Numerical simulation method for analyzing influence of vibration load on stability of front water-containing fault based on extended finite element

Abstract

The invention discloses a numerical simulation method for analyzing the influence of a vibration load on the stability of a front water-containing fault based on an extended finite element, which is used for analyzing the vibration load without causing a water inrush accident caused by activity instability of the front water-containing fault, and can be applied to the industrial fields of coal mining, tunneling and the like. The method can analyze curved surface faults of various dip angles, fault activities are performed according to stick-slip, changes of hydraulic parameters such as permeability in the fault as a fracture zone during fault activities are fully considered, the parameters are arranged according to points, and the influence of heterogeneity can be considered.

Description

Technical Field

[0001] The invention relates to a technology for applying vibration load to rock mass, in particular to a numerical simulation method for analyzing the influence of vibration load on the stability of a front water-bearing fault based on extended finite element. Background Art

[0002] During the construction of coal mining, roadway excavation, tunnel excavation and other projects, it is necessary to apply vibration loads to the rock mass. If there is a water-bearing fault in front of the rock mass, the application of vibration loads is likely to induce instability of the water-bearing fault activity and cause water inrush accidents, posing a threat to engineering facilities and the personal and property safety of construction workers. Therefore, studying and analyzing the numerical solution method of the influence of vibration loads on the stability of the water-bearing fault in front and developing corresponding numerical simulation programs have become key scientific and technological issues that urgently need to be solved in the national economic and social development.

[0003] [B. Jha, R. Juanes. Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquaketriggering [J]. Water Resources Research, 2014, 50: 3776-3808.] Both use the finite element method to study faults. However, when calculating curved surface faults using the finite element method, the grid needs to be constantly re-divided as the shape of the fault interface changes during fault activity, which results in a huge amount of computation. In addition, the Lagrange Multiplier methods are used to deal with the discontinuity on both sides of the fault interface, which increases the number of unknown variables and causes excessive computational complexity. This method is not suitable for studying curved surface faults, and curved surface faults are basically the faults that exist in the real world. Therefore, new methods and technologies need to be developed to overcome this problem. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a numerical solution method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on the extended finite element method, and develops a corresponding numerical simulation program for analyzing whether the vibration load will cause the activity of the front water-bearing fault to become unstable and induce a water inrush accident. The method can be used in industrial fields such as coal mining and tunnel excavation, and can analyze curved surface faults with various inclination angles. The fault activity is based on stick-slip, and the changes in hydraulic parameters such as permeability of the fault as a broken zone during fault activity are fully considered. The parameters are arranged by point, and the influence of heterogeneity can be considered.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] A numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element, comprising the following steps:

[0007] 1) For solid deformation, starting from the momentum balance equation of the solid, the integral equation is constructed through the principle of minimum potential energy, and then the integral region is discretized and divided into grids, and calculations are performed in the grids; for the fluid flow problem in porous media, the present invention starts from the fluid mass conservation equation of a single-phase Newtonian fluid, uses Darcy's law to describe the fluid flow, and constructs the integral equation of the fluid flow by taking both the fluid flow rate and pressure as unknown variables, and then the integral region is discretized and divided into grids, and calculations are performed in the grids;

[0008] 2) The extended finite element method is selected to deal with the discontinuity of rock deformation and fluid flow on both sides of the fault;

[0009] 3) Use the Biot theory of poroelasticity to study the fluid-solid coupling interaction between fluid flow and solid deformation in the surrounding rock porous medium;

[0010] 4) The fixed-stress split method is used to calculate the fluid-solid interaction problem. In this method, the fluid-solid interaction problem is decomposed into a fluid problem and a solid deformation problem. First, the fluid flow problem in the medium is calculated by fixing the total solid stress field, and then the calculation results of the fluid flow problem are used to calculate the solid deformation problem.

[0011] 5) Characterize the fault as a zero-thickness interface. At the same time, a simplified model is used to simplify the fluid flow in the fault as a fracture zone to the fluid flow in a zero-thickness interface to calculate the fluid flow problem in the fault;

[0012] 6) The dynamic coupling problem of fault structure during fault activity is solved by adopting the Nitsche method;

[0013] 7) Apply rate-and state-dependent friction model to calculate the friction characteristics of fault interface.

[0014] The momentum balance equation of the solid in step 1) is

[0015] The fluid mass conservation equation for the single-phase Newtonian fluid in step 1) is:

[0016] Darcy's law in step 1) is

[0017] The Biot theory of poroelasticity in step 3) is ζ=bε v +M -1 δp.

[0018] The simplified model in step 5) is:

[0019]

[0020] coupled with the interface conditions onγ

[0021] onγ,

[0022] and with the boundary conditions on and

[0023]

[0024] Step 7) is specifically as follows:

[0025] Compared with the prior art, the advantages of the present invention are: the present invention selects the extended finite element method (XFEM) to deal with the discontinuity of rock deformation and fluid flow on both sides of the fault, including the discontinuity of various variables such as stress, displacement, fluid pressure and fluid velocity.

[0026] The invention uses the Biot theory of pore elastic mechanics to study the fluid-solid coupling interaction between fluid flow and solid deformation in the surrounding rock porous medium.

[0027] Because the unified calculation of fluid flow and porous solid fluid-solid coupling is very computationally intensive, the present invention adopts a fixed-stress split method to calculate the corresponding fluid-solid coupling problem. In this method, the fluid-solid coupling problem is decomposed into a fluid problem and a solid deformation problem. First, the fluid flow problem in the medium is calculated by fixing the total solid stress field, and then the calculation results of the fluid flow problem are used to calculate the solid deformation problem.

[0028] The present invention regards the fault as a zero-thickness interface and uses a simplified model to consider the hydraulic behavior of fluid flow in the fault as a fracture zone.

[0029] The present invention solves the dynamic coupling problem of fault structure during fault activity by adopting the Nitsche method.

[0030] The present invention applies a rate-and state-dependent friction model (stick-slip model) to calculate the friction characteristics of the fault interface.

[0031] In summary, the present invention can be used to analyze whether the vibration load will cause the instability of the activity of the water-bearing fault in front and induce a water inrush accident. It can be used in industrial fields such as coal mining and tunnel excavation. It can analyze curved surface faults with various inclination angles. The fault activity is performed according to stick-slip, and the changes in hydraulic parameters such as the permeability of the fault as a broken zone during fault activity are fully considered. Compared with previous programs, the present invention can perform the activity of curved surface faults with a very small amount of calculation, which greatly reduces the computing energy consumption, improves the computing efficiency, and solves the technical problems that were difficult to solve with previous programs. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flowchart of the present invention.

[0033] Figure 2 It is a schematic diagram of the vibration load of the present invention.

[0034] Figure 3 Schematic diagram of fluid-solid coupling of the present invention.

[0035] Figure 4 The figure is a schematic diagram of injecting fluid into a rock formation containing a curved fault according to the present invention.

[0036] Figure 5 For the purpose of the present invention, the fluid flow in the fracture zone is simplified as a schematic diagram of the fluid flow in the interface.

[0037] Figure 6 The present invention is a schematic diagram of injecting and pumping fluid into a rock formation containing a curved fault.

[0038] Figure 7 This is a schematic diagram of an earthquake occurring when displacement is applied to both sides of a rock layer containing a vertical fault according to the present invention.

[0039] Figure 8 This is a fault activity curve diagram of the present invention. DETAILED DESCRIPTION

[0040] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0041] like Figure 1-8 As shown, the present invention proposes a numerical solution method for analyzing the influence of vibration load on the stability of the front water-bearing fault by using the extended finite element method to deal with the discontinuity of fluid flow and porous solid, and then predicts whether the fault activity will cause instability and induce water inrush accidents, and develops a corresponding numerical simulation program:

[0042] (1) For rock formation deformation, the present invention uses the momentum balance equation of the solid Starting from the beginning, the integral equation is constructed by the principle of minimum potential energy, and then the integral region is discretized into grids and the calculation is performed in the grids. For the fluid flow problem in porous media, the present invention starts from the fluid mass conservation equation of single-phase Newtonian fluid Let's go and apply Darcy's law To describe the fluid flow, the integral equation of fluid flow is constructed by taking the fluid flow rate and pressure as unknown variables, and then the integral area is discretized into a grid and calculations are performed in the grid.

[0043] (2) The present invention selects the extended finite element method (XFEM) to deal with the discontinuity of rock deformation and fluid flow on both sides of the fault. Thanks to the extended finite element method, the present invention can accurately describe the discontinuity of various variables such as stress, displacement, fluid pressure and fluid velocity on both sides of the curved fault. Compared with the finite element method, the extended finite element method uses a non-embedded grid to calculate the discontinuity by adding discontinuous equations to the nodes on both sides of the discontinuous interface. It can handle curved faults very well, especially when the fault activity becomes unstable and an earthquake occurs, the shape of the fault interface will change. Because the extended finite element is a non-embedded grid, it can well calculate the situation when the active shape of the fault interface changes. The finite element method must constantly re-divide the grid when the active shape of the fault interface changes, and the amount of calculation will be very large.

[0044] (3) The present invention uses the Biot theory of poroelasticity ζ=bε v +M -1 δp is used to study the fluid-solid coupling interaction between fluid flow and solid deformation in the porous medium of the surrounding rock.

[0045] (4) Because the unified calculation of fluid flow and porous solid fluid-solid coupling is very computationally intensive, the present invention adopts a fixed-stress split method to calculate the fluid-solid coupling problem. In this method, the fluid-solid coupling problem is decomposed into a fluid problem and a solid deformation problem. First, the fluid flow problem in the medium is calculated by fixing the total solid stress field, and then the calculation result of the fluid flow problem is used to calculate the solid deformation problem. Compared with other types of decomposition calculation methods, this fixed stress decomposition method has the advantages of unconditional stability, convergence, and higher accuracy in the calculation of a given number of calculation cycles.

[0046] (5) In reality, a fault is a fracture zone with a certain thickness, but the thickness of the fault is very small relative to the macroscopic scale of the geological body being studied. Therefore, in order to study the sliding behavior of the fault when an earthquake occurs after the fault is active, the present invention characterizes the fault according to the zero-thickness interface. At the same time, in order to study the hydraulic behavior of the fluid flow in the fault as a fracture zone, and the changes in the hydraulic radius and permeability of the fault caused by the fault activity, the present invention uses a simplified model to simplify the fluid flow in the fault as a fracture zone into the fluid flow in a zero-thickness interface to calculate the fluid flow problem in the fault:

[0047]

[0048] coupled with the intertace conditions onγ

[0049] onγ,

[0050] and with the boundary conditionS on and

[0051]

[0052] (6) The present invention solves the dynamic coupling problem of fault structure during fault activity by adopting the Nitsche method.

[0053] (7) The present invention uses a rate-and state-dependent friction model (stick-slip model) to calculate the friction characteristics of the fault interface:

[0054]

[0055]

[0056] (8) In order to verify the method of the present invention, the present invention made some examples: for the fluid-solid coupling problems of fluid flow and solid medium mechanics, the present invention solved the Terzaghi problem and the Mandel problem, and verified the correctness of the fluid-solid coupling part of the method of the present invention by comparing them with the results published by predecessors. At the same time, for the solid mechanics problem, the present invention verified the correctness of the solid mechanics part of the method of the present invention by comparing them with the calculation results of commercial simulation software.

Claims

1. A numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element, characterized by the steps include: 1) For solid deformation, starting from the momentum balance equation of the solid, the integral equation is constructed through the principle of minimum potential energy, and then the integral region is discretized and divided into grids, and calculations are performed in the grids; for the fluid flow problem in porous media, the present invention starts from the fluid mass conservation equation of a single-phase Newtonian fluid, uses Darcy's law to describe the fluid flow, and constructs the integral equation of the fluid flow by taking both the fluid flow rate and pressure as unknown variables, and then the integral region is discretized and divided into grids, and calculations are performed in the grids; 2) The extended finite element method is selected to deal with the discontinuity of rock deformation and fluid flow on both sides of the fault; 3) Use the Biot theory of poroelasticity to study the fluid-solid coupling interaction between fluid flow and solid deformation in the surrounding rock porous medium; 4) The fixed-stress split method is used to calculate the fluid-solid interaction problem. In this method, the fluid-solid interaction problem is decomposed into a fluid problem and a solid deformation problem. First, the fluid flow problem in the medium is calculated by fixing the total solid stress field, and then the calculation results of the fluid flow problem are used to calculate the solid deformation problem. 5) Characterize the fault as a zero-thickness interface. At the same time, a simplified model is used to simplify the fluid flow in the fault as a fracture zone to the fluid flow in a zero-thickness interface to calculate the fluid flow problem in the fault; 6) The dynamic coupling problem of fault structure during fault activity is solved by adopting the Nitsche method; 7) Apply rate-and state-dependent friction model to calculate the friction characteristics of fault interface.

2. A numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element according to claim 1, characterized in that The momentum balance equation of the solid in step 1) is 3. The numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element according to claim 1 is characterized in that The fluid mass conservation equation for the single-phase Newtonian fluid in step 1) is:

4. The numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element according to claim 1 is characterized in that Darcy's law in step 1) is 5. The numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element according to claim 1 is characterized in that The Biot theory of poroelasticity in step 3) is ζ=bε v +M -1 δp.

6. The numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element according to claim 1 is characterized in that The simplified model in step 5) is: coupled with the interface conditions onγ and with the boundary conditions on and 7. The numerical simulation method for analyzing the influence of vibration load on the stability of the front water-bearing fault based on extended finite element according to claim 1 is characterized in that Step 7) is specifically as follows:

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