CN-122020955-A - Dynamic fracture analysis and calculation method for concrete panel of earth-rock dam containing cracks

CN122020955ACN 122020955 ACN122020955 ACN 122020955ACN-122020955-A

Abstract

The invention discloses a dynamic fracture analysis and calculation method for a concrete panel of a earth-rock dam containing cracks, and relates to the technical field of dynamic fracture analysis of engineering structures. Obtaining panel, material and load parameters, constructing a discontinuous grid model composed of polygonal units which are not connected with each other, solving Laplace equation based on a proportional boundary finite element method to generate a proportional boundary shape function, establishing material point pairs through near field search, correcting boundary key parameters, combining shape function and material point interaction relation to assemble a global stiffness matrix, after applying boundary conditions and load, carrying out incremental solution by adopting a central difference method to obtain a node displacement field, judging the breaking state of the material point pairs according to a breaking criterion, updating the stiffness matrix, circularly recording the damage variable and displacement data of each incremental step, and outputting a dynamic breaking analysis result. According to the method, three-dimensional grid division is not needed, calculation accuracy and efficiency are considered, the whole crack propagation process can be accurately captured, and technical support is provided for design optimization and safety prevention and control of the earth-rock dam panel.

Inventors

GAN LEI
SUN YIQING
SONG XINWEI
LIU JUN
YU WEI
JIANG ZHENGYI
YE WENBIN
WANG PEIQING
LIU XIAOLI
CHEN LIANG
ZHANG ZHEN

Assignees

西藏农牧大学
大连理工大学
河海大学

Dates

Publication Date: 20260512
Application Date: 20251217

Claims (10)

1. A dynamic fracture analysis and calculation method for a concrete panel of a earth-rock dam containing cracks is characterized by comprising the following steps: parameters of concrete panels, materials and external loads of the earth-rock dam containing the cracks are obtained, wherein the parameters comprise panel geometric dimensions, crack parameters, material mechanical properties and load boundary conditions; Constructing a discontinuous grid model composed of polygonal units which are not connected with each other, solving a Laplace equation based on a proportional boundary finite element method, and generating a proportional boundary shape function corresponding to each polygonal unit; Carrying out neighborhood search on each material point in the model in a near field range with a limited radius, establishing material point pairs, forming interaction keys, and correcting key parameters of a boundary area based on a strain energy density equivalent principle; Calculating the rigidity matrix of each polygonal unit according to the interaction relation between the proportional boundary shape function and the material points, and assembling the rigidity matrix into a global rigidity matrix; Applying boundary conditions and external loads, and obtaining node displacement fields of all incremental steps by solving a system balance equation in an incremental solution cycle; evaluating the deformation state of the material point pairs based on the node displacement field, judging whether bonds are broken according to a preset breaking criterion, and updating the global stiffness matrix if the bonds are broken; recording unit damage variables and node displacement data of each increment step, circularly executing increment solving until all increment steps are completed, and outputting a dynamic fracture analysis result.
2. The method for dynamic fracture analysis and calculation of concrete panels of a concrete dam containing cracks according to claim 1, wherein the construction of the discontinuous grid model is performed in a Cartesian coordinate system Establishing a two-dimensional structure model, establishing a proportional boundary coordinate system by the polygon unit through proportional boundary coordinate transformation, and marking the radial sitting mark as The circumferential sitting mark is A polygonal unit is discretized into a plurality of triangular sector-shaped subfields, each subfield being defined by a similar center and two end points of the line unit, the similar center corresponding to Line unit corresponds to The nodes at the two ends of the line unit are respectively mapped to And The physical coordinates of any point within the subdomain satisfy: , , wherein, As line unit nodes A set of directional coordinates, As line unit nodes A set of directional coordinates, As a function of the shape of the line element.
3. The method for analyzing and calculating the dynamic fracture of the concrete panel of the earth-rock dam with the cracks according to claim 2, wherein the transformation relation between the global coordinates and the proportional boundary coordinates is as follows: , wherein, Is a jacobian matrix of line elements, For any point within a subdomain The physical coordinates of the direction are used, For any point within a subdomain The physical coordinates of the direction are used, Is that For the circumferential coordinates Is used for the partial derivative of (a), Is that For the circumferential coordinates And (2) partial derivatives of , , For a form function For a pair of Partial derivatives of) jacobian matrix 。
4. The method for analyzing and calculating dynamic fracture of concrete panel of earth-rock dam with crack as set forth in claim 1, wherein said solving Laplace equation is characterized in that differential operator The expression of (2) is: , wherein, , Laplace equation , The potential function of a certain point in the triangular sector is converted into a proportional boundary finite element control equation by a weighted residual value method: , wherein, For a radial analytical solution of the potential function, Is that For a pair of Is used for the first partial derivative of (c), Is that For a pair of Is used for the first order partial derivative of (a), 、、 As a matrix of coefficients, Is that Is used to determine the transposed matrix of (a), 。
5. The method for analyzing and calculating dynamic fracture of concrete panel of earth-rock dam with crack according to claim 4, wherein the expression of the proportional boundary shape function is: Wherein, the As a function of the shape of the line elements, As a matrix of feature vectors, As a value of the characteristic(s), Is that An inverse matrix of (a); The finite element format of the shape function is: , wherein, As the number of nodes of the unit, And (5) a proportional boundary shape function component corresponding to each node.
6. The method for dynamic fracture analysis and calculation of concrete panel of earth-rock dam with crack according to claim 1, wherein the material point pairs are established by interpolating unit node coordinates And displacement of Obtaining coordinates of Gaussian points Displacement of : , , wherein, Is Gaussian point The corresponding function of the shape is a function of the shape, Is a set of coordinates for a unit node, A displacement set for the unit node; relative position vector between two Gaussian points , For the coordinates and relative displacement vector of another Gaussian point , Is the displacement of another gaussian point; boundary region key parameter correction is based on strain energy density equivalence, micro modulus function The method meets the following conditions: Wherein, the Is a material point A collection of other material points within the neighborhood, For a near-field radius, Is a material point And neighborhood material point Is used to determine the relative position vector of (a), Is that Is used for the mold length of the mold, Is a neighborhood material point Is defined by the volume of (a), In order to be the modulus of elasticity of the material, Is the Poisson's ratio of the material, and the material point under the condition of conservation of momentum And (3) with Micro modulus therebetween 。
7. The method for dynamic fracture analysis and calculation of concrete panel of earth-rock dam with cracks according to claim 1, wherein the micro-rigidity matrix is introduced when the rigidity matrix of the unit is calculated : , wherein, As a relative position vector And near field radius The relative micro-modulus of the material, Is that Is used for the mold length of the mold, , 、 The x-direction coordinates of the two material points respectively, , 、 The y-direction coordinates of the two material points are respectively; The bond force density vector between the material points satisfies Wherein Is a material point Acting on Is defined by the key force density vector of (a), Is a material point Is defined by the volume of (a), In the form of a matrix of key-force stiffness, 、 The unit stiffness matrix is obtained by circularly summing the key-force stiffness matrix.
8. The method for analyzing and calculating dynamic fracture of concrete panel of earth-rock dam with crack according to claim 1, wherein the incremental solution adopts a central difference method and acceleration And speed of The displacement formula is as follows: , , wherein, For the current time period of time, In a single step of time increment, Is that The node displacement vector of the moment in time, Is that The node displacement vector of the moment in time, Is that Node displacement vector of moment; Equation of motion , In the form of a quality matrix, As a matrix of the global stiffness, External load vector at time t) is: The initial conditions are satisfied Wherein As a result of the initial displacement vector, As a result of the initial velocity vector, , As an external load vector at the initial moment, Is that Is a matrix of inverse of (a).
9. The method for dynamic fracture analysis and calculation of a concrete panel of a earth-rock dam containing a crack according to claim 1, wherein the elongation of bonds in the fracture criteria Wherein Is the initial relative position vector of the material point pair, Is the relative displacement vector of the material point pair, Is that Is used for the mold length of the mold, Is that Is a die length of (2); fracture parameters Wherein The critical elongation is expressed as: , In order for the material to break up in energy, In order to be the modulus of elasticity of the material, Is the radius of the near field; The damage degree quantitative equation is Wherein Is a material point Is used for the damage variable of (a), Is a material point Is provided in the near field region of (c), Is the volume of the micro-element in the near field region.
10. The method for dynamic fracture analysis and calculation of a concrete panel of a earth-rock dam with cracks according to claim 1, wherein after the global stiffness matrix is assembled, the formula of the system momentum equation is as follows Wherein In the form of a quality matrix, As the node acceleration vector, the acceleration vector, As a matrix of the global stiffness, As the displacement vector of the node, Is an external load vector; in the cyclic solving process, each increment step updates the unit damage variable and the global stiffness matrix according to the fracture criterion, and the output dynamic fracture analysis result comprises a damage distribution cloud chart, node displacement time sequence data and a crack propagation path curve of each unit.

Description

Dynamic fracture analysis and calculation method for concrete panel of earth-rock dam containing cracks Technical Field The invention relates to the technical field of dynamic fracture analysis of engineering structures, in particular to a dynamic fracture analysis and calculation method for a concrete panel of a earth-rock dam containing cracks. Background The concrete panel of the earth-rock dam is used as a core component of a dam seepage-proofing system, and the structural integrity of the concrete panel is directly related to the safety and stability of the whole engineering. In the long-term operation process, the concrete panel inevitably generates initial microcracks due to the influence of various factors such as shrinkage, temperature change, uneven settlement of the foundation, external load and the like. More serious, under the action of strong dynamic loads such as earthquake, explosion and the like, the existing cracks are easy to rapidly spread and penetrate, so that the seepage-proofing function of the panel is completely disabled, and catastrophic dam instability and burst are caused. Therefore, the method carries out accurate numerical simulation on the mechanical response, crack propagation path and fracture process of the concrete panel with the cracks under dynamic load, and has important theoretical significance and engineering value for evaluating the safety of the existing structure, carrying out antiknock and antiknock design and formulating a scientific reinforcement and repair scheme. Classical continuous media mechanics frameworks face inherent challenges in modeling material fracture failure. Based on a control equation of a continuous displacement field and a spatial derivative hypothesis, displacement discontinuous areas such as crack tips can fail. In order to overcome the limitation, the academic community develops a plurality of numerical methods, wherein near-field dynamics adopts a non-local integral form to describe interaction force among material points, the damage process is directly simulated through progressive fracture of bonds, the problem of stress singular points at discontinuities is naturally avoided, the method is suitable for simulating the whole process from continuous to complete fracture of materials, and the method is widely applied to fracture analysis in the fields of rock and soil, composite materials, thermal stress and the like. However, near field dynamics itself has problems of high computational cost, significant surface effects, uniform dispersion, complex boundary condition application, and the like. For this reason, researchers have proposed PD and FEM coupling strategies based on the intermittent Galerkin method, which effectively simulate the fracture process while retaining the computational advantage of finite elements. Such methods typically embed PD bond forces in the galy weak form, improve computational efficiency by constructing a symmetric stiffness matrix or reconstructing an integral domain, and develop adaptive coupling techniques based on morphological functions or node transformations. At present, quadrilateral grids are mostly adopted in research, but for complex geometric models, unstructured polygonal grids have better adaptability. The polygonal function is still scarce in its application in such coupling methods due to its difficulty to build in the traditional finite element framework. Therefore, a dynamic fracture computing technology which can be closely attached to the engineering environment of earth and rockfill dams and avoid the limitation of pure theory derivation is needed to fill the gap between the numerical method and the actual demands of hydraulic engineering. Disclosure of Invention Based on the technical problems, the application discloses a dynamic fracture analysis and calculation method for a concrete panel of a earth-rock dam with cracks, which specifically comprises the following steps: parameters of concrete panels, materials and external loads of the earth-rock dam containing the cracks are obtained, wherein the parameters comprise panel geometric dimensions, crack parameters, material mechanical properties and load boundary conditions; Constructing a discontinuous grid model composed of polygonal units which are not connected with each other, solving a Laplace equation based on a proportional boundary finite element method, and generating a proportional boundary shape function corresponding to each polygonal unit; Carrying out neighborhood search on each material point in the model in a near field range with a limited radius, establishing material point pairs, forming interaction keys, and correcting key parameters of a boundary area based on a strain energy density equivalent principle; Calculating the rigidity matrix of each polygonal unit according to the interaction relation between the proportional boundary shape function and the material points, and assembling the rigidity matrix into a global