Method, system, equipment and medium for analyzing reliability of tunnel vault structure

Abstract

The invention discloses a tunnel vault structure reliability analysis method, system, equipment and medium, and relates to the technical field of geotechnical engineering.The tunnel vault structure reliability analysis method comprises the steps that a rock-soil body parameter mean value is obtained, random field discretization is conducted on the rock-soil body parameter mean value, and a discrete rock-soil body parameter random field is generated; the discretized random field unit data and finite element units are mapped one by one, numerical calculation is conducted through finite element software, and a random finite element model is constructed; after the working conditions are simulated and calculated, a calculation result of each working condition is exported, and fitting is carried out by adopting logarithmic normal distribution to represent tunnel vault settlement value probability distribution characteristics; based on the deformation condition of the tunnel vault, various factors influencing the structure function are represented by adopting random variables, the performance function of the structure is constructed, and based on the performance function of the structure, the structure reliability of the tunnel vault under different working conditions is evaluated by adopting the reliability and the failure probability. According to the invention, simulation of spatial variability of rock-soil body parameters is completed, a theoretical system in the field of tunnel engineering can be enriched, and important reference can be provided for practical engineering application, so that further development and optimization of a tunnel engineering technology are promoted.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method, system, equipment and medium for reliability analysis of tunnel arch structures. Background Technology

[0002] During the formation of strata, soil and rock masses are influenced by various factors, such as stress history, environmental conditions, and tectonic movements. These factors can lead to randomness and spatial autocorrelation in soil and rock masses, that is, spatial variability. This characteristic directly affects the surrounding rock after tunnel excavation, including its mechanical properties and deformation.

[0003] In practical engineering projects, some tunnels have complex geological conditions where the values ​​of surrounding rock parameters vary at different locations—this is known as spatial variability of parameters. This characteristic can significantly impact tunnel excavation. Ignoring this spatial variability can sometimes lead to inappropriate designs. Therefore, in-depth research is needed on the deformation patterns of tunnel excavation under such random fields of surrounding rock parameter variability, as well as for reliability analysis. This is a crucial scientific issue, and applying spatial variability theory to practical engineering is of great significance for ensuring the safety of tunnel construction and enhancing the practical value of the project.

[0004] In geotechnical engineering, treating soil and rock masses as homogeneous materials for design and analysis is clearly unrealistic, posing significant challenges to the assessment and precise control of surrounding rock stability after tunnel excavation. Current technologies often employ deterministic calculation methods in tunnel design and reliability analysis, easily overlooking the inherent spatial variability of soil and rock parameters, resulting in typically poor accuracy in reliability analysis results. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a method, system, equipment, and medium for reliability analysis of tunnel arch structures, thereby solving the problems in the prior art.

[0006] The present invention specifically provides the following technical solution: A reliability analysis method for tunnel arch structures includes: The mean values ​​of soil and rock mass parameters are obtained, and the mean values ​​of soil and rock mass parameters are discretized into a random field to generate a discrete random field of soil and rock mass parameters. The soil and rock mass is discretized into several finite element elements, and the discrete random field values ​​of soil and rock mass parameters are mapped one by one into the finite element elements to obtain the random finite element model of soil and rock mass parameters. By changing the vertical correlation distance, horizontal correlation distance, and coefficient of variation of cohesion and internal friction angle in the soil and rock parameters, different working conditions are generated. Each working condition is simulated using a stochastic finite element model of soil and rock parameters to obtain the calculation results for each working condition. The calculation results include the settlement deformation value of the tunnel arch and the settlement deformation value of the ground surface. Based on the calculation results, various factors that affect the structural function are characterized by random variables, a structural function function is constructed, and the structural reliability of the tunnel arch under different working conditions is analyzed and evaluated based on the structural function function.

[0007] Preferably, the step of obtaining the mean values ​​of soil and rock mass parameters and discretizing the mean values ​​of soil and rock mass parameters into a random field to generate a discrete random field of soil and rock mass parameters specifically involves: By combining the known numerical characteristics of random fields, the mean values ​​of soil and rock mass parameters are obtained, and random sampling is performed on the standard normal distribution of the mean values ​​of soil and rock mass parameters to obtain a random sample matrix that follows a standard normal distribution. Z The parameters of the soil and rock mass include cohesion and internal friction angle. The lower triangular matrix is ​​obtained by performing Cholliski decomposition on the correlation coefficient matrix. L and through the lower triangular matrix L Obtaining a standard normal random field H The specific expression is: ; Standard normal random field H The data is transformed into a log-normal random field, and the autocorrelation of soil and rock parameters in spatial location is described by an exponential autocorrelation function to generate a random field of soil and rock parameters.

[0008] Preferably, the step of discretizing the soil and rock mass into several finite element elements and mapping the discrete random field values ​​of the soil and rock mass parameters one by one into the finite element elements to obtain a random finite element model of the soil and rock mass parameters is as follows: Based on the study area, the mechanical parameters of the soil and rock lining are determined, the initial state is calculated and analyzed, the node number and node coordinate data of each unit in the model are extracted, the coordinates of the unit center point are calculated, and a document containing the coordinates of the center point of the grid unit is generated. Read the document containing the coordinates of the center points of the grid cells, substitute the coordinate data into the exponential autocorrelation function, calculate the autocorrelation coefficient matrix of the random field through the autocorrelation function, and decompose the autocorrelation coefficient matrix to obtain the lower triangular matrix; Generate a standard normal random sample matrix and multiply it with a lower triangular matrix to obtain a standard normal random field. Then, convert the standard normal random field into a parametric random field that follows a log-normal distribution. The random field values ​​of the parameters, which follow a log-normal distribution, are mapped one-to-one to the established finite element elements to obtain a first-order random finite element model of the soil and rock parameters. The steps of obtaining the first-order random finite element model of the soil and rock parameters are repeated to obtain the final random finite element model of the soil and rock parameters.

[0009] Preferably, based on the calculation results, the various factors that influence the structural function are characterized by random variables to construct the structural function function, specifically as follows: Obtain n independent random variables, and characterize the various factors that affect the structural function through these random variables to construct a functional function; the specific expression is: ; in, , , Let Z be n independent random variables, and Z be the function.

[0010] Preferably, the structure-based functional analysis evaluates the structural reliability of the tunnel arch under different working conditions, specifically as follows: Reliability P r and failure probability P f The reliability of a structure is evaluated by using the following methods: reliability represents the probability that the structure is reliable, while failure probability represents the probability that the structure will fail. Based on the structural-functional model, probability theory is used to analyze... P r and failure probability P f Solve the problem; the specific expression is: ; ; ; When the function follows a normal distribution or approximately follows a normal distribution, the probability of structural failure is... P r for: ; In standard normal random variables The distribution function is When, the probability of structural failure P r Convert to: ; in, For reliable indicators, the following is adopted: express, Standard deviation This is the expected value.

[0011] Preferably, after obtaining the calculation results for each working condition, the method further includes: Assuming the tunnel arch settlement follows a log-normal distribution, and using the log-normal distribution density function as the fitting formula, the fitted probability density function is obtained; the specific expression is: ; Among them, the settlement of the tunnel arch It follows a log-normal distribution, specifically ln x ~ N ( μ,σ 2 ), x This represents the surface settlement and deformation value. σ 2 For variance; The probability distribution characteristics of tunnel arch settlement are characterized by the fitted probability density function.

[0012] This invention provides a reliability analysis system for tunnel arch structures, comprising: The random field generation module is used to obtain the mean values ​​of soil and rock mass parameters, and to discretize the mean values ​​of soil and rock mass parameters into a random field to generate a discrete random field of soil and rock mass parameters. The model building module is used to discretize the soil and rock mass into several finite element elements, and to map the discrete random field values ​​of soil and rock mass parameters one by one into the finite element elements to obtain the random finite element model of soil and rock mass parameters. The fitting module is used to change the vertical correlation distance, horizontal correlation distance, and coefficient of variation of cohesion and internal friction angle in the soil and rock parameters to generate different working conditions. The module then simulates each working condition using a stochastic finite element model of soil and rock parameters to obtain the calculation results for each working condition. The calculation results include the settlement deformation values ​​of the tunnel arch and the surface settlement deformation values. The evaluation module is used to characterize various factors that affect the structural function using random variables based on the calculation results, construct the structural function function, and analyze and evaluate the structural reliability of the tunnel arch under different working conditions based on the structural function function.

[0013] The present invention provides a computer device, including a memory and a processor. The memory stores a program, and when the program is executed by the processor, the processor performs the steps of the above-described method for reliability analysis of tunnel arch structures.

[0014] The present invention provides a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for reliability analysis of a tunnel arch structure.

[0015] Compared with the prior art, the present invention has the following significant advantages: This invention determines the mean values ​​of soil and rock mass parameters and discretizes them into a random field to obtain a discrete random field of soil and rock mass parameters. Based on this random field, a stochastic finite element model of soil and rock mass parameters is constructed. By changing the relevant parameters of cohesion and internal friction angle in the soil and rock mass parameters, calculation results are generated for different working conditions. This invention employs a research method combining mathematical statistics and finite element numerical simulation to simulate the spatial variability of soil and rock mass parameters. Furthermore, by characterizing various factors that influence the structural function through random variables, a functional function analysis is constructed to assess structural reliability. The impact of spatial variability of parameters on the reliability of the tunnel arch is further analyzed. This not only enriches the theoretical system in the field of tunnel engineering but also provides important references for practical engineering applications, improving the accuracy of reliability analysis in real-world scenarios. Attached Figure Description

[0016] Figure 1 This invention presents the frequency distribution histogram, fitted distribution curve, and related statistical index change curves of the arch settlement values ​​under different vertical correlation distances of cohesion. Figure 2 This invention presents the frequency distribution histogram, fitted distribution curve, and related statistical index change curves of the arch settlement values ​​under different cohesion levels and related distances. Figure 3 The table shows the frequency distribution histogram, fitted distribution curve, and related statistical index change curves of the arch settlement values ​​under different cohesion variation coefficients in this invention. Figure 4 This invention presents the frequency distribution histogram, fitted distribution curve, and related statistical index change curves of the arch settlement values ​​under different vertical correlation distances with different internal friction angles. Figure 5 The present invention includes a frequency distribution histogram, a fitted distribution curve, and a curve showing the change of related statistical indicators for the crown settlement values ​​under different horizontal correlation distances with different internal friction angles. Figure 6 The table shows the frequency distribution histogram, fitted distribution curve, and related statistical index change curves of the arch settlement values ​​under different coefficients of variation of internal friction angles in this invention. Figure 7 The curves showing the changes in reliability index and failure probability with various parameters of cohesion in this invention are shown. Figure 8 The curves showing the changes in reliability index and failure probability with various parameters of the internal friction angle in this invention are shown. Figure 9 This is a flowchart of the calculation process for the stochastic finite element model in this invention; Figure 10 The overall flowchart of a reliability analysis method for tunnel arch structures provided by the present invention is shown. Detailed Implementation

[0017] 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, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0018] like Figure 9 and Figure 10 As shown, this embodiment provides a reliability analysis method for tunnel arch structures, including the following steps: Step S1: Based on the method of establishing and discretizing random fields, combined with the known digital characteristics of random fields, the mean values ​​of soil and rock parameters are obtained, and the mean values ​​of soil and rock parameters are discretized into a random field to generate a discrete random field of soil and rock parameters.

[0019] Things in nature can be broadly categorized into deterministic and random phenomena based on their characteristics. Deterministic phenomena follow definite patterns of change, while random phenomena often exhibit a degree of uncertainty. To better predict and study the patterns of change in random phenomena, the discipline of probability and statistical analysis was born. In probability and statistical analysis, time is relied upon... t A changing random variable is called a stochastic process. If a random variable does not depend on time but changes with its location in space, it is called a random field.

[0020] In geotechnical engineering, due to the influence of complex geological factors such as sedimentary history, stress conditions, and weathering, the parameters of soil and rock masses at different locations in underground space often exhibit differences. This difference is mainly reflected in two aspects: local randomness and overall correlation, collectively referred to as spatial variability of parameters. Random field theory is one of the important theoretical frameworks for studying spatial variability and is often used to describe the spatial variability of parameters. This theory posits that the mechanical characteristics of soil and rock manifest as a random field in space, meaning that the values ​​observed at different locations in space exhibit a certain degree of randomness. This random process is a random function defined in the target space, and its parameter values ​​at different spatial locations exhibit a certain degree of autocorrelation. Random field theory provides a method for characterizing and analyzing the spatial variability of soil and rock masses, effectively characterizing the randomness and autocorrelation of soil and rock masses in space. Applying random field theory allows for a better understanding and explanation of the spatial regularities of natural phenomena, providing important support for design, construction, and decision-making in geotechnical engineering.

[0021] In a random field composed of multidimensional random variables The following numerical characteristics are used for description: (1) Expected (average): That is, the magnitude of the mean of a random variable, if the probability density function of the random variable is... So its expectation Defined as follows (1): (1); (2) Variance, standard deviation, and coefficient of variation: These three numerical features are all used to characterize the dispersion of a random variable around its mean, among which variance... The calculation is as shown in equation (2): (2); Standard deviation is obtained by taking the square root of variance, and coefficient of variation It is defined as the ratio of the standard deviation to the mean, and is a dimensionless value, as shown in equation (3): (3); (3) Covariance and correlation coefficient: covariance Used to describe two random variables The overall error is as shown in equation (4): (4); Correlation coefficient The correlation between two random variables can be described as shown in equation (5): (5); When using random variables to describe the spatial variability of soil and rock parameters, these parameters cannot be considered completely random variables. This is because soil and rock parameters not only exhibit variability in space but also possess a certain degree of correlation. This correlation gradually weakens with increasing spatial distance and is typically quantified using an autocorrelation function. After determining the autocorrelation function, the autocorrelation coefficient matrix affected by spatial distance can be further calculated, i.e., the standardized covariance matrix. This is an important numerical characteristic characterizing the random field of soil and rock parameters. These numerical characteristics form the basis for constructing and generating random fields. If the distribution of random variables in the random field is known, its numerical characteristics can be calculated based on the above methods. For soil and rock masses, their parameters are usually assumed to be a stationary, normally distributed random field, meaning that the soil and rock parameters follow a normal or log-normal distribution.

[0022] The implementation process of a random field for soil and rock mass parameters mainly includes the following two steps: First, based on the methods for establishing and discretizing random fields, and combined with the known digital characteristics of random fields, the target random field is constructed and discretized in MATLAB to generate discrete random field data. Then, the discretized random field element data is mapped one by one to finite element elements, and numerical calculations are performed using finite element software, with ABAQUS selected as the finite element analysis tool. Because the covariance matrix decomposition method has the advantages of simple calculation principles and convenient programming implementation, the covariance matrix decomposition method, namely the Choreski decomposition method, is adopted to construct the random field for soil and rock mass parameters.

[0023] The basic idea of ​​establishing a random field using the covariance matrix decomposition method is as follows: First, the Latin hypercube method is applied to randomly sample from the standard normal distribution to obtain a random sample matrix that follows the standard normal distribution. Z .

[0024] The lower triangular matrix is ​​obtained by performing Cholliski decomposition on the correlation coefficient matrix. L From this, the standard normal random field can be calculated. H .

[0025] (6); For a lower triangular matrix L The solution, the finite element model has n There are 12 grids, and the soil and rock parameters for each grid vary randomly. All soil and rock parameters can be obtained from... n random variables The covariance matrix formed by the covariances of each pair of random variables is: (7); The correlation coefficient matrix is ​​as follows: (8); From equations (7) and (8), it can be seen that both the covariance matrix and the correlation coefficient matrix are symmetric positive definite matrices. Therefore, the matrix... L It can be obtained from equation (9): (9); In equation (9): L It is a lower triangular matrix; LT for L The transpose of the matrix, LT It is an upper triangular matrix. Due to the non-negativity of soil and rock parameters, it is often assumed that the parameters follow a log-normal distribution; therefore, the standard normal random field... H It should be transformed into a log-normal random field H D The conversion formula is as shown in equation (10):

[0026] (10); in, Normal random variable The mean; Normal random variable The standard deviation.

[0027] As can be seen from the solution principle of the covariance matrix decomposition method, the key to constructing a random field lies in the determination of the autocorrelation function, which is used to quantify the relative positional relationship and correlation between points in space. The methods for determining the autocorrelation function usually include two methods: determining the autocorrelation function based on samples and selecting the theoretical autocorrelation function. There are five commonly used autocorrelation functions, as shown in Table 1 below. If the autocorrelation function is determined based on sample data, a large amount of measured engineering data is usually required. The autocorrelation function is derived by calculating the autocorrelation between soil and rock parameters at sample points in space and then applied to the simulation of the random field. However, determining the autocorrelation function based on sample data requires a large sample size, and it is often difficult to obtain a sufficient number of sample data in actual engineering. Therefore, when describing a random field, the theoretical autocorrelation function is chosen to approximate the spatial correlation of soil and rock parameters. Since the exponential autocorrelation function is simple in form and widely used, it is used to describe the autocorrelation of soil and rock parameters in spatial location when generating a random field of soil and rock parameters. The exponential autocorrelation function is shown below (11).

[0028] (11); in, , Let each represent a point in a two-dimensional random field. The relative distance in the direction; , These represent the correlation distances of the random field in the horizontal and vertical directions, respectively.

[0029] An exponential autocorrelation function is used to describe the autocorrelation of soil and rock parameters in spatial location, thereby generating a random field of soil and rock parameters.

[0030] Table 1 Commonly Used Autocorrelation Functions for Soil and Rock Mass Parameters Step S2: Discretize the soil and rock mass into several finite element elements, and map the discrete random field values ​​of soil and rock mass parameters one by one into the finite element elements to obtain the random finite element model of soil and rock mass parameters.

[0031] This paper elucidates the fundamental theory of random fields, focusing on the discretization methods for soil and rock parameters and the construction process of random fields. The Choreskiy central point method is used to discretize the random fields, and all related calculations are performed in the MATLAB environment. In the study of parametric random fields, based on the finite element software ABAQUS 2020, a program is written to map the random field data of soil and rock parameters generated by MATLAB to ABAQUS, thereby constructing a finite element calculation model. The establishment and calculation process of the random finite element model of soil and rock parameters is as follows: Figure 9 As shown, the specific implementation process is as follows:

[0032] (1) After determining the mechanical parameters of the soil and rock lining based on the study area, a finite element model was constructed in ABAQUS2020. The Mohr-Coulomb model was used for the soil and rock mass. After assigning parameters and setting boundary conditions, the initial state was calculated and analyzed. After the calculation, the node numbers and node coordinate data of each element in the model were extracted. Subsequently, a program was written using MATLAB to calculate the coordinates of the center point of the element. After running the program, a document containing the coordinates of the center point of the mesh element was generated.

[0033] (2) In MATLAB, read the document containing the coordinates of the center points of the grid cells and substitute the coordinate data into the exponential autocorrelation function. After determining the correlation distance of the random field with given parameters, calculate the autocorrelation coefficient matrix of the random field using the autocorrelation function, and decompose the matrix using the Cholesky decomposition function to obtain the lower triangular matrix. L .

[0034] (3) In the MATLAB environment, use the lhsnorm function to generate a standard normal random sample matrix, and then combine it with... L Multiplying them together yields the standard normal random field, and then the parametric random field following the log-normal distribution is obtained through the conversion formula between the log-normal and normal distributions.

[0035] (4) The discrete random field values ​​of soil and rock parameters are mapped one-to-one into the established finite element unit to obtain a first-order random finite element model of soil and rock parameters.

[0036] (5) Repeat step (4). N Next, get N The result of random field calculation under sub-sampling conditions. Wherein, the number of sample samplings... N The accuracy and precision of the calculation are determined by the computational precision and efficiency of random fields. To ensure the accuracy and precision of the calculation, this invention... N Set it to 1000.

[0037] Step S3: Change the vertical correlation distance, horizontal correlation distance, and coefficient of variation of cohesion and internal friction angle in the soil and rock parameters to generate different working conditions. Simulate each working condition using a stochastic finite element model of soil and rock parameters to obtain the calculation results for each working condition. Fit the calculation results to a log-normal distribution to characterize the probability distribution characteristics of tunnel arch settlement. The calculation results include tunnel arch settlement deformation value and surface settlement deformation value.

[0038] Settlement of the tunnel lining arch is one of the key indicators in tunnel monitoring and measurement; therefore, this invention uses it as an important basis for evaluating tunnel deformation. After simulating the working conditions, the calculation results for each condition are derived and statistically analyzed. Since the distribution of cohesion and internal friction angle parameters is assumed to be log-normal when establishing the random field, and based on the collection and analysis of literature, it is known that when studying its… c and φ When dealing with independent random fields, the log-normal distribution can better describe the probability distribution characteristics of tunnel arch settlement. Therefore, the calculation results are fitted with a log-normal distribution, and statistical analysis is performed in the plotting software Origin. The fitting formula is chosen as the density function of the log-normal distribution, and the tunnel arch settlement is set as... It follows a log-normal distribution, and its density function is obtained; the specific expression is:

[0039] (12); The settlement of the tunnel arch follows a log-normal distribution, specifically: lnX~N ( μ,σ 2 ), μ The mean, σ The variance is used to study the spatial variability of soil and rock parameters. This invention statistically analyzed the tunnel crown settlement values ​​under different working conditions. A log-normal distribution with good compatibility was used to fit the crown settlement deformation values. Tables 2 to 4 show the relevant statistical indicators under different working conditions. Figures 1-6 They were shown respectively c and φThe histograms (a) and (b) of the frequency distribution of tunnel arch deformation characteristic values ​​under different working conditions in a random field, as well as the curves (c) showing the changes in the average value, coefficient of variation, and 95th quantile of each working condition with respect to the relevant distance and the coefficient of variation of the parameters, are shown. The blue dashed line represents the result of the deterministic calculation model (4.1 mm), the black square dotted line represents the deformation curve of the random calculation mean, the black dotted line represents the deformation curve of the 95th quantile settlement deformation value, and the red upper triangle line represents the deformation curve of the coefficient of variation. Because existing literature and calculation results show that in stochastic finite element analysis, the 95th quantile of the macroscopic deformation value is greater than the randomly calculated mean, which is greater than the deterministic calculated value. In practical engineering, considering the spatial variability of the soil and rock parameters in the target area, using the 95th quantile of the deformation value as the deformation control value is more appropriate. Therefore, the figure not only calculates the average value and coefficient of variation of the arch crown settlement value calculated for each working condition, but also calculates its 95th quantile.

[0040] Table 2 Summary of Statistical Results of Arch Crown Settlement under Different Vertical Relevant Distances Table 3 Summary of statistical results of crown settlement values ​​at different horizontal distances Table 4 Summary of Statistical Results of Arch Crown Settlement under Different Coefficients of Variation Tables 2-4 show the influence of different parameter conditions on the settlement and deformation of the tunnel arch, given the variability of each parameter: (1) In order to clearly show the distribution of the crown settlement under various working conditions, the frequency distribution is divided into intervals of the same size, resulting in Figures 1-6 Figure (a) shows the frequency distribution histogram of the arch settlement values. Figures 1-6As shown in Figure (a), for cohesion and internal friction angle, which follow a log-normal distribution, the distribution of tunnel lining arch deformation values ​​under different working conditions is approximately normal. When the vertical and horizontal correlation distances of cohesion and internal friction angle gradually increase from 0.3 to 8.0 m and 0.3Dm to 8.0Dm (1.86m to 49.6m), respectively, the distribution range of tunnel lining arch deformation values ​​gradually increases, but the change is not significant. When the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, the distribution range of tunnel lining arch deformation values ​​changes more significantly, especially the coefficient of variation of internal friction angle has a greater impact on its distribution range. At the same time, the frequency distribution histogram shows that when the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, the distribution of tunnel lining arch deformation values ​​gradually tends to be left-skewed, which is more obvious when the coefficient of variation is 0.4. This indirectly confirms the results of previous research, so the present invention uses a log-normal distribution for fitting when fitting the frequency distribution histogram.

[0041] (2) From Figures 1-6 The fitted curves under different working conditions show that, for cohesion and internal friction angle, which follow a log-normal distribution, the deformation values ​​of the tunnel lining arch can be well fitted to log-normal distribution curves under different working conditions, and the fitting effect is significant. This indicates that, considering the spatial variability of surrounding rock parameters, the tunnel deformation characteristics exhibit a log-normal distribution. Figure (b) shows that the settlement deformation of the tunnel arch under different vertical correlation distances, horizontal correlation distances, and coefficients of variation for cohesion and internal friction angle is basically symmetrically distributed. When the coefficients of variation for cohesion and internal friction angle are large, the fluctuation range of the tunnel arch settlement deformation values ​​changes significantly and shifts generally to the right, resulting in more cases of large deformation. In general, for each parameter, different working conditions correspond to a separate curve, and the differences between the curves are significant. For each parameter, as the vertical correlation distance, horizontal correlation distance, and coefficient of variation of cohesion and internal friction angle gradually increase within their research range, the range of tunnel arch settlement deformation values ​​also gradually increases. In general, the shape of the fitting curve changes from a 'tall and thin' type to a 'short and fat' type. However, compared with the influence of the parameter correlation distance change on the fitting curve, the influence of cohesion and internal friction angle coefficient of variation on the fitting curve is greater.

[0042] (3) From Figures 1-6As shown in Figure (c), the average value and 95th quantile of the calculated deformation values ​​for each working condition are generally greater than the results of the deterministic calculation. Furthermore, the calculation results also show that the 95th quantile of the deformation values ​​for each working condition > the mean of the random calculation > the deterministic calculation value. This verifies both the conclusions of previous research and the accuracy of the calculation model of this invention. It also indirectly indicates that in actual tunnel support design, neglecting the spatial variability of cohesion and internal friction angle will lead to an underestimation of tunnel lining deformation, thus making the design more risky. Individual analysis of each parameter... Figure 1 and Figure 4 (c) and Table 2 show that when the vertical correlation distance between cohesion and internal friction angle gradually increases from 0.3 m to 8.0 m, the mean, 95th quantile, and coefficient of variation of the calculated results show similar changing patterns, but the degree of change is not entirely the same. When the vertical correlation distance between cohesion and internal friction angle gradually increases from 0.3 m to 8.0 m, the average value of the arch settlement shows a gradually decreasing trend, but the change is not significant. It decreases from 4.19 mm to 4.16 mm and from 4.37 mm to 4.32 mm, respectively, with a decrease percentage of 0.72% and 1.14%. Of course, the influence of the vertical correlation distance on its mean is not constant. When the vertical correlation distance is greater than 5.0 m, the change of the average value tends to stabilize, indicating that... c and φ The vertical correlation distance has a limited impact on the mean. Its 95th percentile shows the opposite trend, when... c and φ When the vertical correlation distance gradually increases from 0.3 m to 8 m, its 95th percentile shows different degrees of increase, increasing from 4.28 mm to 4.31 mm and from 4.55 mm to 4.73 mm, respectively, with percentage increases of 0.70% and 3.96%. c and φ The vertical correlation distance has a limited impact on the 95th percentile; when the vertical correlation distance is greater than 5.0 m, the change in the 95th percentile tends to stabilize. To better understand the results of its stochastic calculations, studying the coefficient of variation of its computational conditions is essential in stochastic finite element analysis. When c and φ As the vertical correlation distance gradually increases from 0.3 m to 8.0 m, the coefficient of variation shows a gradual increasing trend, increasing from 0.0169 to 0.0234 and from 0.0269 to 0.0521, respectively, with percentage increases of 38.46% and 93.6%. However, the growth rates are not the same. cWhen the vertical correlation distance increases from 0.3m to 1.0m, the coefficient of variation of the crown settlement increases rapidly, then gradually slows down until it levels off. In comparison, c The vertical correlation distance showed a relatively large increase in the range of 0.3 m to 5.0 m, and only gradually leveled off after the vertical correlation distance exceeded 5.0 m. In summary, although... c and φ The vertical correlation distance has a limited impact on the crown settlement value. However, relative to... c The vertical correlation distance, its φ The vertical correlation distance has a greater impact on the average value, 95th quantile, and coefficient of variation of the crown settlement under certain working conditions, so it should be given more attention in stochastic finite element analysis. φ The calculation of its vertical correlation distance; by Figure 2 (c) Figure 5 As shown in (c) and Table 3, when the horizontal correlation distance between cohesion and internal friction angle gradually increases from 0.3D m to 8.0D m (1.86 m to 49.6 m), the mean, 95th percentile, and coefficient of variation of the calculated results also show similar changing patterns, but the degree of change is not entirely the same. When the horizontal correlation distance between cohesion and internal friction angle gradually increases from 0.3D m to 8.0D m (1.86 m to 49.6 m), the average value of the arch settlement shows a gradually decreasing trend, but the change is not significant. It decreases from 4.19 mm to 4.17 mm and from 4.37 mm to 4.34 mm, respectively, with a decrease percentage of 0.48% and 0.68%. Similarly, the influence of the horizontal correlation distance on its mean is not constant. When the vertical correlation distance is greater than 5.0D m (31.0 m), the change of its average value tends to stabilize, indicating that... c and φ The horizontal correlation distance has a limited impact on the mean. Its 95th percentile shows the opposite trend, when... c and φ As the horizontal correlation distance gradually increases from 0.3D m to 8.0D m (1.86 m to 49.6 m), its 95th percentile shows varying degrees of increase, increasing from 4.29 mm to 4.35 mm and from 4.55 mm to 4.60 mm, respectively, with percentage increases of 1.39% and 1.10%. c and φ The influence of the horizontal correlation distance on the 95th percentile is also limited; when the horizontal correlation distance is greater than 5.0D m (31.0 m), the change in the 95th percentile tends to stabilize; when... c and φAs the horizontal correlation distance gradually increases from 0.3D m to 8.0D m (1.86 m to 49.6 m), its coefficient of variation shows a gradual increasing trend, increasing from 0.015 to 0.0248 and from 0.0269 to 0.0385, respectively, with percentage increases of 65.33% and 43.12%. However, the growth rate is not the same in each stage. c and φ The coefficient of variation of the crown settlement increased rapidly as the horizontal correlation distance increased from 0.3D m to 5.0D m (1.86 m to 31.0 m), then gradually slowed down until it leveled off. In summary, although... c and φ The horizontal correlation distance has a limited impact on the crown settlement value. However, relative to... c The horizontal correlation distance, its φ The horizontal correlation distance has a greater impact on the average value, 95th quantile, and coefficient of variation of the crown settlement under certain working conditions, so it should be given more attention in stochastic finite element analysis. φ The calculation of its horizontally related distance. (By...) Figure 3 (c) Figure 6 (c) and Table 4 show that when the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, the mean, 95th quantile, and coefficient of variation of their calculated results exhibit similar changing patterns, but the degree of change is not entirely the same. When the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, the average value of the arch crown settlement shows a gradually increasing trend, which can be seen as different from the trend of changing the average value of the arch crown settlement when the relevant distance is changed. c and φ As the correlation distance gradually increases, the correlation between the surrounding rock parameters of the tunnel and the surrounding rock becomes stronger in the horizontal or vertical directions. Therefore, the average value of the calculated results will gradually decrease or the change will become insignificant. However, when... c and φ As the coefficient of variation gradually increases, the heterogeneity of the soil parameters gradually increases, so the average value of the calculated results will gradually increase. The data shows a significant change: when the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, the average value of the crown settlement increases from 4.06 mm to 4.26 mm and decreases from 4.14 mm to 4.73 mm, respectively, representing increases of 4.92% and 4.25%, as shown in the figure. c and φ The coefficients of variation of each factor have different degrees of influence on their mean, but all increase with the increase of their respective coefficients of variation, indicating that... c and φThe coefficient of variation has a significant impact on the mean, and in practical engineering, the parameter... c and φ The calculation of the coefficient of variation and its variation should be given more attention. Its 95th percentile also shows the same trend; when the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, its 95th percentile shows different degrees of increase, increasing from 4.10 mm to 4.47 mm and from 4.26 mm to 5.14 mm, respectively, with percentage increases of 9.02% and 20.66%. When the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, the coefficient of variation of its arch settlement value shows a gradual increasing trend, increasing from 0.0067 to 0.0297 and from 0.018 to 0.0534, respectively, with percentage increases of 343.28% and 196.67%. In summary, although... c and φ The coefficient of variation has a significant impact on the crown settlement value, stronger than the impact of its correlation distance. However, relative to... c The coefficient of variation, its φ The coefficient of variation has a greater impact on the average value, 95th quantile, and coefficient of variation of the crown settlement under the working conditions, so it should be given more attention in stochastic finite element analysis. φ The selection of the coefficient of variation should be carefully considered in actual geological exploration. φ The calculation of the coefficient of variation.

[0043] The probability distribution characteristics of tunnel arch settlement are characterized by a density function.

[0044] Step S4: Based on the deformation of the tunnel arch, i.e. based on the calculation results, various factors that affect the structural function are characterized by random variables, a structural function function is constructed, and based on the structural function function, the structural reliability of the tunnel arch under different working conditions is evaluated by reliability and failure probability analysis.

[0045] Based on the deformation of the tunnel arch, various factors that influence the structural function are characterized using random variables, and a functional function of the structure is constructed as follows: To study structural reliability, random variables are typically used to characterize various factors that influence structural function, and a function function of the structure is constructed based on these variables. This involves obtaining data including... n There are several independent random variables, and a function is constructed using these random variables. The specific expression is as follows:

[0046] (13); in, , , Let Z be n independent random variables, and Z be the function. For equation (13), if Z>0, the structure is reliable; if Z<0, the structure fails; if Z=0, the structure is in a state of limit equilibrium.

[0047] Based on the structural function, the structural reliability of the tunnel arch under different working conditions is evaluated using reliability and failure probability. Specifically: Reliability P r and failure probability P f The reliability of a structure is evaluated by using the following methods: reliability represents the probability that the structure is reliable, while failure probability represents the probability that the structure will fail.

[0048] Based on the structural-functional model, probability theory is used to analyze... P r and failure probability P f Solve the problem; the specific expression is: (14); (15); (16); When the function follows a normal distribution or approximately follows a normal distribution, the probability of structural failure is... P r for: (17); In standard normal random variables The distribution function is When, the probability of structural failure P r Convert to: (18); in, For reliable indicators, the following is adopted: express.

[0049] The reliability index does not need to be obtained through integration. The distribution of the function can be determined by the mean and variance, and the failure probability can be solved by the reliability index through equation (18). The crown settlement values ​​of each working condition follow a log-normal distribution, which is approximately a normal distribution. The function Z calculated from this also follows a log-normal distribution. The reliability index and failure probability obtained from this calculation are conservative, but they will not affect the main laws of the calculation results.

[0050] (19); As can be seen from equations (18) and (19), if one of the failure probability, reliability probability and reliability index of the structure is solved, the other two can be determined.

[0051] Before calculating reliability, the limit state equation of the tunnel structure needs to be established in advance. Lining displacement is the most direct and essential objective reflection of the stability state of the surrounding rock and the tunnel during tunnel construction. The method of evaluating the reliability of tunnel structures based on lining displacement has been widely recognized. According to relevant provisions and combined with the actual engineering situation, the allowable crown settlement value [y] of the tunnel structure can be calculated. Thus, the limit state equation of the tunnel structure can be established as shown in equation (20). According to the "Railway Tunnel Design Code", this invention stipulates that the allowable value of surrounding rock deformation is between 0.1% and 5% of the tunnel radius based on the surrounding rock grade and burial depth. In this example, the allowable crown settlement value [y] is set to 5 mm.

[0052] (20); In the formula: y represents the calculated value of the maximum arch settlement of the tunnel.

[0053] A function was constructed based on the deformation of the tunnel arch. To analyze the impact of the spatial variability of the surrounding rock on tunnel reliability, based on different design parameters and their spatial variability conditions, the tunnel reliability under each condition was calculated. The influence of different parameters on tunnel reliability under changes in vertical correlation distance, horizontal correlation distance, and coefficient of variation was studied to evaluate the sensitivity of tunnel reliability to each parameter. Table 5 shows the tunnel reliability index and failure probability under different conditions.

[0054] Table 5 Reliability indices and failure probabilities under different operating conditions The reliability index and failure probability of the tunnel lining arch exhibit a significant pattern with the variation of the correlation distances of various parameters: as the correlation distance increases, the tunnel reliability index gradually decreases, while the corresponding failure probability gradually increases. However, the degree to which the reliability index and failure probability are affected by the correlation distances of cohesion and internal friction angle varies, and the vertical and horizontal correlation distances for the same parameter also show different degrees of variation. Figure 7 (a) and Figure 8 (a) It can be known that when c and φAs the vertical correlation distance gradually increased from 0.3 m to 8 m, the tunnel reliability index decreased from 11.56 to 7.7 and from 5.39 to 3.0, respectively, representing reductions of 33.40% and 44.34%. The failure probability also increased accordingly with each increase. The vertical correlation distance of cohesion had a small impact on the failure probability, while the vertical correlation distance of the internal friction angle had a stronger impact, increasing to approximately 0.14%. c and φ When the horizontal correlation distance increased from 1.86 m (0.3D) to 49.6 m (8.0D), the reliability index of the tunnel arch decreased from 12.89 to 7.97 and from 5.39 to 3.96, respectively, representing decreases of 38.17% and 26.53%. Similarly, the failure probability also increased to varying degrees with the increase in horizontal correlation distance. The horizontal correlation distance of cohesion had a very small impact on the failure probability; in contrast, the horizontal correlation distance of the internal friction angle had a stronger impact, increasing to approximately 3.74E-03%. This indicates that the spatial correlation of each parameter, i.e., the correlation distance, has a certain influence on the reliability of the tunnel arch; as the correlation distance increases, the reliability index shows a certain degree of decrease.

[0055] From the perspective of the variability of the parameters themselves, combined with Table 3, Figure 7 (c) and Figure 8 (c) It can be seen that the tunnel reliability index gradually decreases as the coefficients of variation of cohesion and internal friction angle gradually increase from 0.1 to 0.4, and the rate of decrease also gradually slows down. The change in reliability index is particularly significant in the stage where the coefficients of variation are between 0.1 and 0.3. Therefore, in practical engineering, more attention should be paid to the calculation of the coefficients of variation of cohesion and internal friction angle in the target area. Based on the specific data, it can be seen that as the coefficients of variation of each parameter increase, the tunnel reliability index shows a gradually decreasing trend, while the corresponding failure probability also shows a gradually increasing trend. The degree to which the reliability index and failure probability are affected by the coefficients of variation of cohesion and internal friction angle also shows different degrees of change. Figure 7 (c) and Figure 8(c) It is evident that neglecting the coefficient of variation of the internal friction angle would further underestimate the reliability index of the tunnel arch. When the coefficients of variation of cohesion and the internal friction angle increase from 0.1 to 0.4, the tunnel reliability index decreases from 34.82 to 5.39 and from 11.39 to 1.07, respectively, representing reductions of 84.45% and 90.6%. The failure probability also increases to varying degrees accordingly. In particular, when the coefficient of variation of the internal friction angle is 0.4, the reliability index and failure probability are 1.07% and 14.3%, respectively, which is far from meeting the safety requirements of actual engineering projects. Therefore, in actual engineering projects, if the coefficient of variation of the calculated internal friction angle in the target area is close to or greater than 0.4, it is crucial to strengthen the support of the construction area to ensure the safety of construction personnel. This indicates that the variability and coefficient of variation of various parameters of the soil and rock mass have a significant impact on tunnel reliability. With the increase of parameter variability, tunnel reliability decreases significantly, and excessive parameter variability can lead to large deformations, thereby threatening tunnel construction safety.

[0056] A comprehensive comparison of the impact of spatial variability of various parameters on tunnel arch reliability reveals that increased spatial variability of the internal friction angle significantly reduces tunnel reliability, while spatial variability of cohesion has a relatively smaller impact. This indicates that the sensitivity of tunnel reliability to various parameters is ranked as follows: internal friction angle > cohesion.

[0057] This invention proposes a reliability analysis system for tunnel arch structures, comprising: a random field generation module, a model building module, a fitting module, and an evaluation module.

[0058] The system comprises several modules: a random field generation module to obtain the mean values ​​of soil and rock parameters, and a random field discretization module to generate discrete random fields of soil and rock parameters; a model building module to discretize the soil and rock mass into several finite element elements, mapping the discrete random field values ​​of soil and rock parameters to each finite element element to obtain a random finite element model of soil and rock parameters; a fitting module to generate different working conditions by changing the vertical correlation distance, horizontal correlation distance, and coefficient of variation of cohesion and internal friction angle in the soil and rock parameters, and to simulate each working condition using the random finite element model of soil and rock parameters to obtain the calculation results for each working condition, including the settlement and deformation values ​​of the tunnel arch and the ground surface; and an evaluation module to characterize various factors that affect the structural function using random variables based on the calculation results, construct the structural function function, and analyze and evaluate the structural reliability of the tunnel arch under different working conditions based on the structural function function.

[0059] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a program, and when the program is executed by the processor, the processor performs the steps of a reliability analysis method for a tunnel arch structure.

[0060] According to the disclosed embodiments, the computer device can communicate with one or more external devices (e.g., keyboard, pointing device, Bluetooth communication, etc.) or with any device that enables the computing device to communicate with one or more other computing devices (e.g., router, demodulator, etc.).

[0061] The present invention also provides a storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the steps of a reliability analysis method for a tunnel arch structure.

[0062] According to the disclosed embodiments, the storage medium can be a non-volatile computer-readable storage medium, such as, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this invention, the storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0063] The above description, in conjunction with specific preferred embodiments, provides a more detailed explanation of the present invention. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention.

Claims

1. A reliability analysis method for tunnel arch structures, characterized in that, include: The mean values ​​of soil and rock mass parameters are obtained, and the mean values ​​of soil and rock mass parameters are discretized into a random field to generate a discrete random field of soil and rock mass parameters. The soil and rock mass is discretized into several finite element elements, and the discrete random field values ​​of soil and rock mass parameters are mapped one by one into the finite element elements to obtain the random finite element model of soil and rock mass parameters. By changing the vertical correlation distance, horizontal correlation distance, and coefficient of variation of cohesion and internal friction angle in the soil and rock parameters, different working conditions are generated. Each working condition is simulated using a stochastic finite element model of soil and rock parameters to obtain the calculation results for each working condition. The calculation results include the settlement deformation value of the tunnel arch and the settlement deformation value of the ground surface. Based on the calculation results, various factors that affect the structural function are characterized by random variables, a structural function function is constructed, and the structural reliability of the tunnel arch under different working conditions is analyzed and evaluated based on the structural function function.

2. The reliability analysis method for a tunnel arch structure as described in claim 1, characterized in that, The process of obtaining the mean values ​​of soil and rock mass parameters and then discretizing these mean values ​​using a random field to generate a discrete random field of soil and rock mass parameters involves the following steps: By combining the known numerical characteristics of random fields, the mean values ​​of soil and rock mass parameters are obtained, and random sampling is performed on the standard normal distribution of the mean values ​​of soil and rock mass parameters to obtain a random sample matrix that follows a standard normal distribution. Z The parameters of the soil and rock mass include cohesion and internal friction angle. The lower triangular matrix is ​​obtained by performing Cholliski decomposition on the correlation coefficient matrix. L and through the lower triangular matrix L Obtaining a standard normal random field H The specific expression is: ； Standard normal random field H The data is transformed into a log-normal random field, and the autocorrelation of soil and rock parameters in spatial location is described by an exponential autocorrelation function to generate a random field of soil and rock parameters.

3. The reliability analysis method for a tunnel arch structure as described in claim 1, characterized in that, The process involves discretizing the soil and rock mass into several finite element elements, and mapping the discrete random field values ​​of the soil and rock mass parameters one by one into the finite element elements to obtain a random finite element model of the soil and rock mass parameters. Specifically: Based on the study area, the mechanical parameters of the soil and rock lining are determined, the initial state is calculated and analyzed, the node number and node coordinate data of each unit in the model are extracted, the coordinates of the unit center point are calculated, and a document containing the coordinates of the center point of the grid unit is generated. Read the document containing the coordinates of the center points of the grid cells, substitute the coordinate data into the exponential autocorrelation function, calculate the autocorrelation coefficient matrix of the random field through the autocorrelation function, and decompose the autocorrelation coefficient matrix to obtain the lower triangular matrix; Generate a standard normal random sample matrix and multiply it with a lower triangular matrix to obtain a standard normal random field. Then, convert the standard normal random field into a parametric random field that follows a log-normal distribution. The random field values ​​of the parameters, which follow a log-normal distribution, are mapped one-to-one to the established finite element elements to obtain a first-order random finite element model of the soil and rock parameters. The steps of obtaining the first-order random finite element model of the soil and rock parameters are repeated to obtain the final random finite element model of the soil and rock parameters.

4. The reliability analysis method for a tunnel arch structure as described in claim 1, characterized in that, Based on the calculation results, various factors that influence the structural function are characterized by random variables, and a functional function of the structure is constructed, specifically as follows: Get including n We define several independent random variables and characterize the various factors that influence the structural function through these random variables, thus constructing a functional function; the specific expression is: ； in, , , for n There are three independent random variables, and Z is a function.

5. The reliability analysis method for a tunnel arch structure as described in claim 4, characterized in that, The structure-based functional analysis evaluates the structural reliability of the tunnel arch under different working conditions, specifically as follows: Reliability P r and failure probability P f The reliability of a structure is evaluated by using the following methods: reliability represents the probability that the structure is reliable, while failure probability represents the probability that the structure will fail. Based on the structural-functional model, probability theory is used to analyze... P r and failure probability P f Solve the problem; the specific expression is: ； ； ； When the function follows a normal distribution or approximately follows a normal distribution, the probability of structural failure is... P r for: ； In standard normal random variables The distribution function is When, the probability of structural failure P r Convert to: ； in, For reliable indicators, the following is adopted: express, Standard deviation This is the expected value.

6. The reliability analysis method for a tunnel arch structure as described in claim 1, characterized in that, After obtaining the calculation results for each working condition, the process also includes: Assuming the tunnel arch settlement follows a log-normal distribution, and using the log-normal distribution density function as the fitting formula, the fitted probability density function is obtained; the specific expression is: ； Among them, the settlement of the tunnel arch It follows a log-normal distribution, specifically ln x ~ N ( μ,σ 2 ), x This represents the surface settlement and deformation value. σ 2 For variance; The probability distribution characteristics of tunnel arch settlement are characterized by the fitted probability density function.

7. A reliability analysis system for tunnel arch structures, characterized in that, include: The random field generation module is used to obtain the mean values ​​of soil and rock mass parameters, and to discretize the mean values ​​of soil and rock mass parameters into a random field to generate a discrete random field of soil and rock mass parameters. The model building module is used to discretize the soil and rock mass into several finite element elements, and to map the discrete random field values ​​of soil and rock mass parameters one by one into the finite element elements to obtain the random finite element model of soil and rock mass parameters. The fitting module is used to change the vertical correlation distance, horizontal correlation distance, and coefficient of variation of cohesion and internal friction angle in the soil and rock parameters to generate different working conditions. The module then simulates each working condition using a stochastic finite element model of soil and rock parameters to obtain the calculation results for each working condition. The calculation results include the settlement deformation values ​​of the tunnel arch and the surface settlement deformation values. The evaluation module is used to characterize various factors that affect the structural function using random variables based on the calculation results, construct the structural function function, and analyze and evaluate the structural reliability of the tunnel arch under different working conditions based on the structural function function.

8. A computer device, characterized in that, The system includes a memory and a processor, wherein the memory stores a program that, when executed by the processor, causes the processor to perform the steps of the reliability analysis method for a tunnel arch structure as described in any one of claims 1 to 6.

9. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the reliability analysis method for a tunnel arch structure according to any one of claims 1 to 6.

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