Method and device for predicting vertical bearing capacity of ultra-high performance tailings pole

Abstract

This invention provides a method and apparatus for predicting the vertical bearing capacity of ultra-high-performance tailings poles, belonging to the field of structural bearing capacity prediction technology. The method includes: establishing a finite element baseline model of the pole, generating an initial stiffness matrix and load vector; obtaining the full stress-strain curve through tailings concrete axial compression tests, extracting the elastic modulus, peak stress, peak strain, and characteristic points of the descending segment, and determining the damage evolution relationship based on the peak strain and the characteristic points of the descending segment; correcting the stiffness matrix and load vector using material constitutive parameters and the damage evolution relationship, and establishing a nonlinear equilibrium equation; iteratively solving the equation using a progressively increasing load method, dynamically updating the damage variables based on the current strain, and reconstructing the stiffness matrix; and outputting the predicted vertical bearing capacity result based on whether the vertical displacement at the top of the pole reaches a preset threshold or the stiffness matrix becomes singular. This invention achieves accurate prediction of the vertical bearing capacity of tailings poles and reduces experimental costs.

Description

Technical Field

[0001] This invention relates to the field of structural bearing capacity prediction technology, specifically to a method and apparatus for predicting the vertical bearing capacity of ultra-high performance tailings poles. Background Technology

[0002] Ultra-high performance tailings poles are pole components made by replacing part of the cement or fine aggregate with mining tailings, offering advantages in solid waste resource utilization and low-carbon environmental protection. However, the complex composition and fluctuating activity of tailings result in significant differences in the constitutive relationship of their concrete materials compared to ordinary concrete, especially exhibiting strong nonlinearity and strain softening characteristics during axial compression. As a key support structure for power and communication lines, the vertical bearing capacity of poles is a core indicator for design, testing, and safety assessment. Traditional bearing capacity prediction methods mainly rely on empirical formulas in ordinary concrete pole design codes or full-scale failure tests. The former cannot reflect the unique damage evolution law of tailings concrete, often resulting in prediction errors exceeding 30%; the latter is costly and time-consuming, making it difficult to use for batch testing and on-site assessment. Therefore, there is an urgent need for a high-precision, low-cost prediction method that can integrate material-level measured constitutive data with component-level nonlinear mechanical responses.

[0003] In the prior art, a method, device, and electronic device for predicting the vertical bearing capacity of prestressed concrete pipe piles (publication number CN117217091A) are disclosed. This method obtains the pipe pile body parameters, self-balancing test influence parameters, pile body soil parameters, and bearing layer soil parameters as inputs, and uses a pre-trained adaptive fuzzy neural network model for prediction processing to obtain the vertical bearing capacity data of the pipe pile. This method is mainly aimed at predicting the bearing capacity of prestressed concrete pipe piles under complex site conditions. Its core lies in establishing a nonlinear mapping relationship between influence parameters and bearing capacity through a neural network model. However, this method belongs to a purely data-driven black-box prediction model and does not involve physical modeling at the material constitutive level. Its input parameters only include macroscopic geometric parameters and empirical soil parameters. It lacks a physical extraction mechanism for constitutive parameters such as the elastic modulus, peak stress, peak strain, and characteristic points of the descending segment of concrete materials, and it does not establish a stiffness degradation model based on damage mechanics. For ultra-high performance tailings poles, their vertical bearing capacity is mainly controlled by the axial compression damage softening behavior of the tailings concrete itself. Pure data-driven models cannot reflect the mechanical coupling mechanism between material damage evolution and structural response, and therefore it is difficult to accurately predict the ultimate bearing capacity and failure process of tailings poles under vertical loads.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for predicting the vertical bearing capacity of ultra-high performance tailings poles, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting the vertical bearing capacity of ultra-high performance tailings poles, the specific steps of which include: Step 1: Obtain the geometric parameters and reinforcement parameters of the ultra-high performance tailings pole to be predicted, and preset the initial elastic modulus of the tailings concrete and steel bars. Input the geometric parameters, reinforcement parameters and initial elastic modulus into the finite element reference model to generate the initial stiffness matrix and initial nodal load vector that only reflect the elastic stage. Step 2: Collect axial stress-strain curve data of the standard test block of tailings concrete used in the ultra-high performance tailings pole during the entire axial compression test, and extract the elastic modulus, peak stress, peak strain and descending segment feature points from the curve data. Use the extracted parameters as material constitutive data. Based on the peak strain and descending segment feature points, use a preset damage evolution equation to determine the damage evolution relationship of damage variables with strain. Step 3: Using the material constitutive parameters and damage evolution relationship, the initial stiffness matrix is ​​modified into a nonlinear stiffness matrix that can be dynamically updated with strain state, and the initial nodal load vector is modified according to the peak stress to establish a nonlinear equilibrium equation. Step 4: Apply loads in progressively increasing steps to iteratively solve the nonlinear equilibrium equations. In each iteration step, update the damage variables and reconstruct the stiffness matrix based on the current strain state until the preset convergence condition is met, and then output the nodal displacement field. If the stiffness matrix becomes singular or non-positive definite during the iteration process, it is determined that the limit state has been reached and the solution is terminated. Step 5: Based on the nodal displacement field, determine the vertical bearing capacity by taking the vertical displacement at the top of the pole as a preset threshold; when the displacement exceeds the limit or the solution is terminated, output the corresponding current load level as the vertical bearing capacity prediction result.

[0007] Furthermore, the generation of the finite element reference model specifically includes: obtaining the pole length, cross-sectional outer diameter, wall thickness, and variable cross-sectional dimensions along the pole direction as geometric parameters, and obtaining the diameter, quantity, distribution circle radius of the longitudinal reinforcement and the diameter and pitch of the spiral stirrups as reinforcement parameters; using solid elements or structural elements to mesh the pole, generating a three-dimensional finite element mesh model composed of nodes and elements, which is the finite element reference model; Initial elastic moduli are assigned to the tailings concrete and steel reinforcement sections respectively, and displacement coordination or bond-slip relationship between the steel reinforcement and concrete is set. Vertical displacement constraints are applied to the bottom of the pole to simulate the actual foundation embedded boundary, constraining displacement in two orthogonal directions in the horizontal plane and rotation about the vertical axis, releasing the vertical displacement degree of freedom. A reference point is established at the centroid of the pole top, and after coupling the reference point with the pole top section, a vertical concentrated load is applied at the reference point. Based on the mesh model, the element stiffness matrix of each element is calculated using the initial elastic moduli and combined into an overall stiffness matrix. At the same time, the equivalent nodal loads are calculated and combined into an overall nodal load vector. The overall stiffness matrix and the overall nodal load vector are used as the initial stiffness matrix and the initial nodal load vector, respectively.

[0008] Furthermore, the logic for obtaining the material constitutive data is as follows: Prepare standard prism or cylindrical specimens of tailings concrete with the same batch and mix ratio as the ultra-high performance tailings pole, and conduct uniaxial compression tests on a servo testing machine. Continuously collect axial stress and axial strain data from the start of loading to the complete failure of the specimen at a preset sampling frequency, and plot the stress-strain curve. The elastic modulus is extracted from the stress-strain curve, and the secant modulus within the initial linear segment of the stress-strain curve is taken as the elastic modulus. The initial linear segment refers to a continuous section in the stress-strain curve in which the axial stress and axial strain have a linear proportional relationship starting from the origin. This section ends when the axial stress reaches 30% of the peak stress, and the relative deviation between the slope of the line connecting any two points in this continuous section and the average slope in the section does not exceed 5%. Extract the peak stress and take it as the maximum stress value in the entire curve; Extract the peak strain and take it as the axial strain value corresponding to the peak stress; Extract the feature point of the descending segment, which is the axial strain value corresponding to the first decrease of the axial stress from the peak stress to 50% of the peak stress; if there is stress fluctuation in the descending segment, causing the peak stress to pass through 50% multiple times during the first descent, then take the minimum axial strain value as the feature point of the descending segment. The elastic modulus, peak stress, peak strain, and characteristic points of the descending segment are used together as the constitutive data of the material.

[0009] Furthermore, based on the peak strain and the characteristic points of the descending segment, a preset damage evolution equation is used to determine the damage evolution relationship of the damage variable with strain, specifically: set up Indicates the current response. This represents the peak strain. Indicates the feature point of the descending segment. Indicates damage variables; The damage evolution mode is determined in the following manner: when At that time, damage variable A value of 0 indicates that the material has not been damaged; when At that time, damage variable Determine by the following formula: when At that time, damage variable A value of 1 indicates that the material has completely lost its load-bearing capacity. in, The range of values ​​is ;when hour, ;when hour, ; The above damage variables With current strain The mapping relationship between them is referred to as the damage evolution relationship, denoted as .

[0010] Furthermore, the establishment of the nonlinear equilibrium equation specifically involves: Obtaining the elastic modulus from material constitutive data and peak stress ; Damage variables are obtained from damage evolution relationships. With current strain Mapping relationship between ; Let the initial stiffness matrix be The initial nodal load vector is Based on the initial stiffness matrix Extract the element stiffness matrix for each element. ; When the strain state is different at different locations in the structure, each element uses the strain at its own integration point to calculate the corresponding damage variable value. The element stiffness matrix of each element is corrected according to the following formula to obtain the corrected element stiffness matrix. : The modified element stiffness matrices are then reassembled into the overall nonlinear stiffness matrix. ; Simultaneously, the ultimate axial force is determined based on the product of the peak stress and the cross-sectional area at the top of the rod. The load values ​​in the initial nodal load vector are scaled proportionally so that the vertical concentrated load value at the reference point at the top of the rod is equal to the ultimate axial force, thereby generating the ultimate load vector. ; From the nonlinear stiffness matrix and ultimate load vector The nonlinear equilibrium equation is formed, and its expression is as follows: in Let be the nodal displacement vector to be solved.

[0011] Furthermore, the method of applying the load in progressively increasing stages specifically involves: applying the ultimate load vector... Divided into equal parts The first load level, the Level load vector Recorded as ,in Indicates the sequence number of the load level. ; Starting with the first level of load, the loads are applied level by level, and the solution under each level of load is used as the initial condition after the previous level converges to the equilibrium state.

[0012] Furthermore, the iterative solution process under each load level is carried out in the following manner: Let the current load level be the first. Level, the nodal displacement vector after convergence of the previous load level is , will the Level load vector The solution is applied to the finite element baseline model and solved iteratively. In the In the iteration, according to the The node displacement vector obtained in the second iteration Calculate the current strain value at each element integration point. The damage evolution relationship Determine the first Damage variable values ​​at each integration point during the next iteration And reconstruct the current overall nonlinear stiffness matrix according to the method described in step 3. : Based on the current node displacement vector Based on the current damage state, the global internal force vector is calculated by integrating the internal forces within the elements. ; Calculate the residual force vector of the current iteration step. : ; Solving for displacement increments : ; Update node displacement vector : ; Calculate the convergence criterion. If the following conditions are met simultaneously: ,and Then determine that the current load level has converged, and output the [number]th load level. Nodal displacement field under level load ,in , These are the preset first convergence tolerance and the second convergence tolerance, respectively. If the reconstructed stiffness matrix is ​​obtained before the convergence condition is met... If the determinant is zero or the main diagonal element is not positive, and the residual force vector does not satisfy the convergence condition. If the structure has reached its limit state, the iteration stops and the application of subsequent load levels is terminated.

[0013] Furthermore, the determination of the vertical bearing capacity in step 5 is specifically as follows: From the The nodal displacement field output after the level load converges Extract the vertical displacement component at the reference point at the top of the rod, denoted as . Compare it with a preset displacement threshold. Comparison: like And the first If the first load is less than the load value corresponding to the ultimate load vector, then the second load shall be applied. Solve for level loads; like Then stop loading and set the current number of pages to [number]. The output of the load value is the predicted result of the vertical bearing capacity of the ultra-high performance tailings pole; If in the 1st If the solution is terminated during the iterative solution of the first-order load due to the stiffness matrix being singular or non-positive definite and the residual force not satisfying the convergence condition, then the solution will be terminated. The level load value is output as the vertical bearing capacity prediction result, and the result is marked as the lower limit estimate of the ultimate bearing capacity; The displacement threshold criterion takes precedence over the stiffness singularity criterion; when a certain load level simultaneously satisfies both the displacement exceeding limit and stiffness singularity conditions, the current load value corresponding to the displacement exceeding limit is used as the bearing capacity prediction result.

[0014] The present invention also provides an ultra-high performance tailings pole vertical bearing capacity prediction device, which is used to execute the above-mentioned ultra-high performance tailings pole vertical bearing capacity prediction method, including: The model initialization module is used to obtain the geometric parameters and reinforcement parameters of the ultra-high performance tailings pole to be predicted, and input the geometric parameters and reinforcement parameters into the finite element reference model to generate an initial stiffness matrix and initial nodal load vector that only reflect the elastic stage. The constitutive parameter extraction module is used to collect axial stress-strain curve data of standard test blocks of tailings concrete used in the ultra-high performance tailings poles during the entire axial compression test, and extract the elastic modulus, peak stress, peak strain and descending segment feature points from the curve data. The extracted parameters are used as material constitutive data. Based on the peak strain and descending segment feature points, a preset damage evolution equation is used to determine the damage evolution relationship of damage variables with strain. The nonlinear equation establishment module is used to modify the initial stiffness matrix into a nonlinear stiffness matrix that can be dynamically updated with strain state by using the material constitutive parameters and damage evolution relationship, and to modify the initial nodal load vector according to the peak stress to establish nonlinear equilibrium equations. The step-by-step iterative solution module is used to iteratively solve the nonlinear equilibrium equation by applying loads in progressively increasing steps. In each iteration step, the damage variables are updated and the stiffness matrix is ​​reconstructed according to the current strain state until the preset convergence condition is met, and then the nodal displacement field is output. If the stiffness matrix becomes singular or non-positive definite during the iteration process, it is determined that the limit state has been reached and the solution is terminated. The bearing capacity determination output module is used to determine the vertical bearing capacity based on the nodal displacement field, with the vertical displacement at the top of the pole reaching a preset threshold as the criterion; when the displacement exceeds the limit or the solution is terminated, the corresponding current load level is output as the vertical bearing capacity prediction result.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention collects the full axial compressive stress-strain curves of standard tailings concrete specimens, extracting the elastic modulus, peak stress, peak strain, and characteristic points of the descending segment as constitutive data. Based on the peak strain and the characteristic points of the descending segment, a damage evolution relationship between damage variables and strain is established, achieving a quantitative characterization of the nonlinear softening characteristics of tailings concrete. Furthermore, using the extracted constitutive parameters and damage evolution relationship, the initial elastic stiffness matrix is ​​modified into a nonlinear stiffness matrix that can be dynamically updated with strain state. The initial nodal load vector is then modified based on the peak stress, establishing a nonlinear equilibrium equation reflecting the mechanical coupling mechanism between material damage evolution and structural response. This overcomes the deficiency of existing purely data-driven models that lack a physical mechanism.

[0016] This invention also employs a progressively increasing load application method to iteratively solve the nonlinear equilibrium equations. In each iteration step, the damage variables are dynamically updated and the stiffness matrix is ​​reconstructed based on the current strain state until a preset convergence condition is met, at which point the nodal displacement field is output. If the stiffness matrix exhibits singularity or non-positive chronology during the iteration process, the structure is deemed to have reached its limit state, and the solution is terminated. Based on this, the vertical bearing capacity is determined using the nodal displacement field and a preset threshold for the vertical displacement at the top of the pole. The displacement threshold criterion is combined with the stiffness singularity criterion, with the displacement criterion being prioritized. This achieves accurate prediction of the ultimate bearing capacity of ultra-high-performance tailings poles and tracks the entire failure process. Compared to traditional empirical formulas, this invention does not rely on correction coefficients for ordinary concrete, significantly improving prediction accuracy. Compared to full-scale failure tests, this invention only requires axial compression tests on standard test blocks, combined with finite element numerical simulation to complete the prediction, greatly reducing testing costs and time, making it suitable for batch testing and on-site evaluation scenarios. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 A dual Y-axis image showing the load level, applied load, and vertical displacement at the top of the rod; Figure 3 A dual Y-axis image showing the load level, vertical displacement at the top of the bar, and maximum damage variable; Figure 4 This is a schematic diagram of the overall device module of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0019] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0020] Example: Please see Figures 1-3 The present invention provides a technical solution: A method for predicting the vertical bearing capacity of ultra-high performance tailings poles, the specific steps of which include: Step 1: Obtain the geometric parameters and reinforcement parameters of the ultra-high performance tailings pole to be predicted, and preset the initial elastic modulus of the tailings concrete and steel bars. Input the geometric parameters, reinforcement parameters and initial elastic modulus into the finite element reference model to generate the initial stiffness matrix and initial nodal load vector that only reflect the elastic stage. In this embodiment, the generation of the finite element reference model specifically includes: obtaining the pole length, cross-sectional outer diameter, wall thickness, and variable cross-sectional dimensions along the pole direction as geometric parameters; and obtaining the diameter, quantity, distribution circle radius of the longitudinal reinforcement and the diameter and pitch of the spiral stirrups as reinforcement parameters; using eight-node hexahedral solid elements to mesh the tailings concrete part, and using two-node linear truss elements to mesh the reinforcing steel part, generating a three-dimensional finite element mesh model composed of nodes and elements, which is the finite element reference model; Initial elastic moduli were assigned to both the tailings concrete and reinforcing steel sections, and a displacement coordination relationship was established between the reinforcing steel and concrete, assuming no relative slippage between the reinforcing steel and the surrounding concrete. This was achieved by coupling the degrees of freedom of the reinforcing steel element nodes with those of the adjacent concrete element nodes. Vertical displacement constraints were applied at the bottom of the pole to simulate the actual fixed boundary of the pier cap, constraining displacements in two orthogonal directions in the horizontal plane and rotations about the vertical axis, thus releasing the vertical displacement degrees of freedom. A reference point was established at the centroid of the pole top, and this reference point was coupled to all nodes of the pole top section using a motion coupling method, ensuring that the pole top section maintained the planar assumption after deformation. A concentrated vertical load was applied at this reference point. Based on the above mesh model, material properties, and boundary conditions, the element stiffness matrix of each element was calculated using the initial elastic moduli and combined into an overall stiffness matrix. Simultaneously, the concentrated vertical load at the pole top was equivalently distributed to each node of the pole top section, and the equivalent nodal loads were calculated and combined into an overall nodal load vector. The overall stiffness matrix and the overall nodal load vector were used as the initial stiffness matrix and the initial nodal load vector, respectively.

[0021] Step 1 involves acquiring the geometric and reinforcement parameters of the ultra-high performance tailings pole to be predicted, and pre-setting the initial elastic moduli of the tailings concrete and steel reinforcement. These parameters are then input into the finite element baseline model to generate an initial stiffness matrix and initial nodal load vector that only reflect the elastic stage. This establishes a basic finite element framework for subsequent material constitutive parameter replacement and nonlinear stiffness correction. This step, using pre-set initial elastic moduli, eliminates the need to wait for axial compression tests to complete the finite element model, enabling parallel processing of geometric modeling and material testing, thus improving the overall efficiency of the prediction process. Simultaneously, the generated initial stiffness matrix and load vector will be replaced and corrected by the actual material constitutive parameters extracted in Step 2. This incorporates the macroscopic geometric features and reinforcement information of the pole into the final load-bearing capacity prediction model, ensuring that the prediction results reflect the actual structural morphology of the pole and avoiding the shortcomings of purely data-driven models that ignore structural geometric features.

[0022] Step 2: Collect axial stress-strain curve data of the standard test block of tailings concrete used in the ultra-high performance tailings pole during the entire axial compression test, and extract the elastic modulus, peak stress, peak strain and descending segment feature points from the curve data. Use the extracted parameters as material constitutive data. Based on the peak strain and descending segment feature points, use a preset damage evolution equation to determine the damage evolution relationship of damage variables with strain. In this embodiment, the logic for obtaining the material constitutive data is as follows: Prepare standard prism or cylindrical specimens of tailings concrete with the same batch and mix ratio as the ultra-high performance tailings pole, and conduct uniaxial compression tests on a servo testing machine. Continuously collect axial stress and axial strain data from the start of loading to the complete failure of the specimen at a preset sampling frequency, and plot the stress-strain curve. Prepare standard prismatic or cylindrical test blocks of tailings concrete from the same batch and mix proportion as the ultra-high performance tailings poles. Specifically, the recommended dimensions for the prismatic test blocks are 100mm×100mm×300mm or 150mm×150mm×450mm, with a height-to-width ratio of 3:1 to obtain a stable descending curve. The recommended diameter for the cylindrical test blocks is 100mm or 150mm, and the height is twice the diameter. The test blocks are poured using the same tailings concrete mix proportion as the poles and cured under standard curing conditions for 28 days. Before the test, the end faces of the test blocks are ground or leveled with sulfur mortar to ensure uniform force transmission under axial compression. A uniaxial compression test is conducted using an electro-hydraulic servo pressure testing machine. The preferred range of the testing machine is 1.5 to 2.5 times the estimated peak load, with an accuracy of not less than ±1%. The specimen is placed at the center of the lower pressure plate of the testing machine, ensuring that the specimen axis coincides with the loading axis of the testing machine, with a deviation not exceeding 0.5% of the specimen's side length. Displacement control is used for loading, with a loading rate set to 0.05 mm / min to 0.2 mm / min to ensure that the specimen's softening behavior is captured completely near the peak stress. Axial stress and axial strain data are continuously collected from the start of loading until complete specimen failure at a preset sampling frequency of 10 Hz. Axial strain is measured using displacement sensors or extensometers mounted on opposite sides of the specimen, with a gauge length of 1 / 2 to 2 / 3 of the specimen height. The average of the measurements from both sides is taken to eliminate bending effects. The test continues until the specimen completely fails, i.e., when the axial stress drops below 30% of the peak stress or the specimen loses its overall load-bearing capacity. The collected data are plotted as a stress-strain curve with axial strain as the abscissa and axial stress as the ordinate.

[0023] The elastic modulus is extracted from the entire stress-strain curve, and the secant modulus within the initial linear segment of the stress-strain curve is taken as the elastic modulus. The initial linear segment refers to a continuous section in the entire stress-strain curve where the axial stress and axial strain exhibit a linear proportional relationship starting from the origin. This section terminates when the axial stress reaches 30% of the peak stress, and the relative deviation between the slope of the line connecting any two points within this continuous section and the average slope within the section does not exceed 5%. This invention uses the secant modulus within the initial linear segment as the elastic modulus, rather than the single-point tangent modulus, because the single-point tangent modulus is easily affected by local noise in the test curve, while the secant modulus, using the average slope of the line connecting two points within the segment, has good noise resistance. The initial linear segment is defined as starting from the origin and ending when the axial stress reaches 30% of the peak stress, based on the following considerations: the stress-strain curve of tailings concrete typically exhibits a good linear relationship in the early loading stage (within 30% of the peak stress). After exceeding this stress level, microcracks begin to initiate, and the curve gradually deviates from linearity. In addition, limiting the relative deviation between the slope of the line connecting any two points in the section and the average slope in the section to no more than five percent is to ensure that the selected section truly satisfies the linear proportional relationship, eliminate nonlinear sections caused by initial centering errors or uneven end faces of the test block, and thus ensure that the extracted elastic modulus is representative and repeatable.

[0024] Extract the peak stress and take it as the maximum stress value in the entire curve; Extract the peak strain and take it as the axial strain value corresponding to the peak stress; The characteristic point of the descending segment is extracted and taken as the axial strain value corresponding to the first decrease of axial stress from the peak stress to 50% of the peak stress. If stress fluctuations occur in the descending segment, causing the axial strain value to pass through 50% of the peak stress multiple times during the initial decrease, the minimum axial strain value among these is taken as the characteristic point of the descending segment. The characteristic point of the descending segment is used to calibrate the second control point in the damage evolution equation, that is, the strain value corresponding to the damage variable reaching 1 (the material completely loses its load-bearing capacity). The reason why this invention takes the axial strain corresponding to the first decrease of axial stress from the peak stress to 50% of the peak stress as the characteristic point of the descending segment is that the softening behavior of tailings concrete usually enters the residual strength stage or the rapid instability stage after the stress decreases to 50% of the peak stress. This point can be used as a criterion for "complete failure" in an engineering sense. For working conditions where stress fluctuates during the descent phase, the minimum axial strain value corresponding to the multiple passages through the stress level during the first descent is taken. The logic is that once the material enters the softening stage, the decrease in its load-bearing capacity is irreversible. Taking the minimum strain value can conservatively estimate the material's deformation capacity, avoiding misjudgment that the material still has a high deformation capacity due to stress fluctuations, thereby ensuring that the load-bearing capacity prediction result is on the safe side.

[0025] The elastic modulus, peak stress, peak strain, and characteristic points of the descending segment are used together as the constitutive data of the material.

[0026] Based on the peak strain and the characteristic points of the descending segment, a preset damage evolution equation is used to determine the damage evolution relationship between the damage variable and strain, specifically: set up Indicates the current response. This represents the peak strain. Indicates the feature point of the descending segment. Indicates damage variables; The damage evolution mode is determined in the following manner: when At that time, the material has not yet entered the damage development stage, and the damage variables... A value of 0 indicates that the material has not been damaged; when At this time, the material enters the damage softening stage, and the damage variable... Determine by the following formula: The core logic of this damage evolution equation lies in establishing a continuous monotonic mapping relationship between strain and damage variables, which is used to quantitatively describe the physical process of gradual stiffness degradation in tailings concrete after peak stress; where This term reflects the reciprocal relationship between the current strain and the peak strain; when the strain is slightly greater than... When this term is slightly less than 1, the damage variable slowly increases from zero; while The term reflects the current strain distance to the point of complete failure. The relative residual deformation capacity gradually approaches zero as strain increases. The product of these two terms constitutes the ratio of the current effective stiffness to the initial stiffness, representing the damage variable. This is equal to 1 minus the ratio, thus achieving a quantitative expression of the stiffness reduction. The equation satisfies the boundary conditions: [Incomplete sentence - likely referring to a specific condition or condition]. hour This ensures that the point of damage initiation corresponds to the point where the material reaches its peak strength; hour It calibrated the strain threshold at which the material completely loses its load-bearing capacity; within the intermediate range Follow The increasing monotonically ensures the continuity and irreversibility of damage evolution. The role of this equation is to provide a calculation basis for subsequent iterative solutions: in each load level and each iteration step, the corresponding damage variables can be quickly calculated by substituting the current strain value of each element integration point into the equation. Then, the stiffness matrix of each element is reduced and corrected according to the formula, so that the finite element model can dynamically reflect the stiffness decay behavior of tailings concrete due to damage accumulation, thereby accurately simulating the entire mechanical response of the pole from elastic deformation, damage initiation, softening development to complete failure.

[0027] when At that time, damage variable A value of 1 indicates that the material has completely lost its load-bearing capacity. in, The range of values ​​is ;when hour, ;when hour, ; The above damage variables With current strain The mapping relationship between them is referred to as the damage evolution relationship, denoted as .

[0028] Step 3: Using the material constitutive parameters and damage evolution relationship, the initial stiffness matrix is ​​modified into a nonlinear stiffness matrix that can be dynamically updated with strain state, and the initial nodal load vector is modified according to the peak stress to establish a nonlinear equilibrium equation. In this embodiment, establishing the nonlinear equilibrium equation specifically involves: Obtaining the elastic modulus from material constitutive data and peak stress ; Damage variables are obtained from damage evolution relationships. With current strain Mapping relationship between ; Let the initial stiffness matrix be The initial nodal load vector is Based on the initial stiffness matrix Extract the element stiffness matrix for each element. ; When the strain state is different at different locations in the structure, each element uses the strain at its own integration point to calculate the corresponding damage variable value. The element stiffness matrix of each element is corrected according to the following formula to obtain the corrected element stiffness matrix. : The modified element stiffness matrices are then reassembled into the overall nonlinear stiffness matrix. ; Simultaneously, the ultimate axial force is determined based on the product of the peak stress and the cross-sectional area at the top of the rod. The load values ​​in the initial nodal load vector are scaled proportionally so that the vertical concentrated load value at the reference point at the top of the rod is equal to the ultimate axial force, thereby generating the ultimate load vector. ; From the nonlinear stiffness matrix and ultimate load vector The nonlinear equilibrium equation is formed, and its expression is as follows: in Let be the nodal displacement vector to be solved.

[0029] In this embodiment, the element extraction function in the finite element program is used to extract the element stiffness matrix of each element in the finite element mesh model, denoted as . superscript This indicates the element number. When the strain state differs at different locations within the structure, each element uses the current strain value at its integration point and substitutes it into the damage evolution relation. The corresponding damage variable value is calculated and denoted as . According to the strain equivalence principle in damage mechanics, the effective stiffness of a damaged material is equal to the initial stiffness multiplied by the damage reduction factor. Based on this, the element stiffness matrix of each element is corrected to obtain the corrected element stiffness matrix. The corrected element stiffness matrices are then reassembled into a global nonlinear stiffness matrix according to the correspondence between element node numbers and global node numbers, denoted as [Mathematical Matrices]. Regarding load correction, based on peak stress... and the cross-sectional area of ​​the top of the pole The product of the initial nodal load vectors determines the ultimate axial force; The load values ​​in the vector are scaled proportionally, i.e., a scaling factor is set so that the vertical concentrated load value at the reference point at the top of the rod after scaling is exactly equal to the ultimate axial force, thus generating the ultimate load vector. This is derived from the aforementioned nonlinear stiffness matrix. and ultimate load vector This forms a nonlinear equilibrium equation, which reflects the force-displacement balance relationship of the pole structure under nonlinear stiffness conditions. Due to the nonlinear stiffness matrix... Damage variables in It depends on the current strain state, which in turn is determined by the nodal displacement vectors. The equation is derived from geometric equations, and therefore is a nonlinear equation in which strain and displacement are coupled, requiring an iterative method to solve it.

[0030] Step 4: Apply loads in progressively increasing steps to iteratively solve the nonlinear equilibrium equations. In each iteration step, update the damage variables and reconstruct the stiffness matrix based on the current strain state until the preset convergence condition is met, and then output the nodal displacement field. If the stiffness matrix becomes singular or non-positive definite during the iteration process, it is determined that the limit state has been reached and the solution is terminated. In this embodiment, the progressively increasing load application method specifically involves: applying the ultimate load vector... Divided into equal parts The first load level, the Level load vector Recorded as ,in Indicates the sequence number of the load level. ; Starting with the first level of load, the loads are applied level by level, and the solution under each level of load is used as the initial condition after the previous level converges to the equilibrium state.

[0031] The iterative solution process for each load level is carried out as follows: Let the current load level be the first. Level, the nodal displacement vector after convergence of the previous load level is , will the Level load vector The solution is applied to the finite element baseline model and solved iteratively. In the In the iteration, according to the The node displacement vector obtained in the second iteration Calculate the current strain value at each element integration point. The damage evolution relationship Determine the first Damage variable values ​​at each integration point during the next iteration And reconstruct the current overall nonlinear stiffness matrix according to the method described in step 3. : Based on the current node displacement vector Based on the current damage state, the global internal force vector is calculated by integrating the internal forces within the elements. ; Calculate the residual force vector of the current iteration step. : ; Solving for displacement increments : ; Update node displacement vector : ; Calculate the convergence criterion. If the following conditions are met simultaneously: ,and Then determine that the current load level has converged, and output the [number]th load level. Nodal displacement field under level load ,in , These are the preset first convergence tolerance and the second convergence tolerance, respectively. If the reconstructed stiffness matrix is ​​obtained before the convergence condition is met... If the determinant is zero or the main diagonal element is not positive, and the residual force vector does not satisfy the convergence condition. If the structure has reached its limit state, the iteration stops and the application of subsequent load levels is terminated.

[0032] This step uses the Newton-Raphson iterative method to solve the nonlinear equilibrium equations. Its logic is based on the following: due to the damage variable... It depends on the current strain state, which in turn is determined by the nodal displacement vectors. The decision leads to the stiffness matrix With displacement vector The structures are interconnected and cannot be solved directly; an iterative approach is necessary to approximate the true solution. Under each load level, the entire load is first applied to the structure. Then, the displacement vector is repeatedly adjusted to bring the internal and external forces into equilibrium. The initial iteration step uses the displacement state after convergence of the previous load level as a starting point. Based on the current displacement, strain is calculated, followed by the damage variable and the current stiffness matrix. The internal forces corresponding to the current displacement are then obtained through internal force integration. The difference between the external and internal forces is the residual force. If the residual force is zero, the equilibrium equation is precisely satisfied; if it is not zero, the displacement is corrected by solving for the displacement increment, gradually reducing the residual force. Essentially, this process transforms a nonlinear problem into a series of linear problems that approximate the true equilibrium state, with each iteration bringing the structural state closer to the actual equilibrium state.

[0033] Regarding the convergence criteria, this invention employs a dual control strategy combining residual force and displacement increment criteria. This is because a single criterion may fail under specific operating conditions. When only the residual force criterion is used, the stiffness matrix tends to be singular when the structure enters the softening phase or approaches the limit state. Even with a large displacement increment, the residual force may appear small due to stiffness degradation, leading to misjudgment of convergence. Conversely, when only the displacement increment criterion is used, the displacement increment itself is very small in the elastic phase, easily meeting the convergence condition prematurely and causing the calculation to terminate prematurely, failing to capture subsequent nonlinear behavior. Therefore, this invention requires the simultaneous satisfaction of two criteria: the residual force criterion... Criteria for ensuring balance between external and internal forces and for determining displacement increment. To ensure that the displacement response tends to be stable, both criteria must be met simultaneously before the current load level can be considered to have reached a true convergence state.

[0034] First convergence tolerance With the second convergence tolerance The range of values ​​is to Recommended value , The determination method is as follows: the initial setting is based on the degree of dispersion of the stress-strain curve of the tailings concrete axial compression test. If the curve is smooth and the data noise is low, a smaller value is taken to improve the accuracy. If the curve fluctuates greatly or the specimen uniformity is poor, the value is appropriately relaxed. Then, through trial calculation and calibration, with the goal of achieving the best fit between the finite element simulation results of a certain standard specimen and the experimentally measured load-displacement curve, the tolerance combination is finely adjusted within the specified range using grid search or gradient descent method. Finally, the value that makes the residual force convergence trajectory stable and the calculation efficiency meets the engineering requirements is determined.

[0035] Step 5: Based on the nodal displacement field, determine the vertical bearing capacity by taking the vertical displacement at the top of the pole as a preset threshold; when the displacement exceeds the limit or the solution is terminated, output the corresponding current load level as the vertical bearing capacity prediction result; In this embodiment, the determination of the vertical bearing capacity in step 5 is specifically as follows: From the The nodal displacement field output after the level load converges Extract the vertical displacement component at the reference point at the top of the rod, denoted as . Compare it with a preset displacement threshold. Comparison: like And the first If the load level is less than the load value corresponding to the ultimate load vector, it indicates that the vertical displacement of the pole under the current load level has not exceeded the allowable limit and has not yet reached the ultimate load state. Therefore, the load level can be increased to the next level. Solve for level loads; like This indicates that the pole has undergone excessive vertical deformation under vertical load, reaching or exceeding the deformation limit allowed under normal serviceability conditions. At this point, loading should be stopped, and the current pole should be... The level load value output is the predicted vertical bearing capacity of the ultra-high performance tailings pole, which corresponds to the bearing capacity under normal serviceability limit state. If in the 1st During the iterative solution of the first-order load, the solution terminates due to the occurrence of singular or non-positive definite stiffness matrices and the failure of residual forces to meet convergence conditions. This indicates that the structure has reached its ultimate limit state, i.e., instability or overall failure has occurred. At this point, the solution is... The level load value is output as the vertical bearing capacity prediction result, and the result is marked as the lower limit estimate of the ultimate bearing capacity; In this design, the displacement threshold criterion takes precedence over the stiffness singularity criterion. When a certain load level simultaneously satisfies both the displacement exceeding limit and stiffness singularity conditions, the current load value corresponding to the displacement exceeding limit is used as the predicted bearing capacity. In this dual-criteria setup, the displacement threshold criterion takes precedence over the stiffness singularity criterion because, for ultra-high-performance tailings poles, excessive vertical displacement often precedes overall instability, and displacement exceeding the limit reaches the ultimate state earlier, reflecting the control effect of the serviceability limit state on the bearing capacity. Therefore, when a certain load level simultaneously satisfies both the displacement exceeding limit and stiffness singularity conditions, the current load value corresponding to the displacement exceeding limit is used as the predicted bearing capacity, ensuring that the predicted result meets the deformation requirements for normal structural use. Through the above criterion combination, this invention can output the bearing capacity prediction result under two modes: when displacement precedes instability, the load value corresponding to the displacement criterion is output; when instability precedes displacement exceeding the limit, the previous level load value corresponding to the stiffness singularity criterion is output, thus comprehensively covering different failure modes of tailings poles.

[0036] The displacement threshold The deformation limit is determined according to the design and usage requirements of the pole or the relevant specifications; for ultra-high performance tailings poles, 1 / 200 to 1 / 300 of the total height of the pole is usually taken as the displacement limit under normal service limit.

[0037] Table 1: Load-displacement-damage relationship data in this embodiment Table 1 summarizes the applied load, vertical displacement at the top of the pole, maximum damage variable, and calculated state of the ultra-high performance tailings pole in this embodiment of the invention during the progressively increasing load process. This data is calculated based on the prediction method described in steps 1 to 5 of this invention. The pole's geometric parameters are set as follows: pole length 12 meters, outer diameter of the annular section 400 mm, wall thickness 100 mm. The reinforcement parameters are set as follows: 12 longitudinal steel bars with a diameter of 18 mm, spiral stirrups with a diameter of 8 mm, and a pitch of 80 mm. The material constitutive parameters are derived from the axial compression test of tailings concrete in the same batch, with peak stress... The peak strain is The characteristic point of the descending segment is 0.0085.

[0038] As shown in Table 1, under the first seven load levels, the vertical displacement at the top of the pole was basically linearly related to the applied load, increasing from 0.8 mm to 5.7 mm. The maximum damage variable remained at 0, indicating that the structure was in a fully elastic stage and no material damage had occurred. Starting with the eighth load level, the damage variable became positive for the first time, marking the entry of the concrete near the pole root into the damage softening stage. Simultaneously, the load-displacement curve began to exhibit nonlinear characteristics, and the displacement growth rate accelerated. As the load continued to increase, the damage variable showed an accelerated growth trend: d=0.156 under the 10th load level of 452.0 kN, d=0.538 (exceeding 0.5) under the 12th load level of 542.4 kN, d=0.886 under the 14th load level of 632.8 kN, and the vertical displacement at the top of the pole reached 44.5 mm under the 15th load level of 656.0 kN, exceeding the preset displacement threshold. In practice, the displacement threshold in this invention can be adjusted according to design requirements. If set to 1 / 300 (40mm), the 44.5mm displacement at the 15th load level of 656.0kN exceeds the limit, and this load level is output as the predicted vertical bearing capacity corresponding to the normal serviceability limit state. Simultaneously, it was observed that during the load increase from 632.8kN to 656.0kN, the load increment was only 23.2kN, while the displacement increment reached 6.3mm, indicating a significantly increased displacement growth rate. This suggests that the structural stiffness has severely degraded, approaching overall instability. The entire data sequence fully demonstrates the complete mechanical behavior of the pole from elastic deformation, damage initiation, accelerated damage development to final displacement exceeding the limit, verifying the effectiveness of the method in this invention in capturing the nonlinear softening characteristics of tailings concrete.

[0039] Please see Figure 4 Ultra-high performance tailings pole vertical bearing capacity prediction device, including: The model initialization module is used to obtain the geometric parameters and reinforcement parameters of the ultra-high performance tailings pole to be predicted, and input the geometric parameters and reinforcement parameters into the finite element reference model to generate an initial stiffness matrix and initial nodal load vector that only reflect the elastic stage. The constitutive parameter extraction module is used to collect axial stress-strain curve data of standard test blocks of tailings concrete used in the ultra-high performance tailings poles during the entire axial compression test, and extract the elastic modulus, peak stress, peak strain and descending segment feature points from the curve data. The extracted parameters are used as material constitutive data. Based on the peak strain and descending segment feature points, a preset damage evolution equation is used to determine the damage evolution relationship of damage variables with strain. The nonlinear equation establishment module is used to modify the initial stiffness matrix into a nonlinear stiffness matrix that can be dynamically updated with strain state by using the material constitutive parameters and damage evolution relationship, and to modify the initial nodal load vector according to the peak stress to establish nonlinear equilibrium equations. The step-by-step iterative solution module is used to iteratively solve the nonlinear equilibrium equation by applying loads in progressively increasing steps. In each iteration step, the damage variables are updated and the stiffness matrix is ​​reconstructed according to the current strain state until the preset convergence condition is met, and then the nodal displacement field is output. If the stiffness matrix becomes singular or non-positive definite during the iteration process, it is determined that the limit state has been reached and the solution is terminated. The bearing capacity determination output module is used to determine the vertical bearing capacity based on the nodal displacement field, with the vertical displacement at the top of the pole reaching a preset threshold as the criterion; when the displacement exceeds the limit or the solution is terminated, the corresponding current load level is output as the vertical bearing capacity prediction result.

[0040] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0041] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0042] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0043] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the vertical bearing capacity of an ultra-high performance tailings pole, characterized in that, The specific steps include: Step 1: Obtain the geometric parameters and reinforcement parameters of the ultra-high performance tailings pole to be predicted, and preset the initial elastic modulus of the tailings concrete and steel bars. Input the geometric parameters, reinforcement parameters and initial elastic modulus into the finite element reference model to generate the initial stiffness matrix and initial nodal load vector that only reflect the elastic stage. Step 2: Collect axial stress-strain curve data of the standard test block of tailings concrete used in the ultra-high performance tailings pole during the entire axial compression test, and extract the elastic modulus, peak stress, peak strain and descending segment feature points from the curve data. Use the extracted parameters as material constitutive data. Based on the peak strain and descending segment feature points, use a preset damage evolution equation to determine the damage evolution relationship of damage variables with strain. Step 3: Using the material constitutive parameters and damage evolution relationship, the initial stiffness matrix is ​​modified into a nonlinear stiffness matrix that can be dynamically updated with strain state, and the initial nodal load vector is modified according to the peak stress to establish a nonlinear equilibrium equation. Step 4: Apply loads in progressively increasing steps to iteratively solve the nonlinear equilibrium equations. In each iteration step, update the damage variables and reconstruct the stiffness matrix based on the current strain state until the preset convergence condition is met, and then output the nodal displacement field. If the stiffness matrix becomes singular or non-positive definite during the iteration process, it is determined that the limit state has been reached and the solution is terminated. Step 5: Based on the nodal displacement field, determine the vertical bearing capacity by taking the vertical displacement at the top of the pole as a preset threshold; when the displacement exceeds the limit or the solution is terminated, output the corresponding current load level as the vertical bearing capacity prediction result.

2. The method for predicting the vertical bearing capacity of the ultra-high performance tailings pole according to claim 1, characterized in that: The generation of the finite element reference model specifically includes: obtaining the pole length, cross-sectional outer diameter, wall thickness, and variable cross-sectional dimensions along the pole direction as geometric parameters, and obtaining the diameter, quantity, distribution circle radius of the longitudinal reinforcement and the diameter and pitch of the spiral stirrups as reinforcement parameters; using solid elements or structural elements to mesh the pole, generating a three-dimensional finite element mesh model composed of nodes and elements, which is the finite element reference model; Initial elastic moduli are assigned to the tailings concrete and steel reinforcement sections respectively, and displacement coordination or bond-slip relationship between the steel reinforcement and concrete is set. Vertical displacement constraints are applied to the bottom of the pole to simulate the actual foundation embedded boundary, constraining displacement in two orthogonal directions in the horizontal plane and rotation about the vertical axis, releasing the vertical displacement degree of freedom. A reference point is established at the centroid of the pole top, and after coupling the reference point with the pole top section, a vertical concentrated load is applied at the reference point. Based on the mesh model, the element stiffness matrix of each element is calculated using the initial elastic moduli and combined into an overall stiffness matrix. At the same time, the equivalent nodal loads are calculated and combined into an overall nodal load vector. The overall stiffness matrix and the overall nodal load vector are used as the initial stiffness matrix and the initial nodal load vector, respectively.

3. The method for predicting the vertical bearing capacity of the ultra-high performance tailings pole according to claim 2, characterized in that: The specific logic for obtaining the material constitutive data is as follows: Prepare standard prism or cylindrical specimens of tailings concrete with the same batch and mix ratio as the ultra-high performance tailings pole, and conduct uniaxial compression tests on a servo testing machine. Continuously collect axial stress and axial strain data from the start of loading to the complete failure of the specimen at a preset sampling frequency, and plot the stress-strain curve. The elastic modulus is extracted from the stress-strain curve, and the secant modulus within the initial linear segment of the stress-strain curve is taken as the elastic modulus. The initial linear segment refers to a continuous section in the stress-strain curve in which the axial stress and axial strain have a linear proportional relationship starting from the origin. This section ends when the axial stress reaches 30% of the peak stress, and the relative deviation between the slope of the line connecting any two points in this continuous section and the average slope in the section does not exceed 5%. Extract the peak stress and take it as the maximum stress value in the entire curve; Extract the peak strain and take it as the axial strain value corresponding to the peak stress; Extract the feature point of the descending segment, which is the axial strain value corresponding to the first decrease of the axial stress from the peak stress to 50% of the peak stress; if there is stress fluctuation in the descending segment, causing the peak stress to pass through 50% multiple times during the first descent, then take the minimum axial strain value as the feature point of the descending segment. The elastic modulus, peak stress, peak strain, and characteristic points of the descending segment are used together as the constitutive data of the material.

4. The method for predicting the vertical bearing capacity of ultra-high performance tailings poles according to claim 3, characterized in that: Based on the peak strain and the characteristic points of the descending segment, a preset damage evolution equation is used to determine the damage evolution relationship between the damage variable and strain, specifically: set up Indicates the current response. This represents the peak strain. Indicates the feature point of the descending segment. Indicates damage variables; The damage evolution mode is determined in the following manner: when At that time, damage variable A value of 0 indicates that the material has not been damaged; when At that time, damage variable Determine by the following formula: when At that time, damage variable A value of 1 indicates that the material has completely lost its load-bearing capacity. in, The range of values ​​is ;when hour, ;when hour, ; The above damage variables With current strain The mapping relationship between them is referred to as the damage evolution relationship, denoted as .

5. The method for predicting the vertical bearing capacity of ultra-high performance tailings poles according to claim 4, characterized in that: The establishment of the nonlinear equilibrium equations specifically involves: Obtaining the elastic modulus from material constitutive data and peak stress ; Damage variables are obtained from damage evolution relationships. With current strain Mapping relationship between ; Let the initial stiffness matrix be The initial nodal load vector is Based on the initial stiffness matrix Extract the element stiffness matrix for each element. ; When the strain state is different at different locations in the structure, each element uses the strain at its own integration point to calculate the corresponding damage variable value. The element stiffness matrix of each element is corrected according to the following formula to obtain the corrected element stiffness matrix. : The modified element stiffness matrices are then reassembled into the overall nonlinear stiffness matrix. ; Simultaneously, the ultimate axial force is determined based on the product of the peak stress and the cross-sectional area at the top of the rod. The load values ​​in the initial nodal load vector are scaled proportionally so that the vertical concentrated load value at the reference point at the top of the rod is equal to the ultimate axial force, thereby generating the ultimate load vector. ; From the nonlinear stiffness matrix and ultimate load vector The nonlinear equilibrium equation is formed, and its expression is as follows: in Let be the nodal displacement vector to be solved.

6. The method for predicting the vertical bearing capacity of ultra-high performance tailings poles according to claim 1, characterized in that: The method of applying the load in a progressively increasing manner is specifically as follows: the ultimate load vector... Divided into equal parts The first load level, the Level load vector Recorded as ,in Indicates the sequence number of the load level. ; Starting with the first level of load, the loads are applied level by level, and the solution under each level of load is used as the initial condition after the previous level converges to the equilibrium state.

7. The method for predicting the vertical bearing capacity of ultra-high performance tailings poles according to claim 6, characterized in that: The iterative solution process for each load level is carried out as follows: Let the current load level be the first. Level, the nodal displacement vector after convergence of the previous load level is , will the Level load vector The solution is applied to the finite element baseline model and solved iteratively. In the In the iteration, according to the The node displacement vector obtained in the second iteration Calculate the current strain value at each element integration point. The damage evolution relationship Determine the first Damage variable values ​​at each integration point during the next iteration And reconstruct the current overall nonlinear stiffness matrix according to the method described in step 3. : Based on the current node displacement vector Based on the current damage state, the global internal force vector is calculated by integrating the internal forces within the elements. ; Calculate the residual force vector of the current iteration step. : ; Solving for displacement increments : ; Update node displacement vector : ; Calculate the convergence criterion. If the following conditions are met simultaneously: ,and Then determine that the current load level has converged, and output the [number]th load level. Nodal displacement field under level load ,in , These are the preset first convergence tolerance and the second convergence tolerance, respectively. If the reconstructed stiffness matrix is ​​obtained before the convergence condition is met... If the determinant is zero or the main diagonal element is not positive, and the residual force vector does not satisfy the convergence condition. If the structure has reached its limit state, the iteration stops and the application of subsequent load levels is terminated.

8. The method for predicting the vertical bearing capacity of ultra-high performance tailings poles according to claim 7, characterized in that: The determination of the vertical bearing capacity in step 5 is specifically as follows: From the The nodal displacement field output after the level load converges Extract the vertical displacement component at the reference point at the top of the rod, denoted as . Compare it with a preset displacement threshold. Comparison: like And the first If the first load is less than the load value corresponding to the ultimate load vector, then the second load shall be applied. Solve for level loads; like Then stop loading and set the current number of pages to [number]. The output of the load value is the predicted result of the vertical bearing capacity of the ultra-high performance tailings pole; If in the 1st If the solution is terminated during the iterative solution of the first-order load due to the stiffness matrix being singular or non-positive definite and the residual force not satisfying the convergence condition, then the solution will be terminated. The level load value is output as the vertical bearing capacity prediction result, and the result is marked as the lower limit estimate of the ultimate bearing capacity; The displacement threshold criterion takes precedence over the stiffness singularity criterion; when a certain load level simultaneously satisfies both the displacement exceeding limit and stiffness singularity conditions, the current load value corresponding to the displacement exceeding limit is used as the bearing capacity prediction result.

9. A high-performance tailings pole vertical bearing capacity prediction device, wherein the high-performance tailings pole vertical bearing capacity prediction device is used to execute the high-performance tailings pole vertical bearing capacity prediction method according to any one of claims 1-8, characterized in that, include: The model initialization module is used to obtain the geometric parameters and reinforcement parameters of the ultra-high performance tailings pole to be predicted, and input the geometric parameters and reinforcement parameters into the finite element reference model to generate an initial stiffness matrix and initial nodal load vector that only reflect the elastic stage. The constitutive parameter extraction module is used to collect axial stress-strain curve data of standard test blocks of tailings concrete used in the ultra-high performance tailings poles during the entire axial compression test, and extract the elastic modulus, peak stress, peak strain and descending segment feature points from the curve data. The extracted parameters are used as material constitutive data. Based on the peak strain and descending segment feature points, a preset damage evolution equation is used to determine the damage evolution relationship of damage variables with strain. The nonlinear equation establishment module is used to modify the initial stiffness matrix into a nonlinear stiffness matrix that can be dynamically updated with strain state by using the material constitutive parameters and damage evolution relationship, and to modify the initial nodal load vector according to the peak stress to establish nonlinear equilibrium equations. The step-by-step iterative solution module is used to iteratively solve the nonlinear equilibrium equation by applying loads in progressively increasing steps. In each iteration step, the damage variables are updated and the stiffness matrix is ​​reconstructed according to the current strain state until the preset convergence condition is met, and then the nodal displacement field is output. If the stiffness matrix becomes singular or non-positive definite during the iteration process, it is determined that the limit state has been reached and the solution is terminated. The bearing capacity determination output module is used to determine the vertical bearing capacity based on the nodal displacement field, with the vertical displacement at the top of the pole reaching a preset threshold as the criterion; when the displacement exceeds the limit or the solution is terminated, the corresponding current load level is output as the vertical bearing capacity prediction result.

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