A method for solving rockfill crushing path

Abstract

This invention discloses a method for solving the rockfill material crushing path, belonging to the technical field of rockfill dam deformation analysis. The method primarily solves the rockfill material crushing path through the following steps: first, using a boundary element numerical solver based on computational solid mechanics to calculate the stress at sample points within the rockfill material numerical model; then, using a crushing factor calculation formula proposed by the yield criterion, solving for the crushing factor at each sample point; then, using the crushing factor at each sample point to plot a three-dimensional surface diagram of the rockfill material; and finally, using the digital elevation-feature line method proposed in this invention, discretizing the three-dimensional surface diagram of the rockfill material and extracting the crushing path. This method demonstrates its effectiveness by establishing a boundary element numerical solver, proposing a formula for solving the crushing factor at each rockfill material sample point, and solving the crushing path for the rockfill material.

Description

Technical Field

[0001] The present invention belongs to the technical field of rockfill dam deformation analysis, and more specifically, relates to a method for solving a rockfill material crushing path. Background Art

[0002] According to statistics, earth-rockfill dams account for over 95% of my country's existing dams. Concrete-faced rockfill dams, as a type of earth-rockfill dam, offer numerous advantages over other dam types, including simple construction techniques, low project costs, access to local materials, and strong adaptability to geological conditions. Consequently, they are widely used in engineering projects. Ensuring dam safety is a prerequisite for engineering construction, and dam body settlement and deformation are among the core issues limiting the service life of rockfill dams. Rockfill, the primary fill material in rockfill dams, is a key factor affecting its performance due to its crushing and deformation.

[0003] Currently, analytical methods for studying rockfill material fragmentation include physical testing and numerical analysis. Numerical simulation methods are rapid, convenient, and effective, and are the mainstream approach for studying the micromechanical properties of rockfill materials. Among these, the discrete element method (DEM) is the most widely used numerical simulation method for discontinuous media mechanics in rockfill materials, effectively reproducing the mechanical laws observed in physical experiments. However, the DEM still has many areas that need improvement. For example: 1) the DEM's rockfill contact model and parameter selection contain numerous simplifications and assumptions; 2) the DEM's fundamental principle is to treat the rockfill material as a rigid body, making it impossible to accurately calculate the internal stress state and fragmentation path. Currently, there are two main types of DEM-based rockfill fragmentation simulation methods: 1) particle-based fragmentation simulation methods, which use a certain number of small particles bonded together to form aggregates. When a certain number of bonds between the small particles fail, the rockfill material fragments. 2) Fragment replacement methods, which simulate particle fragmentation, replace the original fragmented rockfill material with a group of unbonded small particles when the force (maximum contact force or average pressure) on the particles reaches a preset threshold. The above simulation methods are lacking in basic mechanical theory.

[0004] To address these issues, Munjiza et al. proposed the combined finite-discrete element method (FDEM) based on the concept of joint continuous-discrete coupling and performed a comprehensive stress-strain analysis of rockfill aggregates. Bagherzadeh et al. further introduced a stress-failure criterion and performed calculations of rockfill failure paths. However, FDEM requires the subdivision of each rockfill aggregate into individual units, which is computationally expensive for large-scale rockfill aggregates. Furthermore, in 2017, Luo Tao et al. proposed a combined scaled boundary finite element (BFE)-discrete element (DFE) method, applying the BFE method to the calculation of internal stresses in rockfill aggregates. This method offers high computational efficiency, but the particle breakage path is simplified to a straight line and requires further refinement. Overall, numerical methods based on the combined continuous-discrete coupling concept provide a sufficient theoretical basis for mesoscopic numerical studies of rockfill aggregates. They can more realistically account for the effects of rockfill breakage and shape, accurately reflecting the mesoscopic deformation characteristics of rockfill aggregates. However, existing algorithms are computationally intensive, and simulations of realistic breakage paths require improvement. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention proposes a method for solving the rockfill material crushing path, which has extremely high accuracy and effectiveness.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for solving a rockfill material crushing path is provided, comprising:

[0007] Step 1: Establish the displacement boundary integral equation;

[0008] Step 2: Convert the domain integral in the displacement boundary integral equation into a boundary integral;

[0009] Step 3: Construct a boundary element numerical solver and a rockfill crushing path solver;

[0010] Step 4: Model the rockfill material, discretize it using boundary elements, and establish sample points;

[0011] Step 5: Use the boundary element numerical solver to calculate the displacement of the boundary nodes of the rockfill numerical model;

[0012] Step 6: Use the boundary element numerical solver to calculate the stress of the sample points inside the rockfill numerical model;

[0013] Step 7: Establish a calculation formula for the crushing factor based on the yield criterion;

[0014] Step 8: Calculate the crushing factor of the sample points inside the rockfill;

[0015] Step 9: Based on the coordinates and crushing factors of the sample points, draw a three-dimensional surface diagram of the rockfill and discretize it;

[0016] Step 10: Establish digital elevation-feature line method;

[0017] Step 11: Use the digital elevation-feature line method to extract the crushing path of the three-dimensional surface image of the rockfill.

[0018] In some optional embodiments, step 1 includes:

[0019] For rockfill particles subjected to concentrated loads, the concentrated force can be regarded as a special surface force, and the acceleration at a certain moment can be equivalent to the body force. Then, the boundary integral equation of the rockfill can be established:

[0020] Where u is the displacement vector, x and y are the source point and field point in the problem domain respectively, is the coefficient related to the x position, b = ρa is the body force, ρ is the density, a is its acceleration (including gravity), and m is the concentrated force f(z l ) (l=1,…,m). U(x,y) and T(x,y) are the Kelvin fundamental solutions, which can be written as: and where μ is the shear modulus, r = |xy| is the distance between x and y, and n(y) is the unit normal vector at point y.

[0021] In some optional embodiments, step 2 includes:

[0022] The domain integral in the integral equation is converted into a boundary integral using the straight line integration method and solved, where the domain integral is expressed as: W = ∫ Ω E(x,y)qdΩ(y), the domain integral will be converted into an equivalent boundary integral using the straight line integration method. The specific expression is: Among them, Q represents the number of integration lines, F i is the weight factor, L i is the integration line, E(x,y) is the fundamental solution of Green’s function, q is the equivalent body force, and dy1 represents the differential.

[0023] In some optional embodiments, step 4 includes:

[0024] The numerical model of rockfill is divided by Delaunay triangulation algorithm, and the triangle vertices obtained are sorted and numbered, so that the sample points are established.

[0025] In some optional embodiments, step 5 includes:

[0026] Solving the displacement of the boundary nodes of the rockfill numerical model requires discretizing the displacement boundary integral equation. The displacement of a point s on the rockfill boundary can be expressed as Approximately, where s is the coordinate of a point on the boundary, u i (s) is the displacement of point s on the i-th boundary element, N is the number of nodes on the boundary, φ I (s) is node s I Combined with the displacement boundary integral equation, the displacement calculation formula of the boundary node can be derived as follows: Then the displacement of the boundary nodes of the rockfill numerical model can be calculated, where u represents the unknown displacement of all nodes, H -1 、 and M represent the coefficient matrix of displacement, the coefficient matrix of concentrated force, and the coefficient matrix of body force, respectively.

[0027] In some optional embodiments, step 7 includes:

[0028] The calculation formula of the crushing factor based on the yield criterion is: where w k represents the crushing factor, σ1 and σ3 represent the first and third principal stresses respectively, and σ c Represents compressive strength, m b , s and α are material parameters related to rockfill materials. Sample points with a crushing factor greater than 1 are defined as destroyed.

[0029] In some optional embodiments, step 7 includes:

[0030] To establish the digital elevation-feature line method, we first need to sort and number each triangle in the discrete surface map; then number the edges of each triangle; and then number each edge L. i , two triangles that share the same side, solve the formula: Where m is the judgment parameter, x 1i 、x 2i 、y 1i and y 2i L i The x-axis and y-axis coordinates of the vertex and endpoint; the specific expressions of a and b are where z 1i and z 2i L i The z-axis coordinates of the vertex and endpoint, x C 、y C and z C L i The triangle is not on the side L i The x-axis, y-axis, and z-axis coordinates of the vertex on .

[0031] In some optional embodiments, step 7 includes:

[0032] The digital elevation-characteristic line method is used to extract the crushing path of the three-dimensional surface map of the rockfill material. In step 10, it is necessary to traverse and calculate each edge L i After calculating the m values of two adjacent triangles, select the edges whose calculated m values are all greater than zero, and then connect the above edges to form a broken path.

[0033] According to another aspect of the present invention, a rockfill material crushing path solving method is provided, comprising: a boundary element numerical solver and a rockfill material crushing path solver.

[0034] The boundary element numerical solver is used to calculate stress values at the boundaries and inside of rockfill materials, and specifically includes: an input module for receiving material parameters, meshing fraction, mesh type, and boundary condition information of the rockfill material to be solved input by an operator; a solution module for obtaining stress inside the rockfill material to be solved using the rockfill material crushing path solution method and device according to any one of claims 1 to 6; and an output module for outputting stress values of sample points inside the rockfill material.

[0035] The rockfill material crushing path solver is used to solve the rockfill material crushing path.

[0036] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0037] A rockfill material crushing path solving method and device provided by the present invention can accurately solve the rockfill material crushing path, thereby understanding the shape and gradation changes of the rockfill material to ensure the safety and reliability of the engineering structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Figure 1 This is a flow chart of a method and device for solving a rockfill material crushing path provided by an embodiment of the present invention;

[0039] Figure 2 This is a schematic diagram of a surface diagram of a crushing factor of a circular rockfill material provided by an embodiment of the present invention;

[0040] Figure 3 This is a schematic diagram of a circular rockfill crushing path provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining 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 may be combined with each other as long as they do not conflict with each other.

[0042] Based on the basic idea of the intersection of computational geometry and computational solid mechanics, the present invention innovatively invents a method and device for solving the crushing path of rockfill materials, which can effectively solve the crushing path of rockfill materials. The present invention calculates the stress of sample points inside the numerical model of the rockfill material through the proposed boundary element numerical solver based on computational solid mechanics. The present invention also proposes a crushing factor calculation formula based on the yield criterion, which is used to solve the crushing factor of the sample points inside the rockfill material, and then uses the crushing factor of the sample points to draw a three-dimensional surface diagram of the rockfill material. In addition, the present invention also proposes a digital elevation-characteristic line method to discretize the three-dimensional surface diagram of the rockfill material and extract the crushing path. For concentrated loads on rockfill materials, there are certain difficulties in direct calculation using boundary elements. Therefore, the present invention converts concentrated loads into surface forces on boundary elements, eliminating the singularity caused by concentrated loads. For the domain integral in the boundary integral equation, the present invention uses the linear integration method to process it and reduce its dimension to a boundary integral, so only boundary elements need to be used to discretize the boundary, and no volume elements are required.

[0043] like Figure 1 As shown, a method for solving a rockfill material crushing path provided by an embodiment of the present invention includes the following steps:

[0044] Step 1: Establish the displacement boundary integral equation of rockfill materials;

[0045] In the embodiment of the present invention, in order to verify the accuracy and effectiveness, a calculation example of a circular rockfill material with a radius of 0.03 m subjected to pressure from top to bottom is selected.

[0046] In the embodiment of the present invention, the boundary integral equation of the rockfill material is established as follows:

[0047]

[0048] Where u is the displacement vector, x and y are the source point and field point in the problem domain respectively, is the coefficient related to the x position, b = ρa is the body force, ρ is the density, a is its acceleration (including gravity), and m is the concentrated force f(z l ) (l=1,…,m). U(x,y) and T(x,y) are the Kelvin fundamental solutions, which can be written as:

[0049]

[0050] and

[0051]

[0052] where μ is the shear modulus, r = |xy| is the distance between x and y, and n(y) is the unit normal vector at point y.

[0053] Step 2: Convert the domain integral in the displacement boundary integral equation into a boundary integral;

[0054] In the embodiment of the present invention, the domain integral can be expressed as:

[0055] W=∫ Ω E(x,y)qdΩ(y) (4)

[0056] Where Ω is the solution domain, E(x,y) is the fundamental solution of the Green's function, q is the equivalent body force, and dΩ(y) represents the differential with respect to point y.

[0057] The domain integral will be transformed into an equivalent boundary integral using the straight line integration method. The specific expression is:

[0058]

[0059] Among them, Q represents the number of integration lines, F i is the weight factor, L i is the integral line, and dy1 represents the differential of y1.

[0060] Step 3: Construct a boundary element numerical solver and a rockfill crushing path solver;

[0061] The boundary element numerical solver is used to calculate stress values at the boundaries and inside of rockfill materials, and specifically includes: an input module for receiving material parameters, meshing fraction, mesh type, and boundary condition information of the rockfill material to be solved input by an operator; a solving module for obtaining stress inside the rockfill material to be solved using the rockfill material crushing path solving method and device according to any one of claims 1 to 6; and an output module for outputting stress values of sample points inside the rockfill material.

[0062] In this embodiment of the present invention, the material parameters of the rockfill are set as follows: compressive strength of 100 MPa, tensile strength of 20 MPa, elastic modulus of 80 MPa, and Poisson's ratio of 0.15. Boundary conditions are set to apply a concentrated compressive load of 1 MPa at the top, bottom, left, and right endpoints of the rockfill. The boundary of the numerical model of the rockfill is divided into 80 boundary cells.

[0063] Step 4: Model the rockfill material, discretize it using boundary elements, and establish sample points;

[0064] In the embodiment of the present invention, the rockfill numerical model is triangulated using a Delaunay triangulation algorithm, and the triangle vertices obtained by the triangulation are sorted and numbered, thereby establishing sample points.

[0065] Step 5: Use the boundary element numerical solver to calculate the displacement of the boundary nodes of the rockfill numerical model.

[0066] In the embodiment of the present invention, solving the displacement of the boundary nodes of the numerical model of the rockfill material requires discretizing the displacement boundary integral equation. The displacement of a point s on the rockfill material boundary can be approximated by the following formula:

[0067]

[0068] Among them, s is the coordinate of a point on the boundary, u i (s) is the displacement of point s on the i-th boundary element, N is the number of nodes on the boundary, φ I (s) is node s I The shape function at .

[0069] Combined with the displacement boundary integral equation, the displacement calculation formula of the boundary node can be derived as follows:

[0070]

[0071] Where u represents the unknown displacement of all nodes, H -1 、 and M represent the coefficient matrix of displacement, the coefficient matrix of concentrated force, and the coefficient matrix of body force, respectively.

[0072] Then the displacement of the boundary nodes of the rockfill numerical model can be calculated.

[0073] Step 6: Use the boundary element numerical solver to calculate the stress of the sample points inside the rockfill numerical model;

[0074] Step 7: Establish a calculation formula for the crushing factor based on the yield criterion;

[0075] In the embodiment of the present invention, the calculation formula of the crushing factor established based on the yield criterion is:

[0076]

[0077] where w k represents the crushing factor, σ1 and σ3 represent the first and third principal stresses respectively, and σ c Represents compressive strength, m b , s and α are material parameters related to rockfill materials.

[0078] Sample points with a fragmentation factor greater than 1 are defined as destroyed.

[0079] Step 8: Calculate the crushing factor of the sample points inside the rockfill;

[0080] Step 9: Figure 2 As shown in the figure, based on the coordinates of the sample points and the crushing factors, the three-dimensional surface diagram of the rockfill is drawn and discretized;

[0081] Step 10: Establish digital elevation-feature line method;

[0082] In the embodiment of the present invention, the method for establishing digital elevation-feature line first needs to sort and number each triangle in the discrete surface map; then number the edge of each triangle; then number each edge L i , the two triangles that share the same side, the solution formula is:

[0083]

[0084] Among them, m is the judgment parameter, x 1i 、x 2i 、y 1i and y 2i L i The x-axis and y-axis coordinates of the vertex and endpoint; the specific expressions of a and b are

[0085]

[0086] and

[0087]

[0088] Among them, z 1i and z 2i L i The z-axis coordinates of the vertex and endpoint, x C 、y C and z C L i The triangle is not on the side L i The x-axis, y-axis, and z-axis coordinates of the vertex on .

[0089] Step 11: Figure 3 As shown in the figure, the digital elevation-feature line method is used to extract the crushing path of the three-dimensional surface image of the rockfill.

[0090] In the embodiment of the present invention, the digital elevation-characteristic line method is used to extract the crushing path of the three-dimensional surface map of the rockfill material. It is necessary to traverse and calculate each edge L in step 10. i After calculating the m values of two adjacent triangles, select the edges whose calculated m values are all greater than zero, and then connect the above edges to form a broken path.

[0091] The present application also provides a rockfill material crushing path solving method, comprising: a boundary element numerical solver and a rockfill material crushing path solver;

[0092] The boundary element numerical solver is used to calculate stress values at the boundaries and inside of rockfill materials, and specifically includes: an input module for receiving material parameters, meshing fraction, mesh type, and boundary condition information of the rockfill material to be solved input by an operator; a solution module for obtaining stress inside the rockfill material to be solved using the rockfill material crushing path solution method and device according to any one of claims 1 to 6; and an output module for outputting stress values of sample points inside the rockfill material.

[0093] The rockfill material crushing path solver is used to solve the rockfill material crushing path.

[0094] The specific implementation method can refer to the description of the above method embodiment, and the embodiment of the present invention will not be repeated.

[0095] It should be pointed out that, according to the needs of implementation, the various steps / components 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.

[0096] It will be easily understood by those skilled in the art that the above description is merely 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 scope of protection of the present invention.

Claims

1. A method for solving a rockfill material crushing path, characterized in that: include: Step 1: Establish the displacement boundary integral equation: For the rockfill particles subjected to concentrated loads, the concentrated force is regarded as a special surface force, and the acceleration at a certain moment is equivalent to the body force. Then, the boundary integral equation of the rockfill can be established: in, is the displacement vector, and are the source point and field point in the problem domain, for peace The position-dependent coefficient, For physical strength, is the density, is its acceleration, m is the concentrated force The number of (l=1,…,m), and is the Kelvin fundamental solution; Step 2: Convert the domain integral in the displacement boundary integral equation into a boundary integral: Use the straight line integration method to convert the domain integral in the integral equation into a boundary integral and solve it. The domain integral is expressed as: , the domain integral is converted into an equivalent boundary integral using the straight line integration method. The specific expression is: , where Q represents the number of integration lines, is the weight factor, is the integral line, is the fundamental solution of Green’s function, For equivalent physical strength, represents differential; Step 3: Build a boundary element numerical solver and a rockfill crushing path solver; Step 4: Model the rockfill material, discretize it using boundary elements, and establish sample points; Step 5: Calculate the displacement of the boundary nodes of the rockfill numerical model using the boundary element numerical solver; Step 6: Use the boundary element numerical solver to calculate the stress of the sample points inside the rockfill numerical model; Step 7: Establish a calculation formula for the crushing factor based on the yield criterion; Step 8: Calculate the crushing factor of the sample points inside the rockfill; Step 9: Based on the coordinates and crushing factors of the sample points, draw a three-dimensional surface diagram of the rockfill and discretize it; Step 10: Establish digital elevation-feature line method; Step 11: Use the digital elevation-feature line method to extract the crushing path of the three-dimensional surface image of the rockfill.

2. The method for solving a rockfill material crushing path according to claim 1, wherein: Step 1 includes: For a two-dimensional plane strain problem, it can be written as: ,and ， in, is the shear modulus, for and The distance between For the point The unit normal vector at .

3. The method for solving the rockfill material crushing path according to claim 1, characterized in that: Step 4 includes: triangulating the rockfill numerical model using a Delaunay triangulation algorithm, and sorting and numbering the triangle vertices obtained by the triangulation, thereby establishing sample points.

4. The method for solving the rockfill material crushing path according to claim 1, characterized in that: Step 5 includes: solving the displacement of the boundary node of the rockfill numerical model requires discretizing the displacement boundary integral equation, and a certain point on the rockfill boundary The displacement is calculated using the formula Approximately, where is the coordinate of a point on the boundary, is the point on the i-th boundary element The displacement, N is the number of nodes on the boundary, For nodes The shape function at the position; combined with the displacement boundary integral equation, the displacement calculation formula of the boundary node can be derived as follows: Then the displacement of the boundary nodes of the rockfill numerical model can be calculated, where represents the unknown displacements of all nodes, 、 and They represent the coefficient matrix of displacement, the coefficient matrix of concentrated force and the coefficient matrix of body force respectively.

5. The method for solving the rockfill material crushing path according to claim 1, characterized in that: Step 7 includes: the calculation formula of the crushing factor based on the yield criterion is: in represents the fragmentation factor, 、 represent the first and third principal stresses, respectively. Represents compressive strength, 、 and is a material parameter related to rockfill materials, and the sample points with a crushing factor greater than 1 are defined as destroyed.

6. The method for solving the rockfill material crushing path according to claim 1, characterized in that: Step 10 includes: first, the method of establishing digital elevation-feature line needs to sort and number each triangle in the discrete surface map; then, number the edge of each triangle; and then, number each edge. , two triangles that share the same side, solve the formula: , where m is the judgment parameter, 、 、 and Edge The x-axis and y-axis coordinates of the vertex and endpoint; the specific expressions of a and b are: ， ， in and Edge The z-axis coordinates of the vertices and endpoints, 、 and Edge The triangle is not on the side The x-axis, y-axis, and z-axis coordinates of the vertex on .

7. The method for solving a rockfill material crushing path according to claim 1, characterized in that: Step 11 includes: using the digital elevation-characteristic line method to extract the crushing path of the three-dimensional surface map of the rockfill material, and it is necessary to traverse and calculate each edge in step 10. After calculating the m values of two adjacent triangles, select the edges whose calculated m values are all greater than zero, and then connect the above edges to form a broken path.

8. The method for solving the rockfill material crushing path according to claim 1, characterized in that: include: The boundary element numerical solver is used to calculate stress values at the boundaries and inside the rockfill material, and specifically includes: an input module for receiving the material parameters, meshing fraction, mesh type, and boundary condition information of the rockfill material to be solved input by the operator; a solution module for obtaining the stress inside the rockfill material to be solved; and an output module for outputting the stress values of sample points inside the rockfill material. The rockfill material crushing path solver is used to solve the crushing path of the rockfill material.

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