Application method of calcareous sand breakage energy model based on ABAQUS

Abstract

The application relates to the technical field of geotechnical engineering, and particularly provides a calcareous sand breakage energy model application method based on ABAQUS. The method comprises the following steps: constructing a geometric model of soil and a structure; performing pre-processing on the geometric model of the soil and the structure to obtain a particle breakage energy model VUSDFLD subroutine; obtaining stress and strain components of each time increment step based on the subroutine; calculating average effective stress and partial plastic strain at each integration point; calculating calcareous sand particle breakage energy, particle breakage energy change rate and particle breakage angle; calculating a peak friction angle and an expansion angle; updating the peak friction angle and the expansion angle in each cycle step based on a modified Mohr-Coulomb model and entering the next cycle step; after simulation is completed, post-processing is performed on an odb file; and a strength curve and a variable distribution cloud map are drawn to extract a particle breakage energy evolution process, so that the strength evolution characteristics of the soil are better represented.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method for applying a calcareous sand crushing energy model developed based on ABAQUS. Background Technology

[0002] Calcareous sand is a special type of soil and rock medium formed by the in-situ deposition of marine biological remains. Its main component is calcium carbonate, and it is primarily distributed in tropical and subtropical coral reef waters. Its unique biogenic origin gives calcareous sand characteristics such as porosity, irregular shape, and fracturing. Particle fracturing leads to changes in the shape and size distribution of calcareous sand particles, affecting its mechanical behavior and deformation properties. With the development of marine engineering, various projects require construction on calcareous sand foundations, such as offshore wind power, offshore oil, and island construction. Therefore, in-depth research on the engineering properties of calcareous sand and the development of suitable fracturing models are of great significance for marine engineering construction.

[0003] Many studies have incorporated particle breakage into existing theoretical frameworks, proposing constitutive models suitable for particle breakage. However, existing methods primarily measure particle breakage by changes in particle size distribution before and after shearing, known as the particle breakage index. This method fails to capture the continuous evolution of particle breakage during loading. Particle breakage is essentially an energy-consuming plastic behavior; therefore, particle breakage energy is the most direct indicator of particle breakage. However, no studies have yet used particle breakage energy to characterize particle breakage evolution and incorporated it into soil constitutive models.

[0004] Dense calcareous sand exhibits significant strain softening characteristics under conventional confining pressure. This is due to the extremely irregular shape of the calcareous sand particles, resulting in a significant interlocking effect during shearing. Adjacent particles interlock, hindering rearrangement. Therefore, the strength of calcareous sand initially increases to a peak value during shearing, a phenomenon known as pre-peak hardening. When particles overcome interlocking and undergo shear slip, the calcareous sand begins to soften, and its strength gradually decreases to the critical state value. The modified Mohr-Coulomb model, based on the traditional Mohr-Coulomb model, incorporates the sliding friction angle... The expansion angle ψ is expressed as a function of the partial plastic strain ξ and the average effective stress p´. Thus, the soil strength parameters change during shearing, better characterizing the hardening-softening properties of dense soils. However, existing angle evolution methods mostly employ linear evolution, which does not conform to the actual evolution law of soil strength parameters. Summary of the Invention

[0005] In view of this, the present invention provides an application method for a calcareous sand fracturing energy model developed based on ABAQUS, which can better characterize the strength evolution characteristics of soil.

[0006] In a first aspect, the present invention provides a method for applying an energy model for crushing calcareous sand based on ABAQUS, the method comprising:

[0007] Step 1: Construct geometric models of the soil and structure based on the finite element method ABAQUS;

[0008] Step 2: Perform preprocessing settings on the geometric model of the soil and structure to obtain the VUSDFLD user subroutine for the particle crushing energy model;

[0009] Step 3: Obtain the stress and strain components for each time increment step based on the subroutine; calculate the average effective stress and deviatoric plastic strain at each integration point;

[0010] Step 4: Calculate the crushing energy of calcareous sand particles, the rate of change of crushing energy, and the angle of breakage of the particles;

[0011] Step 5: Calculate the peak friction angle and the expansion angle;

[0012] Step 6: Based on the modified Mohr-Coulomb model, update the peak friction angle and expansion angle in each cycle step and proceed to the next cycle step;

[0013] Step 7: After the simulation is completed, post-process the odb file; plot the strength curve and variable distribution cloud map to obtain the structural bearing capacity and particle breakage energy.

[0014] Optionally, step 2 includes:

[0015] Step 21: Define the material properties, interaction properties, loads, and constraints of the soil and structure; assemble the geometric model and mesh the geometric model;

[0016] In soil material properties, the plasticity is modeled using the Mohr-Coulomb model, with the friction angle... and expansion angle Set them as field variables FV1 and FV2 respectively, and the subroutine passes the values ​​of the field variables to the material model;

[0017] Step 22: Perform static stress equilibrium on the soil to simulate the soil consolidation process and obtain the consolidation results;

[0018] Step 23: Import the consolidation results as the initial state into the dynamic analysis step;

[0019] Step 24: Submit the job for calculation. In the User subroutine file, select the VUSDFLD subroutine written in Fortran for the particle breakage energy model.

[0020] Optionally, step 3 includes:

[0021] Mean effective stress The calculation formula is:

[0022] ;

[0023] in, For effective major principal stress, For effective principal stress, For effective small principal stress;

[0024] Plastic strain increment The calculation formula is:

[0025] ;

[0026] in, , , These represent the incremental principal plastic strains.

[0027] Optionally, step 4 includes:

[0028] Energy from crushing calcareous sand particles The calculation formula is:

[0029] ;

[0030] in, , This represents the particle breakage energy corresponding to the critical state. These are the fitting parameters;

[0031] Applying both sides of the above equation simultaneously Differentiate and substitute the peak partial plastic strain The rate of change of particle breakage energy at the peak of deviatoric stress was obtained. :

[0032] ;

[0033] ;

[0034] in, , m is the fitting parameter; Atmospheric pressure;

[0035] Peak particle breakage angle The relationship between the peak particle breakage energy change rate and the formula is:

[0036] ;

[0037] in, The slope is denoted as .

[0038] Optionally, step 5 includes:

[0039] For soil with fragmented particles, the peak friction angle From the initial friction angle Peak expansion angle and peak fracture angle It consists of three parts:

[0040] ;

[0041] Peak expansion angle Calculated using Bolton's formula:

[0042] ;

[0043] ;

[0044] in, Related to the type of soil; It is the relative density index; , , These are the fitting parameters.

[0045] Optionally, step 6 includes:

[0046] The modified Mohr-Coulomb model (MMC) is based on the traditional Mohr-Coulomb model, but incorporates the sliding friction angle... and expansion angle Represented as partial plastic strain and average effective stress The function, where, From the initial friction angle Increase to peak eccentric plastic strain Peak friction angle at Then, from Gradually decrease to the critical state angle Similarly, the expansion angle Increased from 0.1 degrees to Peak expansion angle at Then reduce it to 0.1 degrees, which is the critical state. Each loop step assigns the updated friction angle and expansion angle values ​​to the field variables FV1 and FV2 respectively, and passes the values ​​directly to the main program in the form of a table.

[0047] Optionally, it includes:

[0048] Particle crushing energy The evolution equations were fitted based on the calculated particle breakage energy and a biased plastic strain was used. Replace axial strain The particle breakage energy is calculated based on the stress-expansion breakage model and triaxial test results. Fitting the particle breakage energy is to characterize the particle breakage evolution process, establish the relationship between the peak particle breakage energy and the peak breakage angle, and embed the particle breakage energy into the modified Mohr-Coulomb model.

[0049] Optionally, it includes:

[0050] The hardening stage of calcareous sand uses a power function to increase the hardening rate in the early stage, while the softening stage uses an exponential function to decrease the hardening rate in the early stage, so as to gradually approach the critical state.

[0051] sliding friction angle and expansion angle The rising phase, that is < The evolution formula is:

[0052] ;

[0053] The softening stage is > The evolution formula is:

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] in, The critical state is characterized by partial plastic strain. The relative density of the soil; and The rate of descent during the softening phase is controlled; the softening rate is estimated based on the linear slope from the peak state to the critical state, and multiplied by the corresponding rate correction factor. and These are the fitting parameters.

[0060] The technical solution provided by this invention includes a method that involves constructing a geometric model of soil and structure based on ABAQUS; preprocessing the geometric model of soil and structure to obtain the particle breakage energy model VUSDFLD subroutine; obtaining the stress and strain components at each time increment step based on the subroutine; calculating the average effective stress and partial plastic strain at each integration point; calculating the particle breakage energy, particle breakage energy change rate, and particle breakage angle of calcareous sand; calculating the peak friction angle and expansion angle; updating the peak friction angle and expansion angle at each cycle step based on the modified Mohr-Coulomb model and proceeding to the next cycle step; post-processing the odb file after the simulation; and plotting the strength curve and variable distribution cloud map to extract the particle breakage energy evolution process. This method better characterizes the strength evolution characteristics of soil. Attached Figure Description

[0061] 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.

[0062] Figure 1 A flowchart illustrating the application method of the calcareous sand crushing energy model developed based on ABAQUS, provided in an embodiment of the present invention;

[0063] Figure 2 This is a schematic diagram of a triaxial compression model and mesh generation provided in an embodiment of the present invention;

[0064] Figure 3 A schematic diagram illustrating the nonlinear evolution of the friction angle and expansion angle provided in an embodiment of the present invention;

[0065] Figure 4 A comparison diagram of the deviatoric stress simulation results and experimental results provided in the embodiments of the present invention;

[0066] Figure 5 The distribution cloud diagrams of different variables at the end of shearing under a confining pressure of 500 kPa provided in the embodiments of the present invention are shown in the following: (a) is the distribution cloud diagram of the partial plastic strain, (b) is the distribution cloud diagram of the friction angle, (c) is the distribution cloud diagram of the expansion angle, and (d) is the distribution cloud diagram of the particle breakage energy.

[0067] Figure 6 This is a comparison chart of the simulation results and experimental results of the energy evolution of calcareous sand particle crushing provided in the embodiments of the present invention. Detailed Implementation

[0068] 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.

[0069] 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.

[0070] 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.

[0071] 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.

[0072] 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)."

[0073] Figure 1 A flowchart illustrating the application method of the calcareous sand crushing energy model developed based on ABAQUS provided in this embodiment of the invention is shown below. Figure 1 As shown, the method includes:

[0074] Step 1: Construct geometric models of soil and structure based on the finite element method ABAQUS.

[0075] Step 2: Perform preprocessing settings on the geometric model of the soil and structure to obtain the particle crushing energy model VUSDFLD user subroutine.

[0076] In this embodiment of the invention, step 2 includes:

[0077] Step 21: Define the material properties, interaction properties, loads, and constraints of the soil and structure; assemble the geometric model and mesh the geometric model;

[0078] In soil material properties, the plasticity is modeled using the Mohr-Coulomb model, with the friction angle... and expansion angle Set them as field variables FV1 and FV2 respectively, and the subroutine passes the values ​​of the field variables to the material model;

[0079] Step 22: Perform static stress equilibrium on the soil to simulate the soil consolidation process and obtain the consolidation results;

[0080] The geostress equilibrium is first performed using the Geostatic step; subsequent dynamic analysis steps cannot be performed directly after the Geostatic step.

[0081] Step 23: Import the consolidation results as the initial state into the dynamic analysis step;

[0082] The geostress equilibrium results are imported as the initial state into the Dynamic, Explicit analysis step.

[0083] Step 24: Submit the job for calculation. In the User subroutine file, select the VUSDFLD subroutine written in Fortran for the particle breakage energy model.

[0084] Step 3: Obtain the stress and strain components for each time increment step based on the subroutine; calculate the average effective stress and eccentric plastic strain at each integration point.

[0085] In this embodiment of the invention, step 3 includes:

[0086] Mean effective stress The calculation formula is:

[0087] ;

[0088] in, For effective major principal stress, For effective principal stress, For effective small principal stress;

[0089] Plastic strain increment The calculation formula is:

[0090] ;

[0091] in, , , These represent the incremental principal plastic strains.

[0092] Step 4: Calculate the crushing energy of calcareous sand particles, the rate of change of crushing energy, and the crushing angle of the particles.

[0093] In this embodiment of the invention, step 4 includes:

[0094] Energy from crushing calcareous sand particles The calculation formula is:

[0095] ;

[0096] in, , This represents the particle breakage energy corresponding to the critical state. These are the fitting parameters;

[0097] Applying both sides of the above equation simultaneously Differentiate and substitute the peak partial plastic strain The rate of change of particle breakage energy at the peak of deviatoric stress was obtained. :

[0098] ;

[0099] ;

[0100] in, , m is the fitting parameter; Atmospheric pressure;

[0101] Peak particle breakage angle The relationship between the peak particle breakage energy change rate and the formula is:

[0102] ;

[0103] in, The slope is denoted as .

[0104] In this embodiment of the invention, it includes:

[0105] Particle crushing energy The evolution equations were fitted based on the calculated particle breakage energy and a biased plastic strain was used. Replace axial strain The particle breakage energy is calculated based on the stress-expansion breakage model and triaxial test results. Fitting the particle breakage energy is to characterize the particle breakage evolution process, establish the relationship between the peak particle breakage energy and the peak breakage angle, and embed the particle breakage energy into the modified Mohr-Coulomb model.

[0106] Step 5: Calculate the peak friction angle and the expansion angle.

[0107] In this embodiment of the invention, step 5 includes:

[0108] For soil with fragmented particles, the peak friction angle From the initial friction angle Peak expansion angle and peak fracture angle It consists of three parts:

[0109] ;

[0110] Peak expansion angle Calculated using Bolton's formula:

[0111] ;

[0112] ;

[0113] in, Related to the type of soil; It is the relative density index; , , These are the fitting parameters.

[0114] Step 6: Based on the modified Mohr-Coulomb model, update the peak friction angle and expansion angle in each cycle step and proceed to the next cycle step.

[0115] In this embodiment of the invention, step 6 includes:

[0116] The modified Mohr-Coulomb model (MMC) is based on the traditional Mohr-Coulomb model, but incorporates the sliding friction angle... and expansion angle Represented as partial plastic strain and average effective stress The function of this property allows the soil strength parameters to change during shearing, thus better characterizing the hardening-softening properties of dense soils. From the initial friction angle Increase to peak eccentric plastic strain Peak friction angle at Then, from Gradually decrease to the critical state angle Similarly, the expansion angle Increased from 0.1 degrees to Peak expansion angle at Then reduce it to 0.1 degrees, which is the critical state. Each loop step assigns the updated friction angle and expansion angle values ​​to the field variables FV1 and FV2 respectively, and passes the values ​​directly to the main program in the form of a table.

[0117] In this embodiment of the invention, it includes:

[0118] The hardening stage of calcareous sand uses a power function to increase the hardening rate in the early stage, while the softening stage uses an exponential function to decrease the hardening rate in the early stage, so as to gradually approach the critical state.

[0119] sliding friction angle and expansion angle The rising phase, that is < The evolution formula is:

[0120] ;

[0121] The softening stage is > The evolution formula is:

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] in, The critical state is characterized by partial plastic strain. The relative density of the soil; and The rate of descent during the softening phase is controlled; the softening rate is estimated based on the linear slope from the peak state to the critical state, and multiplied by the corresponding rate correction factor. and These are the fitting parameters.

[0128] Step 7: After the simulation is completed, post-process the odb file; plot the strength curve and variable distribution cloud map to obtain the structural bearing capacity and particle breakage energy.

[0129] The embodiments of the present invention simulate relative density The drained triaxial shear process of 75% calcareous sand (from LedgePoint, Western Australia) under different confining pressures (100 Pa, 300 Pa, 500 kPa) specifically includes the following steps:

[0130] A. In the finite element ABAQUS software, establish soil and loading plate models. The soil is cylindrical with a height of 0.139m and a diameter of 0.0708m. The cylindrical loading plate interface is slightly larger than the soil interface, with a height of 0.005m and a diameter of 0.1m.

[0131] B. Pre-process the soil and loading plate models, including setting Young's modulus E and Poisson's ratio ν to 50 MPa and 0.3 respectively; using the Mohr-Coulomb model for plasticity, and setting the friction angle... and expansion angle Set them as field variables FV1 and FV2 respectively, and the subroutine will pass the values ​​to the material model through the field variables; set the density to 2740 kg / m3; select UserDefined Field, and select user subroutine when submitting the job later; add 11 state variables, which will be used as output variables later, including biased plastic strain, friction angle, expansion angle, particle breakage energy, etc.

[0132] The Young's modulus E and Poisson's ratio ν of the loading plate are taken as 210 GPa and 0.3, respectively; the density is 7850 kg / m3; the soil and upper and lower loading plates are assembled in the assembly module; the triaxial compression model and mesh generation are as follows. Figure 2 As shown, the loading plates at both ends are set as rigid bodies, with the lower loading plate constraining all degrees of freedom. The upper loading plate constrains the horizontal and rotational degrees of freedom, allowing vertical loading. The soil and loading plates are in hard contact in the normal direction and a penalty function in the tangential direction, with a friction coefficient μ=0.1. Both the soil and loading plates are meshed using C3D8R with a size of 0.004m, and the soil is divided into a mesh with 12956 elements.

[0133] First, confining pressures of 100 Pa, 300 Pa, and 500 kPa were applied to the soil to simulate the consolidation process. The Geostatic analysis step was used, and the analysis request was restarted, saving the geostress equilibrium results. These results were then imported as the initial state into the Dynamic Explicit analysis step, with a calculation duration of 1. The corresponding confining pressures were applied, and a vertical displacement loading was applied at the reference point on the upper loading plate, compressing the soil to 35% axial strain. That is, -0.04865m; submit the job again for calculation, and select the VUSDFLD user subroutine written in Fortran in the User subroutine file.

[0134] C. In each increment step, the subroutine obtains the stress and strain components of each time increment step through the internal function VGETVRM; then it calculates the average effective stress and eccentric plastic strain at each integration point.

[0135] D. Calculate the crushing energy of calcareous sand particles. Energy change rate of particle crushing and particle breakage angle Particle crushing energy The evolution equation needs to be fitted based on the calculated particle breakage energy, and the partial plastic strain ξ should be used instead of the axial strain. The particle crushing energy was calculated based on the stress-expansion crushing model and triaxial test results. The particle crushing energy was fitted here to characterize the particle crushing evolution process, further establishing the relationship between peak particle crushing energy and peak crushing angle, and embedding the particle crushing energy into the modified Mohr-Coulomb model; the formula for calculating the crushing energy of calcareous sand particles is:

[0136] ;

[0137] in, , This represents the particle breakage energy corresponding to the critical state. These are the fitting parameters; The best fit of the evolution equation ;

[0138] Applying both sides of the above equation simultaneously Differentiate and substitute the peak partial plastic strain The rate of change of particle breakage energy at the peak of deviatoric stress was obtained. :

[0139] ;

[0140] ;

[0141] Here =0.04, =0.02, m=0.6; The atmospheric pressure is 100 kPa.

[0142] Peak particle breakage angle The relationship between the peak particle breakage energy change rate and the formula is:

[0143] ;

[0144] Among them, slope The optimal value is 0.004.

[0145] E. Calculate the peak friction angle and the expansion angle. For soils with fragmented particles, the peak friction angle... From the initial friction angle Peak expansion angle and peak fracture angle It consists of three parts:

[0146] ;

[0147] Peak expansion angle Calculated using Bolton's formula:

[0148] ;

[0149] ;

[0150] in, Related to soil type (silica sand) =6.25; calcareous sand =12.64); It is the relative density index; =0.8 is consistent with the results of various soil tests; , For calcareous sand, the constant is... =8.8, =1; Initial friction angle of soil It is 33.8°.

[0151] F. The modified Mohr-Coulomb model (MMC) is based on the traditional Mohr-Coulomb model, which incorporates the sliding friction angle... and expansion angle Represented as partial plastic strain and average effective stress The function of this property allows the soil strength parameters to change during shearing, thus better characterizing the hardening-softening properties of dense soils. From the initial friction angle Increase to peak eccentric plastic strain Peak friction angle at Then, from Gradually decrease to the critical state angle Similarly, the expansion angle Increased from 0.1 degrees to Peak expansion angle at Then reduce it to 0.1 degrees, which is the critical state. Each loop step assigns the updated friction angle and expansion angle values ​​to the field variables FV1 and FV2 respectively, and passes the values ​​directly to the main program in the form of a table.

[0152] The hardening stage of calcareous sand adopts a power-law progression to accelerate the early hardening rate; the softening stage adopts an exponential decline to gradually approach the critical state; the angular evolution is as follows: Figure 3 As shown, the friction angle and expansion angle The rising phase < The evolution formula is:

[0153] ;

[0154] The softening stage is > The evolution formula is:

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] in, The critical state partial plastic strain is taken as 0.25; The relative density of the soil is 75% in this case; the critical state angle. The value is set at 36.1°. and The rate of descent during the softening phase is controlled; the softening rate is estimated based on the linear slope from the peak state to the critical state, and multiplied by the corresponding rate correction factor. and These are the fitting parameters; simulation results show that... =13 and =20 conforms to the decreasing pattern during the softening stage.

[0161] G. After the simulation is complete, perform post-processing on the odb file; such as... Figure 4 , Figure 5 (a) to (d) Figure 6 As shown, strength curves and variable distribution cloud maps are plotted to obtain structural bearing capacity and particle breakage energy, so as to extract the particle breakage energy evolution process.

[0162] Compared with the prior art, the present invention has the following advantages:

[0163] I. This invention uses particle crushing energy to characterize the particle crushing evolution process of calcareous sand. By embedding the crushing energy into a modified Mohr-Coulomb model, the evolution process of particle crushing during loading can be observed, providing an effective method for studying the particle crushing evolution and crushing energy consumption of calcareous sand.

[0164] II. In this invention, the friction angle and expansion angle adopt nonlinear evolution, which can better characterize the hardening-softening behavior of dense calcareous sand. The use of power function to increase can accelerate the early hardening speed, while the use of exponential function to decrease can ensure that the soil strength decreases steadily to the critical state value.

[0165] III. This invention, combined with the user subroutine VUSDLD, can be easily implemented in ABAQUS. The use of explicit dynamics can better simulate the nonlinear large deformation behavior of calcareous sand during shearing, providing a foundation for simulating the large deformation interaction between structure and soil on calcareous sand foundations.

[0166] The technical solution provided by this invention includes a method that involves constructing a geometric model of soil and structure based on ABAQUS; preprocessing the geometric model of soil and structure to obtain the particle breakage energy model VUSDFLD subroutine; obtaining the stress and strain components at each time increment step based on the subroutine; calculating the average effective stress and partial plastic strain at each integration point; calculating the particle breakage energy, particle breakage energy change rate, and particle breakage angle of calcareous sand; calculating the peak friction angle and expansion angle; updating the peak friction angle and expansion angle at each cycle step based on the modified Mohr-Coulomb model and proceeding to the next cycle step; post-processing the odb file after the simulation; and plotting the strength curve and variable distribution cloud map to extract the particle breakage energy evolution process. This method better characterizes the strength evolution characteristics of soil.

[0167] 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 applying an energy model for crushing calcareous sand based on ABAQUS, characterized in that, The method includes: Step 1: Construct geometric models of the soil and structure based on the finite element method ABAQUS; Step 2: Perform preprocessing settings on the geometric model of the soil and structure to obtain the VUSDFLD user subroutine for the particle crushing energy model; Step 3: Obtain the stress and strain components for each time increment step based on the subroutine; calculate the average effective stress and deviatoric plastic strain at each integration point; Step 4: Calculate the crushing energy of calcareous sand particles, the rate of change of peak crushing energy, and the peak crushing angle. Step 5: Calculate the peak friction angle and the expansion angle; Step 6: Based on the modified Mohr-Coulomb model, update the friction angle and expansion angle in each cycle step and proceed to the next cycle step; Step 7: After the simulation is completed, post-process the odb file; plot the strength curve and variable distribution cloud map to obtain the structural bearing capacity and particle breakage energy; Step 3 includes: Mean effective stress The calculation formula is: ； in, For effective major principal stress, For effective principal stress, For effective small principal stress; Plastic strain increment The calculation formula is: ； in, , , These are the incremental principal plastic strains; Step 4 includes: Energy from crushing calcareous sand particles The calculation formula is: ； in, , This represents the particle breakage energy corresponding to the critical state. These are the fitting parameters; Applying both sides of the above equation simultaneously Differentiate and substitute the peak partial plastic strain The rate of change of particle breakage energy at the peak of deviatoric stress was obtained. : ； ； in, , m is the fitting parameter; Atmospheric pressure; Peak particle breakage angle The relationship between the peak particle breakage energy change rate and the formula is: ； in, The slope; Step 5 includes: For soil with fragmented particles, the peak friction angle From the initial friction angle Peak expansion angle and peak fracture angle It consists of three parts: ； Peak expansion angle Calculated using Bolton's formula: ； ； in, Related to the type of soil; It is the relative density index; , , These are the fitting parameters; Step 6 includes: The modified Mohr-Coulomb model (MMC) is based on the traditional Mohr-Coulomb model, but incorporates the sliding friction angle... and expansion angle Represented as partial plastic strain and average effective stress The function, where, From the initial friction angle Increase to peak eccentric plastic strain Peak friction angle at Then, from Gradually decrease to the critical state angle Similarly, the expansion angle Increased from 0.1 degrees to Peak expansion angle at Then reduce it to 0.1 degrees, which is the critical state. Each loop step assigns the updated friction angle and expansion angle values ​​to the field variables FV1 and FV2 respectively, and passes the values ​​directly to the main program in the form of a table.

2. The method according to claim 1, characterized in that, Step 2 includes: Step 21: Define the material properties, interaction properties, loads, and constraints of the soil and structure; assemble the geometric model and mesh the geometric model; In soil material properties, the plasticity is modeled using the Mohr-Coulomb model, with the friction angle... and expansion angle Set them as field variables FV1 and FV2 respectively, and the subroutine passes the values ​​of the field variables to the material model; Step 22: Perform static stress equilibrium on the soil to simulate the soil consolidation process and obtain the consolidation results; Step 23: Import the consolidation results as the initial state into the dynamic analysis step; Step 24: Submit the job for calculation. In the User subroutine file, select the VUSDFLD subroutine written in Fortran for the particle breakage energy model.

3. The method according to claim 1, characterized in that, include: Particle crushing energy The evolution equations were fitted based on the calculated particle breakage energy and a biased plastic strain was used. Replace axial strain The particle breakage energy is calculated based on the stress-expansion breakage model and triaxial test results. Fitting the particle breakage energy is to characterize the particle breakage evolution process, establish the relationship between the peak particle breakage energy and the peak breakage angle, and embed the particle breakage energy into the modified Mohr-Coulomb model.

4. The method according to claim 1, characterized in that, include: The hardening stage of calcareous sand is accelerated by using a power function to increase the hardening rate in the early stages. The softening phase decreases exponentially to gradually approach the critical state; sliding friction angle and expansion angle The rising phase, that is < The evolution formula is: ； The softening stage is > The evolution formula is: ； ； ； ； ； in, The critical state is characterized by partial plastic strain. The relative density of the soil; and The rate of descent during the softening phase is controlled; the softening rate is estimated based on the linear slope from the peak state to the critical state, and multiplied by the corresponding rate correction factor. and These are the fitting parameters.

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