wherein, is a subjective weight vector of the specific evaluation index of the land, is an objective weight vector of the specific evaluation index of the land, and are the transpose vectors of the vectors and respectively. Step 4.3, normalize the optimal weight coefficient according to the following formula: ， wherein, and are the optimal weight coefficients of the respective evaluation indicators for the land area. Step 4.4, the optimal combination weight vector obtained by game theory is: ； Step 4.5, according to steps 4.1-4.4, obtain the optimal weight coefficient of each specific evaluation index of the sea area and and the optimal combination weight vector of all indexes ; Step 5, based on the grey correlation analysis method, construct a geological suitability evaluation model, input the optimal comprehensive weight into the evaluation model, calculate the geological suitability score of each geological evaluation unit, and divide the suitability level according to the score range; wherein the construction of the geological suitability evaluation model specifically includes: Step 5.1, for the land evaluation index system, construct an original data matrix containing all geological evaluation units and specific evaluation indexes: ； wherein, represents the value of the i-th geological evaluation unit on the j-th index; m l represents the value of the i-th geological evaluation unit on the j-th index;​ Step 5.2, determine the reference sequence composed of the optimal values of each specific evaluation index of all geological evaluation units and the comparison sequence composed of the actual values, the reference sequence is represented as: ， The comparison sequence is represented as: ； wherein, represents the best value of the i-th index for all the geological evaluation units, the maximum value of the i-th index for all the geological evaluation units is taken for a positive index, and the minimum value of the i-th index for all the geological evaluation units is taken for a negative index, l represents the best value of the i-th index for all the geological evaluation units, the maximum value of the i-th index for all the geological evaluation units is taken for a positive index, and the minimum value of the i-th index for all the geological evaluation units is taken for a negative index, represents the value of the i-th index for the j-th geological evaluation unit; and k represents the value of the i-th index for the j-th geological evaluation unit; and l represents the value of the i-th index for the j-th geological evaluation unit; and Step 5.

3. Normalization of reference sequence and all comparison sequences to obtain dimensionless reference sequence and comparison sequences ; wherein, is the non-dimensionalized value of the reference sequence on the i-th l criterion, is the non-dimensionalized value of the i-th k comparison sequence on the i-th evaluation criterion, l is the non-dimensionalized value of the i-th comparison sequence on the i-th Step 5.4, calculate the correlation coefficients of each geological evaluation unit and the reference sequence on each index, which is expressed as: ； Wherein: is the non-dimensionalized value of the reference sequence on the jth evaluation metric, i is the non-dimensionalized value of the reference sequence on the jth evaluation metric, is the non-dimensionalized value of the reference sequence on the jth evaluation metric, k is the non-dimensionalized value of the reference sequence on the jth evaluation metric, i is the non-dimensionalized value of the reference sequence on the jth evaluation metric, i = 1, 2, …, l ; the absolute difference of the first k comparative sequence on the first i geological suitability evaluation index from the reference sequence; is the minimum value among all the absolute differences; is the maximum difference of two levels, being the maximum value among all the absolute differences. For the resolution coefficient, the value range is (0, 1); Step 5.5, the correlation degree of each comparison sequence and the reference sequence is calculated by weighting the correlation coefficient with the combination weight The correlation degree is the geological suitability score of the geological evaluation unit corresponding to the comparison sequence, and the expression of the correlation degree is: ; wherein, is the combination weight of the i th metric; Step 5.6, according to steps 5.1-5.5, obtain the correlation degree of each geological evaluation unit in the sea area with its reference sequence ; Step 6, according to the geological suitability score, integrate the evaluation results of each geological evaluation unit of land and sea, carry out visual processing, and generate the geological suitability zoning map of land and sea unified underground space development of coastal bedrock city according to the suitability level division standard.

2. The method according to claim 1, wherein the method is characterized by: In step 1, the key geological problem analysis includes geological overview analysis of coastal bedrock city, environmental geological problem analysis affecting the development of coastal bedrock city underground space, and geological cause analysis of cross-sea underground engineering construction accidents.

3. The method according to claim 2, wherein the method is characterized by: The geological overview includes but is not limited to topography, engineering geology, hydrogeology, tectonic zoning and seismic characteristics; The environmental geological problems include but are not limited to soft soil, land subsidence, ground collapse, sand liquefaction, seawater intrusion, storm surge, soil salinization and coastal deposition.

4. The method according to claim 1, wherein the method is characterized by: In step 2, the land and sea basic geological data include but are not limited to digital elevation model DEM, remote sensing image data, land and sea engineering geological drilling and hydrogeological drilling data, geological profile, geotechnical engineering investigation report, single-beam water depth measurement data, coastal erosion and deposition profile measurement data, seabed surface sample and seabed column sample data.

5. The method according to claim 1, wherein the method is characterized by: In step 2, the evaluation index system is divided into a land evaluation index system and a sea area evaluation index system; wherein the land evaluation index system is formed based on natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions and environmental geological problems to identify key indicators; the sea area evaluation index system is formed based on natural geographical conditions, geological conditions and hydrodynamic conditions to identify key indicators; and meanwhile, the coastal bedrock city area is divided into a plurality of geological evaluation units including two types of sub-regions of land and sea areas.

6. The method according to claim 5, wherein the method is characterized by: In step 3, the subjective weight of each specific evaluation index is determined by using the analytic hierarchy process, which specifically includes: In step 3.a1, a hierarchical structure model of target layer, criterion layer and index layer is constructed for the land evaluation index system and the sea area evaluation index system respectively, wherein the target layer of the land hierarchical structure model is the geological suitability of underground space development in land, the criterion layer includes natural geographical conditions, basic geological and hydrogeological conditions, engineering geological conditions and environmental geological problems, and the index layer includes specific evaluation indexes belonging to the indexes of each criterion layer, including but not limited to landform type, slope, Quaternary stratum thickness, aquifer thickness, rock-soil body type, active fault distance, seawater intrusion and collapse and landslide; the target layer of the sea area hierarchical structure model is the geological suitability of underground space development in sea area, the criterion layer includes natural geographical conditions, geological conditions and hydrodynamic conditions, and the index layer includes specific evaluation indexes belonging to the indexes of each criterion layer, including but not limited to water depth, slope, Quaternary sediment thickness, sediment type, active fault distance, erosion and deposition, and sea current; In step 3.a2, a judgment matrix is constructed: using the nine-scale method, the importance of each index in the criterion layer relative to the target layer is compared, and a criterion layer judgment matrix is constructed; for each criterion layer index, the specific evaluation indexes in the index layer thereof are compared in importance using the nine-scale method, and a corresponding index layer judgment matrix is constructed; In step 3.a3, the characteristic vector of each judgment matrix is calculated to obtain the relative weight of the indexes contained therein: The maximum eigenvalue of each judgment matrix is calculated by using the sum-product method the sum-product method includes: normalizing the judgment matrix by column, then summing the normalized matrix by row to obtain a vector, and normalizing the vector to obtain the characteristic vector; max and the corresponding eigenvector ; In step 3.a4, consistency check is performed on each judgment matrix: RI Computing the consistency index where is the matrix order; query the average random consistency index corresponding to the matrix order CR , compute the consistency ratio CI / RI = CR ; when The objective weight of each specific evaluation index is determined by using the entropy weight method, which specifically includes: <0.1, the judgment matrix passes the consistency test, and the relative weight obtained in step 3.a3 is valid. Step 3. a5, determining the final subjective weight: multiplying the relative weight of each specific evaluation index with respect to the guideline layer to which it belongs with the weight of the guideline layer index with respect to the target layer, to obtain the subjective weight of each specific evaluation index with respect to the target layer, i.e., the subjective weight of each specific index of the land area and the subjective weight of each specific index of the sea area ; obtaining a subjective weight vector of the specific evaluation index of the land area based on the subjective weight and a subjective weight vector of the specific evaluation index of the sea area .

7. The method according to claim 6, wherein the method is characterized by: Based on the objective weight, the objective weight vector of the land specific evaluation index is obtained: Step 3.b1, constructing the original evaluation matrix for the land evaluation index system wherein x ki represents the value of the i-th specific evaluation index of the j-th geological evaluation unit; k i m is the total number of geological evaluation units; l is the total number of evaluation indexes;​​ Step 3.b2. Normalization of the original data matrix to eliminate dimension, resulting in a standardized matrix : For the positive indicators, the formula is used: , For the negative indicators, the formula is used: , wherein, and are the first i The maximum and minimum values of the first item of specific evaluation index in all geological evaluation units; Step 3.b3. For the normalized matrix, calculate the feature proportion of the i-th geological evaluation unit under the j-th index: k Step 3.b4. For the normalized matrix, calculate the feature proportion of the i-th geological evaluation unit under the j-th index: i Step 3.b4. For the normalized matrix, calculate the feature proportion of the i-th geological evaluation unit under the j-th index: Step 3.b4. For ， Step 3. b4, calculating the information entropy value of the item index j information entropy value of the item index e i : ， wherein , information entropy e i satisfies , Step 3. b5, calculating the difference coefficient of the item indicators j the difference coefficient of the item indicators d i : ， Step 3.b6, determining the objective weight of each specific evaluation index : ， In step 3.b7, according to steps 3.b1-3.b6, the objective weight vector of the sea area specific evaluation index is obtained: ； According to the geological suitability score, the suitability level is divided, specifically: 。 8. The method according to claim 1, wherein the method is characterized by: the evaluation result with a score in the interval (0, 0.25] is divided into an unsuitable level; the evaluation result with a score in the interval (0.25, 0.5] is divided into a less suitable level; the evaluation result with a score in the interval (0.5, 0.75] is divided into a more suitable level; the evaluation result with a score in the interval (0.75, 1] is divided into a suitable level. ​

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