A macroscopic step-by-step coupled multi-scale stress-deformation calculation method for rockfill dams

Abstract

The present invention discloses a macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dams, which belongs to the technical field of numerical simulation of rockfill dams. The full-scale numerical calculation of the rockfill dam is performed based on the finite element method framework. For areas with serious particle crushing, the strain increment at the Gaussian point calculated in the macroscopic finite element framework is used as the boundary condition, and the boundary element-discrete element joint method is used to simulate the microscopic mechanical evolution process of the characterization element replacing the Gaussian point, so as to consider the microscopic particle crushing phenomenon, and feedback the stress and tangent modulus to the overall stiffness matrix required in the finite element framework solution process at the macroscopic level; for other areas, the stress and tangent modulus at the Gaussian point are directly calculated based on the constitutive model and the strain increment; finally, after the overall stiffness matrix is ​​integrated, the macroscopic mechanical characteristics of the rockfill dam are calculated based on the finite element solver. The present invention improves the calculation efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical calculation of rockfill dams, and more specifically, relates to a macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dams. Background Art

[0002] According to statistics, earth-rock dams account for more than 95% of the dams built in my country. As a type of earth-rock dam, rockfill dams have many advantages compared to other types of dams, such as simple construction technology, low engineering cost, easy access to local materials, strong adaptability to geological conditions, and high seismic performance. Dam settlement and deformation are one of the core issues that restrict the service life of rockfill dams. Uneven settlement and deformation beyond the design range will cause the concrete face plate to be detached from the rockfill body, aggravating uneven force, and then causing cracks, destroying the anti-seepage system, and affecting the safety and stability of the rockfill dam during operation.

[0003] In recent years, with the development of modern dam-building equipment and technology, the design height of rockfill dams has gradually increased. A large number of 200m and 300m high rockfill dams have been put into construction and operation in my country, such as: Nuozadu gravel-soil core rockfill dam (261.5m), Yalong River Lianghekou gravel-soil core rockfill dam (295m), Dadu River Shuangjiangkou gravel-soil core rockfill dam (312m), Lancang River Rumei gravel-soil core rockfill dam (315m). Engineering practice shows that ultra-high rockfill dams exhibit deformation behavior evolution laws that are not completely the same as those of medium and low dams. One of the key reasons is that the natural multi-scale structural characteristics of the rockfill body (the microscopic structural characteristics will affect the macroscopic mechanical properties of the rockfill body) are more prominent in ultra-high rockfill dams. Specifically, due to the complex topography, geology and operating environment of ultra-high rockfill dams, large dam and foundation loads and high stress levels, microscopic characteristics represented by rockfill body crushing (which will cause changes in the engineering design grading of rockfill materials, volume shrinkage and deformation, and thus lead to uneven settlement and deformation of the rockfill dam) are more likely to occur.

[0004] Rockfill dams are composed of discrete particles at the microscopic level, and are usually treated as continua at the macroscopic level. Based on finite element and other continuum mechanics methods, scholars have proposed numerous constitutive models of rockfill bodies, and used these constitutive relations to reflect the nonlinearity, elastic-plasticity, dilatancy and anisotropy of rockfill bodies, which have been widely used in practical engineering problems. However, the stress-strain relationship of rockfill bodies is mainly based on the empirical summary at the macroscopic scale, and it is difficult to reflect the mechanical properties of rockfill bodies from a mechanistic perspective. On the other hand, although the mesoscopic model can accurately simulate the mechanical property process of particle assembly and model the entire macroscopic domain of the particle system as a collection of single particles for numerical simulation, the amount of calculation is too large and it is difficult to achieve an organic balance with the computational efficiency. Therefore, the multi-scale method that combines the numerical model of rockfill at the mesoscopic scale with the continuum model at the macroscopic scale is a reasonable solution, which can make full use of the advantages of both continuous and non-continuous medium mechanics methods to achieve a balance between computational efficiency and computational accuracy.

[0005] At present, the multi-scale calculation methods of rockfill dams are mostly hierarchical multi-scale methods based on homogenization theory, mainly including computational homogenization method and asymptotic homogenization method. In general, it is necessary to use characterization elements to equalize the material properties of the integral points in the macro unit. The final problem is only solved on the macro grid, which generally reduces the degree of freedom and the amount of calculation. Many scholars at home and abroad have applied the computational homogenization method and asymptotic homogenization method included in this method to the multi-scale study of rockfill bodies and have achieved fruitful results. The finite element method is usually used for macro analysis, but due to the large number of integral points, finding a balance between calculation accuracy and efficiency is still an urgent problem to be solved. Generally speaking, the bottom and upstream areas of high rockfill dams in operation are high stress levels, and the dry-wet alternation and freeze-thaw cycles are "severely affected areas", resulting in frequent particle breakage. The microscopic characteristics of the rockfill body have a more significant impact on the macroscopic mechanical properties. If a multi-scale model considering the microscopic structural characteristics is established for this area, and only macroscopic mechanical analysis is performed in the remaining areas, the calculation efficiency can be improved.

[0006] The technical basis of the present invention is established on the basis of the authorized invention patent "Large-scale particle crushing simulation analysis method and device" (publication number: CN112084647A), which provides a theoretical basis and calculation method for numerical calculation of particle stress and crushing representing volume elements.

[0007] The present invention classifies the integral points in the macroscopic finite element model through qualitative analysis of particle breakage rate and strain increment. For the rockfill breakage-prone areas, a multi-scale model is established at the integral points with higher strain increment. The remaining areas are still calculated based on the finite element method and the constitutive model to establish a macro-order coupled multi-scale calculation method. For the multi-scale analysis area, a macro-scale calculation model is established through the finite element method, and the boundary element-discrete element joint method is used to perform the meso-scale calculation of the rockfill characterization element considering particle breakage and shape, and the stress and tangent modulus are fed back to the integral points in the macro-model. Summary of the invention

[0008] In view of the above defects or improvement needs of the prior art, the present invention proposes a macro-order coupled multi-scale stress-deformation calculation method for rockfill dams, which has extremely high accuracy and effectiveness.

[0009] To achieve the above object, according to one aspect of the present invention, a macro-step coupled multi-scale stress-deformation calculation method for a rockfill dam is provided, comprising:

[0010] S1: Model the given rockfill dam model and numerically discretize it using finite element mesh;

[0011] S2: Based on the mechanical parameters of the rockfill material of the given rockfill dam, a representative volume element numerical model is established, triaxial numerical tests are carried out under complex stress paths, and a qualitative analysis of the stress, strain and particle breakage rate of the representative volume element is performed to determine whether the Gaussian integral point in the macroscopic finite element model needs to be replaced by the microscopic representative volume element.

[0012] S3: Give a macro load increment;

[0013] S4: Solve the consistent tangent modulus of each representative volume element;

[0014] S5: Combined with specific boundary conditions, the finite element method is used to preliminarily solve the overall equilibrium equation Kx=r, where K is the overall stiffness matrix; x is the displacement vector of the node to be solved; and r is the load vector of the external node;

[0015] S6: According to the deformation increment Δx of each finite element Gaussian integration point obtained by solving, all integration points are divided into two categories: macroscopic integration points that do not need to be replaced by representative volume elements and microscopic integration points that need to be replaced by representative volume elements;

[0016] S7: For the microscopic integration points that require the replacement calculation of the representative volume element, the deformation increment Δx is used as the boundary condition to simulate the particle stress and crushing of the corresponding representative volume element until it is stable, and the calculated stress σ and tangent modulus D are fed back to the corresponding microscopic integration point;

[0017] S8: For the macroscopic integration point, the constitutive model is used to solve the stress σ and tangent modulus D of the corresponding integration point;

[0018] S9: Utilize formulas Calculate the residual force, where R is the residual force, Ω is the solution domain, and B T is the transposed matrix of the strain matrix, f is the external node load vector;

[0019] S10: Repeat steps S4 to S9 until R is less than the preset allowable residual error, then x is the final solution;

[0020] S11: Return to step S3 and continue with the next load increment step until the current load increment step is smaller than the final load increment step.

[0021] In some optional embodiments, step S2 comprises:

[0022] The boundary of the representative volume element numerical model is a periodic boundary, which is specifically described as the customary structure along the following vector The translation of P α is a basis vector, α is a positive integer, and takes values ​​from 1 to 3.

[0023] In some optional embodiments, step S2 comprises:

[0024] The numerical method for qualitative analysis of stress, strain and particle breakage rate representing volume elements is a high-performance boundary element-discrete element joint method. The main steps of the high-performance boundary element-discrete element joint method include: using a particle interaction solver to simulate the interaction of large-scale particle assemblies; exporting the calculation results of a certain time step in the particle interaction solver, using modeling software to establish a geometric model of the particles to be solved in the particle internal stress solver, inputting the material parameters, meshing fraction, mesh type and boundary conditions of the particle model to be solved exported from the particle interaction solver, and then using the boundary element method to output the internal stress of the particle geometric model to be solved; the concentrated force on each particle boundary is equivalent to the surface force on the boundary; establishing a control equation, and obtaining the displacement from the control equation Boundary integral equation; convert the domain integral caused by volume force in the displacement boundary integral equation into a boundary integral; establish a local coordinate system for each particle and calculate the transformation matrix for similar particles; discretize the single-particle boundary integral equation, divide the boundary elements, and arrange the nodes in the domain; equate the surface force on each particle boundary to the surface force on the boundary element; calculate the coefficient matrix of a single particle and invert the coefficient matrix; solve the displacement of the boundary node; solve the stress and strain values ​​of the nodes in the domain; determine whether the particle is cracked based on the internal stress value, and use the particle replacement method to replace the broken particles, and return the model information of the replaced particles to the particle interaction solver.

[0025] In some optional embodiments, step S2 comprises:

[0026] The stress in the qualitative analysis of stress, strain and particle breakage rate of the representative volume element refers to the homogenized stress of the representative volume element. Calculated, where σ ij is the tensor form of the mean stress σ, N p is the number of particles, V (p) is the volume of particle p, n is the porosity within the representative volume element, N c is the number of contact points of particle p, i and j are traversal values ​​ranging from 1 to N c A positive integer, is the coordinate position of the i-th contact point of particle p, is the coordinate position of the centroid of particle p, The component of the unit normal vector from the particle centroid to the contact point, is the contact force at the jth contact point of particle p.

[0027] In some optional embodiments, step S4 comprises:

[0028] The method of solving the consistent tangent modulus of each representative volume element is: based on the assumption of uniform strain field, using the following formula Calculate, where V is the volume of the volume element, N c is the number of inter-particle releases, k n and k s are the directional and tangential stiffness moduli of the contact points between particles, n c and t c are the external normal and tangential unit vectors of the contact point between particles, respectively; s c is the branch vector.

[0029] In some optional embodiments, step S7 includes:

[0030] The displacement increment Δx needs to be decomposed into strain increment and rotation increment before being applied as a boundary condition.

[0031] In some optional embodiments, step S7 includes:

[0032] The numerical method used to simulate the particle stress and crushing of the corresponding representative volume element is a high-performance boundary element-discrete element method.

[0033] In some optional embodiments, step S8 includes:

[0034] The constitutive model used is the Duncan-Zhang EB model.

[0035] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0036] According to the macro-order coupled multi-scale stress-deformation calculation method of rockfill dam provided by the present invention, compared with the traditional macroscopic finite element model, it can consider the macroscopic stress changes caused by the frequent particle crushing phenomenon of the mesoscopic structure of the rockfill body under high stress levels, and can largely avoid the shortcomings of "high dams are calculated as small, low dams are calculated as large" in the numerical calculation process of the traditional finite element model, and improve the calculation accuracy. Compared with the existing multi-scale calculation method, the Gaussian integral points in the macroscopic finite element model can be divided into macroscopic and mesoscopic integral points according to their strain size, and only the representative volume element is used for the mesoscopic integral point to perform mesoscopic stress calculation, thereby reducing the amount of calculation. In general, the present invention has achieved a good balance between calculation accuracy and calculation efficiency, has feasibility and reliability, and can be applied to high-precision stress analysis of the full scale of rockfill dams to ensure the safety and reliability of engineering structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic diagram of the calculation flow of a macro-order coupled multi-scale stress-deformation calculation method for a rockfill dam provided by an embodiment of the present invention.

[0038] Figure 2 It is a schematic diagram of a calculation model of a macro-order coupled multi-scale stress-deformation calculation method for a rockfill dam provided in an embodiment of the present invention.

[0039] Figure 3 It is a schematic diagram of a representative volume element model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0041] The present invention classifies the integral points in the macroscopic finite element model through qualitative analysis of particle crushing rate and strain increment. For the areas where rockfill crushing is frequent, the integral points with higher strain increment are used to establish a multi-scale model. The remaining areas are still calculated based on the finite element method and the constitutive model, and a macro-order coupled multi-scale calculation method is established; for the multi-scale analysis area, a macro-scale calculation model is established through the finite element method, and the boundary element-discrete element joint method is used to perform the micro-scale calculation of the rockfill representative element considering particle crushing and shape, and the stress and tangent modulus are fed back to the integral points in the macroscopic model. Compared with the traditional macroscopic finite element model, the present invention can consider the macroscopic stress changes caused by the frequent particle crushing phenomenon of the mesoscopic structure of the rockfill body under high stress levels, and can largely avoid the shortcomings of "high dams are calculated small, low dams are calculated large" in the numerical calculation process of the traditional finite element model, and improve the calculation accuracy. Compared with the existing multi-scale calculation method, the Gaussian integral points in the macroscopic finite element model can be divided into macroscopic and microscopic integral points according to their strain size, and only the representative volume element is used for the microscopic integral point to perform the microscopic stress calculation, thereby reducing the amount of calculation. In general, the present invention achieves a good balance between computational accuracy and computational efficiency, has feasibility and reliability, and can be applied to high-precision stress analysis of the entire scale of rockfill dams to ensure the safety and reliability of engineering structures.

[0042] In the embodiment of the present invention, in order to verify the accuracy and effectiveness, a domestic rockfill dam is selected as an example, and a macroscopic hierarchical coupled multi-scale stress and deformation calculation method for rockfill dam provided by the present invention is adopted, such as Figure 1 As shown, the following steps are included:

[0043] S1: Model the given rockfill dam model and numerically discretize it using finite element mesh;

[0044] S2: Based on the mechanical parameters of the given rockfill material of the rockfill dam, a representative volume element numerical model is established, such as Figure 2 As shown, triaxial numerical tests were conducted under complex stress paths, and qualitative analysis of stress, strain and particle breakage rate of representative volume elements was performed to determine the particle breakage rate threshold value whether the Gaussian integral points in the macroscopic finite element model need to be replaced by microscopic representative volume elements;

[0045] in,

[0046] (1) The boundary of the representative volume element numerical model established is a periodic boundary, which is specifically described as the habitual structure along the following vector The translation of P α is a basis vector, α is a positive integer, and takes values ​​from 1 to 3.

[0047] (2) The numerical method for qualitative analysis of stress, strain and particle breakage rate of representative volume elements is a high-performance boundary element-discrete element combined method.

[0048] (3) Qualitative analysis of stress, strain and particle breakage rate of the representative volume element. The stress here refers to the homogenized stress of the representative volume element. The formula is used Calculated, where σ ij is the tensor form of the mean stress σ, N p is the number of particles, V (p) is the volume of particle p, n is the porosity within the representative volume element, N c is the number of contact points of particle p, i and j are traversal values ​​ranging from 1 to N c A positive integer, is the coordinate position of the i-th contact point of particle p, is the coordinate position of the centroid of particle p, The component of the unit normal vector from the particle centroid to the contact point, is the contact force at the jth contact point of particle p.

[0049] S3: Give a macro load increment;

[0050] S4: Solve the consistent tangent modulus of each representative volume element;

[0051] The method for solving the consistent tangent modulus of each representative volume element is: based on the assumption of uniform strain field, using the following formula Calculate, where V is the volume of the volume element, N c is the number of inter-particle releases, k n and k s are the directional and tangential stiffness moduli of the contact points between particles, n c and t c are the external normal and tangential unit vectors of the contact point between particles, respectively; s c is the branch vector.

[0052] S5: Combined with specific boundary conditions, the finite element method is used to preliminarily solve the overall equilibrium equation Kx=r, where K is the overall stiffness matrix; x is the displacement vector of the node to be solved; and r is the load vector of the external node;

[0053] S6: According to the deformation increment Δx of each finite element Gaussian integration point obtained by solving, all integration points are divided into two categories: macroscopic integration points that do not need to be replaced by representative volume elements and microscopic integration points that need to be replaced by representative volume elements;

[0054] S7: For the microscopic integration points that require the replacement calculation of the representative volume element, the deformation increment Δx is used as the boundary condition to simulate the particle stress and crushing of the corresponding representative volume element until it is stable, and the calculated stress σ and tangent modulus D are fed back to the corresponding microscopic integration point;

[0055] in,

[0056] (1) The displacement increment Δx needs to be decomposed into strain increment and rotation increment before being applied as a boundary condition.

[0057] (2) The numerical method for simulating the particle stress and crushing of the corresponding representative volume element is a high-performance boundary element-discrete element combined method.

[0058] S8: For the macroscopic integration point, the constitutive model is used to solve the stress σ and tangent modulus D of the corresponding integration point;

[0059] Among them, the constitutive model used is the Duncan-Zhang EB model.

[0060] S9: Utilize formulas Calculate the residual force, where R is the residual force, Ω is the solution domain, and B T is the transposed matrix of the strain matrix, f is the external node load vector;

[0061] S10: Repeat steps S4 to S9 until R is less than the preset allowable residual error, then x is the final solution;

[0062] S11: Return to step S3 and continue with the next load increment step until the current load increment step is smaller than the final load increment step.

[0063] It should be noted that, according to the needs of implementation, each step / component described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention. It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dams, characterized in that: include: S1: Model the rockfill dam model and numerically discretize it using finite element mesh; S2: Based on the mechanical parameters of the rockfill material of the given rockfill dam, a representative volume element numerical model is established, triaxial numerical tests are carried out under complex stress paths, and a qualitative analysis of the stress, strain and particle breakage rate of the representative volume element is performed to determine whether the Gaussian integral point in the macroscopic finite element model needs to be replaced by the microscopic representative volume element. S3: Give a macro load increment; S4: Solve the consistent tangent modulus of each representative volume element; S5: Combined with specific boundary conditions, the finite element method is used to preliminarily solve the overall equilibrium equation Kx=r, where K is the overall stiffness matrix; x is the displacement vector of the node to be solved; and r is the load vector of the external node; S6: According to the deformation increment Δx of each finite element Gaussian integration point obtained by solving, all integration points are divided into two categories: macroscopic integration points that do not need to be replaced by representative volume elements and microscopic integration points that need to be replaced by representative volume elements; S7: For the microscopic integration points that require the replacement calculation of the representative volume element, the deformation increment Δx is used as the boundary condition to simulate the particle stress and crushing of the corresponding representative volume element until it is stable, and the calculated stress σ and tangent modulus D are fed back to the corresponding microscopic integration point; S8: For the macroscopic integration point, the constitutive model is used to solve the stress σ and tangent modulus D of the corresponding integration point; S9: Use the formula R=∫ Ω B T σdΩ-f, calculate the residual force, where R is the residual force, Ω is the solution domain, and B T is the transposed matrix of the strain matrix, f is the external node load vector; S10: Repeat steps S4 to S9 until R is less than the preset allowable residual error, then x is the final solution; S11: Return to step S3 and continue with the next load increment step until the current load increment step is smaller than the final load increment step.

2. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 1 is characterized in that: The boundary of the representative volume element numerical model established in step S2 is a periodic boundary, which is specifically described as a habit structure along the following vector The translation of P α is a basis vector, α is a positive integer, and takes values ​​from 1 to 3.

3. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 1 is characterized in that: The numerical method for qualitative analysis of stress, strain and particle breakage rate of the representative volume element in step S2 is a high-performance boundary element-discrete element combined method.

4. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 3 is characterized in that: The steps of the high-performance boundary element-discrete element joint method include: using a particle interaction solver to simulate and calculate the interaction of large-scale particle aggregates; exporting the calculation results of a certain time step in the particle interaction solver, using modeling software to establish a geometric model of the particles to be solved in the particle internal stress solver, inputting material parameters, meshing fractions, mesh types and boundary conditions of the particle model to be solved exported from the particle interaction solver, and then using the boundary element method to output the internal stress of the particle geometric model to be solved; equating the concentrated force on each particle boundary to the surface force on the boundary; establishing a control equation, and obtaining the displacement boundary stress from the control equation. boundary integral equation; transform the domain integral caused by volume force in the displacement boundary integral equation into a boundary integral; establish a local coordinate system for each particle respectively, and calculate the transformation matrix for similar particles; discretize the single-particle boundary integral equation, divide the boundary elements, and arrange the nodes in the domain; equate the surface force on each particle boundary to the surface force on the boundary element; calculate the coefficient matrix of the single particle and invert the coefficient matrix; solve the displacement of the boundary node; solve the stress and strain of the nodes in the domain; judge whether the particle is cracked according to the internal stress value, and use the particle replacement method to replace the broken particles, and return the model information of the replaced particles to the particle interaction solver.

5. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 1 is characterized in that: Step S2 is to conduct a qualitative analysis of the stress, strain and particle breakage rate of the representative volume element. The stress refers to the homogenized stress of the representative volume element, using the formula Calculated, where σ ij is the tensor form of the mean stress σ, N p is the number of particles, V (p) is the volume of particle p, n is the porosity within the representative volume element, N c is the number of contact points of particle p, i and j are traversal values ​​ranging from 1 to N c A positive integer, is the coordinate position of the i-th contact point of particle p, is the coordinate position of the centroid of particle p, The component of the unit normal vector from the particle centroid to the contact point, is the contact force at the jth contact point of particle p.

6. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 1 is characterized in that: Step S4 solves the consistent tangent modulus of each representative volume element by: Based on the assumption of uniform strain field, the following formula is used: Calculate, where V is the volume of the volume element, N c is the number of inter-particle releases, k n and k s are the directional and tangential stiffness moduli of the contact points between particles, n c and t c are the external normal and tangential unit vectors of the contact point between particles, respectively; s c is the branch vector.

7. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 1 is characterized in that: The displacement increment Δx in step S7 needs to be decomposed into a strain increment and a rotation increment before being applied as a boundary condition.

8. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 1 is characterized in that: The numerical method for simulating the particle stress and crushing of the corresponding representative volume element in step S7 is a high-performance boundary element-discrete element combined method.

9. The macroscopic hierarchical coupled multi-scale stress-deformation calculation method for rockfill dam according to claim 1 is characterized in that: The constitutive model used in step S8 is the Duncan-Zhang EB model.

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