Deformation analysis method of shield tunneling through existing shield tunnel based on random field theory

Abstract

The present invention discloses a method for analyzing deformation of a shield tunnel passing through an existing shield tunnel based on random field theory. The method comprises the following steps: Step 1: establishing a three-dimensional refined numerical model of shield construction and deriving the center point coordinates of all entity units; Step 2: determining the statistical characteristic values of the spatial variability of the stratum elastic modulus; Step 3: constructing a three-dimensional random field model of the stratum elastic modulus; Step 4: importing the three-dimensional random field model of the stratum elastic modulus into the three-dimensional refined numerical model and conducting numerical calculation and analysis; Step 5: extracting the vertical displacement of the stratum at the axis position of the existing shield tunnel caused by shield construction; Step 6: calculating the deformation of the existing shield tunnel; Step 7: calculating the mean and standard deviation of the maximum vertical deformation of the tunnel. The analysis method of the present invention takes into account the spatial variability characteristics of the stratum mechanical parameters, adopts random field theory and Monte Carlo strategy to predict the deformation of the existing shield tunnel caused by shield construction, and the analysis result is more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering, and in particular to a deformation analysis method for a shield machine passing through an existing shield tunnel based on random field theory. Background Art

[0002] Shield tunneling is a primary construction method for urban rail transit tunnels in my country. In recent years, with the increasing utilization of urban underground space, especially in megacities and large cities, there has been an increasing number of new shield tunneling projects crossing existing shield tunnels, posing significant challenges to the operational safety of existing tunnels. Shield tunnels are modular structures with weak rigidity and easy deformation. During the passage of new shield tunnels, existing shield tunnels may experience excessive deformation, water leakage, cracking, and other defects, seriously threatening their service life. Therefore, a deformation analysis method for shield tunneling through existing shield tunnels was proposed. This method can predict deformation of existing shield tunnels in advance, which is of great significance for ensuring the safety of existing shield tunnels.

[0003] Due to differences in the origin and degree of subsequent weathering, the physical and mechanical parameters of the strata have the characteristics of non-uniform distribution. A large number of statistical results show that the physical and mechanical parameters of the strata are not completely randomly distributed, and often show a certain degree of correlation, which is called spatial variability. Existing shield tunnels are typical linear structures, and the complexity of the stratum conditions that the tunnel passes through is even more prominent. Due to the differences in the mechanical properties of the strata at different spatial locations, the mechanical response of the existing shield tunnel will be different even under the same additional load. Traditional deformation analysis methods for shield tunnels passing through existing shield tunnels are based on the assumption of homogeneous strata, ignoring the spatial variability of stratum mechanical parameters, resulting in large errors in the prediction of deformation of existing shield tunnels. Therefore, there is an urgent need for a deformation analysis method for shield tunnels passing through existing shield tunnels that takes into account the spatial variability of stratum mechanical parameters. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned background technology and provide a deformation analysis method for shield tunneling through existing shield tunnels based on random field theory. This method takes into account the spatial variability characteristics of stratum mechanical parameters and uses random field theory and Monte Carlo strategy to predict the deformation of existing shield tunnels caused by shield construction. Compared with deterministic analysis methods, it is more accurate and provides a reference basis for shield tunnel construction.

[0005] To achieve the above-mentioned object, the present invention provides a deformation analysis method for a shield tunnel passing through an existing shield tunnel based on random field theory, comprising the following steps:

[0006] Step 1: Establish a 3D refined numerical model of shield construction and derive the center point coordinates of all entity units in the 3D refined numerical model;

[0007] Step 2: Determine the statistical characteristic value of the spatial variability of the formation elastic modulus;

[0008] Step 3: Use the covariance matrix decomposition method to construct a three-dimensional random field model of the formation elastic modulus;

[0009] Step 4: Import the 3D random field model of the formation elastic modulus into the 3D refined numerical model and conduct numerical calculation and analysis;

[0010] Step 5: Extract the vertical displacement of the ground at the axis of the existing shield tunnel caused by shield construction;

[0011] Step 6: Calculate the deformation of the existing shield tunnel based on the two-stage method;

[0012] Step 7: Use the Monte Carlo method to calculate the mean and standard deviation of the maximum vertical deformation of the tunnel.

[0013] As a preferred embodiment, in step 1, FLAC3D software is used to establish a three-dimensional refined numerical model reflecting the shield construction process and stratum stratification information, and a FISH language program is written to derive the center point coordinates of all entity units in the three-dimensional refined numerical model as (x i ,y i ,z i ).

[0014] As a preferred embodiment, in step 2, the statistical characteristic value of the spatial variability of the formation elastic modulus is determined to include the mean value μ of the formation elastic modulus. j , mean square error of formation elastic modulus σ j and the autocorrelation function, where j = 1, 2, …, m, and m is the number of strata in the three-dimensional refined numerical model.

[0015] As a preferred embodiment, in step 2, an exponential autocorrelation function is used to describe the spatial variability of the elastic modulus, and the autocorrelation coefficient ρ between any two points in the spatial position is expressed as follows:

[0016]

[0017] Where: θ x ,θ y and θ z are the autocorrelation lengths of the model in the three directions of x, y, and z respectively; τ x , τ y and τ z They represent the relative distances between the center points of any two grid cells in the x, y, and z directions respectively.

[0018] As a preferred embodiment, in step 3, the center point coordinates (xi ,y i ,z i ), according to the unit number in the three-dimensional refined numerical model, the coordinates of the two center points are taken into formula (1) to construct the covariance matrix C:

[0019]

[0020] Where: ρ 1,i Represents the point (x1, y1, z1) and (x i ,y i ,z i ) is the correlation coefficient between them.

[0021] As a preferred implementation, in step 3, the constructed covariance matrix C is subjected to Cholesky decomposition:

[0022] C=LU (3)

[0023] Where: L is the lower triangular matrix, U is the upper triangular matrix;

[0024] Randomly generate a column vector Y, which consists of n random numbers that obey the standard normal distribution; the formation elastic modulus random field model E j It can be expressed as:

[0025] E j =μ j +LYσ j (4)

[0026] Where μ j is the mean value of the formation elastic modulus, σ j is the mean square error of the formation elastic modulus, L is a lower triangular matrix, and Y is a randomly generated column vector.

[0027] Using the above method, the column vector Y is randomly generated multiple times through the Monte Carlo strategy to obtain the formation elastic modulus random field model E j The above calculation process is implemented by writing a calculation program on the MATLAB computing platform.

[0028] As a preferred implementation method, in step 4, based on the FISH language embedded in FLAC3D, the generated three-dimensional random field model of the stratum elastic modulus is imported one-to-one into the three-dimensional refined numerical model in FLAC3D, and numerical calculation and analysis are carried out for the shield construction process.

[0029] As a preferred embodiment, in step 5, the vertical displacement S of the stratum at the axis position of the existing shield tunnel caused by the shield construction is extracted, and the vertical additional load q of the existing shield tunnel caused by the shield construction can be expressed as:

[0030] q=Sk (5)

[0031] Where: k is the stratum base coefficient, which can be calculated by the following formula:

[0032]

[0033] Where: E, μ are the elastic modulus and Poisson's ratio of the stratum respectively; B is the width of the tunnel; EI is the bending stiffness of the tunnel.

[0034] As a preferred embodiment, in step 6, based on a two-stage method, a stratum-tunnel interaction model is used to calculate the deformation of the existing shield tunnel. In the stratum-tunnel interaction model, the existing shield tunnel is simplified to a Timoshenko beam, and the vertical displacement w of the existing shield tunnel under the action of the additional load q satisfies the equilibrium differential equation:

[0035]

[0036] Where: EI and κGA are the bending stiffness and shear stiffness of the shield tunnel, respectively; k is the stratum bed coefficient.

[0037] As a preferred implementation method, in step 7, the Monte Carlo strategy is used to calculate the vertical deformation of the existing shield tunnel under different random field models, the distribution law of the maximum vertical deformation of the tunnel is statistically analyzed, and the mean and standard deviation of the maximum vertical deformation of the tunnel are calculated.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] First, the deformation analysis method of shield tunneling through existing shield tunnels based on random field theory of the present invention takes into account the spatial variability characteristics of stratum mechanical parameters, and uses random field theory and Monte Carlo strategy to predict the deformation of existing shield tunnels caused by shield construction. Compared with deterministic analysis methods, it is more accurate and provides a reference basis for shield tunnel construction.

[0040] Secondly, the deformation analysis method of shield tunneling through existing shield tunnels based on random field theory of the present invention details the specific calculation process, and the method is also applicable to the situation where the shield tunnel passes through the existing shield tunnel in different forms, thereby improving the prediction accuracy of the deformation of the existing shield tunnel and reducing the accident rate.

[0041] Thirdly, a refined numerical model is established in the deformation analysis method of shield tunneling through an existing shield tunnel based on random field theory of the present invention, and the model can take into account the complex construction process and structural characteristics of the shield tunnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1This is a calculation flow chart of the deformation analysis method for shield tunneling through an existing shield tunnel based on random field theory of the present invention;

[0043] Figure 2 A three-dimensional refined numerical model that takes into account the spatial variability of the formation elastic modulus;

[0044] Figure 3 Schematic diagram of the stratum-tunnel interaction model. DETAILED DESCRIPTION

[0045] The following embodiments of the present invention are described in detail, but they are not intended to limit the present invention and are merely examples. The advantages of the present invention will become clearer and easier to understand through the description.

[0046] The present invention provides a deformation analysis method for a shield machine passing through an existing shield tunnel based on random field theory, comprising the following steps:

[0047] Step 1: Use FLAC3D software to build a three-dimensional refined numerical model that reflects the shield construction process and stratum stratification information, write a FISH language program, and export the center point coordinates (x i ,y i ,z i ), used to generate the random field model. In the embodiment, the diameter of the new shield tunnel is 6m, the burial depth is 20m, the diameter of the existing shield tunnel is 6m, and the shield tunnel vertically passes under the existing shield tunnel with a vertical clearance of 5m.

[0048] Step 2: Determine the statistical characteristic values of the spatial variability of the elastic moduli of all formations in the 3D refined numerical model, including the mean value μ of the elastic modulus of the formation j , mean square error of formation elastic modulus σ j And the autocorrelation function (j = 1, 2, ..., m, m is the number of strata in the three-dimensional refined numerical model). The exponential autocorrelation function is used to describe the spatial variability of the elastic modulus, and the autocorrelation coefficient ρ between any two points in the spatial position is expressed as follows:

[0049]

[0050] Where: θ x ,θ y and θ z are the autocorrelation lengths of the model in the three directions of x, y, and z respectively; τ x , τ y and τ y Represents the relative distance between the center points of any two grid cells in the x, y, and z directions. The stratum in the model is of one type, with an elastic modulus mean of 30 MPa and a standard deviation of 5 MPa.x =θ y =20m and θ z =2m.

[0051] Step 3: Use the covariance matrix decomposition method to construct a three-dimensional random field model of the formation elastic modulus. The center point coordinates (x i ,y i ,z i ), take the coordinates of the two center points according to the unit number in the numerical model and put them into formula (1) to construct the covariance matrix C:

[0052]

[0053] Where: ρ 1,i Represents the point (x1, y1, z1) and (x i ,y i ,z i ) is the correlation coefficient between them.

[0054] Perform Cholesky decomposition on the covariance matrix C:

[0055] C=LU (3)

[0056] Where: L is the lower triangular matrix and U is the upper triangular matrix.

[0057] Randomly generate a column vector Y, which consists of n random numbers that obey the standard normal distribution. Formation elastic modulus random field model E j It can be expressed as:

[0058] E j =μ j +LYσ j (4)

[0059] Where μ j is the mean value of the formation elastic modulus, σ j is the mean square error of the formation elastic modulus, L is a lower triangular matrix, and Y is a randomly generated column vector.

[0060] By using the above method, the column vector Y is randomly generated multiple times through the Monte Carlo strategy to obtain the formation elastic modulus random field model E j Multiple implementations of . Similarly, random field models for different strata can also be obtained. The above calculation process was implemented using a program written on the MATLAB computing platform. To reflect the impact of spatial variability in the stratum elastic modulus, the random field model was calculated 500 times.

[0061] Step 4: Based on the embedded FISH language in FLAC3D, the generated formation elastic modulus random field model is imported one-to-one into the 3D refined numerical model in FLAC3D (e.g. Figure 2 As shown in Figure 2, numerical calculation and analysis were carried out for the shield construction process, and the ground loss rate was taken as 0.1%.

[0062] Step 5: Automatically extract the vertical displacement S of the ground at the axis of the existing shield tunnel caused by shield construction. The vertical additional load q of the existing shield tunnel caused by shield construction can be expressed as:

[0063] q=Sk(5)

[0064] Where: k is the stratum base coefficient, which can be calculated by the following formula:

[0065]

[0066] Where: E, μ are the elastic modulus and Poisson's ratio of the stratum respectively; B is the width of the tunnel; EI is the bending stiffness of the tunnel.

[0067] Step 6: Based on the two-stage method, the deformation of the existing shield tunnel is calculated using the stratum-tunnel interaction model. In the stratum-tunnel interaction model, the existing shield tunnel is simplified to a Timoshenko beam. The vertical displacement w of the existing shield tunnel under the action of the additional load q satisfies the equilibrium differential equation:

[0068]

[0069] Where: EI and κGA are the bending stiffness and shear stiffness of the shield tunnel respectively, and EI = 1.51 × 10 8 kN·m 2 , κGA=2.52×10 6 kN; k is the stratum base coefficient.

[0070] Step 7: Use the Monte Carlo method to calculate the vertical deformation of the existing shield tunnel under different random field models, statistically analyze the distribution law of the maximum vertical deformation of the tunnel, and calculate the mean and standard deviation of the maximum vertical deformation of the tunnel.

[0071] The above is only a specific embodiment of the present invention. It should be pointed out that any changes or substitutions that can be easily thought of by any technician familiar with the field within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. The rest not described in detail belong to the prior art.

Claims

1. A deformation analysis method for shield tunneling through an existing shield tunnel based on random field theory, characterized by: The steps include: Step 1: Establish a three-dimensional refined numerical model of shield construction. Use FLAC3D software to establish a three-dimensional refined numerical model that reflects the shield construction process and stratum stratification information. Write a FISH language program to export the center point coordinates of all entity units in the three-dimensional refined numerical model as (x i ,y i ,z i ); Step 2: Determine the statistical characteristic values of the spatial variability of the formation elastic modulus. The statistical characteristic values include the mean μj of the formation elastic modulus, the mean square error σj of the formation elastic modulus, and the autocorrelation function, where j = 1, 2, …, m, and m is the number of formations in the 3D refined numerical model. The exponential autocorrelation function is used to describe the spatial variability of the elastic modulus, and the autocorrelation coefficient ρ between any two points in space is expressed as follows: Where: θx, θy and θz are the autocorrelation lengths of the model in the x, y and z directions respectively; τ x , τ y and τ z Respectively represent the relative distances between the center points of any two grid cells in the x, y, and z directions; Step 3: Use the covariance matrix decomposition method to construct a three-dimensional random field model of the formation elastic modulus; the center point coordinates (x i ,y i ,z i ), according to the unit number in the three-dimensional refined numerical model, the coordinates of the two center points are taken into formula (1) to construct the covariance matrix C: Where: ρ 1,i Represents the point (x1, y1, z1) and (x i ,y i ,z i ) correlation coefficient between them; Perform Cholesky decomposition on the constructed covariance matrix C: C=LU (3) Where: L is the lower triangular matrix, U is the upper triangular matrix; Randomly generate a column vector Y, which consists of n random numbers that obey the standard normal distribution; the formation elastic modulus random field model E j It can be expressed as: E j =μ j +LYσ j (4) Where μ j is the mean value of the formation elastic modulus, σ j is the mean square error of the formation elastic modulus, L is the lower triangular matrix, and Y is a randomly generated column vector; The column vector Y is randomly generated multiple times by Monte Carlo strategy to obtain the formation elastic modulus random field model E j By multiple realizations of , we can obtain three-dimensional random field models of different strata; Step 4: Import the 3D random field model of the formation elastic modulus into the 3D refined numerical model and conduct numerical calculation and analysis; Step 5: Extract the vertical displacement S of the ground at the axis of the existing shield tunnel caused by shield construction. The vertical additional load q of the existing shield tunnel caused by shield construction can be expressed as: q=Sk (5) Where: k is the stratum base coefficient, which can be calculated by the following formula: Where: E, μ are the elastic modulus and Poisson's ratio of the stratum respectively; B is the width of the tunnel; EI is the bending stiffness of the tunnel; Step 6: Based on the two-stage method, the deformation of the existing shield tunnel is calculated using the stratum-tunnel interaction model. In the stratum-tunnel interaction model, the existing shield tunnel is simplified as a Timoshenko beam. The vertical displacement w of the existing shield tunnel under the action of the additional load q satisfies the equilibrium differential equation: Where: EI and κGA are the bending stiffness and shear stiffness of the shield tunnel respectively; k is the stratum bed coefficient; Step 7: Use the Monte Carlo method to calculate the mean and standard deviation of the maximum vertical deformation of the tunnel.

2. The method for analyzing deformation of a shield machine traveling through an existing shield tunnel based on random field theory according to claim 1 is characterized by: In step 4, based on the FISH language embedded in FLAC3D, the generated three-dimensional random field model of the stratum elastic modulus is imported one-to-one into the three-dimensional refined numerical model in FLAC3D, and numerical calculation and analysis are carried out for the shield construction process.

3. The method for analyzing deformation of a shield machine traveling through an existing shield tunnel based on random field theory according to claim 1 or 2, characterized in that: In step 7, the Monte Carlo method is used to calculate the vertical deformation of the existing shield tunnel under different random field models, the distribution law of the maximum vertical deformation of the tunnel is statistically analyzed, and the mean and standard deviation of the maximum vertical deformation of the tunnel are calculated.

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