Method for determining mechanical parameters of surrounding rock of fractured structure

Abstract

The application provides a kind of determination method of fragmented structure surrounding rock mechanics parameter, method includes obtaining fragmented surrounding rock tunnel target section initial support and surrounding rock parameter, based on Mohr-Coulomb criterion selects mechanics parameter as displacement sensitivity influence factor;Secondly, determine parameter value range and horizontal grade, construct orthogonal scheme and establish first numerical model, calculate displacement and carry out sensitivity analysis to determine the parameter to be inverted;Further based on the parameter to be inverted and the first numerical calculation model, a nonlinear regression model with undetermined coefficients is constructed, a second numerical calculation model is established by combining engineering measurement, and a complete regression model is obtained by uniform design and sample verification solution;Finally, the regression model, the measured displacement and the parameter range are input, and the differential evolution algorithm is used for optimization search, and the optimal mechanical parameter value meeting the termination condition is output.The application solves the problem of lacking a determination method of fragmented structure surrounding rock mechanics parameter with strong adaptability, high efficiency and high accuracy in the prior art.

Description

Technical Field

[0001] This invention relates to the field of surrounding rock mechanical parameters acquisition technology, and in particular to a method for determining the surrounding rock mechanical parameters of fractured structures. Background Technology

[0002] Tunnel construction often encounters fractured surrounding rock (fractured granite, fractured basalt, fractured sandstone, fractured mudstone, etc.) when traversing shallowly buried sections under biased pressure or fractured zones. Due to the highly developed and disordered structural surfaces, irregular rock mass morphology, and poor overall integrity, geological disasters such as encroachment, collapse, landslides, and even roof falls frequently occur during construction. The main reason for this is the inability to accurately determine the mechanical parameters of the surrounding rock, thus hindering the development of effective and reasonable excavation and support measures.

[0003] Currently, commonly used methods for determining the mechanical parameters of tunnel surrounding rock include engineering geological analogy, direct indoor and outdoor testing, rock mechanics estimation based on the Hoek-Brown (HB) strength criterion, and displacement back analysis. Among these, the engineering analogy method requires clear and comparable geological structures and hydrological conditions between projects, which is generally difficult to meet. Direct indoor and outdoor testing suffers from uneven spatial distribution of rock mass, long testing cycles, high costs, and unrepresentative results. The rock mechanics estimation method based on the Hoek-Brown (HB) strength criterion relies on the experience of engineers to determine the values ​​of rock geological strength indices and rock disturbance parameters, introducing subjectivity. While existing technologies provide empirical quantitative formulas for rock geological strength indices and rock disturbance parameters, the acoustic wave velocity testing requires drilling into the tunnel wall and applying large amounts of coupling agent, resulting in high costs and long cycles. When the rock mass is fractured or fragmented, drilling becomes even more difficult, hindering widespread application in the field.

[0004] For the reasons mentioned above, a method for obtaining the mechanical parameters of surrounding rock through displacement inverse analysis has been proposed. This method uses any two of the four parameters—deformation modulus, cohesion, internal friction angle, and Poisson's ratio—as inverse parameters, while the other parameters need to be provided based on exploration data or experience. The inverse parameters are obtained by solving equations based on existing observation data such as displacement or stress. This method combines computer technology, numerical analysis methods, optimization design, and field measurement, and can obtain relatively accurate rock mass mechanical parameters. However, it has the problem that the inverse parameters are not unique, making it difficult to choose the optimal combination of parameters.

[0005] Existing patented technologies also fail to effectively solve the technical challenge of accurately determining the mechanical parameters of surrounding rock in fractured structures. For example, the method for obtaining mechanical parameters of tunnel surrounding rock disclosed in related patents increases the number of parameters that need to be adjusted after introducing the firefly algorithm, and the physical meaning of the model is unclear. Furthermore, it requires a large amount of effective training data as support, and the final parameters obtained may not be the optimal combination. Another technology involving the automatic inversion of mechanical parameters of tunnel surrounding rock with joint development is only applicable to jointed rock masses with clearly defined joint dips and angles. It is completely unsuitable for fractured rock masses with chaotic structural surfaces and where the joint orientation cannot be obtained. In summary, the determination of mechanical parameters of surrounding rock in fractured structures currently lacks a dedicated technical method that is highly adaptable, accurate, and engineering-promotable, becoming a critical technical pain point that urgently needs to be addressed in this field. Summary of the Invention

[0006] Based on this, the purpose of this invention is to provide a method for determining the mechanical parameters of the surrounding rock of fractured structures, aiming to solve the problem that there is a lack of a highly adaptable, efficient and accurate method for determining the mechanical parameters of the surrounding rock of fractured structures in the prior art.

[0007] A method for determining the mechanical parameters of surrounding rock in a fractured structure according to an embodiment of the present invention, the method comprising:

[0008] The initial support and related parameters of the surrounding rock at the target section of the fractured surrounding rock tunnel were obtained, and the target mechanical parameters were selected as influencing factors for displacement sensitivity analysis based on the Mohr-Coulomb criterion.

[0009] The range of values ​​for each of the target mechanical parameters is determined and the level is divided. An orthogonal design scheme is determined based on the range of values ​​and level of each parameter. A first numerical calculation model of a fractured surrounding rock tunnel is established according to the relevant parameters and the orthogonal design scheme. After calculating the first peripheral displacement, displacement sensitivity analysis is carried out on each of the target mechanical parameters to determine the parameters to be inverted.

[0010] Based on the parameters to be inverted and the first numerical calculation model, a first nonlinear regression model with undetermined coefficients and the surrounding displacement varying with the parameters to be inverted is constructed through a preset scheme. A second numerical calculation model is established by combining specific engineering site detection information. The parameters to be inverted are uniformly designed to obtain a parameter combination scheme. The parameter combination scheme is substituted into the second numerical calculation model to obtain the second surrounding displacement. Based on the parameter combination scheme, the second surrounding displacement, and the first nonlinear regression model, a complete second nonlinear regression model is determined through a preset method.

[0011] Using the second nonlinear regression model, the measured displacement data of the surrounding area of ​​the tunnel, and the range of values ​​of the parameters to be inverted at each monitoring section as input, the differential evolution algorithm is used to optimize and search for the parameters to be inverted in the fractured surrounding rock, and outputs the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions.

[0012] In addition, the method for determining the mechanical parameters of fractured surrounding rock according to the above embodiments of the present invention may also have the following additional technical features:

[0013] Furthermore, the step of constructing a first nonlinear regression model with undetermined coefficients, based on the parameters to be inverted and the first numerical calculation model, through a preset scheme, includes:

[0014] The controlled variable method is used to calculate the displacement around the tunnel under the corresponding working condition through the first numerical calculation model in sequence, and the single-factor calculation of all parameters to be inverted is completed in sequence to obtain the displacement data around the tunnel corresponding to a single change of each parameter to be inverted.

[0015] Function fitting was performed on the surrounding displacement data corresponding to each parameter to be inverted to obtain the single-factor relationship between the surrounding displacement and each parameter to be inverted;

[0016] By integrating all single-factor relationships, a first nonlinear regression model with undetermined coefficients is constructed, which describes the displacement around the tunnel as a function of deformation modulus, internal friction angle, and cohesion.

[0017] The formula for the first nonlinear regression model is:

[0018]

[0019] in, For the surrounding displacement, For deformation modulus, It is the internal friction angle. For cohesion, , , , , and The fitting coefficients are denoted as .

[0020] Furthermore, the second peripheral displacement includes the arch subsidence displacement and the clearance convergence displacement. The steps for determining the complete second nonlinear regression model using a preset method based on the parameter combination scheme, the second peripheral displacement, and the first nonlinear regression model include:

[0021] The parameter combination scheme is matched one-to-one with the second peripheral displacement to construct a combined dataset. The parameter combination scheme is a preset number of representative combinations generated for the parameters to be inverted. Each parameter combination corresponds to a set of arch settlement displacement values ​​and net clearance convergence displacement values. The parameters to be inverted include deformation modulus, internal friction angle, and cohesion.

[0022] Substitute the combined dataset into the first nonlinear regression model, and use MATLAB software to solve the coefficients of the first nonlinear regression model from the two indicators of arch subsidence displacement and net clearance convergence displacement, respectively, to obtain the second nonlinear regression model.

[0023] Furthermore, using the second nonlinear regression model, the measured displacement data around the tunnel site, and the range of values ​​for the parameters to be inverted at each monitoring section as input, the steps for optimizing and searching the parameters to be inverted in the fractured surrounding rock based on the differential evolution algorithm, and outputting the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions, include:

[0024] Determine the initial parameters of the differential evolution algorithm. The initial parameters include at least the number of optimization variables, the number of populations, the mutation factor, the crossover probability, the maximum number of iterations, and the convergence accuracy, wherein the number of optimization variables is consistent with the number of parameters to be inverted.

[0025] The objective function is the sum of squared errors between the calculated and measured values ​​of the displacement around the tunnel section. The calculated value of the displacement around the tunnel section is obtained through a complete nonlinear regression model of the displacement around the tunnel section. Based on the geological data of the monitoring section of the fractured rock tunnel in the specific project, the range of values ​​of the parameters to be inverted for each monitoring section and the fixed values ​​of the parameters not involved in the inversion are determined.

[0026] Within the range of values ​​for the parameters to be inverted, a set of parent populations is randomly generated to substitute the mechanical parameters of each body in the parent population into the complete nonlinear regression model of the surrounding displacement and calculate the objective function value of each body.

[0027] The mutation operation is performed according to the preset mutation formula. Different individuals are randomly selected from the parent population to generate a set of mutated individuals. The crossover operation is performed according to the preset crossover rule to cross the target vector of the parent population with the mutated vector of the set of mutated individuals to generate a new population.

[0028] The objective function value of each individual in the new population is calculated, and an evolutionary selection operation is performed according to a preset selection formula to select high-quality individuals from the parent population and the new population to form the offspring population, so as to calculate the objective function value of each individual in the offspring population.

[0029] If the minimum objective function value of an individual in the offspring population satisfies the termination condition, the calculation ends, and the individual corresponding to the minimum objective function value is the mechanical parameter value of the fractured surrounding rock. If the minimum objective function value of an individual in the offspring population satisfies the termination condition, the offspring population is used as the new parent population, and the step of performing the mutation operation according to the preset mutation formula and randomly selecting different individuals from the parent population to generate a set of mutated individuals is repeated until the parameter value that satisfies the termination condition is obtained.

[0030] Furthermore, both the first and second numerical calculation models are FLAC3D numerical calculation models. When establishing the FLAC3D numerical calculation model, the surrounding rock adopts the Mohr-Coulomb elastoplastic constitutive model, and the initial support adopts the linear elastic constitutive model.

[0031] The surrounding displacements include the arch subsidence displacement and the clearance convergence displacement; the displacement sensitivity analysis adopts a combination of range analysis and variance analysis.

[0032] Furthermore, the steps of determining the value range of each of the target mechanical parameters and classifying them into level categories, so as to determine the orthogonal design scheme based on the value range and level category of each parameter, include:

[0033] The target mechanical parameters include deformation modulus, internal friction angle, cohesion and Poisson's ratio. The value range of the target mechanical parameters is divided into 5 levels, and the values ​​of each level of the parameter are in an arithmetic sequence.

[0034] The orthogonal design scheme is based on An orthogonal array was constructed, resulting in 25 effective parameter combinations.

[0035] Furthermore, the relationship between the peripheral displacement and the deformation modulus and cohesion was fitted using a quadratic function, while the relationship between the peripheral displacement and the internal friction angle was fitted using a linear function.

[0036] By unifying the fitted relationships between the peripheral displacements and the deformation modulus, internal friction angle, and cohesion, the first nonlinear regression model can be obtained.

[0037] Another objective of this invention is to provide a system for determining the mechanical parameters of surrounding rock in fractured structures, used to implement the aforementioned method for determining the mechanical parameters of surrounding rock in fractured structures, the system comprising:

[0038] The data determination module is used to obtain the initial support and related parameters of the surrounding rock at the target section of the fractured rock tunnel, and selects the target mechanical parameters as the influencing factors for displacement sensitivity analysis based on the Mohr-Coulomb criterion.

[0039] The inversion parameter determination module is used to determine the value range of each of the target mechanical parameters and classify the level, so as to determine the orthogonal design scheme based on the value range and level of each parameter, and to establish a first numerical calculation model of the fractured surrounding rock tunnel according to the relevant parameters and the orthogonal design scheme. After calculating the first peripheral displacement, displacement sensitivity analysis is carried out on each of the target mechanical parameters to determine the parameters to be inverted.

[0040] The model building module is used to construct a first nonlinear regression model with undetermined coefficients and the surrounding displacement varying with the parameters to be inverted based on the parameters to be inverted and the first numerical calculation model through a preset scheme, and to establish a second numerical calculation model in combination with specific engineering site detection information. The parameters to be inverted are uniformly designed to obtain a parameter combination scheme, and the parameter combination scheme is substituted into the second numerical calculation model to obtain the second surrounding displacement. Based on the parameter combination scheme, the second surrounding displacement and the multivariate nonlinear regression model, the complete second nonlinear regression model is determined through a preset method.

[0041] The optimal parameter determination module is used to optimize and search for the parameters to be inverted in the fractured surrounding rock based on the differential evolution algorithm, taking the second nonlinear regression model, the measured displacement data of the surrounding rock at the tunnel site, and the range of values ​​of the parameters to be inverted at each monitoring section as input, and output the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions.

[0042] Another objective of this invention is to provide a storage medium storing a computer program that, when executed by a processor, implements the steps of the method for determining the mechanical parameters of the surrounding rock in a fractured structure as described above.

[0043] Another objective of this invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method for determining the mechanical parameters of the surrounding rock of the fractured structure described above.

[0044] This invention selects the deformation modulus, internal friction angle, cohesion, and Poisson's ratio—mechanical parameters of fractured rock masses—as influencing factors for sensitivity analysis based on the Mohr-Coulomb criterion. An orthogonal experimental scheme is designed, and numerical simulation analysis of tunnel excavation is conducted. Based on the peripheral displacement calculated by numerical simulation, sensitivity analysis is performed to determine the parameters to be inverted as deformation modulus, internal friction angle, and cohesion. Using the controlled variable method, a ternary nonlinear regression model is constructed to express the relationship between peripheral displacement and deformation modulus, internal friction angle, and cohesion, based on the peripheral displacement calculated by numerical simulation. Combined with specific engineering survey data and a uniform design scheme for the parameters to be inverted, the coefficients of the nonlinear regression model of peripheral displacement are obtained through numerical simulation calculations, resulting in a complete nonlinear regression model of peripheral displacement for the specific project. Using the variance between the calculated and measured values ​​of peripheral displacement as the objective function, the DE algorithm is used to obtain the optimal solution for the mechanical parameters to be inverted. This scheme requires fewer parameters to be adjusted, the objective function has a clear meaning, does not require repeated calls to FLAC3D software, and does not require a large amount of training data, making the calculation fast and efficient. Furthermore, this scheme does not require knowledge of the specific occurrence of the rock mass. Therefore, this invention solves the problem of the lack of a highly adaptable, efficient, and accurate method for determining the mechanical parameters of fractured rock surrounding structures in the prior art. Attached Figure Description

[0045] Figure 1 This is a flowchart of the method for determining the mechanical parameters of the surrounding rock of the fractured structure in the first embodiment of the present invention;

[0046] Figure 2 This is a schematic diagram of the system for determining the mechanical parameters of the surrounding rock in a fractured structure according to the second embodiment of the present invention.

[0047] Figure 3 This is a schematic diagram of the structure of the electronic device in the third embodiment of the present invention;

[0048] Figure 4 This is a schematic diagram of a tunnel model according to one embodiment of the present invention;

[0049] Figure 5 This is a schematic diagram of an advanced small catheter model in one embodiment of the present invention;

[0050] Figure 6 This is a schematic diagram of an anchor bolt support and advanced pipe roof model in one embodiment of the present invention;

[0051] Figure 7 This is a schematic diagram of the initial shotcrete support model in one embodiment of the present invention.

[0052] Figure 8 This is a schematic diagram of the simulation results of deformation modulus and arch settlement in one embodiment of the present invention;

[0053] Figure 9This is a schematic diagram of the simulation results of deformation modulus and horizontal convergence in one embodiment of the present invention;

[0054] Figure 10 This is a schematic diagram of the simulation results of the internal friction angle and the crown settlement in one embodiment of the present invention;

[0055] Figure 11 This is a schematic diagram of the simulation results of the internal friction angle and horizontal convergence in one embodiment of the present invention;

[0056] Figure 12 This is a schematic diagram of the simulation results of cohesion and arch settlement in one embodiment of the present invention;

[0057] Figure 13 This is a schematic diagram of the simulation results of cohesion and horizontal convergence in one embodiment of the present invention;

[0058] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0059] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Several embodiments of the invention are illustrated in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0060] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0061] Example 1

[0062] Please see Figure 1 The figure shows a method for determining the mechanical parameters of the surrounding rock of a fractured structure in the first embodiment of the present invention, the method specifically including S01-S04.

[0063] S01, obtain the initial support and related parameters of the surrounding rock at the target section of the fractured rock tunnel, and select the target mechanical parameters as the influencing factors for displacement sensitivity analysis based on the Mohr-Coulomb criterion.

[0064] Specifically, the relevant parameters include at least the support type, as well as the geometric and physical-mechanical parameters of the surrounding rock and support structure. By collecting the basic geometric and physical-mechanical parameters of the initial tunnel support, the modeling is ensured to closely align with the actual engineering situation. Mechanical parameters are selected based on the Mohr-Coulomb elastoplastic criterion to match the deformation and failure characteristics of the fractured surrounding rock. This clarifies the basic input conditions for numerical modeling and sensitivity analysis, identifies the core mechanical parameters strongly correlated with the deformation of the fractured surrounding rock, and avoids irrelevant parameters interfering with subsequent analysis processes.

[0065] S02, determine the value range of each of the target mechanical parameters and classify the level, determine the orthogonal design scheme based on the value range and level of each parameter, and establish the first numerical calculation model of the fractured surrounding rock tunnel according to the relevant parameters and the orthogonal design scheme. After calculating the first peripheral displacement, conduct displacement sensitivity analysis on each of the target mechanical parameters to determine the parameters to be inverted.

[0066] In practice, by defining reasonable ranges for parameter values, constructing an orthogonal experimental scheme, and then establishing a FLAC3D numerical model to calculate displacement, sensitivity analysis is used to determine the degree of influence of each parameter, and low-sensitivity parameters are eliminated. This significantly reduces the amount of simulation computation while ensuring analytical accuracy, quickly and accurately determining the core parameters to be inverted, and solving the problems of excessive inversion parameters and computational redundancy.

[0067] Specifically, the target mechanical parameters include deformation modulus, internal friction angle, cohesion, and Poisson's ratio. The value ranges of these target mechanical parameters are divided into five levels, and the levels of each parameter follow an arithmetic progression. The orthogonal design scheme is based on... An orthogonal array was constructed, resulting in 25 effective parameter combinations. In practice, by standardizing the parameter level division rules, a balanced and representative orthogonal experimental scheme was constructed to cover the entire parameter space with the fewest possible experiments. Furthermore, the parameter combinations exhibit balanced distribution and comparable characteristics; the 25 effective parameter combinations can fully cover the parameter variation range, significantly reducing the computational and time costs of numerical simulation.

[0068] In addition, both the first and second numerical calculation models are FLAC3D numerical calculation models. When establishing the FLAC3D numerical calculation model, the surrounding rock adopts the Mohr-Coulomb elastoplastic constitutive model, and the initial support adopts the linear elastic constitutive model. The peripheral displacement includes the crown settlement displacement and the net clearance convergence displacement. The displacement sensitivity analysis adopts a combination of range analysis and variance analysis.

[0069] In practical implementation, the Mohr-Coulomb elastoplastic model was selected for the surrounding rock to match the elastoplastic deformation characteristics of the fractured structure. A linear elastic model was used for simplified calculations in the initial support phase. Simultaneous monitoring of crown settlement and clearance convergence displacements was conducted to comprehensively reflect the surrounding rock deformation. Then, range analysis and variance analysis were combined to quantitatively determine the significance of parameter influences. Thus, by establishing a numerical model that closely matches the engineering characteristics of fractured surrounding rock, and employing dual displacement indices and dual analysis methods, the accuracy and reliability of sensitivity analysis were improved. This ensures that the numerical model calculation results closely match the actual engineering situation, that the dual displacement indices comprehensively reflect the deformation state, and that the sensitivity analysis results can accurately distinguish the strength of parameter influences, providing a scientific basis for selecting parameters to be inverted.

[0070] S03, based on the parameters to be inverted and the first numerical calculation model, a first nonlinear regression model with undetermined coefficients and the surrounding displacement varying with the parameters to be inverted is constructed through a preset scheme. A second numerical calculation model is established by combining specific engineering site detection information. The parameters to be inverted are uniformly designed to obtain a parameter combination scheme. The parameter combination scheme is substituted into the second numerical calculation model to obtain the second surrounding displacement. Based on the parameter combination scheme, the second surrounding displacement, and the first nonlinear regression model, a complete second nonlinear regression model is determined through a preset method.

[0071] In practical implementation, a ternary nonlinear regression model with undetermined coefficients is first constructed. Then, the coefficients are solved and the accuracy is verified using engineering measured data and uniform design, ultimately obtaining a fast calculation model specific to the project. This improves inversion efficiency by establishing an explicit nonlinear correlation model between surrounding rock mechanical parameters and surrounding displacements, replacing repeated calls to FLAC3D for displacement calculations.

[0072] Specifically, the controlled variable method is used to calculate the tunnel periphery displacement under the corresponding working conditions through the first numerical calculation model in sequence, and the single-factor calculation of all parameters to be inverted is completed in sequence to obtain the tunnel periphery displacement data corresponding to a single change of each parameter to be inverted; the periphery displacement data corresponding to each parameter to be inverted are fitted with functions to obtain the single-factor relationship between the periphery displacement and each parameter to be inverted; all single-factor relationships are integrated to construct a first nonlinear regression model with undetermined coefficients, in which the tunnel periphery displacement changes with deformation modulus, internal friction angle and cohesion.

[0073] The formula for the first nonlinear regression model is:

[0074]

[0075] in, For the surrounding displacement, For deformation modulus, It is the internal friction angle. For cohesion, , , , , and The coefficients represent the fitting values. In practice, the independence of the single-factor analysis is ensured by using the control variable method, and the fitting form is selected according to the deformation law to integrate the single-factor relationships to obtain a ternary model that covers all core parameters to be inverted. This eliminates coupling interference between parameters, accurately describes the deformation law of single parameters and displacement, and integrates them to obtain a ternary nonlinear regression model with clear physical meaning.

[0076] Furthermore, the parameter combination scheme is mapped one-to-one with the second peripheral displacement to construct a combined dataset. The parameter combination scheme is a preset number of representative combinations generated for the parameters to be inverted. Each parameter combination corresponds to a set of arch crown settlement displacement values ​​and net clearance convergence displacement values. The parameters to be inverted include deformation modulus, internal friction angle, and cohesion. The combined dataset is substituted into the first nonlinear regression model, and the coefficients of the first nonlinear regression model are solved based on the arch crown settlement displacement and net clearance convergence displacement using MATLAB software to obtain the second nonlinear regression model.

[0077] In addition, the accuracy of the second nonlinear regression model needs to be verified. Multiple sets of independent parameter test samples are generated. The test samples are substituted into the second nonlinear regression model to obtain the predicted value of the surrounding displacement. At the same time, the test samples are substituted into the second numerical calculation model to obtain the calculated value of the surrounding displacement. The relative error between the predicted value and the calculated value is compared. If the relative error is within the preset range, the accuracy verification is deemed qualified. The second nonlinear regression model after verification is the complete second nonlinear regression model. This model can directly calculate the tunnel arch settlement displacement and net clearance convergence displacement through the parameters to be inverted.

[0078] In practical implementation, a dataset is constructed by generating representative parameter combinations through uniform design, and the coefficients are solved using MATLAB with dual indices to ensure that the model is suitable for calculating arch settlement and clearance convergence. Furthermore, the model's accuracy is verified through independent samples to ensure its reliability. This yields a complete regression model for the specific project, with the relative error of displacement prediction controlled within 5%. This model can completely replace FLAC3D for rapid displacement calculation, significantly improving the efficiency of subsequent parameter inversion.

[0079] Furthermore, the relationships between peripheral displacement and deformation modulus and cohesion are fitted using quadratic functions, while the relationship between peripheral displacement and internal friction angle is fitted using a linear function. By unifying the fitted expressions for peripheral displacement with deformation modulus, internal friction angle, and cohesion, the first nonlinear regression model can be obtained. In practical implementation, the fitting function is selected according to the parameter deformation law, and the unified integration rules are used to avoid a chaotic model structure. This ensures that the first nonlinear regression model has a regular structure, the coefficients are easy to solve, and the subsequent calculation process is stable and the results are accurate.

[0080] S04 takes the second nonlinear regression model, the measured displacement data of the surrounding area of ​​the tunnel, and the range of values ​​of the parameters to be inverted at each monitoring section as inputs. Based on the differential evolution algorithm, it optimizes and searches for the parameters to be inverted in the fractured surrounding rock and outputs the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions.

[0081] Specifically, the initial parameters of the differential evolution algorithm are determined. These initial parameters include at least the number of optimization variables, the number of populations, the mutation factor, the crossover probability, the maximum number of iterations, and the convergence accuracy. The number of optimization variables is consistent with the number of parameters to be inverted. The objective function is the sum of squared errors between the calculated and measured values ​​of the displacement around the tunnel section. The calculated displacement values ​​are obtained through a complete nonlinear regression model of the displacement around the tunnel. Based on the geological data of the monitoring sections of the fractured surrounding rock tunnel in the specific engineering project, the value range of the parameters to be inverted at each monitoring section, as well as the fixed values ​​of the parameters not involved in the inversion, are determined. Within the value range of the parameters to be inverted, a set of parent populations is randomly generated. The mechanical parameters of each individual in the parent population are substituted into the complete nonlinear regression model of the displacement around the tunnel to calculate the objective function value of each individual. The mutation operation is performed according to a preset mutation formula, and mutually exclusive values ​​are randomly selected from the parent population. Identical individuals generate a set of mutated individuals, and crossover operations are performed according to preset crossover rules. The target vector of the parent population is crossbred with the mutated vector of the set of mutated individuals to generate a new population. The target function value of each individual in the new population is calculated, and evolutionary selection operations are performed according to preset selection formulas to select high-quality individuals from the parent population and the new population to form the offspring population, so as to calculate the target function value of each individual in the offspring population. If the minimum target function value of an individual in the offspring population meets the termination condition, the calculation ends, and the individual with the minimum target function value is the mechanical parameter value of the fractured surrounding rock. If the minimum target function value of an individual in the offspring population meets the termination condition, the offspring population is used as the new parent population, and the step of performing mutation operations according to preset mutation formulas and randomly selecting distinct individuals from the parent population to generate a set of mutated individuals is repeated until the parameter value that meets the termination condition is obtained.

[0082] In practical implementation, the initial values ​​for the differential evolution algorithm are first determined. Specific steps include: optimizing the number of variables, i.e., the number of parameters to be inverted. D Population size NP ; variable factor F Crossover probability CR Maximum number of iterations (max-iter); Convergence accuracy tol ;

[0083] Secondly, determine the objective function. Specifically, take the tunnel's first... k Calculated values ​​of displacement around each cross section Compared with the measured displacement value u The sum of squared errors is used as the objective function, also known as the fitness value, i.e.:

[0084]

[0085] in, This is the sum of squared errors, also known as the fitness value; This corresponds to a set of surrounding rock mechanical parameters to be inverted; , The calculated values ​​of the crown displacement and horizontal clearance displacement of the k-th section are obtained through a complete nonlinear regression model of the surrounding displacements. , These are the measured values ​​of the crown displacement and the horizontal clearance displacement at the k-th section, respectively.

[0086] Then, based on the geological data of the specific monitoring section of the fractured surrounding rock tunnel of a certain project, the range of values ​​for the parameters to be inverted under each working condition and the values ​​of the parameters not involved in the inversion were determined.

[0087] Next, a parent population is generated. Specifically, within the range of values ​​for the parameters to be inverted, a set of parent populations is randomly generated: , NP is usually taken as 5D-10D, where D is the number of parameters to be inverted; The surrounding rock mechanical parameters corresponding to the j-th individual in the population The initial value;

[0088] Then, the surrounding rock mechanical parameters are substituted into the complete nonlinear regression model of the peripheral displacement to calculate the objective function value of each individual in the parent population, i.e. ,That i For the algebra of evolution;

[0089] Then perform the mutation operation, specifically by generating mutated individuals according to the following formula. :

[0090]

[0091] In the formula, ; ; , , It involves randomly selecting three distinct individuals from the parent population, i.e. , , for The random integers in the set are all distinct. F This is a variable factor, which is a preset value, ranging from 0.5 to 0.9;

[0092] Then, a crossover operation is performed, specifically involving the target vector. With the mutation vector New sample vectors are generated by hybridization according to the following rules.

[0093]

[0094] In the formula, Individuals resulting from crossover. It is taken from [0,1]. j A random number; CR represents the crossover probability; Is The first random value within the range j A random integer variable;

[0095] Next, calculate the population after the crossover operation. individual objective function values ;

[0096] Next, evolutionary selection is performed. The specific formula for selecting the offspring population is as follows:

[0097]

[0098] In the formula, , , They are respectively and The objective function value.

[0099] Finally, the test is terminated by calculating the values ​​of each individual in the offspring generation. If the minimum objective function value of an individual satisfies the termination condition, i.e., the convergence accuracy or the maximum number of iterations is reached, the calculation ends, and the individual corresponding to the minimum objective function value is the rock mass mechanical parameter value of the fractured surrounding rock tunnel; otherwise, the mutation operation step is repeated until the termination detection step is found until the parameter value that satisfies the termination condition is found.

[0100] As an example, and not a limitation, in some alternative embodiments, an example of applying the above method to a tunnel project is given below to facilitate a better understanding of the solution. The specific steps are as follows:

[0101] 1. Model building and parameter setting

[0102] The project overview is as follows: This is a two-way, four-lane separated tunnel, with the tunnel's starting and ending mileage markers ranging from K31+229 to K34+406. The tunnel's designed clearance dimensions are 11.0 m (width) × 5.0 m (height). The surrounding rock at the left tunnel entrance section ZK31+250 to ZK31+280 exhibits a loose rock structure (Class V), with ZK indicating its number. The maximum burial depth is 29.31 meters, and the average burial depth is 27.24 m, classifying it as a shallow tunnel. It contains one fault, with obvious bedding and well-developed joints, and the surrounding rock lithology is complex and variable.

[0103] 1.1 Numerical Model Establishment for Tunnels in Bulk Rock Sections

[0104] A three-dimensional numerical model was established based on the excavation outline of the tunnel cross-section design. The tunnel excavation dimensions are 12m × 10m, with a burial depth of 27m. To eliminate boundary effects, 30m was taken on each side of the tunnel, 27m downwards, and 50m along the tunnel length. Horizontal displacement constraints were applied to the left and right (X-direction) and front and back (Y-direction) boundaries of the model, the bottom (Z-direction) boundary was fixed, and the top was a free boundary to simulate the ground surface. The model was discretized into 277,440 elements and 287,716 nodes, and the Mohr-Coulomb elastoplastic model was adopted for the rock mass constitutive relation. The convergence criterion was that the ratio of the maximum unbalanced force to the typical internal force of the system was less than 1 × 10⁻⁶. -5 Once the conditions are met, the next excavation step calculation is performed. In the simulation, the tunnel excavation advance per cycle is set to 1 m, for a total advance of 30 m. The tunnel's three-dimensional geometry and support structure are as follows: Figures 4-7 As shown.

[0105] 1.2 Simulation Parameter Settings

[0106] The mechanical parameters of various structures in the model were mainly determined based on the "Specifications for Design of Highway Tunnels" (JTG 3370.1-2018), tunnel-specific design documents, and relevant research literature. The numerical simulation element types for each structure are shown in Table 1: the surrounding rock was simulated using solid elements; the anchor bolt support and advanced pipe roof were simulated using cable structural elements; and the initial shotcrete support was simulated using shell structural elements.

[0107] Table 1 Selection of Tunnel Simulation Units

[0108]

[0109] The parameters of each element are as follows:

[0110] Initial support uses a combined support system (system anchor bolts + steel arch frame + shotcrete):

[0111] The composite structure consisting of a steel arch frame and shotcrete was simulated using Shell elements with a thickness of 0.3 m and an equivalent modulus of elasticity. The mechanical parameters of the composite structure are shown in Table 2.

[0112] Table 2 Mechanical parameters of Shell unit

[0113]

[0114] The system anchor bolts are 4.0 m long, spaced 0.75 m apart, and arranged in a staggered pattern with a row spacing of 1.0 m. The elastic modulus of the anchor bolts (Cable units) is 200 GPa, and their bond strength with the surrounding rock is provided by cement grout and set at 2.0 MPa. Specific parameters of the Cable units are shown in Table 3.

[0115] Table 3 Specific parameters of the cable unit for anchor bolt support

[0116]

[0117] Advanced support consists of advanced small guide pipes and advanced pipe roofs:

[0118] The advanced guide pipes are arranged within a 120° range of the arch cross-section, with an outward insertion angle of 15°. They are made of Φ42mm×3.5mm hot-rolled seamless steel pipes, with a length of 4.5m, a circumferential spacing of 0.4m, and a row spacing of 1.0m. Their mechanical parameters are shown in Table 4.

[0119] Table 4 Mechanical parameters of advanced small catheters

[0120]

[0121] The advanced pipe roof uses Φ108mm×6mm hot-rolled seamless steel pipes with a circumferential spacing of 0.4m and a length of 16m. Its mechanical parameters are shown in Table 5.

[0122] Table 5 Mechanical parameters of advanced pipe shed

[0123]

[0124] 2. Parameter sensitivity analysis based on orthogonal experiments

[0125] This study employs a combination of orthogonal experimental design and variance analysis to conduct sensitivity analysis on four mechanical parameters of surrounding rock: deformation modulus E, Poisson's ratio μ, internal friction angle φ, and cohesion c.

[0126] 2.1 Orthogonal Experimental Design Scheme

[0127] Based on the measured data provided in the tunnel engineering geological survey report, the benchmark values ​​for the surrounding rock mechanical parameters were determined (Table 6). Each parameter was divided into five levels, with specific values ​​shown in Table 7. The test scheme was based on L...25 (5 6 The orthogonal array was constructed, resulting in 25 effective parameter combinations (Table 8).

[0128] Table 6 Range of values ​​for back analysis parameters

[0129]

[0130] Table 7. Level values ​​of back analysis parameters

[0131]

[0132] Table 8 Orthogonal Experiment Combination Table

[0133]

[0134] 2.2 Numerical Simulation Results

[0135] For the 25 orthogonal test schemes established in Table 8, the FLAC3D numerical simulation software was used to calculate the parameter combinations of each group, and the settlement of the tunnel arch and the displacement data of horizontal convergence were obtained, as shown in Table 9.

[0136] Table 9 Numerical Model Calculation Results

[0137]

[0138] 2.3 Sensitivity Analysis of Displacement Back Analysis Parameters

[0139] Sensitivity analyses were performed using range analysis and variance analysis relative to deformation modulus, cohesion, internal friction angle, and Poisson's ratio. The results are shown in Tables 10, 11, 12, and 13.

[0140] Table 10 Results of the range analysis of the settlement of the arch crown

[0141]

[0142] The order of influence from greatest to least is: deformation modulus E > cohesion c > friction angle φ > Poisson's ratio ν.

[0143] Table 11 Results of ANOVA on Variance Analysis of Variance in Crown Settlement

[0144]

[0145] The order of influence is: deformation modulus E > cohesion c > friction angle φ > Poisson's ratio ν.

[0146] Table 12 Results of Horizontal Convergence Range Analysis

[0147]

[0148] The order of influence from greatest to least is: deformation modulus E > cohesion c > friction angle φ > Poisson's ratio ν.

[0149] Table 13 Results of Horizontal Convergence ANOVA

[0150]

[0151] The order of influence is as follows: deformation modulus E > cohesion c > friction angle φ > Poisson's ratio ν. The number of asterisks (*) below the significance level indicates the degree of significance; the more asterisks, the higher the significance.

[0152] It can be seen that among the four mechanical parameters affecting the deformation of the surrounding rock of the tunnel, the deformation modulus E and cohesion c are the key sensitive parameters, followed by the influence of the internal friction angle φ; while the influence of Poisson's ratio ν is not significant.

[0153] 3. Establishment of a nonlinear regression model for displacement inverse analysis

[0154] By controlling the variables, changing one of E, c, and φ while keeping the others constant, numerical simulations were performed using FLAC3D to obtain the relationship between the surrounding displacement and each parameter. Furthermore, an explicit nonlinear relationship was established between the three parameters: the tunnel surrounding displacement u0. .

[0155] Based on the geological survey data of the ZK31+250~ZK31+280 section of the left tunnel, the values ​​of each inversion parameter are determined as follows: deformation modulus E is 0.2~1.0 GPa, cohesion c is 20~60 kPa, friction angle φ is 18~28°, and Poisson's ratio is taken as a fixed value ν=0.3.

[0156] 3.1 Single-factor relationship between peripheral displacement and deformation modulus E

[0157] Under the conditions of cohesion c = 40 kPa and internal friction angle φ = 23°, with other parameters fixed, the deformation modulus E was divided into 9 levels within the range of 0.2-1.0 GPa. FLAC3D numerical simulations were performed on each group under the conditions of lateral pressure coefficient λ = 1.0, 0.8, 0.6, and 0.4. The simulation results are as follows: Figure 8 and Figure 9 .

[0158] The figure shows that the crown settlement displacement and the horizontal convergent displacement have the same fitting relationship with the deformation modulus E. A quadratic function relationship can be established between u0 and E:

[0159]

[0160] In the formula: This indicates displacement around the tunnel, including crown settlement. and horizontal convergence ; , The coefficients are the fitting coefficients of the relation.

[0161] 3.2 Single-factor relationship between peripheral displacement and internal friction angle φ

[0162] With a deformation modulus E = 0.6 GPa and cohesion c = 40 kPa, and other parameters fixed, the internal friction angle φ was controlled to vary in 11 levels within the range of 18° to 28°. FLAC3D numerical simulations were performed on each of the above groups under the conditions of lateral pressure coefficients λ = 1.0, 0.8, 0.6, and 0.4. The simulation results are as follows: Figure 10 and Figure 11 .

[0163] The figure shows that the crown settlement displacement and the horizontal convergent displacement have the same fitting relationship with the internal friction angle φ. A linear relationship between u0 and φ can be established.

[0164]

[0165] In the formula: , The fitting coefficients are denoted as .

[0166] 3.3 Single-factor relationship between peripheral displacement and cohesion c

[0167] With a deformation modulus E = 0.6 GPa and an internal friction angle φ fixed at 23°, and other parameters constant, the cohesion c was controlled to vary at nine levels within the range of 20–60 kPa. FLAC3D numerical simulations were performed on each of the above groups under the conditions of lateral pressure coefficients λ = 1.0, 0.8, 0.6, and 0.4. The simulation results are as follows: Figure 12 and Figure 13 As shown.

[0168] The figure shows that the crown settlement displacement and the horizontal convergent displacement have the same fitting relationship with the cohesion c. A quadratic function relationship can be established between u0 and c:

[0169]

[0170] In the formula: , , The fitting coefficients are denoted as .

[0171] 3.4 Establishment of a Multivariate Nonlinear Regression Model

[0172] To establish the relationship between the displacement around the tunnel and key mechanical parameters (deformation modulus E, internal friction angle φ, and cohesion c), a nonlinear regression model of the following form is established:

[0173]

[0174] In the formula: The displacement around the tunnel is expressed in mm; E is the deformation modulus in GPa; φ is the internal friction angle in °; and c is the cohesion in kPa. , , , , , These are the fit coefficients of the regression model.

[0175] Using a uniform design method, 29 representative sample points were generated within the range of parameters E (0.2~1.0 GPa), φ (18°~28°), and c (20~60 kPa). The crown settlement corresponding to each set of parameters was calculated using FLAC3D numerical simulation. and horizontal convergence The specific calculation results are listed in Table 14.

[0176] Table 14 Numerical Model Calculation Results

[0177]

[0178] Based on the numerical simulation results in Table 14, the settlement of the arch crown was obtained through nonlinear regression analysis. and horizontal convergence A quantitative relationship model between rock mass parameters (deformation modulus E, internal friction angle φ, cohesion c) and the parameters is established. The fitting results are as follows:

[0179] For the settlement of the arch The obtained coefficient is = 18.286、 = -0.849、 = 0.003、 = -0.916、 = -0.468、 = 36.013, correlation coefficient R² = 0.9826. Its expression is:

[0180]

[0181] For horizontal convergence The obtained coefficient is = 11.841、 = -0.881、 = 0.003、 = -0.355、 = -0.359、 = 20.829, correlation coefficient R² = 0.9838. Its expression is:

[0182]

[0183] 3.5 Regression Model Testing

[0184] To verify the reliability of the regression model, five independent test samples were generated using a new uniform design table U5(53). FLAC3D numerical calculations and the predicted values ​​from the regression model were performed, and the results were compared. Error analysis is shown in Table 15.

[0185] Table 15 Relative Errors Between Regression Model Predictions and FLAC3D Calculations

[0186]

[0187] The test results show that the arch has settled. The relative error of the predicted values ​​ranges from 0.50% to 4.97%, and the predictions are horizontally convergent. The relative error range of the predicted values ​​is 0.29% to 4.73%, with all errors controlled within 5%. This result demonstrates that the established multivariate nonlinear regression model has high prediction accuracy and reliability, and can effectively replace the complex FLAC3D full model for rapid computation.

[0188] 4. Inverse analysis of mechanical parameters based on differential evolution algorithm

[0189] The differential evolution algorithm parameters set for this inverse analysis are: population size NP = 50, maximum number of iterations = 200, scaling factor F = 0.8, and crossover probability CR = 0.9.

[0190] The range of inverted values ​​for rock mass mechanical parameters at each monitoring section is determined based on engineering geological conditions, as shown in Table 16.

[0191] Table 16 Range of values ​​for inverse analysis mechanical parameters

[0192]

[0193] The inversion was performed using the above method, and the results are shown in Table 17. As can be seen from the table, the relative errors of the crown settlement and horizontal convergence were controlled between 2.18% and 9.71% and 0.96% and 11.28%, respectively. These results comprehensively verify the effectiveness of the displacement inversion analysis method based on the combination of the DE algorithm and the regression model.

[0194] Table 17 Results of inverse analysis of mechanical parameters

[0195]

[0196] In summary, this invention uses orthogonal analysis, FLAC3D numerical simulation, and sensitivity analysis of mechanical parameters to determine the deformation modulus, cohesion, and internal friction angle as the parameters to be inverted. Using the controlled variable method and FLAC3D numerical simulation, the relationships between the peripheral displacement and the deformation modulus, cohesion, and internal friction angle are obtained, and a ternary nonlinear regression model of the peripheral displacement as a function of these parameters is constructed. A nonlinear regression model based on the Mohr-Coulomb criterion is established using FLAC3D numerical simulation and regression analysis. The sum of squared errors between the calculated and measured values ​​of the tunnel cross-section peripheral displacement is taken as the objective function. The process involves: determining the range of values ​​for the parameters to be inverted and randomly generating a parent population; substituting the mechanical parameters into a ternary nonlinear regression model of the surrounding displacement and calculating the objective function value of each individual in the parent population; performing mutation and crossover operations; calculating the objective function value of each individual in the population after the crossover operation; performing evolutionary selection operations; calculating the objective function value of each individual in the generated offspring; if the minimum objective function value of an individual satisfies the termination condition, the calculation ends, and the individual with the minimum objective function value is the mechanical parameter value of the fractured surrounding rock; otherwise, the calculation continues iteratively from the mutation and crossover operation until a parameter value that satisfies the termination condition is found.

[0197] Example 2

[0198] Please see Figure 2 The diagram shows a structural block diagram of the system for determining the mechanical parameters of fractured surrounding rock proposed in the second embodiment of the present invention. This system 200 includes: a data determination module 21, an inversion parameter determination module 22, a model construction module 23, and an optimal parameter determination module 24, wherein:

[0199] The data determination module 21 is used to obtain the initial support and related parameters of the surrounding rock at the target section of the fractured rock tunnel, and select the target mechanical parameters as the influencing factors for displacement sensitivity analysis based on the Mohr-Coulomb criterion.

[0200] The inversion parameter determination module 22 is used to determine the value range of each of the target mechanical parameters and classify the level, so as to determine the orthogonal design scheme based on the value range and level of each parameter, and to establish a first numerical calculation model of the fractured surrounding rock tunnel according to the relevant parameters and the orthogonal design scheme. After calculating the first peripheral displacement, displacement sensitivity analysis is carried out on each of the target mechanical parameters to determine the parameters to be inverted.

[0201] The model building module 23 is used to construct a first nonlinear regression model with undetermined coefficients and the surrounding displacement varying with the parameters to be inverted based on the parameters to be inverted and the first numerical calculation model through a preset scheme, and to establish a second numerical calculation model in combination with specific engineering site detection information. The parameters to be inverted are uniformly designed to obtain a parameter combination scheme, and the parameter combination scheme is substituted into the second numerical calculation model to obtain the second surrounding displacement. Based on the parameter combination scheme, the second surrounding displacement and the multivariate nonlinear regression model, the complete second nonlinear regression model is determined through a preset method.

[0202] The optimal parameter determination module 24 is used to optimize and search for the parameters to be inverted in the fractured surrounding rock based on the differential evolution algorithm, taking the second nonlinear regression model, the measured displacement data of the surrounding rock at the tunnel site and the range of values ​​of the parameters to be inverted in each monitoring section as input, and output the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions.

[0203] Example 3

[0204] In another aspect, the present invention also proposes an electronic device, please refer to [link to relevant documentation]. Figure 3 The diagram shows an electronic device according to the third embodiment of the present invention, including a memory 20, a processor 10, and a computer program 30 stored in the memory and executable on the processor. When the processor 10 executes the computer program 30, it implements the method for determining the mechanical parameters of the surrounding rock of the fractured structure as described above.

[0205] In some embodiments, the processor 10 may be a central processing unit (CPU), controller, microcontroller, microprocessor or other data processing chip, used to run program code stored in memory 20 or process data, such as executing access restriction programs.

[0206] The memory 20 includes at least one type of readable storage medium, such as flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 20 can be an internal storage unit of an electronic device, such as the hard disk of the electronic device. In other embodiments, the memory 20 can also be an external storage device of the electronic device, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. Furthermore, the memory 20 can include both internal and external storage units of the electronic device. The memory 20 can be used not only to store application software and various types of data of the electronic device, but also to temporarily store data that has been output or will be output.

[0207] It should be pointed out that, Figure 3 The structure shown does not constitute a limitation on the electronic device. In other embodiments, the electronic device may include fewer or more components than shown, or combine certain components, or have different component arrangements.

[0208] This invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for determining the mechanical parameters of the surrounding rock in a fractured structure as described above.

[0209] Those skilled in the art will understand that the logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can mean any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0210] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0211] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0212] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0213] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A method for determining the mechanical parameters of surrounding rock in a fractured structure, characterized in that, The method includes: The initial support and related parameters of the surrounding rock at the target section of the fractured surrounding rock tunnel were obtained, and the target mechanical parameters were selected as influencing factors for displacement sensitivity analysis based on the Mohr-Coulomb criterion. The range of values ​​for each of the target mechanical parameters is determined and the level is divided. An orthogonal design scheme is determined based on the range of values ​​and level of each parameter. A first numerical calculation model of a fractured surrounding rock tunnel is established according to the relevant parameters and the orthogonal design scheme. After calculating the first peripheral displacement, displacement sensitivity analysis is carried out on each of the target mechanical parameters to determine the parameters to be inverted. Based on the parameters to be inverted and the first numerical calculation model, a first nonlinear regression model with undetermined coefficients and the surrounding displacement varying with the parameters to be inverted is constructed through a preset scheme. A second numerical calculation model is established by combining specific engineering site detection information. The parameters to be inverted are uniformly designed to obtain a parameter combination scheme. The parameter combination scheme is substituted into the second numerical calculation model to obtain the second surrounding displacement. Based on the parameter combination scheme, the second surrounding displacement, and the first nonlinear regression model, a complete second nonlinear regression model is determined through a preset method. Using the second nonlinear regression model, the measured displacement data of the surrounding area of ​​the tunnel, and the range of values ​​of the parameters to be inverted at each monitoring section as input, the parameters to be inverted in the fractured surrounding rock are optimized and searched based on the differential evolution algorithm, and the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions are output. The steps of constructing a first nonlinear regression model with undetermined coefficients and the surrounding displacement varying with the parameters to be inverted, based on the parameters to be inverted and the first numerical calculation model, through a preset scheme, include: The controlled variable method is used to calculate the displacement around the tunnel under the corresponding working condition through the first numerical calculation model in sequence, and the single-factor calculation of all parameters to be inverted is completed in sequence to obtain the displacement data around the tunnel corresponding to a single change of each parameter to be inverted. Function fitting was performed on the surrounding displacement data corresponding to each parameter to be inverted to obtain the single-factor relationship between the surrounding displacement and each parameter to be inverted; By integrating all single-factor relationships, a first nonlinear regression model with undetermined coefficients is constructed, which describes the displacement around the tunnel as a function of deformation modulus, internal friction angle, and cohesion. The formula for the first nonlinear regression model is: in, For the surrounding displacement, For deformation modulus, It is the internal friction angle. For cohesion, , , , , and These are the fitting coefficients; The second peripheral displacement includes the arch settlement displacement and the clearance convergence displacement. The steps for determining the complete second nonlinear regression model using a preset method based on the parameter combination scheme, the second peripheral displacement, and the first nonlinear regression model include: The parameter combination scheme is matched one-to-one with the second peripheral displacement to construct a combined dataset. The parameter combination scheme is a preset number of representative combinations generated for the parameters to be inverted. Each parameter combination corresponds to a set of arch settlement displacement values ​​and net clearance convergence displacement values. The parameters to be inverted include deformation modulus, internal friction angle, and cohesion. Substitute the combined dataset into the first nonlinear regression model, and use MATLAB software to solve the coefficients of the first nonlinear regression model from the two indicators of arch subsidence displacement and net clearance convergence displacement, respectively, to obtain the second nonlinear regression model. Both the first and second numerical calculation models are FLAC3D numerical calculation models. When establishing the FLAC3D numerical calculation model, the surrounding rock adopts the Mohr-Coulomb elastoplastic constitutive model, and the initial support adopts the linear elastic constitutive model. The surrounding displacements include the arch subsidence displacement and the clearance convergence displacement; the displacement sensitivity analysis adopts a combination of range analysis and variance analysis.

2. The method for determining the mechanical parameters of the surrounding rock in a fractured structure according to claim 1, characterized in that, The steps of optimizing and searching for the parameters to be inverted in the fractured surrounding rock based on the differential evolution algorithm, using the second nonlinear regression model, the measured displacement data of the surrounding rock at the tunnel site, and the range of values ​​of the parameters to be inverted at each monitoring section as input, and outputting the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions, include: Determine the initial parameters of the differential evolution algorithm. The initial parameters include at least the number of optimization variables, the number of populations, the mutation factor, the crossover probability, the maximum number of iterations, and the convergence accuracy, wherein the number of optimization variables is consistent with the number of parameters to be inverted. The objective function is the sum of squared errors between the calculated and measured values ​​of the displacement around the tunnel section. The calculated value of the displacement around the tunnel section is obtained through a complete nonlinear regression model of the displacement around the tunnel section. Based on the geological data of the monitoring section of the fractured rock tunnel in the specific project, the range of values ​​of the parameters to be inverted for each monitoring section and the fixed values ​​of the parameters not involved in the inversion are determined. Within the range of values ​​for the parameters to be inverted, a set of parent populations is randomly generated to substitute the mechanical parameters of each body in the parent population into the complete nonlinear regression model of the surrounding displacement and calculate the objective function value of each body. The mutation operation is performed according to the preset mutation formula. Different individuals are randomly selected from the parent population to generate a set of mutated individuals. The crossover operation is performed according to the preset crossover rule to cross the target vector of the parent population with the mutated vector of the set of mutated individuals to generate a new population. The objective function value of each individual in the new population is calculated, and an evolutionary selection operation is performed according to a preset selection formula to select high-quality individuals from the parent population and the new population to form the offspring population, so as to calculate the objective function value of each individual in the offspring population. If the minimum objective function value of an individual in the offspring population satisfies the termination condition, the calculation ends, and the individual corresponding to the minimum objective function value is the mechanical parameter value of the fractured surrounding rock. If the minimum objective function value of an individual in the offspring population does not satisfy the termination condition, the offspring population is used as a new parent population, and the process returns to the step of performing mutation operation according to the preset mutation formula, randomly selecting distinct individuals from the parent population to generate a set of mutated individuals, until the parameter value that satisfies the termination condition is obtained.

3. The method for determining the mechanical parameters of the surrounding rock in a fractured structure according to claim 1, characterized in that, The steps for determining the value range of each target mechanical parameter and classifying the level levels, and then determining the orthogonal design scheme based on the value range and level level of each parameter, include: The target mechanical parameters include deformation modulus, internal friction angle, cohesion and Poisson's ratio. The value range of the target mechanical parameters is divided into 5 levels, and the values ​​of each level of the parameter are in an arithmetic sequence. The orthogonal design scheme is based on An orthogonal array was constructed, resulting in 25 effective parameter combinations.

4. The method for determining the mechanical parameters of the surrounding rock in a fractured structure according to claim 3, characterized in that, The relationship between peripheral displacement and deformation modulus and cohesion was fitted using a quadratic function, while the relationship between peripheral displacement and internal friction angle was fitted using a linear function. By unifying the fitted relationships between the peripheral displacements and the deformation modulus, internal friction angle, and cohesion, the first nonlinear regression model can be obtained.

5. A system for determining the mechanical parameters of surrounding rock in fractured structures, characterized in that, The method for determining the mechanical parameters of fractured surrounding rock according to any one of claims 1 to 4, the system comprising: The data determination module is used to obtain the initial support and related parameters of the surrounding rock at the target section of the fractured rock tunnel, and selects the target mechanical parameters as the influencing factors for displacement sensitivity analysis based on the Mohr-Coulomb criterion. The inversion parameter determination module is used to determine the value range of each of the target mechanical parameters and classify the level, so as to determine the orthogonal design scheme based on the value range and level of each parameter, and to establish a first numerical calculation model of the fractured surrounding rock tunnel according to the relevant parameters and the orthogonal design scheme. After calculating the first peripheral displacement, displacement sensitivity analysis is carried out on each of the target mechanical parameters to determine the parameters to be inverted. The model building module is used to construct a first nonlinear regression model with undetermined coefficients and the surrounding displacement varying with the parameters to be inverted based on the parameters to be inverted and the first numerical calculation model through a preset scheme, and to establish a second numerical calculation model in combination with specific engineering site detection information. The parameters to be inverted are uniformly designed to obtain a parameter combination scheme, and the parameter combination scheme is substituted into the second numerical calculation model to obtain the second surrounding displacement. Based on the parameter combination scheme, the second surrounding displacement and the multivariate nonlinear regression model, the complete second nonlinear regression model is determined through a preset method. The optimal parameter determination module is used to optimize and search for the parameters to be inverted in the fractured surrounding rock based on the differential evolution algorithm, taking the second nonlinear regression model, the measured displacement data of the surrounding rock at the tunnel site, and the range of values ​​of the parameters to be inverted at each monitoring section as input, and output the optimal mechanical parameter values ​​of the fractured surrounding rock that meet the termination conditions.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method for determining the mechanical parameters of the surrounding rock of the fractured structure as described in any one of claims 1 to 4.

7. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for determining the mechanical parameters of the surrounding rock of the fractured structure as described in any one of claims 1-4.

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