Calcarenaceous sand particle breakage energy calculation method and system improved by particle swarm optimization

Abstract

The present application relates to geotechnical engineering technical field, especially provide a kind of particle swarm optimization improved calcareous sand particle breakage energy calculation method and system.The method includes obtaining triaxial test data and peak point data;According to triaxial test data and peak point data, based on stress-expansion breakage model framework, construct multi-objective optimization function;Multi-objective optimization function minimum value is solved using particle swarm optimization algorithm, and the optimal value of optimization parameter is obtained, and the initial friction angle of calcareous sand is calibrated;According to initial friction angle, calculate critical state angle, establish evolution equation in the process of friction angle shear;Corresponding stress-expansion breakage model equation is changed, combined with calcareous sand triaxial test data, the breakage energy of calcareous sand particle is calculated, the breakage energy evolution process is fitted, and the breakage energy evolution equation of calcareous sand particle is established;The method calculates the breakage energy of calcareous sand particle, can continuously characterize the evolution process of particle breakage and establish corresponding evolution equation.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method and system for calculating the crushing energy of calcareous sand particles through particle swarm optimization. Background Technology

[0002] With the development of marine engineering, an increasing number of projects are being carried out in geological environments containing calcareous sand, including anchoring structures for offshore renewable energy, foundations for oil and gas platforms, and land reclamation. Calcareous sand differs from traditional terrestrial sand in that it is porous, angular, has low strength, and is easily broken. Breaking alters the soil gradation, significantly affecting the mechanical behavior and deformation characteristics of calcareous sand.

[0003] However, existing methods for measuring particle breakage primarily rely on changes in particle size before and after shearing, known as particle breakage indices. This method cannot continuously capture the evolution of particle breakage. Furthermore, current energy consumption during triaxial shearing is mainly characterized by plastic work. Plastic work encompasses both the energy consumed by friction and the energy consumed during particle breakage; existing methods cannot calculate the particle breakage energy during the triaxial shearing process of calcareous sand. Summary of the Invention

[0004] In view of this, the present invention provides a particle swarm optimization-based method and system for calculating the crushing energy of calcareous sand particles, which can calculate the crushing energy of calcareous sand particles, continuously characterize the evolution process of particle crushing, and establish corresponding evolution equations.

[0005] In a first aspect, the present invention provides a particle swarm optimization-improved method for calculating the crushing energy of calcareous sand particles, the method comprising:

[0006] Step 1: Conduct a triaxial drainage test on calcareous sand to obtain triaxial test data and peak point data, including peak stress ratio and volumetric strain rate;

[0007] Step 2: Based on the triaxial experimental data and peak point data, construct a multi-objective optimization function based on the stress-expansion fracture model framework;

[0008] Step 3: Use the particle swarm optimization algorithm to solve for the minimum value of the multi-objective optimization function, obtain the optimal value of the optimization parameters, and calibrate the initial friction angle of the calcareous sand;

[0009] Step 4: Calculate the critical state angle based on the initial friction angle and establish the evolution equation for the friction angle shear process;

[0010] Step 5: Modify the stress-expansion crushing model equation and calculate the crushing energy of calcareous sand particles by combining the triaxial experimental data of calcareous sand.

[0011] Step 6: Fit the energy evolution process of crushing and establish the energy evolution equation for crushing calcareous sand particles.

[0012] Optionally, step 1 includes:

[0013] Using a triaxial soil testing apparatus, the same density D was measured. r Calcareous sand under different confining pressures Drained shear tests were conducted to obtain triaxial experimental data under different confining pressures, including deviatoric stress q and axial strain. Body strain Axial strain Data shows that the deviatoric stress q is the effective major principal stress. With effective minor principal stress The difference, Simultaneously, peak point data were acquired, including the peak stress ratio under different confining pressures measured experimentally. and peak volumetric strain rate , where j represents different confining pressures, j=1,2,…m; p represents the peak point.

[0014] Optionally, step 2 includes:

[0015] Based on the stress-expansion fracture model framework, the theoretical peak stress ratio is calculated according to the experimentally measured peak volumetric strain rate; the absolute values ​​of the differences between the peak stress ratios measured by triaxial experiments under different confining pressures and the theoretical peak stress ratios are weighted and summed to construct a multi-objective optimization function.

[0016] Based on the stress-expansion fracture model framework, the theoretical peak stress ratio under the j-th level confining pressure is... The calculation formula is: ;

[0017] in, The peak volumetric strain rate measured experimentally; initial friction angle. and the rate of change of energy in particle crushing The optimization parameters for the particle swarm optimization algorithm; initial friction angle. For the same soil mass remaining unchanged, The value is related to the confining pressure; as the confining pressure increases, the degree of particle breakage continuously increases. It continues to rise;

[0018] Multi-objective function of particle swarm optimization algorithm The weighted summation of the absolute values ​​of the differences between the theoretical peak stress ratio and the experimental peak stress ratio under different confining pressures is calculated using the following formula:

[0019] ;

[0020] in, , This represents the weight of the confining pressure error value at level j.

[0021] Optionally, step 3 includes:

[0022] The particle swarm optimization algorithm was used to solve for the minimum value of the multi-objective function, and the initial friction angle of the calcareous sand was obtained. To find the optimal value, the particle swarm optimization algorithm first initializes the particle i within a given search space, assigning it an initial velocity V. i and position X i Then, the particle's V is continuously updated iteratively. i and X i The optimal position is found based on a predefined objective function; the V of the particle in the particle swarm optimization algorithm. i and X i The update satisfies the following equation:

[0023] ;

[0024] ;

[0025] in, This represents the current iteration number. This represents the maximum number of iterations. The inertial weight determines the degree to which the particle's previous velocity contributes to its current velocity. Linear dynamic inertia weights are used. This is used to ensure that the particle swarm optimization algorithm uses different search strategies at different stages. Take 0.9, Take 0.4; The contraction coefficient is used to control the dynamic characteristics of particles. , ∈(0,1], which determines the balance between particle development and exploration; and These are cognitive and social parameters, used to reflect the influence of the particle velocity on its own and the group's optimal values, and then multiplied by random numbers r1 and r2 between [0,1] respectively; pbest is the optimal position found by a single particle, and gbest is the optimal position found by the entire particle swarm.

[0026] Optionally, when using the particle swarm optimization algorithm to solve for the minimum value of the multi-objective function, the search range of the parameters needs to be given first; in the stress-expansion fracture model, the minimum confining pressure in the experiment is used as the minimum value. and Substitute the values ​​into the equation to calculate the friction angle, which includes particle breakage but excludes expansion. , Including the effect of particle breakage under minimum confining pressure, it is greater than , as the upper limit of the search:

[0027] ;

[0028] The smaller the confining pressure, the smaller the contribution to particle breakage; therefore, The search scope is set to [ -β, When the confining pressure increases, The value increases accordingly; limitations apply. After the range, The range of values ​​will be adjusted accordingly based on the search results.

[0029] Optionally, since particle swarm optimization is essentially a random search, the solutions obtained in each search will differ. The quality of the solutions is judged according to the following principles: (1) the objective function value; the smaller the objective function value, the higher the accuracy of the solution; (2) the actual physical meaning. The value of increases continuously with the increase of confining pressure, and the solution must satisfy the actual physical meaning; (3) boundary conditions, the searched solution must be located inside the given space; The value is the average of the search results obtained from three iterations of the particle swarm optimization algorithm.

[0030] Optionally, step 4 includes:

[0031] Critical state angle of calcareous sand The calculation formula is:

[0032] ;

[0033] in, The initial friction angle is... This represents the contribution of particle rearrangement to strength during soil shearing to the critical state. Estimation was made based on the results of triaxial experiments on calcareous sand;

[0034] Friction angle The evolution equation is expressed as:

[0035] ;

[0036] in, The axial strain required to reach the critical state.

[0037] Optionally, step 5 includes:

[0038] Energy consumption per unit volume of crushed particles is calculated using inverse integral calculation. The evolutionary process:

[0039] ;

[0040] Input triaxial experimental data and And combined with the friction angle The evolution equation, that is, the particle breakage energy during the triaxial shear process, is obtained. .

[0041] Optionally, step 6 includes:

[0042] To incorporate the energy of calcareous sand particle breakage into the constitutive model, a corresponding energy evolution equation must be established to describe and characterize the breakage process; particle breakage evolution and mean effective stress and axial strain The relevant energy for breakage is represented by the following nonlinear equation:

[0043] ;

[0044] in, The fitting parameters are based on the actual particle crushing energy values. This represents the particle breakage energy at the critical state. .

[0045] Secondly, the present invention provides a particle swarm optimization-improved energy calculation system for crushing calcareous sand particles, the system comprising:

[0046] The data reading module is used to conduct triaxial drainage experiments on calcareous sand, and to acquire triaxial experimental data and peak point data, including peak stress ratio and volumetric strain rate.

[0047] The mathematical model building module is used to construct a multi-objective optimization function based on the stress-expansion fracture model framework, using triaxial experimental data and peak point data.

[0048] The particle swarm optimization module is used to solve for the minimum value of the multi-objective optimization function using the particle swarm optimization algorithm, obtain the optimal value of the optimization parameters, and calibrate the initial friction angle of the calcareous sand.

[0049] The particle crushing energy calculation module calculates the critical state angle based on the initial friction angle and establishes the evolution equation during the friction angle shearing process; it modifies the stress-expansion crushing model equation and calculates the crushing energy of calcareous sand particles by combining triaxial experimental data of calcareous sand; it fits the crushing energy evolution process and establishes the calcareous sand particle crushing energy evolution equation.

[0050] Thirdly, embodiments of the present invention provide a computer-readable storage medium comprising a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to execute the particle swarm optimization improved method for calculating the crushing energy of calcareous sand particles in the first aspect or any possible implementation thereof.

[0051] Fourthly, embodiments of the present invention provide an electronic device, comprising: one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions that, when executed by the device, cause the device to perform the particle swarm optimization-improved energy calculation method for crushing calcareous sand particles in the first aspect or any possible implementation of the first aspect.

[0052] The technical solution provided by this invention includes a method comprising conducting a triaxial drainage experiment on calcareous sand to obtain triaxial experimental data and peak point data, including peak stress ratio and volumetric strain rate; constructing a multi-objective optimization function based on the triaxial experimental data and peak point data and a stress-expansion fracture model framework; solving for the minimum value of the multi-objective optimization function using a particle swarm optimization algorithm to obtain the optimal value of the optimization parameters and calibrating the initial friction angle of the calcareous sand; calculating the critical state angle based on the initial friction angle and establishing the evolution equation in the friction angle shear process; modifying the stress-expansion fracture model equation and combining it with the triaxial experimental data of calcareous sand to calculate the crushing energy of calcareous sand particles, fitting the evolution process of crushing energy, and establishing the evolution equation of crushing energy of calcareous sand particles; this method calculates the crushing energy of calcareous sand particles, can continuously characterize the evolution process of particle crushing, and establishes the corresponding evolution equation. Attached Figure Description

[0053] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 A flowchart of a particle swarm optimization-improved method for calculating the crushing energy of calcareous sand particles, provided in an embodiment of the present invention;

[0055] Figure 2 A flowchart illustrating another particle swarm optimization-improved method for calculating the crushing energy of calcareous sand particles, provided in an embodiment of the present invention;

[0056] Figure 3 A diagram showing triaxial experimental data of calcareous sand provided in an embodiment of the present invention;

[0057] Figure 4 A curve showing the fitting results of particle crushing energy provided in an embodiment of the present invention;

[0058] Figure 5 A comparison chart between particle crushing energy and crushing index provided in an embodiment of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0061] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” used in the embodiments of this invention are also intended to include the plural forms unless the context clearly indicates otherwise.

[0062] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0063] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0064] This invention provides a particle swarm optimization-based method for calculating the energy of calcareous sand particle crushing, such as... Figure 1 and Figure 2 As shown, the method includes:

[0065] Step 1: Conduct a triaxial drainage test on calcareous sand to obtain triaxial test data and peak point data, including peak stress ratio and volumetric strain rate.

[0066] In this embodiment of the invention, step 1 includes:

[0067] Using a triaxial soil testing apparatus, the same density D was measured. r Calcareous sand under different confining pressures Drained shear tests were conducted to obtain triaxial experimental data under different confining pressures, including deviatoric stress q and axial strain. Body strain Axial strain Data shows that the deviatoric stress q is the effective major principal stress. With effective minor principal stress The difference, Simultaneously, peak point data were acquired, including the peak stress ratio under different confining pressures measured experimentally. and peak volumetric strain rate , where j represents different confining pressures, j=1,2,…m; p represents the peak point.

[0068] In this embodiment of the invention, samples of the same density D were collected. r This data represents drained triaxial experimental data for 75% calcareous sand (from LedgePoint, Western Australia) under confining pressures of 100 Pa, 300 Pa, and 500 kPa, including deviatoric stress q and axial strain. Body strain Axial strain Data, such as Figure 3 As shown. The experimental data were processed to locate the peak point of the deviatoric stress and obtain the peak stress ratio at that point. and peak volumetric strain rate .

[0069] Step 2: Based on the triaxial experimental data and peak point data, construct a multi-objective optimization function based on the stress-expansion fracture model framework.

[0070] In this embodiment of the invention, step 2 includes:

[0071] Based on the stress-expansion fracture model framework, the theoretical peak stress ratio is calculated according to the experimentally measured peak volumetric strain rate; the absolute values ​​of the differences between the peak stress ratios measured by triaxial experiments under different confining pressures and the theoretical peak stress ratios are weighted and summed to construct a multi-objective optimization function.

[0072] Based on the stress-expansion fracture model framework, the theoretical peak stress ratio under the j-th level confining pressure is... The calculation formula is:

[0073] ;

[0074] in, The peak volumetric strain rate measured experimentally; initial friction angle. and the rate of change of energy in particle crushing The optimization parameters for the particle swarm optimization algorithm; initial friction angle. For the same soil mass remaining unchanged, The value is related to the confining pressure; as the confining pressure increases, the degree of particle breakage continuously increases. It continues to rise;

[0075] The peak volumetric strain rate measured in the experiment Substitute the initial friction angle and the rate of change of energy in particle crushing These are the optimization parameters for the particle swarm optimization algorithm.

[0076] Multi-objective function of particle swarm optimization algorithm The weighted summation of the absolute values ​​of the differences between the theoretical peak stress ratio and the experimental peak stress ratio under different confining pressures is calculated using the following formula:

[0077] ;

[0078] in, , This represents the weight of the confining pressure error value at level j. Different confining pressure data contribute equally to the multi-objective function, so it is set to 1.

[0079] Step 3: Use the particle swarm optimization algorithm to solve for the minimum value of the multi-objective optimization function, obtain the optimal value of the optimization parameters, and calibrate the initial friction angle of the calcareous sand.

[0080] The optimal parameter is the value that minimizes the difference between the theoretical stress ratio and the experimental stress ratio, thus determining the initial friction angle of the calcareous sand.

[0081] In this embodiment of the invention, step 3 includes:

[0082] The particle swarm optimization algorithm was used to solve for the minimum value of the multi-objective function, and the initial friction angle of the calcareous sand was obtained. To find the optimal value, the particle swarm optimization algorithm first initializes the particle i within a given search space, assigning it an initial velocity V. i and position X i Then, the particle's V is continuously updated iteratively. i and X i The particle swarm optimization (PSO) algorithm finds the optimal position based on a predefined objective function. The key to the PSO algorithm lies in the mutual learning, inheritance, and evolution of particles during their flight. The velocity of a particle in the next iteration is influenced by its own flight velocity and the flight results of its companions. The velocity V of a particle in the PSO algorithm... i and X i The update satisfies the following equation:

[0083] ;

[0084] ;

[0085] in, This represents the current iteration number. To maximize the number of iterations and improve search accuracy, and to avoid getting trapped in local optima, the maximum number of iterations is set to 50,000. The inertial weight determines the degree to which the particle's previous velocity contributes to its current velocity. Linear dynamic inertia weights are used. This is used to ensure that the particle swarm optimization algorithm uses different search strategies at different stages. Take 0.9, Take 0.4; The contraction coefficient is used to control the dynamic characteristics of particles. , The region ∈(0,1] determines the balance between particle development and exploration. Set it to 1; and These are cognitive and social parameters, used to reflect the influence of the particle velocity on its own and the group's optimal values, and then multiplied by random numbers r1 and r2 between [0,1] respectively; , and Both are set to 2.05; pbest is the best position found by a single particle, and gbest is the best position found by the entire particle swarm.

[0086] In this embodiment of the invention, when using the particle swarm optimization algorithm to solve for the minimum value of a multi-objective function, the search range of the parameters must first be given; in the stress-expansion fracture model, dE is not considered. B The term refers to the minimum confining pressure in the experiment. and Substitute the values ​​into the equation to calculate the friction angle, which includes particle breakage but excludes expansion. , Including the effect of particle breakage under minimum confining pressure, it is greater than , as the upper limit of the search:

[0087] ;

[0088] The smaller the confining pressure, the smaller the contribution to particle breakage. The closer ,therefore, The search scope is set to [ -β, Under a confining pressure of 100 kPa, particle breakage is still not significant, and the contribution of particle breakage strength is small. The value can be taken as 2°; as the confining pressure increases, The value increases accordingly; limitations apply. After the range, The range of values ​​will be adjusted accordingly based on the search results.

[0089] In this embodiment of the invention, the particle swarm optimization algorithm is essentially a random search, and the solutions obtained in each search will differ. The quality of the solutions is judged according to the following principles: (1) the objective function value. The smaller the objective function value, the higher the accuracy of the solution. The algorithm proposed above can guarantee that the objective function value is exactly equal to 0; (2) the actual physical meaning. The value of increases continuously with the increase of confining pressure, and the solution must satisfy the actual physical meaning; (3) Boundary conditions: the searched solution must be located inside the given space to avoid the parameter taking the boundary value; The value is the average of the search results obtained from three iterations of the particle swarm optimization algorithm.

[0090] In this embodiment of the invention, the calcareous sand obtained by the particle swarm optimization algorithm The optimal value is 33.35°, obtained through experimental fitting and calibration. The value is 34°, and the relative error between the two is only 2%, which proves the effectiveness of the method of the present invention.

[0091] Step 4: Calculate the critical state angle based on the initial friction angle and establish the evolution equation in the friction angle shear process.

[0092] In this embodiment of the invention, step 4 includes:

[0093] Due to the extreme irregularity of calcareous sand particles and their extremely complex internal structure, it is often difficult to reach a strictly critical state in triaxial experiments on calcareous sand. The critical state angle for calcareous sand is... Selection is relatively difficult; critical state angle of calcareous sand The results obtained by particle swarm optimization algorithm The values ​​are not significantly different; the difference lies in the contribution of particle rearrangement to strength during soil shearing to the critical state. . Represented as and The sum; critical state angle of calcareous sand The calculation formula is:

[0094] ;

[0095] in, The initial friction angle is... This represents the contribution of particle rearrangement to strength during soil shearing to the critical state. Estimation was made based on the results of triaxial experiments on calcareous sand;

[0096] Estimated based on experimental results of different calcareous sands The value is 3°. .

[0097] Friction angle The evolution equation is expressed as:

[0098] ;

[0099] in, The axial strain required to reach the critical state.

[0100] In this embodiment of the invention, ; The strain at the end of the triaxial experiment was taken as 35%.

[0101] Step 5: Modify the stress-expansion crushing model equation and calculate the crushing energy of calcareous sand particles by combining the triaxial experimental data of calcareous sand.

[0102] In this embodiment of the invention, step 5 includes:

[0103] Energy consumption per unit volume of crushed particles is calculated using inverse integral calculation. The evolutionary process:

[0104] ;

[0105] Input triaxial experimental data and And combined with the friction angle The evolution equation, that is, the particle breakage energy during the triaxial shear process, is obtained. .

[0106] In embodiments of the present invention, such as Figure 4 As shown, particle breakage increases with ε1 during shearing, and tends to stabilize at the critical state. This is consistent with experimental observations, indicating that particle breakage does not continue indefinitely; eventually, the particle size distribution develops towards fractals, and particle breakage ceases. B The values ​​all increase significantly with increasing confining pressure, indicating that particle breakage is necessarily related to the stress state.

[0107] Before particle breakage, it is mainly quantified by the change in particle size before and after loading. Hardin proposed the relative breakage B... r Widely used. Different calcareous sand samples are sheared to different axial strain points and then sieved to obtain B at different strain points after crushing. r To verify the correctness of the calculated particle breakage energy, Figure 4 B was drawn r Regarding E B The scatter plot shows that the linear relationship between the two is very significant, and the linear fit is R0. 2 Greater than 0.95, which indicates that the E value sought in this invention is... B With B r The correlation is strong, verifying the use of E BThe rationale for characterizing the particle breakage evolution of calcareous sand is demonstrated. Therefore, the particle breakage energy calculated in this invention can continuously characterize the particle breakage evolution of calcareous sand instead of particle breakage indices.

[0108] Step 6: Fit the energy evolution process of crushing and establish the energy evolution equation for crushing calcareous sand particles.

[0109] In this embodiment of the invention, step 6 includes:

[0110] To incorporate the energy of calcareous sand particle breakage into the constitutive model, a corresponding energy evolution equation must be established to describe and characterize the breakage process; particle breakage evolution and mean effective stress and axial strain The relevant energy for breakage is represented by the following nonlinear equation:

[0111] ;

[0112] in, The fitting parameters are based on the actual particle crushing energy values. This represents the particle breakage energy at the critical state. .

[0113] In this embodiment of the invention, the fitting result is as follows: Figure 4 As shown, the fitted curve almost perfectly matches the calculated energy of particle crushing, R 2 Greater than 0.95. The energy evolution equation for the breakage of calcareous sand particles is a function of the average effective stress p′ and the axial strain ε1. It can be embedded into the corresponding soil constitutive model, and the corresponding particle breakage energy can be calculated based on the stress-strain state of the soil, thereby characterizing the particle breakage evolution.

[0114] This invention provides a particle swarm optimization-based energy calculation system for crushing calcareous sand particles, the system comprising:

[0115] The system comprises the following modules: a data acquisition module for conducting triaxial drainage experiments on calcareous sand, acquiring triaxial experimental data and peak point data, including peak stress ratio and volumetric strain rate; a mathematical model construction module for constructing a multi-objective optimization function based on the triaxial experimental data and peak point data, using a stress-expansion fracture model framework; a particle swarm optimization module for solving the minimum value of the multi-objective optimization function using the particle swarm optimization algorithm, obtaining the optimal values ​​of the optimization parameters, and calibrating the initial friction angle of the calcareous sand; and a particle crushing energy calculation module for calculating the critical state angle based on the initial friction angle, establishing the evolution equation during the friction angle shearing process, modifying the stress-expansion fracture model equation, and calculating the particle crushing energy of calcareous sand by combining the triaxial experimental data; and fitting the crushing energy evolution process to establish the particle crushing energy evolution equation for calcareous sand.

[0116] Compared with the prior art, the present invention has the following beneficial effects:

[0117] First, this invention is based on the stress-expansion fracture model framework and uses a particle swarm optimization algorithm to calibrate the initial friction angle of calcareous sand. This method avoids the cumbersome steps of traditional experimental fitting calibration, has good scalability, and can quickly calibrate the initial friction angle of different types of calcareous sand.

[0118] Secondly, this invention calculates the particle crushing energy during the shearing process of calcareous sand, separating the particle crushing energy from the energy consumed by friction, thus providing a deeper understanding of the energy dissipation mechanism of calcareous sand during the stress process.

[0119] Next, the particle crushing energy calculated by this invention can replace the particle crushing index and continuously characterize the evolution process of particle crushing, avoiding the process of obtaining particle crushing index through screening.

[0120] Finally, this invention fits the evolution equation of the crushing energy of calcareous sand particles, which can be embedded into existing soil constitutive models, providing an effective crushing characterization method for establishing calcareous sand crushing models.

[0121] The technical solution provided by this invention includes a method comprising conducting a triaxial drainage experiment on calcareous sand to obtain triaxial experimental data and peak point data, including peak stress ratio and volumetric strain rate; constructing a multi-objective optimization function based on the triaxial experimental data and peak point data and a stress-expansion fracture model framework; solving for the minimum value of the multi-objective optimization function using a particle swarm optimization algorithm to obtain the optimal value of the optimization parameters and calibrating the initial friction angle of the calcareous sand; calculating the critical state angle based on the initial friction angle and establishing the evolution equation in the friction angle shear process; modifying the stress-expansion fracture model equation and combining it with the triaxial experimental data of calcareous sand to calculate the crushing energy of calcareous sand particles, fitting the evolution process of crushing energy, and establishing the evolution equation of crushing energy of calcareous sand particles; this method calculates the crushing energy of calcareous sand particles, can continuously characterize the evolution process of particle crushing, and establishes the corresponding evolution equation.

[0122] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the grain breakage energy of calcareous sand particles using particle swarm optimization, characterized by, The method comprises: Step 1, performing a calcareous sand triaxial drainage experiment, obtaining triaxial experiment data and peak point data, including peak stress ratio and volumetric strain rate; Step 2, based on the stress-dilatancy failure model framework, a multi-objective optimization function is constructed according to the triaxial experiment data and the peak point data; Step 3, the minimum value of the multi-objective optimization function is solved by using the particle swarm optimization algorithm, and the optimal value of the optimization parameter is obtained, and the initial friction angle of the calcareous sand is calibrated; Step 4, the critical state angle is calculated according to the initial friction angle, and the evolution equation in the friction angle shear process is established; Step 5, the stress-dilatancy failure model equation is changed, and the calcareous sand particle crushing energy is calculated combined with the triaxial experiment data of the calcareous sand; Step 6, the crushing energy evolution process is fitted, and the calcareous sand particle crushing energy evolution equation is established; The step 2 comprises: Based on the stress-dilatancy failure model framework, the theoretical peak stress ratio is calculated according to the measured peak volumetric strain rate; the absolute values of the differences between the peak stress ratios measured under different confining pressures and the theoretical peak stress ratios are weighted and summed to construct a multi-objective optimization function; Based on the stress-dilatancy failure model framework, the theoretical peak stress ratio under the jth stage confining pressure is The calculation formula is: ; wherein, is the experimentally measured peak volumetric strain rate; initial friction angle and the rate of change of particle breakage energy is the optimization parameter of the particle swarm algorithm; initial friction angle , for the same soil body, The value of is related to the confining pressure, and with the increase of confining pressure, the degree of particle breakage, continuously increases; Multi-objective function of particle swarm optimization algorithm The absolute value of the difference between the theoretical peak stress ratio and the experimental peak stress ratio under different confining pressures is weighted and summed, and the calculation formula is: ； wherein , represents the weight of the jth level confining pressure error value; The step 6 comprises: To embed the energy of calcareous sand particle breakage into the constitutive model, the corresponding energy evolution equation should be established to describe the breakage process; the evolution of particle breakage is related to the average effective stress and axial strain ; the breakage energy is expressed by the following nonlinear equation: ； wherein, is a fitting parameter, fitted according to actual particle breakage energy values; is the particle breakage energy at the critical state, .

2. The method of claim 1, wherein, The step 1 comprises: Through the triaxial test instrument of soil, the drained shear test of calcareous sand with the same density D r under different confining pressures was carried out, and the triaxial test data under different confining pressures were obtained, including the deviatoric stress q, the axial strain , the volumetric strain , the axial strain data, the deviatoric stress q being the difference between the effective major stress and the effective minor stress , ; at the same time, the peak point data were obtained, including the peak stress ratio and the peak volumetric strain rate under different confining pressures measured by the experiment, wherein j represents different confining pressures, j = 1, 2, … m; p represents the peak point.

3. The method of claim 1, wherein, The step 3 comprises: The particle swarm optimization algorithm is used to solve the minimum value of the multi-objective function, and the optimal value of the initial friction angle of calcareous sand is obtained The particle swarm optimization algorithm is initialized in a given search space, and the initial velocity V i and position X i of particle i are assigned; then the V i and X i of the particle are iteratively updated to find the best position according to the predefined objective function; the update of the V i and X i of the particle in the particle swarm optimization algorithm satisfies the following equation: ； ； wherein, is the current iteration number, is the maximum iteration number; is the inertia weight, which determines the contribution of the previous velocity to the current velocity, , a linear dynamic inertia weight is adopted to ensure that the PSO algorithm adopts different search strategies at different stages, takes 0.9, takes 0.4; is the contraction coefficient, which is used to control the dynamic characteristics of the particles, , ∈(0, 1], which determines the balance between the development and exploration of the particles; and are the cognitive parameter and the social parameter, respectively, which are used to reflect that the velocity of the particles is affected by the individual and group optimal values, and are multiplied by random numbers r1 and r2 between 0 and 1, respectively; pbest is the optimal position searched by a single particle, and gbest is the optimal position searched by the entire particle swarm.

4. The method of claim 3, wherein, The minimum value of the multi-objective function is solved by using the particle swarm optimization algorithm, which needs to give the search range of parameters; in the stress-dilation crushing model, the minimum confining pressure in the experiment and The friction angle is calculated by including particle crushing and excluding dilation , Including the influence of particle crushing at the lowest confining pressure, which is greater than as the upper limit value of the search ； The smaller the confining pressure, the smaller the contribution of particle crushing, and thus, The search range is taken as -β, When the confining pressure increases, the value of correspondingly increases; the value of is adjusted according to the search result after the range is limited. is adjusted according to the search result after the range is limited.

5. The method of claim 4, wherein, Particle swarm optimization is essentially a random search, and the solutions obtained in each search will differ. The quality of the solutions is judged according to the following principles: (1) the objective function value; the smaller the objective function value, the higher the accuracy of the solution; (2) the actual physical meaning. The value of increases continuously with the increase of confining pressure, and the solution must satisfy the actual physical meaning; (3) boundary conditions, the searched solution must be located inside the given space; The value is the average of the search results obtained from three iterations of the particle swarm optimization algorithm.

6. The method of claim 5, wherein, The step 4 comprises: Calcitic sand critical state angle The formula for calculating the critical state angle is: ； where, is the initial friction angle, is the contribution of particle rearrangement to the strength during the process of soil shear to critical state, is estimated from the results of triaxial tests on calcareous sand; friction angle The evolution equation for is given by ； wherein, is the axial strain at the critical state.

7. The method of claim 6, wherein, The step 5 comprises: Evolution of the process of integral back-calculation of the energy of breaking of particles per unit volume of the particles ； The triaxial test data are brought in and combined with the evolution equation of friction angle , the particle breakage energy during triaxial shearing is obtained .

8. A system for calculating the breakage energy of calcareous sand particles using particle swarm optimization, characterized by, The system is used to realize the particle swarm optimization improved calcareous sand particle crushing energy calculation method of claim 1, and the system comprises: A data reading module is used to perform a calcareous sand triaxial drainage experiment, obtain triaxial experiment data and peak point data, including peak stress ratio and volumetric strain rate; A mathematical model construction module is used to construct a multi-objective optimization function based on the stress-dilatancy failure model framework according to the triaxial experiment data and the peak point data; A particle swarm optimization algorithm optimization module is used to solve the minimum value of the multi-objective optimization function by using the particle swarm optimization algorithm, and the optimal value of the optimization parameter is obtained, and the initial friction angle of the calcareous sand is calibrated; A particle crushing energy calculation module is used to calculate the critical state angle according to the initial friction angle, establish the evolution equation in the friction angle shear process, change the stress-dilatancy failure model equation, calculate the calcareous sand particle crushing energy combined with the triaxial experiment data of the calcareous sand, and fit the crushing energy evolution process to establish the calcareous sand particle crushing energy evolution equation.

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