Number and object fusion method for railway foundation deformation analysis under fault zone dislocation

Abstract

The invention relates to the technical field of railway foundation deformation, and discloses a number and object fusion method for railway foundation deformation analysis under fault zone dislocation, which comprises the following steps: establishing a physical experiment platform, a simulation model and a fault zone spatial dislocation deformation statistical model, and obtaining boundary conditions; loading boundary conditions on the physical experiment platform and the simulation model to obtain space deformation of the tunnel structure; and comparing the space deformation of the tunnel structure under the physical experiment condition with the space deformation of the tunnel structure under the analogue simulation condition, and outputting a displacement curve of the tunnel inverted arch in the fault dislocation direction after the conditions are met. According to the method, an active fault zone-tunnel structure physical experiment platform and a simulation model are effectively combined, simulation model parameters are guided and corrected through physical experiment results, the fault zone-tunnel structure system deformation evolution and the space-time law thereof are accurately analyzed, the types of working conditions capable of being simulated are rich, and the simulation efficiency is high. And the method is suitable for the pre-research requirements of railway construction in the western fault zone frequently-occurring areas, and has relatively high accuracy and robustness.

Description

Technical Field

[0001] The invention relates to the technical field of railway foundation deformation, and in particular to a mathematical-physical fusion method for railway foundation deformation analysis under fault zone dislocation. Background Art

[0002] It is not easy to build high-speed railways in western my country. The natural disasters it faces, such as active fault zones, large deformation of soft rocks, frequent earthquakes, high cold weather, frozen soil, strong winds, etc., will cause large structural deformation of the railway infrastructure during service. The offline foundation has almost no resistance to large deformation of the surrounding rock and soil. This is also the reason why ballasted tracks with a wider adjustment range and lower train speeds were widely used when building railways in western China. However, the slab ballastless track commonly used in high-speed railways has a large structural stiffness. If it cannot be well coordinated with the deformation of the offline foundation, it will cause the overall geometric behavior of the line to deteriorate or even cause large-scale damage and de-airing, increase the maintenance and repair costs of railway infrastructure, and even affect the operating safety of high-speed trains.

[0003] The research on the spatiotemporal laws of deformation of active fault zone-underline tunnel foundation is still in its infancy both at home and abroad. The difficulties are: 1) Most of the current experiments take into account fewer objective factors, and most of them are aimed at a single fault dip (45°, 60°, 75°) and a single active fault zone type (normal, reverse fault, strike-slip fault), lacking a more systematic experimental platform; 2) It is difficult to consider the coexistence of complex geostress and active faults, and it is impossible to simulate multi-degree-of-freedom acceleration excitation at the boundary; 3) Complex active faults include different types such as strike-slip, normal faults, reverse faults, and combined faults, and most current platforms are unable to simulate complex faults; 4) Most simulation results lack practical engineering demonstration.

[0004] In summary, there is an urgent need for a method for analyzing railway foundation deformation under fault zone dislocation that is highly reliable and has strong engineering practical significance to solve the problems existing in the prior art. Summary of the invention

[0005] The purpose of the present invention is to provide a method for integrating data and physics for railway foundation deformation analysis under fault zone dislocation, which has high reliability and strong engineering practical significance. The specific technical scheme is as follows:

[0006] A mathematical-physical fusion method for railway foundation deformation analysis under fault zone dislocation includes the following steps:

[0007] Step 1: Establish an active fault zone-tunnel structure physical experiment platform; establish a simulation model; establish a statistical model of spatial displacement deformation of the fault zone and obtain physical experiment boundary conditions and simulation boundary conditions;

[0008] Step 2: Load the physical experiment boundary conditions on the active fault zone-tunnel structure physical experiment platform to obtain the spatial deformation of the tunnel structure under the physical experiment conditions; load the simulation boundary conditions on the simulation model to obtain the spatial deformation of the tunnel structure under the simulation conditions; the spatial deformation of the tunnel structure includes the vertical deformation and lateral deformation of the invert along the longitudinal distribution;

[0009] Step 3: Compare the spatial deformation of the tunnel structure under physical experimental conditions with the spatial deformation of the tunnel structure under simulation conditions, and output the displacement curve of the tunnel invert along the fault dislocation direction when the conditions are met.

[0010] Preferably, in step 3: taking the center position where the fault and the line intersect as point 0, the displacement curve of the tunnel invert along the fault displacement direction includes:

[0011] For normal faults or reverse faults, the vertical deformation curve of the tunnel invert is calculated using the following formula:

[0012]

[0013] Where: z is the vertical deformation of the tunnel invert; x is the longitudinal coordinate value of the tunnel; u1 is the displacement deformation of the normal fault or reverse fault; L R is the width of the fault; D is the diameter of the tunnel;

[0014] For strike-slip faults, the lateral deformation curve of the tunnel invert is calculated using the following formula:

[0015]

[0016] Among them: y is the lateral deformation of the tunnel invert; u2 is the displacement deformation of the strike-slip fault.

[0017] Preferably, the step 2 specifically includes:

[0018] Step 2.1, measuring material parameters, including:

[0019] For rock and soil, a triaxial shear test is used: the soil sample is placed in a triaxial apparatus, confining pressure and axial stress are applied, and then sheared, and the axial stress σ and shear displacement τ are recorded; the internal friction angle φ and cohesion c are calculated based on the τ-σ curve and the formula τ=c+σ×tan(φ);

[0020] For concrete and rock materials, uniaxial tension test or compression test is carried out: E = σ / ∈; where: E is the elastic modulus of the material; σ and ∈ are the axial stress and strain of the material under tension or compression;

[0021] For Poisson's ratio, it is determined by the ratio of the transverse strain to the axial strain ∈y: ν = -∈y / ∈x;

[0022] Step 2.2, based on the material parameters tested in step 2.1, the physical parameters under real conditions are calculated using the scale ratio and used as the parameters of the simulation model;

[0023] Step 2.3, the physical experiment boundary conditions are applied in sections. After a section is loaded, the spatial deformation of the tunnel structure under the physical experiment boundary conditions is saved in real time, which is recorded as X1;

[0024] Step 2.4: Calculate the spatial deformation of the tunnel structure under the current boundary conditions using the simulation model, and save the spatial deformation of the tunnel structure under the simulation conditions in real time, which is recorded as X2.

[0025] Preferably, in step three: comparing the spatial deformation of the tunnel structure under physical experimental conditions with the spatial deformation of the tunnel structure under simulation conditions is specifically:

[0026] The error ΔX is calculated using the following formula:

[0027] ΔX=C u -1 X1-X2;

[0028] Where: C u is the displacement scale ratio;

[0029] When ||ΔX||2<α, the condition is considered to be satisfied; α is the convergence condition; otherwise, the Newton-Raphson iteration method is used to iteratively calculate the perturbation amount ΔE of a parameter variable of the material elastic modulus. If ΔX=C u -1 X1-X2>0, then the updated material elastic modulus is E-ΔE; if ΔX=C u -1 If X1-X2<0, the updated material elastic modulus is E+ΔE.

[0030] Preferably, establishing an active fault zone-tunnel structure physical experimental platform specifically includes:

[0031] Build a loading device that meets the boundary conditions required for fault zone dislocation; the loading device includes a hydraulic oil pump, a jack, a detachable steel block and a sensor;

[0032] According to the tunnel structure design drawings, a scaled experimental model was established with a ratio of 1:30 to 1:60;

[0033] Calculate the amount of rock, soil, rubber, gypsum and PVC board materials required for the experiment according to the scale ratio to make a tunnel model;

[0034] A tunnel model is installed in a physical experiment model box, and required displacement meters and strain meters are installed around the tunnel model; surrounding rock is set around the tunnel model by landfill; and when setting the surrounding rock, prefabricated fault fracture zone materials are installed and viscous materials are applied to simulate the creep of the upper and lower plates of the fault; the physical experiment model box has fixed boundaries at the ends, free boundaries on both sides, and a jack is used to apply displacement boundaries at the bottom.

[0035] Preferably, the simulation model is established by: according to the tunnel structure design drawings, a 1:1 simulation model is established by using finite element method, finite difference method or discrete element method analysis software; the simulation model is a tunnel-surrounding rock-fault interaction numerical model, and the Moore-Coulomb model and CDP model are introduced respectively to characterize the damage characteristics of rock and soil and concrete.

[0036] Preferably, establishing a statistical model of spatial displacement deformation of the fault zone and obtaining physical experimental boundary conditions and simulation boundary conditions specifically include:

[0037] Real-time monitoring of the deformation of the fault zone on a line to obtain the fault zone type, vertical creep deformation and lateral creep deformation at different locations; Investigate the engineering geological data and relevant literature near the foundation structure of the railway tunnel laid in the existing fault zone, and classify the fault zone deformation data recorded in the data;

[0038] The statistically analyzed spatial deformation of the fault zone is fitted, and the representative value of the deformation in each time unit is obtained by using a fixed time unit as the measurement unit, and the distribution type of the representative value is calculated and fitted; the distribution types include extreme value type I and extreme value type II;

[0039] The sampling method in statistical analysis is used to extract the deformation value of the fault zone with 95% confidence level in the statistical model; the inversion is performed according to the experimental conditions, and the simulated data are used as the physical experimental boundary conditions and the simulation boundary conditions.

[0040] Preferably, the simulated data include annual vertical and strike-slip displacements of the fault zone.

[0041] The technical scheme of the present invention has the following beneficial effects: the present invention first establishes an active fault zone-tunnel structure physical experiment platform; establishes a simulation model; establishes a statistical model of spatial displacement deformation of the fault zone and obtains physical experiment boundary conditions and simulation boundary conditions; then loads the physical experiment boundary conditions on the active fault zone-tunnel structure physical experiment platform to obtain the spatial deformation of the tunnel structure under the physical experiment conditions; loads the simulation boundary conditions on the simulation model to obtain the spatial deformation of the tunnel structure under the simulation conditions; the spatial deformation of the tunnel structure includes the vertical deformation and lateral deformation of the invert distributed in the longitudinal direction; finally, the spatial deformation of the tunnel structure under the physical experiment conditions and the spatial deformation of the tunnel structure under the simulation conditions are compared, and the displacement curve of the tunnel invert along the fault displacement direction is output when the conditions are met. The active fault zone-tunnel structure physical experiment platform and the simulation model are effectively combined, and the simulation model parameters are guided and corrected by the physical experiment results. When the conditions are met, the displacement curve of the tunnel invert along the fault displacement direction is output, and the deformation evolution of the fault zone-tunnel structure system and its temporal and spatial laws are accurately analyzed. The simulated working conditions are rich in types, which meet the pre-research needs of railway construction in fault-prone areas in the west, and have high accuracy and robustness.

[0042] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0044] Figure 1 It is a flow chart of the mathematical-physical integration method for railway foundation deformation analysis under fault zone dislocation in the present invention;

[0045] Figure 2 It is a schematic diagram of the arrangement of measuring points of displacement and strain sensors set on the scaled tunnel specimen in the present invention;

[0046] Figure 3 Schematic diagram of the overall structure of the physical experiment platform and the loading method of the platform in the present invention, wherein: (a) is an end view of the platform; (b) is a side view of the platform; (c) is a schematic diagram of the loading method for normal and reverse fault simulation; (d) is a schematic diagram of the loading method for strike-slip fault simulation;

[0047] Figure 4 It is a schematic diagram of the simulation analysis model of the temporal and spatial law of deformation of the active fault zone-tunnel foundation in the present invention;

[0048] Figure 5Schematic diagram of the spatial displacement deformation statistical model of the fault zone in the present invention, wherein: (a) is the annual vertical displacement; (b) is the annual strike-slip displacement;

[0049] Figure 6 is the vertical deformation of the tunnel invert in the present invention along the longitudinal distribution, wherein: (a) is the vertical deformation of the tunnel invert along the longitudinal distribution after the first iteration; (b) is the vertical deformation of the tunnel invert along the longitudinal distribution after the second iteration; (c) is the vertical deformation of the tunnel invert along the longitudinal distribution after the third iteration;

[0050] Figure 7 is the lateral deformation of the tunnel invert along the longitudinal distribution in the present invention, wherein: (a) is the lateral deformation of the tunnel invert along the longitudinal distribution after the first iteration; (b) is the lateral deformation of the tunnel invert along the longitudinal distribution after the second iteration; (c) is the lateral deformation of the tunnel invert along the longitudinal distribution after the sth third iteration;

[0051] Figure 8 It is the spatial distribution and evolution law of tunnel structure deformation in the present invention, wherein: (a) is the vertical deformation of the tunnel arch under a normal fault; (b) is the vertical deformation of the tunnel arch under a reverse fault; (c) is the lateral deformation of the tunnel arch under a strike-slip fault. DETAILED DESCRIPTION

[0052] The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0053] Example:

[0054] See also Figure 1 A mathematical-physical fusion method for railway foundation deformation analysis under fault zone dislocation includes the following steps:

[0055] Step 1: Establish an active fault zone-tunnel structure physical experiment platform; establish a simulation model; establish a statistical model of spatial displacement deformation of the fault zone and obtain physical experiment boundary conditions and simulation boundary conditions;

[0056] Step 2: Load the physical experiment boundary conditions on the active fault zone-tunnel structure physical experiment platform to obtain the spatial deformation of the tunnel structure under the physical experiment conditions; load the simulation boundary conditions on the simulation model to obtain the spatial deformation of the tunnel structure under the simulation conditions; the spatial deformation of the tunnel structure includes the vertical deformation and lateral deformation of the invert along the longitudinal distribution;

[0057] Step 3: Compare the spatial deformation of the tunnel structure under physical experimental conditions with the spatial deformation of the tunnel structure under simulation conditions, and output the displacement curve of the tunnel invert along the fault dislocation direction when the conditions are met.

[0058] Preferably, in this embodiment, establishing an active fault zone-tunnel structure physical experiment platform comprises the following steps:

[0059] Step A: Build a loading device that meets the boundary conditions required for the fault zone displacement, which is mainly composed of a hydraulic oil pump, a jack, a detachable steel block, and a sensor; the detachable steel block is mainly used to simulate different displacement angles of the fault zone; the loading platform can realize the simulation of three-dimensional confining pressure and acceleration boundary;

[0060] Step B: According to the construction site drawings or the design drawings of the tunnel structure laid on the existing active fault zone, a scaled experimental model is established at a ratio of 1:60; since the deformation of the fault zone itself is greatly affected by geological structure, geological movement and environmental factors, the experiment on the deformation law of the fault zone itself has a strong randomness, so the experimental conditions and results are difficult to reproduce, and may not be suitable for the study of the deformation-destruction mechanism of the tunnel-surrounding rock structure under fault dislocation. Based on the actual geological conditions provided by the design data, the experiment can be mainly summarized as follows: (I) different fault zone inclinations; (II) normal / reverse faults; (III) different surrounding rock grades; (IV) tunnel-fault zone penetration angle; (V) reserved volume and deformation law of segmented tunnels.

[0061] Step C, calculating the amount of rock and soil, rubber, gypsum and PVC board materials required for the experiment according to the scale ratio;

[0062] The specific scale ratios of various physical parameters are shown in the following table:

[0063] Table 1 Specific scale ratio statistics of various physical parameters

[0064] Physical quantity symbol Similarity Ratio Similarity ratio length l <![CDATA[C l ]]> 1 / 60 density ρ <![CDATA[C ρ ]]> 1 / 1 Elastic modulus E <![CDATA[C E ]]> 1 / 30 force F <![CDATA[C F =C l 3 C ρ ]]> 1 / 216000 strain ε <![CDATA[C ε =C l C ρ C E -1 ]]> 1 / 2 stress σ <![CDATA[C σ =C E C ε ]]> 1 / 60 Acceleration a <![CDATA[C a =a m / a p ]]> 1 / 1 speed v <![CDATA[C v =C E 0.5 C ρ -0.5 ]]> 1 / 5.477 Displacement u <![CDATA[C u =C l C ε ]]> 1 / 120 time t <![CDATA[C ε =C l C ρ 0.5 C E -0.5 ]]> 1 / 10.955 frequency ω <![CDATA[C ε =C t -1 ]]> 1 / 0.0913

[0065] The materials used in the experiment are as follows:

[0066] a. Experimental surrounding rock materials: fly ash, river sand and motor oil are used to configure similar materials of different surrounding rock grades; b. Scaled tunnel specimens: gypsum, water and barite are used to configure similar lining materials; c. Fault zone filling materials: two layers of PVC boards with butter in the middle.

[0067] Step D: Purchase a physical experiment model box, install the required displacement gauges and strain gauges around the tunnel on the prefabricated tunnel plaster model, and fill the rock material around the tunnel by landfill;

[0068] For the displacement and strain sensors in the experiment, the measuring points are arranged as follows: Figure 2As shown, CD1-CD8 are the measuring point numbers installed on the tunnel wall, CD1 is located at the top of the tunnel segment, CD2 and CD8 are located at the connection between the upper step and the middle step on both sides, CD3 and CD7 are located at the connection between the middle step and the lower step on both sides, CD4 and CD6 are located at the connection between the lower step and the invert on both sides, and CD5 is located at the bottom of the invert.

[0069] Step E: installing the prefabricated fault fracture zone material and applying the viscous material to simulate the creep of the upper wall and the lower wall of the fault when filling the surrounding rock;

[0070] Step F: Apply model constraints, specifically: apply fixed hinges at both ends of the experimental box tunnel opening. The overall structure of the physical experiment platform and the platform loading method are as follows: Figure 3 As shown, a steel block with an inclined angle of 60° is used to simulate the displacement of the fault zone, where: (a) and (b) are the front view and side view of the test platform, (c) is the principle diagram of the bottom lifting simulation of the normal-reverse fault, and (d) is the principle diagram of the lateral lifting simulation of the slip fault. It can be used to simulate the lifting and lateral displacement of the upper plate of the normal fault to simulate the boundary conditions of the normal-reverse fault and the strike-slip fault. The boundary conditions at both ends of the experimental box are fixed constraints.

[0071] Preferably, in this embodiment, establishing the simulation model specifically includes:

[0072] A simulation model with the same working conditions as the model experiment was established using commercial finite element software. The model size is 100m (width) × 100m (height), the inclination angle is 60°, and the thickness of the overlying rock layer is 45m. The soil constitutive model obeys the Mohr-Coulomb yield criterion, and the CDP model is used for the concrete track structure to characterize the material damage characteristics under large deformation. The mechanical parameters of the soil, fault zone and tunnel lining are shown in Table 2. The soil and the tunnel are set to "face-to-face contact", the tangential direction is "penalty" friction, the friction coefficient is 0.3, and the normal direction is "hard" contact. The main parameters of the simulation model are determined according to physical experiments and scale ratios, see Table 2. The schematic diagram of the simulation analysis model of the spatiotemporal law of deformation of the active fault zone-tunnel foundation is shown in Figure 4 As shown (D is the diameter of the tunnel segment, θ is the displacement angle of the fault zone, L S is the longitudinal length of the tunnel model, L R is the longitudinal length of the fault zone).

[0073] Table 2 Mechanical parameters of soil, fault zone and tunnel lining

[0074]

[0075]

[0076] In this embodiment, preferably, the statistical model of spatial displacement deformation of the fault zone is established and the physical experimental boundary conditions and simulation boundary conditions are obtained as follows: Taking the deformation of the Jiali fault zone in the past three years as an example, a preliminary statistical model of the deformation of the fault zone is established. The measured data on site are shown in Table 3 below:

[0077] Table 3 Field measured data

[0078] Measuring point Vertical component 1 (mm / a) Vertical component 2 (mm / a) Strike-slip component 1 (mm / a) Strike-slip component 2 (mm / a) 1 19.55 6.58 1.79 1.71 2 18.23 8.93 1.57 1.56 3 20.18 10.25 1.66 1.64 4 19.28 5.77 2 1.79 5 20.07 5.42 1.65 1.64 6 18.68 7.47 2.19 2.15 7 19.78 4 2.02 1.98 8 20.66 5.33 1.64 1.71 9 21.46 8.23 1.69 1.67 10 21.97 7.68 1.83 1.82 11 23.31 10.19 1.99 2.06 12 24.22 16.2 1.87 1.84 13 24.17 16.08 1.77 1.79 14 21.9 10.38 1.86 1.73 15 19.97 13.48 2.56 2.26 16 17.9 10.57 1.95 1.92 17 19.54 5.59 1.63 1.63 18 15.48 4.85 1.94 1.84 19 18.54 0.95 1.9 1.88 20 20.06 2.8 2.3 2.21 21 18.43 9.15 1.77 1.75 22 17.75 7.07 2.33 2.25 23 18.23 9.15 1.81 1.82

[0079] Taking the annual deformation of the fault zone as the basic parameter, a statistical model of spatial displacement deformation of the fault zone is established, such as Figure 5 As shown in (a). According to the statistical results, it can be considered that the annual variation of the Jiali fault zone conforms to the normal distribution law. The vertical and strike-slip deformation of the fault zone are fitted with the normal distribution function, and it can be obtained that the average annual vertical displacement of the fault zone is 20.7078mm, and the standard deviation of the annual vertical displacement of the fault zone is 1.38mm; the average annual displacement of the fault zone is 2.5265mm, and the standard deviation of the annual displacement of the fault zone is 0.32141mm.

[0080] The Monte-Carlo method used in traditional statistical analysis is used to perform random sampling in the statistical model, and the sampling results meet the 95% confidence level. Figure 5 As shown in (b), the random sampling points are evenly distributed around the mean, indicating that the random samples can better represent the basic probability characteristics of the statistical model. According to the "3σ" principle in probability theory, combined with the annual variation mean and standard deviation obtained from the above statistics, it can be preliminarily estimated that the annual variation range of the Jiali Fault Zone is [16.56, 24.85] mm vertically and [1.56, 3.49] mm in strike slip. The established fault zone statistical model can be used to generate annual displacement samples of the fault zone vertically and strike slip and can be used as the boundary conditions of the numerical model.

[0081] In this embodiment, preferably, loading the physical experiment boundary conditions on the active fault zone-tunnel structure physical experiment platform to obtain the spatial deformation of the tunnel structure under the physical experiment conditions and loading the simulation boundary conditions on the simulation model to obtain the spatial deformation of the tunnel structure under the simulation conditions specifically include:

[0082] Physical experiment boundary condition loading is implemented by using Figure 3 The hydraulic oil pump shown in (a) and (b) applies a thrust to the bottom of the footwall or the right boundary. The thrust recorded by the jack is compared with the applied deformation. When the current deformation is reached, the model loading is stopped. Reverse faults, normal faults, and strike-slip fault boundary conditions can be simulated based on upward, downward, and lateral loading.

[0083] The specific steps of correcting the simulation model parameters using the physical test results are as follows:

[0084] (1) Test the basic physical parameters of the experimental materials. Use the scale ratio to calculate the physical parameters in real situations and use them as the parameters of the simulation model, as shown in Table 4:

[0085] Table 4 Physical parameters in real situations and used as parameter table of simulation model

[0086]

[0087]

[0088] (2) Apply the boundary conditions in sections. After loading a section, record the physical experiment results: the spatial deformation of the tunnel structure. The spatial deformation of the tunnel structure under the current boundary conditions obtained in B is saved in real time through the cloud PC and recorded as X1.

[0089] (3) Use the simulation model to calculate the spatial deformation of the tunnel structure under the current boundary conditions, that is, the vertical and lateral deformation of the tunnel invert along the longitudinal distribution, such as Figure 6 (a) and 7(a).

[0090] In this embodiment, the spatial deformation of the tunnel structure under physical experimental conditions is compared with the spatial deformation of the tunnel structure under simulation conditions. When the conditions are met, the displacement curve of the tunnel invert along the fault dislocation direction is output. The details are as follows:

[0091] The saved spatial deformation X1 of the tunnel structure is compared with the simulated spatial deformation X2 of the tunnel structure. If there is an error, it can be expressed as ΔX = C u -1 X1-X2 Where: C u is the displacement scale ratio;

[0092] An iterative convergence criterion (i.e., error tolerance α) is preset, the simulation calculation results and the experimental results are iterated, and the elastic modulus E in the numerical model is updated until the model meets the convergence condition ||ΔX||2<α. Specifically, if the second-order norm of ΔX exceeds the preset error tolerance α (the value is 1e-7 in this embodiment), it is necessary to use iteration to update the physical parameters of the current model; the iterative method specifically adopts the Newton-Raphson iteration method to treat the simulation model as a nonlinear system, calculate the residual between the current result and the physical experimental result after correcting the parameters, and continuously iterate and update the simulation model parameters so that the current simulation result X2 is consistent with the physical experimental result C u -1If the residual between X1 is less than the convergence condition (i.e., the error tolerance α), it can be considered that the current simulation model can represent the specific working conditions simulated by the current physical experiment. By presetting a perturbation amount ΔE of a parameter variable for the elastic modulus of the material, the calculation result of the model after the parameter perturbation is calculated, that is, the numerical model is updated with the parameter E+ΔE and the structural response X is calculated. 2,j (j represents the result after the jth iteration), based on the experimental results C u -1 X1 is the true value. After n iterations, the disturbance Δa that satisfies the accuracy can be obtained. n As the final updated parameter value a+Δa of the current model n The iteration formula can be calculated according to the following formula:

[0093] (K j (E+ΔE)X 2,j -F j ) / K′ j (E+ΔE)-C u -1 X1=0;

[0094] Where: K j is the stiffness matrix at the jth iteration step, and the elastic modulus is E+ΔE; F j is the equivalent load matrix of the current boundary condition; K′ j is the tangent stiffness matrix at the jth iteration step; E and ΔE are the elastic modulus and its perturbation respectively; C u is the displacement scale ratio; X 2,j is the displacement after the jth iteration step.

[0095] If the calculated ΔX j =C u -1 X1-X 2,j >0, the disturbance ΔE can be reduced (i.e., E-ΔE is taken), otherwise ΔE is increased (i.e., E+ΔE is taken), until after iteration ||ΔX j ||2<α, the iteration ends. You can refer to the following iteration formula:

[0096]

[0097] Where ||ΔX j ||2 is ΔX j The norm of ΔX j (1) ΔX j (2), ..., ΔX j (n) represents the vector ΔX j The 1st, 2nd, …, nth elements in .

[0098] In this case, the elastic model disturbance ΔE=2GPa is preset. After 2 iterations, the final deformation can be obtained as follows: Figure 6 (b) and (c) and Figure 7 As shown in (b) and (c).

[0099] Repeat the physical experimental boundary condition loading and use the physical test results to correct the simulation model parameters, and realize the multi-scale analysis of the spatial deformation distribution and evolution mechanism of the active fault zone-railway tunnel foundation based on the fusion of mathematics and physics.

[0100] Repeat the physical experiment boundary condition loading and use the physical test results to correct the simulation model parameters:

[0101] Complete the result calculation of the first iteration according to the above steps and save the current model calculation parameters;

[0102] according to Figure 5 The deformation sampling data of the fault zone in (a) and (b) continue to implement the physical experiment boundary condition loading, that is, continue to apply the current boundary conditions to the physical experiment model;

[0103] Repeatedly use the physical test results to correct the simulation model parameters, that is, to recalculate the unknown parameters in the simulation model represented by the current experimental results, and again iterate the simulation model and correct the model parameters, and obtain the spatial distribution and evolution law of the tunnel structure deformation under the fault zone deformation condition, such as Figure 8 As shown (where: (a) is the vertical deformation of the tunnel arch under the normal fault; (b) is the vertical deformation of the tunnel arch under the reverse fault; (c) is the lateral deformation of the tunnel arch under the strike-slip fault). Taking the boundary conditions of 50mm, 100mm, 150mm, 200mm for normal and reverse faults; 20mm, 40mm, 60mm, 80mm for strike-slip faults as examples, according to the loading of different boundary conditions, the deformation curve of the tunnel structure under the fault zone dislocation condition can be obtained by the curve interpolation fitting method. From the calculation results, it can be seen that the displacement curves of the tunnel arches along the fault dislocation direction of the three types of fault dislocation are all "S" shaped, which can be summarized as follows:

[0104] (1) Taking the center of the intersection of the fault and the line as the zero point, for normal faults or reverse faults, the vertical deformation curve of the tunnel invert is calculated using the following formula:

[0105]

[0106] Where: z is the vertical deformation of the tunnel arch (mm); x is the longitudinal coordinate of the tunnel (m); u1 is the displacement deformation of the positive / reverse fault (mm), where the displacement of the reverse fault is negative and the displacement of the positive fault is positive; L R is the width of the fault (m); D is the diameter of the tunnel (m);

[0107] (2) Taking the center of the intersection of the fault and the line as the zero point, for the strike-slip fault, the lateral deformation curve of the tunnel invert is calculated using the following formula:

[0108]

[0109] Where: y is the lateral deformation of the tunnel invert (mm); x is the longitudinal coordinate of the tunnel (m); u2 is the longitudinal displacement of the strike-slip fault (mm); L R is the width of the fault (m); D is the diameter of the tunnel (m).

[0110] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A mathematical-physical fusion method for railway foundation deformation analysis under fault zone dislocation, characterized in that: The following steps are involved: Step 1: Establish an active fault zone-tunnel structure physical experiment platform; establish a simulation model; establish a statistical model of spatial displacement deformation of the fault zone and obtain physical experiment boundary conditions and simulation boundary conditions; Step 2: Load the physical experiment boundary conditions on the active fault zone-tunnel structure physical experiment platform to obtain the spatial deformation of the tunnel structure under the physical experiment conditions; load the simulation boundary conditions on the simulation model to obtain the spatial deformation of the tunnel structure under the simulation conditions; the spatial deformation of the tunnel structure includes the vertical deformation and lateral deformation of the invert along the longitudinal distribution; Step 3: Compare the spatial deformation of the tunnel structure under physical experimental conditions with the spatial deformation of the tunnel structure under simulation conditions, and output the displacement curve of the tunnel invert along the fault dislocation direction when the conditions are met.

2. The method for integrating mathematics and physics for railway foundation deformation analysis under fault zone dislocation according to claim 1 is characterized in that: In step 3: the center of the intersection of the fault and the line is taken as the 0 point, and the displacement curve of the tunnel arch along the fault displacement direction includes: For normal faults or reverse faults, the vertical deformation curve of the tunnel invert is calculated using the following formula: Where: z is the vertical deformation of the tunnel invert; x is the longitudinal coordinate value of the tunnel; u1 is the displacement deformation of the normal fault or reverse fault; L R is the width of the fault; D is the diameter of the tunnel; For strike-slip faults, the lateral deformation curve of the tunnel invert is calculated using the following formula: Among them: y is the lateral deformation of the tunnel invert; u2 is the displacement deformation of the strike-slip fault.

3. The method for integrating mathematics and physics for railway foundation deformation analysis under fault zone dislocation according to claim 1 is characterized in that: Step 2 specifically includes: Step 2.1, measuring material parameters, including: For rock and soil, triaxial shear test is used to obtain parameters. Specifically, the soil sample is placed in a triaxial apparatus, confining pressure and axial stress are applied, and then shearing is performed. The axial stress σ and shear displacement τ are recorded. The internal friction angle φ and cohesion c are calculated based on the τ-σ curve and the formula τ=c+σ×tan(φ). For concrete and rock materials, uniaxial tension test or compression test is used to obtain parameters, E = σ / ∈, where: E is the elastic modulus of the material; σ and ∈ are the axial stress and strain of the material under tension or compression; For Poisson's ratio, it is determined by the ratio of the transverse strain to the axial strain ∈y: ν = -∈y / ∈x; Step 2.2, based on the material parameters tested in step 2.1, the physical parameters under real conditions are calculated using the scale ratio and used as the parameters of the simulation model; Step 2.3, the physical experiment boundary conditions are applied in sections. After a section is loaded, the spatial deformation of the tunnel structure under the physical experiment boundary conditions is saved in real time, which is recorded as X1; Step 2.4: Calculate the spatial deformation of the tunnel structure under the current boundary conditions using the simulation model, and save the spatial deformation of the tunnel structure under the simulation conditions in real time, which is recorded as X2.

4. The method for integrating mathematics and physics for railway foundation deformation analysis under fault zone dislocation according to claim 3 is characterized in that: In the step 3, the spatial deformation of the tunnel structure under the physical experimental conditions and the spatial deformation of the tunnel structure under the simulation conditions are compared specifically: The error ΔX is calculated using the following formula: ΔX=C u -1 X1-X2; Where: C u is the displacement scale ratio; When ||ΔX||2<α, the condition is considered to be satisfied, where α is the convergence condition; otherwise, the Newton-Raphson iteration method is used to iteratively calculate the disturbance ΔE of a parameter variable of the material elastic modulus to make a judgment: If ΔX=C u -1 X1-X2>0, then the updated material elastic modulus is E-ΔE; If ΔX=C u -1 If X1-X2<0, the updated material elastic modulus is E+ΔE.

5. The method for integrating mathematics and physics for railway foundation deformation analysis under fault zone dislocation according to any one of claims 1 to 4, characterized in that: The establishment of an active fault zone-tunnel structure physical experimental platform specifically includes: Build a loading device that meets the boundary conditions required for fault zone dislocation; the loading device includes a hydraulic oil pump, a jack, a detachable steel block and a sensor; According to the tunnel structure design drawings, a scaled experimental model was established with a ratio of 1:30 to 1:60; Calculate the amount of rock, soil, rubber, gypsum and PVC board materials required for the experiment according to the scale ratio to make a tunnel model; A tunnel model is installed in a physical experiment model box, and required displacement meters and strain meters are installed around the tunnel model; surrounding rock is set around the tunnel model by landfill; and when setting the surrounding rock, prefabricated fault fracture zone materials are installed and viscous materials are applied to simulate the creep of the upper and lower plates of the fault; the physical experiment model box has fixed boundaries at the ends, free boundaries on both sides, and a jack is used to apply displacement boundaries at the bottom.

6. The method for integrating mathematics and physics for railway foundation deformation analysis under fault zone dislocation according to claim 5 is characterized in that: The specific steps of establishing the simulation model are as follows: according to the tunnel structure design drawings, a 1:1 simulation model is established by using finite element method, finite difference method or discrete element method analysis software; the simulation model is a tunnel-surrounding rock-fault interaction numerical model, and the Mohr-Coulomb model and CDP model are introduced respectively to characterize the damage characteristics of rock and soil and concrete.

7. The method for integrating mathematics and physics for railway foundation deformation analysis under fault zone dislocation according to claim 5 is characterized in that: Establishing a statistical model of spatial displacement deformation of the fault zone and obtaining physical experimental boundary conditions and simulation boundary conditions specifically include: Real-time monitoring of the deformation of the fault zone on a line to obtain the fault zone type, vertical creep deformation and lateral creep deformation at different locations; Investigate the engineering geological data near the foundation structure of the railway tunnel laid in the existing fault zone and classify it according to the deformation data of the fault zone recorded in the data; The statistically analyzed spatial deformation of the fault zone is fitted, and the representative value of the deformation in each time unit is obtained by using a fixed time unit as the measurement unit, and the distribution type of the representative value is calculated and fitted; the distribution types include extreme value type I and extreme value type II; The sampling method in statistical analysis is used to extract the deformation value of the fault zone with 95% confidence level in the statistical model; the inversion is performed according to the experimental conditions, and the simulated data are used as the physical experimental boundary conditions and the simulation boundary conditions.

8. The method for integrating mathematics and physics for railway foundation deformation analysis under fault zone dislocation according to claim 7 is characterized in that: The simulated data include the annual vertical and strike-slip displacement of the fault zone.

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