A method for analyzing the behavior changes of tension cracks in clay core walls under fluid-solid coupling

Abstract

The present invention belongs to the technical field of clay core wall crack analysis, and specifically relates to a method for analyzing the change in properties of clay core wall tension cracks under fluid-solid coupling. The method includes: establishing a mixed flow fluid-solid coupling analysis model of a clay core wall with tension cracks based on an extended finite element method; analyzing the model calculation domain, setting boundary conditions, introducing virtual displacement and virtual seepage pressure, and obtaining the weak form of the soil fluid-solid coupling equation and the weak form of the crack seepage equation according to the divergence theorem and introducing boundary conditions; discretizing the weak form of the soil fluid-solid coupling equation and the weak form of the crack seepage equation in the space domain and the time domain; jointly solving the discrete form of the soil fluid-solid coupling equation and the discrete form of the crack seepage equation, and outputting the calculation results. The present invention uses an extended finite element method, and there is no need to predetermine the crack path, which simplifies the calculation process and reduces the need for mesh encryption.

Description

Technical Field

[0001] The invention belongs to the technical field of clay core wall crack analysis, and in particular relates to a method for analyzing property changes of clay core wall tension cracks under fluid-solid coupling. Background Art

[0002] When the conventional finite element method is used to numerically solve the mixed flow fluid-solid coupling analysis model of clay core wall with tension cracks, the cracks are usually characterized by diffuse units, that is, thin layer units are set at the crack site to simulate the cracks by reducing the deformation modulus of the unit and increasing the permeability coefficient. In the process of analyzing the crack extension, this method needs to determine the crack extension path in advance and encrypt the mesh near the crack. However, in actual analysis, the specific path of crack extension is not known in advance, and the full-area encrypted mesh is bound to cause difficulty in solving. Therefore, it is necessary to determine the important influence of the tension cracks in the clay core wall on the stability and seepage characteristics of the wall under the action of fluid-solid coupling. When analyzing the crack extension path, the traditional method needs to determine the crack extension path in advance and encrypt the mesh near the crack, which increases the complexity and workload of the calculation. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to address the deficiencies of the prior art and to provide a method for analyzing the changes in the properties of tension cracks in clay core walls under fluid-solid coupling. The analysis method based on the extended finite element method (XFEM) can simulate the crack propagation without predetermining the crack path, thereby simplifying the calculation process and solving the problems of complex calculations and heavy workload in the prior art.

[0004] Technical solution: The method for analyzing the change of tensile crack properties of clay core wall under fluid-solid coupling of the present invention comprises the following steps:

[0005] S1: Based on the extended finite element method, a fluid-solid coupling analysis model of mixed flow in clay core wall with tension cracks is established, and the extended finite element expressions of displacement and seepage pressure under fluid-solid coupling are determined;

[0006] S2: Analysis model calculation domain, including soil calculation domain and crack calculation domain , set boundary conditions; construct the basic equation of soil fluid-solid coupling, introduce virtual displacement and virtual osmotic pressure , substitute the basic equation and integrate the soil calculation domain to obtain the weak form of the soil fluid-solid coupling equation. According to the divergence theorem and the introduction of boundary conditions, the weak form of the soil fluid-solid coupling equation related to the boundary conditions is obtained; the basic equation of fracture seepage is constructed and the virtual seepage pressure is introduced. , substitute the basic fracture seepage equation to integrate the fracture solution domain, and obtain the weak form of the fracture seepage equation. According to the divergence theorem and introducing boundary conditions, the weak form of the fracture seepage equation related to the boundary conditions is obtained;

[0007] S3: Substitute the extended finite element expressions of displacement and seepage pressure into the weak form of the soil fluid-solid coupling equation and the weak form of the fracture seepage equation, and discretize them in the space domain and time domain to obtain the discrete form of the soil fluid-solid coupling equation and the discrete form of the fracture seepage equation;

[0008] S4: The discrete form of the soil fluid-solid coupling equation and the discrete form of the fracture seepage equation are jointly solved, the initial crack width and seepage pressure value are set, the crack width and seepage pressure value are updated through iterative calculation until the convergence conditions are met, and the calculation results are output.

[0009] To further improve the above technical solution, the extended finite element expression of the displacement under the fluid-solid coupling in S1 is:

[0010] ;

[0011] in, is the set of all displacement nodes; Strengthen the displacement node set for the crack penetration unit; Strengthen the displacement node set for the crack tip element; is the displacement of the continuous deformation of the displacement node; Strengthen the additional degrees of freedom of node displacement for crack penetration elements; Strengthen the node displacement additional degrees of freedom for the crack tip element; is the conventional osmotic pressure shape function; is the displacement enhancement function of the crack penetrating unit; is the displacement enhancement function of the crack tip unit, where the first term on the right side is the continuous displacement of the conventional finite element part, and the second and third terms are the discontinuous displacement part;

[0012] The extended finite element expression of the seepage pressure under the fluid-solid coupling in S1 is:

[0013] ;

[0014] in, is the set of all percolation nodes; Strengthen the seepage node set for the fracture penetration unit; Strengthen the seepage node set for the crack tip unit; is the conventional continuous osmotic pressure value; , They are the additional degrees of freedom for seepage pressure of the crack penetration unit and the crack tip unit respectively; is the conventional osmotic pressure shape function; is the permeability enhancement function of the fracture penetrating unit; is the crack tip unit seepage pressure enhancement function, where the first term on the right side is the continuous seepage pressure of the conventional finite element part, and the second and third terms are the weak discontinuous seepage pressure parts.

[0015] Furthermore, the boundary conditions in S2 include load boundary, displacement boundary, seepage pressure boundary, flow boundary and fracture boundary;

[0016] The basic equation of soil fluid-solid coupling is expressed as:

[0017] exist Within the domain

[0018] The corresponding boundary conditions are:

[0019] ;

[0020] in, is the total stress tensor, For physical strength, is the mixed flow bulk density; is the permeability coefficient; is the bulk modulus of the mixed fluid in the pore; is the mixed flow osmotic pressure; is the displacement tensor; For flow; is the displacement change rate tensor; is the osmotic pressure change rate; is the adhesion tensor within the crack surface; is the seepage pressure at the fracture surface; is the flow rate from the crack surface into the soil medium They are boundary surface load, displacement constraint, seepage pressure and seepage flow constraint; is the mixed fluid flow rate; express , and represent the positive and negative velocity components of the mixed fluid respectively;

[0021] The basic equation of fracture seepage is expressed as:

[0022] ;

[0023] in: is the permeability coefficient of mixed flow in the fracture; For seam end flow rate; For seam end Osmotic pressure.

[0024] Furthermore, the weak form of the soil fluid-solid coupling equation is:

[0025] ;

[0026] According to the divergence theorem, the boundary conditions are substituted and the weak form of the soil fluid-solid coupling equation related to the boundary conditions is obtained, which is expressed as follows:

[0027] ;

[0028] ;

[0029] in: , Indicates the amount of leakage from the crack surface into the soil, symbol express , and represent the positive and negative velocity components of the mixed fluid respectively;

[0030] Introducing virtual osmotic pressure , and integrate the fracture solution domain to obtain the weak form of the fracture seepage equation, which is expressed as:

[0031] ;

[0032] According to the divergence theorem, the boundary conditions are substituted and the weak form of the fracture seepage equation related to the boundary conditions is obtained, which is expressed as follows:

[0033] .

[0034] Furthermore, S3 discretizes the weak form of the soil fluid-solid coupling equation and expresses it in a matrix as follows:

[0035] ;

[0036] ;

[0037] in:

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045]

[0046] in: is the shape function of the standard finite element; is the displacement enhancement function of the crack penetrating unit; is the crack tip unit displacement enhancement function; is the permeability enhancement function of the fracture penetrating unit; is the crack tip unit seepage enhancement function.

[0047] The weak form of the fracture seepage equation is discretized in the spatial domain, and its expression is:

[0048] ;

[0049] Where: , , , , is the seepage rate at the crack end.

[0050] Furthermore, the extended finite element form of the weak form equation is discretized in time, and the soil fluid-solid coupling equation is discretized in the time domain, and its expression is:

[0051] ;

[0052] ;

[0053] In short:

[0054] ;

[0055] ;

[0056] The mixed fluid seepage equation in the fracture is discretized in the time domain, and its expression is:

[0057] .

[0058] Furthermore, the joint solution is divided into two parts: soil fluid-solid coupling solution and fracture seepage solution.

[0059] The soil fluid-solid coupling analysis process is as follows:

[0060] S401: Divide the soil grid and arrange the initial crack positions;

[0061] S402: Apply loads and boundary conditions within the load increment step;

[0062] S403: Assign initial parameters to materials , including deformation modulus, bulk modulus, mixed fluid bulk modulus, permeability coefficient and crack aperture, to construct the stiffness matrix and adhesion stiffness matrix of the soil;

[0063] S404: Determine the seepage pressure boundary and water pressure load at the fracture surface;

[0064] S405, calculating the displacement field, stress field, and seepage pressure field, and calculating the soil deformation modulus, bulk modulus, mixed fluid bulk modulus, permeability coefficient, and crack opening according to the calculated deformation, stress, and seepage pressure;

[0065] S406. Compare the calculated material parameters mat with the initial parameters , if it is within the given error range, continue; if it is not within the range, update the parameters and repeat the calculation;

[0066] S407, calculating the leakage amount of soil at the crack surface;

[0067] S408, compare the calculated fracture surface leakage q1 with the initial leakage q0 of the fracture seepage part, if it is within the given error range, then enter S409, otherwise set q0=q1, go to the fracture seepage part, go to step S413 of the fracture seepage part, perform fracture seepage, obtain the seepage pressure at the fracture surface and then return to S404;

[0068] S409, judging whether the cracking criterion is satisfied, if the cracking criterion is satisfied, then the updated level set of crack extension returns to S403, and at the same time goes to step S411 of the fracture seepage solution, otherwise, execute S410;

[0069] S410, determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to S402, if the load step is completed, output the calculation results;

[0070] The fracture seepage solution process is:

[0071] S411, dividing the crack grid, and reading the unit and node information;

[0072] S412, assigning material parameters and establishing a stiffness matrix of the crack;

[0073] S413, applying fracture boundary conditions and giving an initial leakage amount q0;

[0074] S414. Solve the seepage pressure and enter the soil fluid-solid coupling analysis step S404.

[0075] Beneficial effects: Compared with the prior art, the advantages of the present invention are: the present invention uses the extended finite element method to simulate the expansion of cracks without predetermining the crack path. The extended finite element method divides the deformation into two parts: continuous deformation and discontinuous deformation, and uses the enhancement function to handle the discontinuous deformation at the crack; when the seepage field at the crack changes, the seepage pressure is decomposed into two parts: continuous seepage pressure and weak discontinuous seepage pressure, and the seepage field at the crack is handled by the extended finite element method. This process does not require the predetermination of the crack path, reduces the need for mesh encryption, thereby simplifying the calculation process, reducing the calculation complexity and workload; the analysis method can flexibly adapt to the situation where the crack expansion path is uncertain in practice, and is more in line with the actual needs of the project.

[0076] Through the expressions of displacement and seepage pressure, the continuous deformation and discontinuous deformation, continuous seepage pressure and weak discontinuous seepage pressure at the crack are expressed respectively, which enhances the ability to describe the behavior at the crack; virtual displacement and virtual seepage pressure are introduced to perform weak form treatment on the fluid-solid coupling equation and the fracture seepage equation, and the divergence theorem is applied in combination with boundary conditions to improve the operability of equation solving; based on the back difference method, any field variable is discretized in the time domain to ensure the stability of the time stepping solution; the soil fluid-solid coupling equation and the fracture seepage equation are jointly solved iteratively to ensure the convergence and accuracy of the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 It is a schematic diagram of the boundary of the seam body in the present invention;

[0078] Figure 2 It is a schematic diagram of the boundary conditions of the crack part of the clay core wall in the present invention;

[0079] Figure 3 It is a flow chart of the analysis of the change of properties of the tensile cracks in the clay core wall by iteratively solving the cracks and soil seepage in the present invention;

[0080] Figure 4 It is a schematic diagram of the dam body material partitioning in the present invention.

[0081] Figure 5 It is a schematic diagram of the change of pore water pressure at the E5 position of the center wall of the present invention;

[0082] Figure 6 It is a schematic diagram of the change of pore water pressure at the E6 position of the center wall of the present invention;

[0083] Figure 7 It is a schematic diagram of the change of pore water pressure at position E7 of the central wall of the present invention. DETAILED DESCRIPTION

[0084] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0085] Example 1: When tension cracks appear in the clay core wall, the displacement jumps at the cracks, resulting in discontinuous deformation. The extended finite element method divides the deformation into two parts: continuous deformation and discontinuous deformation. The corresponding displacement expression is:

[0086] ;

[0087] in, is the set of all displacement nodes; Strengthen the displacement node set for the crack penetration unit; Strengthen the displacement node set for the crack tip element; is the displacement of the continuous deformation of the displacement node; Strengthen the additional degrees of freedom of node displacement for crack penetration elements; Strengthen the node displacement additional degrees of freedom for the crack tip element; is the conventional osmotic pressure shape function; is the displacement enhancement function of the crack penetrating unit; is the displacement enhancement function of the crack tip unit; the first term on the right side is the continuous displacement of the conventional finite element part, and the second and third terms are the discontinuous displacement parts.

[0088] When tension cracks appear in the clay core wall, the seepage field at the cracks will change. The seepage pressure distribution at the cracks remains continuous, but the seepage pressure gradient is discontinuous (weakly discontinuous). Based on the idea of ​​extended finite element solution for discontinuous deformation, the seepage pressure at the cracks is decomposed into continuous seepage pressure and weakly discontinuous seepage pressure. The expression is:

[0089] ;

[0090] Where: is the set of all percolation nodes; Strengthen the seepage node set for the fracture penetration unit; Strengthen the seepage node set for the crack tip unit; is the conventional continuous osmotic pressure value; , They are the additional degrees of freedom for seepage pressure of the crack penetration unit and the crack tip unit respectively; is the conventional osmotic pressure shape function; is the permeability enhancement function of the fracture penetrating unit; is the crack tip unit seepage enhancement function. The first term on the right side of the formula is the continuous seepage of the conventional finite element part, and the second and third terms are the weak discontinuous seepage part.

[0091] The computational domain of the mixed flow fluid-solid coupling analysis model of clay core wall with tension cracks includes the soil part and the crack part, among which the computational domain of the clay core wall soil part is like Figure 1 As shown, the domain contains a crack , boundary conditions include load boundary , displacement boundary , osmotic pressure boundary , Traffic Boundary and crack boundaries For the computational domain When the incremental method is used to solve, assuming that the permeability coefficient is a constant in each incremental step, the fluid-solid coupling equation of the clay core wall soil can be expressed as:

[0092]

[0093] The corresponding boundary conditions are:

[0094] ;

[0095] in, is the total stress tensor, For physical strength, is the mixed flow bulk density; is the permeability coefficient; is the bulk modulus of the mixed fluid in the pore; is the mixed flow osmotic pressure; is the displacement tensor; For flow; is the displacement change rate tensor; is the osmotic pressure change rate; is the adhesion tensor within the crack surface; is the seepage pressure at the fracture surface; is the flow rate from the crack surface into the soil medium They are boundary surface load, displacement constraint, seepage pressure and seepage flow constraint; is the mixed fluid flow rate; express , and They represent the positive and negative velocity components of the mixed fluid respectively.

[0096] For the crack calculation domain in the clay core wall, Figure 2 As shown, the boundary conditions include the osmotic pressure boundary and flow boundaries When the incremental method is used to solve the problem, assuming that the permeability coefficient is a constant in each incremental step, the fracture fluid seepage equation can be expressed as:

[0097] ;

[0098] in: is the permeability coefficient of mixed flow in the fracture; For seam end flow rate; For seam end Osmotic pressure.

[0099] Introducing virtual displacement and virtual seepage pressure, substituting them into the soil fluid-solid coupling equation and integrating the soil solution area, the weak form of the clay core wall soil fluid-solid coupling equation is obtained, and its expression is:

[0100]

[0101]

[0102] According to the divergence theorem, the boundary conditions are substituted and the weak form of the soil fluid-solid coupling equation related to the boundary conditions is obtained, which is expressed as follows:

[0103]

[0104]

[0105] in: , Indicates the amount of leakage from the crack surface into the soil, symbol express , and They represent the positive and negative velocity components of the mixed fluid respectively.

[0106] Introducing virtual osmotic pressure , substituted into the fracture fluid seepage equation and integrated over the fracture solution domain, the weak form of the fracture seepage equation is obtained, which is expressed as:

[0107]

[0108] According to the divergence theorem, the boundary conditions are substituted and the weak form of the fracture seepage equation related to the boundary conditions is obtained, which is expressed as follows:

[0109] .

[0110] According to the Galerkin variational principle, the weak form equations of displacement field and seepage pressure field are discretized and expressed in matrices as follows:

[0111]

[0112]

[0113] in:

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125] in: is the shape function of the standard finite element; is the displacement enhancement function of the crack penetrating unit; is the crack tip unit displacement enhancement function; is the permeability enhancement function of the fracture penetrating unit; is the crack tip unit seepage enhancement function.

[0126] The load matrix is:

[0127] ;

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] ;

[0133] in: They are surface load, body load and node load in the calculation domain respectively; is the water pressure load in the crack; It is the other loads in the calculation domain except the crack surface adhesion and water pressure load.

[0134] The flow value is:

[0135] ;

[0136] ;

[0137] in: is the seepage amount from the crack surface into the soil; is the seepage volume other than the fracture in the calculation domain.

[0138] The weak form of the fracture seepage equation is discretized in the spatial domain, and its expression is:

[0139] ;

[0140] Where: , , , , , is the seepage rate at the crack end.

[0141] The extended finite element form of the weak form equation is discretized in time. According to the back difference method, for any field variable in time arrive The rate of change of the internal field variable can be expressed as:

[0142] .

[0143] The variable change rate formula is used to discretize the variables in the weak form of the soil fluid-solid coupling equation in the time domain, and its expression is:

[0144] ;

[0145] ;

[0146] The above formula can be abbreviated as:

[0147] ;

[0148] ;

[0149] The variable change rate formula is used to discretize the variables in the mixed fluid seepage equation in the fracture in the time domain, and its expression is:

[0150] .

[0151] When there are cracks or weak permeable layers (regarded as a type of crack) on the upstream surface of the clay core wall, it is necessary to jointly solve the soil fluid-solid coupling equation and the fracture seepage equation in the process of analyzing the change in the tensile crack properties of the clay core wall.

[0152] For the soil fluid-solid coupling equation, the water pressure load on the crack surface The fracture width and the seepage volume of the fracture surface are unknown. is unknown and needs to be calculated through the soil fluid-solid coupling equation. Therefore, when solving the soil fluid-solid coupling equation and the fracture seepage equation, both need to be solved iteratively. The solution process is as follows: Figure 3 As shown in the figure, the solution is divided into two parts: fluid-solid coupling analysis of the soil medium part and seepage analysis of the crack part.

[0153] The soil fluid-solid coupling analysis process is as follows:

[0154] S401: Divide the soil grid and arrange the initial crack positions;

[0155] S402: Apply loads and boundary conditions within the load increment step;

[0156] S403: Assign initial parameters to materials , including deformation modulus, bulk modulus, mixed fluid bulk modulus, permeability coefficient and crack aperture, to build stiffness matrix and adhesion stiffness matrix, and to establish stiffness matrix and adhesion stiffness matrix of soil part;

[0157] S404: Determine the seepage pressure boundary and water pressure load at the fracture surface;

[0158] S405, calculating the displacement field, stress field, and seepage pressure field, and calculating the soil deformation modulus, bulk modulus, mixed fluid bulk modulus, permeability coefficient, and crack opening according to the calculated deformation, stress, and seepage pressure;

[0159] S406. Compare the calculated material parameters mat with the initial parameters , if it is within the given error range, continue; if it is not within the range, update the parameters and repeat the calculation;

[0160] S407, calculating the leakage amount of soil at the crack surface;

[0161] S408, compare the calculated fracture surface leakage q1 with the initial leakage q0 of the fracture seepage part, if it is within the given error range, then enter S409, otherwise set q0=q1, go to the fracture seepage part, go to step S413 of the fracture seepage part, perform fracture seepage, obtain the seepage pressure at the fracture surface and then return to S404;

[0162] S409, judging whether the cracking criterion is satisfied, if the cracking criterion is satisfied, then the updated level set of crack extension returns to S403, and at the same time goes to step S411 of the fracture seepage solution, otherwise, execute S410;

[0163] S410, determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to S402, if the load step is completed, output the calculation results;

[0164] The fracture seepage solution process is:

[0165] S411, dividing the crack grid, and reading the unit and node information;

[0166] S412, assigning material parameters and establishing a stiffness matrix;

[0167] S413, applying fracture boundary conditions and giving an initial leakage amount q0;

[0168] S414. Solve the seepage pressure and enter the soil fluid-solid coupling analysis step S404.

[0169] Example 2: The mixed flow-solid coupling extended finite element program for clay core with tension cracks provided in Example 1 is used to analyze the behavior changes of tension cracks in the core of the Hyttejuvet narrow core rockfill dam in Norway.

[0170] The Hyttejuvet Dam in Norway is a narrow core rockfill dam with a crest elevation of 749m, a maximum dam height of 93m, a crest length of nearly 400m, and a normal water level of 745m. Figure 4 As shown in the figure, there are three measuring points E5, E6 and E7. The dam body materials are mainly composed of ① moraine soil, ② transition material, ③ gravel, ④ excavated material, ⑤ rockfill material and ⑥ block stone. The dam body filling process is divided into two phases of construction. The first phase is constructed to an elevation of 700m. The pore pressure sensor monitoring shows that the excess pore water pressure inside the core wall is too high. During the second phase of construction, the pore water pressure dissipation is accelerated by reducing the thickness of the core wall. Above the elevation of 727.8m, a vertical narrow core wall with a width of 4m is used.

[0171] Water storage began in May 1966, and reached the normal water level of 745m in October 1966. Before the water level reached 738m, the seepage rate measured by the downstream water measuring weir was less than 1~2L / s. After exceeding 738m, the downstream seepage rate increased significantly, reaching a maximum of 63L / s, and the seepage water was turbid, indicating a serious leakage problem. Subsequently, the water storage speed slowed down and the seepage rate began to decrease. A few months later, the reservoir was emptied, and when the water level dropped to 717m, the seepage rate dropped to less than 10L / s. Afterwards, the accident was analyzed and it was believed that the increase in leakage was caused by hydraulic fracturing in the core wall. After investigation, it was believed that the hydraulic fracturing occurred at the core wall at an elevation of 710m~730m.

[0172] The mixed flow-solid coupling extended finite element analysis method of clay core with tension cracks developed by the present invention is used to calculate and analyze the change of tension crack properties of Hyttejuvet core rockfill dam. For the convenience of research, it is assumed that the soil parameters of the filter layer and transition layer are the same as those of the dam shell rockfill material, and the extended Duncan EB model is used for the tension part. Many scholars believe that the existence of a weak seepage surface on the upstream side of the core wall is a necessary condition for hydraulic fracturing when analyzing the accident of sudden increase in seepage of Hyttejuvet core rockfill dam. Therefore, when analyzing the change of tension crack properties of the core wall, a 20cm thick and 2m long weak seepage layer is arranged at an elevation of 720m on the upstream side of the core wall, and the permeability coefficient of the weak seepage layer is 1m / d. According to the geometric dimensions of the dam body and the core wall, a two-dimensional or three-dimensional geometric model is established, including the soil body and the core wall.

[0173] Set material parameters according to the properties of different materials, such as deformation modulus, permeability coefficient, density, etc.

[0174] Characterization of cracks in the core wall using displacement enhancement functions in XFEM:

[0175] Crack propagation path: Determine the possible crack propagation path based on the initial pore water pressure and stress state;

[0176] Displacement Enhancement Function: Use displacement enhancement function to simulate deformation discontinuity at cracks.

[0177] According to the seepage pressure changes of the core wall and soil, the seepage pressure model is constructed, and the seepage pressure is decomposed into two parts: continuous seepage pressure and weak discontinuous seepage pressure.

[0178] Initial condition setting: Set the initial stress and seepage pressure conditions, including the initial water level, the initial stress state of the dam material, etc.

[0179] Boundary condition setting: Boundary conditions are set according to the actual situation of the dam body, including: water pressure boundary conditions: the pressure of water on the dam body, foundation constraint boundary conditions: the constraint of the foundation on the dam body.

[0180] The behavior changes of the core wall tension cracks are simulated by using the iterative solution method of XFEM combined with the fluid-solid coupling equation.

[0181] Solution process:

[0182] Initial iteration: Calculate the initial stress and seepage pressure distribution;

[0183] Iterative update: Update the displacement and seepage pressure fields at each time step;

[0184] Convergence judgment: Determine whether the convergence conditions are met. If not, continue iterating.

[0185] According to the numerical solution results, the expansion path of the core wall cracks and the changes in crack morphology are analyzed;

[0186] Analyze the changes in seepage pressure at the cracks and inside the entire core wall to evaluate the effect of pore water pressure dissipation;

[0187] Through the calculation results, the displacement and stress field distribution of the core wall and dam body are obtained, and the structural stability is evaluated.

[0188] Figure 5~Figure 7 The calculated values ​​and monitored values ​​of the pore water pressure at the E5, E6, and E7 measuring points inside the core wall during the construction period and the water storage period are compared. It can be seen that during the filling period, as the filling height increases, the pore water pressure in each part of the core wall increases synchronously; during the construction interval and from the completion of filling to the water storage, the pore water pressure dissipates; during the water storage process, as the upstream water level rises, the pore water pressure inside the core wall also gradually increases. The calculated pore water pressure values ​​are generally close to the measured values, which shows the reliability of the calculation method.

[0189] During the construction and water storage process, as the load on the upper soil increases during the filling process, the vertical stress at the end gradually increases; in the period from the completion of filling to the water storage, the vertical stress at the end increases slightly due to the partial dissipation of the pore water pressure; when the water storage level exceeds the weak layer, the reservoir water flows into the weak layer, and the water load generated by the reservoir water produces a tensile effect on the layer surface. As the water level rises, the vertical compressive stress at the end gradually decreases. After the water storage exceeds 738m, tensile stress is generated. When the tensile cracking criterion is met, cracks will occur. Finally, the cracks penetrate the core wall to form a concentrated leakage channel.

[0190] The above calculation and analysis show that the leakage accident of the Hyttejuvet core rockfill dam is mainly caused by hydraulic fracturing at the core wall. The uneven settlement of the rockfill body and the core wall and the pore water pressure during the filling process reduce the vertical stress of the core wall, but no tensile stress occurs. During the water storage process, the existence of the weak seepage layer on the upstream surface of the core wall is the direct cause of hydraulic fracturing. The water load exerts a tensile effect on the weak layer, causing the core wall to crack. Finally, the tensile cracks penetrate the core wall and form a concentrated leakage channel. The analysis results of this embodiment are basically consistent with the on-site monitoring and accident phenomena, indicating that the fluid-solid coupling expansion finite element simulation of cracks with tensile cracks proposed in this embodiment is feasible.

[0191] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A method for analyzing the behavior change of tension cracks in clay core wall under fluid-solid coupling, characterized in that: The steps include: S1: Based on the extended finite element method, a fluid-solid coupling analysis model of mixed flow in clay core wall with tension cracks is established, and the extended finite element expressions of displacement and seepage pressure under fluid-solid coupling are determined; The extended finite element expression of displacement under fluid-solid coupling in S1 is: ； in, is the set of all displacement nodes; Strengthen the displacement node set for the crack penetration unit; Strengthen the displacement node set for the crack tip element; is the displacement of the continuous deformation of the displacement node; Strengthen the additional degrees of freedom of node displacement for crack penetration elements; Strengthen the node displacement additional degrees of freedom for the crack tip element; is the conventional osmotic pressure shape function; is the displacement enhancement function of the crack penetrating unit; is the displacement enhancement function of the crack tip unit; the first term on the right side is the continuous displacement of the conventional finite element part, and the second and third terms are the discontinuous displacement part; The extended finite element expression of the seepage pressure under the fluid-solid coupling in S1 is: ； in, is the set of all percolation nodes; Strengthen the seepage node set for the fracture penetration unit; Strengthen the seepage node set for the crack tip unit; is the conventional continuous osmotic pressure value; , They are the additional degrees of freedom for seepage pressure of the crack penetration unit and the crack tip unit respectively; is the conventional osmotic pressure shape function; is the permeability enhancement function of the fracture penetrating unit; is the crack tip unit seepage pressure enhancement function, where the first term on the right side is the continuous seepage pressure of the conventional finite element part, and the second and third terms are the weak discontinuous seepage pressure part; S2: Analysis model calculation domain, including soil calculation domain and crack calculation domain , set boundary conditions; construct the basic equation of soil fluid-solid coupling, introduce virtual displacement and virtual osmotic pressure , substitute the basic equation and integrate the soil calculation domain to obtain the weak form of the soil fluid-solid coupling equation. According to the divergence theorem and the introduction of boundary conditions, the weak form of the soil fluid-solid coupling equation related to the boundary conditions is obtained; the basic equation of fracture seepage is constructed and the virtual seepage pressure is introduced. , substitute the basic fracture seepage equation to integrate the fracture solution domain, and obtain the weak form of the fracture seepage equation. According to the divergence theorem and introducing boundary conditions, the weak form of the fracture seepage equation related to the boundary conditions is obtained; S3: Substitute the extended finite element expressions of displacement and seepage pressure into the weak form of the soil fluid-solid coupling equation and the weak form of the fracture seepage equation, and discretize them in the space domain and time domain to obtain the discrete form of the soil fluid-solid coupling equation and the discrete form of the fracture seepage equation; S4: The discrete form of the soil fluid-solid coupling equation and the discrete form of the fracture seepage equation are jointly solved, the initial crack width and seepage pressure value are set, the crack width and seepage pressure value are updated through iterative calculation until the convergence conditions are met, and the calculation results are output.

2. The method for analyzing the change of properties of tensile cracks in clay core wall under fluid-solid coupling according to claim 1 is characterized in that: The boundary conditions in S2 include load boundary, displacement boundary, seepage pressure boundary, flow boundary and fracture boundary; The basic equation of soil fluid-solid coupling is expressed as: ； The corresponding boundary conditions are: ； in, is the total stress tensor, For physical strength, is the mixed flow bulk density; is the permeability coefficient; is the bulk modulus of the mixed fluid in the pore; is the mixed flow osmotic pressure; is the displacement tensor; For flow; is the displacement change rate tensor; is the osmotic pressure change rate; is the adhesion tensor within the crack surface; is the seepage pressure at the fracture surface; is the flow rate from the crack surface into the soil medium They are boundary surface load, displacement constraint, seepage pressure and seepage flow constraint; is the mixed fluid flow rate; express , and represent the positive and negative velocity components of the mixed fluid respectively; The basic equation of fracture seepage is expressed as: ； in: is the permeability coefficient of mixed flow in the fracture; For seam end flow rate; For seam end Osmotic pressure.

3. The method for analyzing the change of properties of tensile cracks in clay core wall under fluid-solid coupling according to claim 2 is characterized in that: The weak form of the soil fluid-solid coupling equation is: ； According to the divergence theorem, the boundary conditions are substituted and the weak form of the soil fluid-solid coupling equation related to the boundary conditions is obtained, which is expressed as follows: ； ； in: , Indicates the amount of leakage from the crack surface into the soil, symbol express , and represent the positive and negative velocity components of the mixed fluid respectively; Introducing virtual osmotic pressure , and integrate the fracture solution domain to obtain the weak form of the fracture seepage equation, which is expressed as: ； According to the divergence theorem, the boundary conditions are substituted and the weak form of the fracture seepage equation related to the boundary conditions is obtained, which is expressed as follows: 。 4. The method for analyzing the change of tensile crack properties of clay core wall under fluid-solid coupling according to claim 3 is characterized in that: The S3 discretizes the weak form of the soil fluid-solid coupling equation and is expressed in a matrix as follows: ； ； in: ; ； ； ； ； ； ； ； ； ； ； in: is the shape function of the standard finite element; is the displacement enhancement function of the crack penetrating unit; is the crack tip unit displacement enhancement function; is the permeability enhancement function of the fracture penetrating unit; is the crack tip unit seepage enhancement function; The weak form of the fracture seepage equation is discretized in the spatial domain, and its expression is: ； Where: , , , , , is the seepage rate at the crack end.

5. The method for analyzing the change of properties of tension cracks in clay core wall under fluid-solid coupling according to claim 4 is characterized in that: The extended finite element form of the weak form equation is discretized in time, and the soil fluid-solid coupling equation is discretized in the time domain, and its expression is: ； ； In short: ； ； The mixed fluid seepage equation in the fracture is discretized in the time domain, and its expression is: 。 6. The method for analyzing the change of properties of tension cracks in clay core wall under fluid-solid coupling according to claim 5 is characterized in that: The joint solution is divided into two parts: soil fluid-solid coupling solution and fracture seepage solution. The soil fluid-solid coupling analysis process is as follows: S401: Divide the soil grid and arrange the initial crack positions; S402: Apply loads and boundary conditions within the load increment step; S403: Assign initial parameters to materials , including deformation modulus, bulk modulus, mixed fluid bulk modulus, permeability coefficient and crack aperture, to construct the stiffness matrix and adhesion stiffness matrix of the soil; S404: Determine the seepage pressure boundary and water pressure load at the fracture surface; S405, calculating the displacement field, stress field, and seepage pressure field, and calculating the soil deformation modulus, bulk modulus, mixed fluid bulk modulus, permeability coefficient, and crack opening according to the calculated deformation, stress, and seepage pressure; S406. Compare the calculated material parameters mat with the initial parameters , if it is within the given error range, continue; if it is not within the range, update the parameters and repeat the calculation; S407, calculating the leakage amount of soil at the crack surface; S408, compare the calculated fracture surface leakage q1 with the initial leakage q0 of the fracture seepage part, if it is within the given error range, then enter S409, otherwise set q0=q1, go to the fracture seepage part, go to step S413 of the fracture seepage part, perform fracture seepage, obtain the seepage pressure at the fracture surface and then return to S404; S409, judging whether the cracking criterion is satisfied, if the cracking criterion is satisfied, then the updated level set of crack extension returns to S403, and at the same time goes to step S411 of the fracture seepage solution, otherwise, execute S410; S410, determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to determine whether the load step is completed, if not enter the next increment, return to S402, if the load step is completed, output the calculation results; The fracture seepage solution process is: S411, dividing the crack grid, and reading the unit and node information; S412, assigning material parameters and establishing a stiffness matrix of the crack; S413, applying fracture boundary conditions and giving an initial leakage amount q0; S414. Solve the seepage pressure and enter the soil fluid-solid coupling analysis step S404.

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