High-head concrete lining tunnel bearing ratio numerical method based on seepage stress cracking model

Abstract

The invention relates to a high-head concrete lining tunnel bearing ratio numerical method based on a seepage stress cracking model. According to the method, discrete element calculation and analysis are adopted, a three-dimensional geological discrete element unit grid model of the high-head tunnel is established, mechanical calculation is carried out by utilizing a three-dimensional breaking strength criterion, a seepage stress cracking model is established to carry out pore crack seepage stress coupling analysis, and surrounding rock damage and deformation control double indexes for controlling the lining application time are put forward. A local and overall bearing ratio calculation formula of the lining and the surrounding rock is established, and the overall and local bearing sharing ratio of the reinforced concrete lining and the surrounding rock in the water filling process, the stress and strain of steel bars in the lining and the cracking degree of lining cracks are calculated; according to the seepage stress cracking model and the discrete element numerical method thereof provided by the invention, a simulation result better conforms to an actual working condition, and the spatio-temporal evolution law of lining and surrounding rock joint to non-joint bearing (overall bearing ratio and local bearing ratio) in the gradual hydraulic coupling cracking process of the concrete lining is reasonably quantified.

Description

Technical Field

[0001] The invention belongs to the technical field of high-head reinforced concrete lined tunnel construction for water conservancy and hydropower, and in particular relates to a numerical method for the bearing ratio of a high-head concrete lined tunnel. Background Art

[0002] With the development of water conservancy projects such as pumped storage power stations, the construction of high-head tunnels is increasing. These tunnels are usually used for water transportation, power generation or other water conservancy purposes. Reinforced concrete lining has become the preferred lining structure type for the diversion pressure tunnel of high-head pumped storage power stations. This is due to its own high strength, durability, and good rigidity of reinforced concrete, which can withstand high water pressure and resist water erosion, as well as its suitability for on-site casting, suitable for various tunnel shapes and sizes, and its economic advantages. As the preferred lining structure type for the diversion pressure tunnel of pumped storage power stations, reinforced concrete lining has been widely used in the construction of large-scale pumped storage power stations with high water heads, and the project construction has achieved huge economic benefits.

[0003] Although reinforced concrete lining structures are favored by designers of high-head pumped-storage power stations, the problems exposed in reinforced concrete lined tunnel projects show that the current design theory and analysis methods for reinforced concrete pressure tunnels are still immature, which brings many challenges to engineering design. The measured data of the built projects show that during the water filling process of the pressure tunnel, when the water filling pressure reaches a certain critical value, the reinforced concrete lining will crack. After the cracking, the high-pressure water flow will cause the lining and the surrounding rock to separate, causing the working properties of the lining and the surrounding rock to change from displacement continuity to hydraulic continuity, and the bearing characteristics will also change from joint bearing to non-joint bearing. At the same time, the seepage effect in the tunnel is composed of the coupled seepage effect of pores (the contact surface between the lining and the surrounding rock) and cracks (lining cracks and cracks between the surrounding rock and the lining). It can be seen that the cracking of the reinforced concrete lining will affect the working mechanism of the tunnel, especially the joint bearing mechanism of the lining and the surrounding rock. Therefore, in order to ensure the safety and rationality of the design when designing high-head tunnels, numerical simulation methods can be used to determine the non-combined bearing evolution mechanism of the reinforced concrete lining and surrounding rock of high-head tunnels, providing guidance for the design of high-head tunnels.

[0004] However, there are several problems in determining the evolution mechanism of non-combined bearing between reinforced concrete lining and surrounding rock in high-head tunnels:

[0005] 1. When studying the joint bearing mechanism of reinforced concrete lining and surrounding rock in tunnels, technicians in this field mostly use equivalent continuous models to simulate lining cracks and water seepage, and regard the lining and surrounding rock as a whole, ignoring the separation of the lining and surrounding rock caused by the infiltration of high-pressure water after the lining cracks, as well as the flow of high-pressure water in the gap between the lining and the surrounding rock. This is inconsistent with the actual operating mechanism of the pressure tunnel, resulting in a large discrepancy between the simulation results and the actual engineering situation;

[0006] 2. Some technicians insert cohesive units with pore pressure into the finite element model to simulate the separation of lining and surrounding rock, as well as the flow characteristics of high-pressure water in lining cracks and gaps between lining and surrounding rock. Although this method can describe the operating mechanism of the water diversion tunnel after the cracking of the pressure tunnel lining, it is currently limited to two-dimensional plane analysis and cannot achieve three-dimensional analysis. Therefore, in the analysis, it is impossible to consider the influence of the spacing of the annular steel bars inside the reinforced concrete lining and the spacing of the anchor rods inside the surrounding rock on the non-combined bearing evolution mechanism of the reinforced concrete lining and the surrounding rock of the high-head tunnel, and it is impossible to achieve model mechanical calculations under the three-dimensional stress field under the three-dimensional failure strength criterion, which leads to a large deviation between the analysis results and the actual operating characteristics of the pressure tunnel;

[0007] 3. At present, for the numerical simulation of high-head tunnels, lining is often applied directly after the tunnel excavation is completed, without considering the surrounding rock deformation after tunnel excavation controlled by the surrounding rock grade. The deformation size and degree of damage of the surrounding rock will affect the timing of lining application and the stress redistribution after tunnel excavation, resulting in the tunnel simulation conditions not being consistent with the actual project;

[0008] 4. The existing analysis methods of pressure tunnel filling process are often implemented by finite element method based on continuum mechanics. This method is more complicated when dealing with non-continuous mechanics problems such as cracking of reinforced concrete lining and separation of lining and surrounding rock, and has low calculation efficiency and poor stability. Summary of the invention

[0009] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a numerical method for the bearing ratio of a high-head concrete lining tunnel based on a seepage stress cracking model, which solves the problems in the above-mentioned background technology of ignoring the separation of the lining and the surrounding rock caused by the seepage of high-pressure water after the lining cracks, the flow characteristics of the high-pressure water in the lining cracks and the gaps between the lining and the surrounding rock, and the inability to perform three-dimensional analysis of the high-head tunnel model, not considering the timing of lining application, and the low computational efficiency of the existing simulation methods when dealing with non-continuous mechanical problems such as reinforced concrete lining cracks and separation of the lining and the surrounding rock.

[0010] In order to achieve the above object, the technical solution of the present invention is as follows:

[0011] A numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model, comprising the following steps:

[0012] Step 1: Establish a 3D geological discrete element unit grid model of a high-head tunnel. According to the design plan of the high-head tunnel, the following factors are comprehensively considered: the physical properties of the reinforced concrete lining material, the design size of the tunnel, the tunnel shape, the distribution of steel bars in the reinforced concrete lining, the change process of the contact state between the lining and the surrounding rock, the setting of anchors inside the surrounding rock, the permeability characteristics of the lining, surrounding rock and contact surface, and the geological conditions of the surrounding rock;

[0013] Step 2: Establish a three-dimensional discrete element seepage stress cracking model for high-head tunnels;

[0014] The three-dimensional discrete element seepage stress cracking model of high-head tunnel is composed of a discrete element unit grid mechanical model and Flowknots and Flowplanes models for pore crack seepage calculation;

[0015] The discrete element unit grid mechanical model realizes the mechanical calculation and analysis of high head tunnels. The constitutive model of mechanical calculation adopts the Mogi-Coulomb three-dimensional failure strength criterion considering the effect of intermediate principal stress. The preset cracks on the lining and the contact surface between the lining and the surrounding rock are set as the Mogi-Coulomb joint model. The calculation formula is as follows:

[0016] The unit strength in the model is calculated by the octahedral shear stress τ oct and the effective mean stress σ m,2 The linear relationship between them is expressed as:

[0017] τ oct =a+bσ m,2 ;

[0018] Where: a and b are material parameters,

[0019]

[0020]

[0021] When the yield function f < 0, the rock is in an elastic state; when f = 0, it is in a plastic state. The plastic yield state is divided into shear yield and tensile yield. The stress is defined as positive tension and negative compression (σ1≤σ2≤σ3). The shear yield function f of the three-dimensional mechanical model is s as follows:

[0022]

[0023]

[0024] Where c and are cohesion and internal friction angle, respectively. are non-zero material parameters, p, q, and θ σ are the mean effective stress, equivalent shear stress and Lode's angle, respectively;

[0025] Tensile yield function f t Defined as:

[0026] f t =p-σ t ;

[0027] where σ t is the tensile strength of rock, and the maximum value of tensile strength is

[0028] The Flowknots and Flowplanes models are used for seepage analysis of pore cracks in tunnels under high water head. The seepage stress cracking model is used to realize the three-dimensional discrete element pore crack seepage stress coupling analysis of high water head tunnels, thereby realizing the numerical simulation and evolution characteristic analysis of the non-combined bearing evolution of reinforced concrete lining and surrounding rock under high water head. The basic equation and seepage equation of the seepage stress cracking model are as follows:

[0029] Balanced equation:

[0030] σ i ' j,j +F j +(αp w ) ,j =0;

[0031] Geometric equations:

[0032]

[0033] Physics equation:

[0034] σ i ' j =σ ij -αp w δ ij =E ij ε-αp w δ ij ;

[0035] Mechanical boundary conditions:

[0036] P i =σ i ' j n j ;

[0037] Displacement boundary conditions:

[0038]

[0039] Where σ i ' j,j is the effective stress tensor, F j is the body force, α is the equivalent pore pressure coefficient, p w is the pore water pressure, E ij is the elastic stiffness matrix, ε ij is the strain tensor, u j,i 、u i,j is the displacement tensor, δ ij is the Kronecker symbol, P i is the external force, n j is the direction cosine of the external normal on the boundary, u i is the boundary displacement, is the average displacement of the boundary element;

[0040] The governing equation for the seepage of water in the cracks of the lining and the contact surface between the reinforced concrete lining and the surrounding rock follows the cubic theorem:

[0041] (k j φ, i ρu), i =0;

[0042] Where: u = x i is the distance x between the impervious boundaries at a point i (i=1,2) is the hydraulic opening, φ, i is the pressure head gradient in the i-th direction, φ=z+p / ρg, z is the elevation, p is the pore water pressure, ρ is the fluid density, and g is the gravitational acceleration; from the above formula, the flow rate per unit width of the crack can be deduced as:

[0043] q i =k j φ, i ρu;

[0044] Where: q i is the flow rate per unit crack width, μ is the fluid viscosity, k j is the hydraulic conductivity coefficient, and the hydraulic conductivity coefficient and the contact surface stress and strain satisfy the equation:

[0045]

[0046] Where: k0 is the initial hydraulic conductivity, a is a constant, σ n is the normal stress; The calculation formula of the hydraulic opening u is:

[0047] u=u0+fΔu n ;

[0048] Where: u0 is the hydraulic opening when the normal stress is zero, Δu n is the change in opening caused by effective stress; f is the proportionality coefficient;

[0049] According to Darcy's law, the calculation formula for the pore seepage of water-filled flow in reinforced concrete lining and surrounding rock can be obtained:

[0050] q i =-k i [p-ρ f x j g] ,l ;

[0051] Where: q i is the unit flow at a specific location, k i (i=1,2,3) is the permeability coefficient at a specific location, p is the pore water pressure, ρ f is the fluid density, g is the gravitational acceleration;

[0052] The permeability coefficient calculation formula is:

[0053]

[0054] where k i0 is the initial permeability coefficient, σ 1-0 , σ 2-0 , σ 3-0 is the initial principal stress, is the corresponding crack compression rate in the three principal stress directions, and the calculation formula is as follows:

[0055]

[0056] Where α1, α2 and α3 are the decreasing rates of pore compressibility with the increase of corresponding principal stress;

[0057] Step 3: Apply stress and displacement boundary conditions on the model boundary and geostress conditions inside the model, perform stress balance iterative calculation, and obtain a discrete element model under the initial geostress field;

[0058] Step 4: Inversely determine the model parameters according to the range of the model failure zone and the deformation state of the surrounding rock after stress equilibrium;

[0059] Step 5: Assign the unit grid model parameters and mechanical model parameters obtained by inversion in step 4 to the corresponding model to simulate tunnel excavation. Through stress balance iterative calculation, obtain the discrete element model after stress release and redistribution caused by tunnel excavation, and save the model unit stress field data of the whole process of stress release and redistribution. According to the degree of damage and deformation of the potential damage zone of the surrounding rock, establish dual control indicators under different surrounding rock grades to determine the timing of lining application; call the three-dimensional geological discrete element unit grid model of the high-head tunnel established in the previous step, delete the surrounding rock unit in the tunnel excavation area, and import the model unit stress field data of the whole process of stress release and redistribution after tunnel excavation into the model in chronological order; observe the degree of damage and deformation of the potential damage zone of the surrounding rock at each moment. When the degree of damage and deformation of the potential damage zone of the surrounding rock meet the dual indicators of lining application, apply lining and apply anchors inside the surrounding rock;

[0060] Step 5.1: assign the unit grid model parameters and mechanical model parameters obtained by inversion in step 4 to the corresponding model;

[0061] Step 5.2: Perform tunnel excavation simulation, and perform discrete element iterative calculation during the excavation process to obtain a discrete element model after stress release and redistribution caused by tunnel excavation;

[0062] During the iterative calculation process, the iterative calculation is completed when the following equation is established:

[0063]

[0064] In the formula, i and j represent the three directions of the model coordinate axis, n is the number of nodes in the model, abs() is the absolute value function, Δf i is the unbalanced nodal force in the direction of a certain node i, f i is the nodal force in the direction of a certain node i, ε is the tolerance, which is 5.0e -8 ;

[0065] Step 5.3: Traverse all units in the tunnel model and derive the stress components of the model units in the whole process of stress release and redistribution in sequence;

[0066] The stress components of the element include σ xx , σ xy , σ xz , σ yy , σ yz , σ zz ;

[0067] Step 5.4: Call the high-head tunnel 3D discrete element seepage stress cracking model established in step 2, set the unit constitutive model of the model tunnel location to NULL, evenly arrange n command recording points along the tunnel wall, arrange m command recording points in the potential damage area of ​​the surrounding rock, and excavate the unit at the location of the tunnel;

[0068] The monitoring point records and calculates the stress and strain data of the surrounding rock unit during the tunnel excavation process;

[0069] Step 5.5: Using the obtained stress field in the stress release and redistribution process after tunnel excavation, the stress of each unit is traversed and imported in sequence according to the number of the surrounding rock unit;

[0070] Step 5.6: According to the degree of damage and deformation of the potential damage zone of the surrounding rock, establish dual control indicators under different surrounding rock grades to determine the timing of lining application, and apply anchors inside the surrounding rock;

[0071] The degree of damage to the potential damage zone of the surrounding rock is determined by the rock damage degree RDD, and the calculation formula of the rock damage degree RDD is as follows:

[0072]

[0073] Where: ω is the complementary parameter of yield proximity, ω = 1-YAR, YAR is the yield proximity, and the calculation formula is as follows:

[0074]

[0075] Where I1 is the first invariant of the stress tensor, J2 is the second invariant of the deviatoric stress tensor, θ σ is the stress Lode angle, c is the cohesion, and φ is the friction angle;

[0076]

[0077] in is the plastic shear strain, is the ultimate plastic shear strain of the material;

[0078] The average rock damage The calculation formula is as follows:

[0079]

[0080] Where: Z i Represents the command record point with sequence number i;

[0081] The deformation degree of the potential damage zone of the surrounding rock is determined by the displacement release rate η, and the calculation formula of the displacement release rate η is as follows:

[0082]

[0083]

[0084] Where μ imax is the maximum radial displacement of the surrounding rock unit simulated and predicted by the command recording points in each potential failure zone of the surrounding rock, μ i is the real-time radial displacement of the surrounding rock unit simulated and predicted by the command recording points in each potential failure zone of the surrounding rock, η i The simulated predicted displacement release rate of the command recording points in each potential failure zone of the surrounding rock;

[0085] When the potential damage zone of the surrounding rock reaches the damage degree or deformation degree under the surrounding rock grade, lining is applied and anchor rods are applied inside the surrounding rock. The control indicators of damage degree and deformation degree corresponding to the timing of applying lining under different surrounding rock grades are as follows:

[0086]

[0087] Step 6: Determine the step-by-step water filling scheme for the high-head tunnel, use the three-dimensional discrete element seepage stress cracking model of the high-head tunnel to simulate the process of gradually increasing the water filling pressure of the tunnel, and save the simulation results at each level of water filling pressure separately;

[0088] Step 7: Based on the saved simulation results at each level of water filling pressure, calculate the global and local non-combined load-bearing sharing ratios between the reinforced concrete lining and the surrounding rock during the water filling process, the stress and strain of the steel bars inside the lining, and the cracking degree of the lining cracks;

[0089] The calculation formula for the local share ratio of the non-combined load of reinforced concrete lining and surrounding rock is as follows:

[0090]

[0091]

[0092] Where (R pl ) i and (R ps ) i are the load sharing ratios of the ith lining and surrounding rock unit on the contact surface, (σ pnl ) i and (σ pns ) i are the normal stresses on the ith lining and surrounding rock unit on the contact surface, (p pw ) i is the pore water pressure on the i-th lining and surrounding rock unit on the contact surface, i = 1, 2, 3…n, where n is the number of units on the lining and surrounding rock;

[0093] The global sharing ratio calculation formula of the non-combined load of reinforced concrete lining and surrounding rock is as follows:

[0094]

[0095]

[0096] Where: R ns With R nl are the load sharing ratios of reinforced concrete lining and surrounding rock on the contact surface, σ anl is the average normal stress of reinforced concrete lining on the contact surface, σ ans is the average normal stress of the surrounding rock on the contact surface, p w is the average pore water pressure at the contact surface between reinforced concrete lining and surrounding rock;

[0097] The calculation formula of the cracking degree of the lining crack is as follows:

[0098]

[0099] Where: u h0 is the hydraulic opening of the lining when the normal stress is zero, u h is the cracking degree of lining crack, σ' n is the normal effective stress of the lining crack, k n is the normal stiffness of the lining crack;

[0100] Step 8: Based on the calculation results, draw the local non-combined load cloud diagram of the reinforced concrete lining and the surrounding rock during the water filling process, as well as the global non-combined load evolution characteristic curve, the stress state change curve of the steel bar, and the cracking degree change curve of the lining crack;

[0101] The beneficial effects of the present invention are mainly manifested in:

[0102] 1. The numerical method of bearing ratio of high-head concrete lining tunnel based on seepage stress cracking model involved in the present invention takes into account the separation of lining and surrounding rock caused by high-pressure water seepage after lining cracking, as well as the flow of high-pressure water in the gap between lining and surrounding rock, which is more in line with the operation mechanism of steel reinforced concrete lining structure tunnel, and the simulation results are more in line with the actual engineering situation;

[0103] 2. This method can realize the three-dimensional analysis of the numerical model of reinforced concrete lined tunnels, and can consider the influence of the spacing of the annular steel bars inside the reinforced concrete lining and the spacing of the anchors inside the surrounding rock on the non-combined bearing evolution mechanism of the reinforced concrete lining and the surrounding rock of the high-head tunnel, and can realize the model mechanical calculation under the three-dimensional failure strength criterion;

[0104] 3. This method takes into account the dual indicators of surrounding rock damage degree and deformation degree under different surrounding rock grades to control the timing of lining application and consider the redistribution of internal forces under different surrounding rock grades;

[0105] 4. This method adopts the discrete element calculation and analysis method, which can efficiently and stably calculate non-continuous mechanical problems such as the separation of reinforced concrete lining and surrounding rock. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 The flowchart of the numerical determination method for the non-combined load evolution of reinforced concrete lining and surrounding rock in high-head tunnels is provided;

[0107] Figure 2 It is the front view of the three-dimensional geometric unit grid model of the high-head tunnel discrete element in all directions;

[0108] Figure 3 This is a three-dimensional geometric unit grid model diagram of a high-head tunnel discrete element;

[0109] Figure 4 It is the three-dimensional geometric unit grid model diagram of surrounding rock discrete element;

[0110] Figure 5 It is the 3D geometric unit mesh model diagram of lining and tunnel discrete element;

[0111] Figure 6 This is the Flowplane unit grid model diagram;

[0112] Figure 7 It is the cloud diagram of the load sharing ratio between surrounding rock and lining under various levels of water filling pressure;

[0113] Figure 8 It is the axial stress cloud diagram of reinforced concrete lining steel bars;

[0114] Fig. 9 This is a diagram of the step-by-step pressurization and pressure stabilization scheme for high water head pressure tunnels;

[0115] Fig.10 The change process of the contact normal stress between the lining and the surrounding rock with the water filling pressure and the non-combined bearing evolution characteristic curve of the reinforced concrete lining and the surrounding rock;

[0116] Fig.11 It is the curve diagram of the stress change process of the steel bars inside the lining;

[0117] Fig.12 It is the curve diagram of the change process of lining crack width;

[0118] In the figure: 1-surrounding rock; 2-lining; 3-tunnel; 4-virtual preset lining crack; 5-contact surface between lining and surrounding rock; 6-Flowplane unit grid model of contact surface between lining and surrounding rock; 7-Flowplane unit grid model of crack on tunnel surface; 8-Flowplane unit grid model of virtual preset lining crack. DETAILED DESCRIPTION

[0119] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0120] like Figures 1 to 12 As shown, a numerical method for the bearing ratio of high-head concrete lining tunnels based on the seepage stress cracking model is presented. By using the discrete element numerical simulation method, a three-dimensional discrete element unit model of the high-head tunnel is established, and a three-dimensional discrete element seepage stress cracking model is constructed to simulate the hydraulic behavior during the water filling and pressurization process. The unit three-dimensional failure strength criterion constitutive model is set for mechanical calculation. At the same time, the timing of lining application and the application of anchor rods and steel bars are considered. This method realizes the study of the non-combined bearing evolution mechanism of reinforced concrete lining and surrounding rock in high-head tunnels by gradually increasing the water filling pressure.

[0121] In this embodiment:

[0122] A discrete element model of a high-head tunnel with a diameter of 6.2m is constructed, and its outline is horseshoe-shaped. The evolution mechanism of the non-joint bearing capacity of the reinforced concrete lining and surrounding rock in the high-head tunnel is studied by step-by-step water filling and pressurization.

[0123] A numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model, using discrete element numerical simulation method, includes the following steps:

[0124] Step 1: Establish a three-dimensional geological discrete element unit grid model of a high-head tunnel. According to the design plan of the high-head tunnel, the following factors are comprehensively considered: the material physical properties of the reinforced concrete lining 2, the design size of the tunnel 3, the tunnel shape, the distribution of steel bars in the reinforced concrete lining 2, the change process of the contact state between the lining 2 and the surrounding rock 1, the setting of anchors inside the surrounding rock 1, the permeability characteristics of the lining 2, the surrounding rock 1 and the contact surface 5, and the geological conditions of the surrounding rock 1;

[0125] The specific method for establishing a three-dimensional geological discrete element grid model of a high-head tunnel is as follows:

[0126] Step 1.1: According to the design diameter of tunnel 3 in the design scheme of the high-head tunnel and the longitudinal arrangement spacing of the annular steel bars in the reinforced concrete lining 2, the size of the three-dimensional geological discrete element unit grid model of the high-head tunnel is determined. The calculation formula for determining the size is as follows:

[0127]

[0128] Wherein L is the length of the three-dimensional geological discrete element unit grid geometric model of the high-head tunnel, D is the diameter of the tunnel 3, W is the width of the three-dimensional geological discrete element unit grid geometric model of the high-head tunnel, H is the height of the three-dimensional geological discrete element unit grid geometric model of the high-head tunnel, and d is the longitudinal arrangement spacing of the annular steel bars in the reinforced concrete lining 2;

[0129] In this example, the hole diameter is 6.2 m. Therefore, the length and width of the geometric model of the discrete element unit grid are set to 40 m, and the longitudinal arrangement spacing of the annular steel bars in the steel reinforced concrete lining 2, that is, the thickness of the unit model is set to 0.1 m. In order to facilitate the subsequent application of displacement and stress boundary conditions, we use the Cartesian space coordinate system to define the model size, where the length direction is the X axis, the width direction is the Z axis, and the thickness direction is the Y axis (see Figure 2 shown).

[0130] Step 1.2: According to the size of the high-head tunnel 3D geological discrete element unit grid model determined in step 1.1 and the geological conditions of the surrounding rock, a high-head tunnel 3D geological discrete element geometric model is established; the preset lining 2 and the surrounding rock at the location of the tunnel 3 are grouped, and a water seepage crack 4 is preset on the tunnel lining to simulate the cracking of the lining under the action of high water head, and a contact surface 5 without thickness is set between the preset lining 2 and the surrounding rock 1 (see Figure 3 It is used to simulate the influence of water seepage from cracks in lining 2 and water seepage from contact surface 5 on the evolution of non-combined bearing capacity of reinforced concrete lining 2 and surrounding rock 1 under high water head.

[0131] The preset water seepage cracks 4 are set on the top of the reinforced concrete lining 2 to simulate the cracking phenomenon of the lining 2 of the pressure tunnel after being filled with water and pressurized; the contact surface 5 without thickness is used to simulate the situation that after the lining cracks, the contact surface 5 between the lining and the surrounding rock will be water-permeable and separated due to the seepage effect of high-pressure water flow;

[0132] Step 1.3: Divide the three-dimensional geological discrete element geometric model of the high-head tunnel established in step 1.2 by tetrahedral unit meshes to establish a three-dimensional geological discrete element unit mesh model of the high-head tunnel;

[0133] Step 2: Establish a three-dimensional discrete element seepage stress cracking model for high-head tunnels;

[0134] The three-dimensional discrete element seepage stress cracking model for high-head tunnels is composed of a discrete element unit grid mechanical model and Flowknots and Flowplanes models for pore crack seepage calculation (see Figure 6 shown);

[0135] The discrete element unit grid mechanical model realizes the mechanical calculation and analysis of the high head tunnel 3. The constitutive model of the mechanical calculation adopts the Mogi-Coulomb three-dimensional failure strength criterion considering the intermediate principal stress effect. The preset cracks 4 on the lining and the contact surface between the lining 2 and the surrounding rock 1 are set as the Mogi-Coulomb joint model. The calculation formula is as follows:

[0136] The unit strength in the model is calculated by the octahedral shear stress τ oct and the effective mean stress σ m,2 The linear relationship between them is expressed as:

[0137] τ oct =a+bσ m,2 ;

[0138] Where: a and b are material parameters,

[0139]

[0140]

[0141] When the yield function f < 0, the rock is in an elastic state; when f = 0, it is in a plastic state. The plastic yield state is divided into shear yield and tensile yield. The stress is defined as positive tension and negative compression (σ1≤σ2≤σ3). The shear yield function f of the three-dimensional mechanical model is s as follows:

[0142]

[0143]

[0144] Where c and are cohesion and internal friction angle, respectively. are non-zero material parameters, p, q, and θ σ are the mean effective stress, equivalent shear stress and Lode's angle, respectively;

[0145] Tensile yield function f t Defined as:

[0146] f t =p-σ t ;

[0147] where σ t is the tensile strength of rock, and the maximum value of tensile strength is The Flowknots and Flowplanes models are used for seepage analysis of pore cracks in tunnel 3 under high water head. The seepage stress cracking model is used to realize the three-dimensional discrete element pore crack seepage stress coupling analysis of high water head tunnel, and then the numerical simulation and evolution characteristic analysis of the non-combined bearing evolution of reinforced concrete lining 2 and surrounding rock 1 in tunnel 3 under high water head are realized; the basic equation and seepage equation of the seepage stress cracking model are as follows:

[0148] Balanced equation:

[0149] σ i ' j,j +F j +(αp w ) ,j =0;

[0150] Geometric equations:

[0151]

[0152] Physics equation:

[0153] σ i ' j =σ ij -αp w δ ij =E ij ε-αp w δ ij ;

[0154] Mechanical boundary conditions:

[0155] P i =σ i ' j n j ;

[0156] Displacement boundary conditions:

[0157]

[0158] Where σ i ' j,j is the effective stress tensor, F j is the body force, α is the equivalent pore pressure coefficient, p w is the pore water pressure, E ij is the elastic stiffness matrix, ε ij is the strain tensor, u j,i 、u i,j is the displacement tensor, δ ij is the Kronecker symbol, P i is the external force, n j is the direction cosine of the external normal on the boundary, u iis the boundary displacement, is the average displacement of the boundary element;

[0159] The governing equation for the seepage of water in the lining crack 4 and the contact surface 5 between the reinforced concrete lining and the surrounding rock follows the cubic theorem:

[0160] (k j φ, i ρu), i =0;

[0161] Where: u = x i is the distance x between the impervious boundaries at a point i (i=1,2) is the hydraulic opening, φ, i is the pressure head gradient in the i-th direction, φ=z+p / ρg, z is the elevation, p is the pore water pressure, ρ is the fluid density, and g is the gravitational acceleration; the flow rate per unit width of the crack can be deduced as:

[0162] q i =k j φ, i ρu;

[0163] Where: q i is the flow rate per unit crack width, μ is the fluid viscosity, k j is the hydraulic conductivity coefficient, and the hydraulic conductivity coefficient and the contact surface stress and strain satisfy the equation:

[0164]

[0165] Where: k0 is the initial hydraulic conductivity, a is a constant, σ n is the normal stress; The calculation formula of the hydraulic opening u is:

[0166] u=u0+fΔu n ;

[0167] Where: u0 is the hydraulic opening when the normal stress is zero, Δu n is the change in opening caused by effective stress; f is the proportionality coefficient, which takes into account the irregularity of the joint surface and its value range is 0.5 to 1.0;

[0168] According to Darcy's law, the calculation formula for the pore seepage of water-filled flow in reinforced concrete lining 2 and surrounding rock 1 can be obtained:

[0169] q i =-k i [p-ρ f x j g] ,l ;

[0170] Where: q i is the unit flow at a specific location, k i (i=1,2,3) is the permeability coefficient at a specific location, p is the pore water pressure, ρ f is the fluid density, g is the gravitational acceleration; The permeability coefficient calculation formula is:

[0171]

[0172] where k i0 is the initial permeability coefficient, σ 1-0 , σ 2-0 , σ 3-0 is the initial principal stress, is the corresponding crack compression rate in the three principal stress directions, and the calculation formula is as follows:

[0173]

[0174] Where α1, α2 and α3 are the decreasing rates of pore compressibility with the increase of corresponding principal stress;

[0175] Step 2.1: Traverse all nodes on the contact surface of each group of blocks in the high-head tunnel three-dimensional geological discrete element unit grid model established in step 1, and determine the attributes of each node according to the relationship between the block groups to which the nodes belong;

[0176] For nodes on the contact surface, if there are no other nodes with the same group of blocks as this node on the contact surface, this node can be defined as a Flowknot; if there are other nodes with the same group of blocks as this node on the contact surface, this node will not be defined as a Flowknot; a contact surface with a series of Flowknots can be defined as a Flowplane;

[0177] In this example, the pre-lining crack 4 and the contact surface between the reinforced concrete lining 2 and the surrounding rock 1 are Flowplanes, and a series of Flowknots are spread on the Flowplane. Through the Flowplane and Flowknots, hydraulic calculations can be performed on the lining crack 4 and the contact surface 5 when high-pressure water flow penetrates;

[0178] Step 2.2: According to the node attributes on the contact surface of each group of blocks in the three-dimensional geological discrete element unit grid model of the high-head tunnel, and according to the condition that the pore crack seepage stress acts continuously on Flowknots and Flowplanes, a three-dimensional discrete element seepage stress cracking model for calculating the high-head tunnel can be established;

[0179] Step 3: Apply stress and displacement boundary conditions on the model boundary and geostress conditions inside the model, perform stress balance iterative calculation, and obtain a discrete element model under the initial geostress field;

[0180] Step 3.1: Set the mechanical parameters in the constitutive model. The specific parameters of the example are shown in the table below: Table 1 Mechanical calculation parameters Table 2 Seepage calculation parameters

[0181] Step 3.2: Apply stress and displacement boundary conditions on the model boundary and geostress conditions inside the model;

[0182] The stress and displacement boundary conditions of the model boundary are as follows: the unit nodes on each boundary of the model are in a fixed state, the top and lateral boundaries of the model are subject to stress boundary conditions caused by the ground stress, and the ground stress condition inside the model is a uniform stress field generated by gravity;

[0183] Step 3.3: Perform stress balance iterative calculation to obtain the discrete element model under the initial geostress field;

[0184] During the iterative calculation process, the iterative calculation is completed when the following equation is established:

[0185]

[0186] In the formula, i and j represent the three directions of the model coordinate axis, n is the number of nodes in the model, abs() is the absolute value function, Δf i is the unbalanced nodal force in the direction of a certain node i, f i is the nodal force in the direction of a certain node i, ε is the tolerance, which is 5.0e -8 ;

[0187] Step 4: Inversely determine the model parameters according to the range of the model failure zone after stress equilibrium and the deformation state of the surrounding rock 1;

[0188] Step 4.1: Save the initial geostress balance iterative calculation results obtained from step 3, and derive the range of the failure zone of the pressure tunnel model and the deformation state data of the surrounding rock 1;

[0189] Step 4.2: Compare the derived data of the damage area of ​​the pressure tunnel model and the deformation state of the surrounding rock 1 with the results of the on-site engineering survey, and then perform inverse optimization of the model parameters. This process will be iterated until the error between the predicted damage area of ​​the pressure tunnel and the deformation state of the surrounding rock 1 and the actual survey data is controlled within an acceptable accuracy range;

[0190] Step 5: Assign the unit grid model parameters and mechanical model parameters obtained by inversion in step 4 to the corresponding model to simulate the excavation of tunnel 3. Through stress balance iterative calculation, the discrete element model after stress release and redistribution caused by the excavation of tunnel 3 is obtained, and the model unit stress field data of the whole process of stress release and redistribution is saved. According to the degree of damage and deformation of the potential damage zone of surrounding rock 1, dual control indicators under different surrounding rock grades are established to determine the timing of applying lining 2; call the three-dimensional geological discrete element unit grid model of the high-head tunnel established in the previous step, delete the surrounding rock unit in the excavation area of ​​tunnel 3, and import the model unit stress field data of the whole process of stress release and redistribution after the excavation of tunnel 3 into the model in chronological order; observe the degree of damage and deformation of the potential damage zone of surrounding rock 1 at each moment. When the degree of damage and deformation of the potential damage zone of surrounding rock 1 meet the dual indicators for applying lining 2, apply lining 2 and apply anchors inside the surrounding rock 1;

[0191] Step 5.1: assign the unit grid model parameters and mechanical model parameters obtained by inversion in step 4 to the corresponding model;

[0192] Step 5.2: Perform tunnel excavation 3 simulation, and perform discrete element iterative calculation during the excavation process to obtain a discrete element model after stress release and redistribution caused by tunnel 3 excavation;

[0193] During the iterative calculation process, the iterative calculation is completed when the following equation is established:

[0194]

[0195] In the formula, i and j represent the three directions of the model coordinate axis, n is the number of nodes in the model, abs() is the absolute value function, Δf i is the unbalanced nodal force in the direction of a certain node i, f i is the nodal force in the direction of a certain node i, ε is the tolerance, which is 5.0e -8 ;

[0196] Step 5.3: Traverse all units in the tunnel model and derive the stress components of the model units in the whole process of stress release and redistribution in sequence;

[0197] The stress components of the element include σ xx , σ xy , σ xz , σ yy , σ yz , σ zz ;

[0198] Step 5.4: Call the high-head tunnel 3D discrete element seepage stress cracking model established in step 2, set the unit constitutive model of the model tunnel location to NULL, evenly arrange n command recording points along the tunnel wall of tunnel 3, arrange m command recording points in the potential damage area of ​​surrounding rock 1, and excavate the unit at the location of tunnel 3;

[0199] The monitoring point records and calculates the stress and strain data of the surrounding rock unit during the excavation of the tunnel 3;

[0200] Step 5.5: Using the obtained stress field in the stress release and redistribution process after the excavation of tunnel 3, the stress of each unit is traversed and imported in sequence according to the number of the surrounding rock unit;

[0201] Step 5.6: According to the damage degree and deformation degree of the potential damage zone of surrounding rock 1, establish the double control index under different surrounding rock grades to determine the timing of applying lining 2, and apply anchor bolts inside surrounding rock 1;

[0202] The damage degree of the potential damage zone of the surrounding rock 1 is determined by the rock damage degree RDD, and the calculation formula of the rock damage degree RDD is as follows:

[0203]

[0204] Where: ω is the complementary parameter of yield proximity, ω = 1-YAR, YAR is the yield proximity, and the calculation formula is as follows:

[0205]

[0206] Where I1 is the first invariant of the stress tensor, J2 is the second invariant of the deviatoric stress tensor, θ σ is the stress Lode angle, c is the cohesion, and φ is the friction angle;

[0207]

[0208] in is the plastic shear strain, is the ultimate plastic shear strain of the material;

[0209] The average rock damage The calculation formula is as follows:

[0210]

[0211] Where: Z i Represents the command record point with sequence number i;

[0212] The deformation degree of the potential damage zone of the surrounding rock 1 is determined by the displacement release rate η, and the calculation formula of the displacement release rate η is as follows:

[0213]

[0214]

[0215] Where μ imax is the maximum radial displacement of the surrounding rock unit simulated and predicted by the command recording points in each potential failure zone of surrounding rock 1, μ i is the real-time radial displacement of the surrounding rock unit simulated and predicted by the command recording points in each potential failure zone of the surrounding rock 1, η i The displacement release rate simulated and predicted for each command recording point in the potential failure zone of surrounding rock 1;

[0216] When the potential damage zone of surrounding rock 1 reaches the damage degree or deformation degree under the surrounding rock grade, lining 2 is applied and anchors are applied inside surrounding rock 1. The control indicators of damage degree and deformation degree corresponding to the timing of applying lining 2 under different surrounding rock grades are shown in Table 1;

[0217] Step 6: Determine the step-by-step water filling scheme for high-head tunnels (see Fig. 9 As shown in the figure, the high-head tunnel 3D discrete element seepage stress cracking model is used to simulate the process of gradually increasing the water filling pressure in the tunnel, and the simulation results under each level of water filling pressure are saved separately;

[0218] Step 6.1: According to the design plan of the high-head tunnel and the on-site survey report, determine the maximum design water filling pressure, initial water filling pressure and the change in each level of water filling and pressurization of Tunnel 3, and calculate the number of steps of water filling and pressurization step by step: the calculation formula is as follows:

[0219]

[0220] Where, s is the number of steps of water filling and pressurization; p1 is the maximum design water filling pressure of tunnel 3; p0 is the initial water filling pressure; Δp is the change of water filling and pressurization at each level;

[0221] Step 6.2: According to the water filling pressure that the reinforced concrete lining 2 of the high-head tunnel can withstand before cracking, determine the number of steps of water filling and pressurization when the lining 2 cracks. The calculation formula is as follows:

[0222]

[0223] In the formula, s c is the number of steps of water filling and pressurization step by step when lining 2 cracks; p c is the water filling pressure that the reinforced concrete lining 2 of the high-head tunnel can withstand before cracking; math.floor() is the minimum positive integer of the variable;

[0224] In the embodiment, the maximum design water filling pressure p1 = 3MPa, the initial water filling pressure p0 = 0.25MPa, the change of each level of water filling pressure Δp = 0.25MPa, and the number of steps of step-by-step water filling pressure s = 12; the water filling pressure p that the reinforced concrete lining 2 of the high head tunnel can withstand before cracking c =1.25MPa, then the number of steps of water filling and pressurization during cracking is s c =5;

[0225] Step 6.3: Determine the pressure stabilization time for each level of water filling and pressurization. The calculation formula is as follows:

[0226]

[0227] Where, T k is the pressure stabilization time of the k-th level of flushing and pressurization, and k is the number of steps of flushing and pressurization step by step;

[0228] Step 6.4: Open the seepage calculation mode and set the boundary conditions of the model to make all the boundaries of the model impermeable and the inner boundary of the lining uniformly stressed;

[0229] Step 6.5: According to the step-by-step water filling scheme of the pressure tunnel, water filling pressure is applied step by step to the inner surface of lining 2, and a step-by-step water filling simulation is performed using the three-dimensional discrete element seepage stress cracking model of the high-head tunnel;

[0230] In the process of simulating the step-by-step increase of the water filling pressure in the tunnel, at any level of water filling pressure, the seepage stress coupling calculation of crack 4 and the contact surface 5 between lining 2 and surrounding rock 1 is first performed. After the calculation results are obtained, the calculation results of the seepage stress coupling calculation of crack 4 are used as the boundary conditions for the pore seepage calculation of lining 2 and surrounding rock 1, and then the pore seepage calculation of lining 2 and surrounding rock 1 is performed;

[0231] Step 6.6: In the process of simulating the step-by-step increase of the water filling pressure of Tunnel 3, after the water pressure increase and pressure stabilization of the first level are completed, the water pressure increase and pressure stabilization simulation of the next level is performed, and after the final level of the water filling and pressure stabilization simulation of Tunnel 3 is completed, the simulation results are saved;

[0232] Step 7: Based on the saved simulation results at each level of water filling pressure, calculate the global and local non-combined load sharing ratios between the reinforced concrete lining 2 and the surrounding rock 1, the stress and strain of the steel bars inside the lining 2, and the cracking degree of the lining crack 4 during the water filling process;

[0233] The calculation formula for the local share ratio of the non-combined load of the reinforced concrete lining 2 and the surrounding rock 1 is as follows:

[0234]

[0235]

[0236] Where (R pl ) i and (R ps ) i are the load sharing ratios of the ith lining 2 and surrounding rock 1 units on the contact surface 5, (σ pnl ) i and (σ pns ) i are the normal stresses on the i-th lining 2 and surrounding rock 1 unit on the contact surface 5, (p pw ) i is the pore water pressure on the i-th unit of lining 2 and surrounding rock 1 on the contact surface 5, i = 1, 2, 3…n, where n is the number of units on lining 2 and surrounding rock 1;

[0237] The global sharing ratio calculation formula of the non-combined load of the reinforced concrete lining 2 and the surrounding rock 1 is as follows:

[0238]

[0239]

[0240] Where: R ns With R nl are the load sharing ratios of reinforced concrete lining 2 and surrounding rock 1 on contact surface 5, σ anl is the average normal stress of reinforced concrete lining 2 on contact surface 5, σ ans is the average normal stress of surrounding rock 1 on contact surface 5, p w is the average pore water pressure at the contact surface 5 between reinforced concrete lining and surrounding rock;

[0241] The calculation formula for the cracking degree of the lining crack 4 is as follows:

[0242]

[0243] Where: u h0 is the hydraulic opening of lining 2 when the normal stress is zero, u h is the cracking degree of lining crack 4, σ' n is the normal effective stress of lining crack 4, k n is the normal stiffness of lining crack 4;

[0244] Step 7.1: The simulation results of the water filling and pressurization of the tunnel 3 at various levels are respectively exported, and then the local share ratio of the non-combined load of the reinforced concrete lining 2 and the surrounding rock 1 is calculated according to the above-mentioned preset calculation formula;

[0245] The calculation method of the local share ratio of the non-combined load of the reinforced concrete lining 2 and the surrounding rock 1 is as follows:

[0246] Step 7.1.1: Traverse all units on the contact surface 5 between the reinforced concrete lining and the surrounding rock, and derive the normal stress, pore water pressure, and stress area value of each unit on the contact surface 5 under different water filling pressures;

[0247] Step 7.1.2: Calculate the local load ratio by using the derived normal stress, pore water pressure and stress area values ​​of each unit of the contact surface 5 under different water filling pressures and the local load ratio calculation formula of the non-combined load of the reinforced concrete lining 2 and the surrounding rock 1;

[0248] Step 7.2: Based on the calculated local sharing ratio of the non-combined load of the reinforced concrete lining 2 and the surrounding rock 1, the global sharing ratio is calculated according to the above-mentioned global sharing ratio calculation formula of the non-combined load of the reinforced concrete lining 2 and the surrounding rock 1;

[0249] Step 7.3: Calculate the stress-strain value of the steel bar and the cracking degree of lining crack 4 during the water filling process through the simulation results at each level of water filling pressure;

[0250] Step 8: Based on the calculation results, draw the local non-combined bearing cloud diagram of the reinforced concrete lining 2 and the surrounding rock 1 during the water filling process (see Figure 7 as shown) and the axial stress cloud diagram of the internal reinforcement of lining 2 (see Figure 8 As shown), the global non-joint load evolution characteristic curve (see Fig.10 The stress state change curve of the wire and steel bar (see Fig.11 ), the cracking degree variation curve of lining crack 4 (see Fig.12 shown);

[0251] Matters not covered by the present invention are known technologies.

[0252] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model, characterized in that: The steps include: Step 1: Establish a 3D geological discrete element unit grid model of a high-head tunnel. According to the design plan of the high-head tunnel, the following factors are comprehensively considered: the physical properties of the reinforced concrete lining material, the design size of the tunnel, the shape of the tunnel, the distribution of steel bars in the reinforced concrete lining, the change process of the contact state between the lining and the surrounding rock, the setting of anchors inside the surrounding rock, the lining and its preset cracks, the surrounding rock, the permeability characteristics of the contact surface, and the geological conditions of the surrounding rock; Step 2: Establish a three-dimensional seepage stress cracking model for high-head tunnels; The three-dimensional seepage stress cracking model of high-head tunnel is composed of a discrete element unit mechanical model and Flowknots and Flowplanes models for pore crack seepage calculation; the discrete element unit mechanical model adopts a three-dimensional failure strength criterion considering the effect of intermediate principal stress, and the preset cracks on the lining and the contact surface between the lining and the surrounding rock are set as the Mohr-Coulomb Joint model; Step 3: Apply stress and displacement boundary conditions to the boundaries of the three-dimensional geological discrete element unit grid model, apply geostress body conditions inside the model, perform stress balance iterative calculations, and obtain a discrete element model under the initial geostress field; Step 4: According to the on-site monitoring results of the engineering excavation, the 3D geological discrete element unit grid model is excavated, and the unit grid model parameters and mechanical model parameters are inverted according to the scope of the damage zone and the deformation state of the surrounding rock; Step 5: Assign the unit grid model parameters and mechanical model parameters obtained by inversion in step 4 to the corresponding model to simulate tunnel excavation; obtain the discrete element model after stress release and redistribution caused by tunnel excavation through stress balance iterative calculation, and save the model unit stress field data of the whole process of stress release and redistribution; According to the degree of damage and deformation of the potential damage zone of the surrounding rock, dual control indicators under different surrounding rock grades are established to determine the timing of lining application; the three-dimensional geological discrete element unit grid model of the high-head tunnel established in the previous step is called, the surrounding rock unit of the tunnel excavation area is deleted, and the model unit stress field data of the whole process of stress release and redistribution after tunnel excavation are sequentially imported into the model in chronological order; the degree of damage and deformation of the potential damage zone of the surrounding rock at each moment is observed, and when the degree of damage and deformation of the potential damage zone of the surrounding rock meets the dual indicators of lining application, the lining is applied, and anchors are applied inside the surrounding rock; Step 6: Determine the step-by-step water filling scheme for the high-head tunnel, use the 3D discrete element seepage stress cracking model for the high-head tunnel, simulate the process of gradually increasing the water filling pressure in the tunnel, and save the simulation results at each level of water filling pressure separately; Step 7: Based on the saved simulation results at each level of water filling pressure, calculate the global and local non-combined load-bearing sharing ratios between the reinforced concrete lining and the surrounding rock during the water filling process, the stress and strain of the steel bars inside the lining, and the cracking degree of the lining cracks; The calculation formula for the local share ratio of the non-combined load of reinforced concrete lining and surrounding rock is as follows: Where (Rp l )i and (Rps)i are the load sharing ratios of the ith lining and surrounding rock units on the contact surface, respectively. pnl ) i and (σ pns ) i are the normal stresses on the ith lining and surrounding rock unit on the contact surface, (p pw ) i is the pore water pressure on the i-th lining and surrounding rock unit on the contact surface, i = 1, 2, 3…n, where n is the number of units on the lining and surrounding rock; The global sharing ratio calculation formula of the non-combined load of reinforced concrete lining and surrounding rock is as follows: Where: R ns With R nl are the load sharing ratios of reinforced concrete lining and surrounding rock on the contact surface, σ anl is the average normal stress of reinforced concrete lining on the contact surface, σ ans is the average normal stress of the surrounding rock on the contact surface, p w is the average pore water pressure at the contact surface between reinforced concrete lining and surrounding rock; The calculation formula of the cracking degree of the lining crack is as follows: Where: u h0 is the hydraulic opening of the lining when the normal stress is zero, u h is the cracking degree of lining crack, σ' n is the normal effective stress of the lining crack, k n is the normal stiffness of the lining crack; Step 8: Based on the calculation results, draw the local non-combined load-bearing cloud map of reinforced concrete lining and surrounding rock during water filling, the axial stress cloud map of the steel bars inside the lining, the global non-combined load-bearing evolution characteristic curve, the stress state change curve of the steel bars, and the cracking degree change curve of the lining cracks to provide design guidance for the design of reinforced concrete lining of high head tunnels.

2. The numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model according to claim 1 is characterized in that: the specific method for establishing the three-dimensional geological discrete element unit grid model of the high head tunnel is: Step 1.1: According to the design diameter of the tunnel in the design scheme of the high-head tunnel and the longitudinal arrangement spacing of the annular steel bars in the reinforced concrete lining, determine the size of the three-dimensional geological discrete element unit grid model of the high-head tunnel. The calculation formula for determining the size is as follows: Where L is the length of the three-dimensional geological discrete element unit grid geometric model of the high-head tunnel, D is the diameter of the tunnel, W is the width of the three-dimensional geological discrete element unit grid geometric model of the high-head tunnel, H is the height of the three-dimensional geological discrete element unit grid geometric model of the high-head tunnel, and d is the longitudinal arrangement spacing of the annular steel bars in the reinforced concrete lining; Step 1.2: According to the size of the high-head tunnel 3D geological discrete element unit grid model determined in step 1.1 and the geological conditions of the surrounding rock, a high-head tunnel 3D geological discrete element geometric model is established; the preset lining and the surrounding rock at the tunnel location are grouped, and a seepage crack is preset on the tunnel lining to simulate the cracking of the lining under the action of high water head, and a contact surface with no thickness is set between the preset lining and the surrounding rock; Step 1.3: Divide the three-dimensional geological discrete element geometric model of the high-head tunnel established in step 1.2 by tetrahedral unit mesh to establish a three-dimensional geological discrete element unit mesh model of the high-head tunnel.

3. The numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model according to claim 1 is characterized by: The method for establishing the three-dimensional discrete element seepage stress cracking model of high head tunnel in step 2 is: Step 2.1: Traverse all nodes on the contact surface of each group of blocks in the high-head tunnel three-dimensional geological discrete element unit grid model established in step 1, and determine the attributes of each node according to the relationship between the block groups to which the nodes belong; For nodes on the contact surface, if there are no other nodes with the same group of blocks as this node on the contact surface, this node can be defined as a Flowknot; if there are other nodes with the same group of blocks as this node on the contact surface, this node will not be defined as a Flowknot; a contact surface with a series of Flowknots can be defined as a Flowplane; Step 2.2: According to the node attributes on the contact surface of each group of blocks in the three-dimensional geological discrete element unit grid model of the high-head tunnel, and according to the condition that the pore crack seepage stress acts continuously on Flowknots and Flowplanes, a three-dimensional discrete element seepage stress cracking model for calculating the high-head tunnel can be established; The basic equation and seepage equation of the three-dimensional seepage stress cracking model are as follows: Balanced equation: s i ′ j,j +F j +(αp w ) ,j =0; Geometric equations: Physics equation: s i ′ j =s ij -αp w d ij =E ij e-ap w d ij ; Mechanical boundary conditions: P i =s i ′ j n j ; Displacement boundary conditions: Where σ i ' j,j is the effective stress tensor, F j is the body force, α is the equivalent pore pressure coefficient, p w is the pore water pressure, E ij is the elastic stiffness matrix, ε ij is the strain tensor, u j,i 、u i,j is the displacement tensor, δ ij is the Kronecker symbol, P i is the external force, n j is the direction cosine of the external normal on the boundary, u i is the boundary displacement, is the average displacement of the boundary element; The governing equation for the seepage of water in the cracks of the lining and the contact surface between the reinforced concrete lining and the surrounding rock follows the cubic theorem: (k j f, i ru), i =0; Where: u = x i is the distance x between the impervious boundaries at a point i (i=1,2) is the hydraulic opening, φ, i is the pressure head gradient in the i-th direction, φ=z+p / ρg, z is the elevation, p is the pore water pressure, ρ is the fluid density, and g is the gravitational acceleration; according to the above formula, the flow rate per unit width of the crack can be deduced as: q i =k j f, i ru; Where: q i is the flow rate per unit crack width, μ is the fluid viscosity, k j is the hydraulic conductivity coefficient, and the hydraulic conductivity coefficient and the contact surface stress and strain satisfy the equation: k j =k0e -aσn ; Where: k0 is the initial hydraulic conductivity, a is a constant, σ n is the normal stress; The calculation formula of the hydraulic opening u is: u=u0+fΔu n ; Where: u0 is the hydraulic opening when the normal stress is zero, Δu n is the change in opening caused by effective stress; f is the proportionality coefficient; According to Darcy's law, the calculation formula for the pore seepage of water-filled flow in reinforced concrete lining and surrounding rock can be obtained: q i 1-k i [p-ρ f x j g] ,l 100. Where: q i is the unit flow at a specific location, k i (i=1,2,3) is the permeability coefficient at a specific location, p is the pore water pressure, ρ f is the fluid density, g is the gravitational acceleration; The permeability coefficient calculation formula is: where k i0 is the initial permeability coefficient, σ 10 , σ 20 , σ 30 is the initial principal stress, is the corresponding crack compression rate in the three principal stress directions, and the calculation formula is as follows: Where α1, α2 and α3 are the decreasing rates of pore compressibility with the increase of corresponding principal stress.

4. The numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model according to claim 1 is characterized by: The degree of damage to the potential damage zone of the surrounding rock is determined by the rock damage degree RDD, and the calculation formula of the rock damage degree RDD is as follows: Where: ω is the complementary parameter of yield proximity, ω = 1-YAI, YAI is the yield proximity, and the calculation formula is as follows: Where I1 is the first invariant of the stress tensor, J2 is the second invariant of the deviatoric stress tensor, θ σ is the stress Lode angle, c is the cohesion, and φ is the friction angle; in is the plastic shear strain, is the ultimate plastic shear strain of the material; The average rock damage The calculation formula is as follows: Where: Z i Represents the command record point with sequence number i; The deformation degree of the potential damage zone of the surrounding rock is determined by the displacement release rate η, and the calculation formula of the displacement release rate η is as follows: Where μ imax is the maximum radial displacement of the surrounding rock unit simulated and predicted by the command recording points in each potential failure zone of the surrounding rock, μ i is the real-time radial displacement of the surrounding rock unit simulated and predicted by the command recording points in each potential failure zone of the surrounding rock, η i The simulated predicted displacement release rate of the command recording points in each potential failure zone of the surrounding rock; When the potential damage zone of the surrounding rock reaches the damage degree or deformation degree under the surrounding rock grade, lining is applied and anchor rods are applied inside the surrounding rock. The control indicators of damage degree and deformation degree corresponding to the timing of applying lining under different surrounding rock grades are as follows:

5. The numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model according to claim 1 is characterized by: The method for determining the step-by-step water filling scheme for the high-head tunnel is as follows: Step 6.1: According to the design plan of the high-head tunnel and the on-site survey report, determine the maximum design water filling pressure, initial water filling pressure and the change in each level of water filling and pressurization, and calculate the number of steps for step-by-step water filling and pressurization: the calculation formula is as follows: In the formula, s is the number of steps of water filling and pressurization; p1 is the maximum design water filling pressure of the tunnel; p0 is the initial water filling pressure; Δp is the change of water filling and pressurization at each level; Step 6.2: According to the water filling pressure that the reinforced concrete lining of the high-head tunnel can withstand before cracking, determine the number of steps of water filling and pressurization when the lining cracks. The calculation formula is as follows: In the formula, s c The number of steps of water filling and pressurization step by step when the lining cracks; p c is the water filling pressure that the reinforced concrete lining of a high-head tunnel can withstand before cracking; math.floor() is the minimum positive integer of the variable; Step 6.3: Determine the pressure stabilization time for each level of water filling and pressurization. The calculation formula is as follows: Where, T k is the pressure stabilization time of the kth level of flushing pressurization, and k is the number of steps of flushing pressurization step by step.

6. The numerical method for bearing ratio of high head concrete lining tunnel based on seepage stress cracking model according to claim 1 is characterized by: The method for simulating the process of gradually increasing the water filling pressure of the tunnel and saving the simulation results at each level of water filling pressure is: Step 6.4: Open the seepage calculation mode and set the boundary conditions of the model to make all the boundaries of the model impermeable and the inner boundary of the lining uniformly stressed; Step 6.5: According to the step-by-step water filling scheme of the pressure tunnel, water filling pressure is applied step by step to the inner surface of the lining, and a step-by-step water filling simulation is performed using the three-dimensional discrete element seepage stress cracking model of the high-head tunnel; In the process of simulating the step-by-step increase of water filling pressure in the tunnel, at any level of water filling pressure, the crack and the seepage stress coupling calculation of the contact surface between the lining and the surrounding rock are first performed. After the calculation results are obtained, the crack seepage stress coupling calculation results are used as the boundary conditions for the pore seepage calculation of the lining and the surrounding rock, and then the pore seepage calculation of the lining and the surrounding rock is performed; Step 6.6: In the process of simulating the step-by-step increase of the water filling pressure in the tunnel, after the water pressure increase and pressure stabilization of the first level are completed, the water pressure increase and pressure stabilization simulation of the next level is carried out. After the final level of tunnel water filling and pressure simulation is completed, the simulation results are saved.

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