Random field theory-based deformation analysis method for shield to pass through existing shield tunnel

Abstract

The invention discloses a random field theory-based deformation analysis method for a shield to pass through an existing shield tunnel, and the method comprises the following steps: 1, building a shield construction three-dimensional refined numerical model, and exporting central point coordinates of all entity units; 2, determining a statistical characteristic value of the spatial variability of the elastic modulus of the stratum; 3, constructing a three-dimensional random field model of the stratum elastic modulus; 4, importing the three-dimensional random field model of the stratum elasticity modulus into the three-dimensional refined numerical model, and carrying out numerical calculation and analysis; 5, vertical displacement, caused by shield construction, of the stratum at the axis position of the existing shield tunnel is extracted; 6, deformation of the existing shield tunnel is calculated; and 7, calculating the mean value and the standard deviation of the maximum vertical deformation of the tunnel. According to the analysis method, spatial variability characteristics of stratum mechanical parameters are considered, the random field theory and the Monte Carlo strategy are adopted to predict existing shield tunnel deformation caused by shield construction, and the analysis result is more accurate.

Description

Technical Field

[0001] The 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] The shield method is one of the most important construction methods for urban rail transit tunnel construction in my country. In recent years, with the increasing utilization of urban underground space, especially in super-large and large cities, there are more and more new shield tunnels passing through existing shield tunnels, which brings great challenges to the operational safety of existing tunnels. The shield tunnel itself is an assembled structure with weak rigidity and easy deformation. During the crossing of the new shield tunnel, the existing shield tunnel may suffer from excessive deformation, water leakage, cracking and other defects, which seriously threaten its service life. Such engineering accidents have occurred in many cities in my country. Therefore, a deformation analysis method for shield tunnels passing through existing shield tunnels is proposed, which can predict the deformation of existing shield tunnels in advance, which is of great significance to ensuring the safety of existing shield tunnels.

[0003] Due to differences in the origin and degree of later 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 more prominent. Due to the differences in the mechanical properties of the strata at different spatial locations, even under the same additional load, the mechanical response of the existing shield tunnel will be different. 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 predicting the 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 an existing shield tunnel based on random field theory. The 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 the existing shield tunnel 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 object, 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:

[0006] Step 1: Establish a three-dimensional refined numerical model of shield construction and derive the center point coordinates of all entity units of the three-dimensional 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 three-dimensional random field model of the formation elastic modulus into the three-dimensional refined numerical model and carry out numerical calculation and analysis;

[0010] Step 5: Extract the vertical displacement of the stratum 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 implementation method, 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 export 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, determining the statistical characteristic value of the spatial variability of the formation elastic modulus includes 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 implementation, 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 y Respectively represent the relative distance between any two grid unit center points in the x, y, and z directions.

[0018] As a preferred implementation, in step 3, 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 and substituted into formula (1) to construct the covariance matrix C:

[0019]

[0020] Where: 1,i Represents a point (x 1 ,y 1 ,z 1 ) 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] In the formula, 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.

[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 realized 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 is carried out for the shield construction process.

[0029] As a preferred implementation, 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 bed 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 implementation method, 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] Firstly, the deformation analysis method of shield tunneling through existing shield tunnel 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 tunnel caused by shield construction. It is more accurate than the deterministic analysis method 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 1 It is a calculation flow chart of the deformation analysis method of 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 considering the spatial variability of formation elastic modulus;

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

[0045] The following embodiments are used to describe the implementation of the present invention in detail, but they do not limit the present invention and are only used as examples. At the same time, the advantages of the present invention will become clearer and easier to understand.

[0046] A deformation analysis method for shield tunneling through an existing shield tunnel based on random field theory of the present invention comprises the following steps:

[0047] Step 1: 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, and export the center point coordinates (x i ,y i ,z i ), used for the generation of random field models. In the embodiment, the diameter of the newly built shield tunnel is 6m, the buried depth is 20m, the diameter of the existing shield tunnel is 6m, the shield tunnel vertically passes under the existing shield tunnel, and the vertical clearance is 5m.

[0048] Step 2: Determine the statistical characteristic values ​​of the spatial variability of the elastic moduli of all formations in the three-dimensional 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 zare the autocorrelation lengths of the model in the three directions of x, y, and z respectively; τ x , τ y and τ y Respectively represent the relative distance between the center points of any two grid cells in the three directions of x, y, and z. There is one type of stratum in the model, with a mean elastic modulus 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. i ,y i ,z i ), according to the unit number in the numerical model, take the coordinates of the two center points and substitute them into formula (1) to construct the covariance matrix C:

[0052]

[0053] Where: 1,i Represents a point (x 1 ,y 1 ,z 1 ) 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. Random field model of formation elastic modulus E j It can be expressed as:

[0058] E j =μ j +LYσ j (4)

[0059] In the formula, 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.

[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 jSimilarly, the random field model of different strata can also be obtained. The above calculation process is implemented by writing a calculation program on the MATLAB computing platform. In order to reflect the influence of the spatial variability of the stratum elastic modulus, the random field model calculation times are taken as 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 three-dimensional refined numerical model in FLAC3D (such as Figure 2 As shown in Figure 2, numerical calculation and analysis were carried out on 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 stratum at the axis position 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 bed 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 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:

[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 formation base coefficient.

[0070] Step 7: Use the Monte Carlo strategy 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 are only specific embodiments 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 within the protection scope of the present invention, and 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 and derive the center point coordinates of all entity units of the three-dimensional refined numerical model; Step 2: Determine the statistical characteristic value of the spatial variability of the formation elastic modulus; Step 3: Use the covariance matrix decomposition method to construct a three-dimensional random field model of the formation elastic modulus; Step 4: Import the three-dimensional random field model of the formation elastic modulus into the three-dimensional refined numerical model and carry out numerical calculation and analysis; Step 5: Extract the vertical displacement of the stratum at the axis of the existing shield tunnel caused by shield construction; Step 6: Calculate the deformation of the existing shield tunnel based on the two-stage method; 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 passing through an existing shield tunnel based on random field theory according to claim 1 is characterized by: 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 export the center point coordinates of all entity units in the three-dimensional refined numerical model as (x i ,y i ,z i ).

3. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to claim 2 is characterized by: In step 2, the statistical characteristic values ​​of the spatial variability of the formation elastic modulus are 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.

4. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to claim 3 is characterized by: 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: 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 Respectively represent the relative distance between any two grid unit center points in the x, y, and z directions.

5. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to claim 4 is characterized by: In step 3, 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 and substituted into formula (1) to construct the covariance matrix C: Where: 1,i Represents the point (x1, y1, z1) and (x i ,y i ,z i ) is the correlation coefficient between them.

6. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to claim 5 is characterized in that: In step 3, the constructed covariance matrix C is subjected to Cholesky decomposition: 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) In the formula, 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 the 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.

7. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to claim 6 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 is carried out for the shield construction process.

8. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to claim 7 is characterized by: 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: q=Sk(5) Where: k is the stratum bed 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.

9. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to claim 8 is characterized by: In step 6, based on the two-stage method, the 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: Where: EI and κGA are the bending stiffness and shear stiffness of the shield tunnel respectively; k is the stratum bed coefficient.

10. The method for analyzing deformation of a shield machine passing through an existing shield tunnel based on random field theory according to any one of claims 1 to 9, characterized in that: 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.

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