Shield engineering stratum identification and construction parameter optimization method based on BIM
By using a BIM-based method for identifying geological formations in tunnel boring machines (TBMs), and combining the Sparrow Search algorithm and the Random Forest algorithm, an RF-SSA model was constructed. This solved the problem of inaccurate identification of geological parameters in traditional TBM construction, enabled dynamic optimization of TBM construction parameters, improved construction efficiency, and reduced costs.
Patent Information
- Application Number
- CN202511381298.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-25
- Publication Date
- 2025-12-23
AI Technical Summary
Traditional shield tunneling relies on experience and limited geological survey data for identifying geological parameters, making it difficult to adapt to complex and ever-changing construction environments, resulting in high uncertainty and risk during construction.
A BIM-based method for identifying geological formations in tunnel boring machines (TBMs) was adopted. By combining the Sparrow Search algorithm and the Random Forest algorithm, an RF-SSA geological inverse analysis identification model and an RF-SSA TBM construction parameter inverse analysis model were constructed. Through simulation and data optimization, rapid and accurate identification of geological parameters and dynamic optimization of construction parameters were achieved.
It enables rapid and accurate identification of geological parameters during shield tunneling, adapts to complex and ever-changing construction environments, improves construction efficiency, and reduces construction costs.
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Figure CN121189178A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of shield tunneling construction management technology, and in particular to a BIM-based method for identifying geological formations and optimizing construction parameters in shield tunneling projects. Background Technology
[0002] In the context of the information age, engineering informatization is developing rapidly, and the application of BIM-based 3D technology is unstoppable, subtly influencing the construction mode of tunnel boring machines (TBMs) and gradually permeating the TBM construction field. During TBM tunnel construction, accurate identification of geological parameters is crucial for determining construction parameters, and optimizing these parameters is key to ensuring construction efficiency and reducing costs. Traditional methods rely primarily on experience and limited geological survey data, making them ill-suited to complex and ever-changing construction environments, resulting in high uncertainty and risk during construction. Summary of the Invention
[0003] This invention provides a BIM-based method for identifying geological formations and optimizing construction parameters in tunnel boring machine (TBM) projects, in order to overcome the aforementioned technical problems.
[0004] To achieve the above objectives, the technical solution of the present invention is as follows: A BIM-based method for geological formation identification and construction parameter optimization in tunnel boring machine (TBM) projects, comprising the following steps: S1: Establish a shield tunneling simulation model based on BIM modeling software to realize the shield deformation data analysis process from stratum parameters and construction parameters; The formation parameters include at least the elastic modulus, internal friction angle, cohesion, and density; The construction parameters include at least the excavation advance, soil pressure, and grouting range; The shield deformation data includes at least the settlement deformation of the arch crown, ground surface, and building, as well as the horizontal displacement of the arch waist; S2: Based on expert experience, determine the range of values for the formation parameters, and use the known orthogonal test method to obtain the orthogonal scheme of the formation parameters according to the range of values; and based on the shield tunneling simulation model, simulate and obtain shield deformation data according to the orthogonal scheme of the formation parameters; use the formation parameters and the corresponding shield deformation data as the first sample data. Based on the Sparrow Search algorithm and the first random forest algorithm model, an RF-SSA stratigraphic inverse analysis identification model is constructed using the first sample data, and the inverted stratigraphic parameters are obtained by inverting the RF-SSA stratigraphic inverse analysis identification model. S3: Set the stratum parameters during the shield tunneling simulation excavation process, and determine the range of shield tunnel construction parameters based on expert experience; use known orthogonal test method and uniform design test method to obtain the orthogonal scheme and uniform scheme of construction parameters according to the range of shield tunnel construction parameters, and simulate and obtain shield deformation data based on the shield construction simulation model according to the orthogonal scheme and uniform scheme of construction parameters to obtain the second sample data. Based on the Sparrow Search algorithm and the second random forest algorithm model, an RF-SSA shield tunneling parameter back analysis model is constructed using the second sample data. The optimized shield tunneling parameters are then obtained by inverting the RF-SSA shield tunneling parameter back analysis model. S4: Based on the RF-SSA stratum inverse analysis identification model and the RF-SSA shield construction parameter inverse analysis model, the stratum identification and construction parameter optimization of the shield project are realized according to the measured shield deformation data.
[0005] Furthermore, the method for constructing the RF-SSA stratigraphic inverse analysis identification model using the first sample data in step S2 specifically includes the following steps: S21: Initialize a sparrow population containing N individuals. Define the combination of the number of decision trees and the feature quantity parameter of the smallest leaf node in the first random forest RF model as the position of each sparrow individual. Based on the sparrow search algorithm SSA, optimize and update the number of decision trees and the feature quantity parameter of the smallest leaf node in the random forest RF model according to the fitness function of the model parameter combination. S22: Divide the first sample data into a first training set and a first validation set according to a preset ratio; Furthermore, shield deformation data is used as feature data of the first sample data, and stratum parameters are used as label data of the first sample data. S23: Train the first random forest (RF) model using the first training set in conjunction with step S21, specifically including: S231: Input the sample data from the first training set into the first random forest RF model for model training, and obtain the trained first random forest RF model; S232: Based on the root mean square error function, confirm whether the output of the first random forest RF model after training has converged through the first validation set; if yes, then use the first random forest RF model after training at this time as the RF-SSA stratigraphic inverse analysis identification model; if not, then based on the fitness function of the model parameter combination, combine the sparrow search algorithm SSA to optimize and update the number of decision trees and the feature quantity of the smallest leaf node in the first random forest RF model after training, and repeat step S231.
[0006] Furthermore, the fitness function for the model parameter combination in S232 is expressed as follows: RMSE= , In the formula: RMSE represents the fitness value of the model parameter combination; This represents the output prediction value of the trained Random Forest (RF) model; Represents the actual value; Indicates the number of samples.
[0007] Furthermore, the method for constructing an RF-SSA shield tunneling construction parameter back analysis model using second sample data in S3 specifically includes the following steps: S31: Initialize a sparrow population containing N individuals. Define the combination of the number of decision trees and the feature quantity parameter of the smallest leaf node in the second random forest RF model as the position of each sparrow individual. Construct a shield tunneling construction parameter fitness function by introducing construction cost, and optimize and update the number of decision trees and the feature quantity parameter of the smallest leaf node in the random forest RF model by combining the sparrow search algorithm SSA. S32: Use the orthogonal schemes and corresponding shield deformation data in the second sample data as the second training set, and use the uniform schemes and corresponding shield deformation data in the second sample data as the second validation set. Furthermore, the geological parameters and shield deformation data are used as feature data of the second sample data, and the shield tunnel construction parameters are used as label data of the second sample data. S33: Train the second random forest (RF) model using the second training set in conjunction with step S31, specifically including: S331: Input the sample data from the second training set into the second random forest RF model for model training, and obtain the trained second random forest RF model; S332: Based on the root mean square error function, confirm whether the output of the trained second random forest RF model has converged through the second validation set; if yes, then use the trained second random forest RF model as the RF-SSA shield construction parameter back analysis model; if not, then based on the shield construction parameter fitness function, combine the sparrow search algorithm SSA to optimize and update the number of decision trees and the number of features of the smallest leaf node in the trained second random forest RF model, and repeat step S331.
[0008] Furthermore, the fitness function of the shield tunneling construction parameters described in S332 Its expression is , In the formula: This represents the combination of construction parameters, including soil pressure, shield advance, and grouting depth; L represents the length of the shield tunnel section. Indicates the pressure of the earthwork; This indicates the basic cost per meter; Indicates the pressure adjustment factor; Indicates the progress of the tunnel boring machine; This represents the construction cost of one tunnel boring machine advance. This indicates the cost per cubic meter of grouting required in the construction cost; Indicates the grouting depth; This indicates the annular area of the grouting layer.
[0009] Beneficial effects: This invention provides a BIM-based method for identifying geological formations and optimizing construction parameters in tunnel boring machines (TBMs). By introducing a sparrow search algorithm based on a random forest algorithm model, a ground parameter inverse analysis identification model based on RF-SSA and a TBM construction parameter inverse analysis model based on RF-SSA are constructed. Through the optimization method combining the two, rapid and accurate identification of ground parameters for TBM construction is achieved, which can adapt to complex and ever-changing construction environments and further enable dynamic optimization of TBM construction parameters. Attached Figure Description
[0010] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0011] Figure 1 This is a flowchart of the method for BIM-based shield tunneling engineering stratum identification and construction parameter optimization according to the present invention; Figure 2 This is a diagram showing the deformation during shield tunneling construction viewed through a BIM construction system in this embodiment; Figure 3 This is a schematic diagram of the blocks in the FLAC3D simulation model pre-built using BIM modeling software in this embodiment. Detailed Implementation
[0012] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0013] This embodiment provides a BIM-based method for geological strata identification and construction parameter optimization in tunnel boring machine (TBM) projects, such as... Figure 1 As shown, the specific steps include: S1: Establish a shield tunneling simulation model based on BIM modeling software to realize the shield deformation data analysis process from stratum parameters and construction parameters; The geological parameters include at least the elastic modulus, internal friction angle, cohesion, and density; the construction parameters include at least the excavation advance, soil chamber pressure, and grouting range; and the shield deformation data include at least the settlement deformation of the arch crown, ground surface, and structure, as well as the horizontal displacement of the arch waist. Specifically, the BIM modeling software in this embodiment includes the following functions: (1) Assisting construction technology: BIM technology can use its unique three-dimensional visualization model to carry out technical briefings and provide detailed demonstrations of construction plans, helping technical personnel to better understand and implement construction plans; (2) Refined management: BIM technology is an important means of controlling construction data and costs, and also undertakes the refined management of subway construction to a certain extent; (3) Data support: BIM technology can establish a three-dimensional visualization construction model and input information such as the specific construction progress plan of the subway project into the software, so that the planned progress is compared with the actual progress, thereby achieving scientific control; (4) Preventing ground settlement: BIM technology can perform three-dimensional modeling and simulation analysis, and then formulate measures in advance to prevent ground settlement from exceeding the monitoring allowable value; S2: Based on expert experience, determine the range of values for the formation parameters, and use the known orthogonal test method to obtain the orthogonal scheme of the formation parameters according to the range of values; and based on the shield tunneling simulation model, simulate and obtain shield deformation data according to the orthogonal scheme of the formation parameters; use the formation parameters and the corresponding shield deformation data as the first sample data. Specifically, such as Figure 3 As shown, the blocks of the FLAC3D simulation model are pre-built based on BIM modeling software, and the blocks are divided using hexahedral solid elements. The method of using hexahedral solid elements for block division is a well-known existing technique and will not be elaborated further here. The FLAC3D simulation model has a length of 80 m in the X direction, 30 m in the Y direction, and 10 m in the Z direction; it contains 9324 hexahedral solid elements and 24635 nodes. Multiple sensor monitoring points are pre-set in the FLAC3D simulation model, and the automated monitoring function for tunnel boring machine (TBM) construction is integrated into the existing intelligent TBM construction BIM system. This function window displays the deformation data of the corresponding sensor monitoring points during construction, such as... Figure 2As shown, the monitoring data from the sensor monitoring points include at least the settlement of the left tunnel arch (α), the horizontal convergence displacement around the left tunnel (Ɛ), the settlement of the ground surface center (t), and the building settlement (b). The simulation parameters are those of the design and construction scheme: grouting depth 30 cm, soil chamber pressure 0.5 MPa, and excavation advance 1.2 m. The range of values for the strata parameters is determined based on expert experience, and the simulated strata parameters and their ranges are as follows: elastic modulus of silty clay... internal friction angle of silty clay Elastic modulus of medium sand internal friction angle of medium sand ; elastic modulus of gravel and the internal friction angle of the pebble The above schemes were grouped into equal groups, and orthogonal experiments were performed based on the orthogonal experimental method. The 25 orthogonal schemes were then used in the established shield tunneling simulation model for simulation. The simulation commands were implemented using the FISH statement in FLAC, which refers to the command flow in FLAC3D. Using the FISH language can enhance the targeting of the modeling. The 25 sets of data were obtained and organized into the first sample data T1, as shown in Table 1. They were divided into the first training set T1a and the first validation set T1b in a 4:1 ratio. Table 1. First Sample Data
[0014] Based on the Sparrow Search algorithm and the first random forest algorithm model, an RF-SSA stratigraphic inverse analysis identification model is constructed using the first sample data, and the inverted stratigraphic parameters are obtained by inverting the RF-SSA stratigraphic inverse analysis identification model. The method for constructing an RF-SSA stratigraphic inverse analysis identification model using first sample data in this embodiment specifically includes the following steps: S21: Initialize a sparrow population containing N individuals. Define the combination of the number of decision trees and the feature quantity parameter of the smallest leaf node in the first random forest RF model as the position of each sparrow individual. Based on the sparrow search algorithm SSA, optimize and update the number of decision trees and the feature quantity parameter of the smallest leaf node in the random forest RF model according to the fitness function of the model parameter combination. S22: Divide the first sample data into a first training set and a first validation set according to a preset ratio; Furthermore, shield deformation data is used as feature data of the first sample data, and stratum parameters are used as label data of the first sample data. S23: Train the first random forest (RF) model using the first training set in conjunction with step S21, specifically including: S231: Input the sample data from the first training set into the first random forest RF model for model training, and obtain the trained first random forest RF model; S232: Based on the root mean square error function, confirm whether the output of the first random forest RF model after training has converged through the first validation set; if yes, then use the first random forest RF model after training at this time as the RF-SSA stratum inverse analysis identification model; if not, then based on the fitness function of the model parameter combination, combine the sparrow search algorithm SSA to optimize and update the number of decision trees and the feature number of the smallest leaf node in the first random forest RF model after training, and repeat step S231. Specifically, the expression for the fitness function of the model parameter combination is: RMSE= , In the formula: RMSE represents the fitness value of the model parameter combination; This represents the output prediction value of the trained Random Forest (RF) model; Represents the actual value; Indicates the number of samples.
[0015] S3: Set the stratum parameters during the shield tunneling simulation excavation process, and determine the range of shield tunnel construction parameters based on expert experience; use known orthogonal test method and uniform design test method to obtain the orthogonal scheme and uniform scheme of construction parameters according to the range of shield tunnel construction parameters, and simulate and obtain shield deformation data based on the shield construction simulation model according to the orthogonal scheme and uniform scheme of construction parameters to obtain the second sample data. Specifically, the simulated stratum parameters are obtained through back analysis of the stratum parameters of the building section. By combining the simulated construction parameters with the actual working conditions on site, the range of values for construction parameters such as soil pressure, shield advance, and grouting depth are determined. Orthogonal experimental design or uniform scheme design is carried out on the shield construction parameters to establish an orthogonal design table or a uniform design table for construction parameters. The data in the orthogonal design table is used as the training sample T2a, i.e., the second training set, and the data in the uniform design table is used as the test sample T2b, i.e., the second validation set. The construction parameters of different combination schemes are used as inputs, and the monitored target settlement values are used as outputs to train the RF model and establish the mapping relationship between construction parameters and target settlement values. The training sample T2a is shown in Table 2. Table 2. Second Training Set
[0016] Table 3. Second Validation Set
[0017] Based on the Sparrow Search algorithm and the second random forest algorithm model, an RF-SSA shield tunneling parameter back analysis model is constructed using the second sample data. The optimized shield tunneling parameters are then obtained by inverting the RF-SSA shield tunneling parameter back analysis model. The method for constructing an RF-SSA shield tunneling parameter back analysis model using second sample data in this embodiment specifically includes the following steps: S31: Initialize a sparrow population containing N individuals. Define the combination of the number of decision trees and the feature quantity parameter of the smallest leaf node in the second random forest RF model as the position of each sparrow individual. Construct a shield tunneling construction parameter fitness function by introducing construction cost, and optimize and update the number of decision trees and the feature quantity parameter of the smallest leaf node in the random forest RF model by combining the sparrow search algorithm SSA. S32: Use the orthogonal schemes and corresponding shield deformation data in the second sample data as the second training set, and use the uniform schemes and corresponding shield deformation data in the second sample data as the second validation set. Furthermore, the geological parameters and shield deformation data are used as feature data of the second sample data, and the shield tunnel construction parameters are used as label data of the second sample data. S33: Train the second random forest (RF) model using the second training set in conjunction with step S31, specifically including: S331: Input the sample data from the second training set into the second random forest RF model for model training, and obtain the trained second random forest RF model; S332: Based on the root mean square error function, confirm whether the output of the trained second random forest RF model has converged through the second validation set; if yes, then use the trained second random forest RF model as the RF-SSA shield tunneling construction parameter back analysis model; if not, then based on the shield tunneling construction parameter fitness function, combine the sparrow search algorithm SSA to optimize and update the number of decision trees and the feature quantity of the smallest leaf node in the trained second random forest RF model, and repeat step S331. Specifically, the fitness function of the tunnel boring machine construction parameters The expression for the ground is , In the formula: This represents the combination of construction parameters, including soil pressure, shield advance, and grouting depth; L represents the length of the shield tunnel section. Indicates the pressure of the earthwork; This indicates the basic cost per meter; Indicates the pressure adjustment factor; Indicates the progress of the tunnel boring machine; This represents the construction cost of one tunnel boring machine advance. This indicates the cost per cubic meter of grouting required in the construction cost; Indicates the grouting depth; Indicates the annular area of the grouting layer; S4: Based on the RF-SSA stratum inverse analysis identification model and the RF-SSA shield tunneling parameter inverse analysis model, the stratum identification and construction parameter optimization of the shield tunneling project are achieved based on the measured shield deformation data. Furthermore, this embodiment also displays the stratum parameter update and construction parameter optimization status through an intelligent shield tunneling construction BIM system integrating shield tunneling parameter query functions. The method described in this embodiment, by introducing a sparrow search algorithm based on a random forest algorithm model, constructs an RF-SSA stratum parameter inverse analysis identification model and an RF-SSA shield tunneling parameter inverse analysis model. Through the optimization method combining these two models, rapid and accurate identification of stratum parameters for shield tunneling construction is achieved, adapting to complex and changing construction environments. This further enables dynamic optimization of shield tunneling project construction parameters, significantly improving construction efficiency.
[0018] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A BIM-based method for geological formation identification and construction parameter optimization in tunnel boring machine (TBM) projects, characterized in that, Specifically, the following steps are included: S1: Establish a shield tunneling simulation model based on BIM modeling software to realize the shield deformation data analysis process from stratum parameters and construction parameters; The formation parameters include at least the elastic modulus, internal friction angle, cohesion, and density; The construction parameters include at least the excavation advance, soil pressure, and grouting range; The shield deformation data includes at least the settlement deformation of the arch crown, ground surface, and building, as well as the horizontal displacement of the arch waist; S2: Based on expert experience, determine the range of values for the formation parameters, and use known orthogonal test methods to obtain orthogonal schemes for the formation parameters according to the range of values; and based on the shield tunneling simulation model, simulate and obtain shield deformation data according to the orthogonal schemes for the formation parameters. The geological parameters and the corresponding shield deformation data were used as the first sample data. Based on the Sparrow Search algorithm and the first random forest algorithm model, an RF-SSA stratigraphic inverse analysis identification model is constructed using the first sample data, and the inverted stratigraphic parameters are obtained by inverting the RF-SSA stratigraphic inverse analysis identification model. S3: Set the stratum parameters during the shield tunneling simulation excavation process, and determine the range of shield tunnel construction parameters based on expert experience; use known orthogonal test method and uniform design test method to obtain the orthogonal scheme and uniform scheme of construction parameters according to the range of shield tunnel construction parameters, and simulate and obtain shield deformation data based on the shield construction simulation model according to the orthogonal scheme and uniform scheme of construction parameters to obtain the second sample data. Based on the Sparrow Search algorithm and the second random forest algorithm model, an RF-SSA shield tunneling parameter back analysis model is constructed using the second sample data. The optimized shield tunneling parameters are then obtained by inverting the RF-SSA shield tunneling parameter back analysis model. S4: Based on the RF-SSA stratum inverse analysis identification model and the RF-SSA shield construction parameter inverse analysis model, the stratum identification and construction parameter optimization of the shield project are realized according to the measured shield deformation data.
2. The method for BIM-based geological formation identification and construction parameter optimization in shield tunneling projects according to claim 1, characterized in that, The method for constructing the RF-SSA stratigraphic inverse analysis identification model using the first sample data in S2 specifically includes the following steps: S21: Initialize a sparrow population containing N individuals. Define the combination of the number of decision trees and the feature quantity parameter of the smallest leaf node in the first random forest RF model as the position of each sparrow individual. Based on the sparrow search algorithm SSA, optimize and update the number of decision trees and the feature quantity parameter of the smallest leaf node in the random forest RF model according to the fitness function of the model parameter combination. S22: Divide the first sample data into a first training set and a first validation set according to a preset ratio; Furthermore, shield deformation data is used as feature data of the first sample data, and stratum parameters are used as label data of the first sample data. S23: Train the first random forest (RF) model using the first training set in conjunction with step S21, specifically including: S231: Input the sample data from the first training set into the first random forest RF model for model training, and obtain the trained first random forest RF model; S232: Based on the root mean square error function, confirm whether the output of the first random forest RF model after training has converged through the first validation set; if yes, then use the first random forest RF model after training at this time as the RF-SSA stratigraphic inverse analysis identification model; if not, then based on the fitness function of the model parameter combination, combine the sparrow search algorithm SSA to optimize and update the number of decision trees and the feature quantity of the smallest leaf node in the first random forest RF model after training, and repeat step S231.
3. The method for BIM-based geological formation identification and construction parameter optimization in shield tunneling projects according to claim 1, characterized in that, The fitness function for the model parameter combination in S232 is expressed as follows: RMSE= In the formula: RMSE represents the fitness value of the model parameter combination; This represents the output prediction value of the trained Random Forest (RF) model; Represents the actual value; Indicates the number of samples.
4. The method for BIM-based geological formation identification and construction parameter optimization in shield tunneling projects according to claim 3, characterized in that, The method for constructing an inverse analysis model of RF-SSA shield tunneling construction parameters using second sample data in S3 specifically includes the following steps: S31: Initialize a sparrow population containing N individuals. Define the combination of the number of decision trees and the feature quantity parameter of the smallest leaf node in the second random forest RF model as the position of each sparrow individual. Construct a shield tunneling construction parameter fitness function by introducing construction cost, and optimize and update the number of decision trees and the feature quantity parameter of the smallest leaf node in the random forest RF model by combining the sparrow search algorithm SSA. S32: Use the orthogonal schemes and corresponding shield deformation data in the second sample data as the second training set, and use the uniform schemes and corresponding shield deformation data in the second sample data as the second validation set. Furthermore, the geological parameters and shield deformation data are used as feature data of the second sample data, and the shield tunnel construction parameters are used as label data of the second sample data. S33: Train the second random forest (RF) model using the second training set in conjunction with step S31, specifically including: S331: Input the sample data from the second training set into the second random forest RF model for model training, and obtain the trained second random forest RF model; S332: Based on the root mean square error function, confirm whether the output of the trained second random forest RF model has converged through the second validation set; if yes, then use the trained second random forest RF model as the RF-SSA shield construction parameter back analysis model; if not, then based on the shield construction parameter fitness function, combine the sparrow search algorithm SSA to optimize and update the number of decision trees and the number of features of the smallest leaf node in the trained second random forest RF model, and repeat step S331.
5. The method for BIM-based geological formation identification and construction parameter optimization in shield tunneling projects according to claim 4, characterized in that, Fitness function of shield tunneling construction parameters described in S332 Its expression is In the formula: This represents the combination of construction parameters, including soil pressure, shield advance, and grouting depth; L represents the length of the shield tunnel section. Indicates the pressure of the earthwork; This indicates the basic cost per meter; Indicates the pressure adjustment factor; Indicates the progress of the tunnel boring machine; This represents the construction cost of one tunnel boring machine advance. This indicates the cost per cubic meter of grouting required in the construction cost; Indicates the grouting depth; This indicates the annular area of the grouting layer.