A discrete element modeling and numerical simulation method for the deformation process of shield tunnel segments

Abstract

A discrete element modeling and numerical simulation method for the deformation process between adjacent segments of a shield tunnel comprises: 1) inputting length, width and height to establish a three-dimensional rectangular parallelepiped model box; 2) importing the material properties of the optical fiber material and the segment material required in the model, namely, Young's modulus, Poisson's ratio, tensile strength, compressive strength, internal friction coefficient and density, a total of six parameters, into the model; 3) inputting the radius and length of the tunnel to establish two tunnel models of exactly the same size; 4) setting the spacing between the two tunnel models; 5) inputting the length of the optical fiber model to establish four exactly the same optical fiber models; (6) adjusting the positions of the four optical fiber models in the model so that the four segments of the optical fiber model are located at 0°, 135°, 180° and 225° on the cross section of the tunnel; 7) setting the displacement of the tunnel on the other side in the Z direction so that it moves in the Z direction. The discrete element quantitative modeling of the displacement deformation between the segments of the shield tunnel is completed.

Description

Technical Field

[0001] The invention is a discrete element numerical simulation process of the deformation process of the shield tunnel connection (adjacent segments), which can be used for quantitative calculation. Background Art

[0002] Subway is an important part of urban rail transit. In recent years, in order to solve the problem of urban traffic congestion, subways have been built on a large scale. As the main carrier of urban subways, shield tunnels have been widely used in major cities in China. During the construction of shield tunnels, due to the excavation of foundation pits, ground loading and unloading, and changes in geological conditions, the soil around the tunnel will be subject to additional stress. With the increase in service time, the tunnel will be subjected to the long-term effect of additional stress, and will experience deformation and damage to varying degrees. At present, there are two main research methods for the longitudinal settlement deformation of shield tunnels. The first is the theoretical analysis method, and the second is the numerical simulation analysis method. Distributed fiber optic sensing technology has been widely used in the process of tunnel deformation monitoring, but it is mostly qualitative analysis, and quantitative analysis is still an urgent problem to be solved. Summary of the invention

[0003] To solve the above problems, the purpose of the present invention is to propose a three-dimensional tunnel discontinuous segment deformation numerical simulator based on discrete element algorithm, and to perform discrete element modeling and numerical simulation of the longitudinal settlement deformation of the shield tunnel (adjacent segments). According to the physical properties of the optical fiber and the tunnel, the optical fiber model and the tunnel model are established. By setting the displacement of the longitudinal settlement of the tunnel, the strain data of the optical fiber model are obtained, which can be compared with the actual measured value to provide a basis for quantitative analysis.

[0004] The present invention proposes a solution to solve the difficulty of quantitative analysis of tunnel deformation: a discrete element modeling and numerical simulation method for the deformation process between adjacent segments of a shield tunnel, the steps of which include:

[0005] (1) Establish a model box model for adjacent segments of a shield tunnel; establish a model box according to the input dimensions, with a pressure plate on the top of the model box; and do not contain particle units in the model box;

[0006] (2) Given mechanical properties Input the specified macroscopic mechanical properties, including: Young's modulus, Poisson's ratio, tensile strength, compressive strength, internal friction coefficient, density;

[0007] (3) Establish adjacent segment models of shield tunnels; input the specified radius and length to establish two tunnel segment models of exactly the same size; input the specified length to establish four fiber models of exactly the same size consisting of continuous particle units;

[0008] (4) Adjust the position of adjacent segment models of shield tunnels: In the model box, input the specified displacement vector and adjust the relative position of the two tunnel segment models so that their center lines coincide with each other and the spacing is 2 cm; at the same time, adjust the position of the four fiber models so that the fiber fits the tunnel segment model, and on the tunnel cross section, the four fiber models for strain and temperature measurement are located at 0°, 135°, 180°, and 225° respectively; 0° is the top of the tunnel;

[0009] (5) Locking the degrees of freedom: Lock the degrees of freedom of the first tunnel segment model in the X, Y, and Z directions, and at the same time lock the degrees of freedom of the second tunnel segment model in the X and Y directions, so that it can only move in the Z direction, that is, perpendicular to the horizontal position;

[0010] (6) Standard balance: After the tunnel segment model is established, the forces, energy and heat in the tunnel segment model are balanced to make the state of the entire tunnel segment model stable;

[0011] (7) Numerical simulation; set the displacement of the tunnel segment model in the Z direction, the number of cycles and the time step; the displacement applied in each step during the numerical simulation = total displacement / (number of cycles × time step). The more cycles and the larger the time step, the smaller the displacement in each step and the more accurate the simulation process.

[0012] Beneficial effects: To solve the difficulty of quantitative analysis of tunnel deformation, a solution is proposed to model the longitudinal settlement deformation of shield tunnel (adjacent segments) using discrete element method and numerical simulation. According to the physical properties of optical fiber and tunnel, an optical fiber model and a tunnel model are established. By setting the displacement of longitudinal settlement of the tunnel, the strain data of the optical fiber model is obtained, which can be compared with the actual measured value to provide a basis for quantitative analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A flow chart of a discrete element modeling and numerical simulation method for the deformation process between adjacent segments of a shield tunnel; Figure 1A Schematic diagram of shield tunnel model structure;

[0014] Figure 2 Establish a 3D model box flow chart;

[0015] Figure 3 Assign materials and modeling flow chart;

[0016] Figure 4 Balance model flow chart;

[0017] Figure 5 Schematic diagram of the test device;

[0018] Figure 6 Schematic diagram of optical fiber cross-section layout;

[0019] Figure 7 Principle of quantitative calculation of shear test;

[0020] Figure 8 For the quantitative calculation results of the tunnel shear test, the first three level curves are selected for quantitative calculation. DETAILED DESCRIPTION

[0021] Figure 1 The figure is a flow chart of a discrete element modeling and numerical simulation method for the deformation process between adjacent segments of a shield tunnel.

[0022] Step 10 generates a three-dimensional model box of a specific size according to the set length, width and height. The specific size only needs to be larger than the tunnel model in all directions.

[0023] Step 11 Material properties include six parameters, namely: Young's modulus, Poisson's ratio, tensile strength, compressive strength, internal friction coefficient, and density. Store the material properties in a document and then import them into the model.

[0024] Step 12: Establish a 3D model of adjacent tunnel segments by setting the cross-sectional radius and axial length. The radius is 0.05m, the length is 0.45m, and the ratio of the model to the actual model is 1:1.

[0025] Step 13 establishes an optical fiber model consisting of a string of particle units by setting the length.

[0026] Step 14 adjusts the relative positions between two identical adjacent tunnel segment models and four identical optical fiber models in the model box.

[0027] Step 15: lock the degrees of freedom of one section of the tunnel model in the X, Y, and Z directions; at the same time, lock the degrees of freedom of another section of the tunnel model in the X and Y directions so that it can only move in the Z direction.

[0028] Step 16 performs standard equilibrium operations to make the energy, heat and force in the model tend to a steady state.

[0029] Step 17 sets the total displacement during the simulation and performs numerical simulation.

[0030] Figure 2 In step 20, the average radius of the basic particle units in the model is determined according to the set particle radius.

[0031] Step 21 determines the size of the three-dimensional model box according to the set length, width and height.

[0032] Step 22 selects whether the model box contains a particle unit according to a Boolean value, 0 represents not contained, and 1 represents contained.

[0033] Step 23 controls the relative size of the maximum particle size and the minimum particle size of the particles in the model box according to the input dispersion coefficient distriRate. max / R min =(1+rate)^2, where: R max With R min is the maximum and minimum particle size, and rate is the dispersion coefficient. For example, if the dispersion coefficient is set to 0.25, then according to the calculation formula, in the accumulation model, the ratio of the maximum particle size to the minimum particle size is (1+0.25)^2. This coefficient is specially set for the gradation of soil particles (i.e. the distribution of particle size) in geotechnical engineering.

[0034] Step 24: According to the Boolean matrix, select the number of pressure plates. The model box contains at most six pressure plates, namely, left, right, front, back, bottom, and top. The Boolean matrix is ​​controlled by two numbers, 0 and 1. 0 means that the pressure plate does not exist, and 1 means that the pressure plate exists. When modeling, you only need to use equation assignment.

[0035] Step 25 performs initialization operation and establishes a three-dimensional model box according to the initial setting information.

[0036] Step 26: If the model box contains particle units in step 22, a gravity deposition operation is performed. After initialization, the particles in the model box are in a regularly arranged non-densely packed state, and after the gravity deposition operation, the particles are in a densely packed state.

[0037] Step 27 determines the friction coefficient between particles based on the input parameters.

[0038] If the model box is selected to contain particles according to the Boolean matrix (i.e., 0, 1 values) in step 22, then the deposition operation of step 26 needs to be performed; if the model box is selected to be empty in step 22, i.e., there are no particles, then step 26 is not required and step 27 can be performed directly.

[0039] Figure 3 Provide a flow chart for assigning materials and modeling.

[0040] Step 30 stores the material parameters (Young's modulus, Poisson's ratio, tensile strength, compressive strength, internal friction coefficient, density) in a file.

[0041] Step 31 Import the material information in the document into the model.

[0042] Step 32 determines the particle radius of the established model according to the input value.

[0043] Step 33 establishes two identical tunnel models according to the particle radius set in step 32, as well as the cross-sectional radius and axial length of the tunnel.

[0044] Step 34 establishes four identical optical fiber models consisting of a string of particle units according to the particle radius set in step 32 and the input length at the same time.

[0045] Step 35: Adjust the relative positions of the fiber model and the tunnel model so that the central axes of the two tunnel models coincide and are parallel to the X-axis direction, with a spacing of 2 cm. The four sections of optical fiber are all along the X-axis direction, and are located at 0° (assuming the top of the tunnel), 135°, 180°, and 225° on the tunnel cross section, and the fiber model and the tunnel model are exactly in contact (tangent to the particle surface).

[0046] Step 36 bonds the group where the tunnel model is located with the group where the optical fiber model is located, that is, declares that the connection cannot be broken.

[0047] Step 37 locks the degrees of freedom of one section of the tunnel model in the X, Y, and Z directions; at the same time, locks the degrees of freedom of another section of the tunnel model in the X and Y directions so that it can only move in the Z direction.

[0048] Figure 4 Flow chart of numerical simulation

[0049] Step 40 determines the number of cycles according to the input parameters, that is, the total displacement of the numerical simulation process is achieved through how many cycles.

[0050] Step 41 determines the number of steps contained in each cycle according to the input parameters, that is, the displacement represented by each cycle is divided into several steps for execution.

[0051] Step 42 determines the total displacement of the numerical simulation process according to the input parameters.

[0052] Step 43 determines the displacement of each time step according to steps 51 and 52, that is, total displacement / (number of cycles×number of steps included in each cycle).

[0053] Step 44 completes the numerical simulation process by cyclically applying loads.

[0054] Comparison of numerical simulation and indoor test results:

[0055] Indoor test process: Before the indoor test begins, four dial indicators are placed above the two pipes, with a spacing of 10 cm between each dial indicator and a displacement indicator rod placed below each. The displacement indicator rod is a steel rod with a diameter of 4 mm and a length of 40 cm. One end of the steel rod is vertically welded to the center of a steel sheet with a thickness of 5 mm and a diameter of 1.5 cm. One end of the displacement indicator rod is in direct contact with the pipe through gravity, and one end of the welded steel sheet is in direct contact with the dial indicator. The displacement indicator rod is used to monitor the displacement of the pipe in the vertical direction in real time. See the figure for a schematic diagram of the test device.

[0056] The test uses two steel pipes with a diameter of 5cm and a length of 45cm, and sticks a polyurethane optical fiber with a diameter of 2mm to the outer wall of the steel pipe. The preset distance between the two sections of the pipe is 2cm. In the cross-sectional direction, the optical fiber is arranged at 0°, 135°, 180°, and 225°; the optical fibers at 0° and 180° are used for quantitative calculations, and the optical fibers at 135° and 225° are used to correct the results of quantitative calculations. On the side wall of the pipe, the optical fiber is arranged in an "S" shape. The range of the dial indicator used in the test is 2cm, the accuracy is 0.01mm, and it is numbered 1-8 from left to right. See the schematic diagram of the optical fiber cross-sectional layout. Figure 5 .

[0057] During the shear test, the left section of the pipe was placed on two lifting platforms of the same height, and the right section of the pipe was placed on a separate lifting platform. During the entire test, the height of the two lifting platforms carrying the left section of the pipe remained unchanged. We lowered the height of the lifting platform under the right section of the pipe to create a height difference between the two sections of the pipe. A total of 6 displacement levels were applied.

[0058] Each test process lasted about 15 minutes, and the tests were all carried out in a constant temperature laboratory at room temperature of 23.5°, so the effect of temperature on the strain value of the optical fiber was not considered.

[0059] Quantitative calculation principle of shear test:

[0060] The distance L between A and B is a known quantity; when the tunnel undergoes vertical shear deformation, the free section of the optical fiber is stretched by a distance of ΔL, and the distance between A and B is (L+ΔL). We use the peak strain to calculate the value of ΔL, and then we can calculate the vertical shear deformation of the tunnel. The quantitative calculation principle of the shear test is shown in Figure 7 .

[0061] The calculation formula derivation process is as follows:

[0062] ε=ΔL÷L (1)

[0063]

[0064] therefore:

[0065]

[0066] Where: ε is the axial strain of the optical fiber, ΔL is the change in the length of the optical fiber, L is the original length of the optical fiber, and x is the shear deformation of the tunnel.

[0067] Results comparison:

[0068] The actual monitored displacement of the shear test was compared with the optical fiber calculated value, and the details are shown in Table 1. The error between the displacement calculated by the optical fiber and the measured displacement is between 0.9% and 16.8%. This shows that the proposed quantitative calculation method for displacement in the tunnel shear process is effective and greatly improves the calculation accuracy.

[0069] Table 1

[0070]

[0071] Figure 8 The quantitative calculation results of the tunnel shear test are shown in the figure. The first three curves are selected for quantitative calculation. The three broken lines in the figure are the measured value, the calculated value and the simulated value. Taking the displacement actually measured by the dial gauge as the benchmark, the displacement calculation value is obtained using the quantitative calculation method proposed in the article, and finally the numerical simulation results are calculated to obtain the simulated value. It can be found that the measured value is between 2 and 3 mm. The calculated values ​​are all smaller than the measured values, between 0.75 and 1.25 mm. The simulated values ​​are all larger than the measured values, between 3 and 4.5 mm.

Claims

1. A discrete element modeling and numerical simulation method for the deformation process between adjacent segments of a shield tunnel, characterized in that the steps include: (1) Establish a model box model for adjacent segments of a shield tunnel; establish a model box according to the input dimensions, with a pressure plate on the top of the model box; The model box does not contain particle units; (2) Given mechanical properties Input the specified macroscopic mechanical properties, including: Young's modulus, Poisson's ratio, tensile strength, compressive strength, internal friction coefficient, density; (3) Establish adjacent segment models of shield tunnels; input the specified radius and length to establish two tunnel segment models of exactly the same size; input the specified length to establish four fiber models of exactly the same size consisting of continuous particle units; (4) Adjust the position of adjacent segment models of shield tunnels: In the model box, input the specified displacement vector and adjust the relative position of the two tunnel segment models so that their center lines coincide with each other and the spacing is 2 cm; at the same time, adjust the position of the four fiber models so that the fiber fits the tunnel segment model, and on the tunnel cross section, the four fiber models for strain and temperature measurement are located at 0°, 135°, 180°, and 225° respectively; 0° is the top of the tunnel; (5) Locking the degrees of freedom: Lock the degrees of freedom of the first tunnel segment model in the X, Y, and Z directions, and at the same time lock the degrees of freedom of the second tunnel segment model in the X and Y directions, so that it can only move in the Z direction, that is, perpendicular to the horizontal position; (6) Standard balance: After the tunnel segment model is established, the forces, energy and heat in the tunnel segment model are balanced to make the state of the entire tunnel segment model stable; (7) Numerical simulation; set the displacement of the tunnel segment model in the Z direction, the number of cycles and the time step; the displacement applied in each step during the numerical simulation = total displacement / (number of cycles × time step). The more cycles and the larger the time step, the smaller the displacement in each step and the more accurate the simulation process.

2. The modeling and numerical simulation method according to claim 1, characterized in that: The test used two steel pipes with a diameter of 5 cm and a length of 45 cm, and pasted polyurethane optical fibers with a diameter of 2 mm on the outer wall of the steel pipes. The preset distance between the two sections of the pipes was 2 cm. In the cross-sectional direction, the optical fibers were arranged at 0°, 135°, 180°, and 225°. The optical fibers at 0° and 180° were used for quantitative calculations, and those at 135° and 225° were used to correct the results of quantitative calculations. On the side wall of the pipe, the optical fibers were arranged in an "S" shape.

3. The modeling and numerical simulation method according to claim 1 is characterized in that: The distance L between A and B is a known quantity. When the tunnel undergoes vertical shear deformation, the free segment of the optical fiber is stretched by a distance of ΔL. At this time, the distance between A and B is (L+ΔL). We use the peak strain to calculate the value of ΔL, and then we can calculate the vertical shear deformation of the tunnel: ε=ΔL÷L (1) therefore: Where: ε is the axial strain of the optical fiber, ΔL is the change in the length of the optical fiber, L is the original length of the optical fiber, and x is the shear deformation of the tunnel.

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