Discrete Element Parameter Calibration Method for Co-Nodal DEM-SPH Sea Ice Model

Abstract

The present invention relates to the field of computer digital simulation technology, and in particular to a method for calibrating discrete element parameters of a co-node DEM-SPH sea ice model, which comprises the following steps: selection of macroscopic mechanical parameters of sea ice; selection of friction coefficient between sea ice and structure; uniaxial compression discrete element numerical simulation; three-point bending discrete element numerical simulation; secondary uniaxial compression discrete element numerical simulation; calibration of discrete element parameters of sea ice specimens. Thus, in the process of performing numerical simulation analysis on ice loads of ocean structures, by combining theoretical analysis and numerical simulation, it comprehensively and fully considers the influencing factors of the macroscopic strength of the structure to be simulated, and establishes a functional relationship between microscopic parameters and macroscopic parameters, so as to quickly determine the discrete element parameters of sea ice with different strengths, and finally make the results obtained by discrete element parameter calibration more comprehensive and efficient.

Description

Technical Field

[0001] The present invention relates to the technical field of computer digital simulation, and in particular to a method for calibrating discrete element parameters of a co - node DEM - SPH sea ice model. Background Art

[0002] With the increasing frequency of human activities in the development of marine resources in cold regions (Antarctica, the Arctic, and high - latitude sea areas), the interaction between sea ice and marine structures can easily pose a serious threat to structural stability and personnel safety. Therefore, extensive research has been carried out on the physical and mechanical properties of sea ice and structural ice loads.

[0003] Sea ice is a composite material with complex properties, featuring discontinuity, anisotropy, etc. Its mechanical properties are mainly affected by internal structures such as ice crystal size, temperature, salinity, etc. The ice load on marine structures is mainly affected by the physical properties of sea ice. Only by reasonably applying the constitutive model, failure criterion, and mechanical parameters of sea ice can the ice load on marine engineering structures be accurately calculated.

[0004] The discrete element method is a numerical simulation method specifically used to solve problems of discontinuous media. Due to its natural advantages in simulating the failure of brittle materials, it has been widely applied to the simulation and research analysis of various solid materials such as rocks, concrete, ceramics, and sea ice. Since sea ice is a natural composite material with complex properties, its mechanical properties are affected by its internal structure and external loading environment, showing strong discrete characteristics. Therefore, in recent years, the discrete element method with bonding and crushing functions has been widely used in the research of simulating engineering sea ice.

[0005] The accuracy of simulating the mechanical properties of materials by the discrete element method is closely related to the basic particle parameters and the contact and cementation parameters between particles. Therefore, in the actual simulation process, the selection of discrete element microscopic parameters is extremely important. In terms of the current research status, the traditional calibration of discrete element parameters for sea ice models mostly uses the trial - and - error iteration method. Although it can quickly derive the simulation analysis results and thus provide theoretical support for the construction, operation, and later maintenance of marine structures, the parameters affecting the macroscopic mechanical properties of discrete elements are not comprehensively considered, and the accuracy and applicability of the final results cannot be guaranteed. Moreover, in the traditional method for calibrating discrete element parameters of sea ice models, there is no unified and reasonable standard method for determining the relationship between the microscopic parameters of sea ice discrete elements and the macroscopic parameters of sea ice, and for selecting the microscopic parameters of sea ice materials. The subjective factors of the simulator (mainly including the correctness of determining the relationship between the microscopic parameters of sea ice discrete elements and the macroscopic parameters of sea ice and the determination of the range of microscopic parameters of sea ice materials) will have a great impact on the simulation results, and thus will inevitably affect the reliability of the simulation results. Therefore, it provides a new research direction for the members of this research group. Summary of the Invention

[0006] Therefore, in view of the above existing problems and defects, the research group of the present invention collected relevant materials, conducted multi-party evaluations and considerations, and through continuous discussions and design improvements by the research group members, finally led to the emergence of the discrete element parameter calibration method for the co - node DEM - SPH sea ice model.

[0007] In order to solve the above - mentioned technical problems, the present invention relates to a discrete element parameter calibration method for a co - node DEM - SPH sea ice model, which is characterized by including the following steps:

[0008] S1. Selection of macroscopic mechanical parameters of sea ice;

[0009] S2. Selection of the friction coefficient between sea ice and structure;

[0010] S3. Uniaxial compression discrete element numerical simulation;

[0011] S4. Three - point bending discrete element numerical simulation;

[0012] S5. Secondary uniaxial compression discrete element numerical simulation;

[0013] S6. Calibration of discrete element parameters of sea ice specimens.

[0014] As a further improvement of the technical solution disclosed by the present invention, step S1 includes the following sub - steps:

[0015] S11: Through uniaxial compression tests and three - point bending tests, determine the compressive elastic modulus E c0 of the sea ice specimen to be simulated, the uniaxial compression strength σ c0 and the bending strength σ b0 ;

[0016] S12: Take the compressive elastic modulus E c0 , the uniaxial compression strength σ c0 and the bending strength σ b0 obtained in step S11 as the target values of the discrete element sea ice model.

[0017] As a further improvement of the technical solution disclosed by the present invention, step S2 includes the following sub - steps:

[0018] S21: Determine the friction coefficient between sea ice and structure in research or actual projects.

[0019] S22: Take the result in step S21 as the friction coefficient μ between sea ice and structure in discrete element simulation.

[0020] As a further improvement of the technical solution disclosed by the present invention, step S3 includes the following sub - steps:

[0021] S31: Select the particle radius r for constructing the discrete element sea ice model;

[0022] S32: Regularly arrange the spherical particles selected in step S31 to establish a discrete element uniaxial compression model of sea ice, with the model size being a×a×l;

[0023] S33: Select the elastic modulus of the particles as E, and the value is the target value E in step S12 c0 ; Select the Poisson's ratio of the particles as u; Select the normal stiffness coefficient of the particles as N k ;

[0024] S34: Determine the number of particles n in unilateral contact between the discrete element sea ice model and the structure during uniaxial compression;

[0025] S35: Select the expected average overlap x between the discrete element sea ice model and the structure, where Δl is the compression displacement value;

[0026] S36: Calculate the contact stiffness proportionality factor SFP according to the uniaxial compression strain formula, stress-strain relationship, pressure-stress relationship, and discrete element theory formula. The formula is:

[0027]

[0028] S37: Introduce SPH particles with fluid properties into each particle unit in the discrete element uniaxial compression sea ice model to establish a co-node DEM-SPH uniaxial compression model of sea ice;

[0029] S38: Set the SPH particle parameters;

[0030] S39: Set the normal bonding strength pb_n and tangential bonding strength pb_s of the cementation.

[0031] S310: Estimate the normal stiffness value pb_k of the cementation according to the target value E in step S11 c0 , and its estimation formula is: n , and its estimation formula is:

[0032]

[0033] S311: Set the ratio of the tangential to normal stiffness of the cementation pb_k s / pb_k n =Ω, and 0.29 < Ω < 0.32; Conduct uniaxial compression numerical simulations on discrete element models with different normal stiffnesses of cementation, and set the acting force as F when the compression displacement is Δl. Then the compression elastic modulus result of the discrete element model is:

[0034]

[0035] S312: Analyze the compression elastic modulus E of the discrete element model from the data obtained in step S311 cRelationship between the normal stiffness pb_k of cementation and n E c = k1pb_k n Let E c = k1pb_k n = E c0 to obtain pb_k n = E c0 / k1;

[0036] S313: Take the normal stiffness pb_k of cementation n = E c0 / k1, conduct uniaxial compression numerical simulation on the discrete element model with different ratios of tangential to normal stiffness of cementation, and obtain the compression elastic modulus results of the discrete element model;

[0037] S314: From the data obtained in step S313, analyze and obtain the relationship between the compression elastic modulus Ec of the discrete element model and the ratio of tangential to normal stiffness of cementation pb_k s / pb_k n is E c = b + k2pb_k s / pb_k n ;

[0038] S315: Obtain the relationship between the compression elastic modulus E c of the discrete element model, the normal stiffness pb_k of cementation n , and the ratio of tangential to normal stiffness of cementation pb_k s / pb_k n is E c = F(pb_k n , pb_k s / pb_k n ), and its formula is:

[0039] S316: Determine multiple sets of values of the normal stiffness of cementation and the ratio of tangential to normal stiffness of cementation, make the relational expression obtained in step S315 equal to E c0 , pb_k s / pb_k n take 0.1, 0.2, 0.3, 0.4... respectively, and obtain the value of pb_k n .

[0040] As a further improvement of the technical solution disclosed in the present invention, step S4 includes the following sub-steps:

[0041] S41: Regularly arrange the spherical particles selected in step S31, introduce SPH particles into each particle unit, and establish a co-node DEM-SPH sea ice three-point bending model with the model size of h×h×b;

[0042] S42: Select the particle elastic modulus E, particle Poisson's ratio u, and particle normal stiffness coefficient N k , and the values are the same as those in sub-step S33;

[0043] S43: Select the contact stiffness proportionality factor SFP, and the value is the same as that in sub-step S36;

[0044] S44: Set the values of the cement normal bonding strength pb_n and the cement tangential bonding strength pb_s, and the initial estimated values are taken as pb_n = pb_s = σ b0 / 2;

[0045] S45: Select a set of cement normal stiffness pb_k in sub-step S316 n and the ratio of the cement tangential to the legal system stiffness pb_k s / pb_k n values;

[0046] S46: Conduct numerical simulation. If the acting force when the discrete element sea ice model fractures is F, then the bending strength result of the discrete element sea ice model is:

[0047]

[0048] S47: The bending strength result of the discrete element sea ice model is linearly related to the cement bonding strength. According to the bending strength σb obtained in sub-step S46, adjust the values of the cement normal bonding strength pb_n and the cement tangential bonding strength pb_s, and its calculation formula is:

[0049]

[0050] S48: Repeat sub-steps S45 - S47;

[0051] S49: Establish the relationship between the cement normal bonding strength pb_n obtained in step S47 and the ratio of the cement tangential to the legal system stiffness pb_ks / pb_kn selected in step S45 as pb_n = G(pb_ks / pb_kn).

[0052] As a further improvement of the technical solution disclosed in the present invention, step S5 includes the following sub-steps:

[0053] S51: Adopt the same co-node DEM-SPH sea ice uniaxial compression model as in step S3;

[0054] S52: Select a set of values of the cement normal stiffness pb_kn and the ratio of the cement tangential to the legal system stiffness pb_ks / pb_kn in sub-step S316, and obtain the corresponding value of the cement normal stiffness pb_n from step S47;

[0055] S53: Take different tangential bonding strengths pb_s of cementation, and the ratios of them to the normal bonding strength pb_n of cementation are 1, 1.5, 2, 2.5...;

[0056] S54: Conduct uniaxial compression numerical simulations on discrete element models with different ratios of tangential to normal stiffness of cementation. If the acting force at the failure of the discrete element sea ice model is F, then the uniaxial compression strength of the discrete element sea ice model is obtained as:

[0057]

[0058] S55: Repeat sub-steps S52 - S54;

[0059] S56: For the compression strength σc obtained in sub-step S54, its maximum compression strength is denoted as (σc)max, and the corresponding minimum tangential to normal bonding strength of cementation is denoted as (pb_s / pb_n)min;

[0060] S57: Let the ratio of the maximum compression strength (σc)max obtained in sub-step S56 to the flexural strength σ b0 be e;

[0061] S58: Establish the relationship between the ratio of tangential to normal stiffness of cementation pb_k s / pb_k n selected in sub-step S52 and the ratio e obtained in sub-step S57 as pb_k s / pb_k n = H(e);

[0062] S59: Establish the relationship between the minimum tangential to normal bonding strength of cementation (pb_s / pb_n)min obtained in sub-step S56 and the ratio of tangential to normal stiffness of cementation pb_k s / pb_k n selected in sub-step S52 as (pb_s / pb_n)min = I(pb_k s / pb_k n ).

[0063] As a further improvement of the technical solution disclosed in the present invention, when performing discrete element parameter calibration operations on the sea ice specimen to be simulated in sub-step S11, step S6 includes the following sub-steps:

[0064] S61: Calculate the ratio e0 of the uniaxial compression strength σ c0 obtained in sub-step S11 to the flexural strength σ b0 ;

[0065] S62: From the relationship pb_k s / pb_k n= H(e) determines the value of the ratio of the cementation tangential stiffness to the normal stiffness pb_k with the ratio e0 obtained in sub-step S61 s0 / pb_k n0 = H(e0);

[0066] S63: Determine the cementation normal stiffness pb_k such that the value satisfies E c = F(pb_k n , pb_k s / pb_k n ) and the ratio of the cementation tangential stiffness to the normal stiffness pb_k obtained in sub-sub-step S612 s0 / pb_k n0 using the compressive elastic modulus Ec0 obtained in sub-step S11, the relationship E n0 = F(pb_k c0 , pb_k n0 , pb_k s0 / pb_k n0 ).

[0067] S64: Determine the value of the cementation normal bonding strength pb_n0 = G(pb_k s / pb_k n ) using the relationship pb_n = G(pb_k s0 / pb_k n0 ) obtained in sub-step S49 and the ratio of the cementation tangential stiffness to the normal stiffness pb_k obtained in sub-step S62 s0 / pb_k n0 ).

[0068] S65: Determine the value of the cementation tangential bonding strength pb_s0 = pb_n0I(pb_k s / pb_k n ) using the relationship (pb_s / pb_n)min = I(pb_k s0 / pb_k n0 ) obtained in sub-step S59, the ratio of the cementation tangential stiffness to the normal stiffness pb_k obtained in sub-sub-step S62 s0 / pb_k n0 ) and the cementation normal bonding strength pb_n0 obtained in sub-sub-step S64

[0069] Of course, as another application scenario selection of the above-disclosed technical solution, when performing discrete element parameter calibration operations on other sea ice specimens to be simulated, step S6 includes the following sub-steps:

[0070] S61': Determine the compressive elastic modulus E c1 , uniaxial compressive strength σ c1 and flexural strength σ of the other sea ice specimens to be simulated through uniaxial compression tests and three-point bending testsb1 ;

[0071] S62’: Calculate the ratio e1 of the uniaxial compressive strength σ obtained in sub-step S61’ c1 to the flexural strength σ b1 ;

[0072] S63’: Determine the value of the ratio of the cementation tangential stiffness to the normal stiffness as pb_k s / pb_k n = H(e) from the relationship pb_k s1 / pb_k n1 = H(e1) obtained in sub-step S62’;

[0073] S64’: Determine that the value of the cementation normal stiffness pb_k c1 satisfies E c = F(pb_k n , pb_k s / pb_k n ) and the ratio of the cementation tangential stiffness to the normal stiffness pb_k s1 / pb_k n1 obtained in sub-step S63’; n1 where E c1 = F(pb_k n1 , pb_k s1 / pb_k n1 );

[0074] S65’: Determine the value of the cementation normal bonding strength as pb_n1 = (σb1 / σb0)G(pb_k s / pb_k n ) from the relationship pb_n = G(pb_k s1 / pb_k n1 ) obtained in sub-step S49, the ratio of the cementation tangential stiffness to the normal stiffness pb_k b1 / pb_k b0 obtained in sub-step S63’, and the ratio of the flexural strength σ s1 / pb_k n1 ;

[0075] S66’: Determine the value of (pb_s / pb_n)min = I(pb_k s / pb_k n ) from the relationship obtained in sub-step S59, the ratio of the cementation tangential stiffness to the normal stiffness pb_k s1 / pb_k n1and the value of the cemented tangential bond strength pb_s1 is determined from the normal bond strength pb_n1 obtained in step S65' of Sun as pb_s1 = pb_n1I(pb_k s1 / pb_k n1 ).

[0076] In the technical solution disclosed in the present invention, through the combination of theoretical analysis and numerical simulation, the influencing factors of the macroscopic strength of the structure to be simulated are comprehensively and fully considered, and the functional relationship between the microscopic parameters and the macroscopic parameters is established, so as to quickly determine the discrete element parameters of sea ice with different strengths, making the results obtained by the calibration of the discrete element parameters more comprehensive and efficient.

[0077] In addition, it should be noted here that in the process of solving the structure to be simulated by means of the discrete element parameter calibration method of the co - nodal DEM - SPH sea ice model, based on the potential physical connection between the macro - and micro - strength parameters of sea ice, the matching error of the uniaxial compressive strength and the three - point bending flexural strength parameters is converged to a small range, making the results obtained by the calibration of the discrete element parameters more accurate. Brief Description of the Drawings

[0078] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0079] Figure 1 It is a flowchart of the discrete element parameter calibration method for the co - nodal DEM - SPH sea ice model of the present invention.

[0080] Figure 2 It is a schematic diagram of the uniaxial compression DEM model in the discrete element parameter calibration method for the co - nodal DEM - SPH sea ice model of the present invention.

[0081] Figure 3 It is a schematic diagram of the main uniaxial compression DEM - SPH model in the discrete element parameter calibration method for the co - nodal DEM - SPH sea ice model of the present invention.

[0082] Figure 4 It is a schematic diagram of the relationship between the compression elastic modulus and the cemented normal stiffness in the discrete element parameter calibration method for the co - nodal DEM - SPH sea ice model of the present invention.

[0083] Figure 5 It is a schematic diagram of the relationship between the compression elastic modulus and the ratio of the cemented tangential stiffness to the normal stiffness in the discrete element parameter calibration method for the co - nodal DEM - SPH sea ice model of the present invention.

[0084] Figure 6Schematic diagram of the main three-point bending DEM-SPH model in the discrete element parameter calibration method of the co-node DEM-SPH sea ice model of the present invention.

[0085] Figure 7 Relationship diagram of compressive strength, ratio of cemented tangential stiffness to normal stiffness, and ratio of cemented tangential bond strength to normal bond strength in the discrete element parameter calibration method of the co-node DEM-SPH sea ice model of the present invention. Detailed implementation method

[0086] Based on the project "Risk Assessment of Aging Jacket Platforms in the Bohai Sea" carried out by the research group and CNOOC Technology & Inspection Co., Ltd., a comprehensive, accurate and efficient method is proposed in the following embodiments to determine the microscopic parameters of Bohai sea ice materials during the discrete element simulation process. This is of great theoretical significance and practical value for the study of the mechanical properties of Bohai sea ice and the ice load of aging jacket offshore platforms. The specific content is as follows:

[0087] Reference Figure 1 , this embodiment provides a discrete element parameter calibration method for the co-node DEM-SPH sea ice model to determine the cemented normal stiffness pb_k n , ratio of cemented tangential stiffness to normal stiffness pb_k s / pb_k n , cemented normal bond strength pb_n, and cemented tangential bond strength pb_s.

[0088] In this embodiment, the sea ice in the Bohai Sea area is selected as the applicable object of the discrete element parameter calibration method of the co-node DEM-SPH sea ice model.

[0089] The discrete element parameter calibration method of the co-node DEM-SPH sea ice model includes the following steps:

[0090] Step 1: Selection of macroscopic mechanical parameters of sea ice:

[0091] Step 1.1: Through uniaxial compression tests and three-point bending tests, determine the compression elastic modulus E c0 = 1200 MPa, uniaxial compression strength σ c0 = 4.2 MPa, and bending strength σ b0 = 1.4 MPa of the sea ice specimen to be simulated.

[0092] Step 1.2: Take the compression elastic modulus E c0 = 1200 MPa, uniaxial compression strength σ c0 = 4.2 MPa, and bending strength σ b0 = 1.4 MPa obtained in Step 1.1 as the target values of the discrete element sea ice model.

[0093] Step 2: Selection of the friction coefficient between sea ice and the structure:

[0094] Step 2.1: Determine that the friction coefficient between sea ice and the structure in the research or actual project is 0.014.

[0095] Step 2.2: Use the result in Step 2.1 as the friction coefficient μ = 0.014 between sea ice and the structure in the discrete element simulation.

[0096] Step 3: Uniaxial compression discrete element numerical simulation:

[0097] Step 3.1: Select the particle radius r = 10 mm for constructing the discrete element sea ice model.

[0098] Step 3.2: Arrange the spherical particles selected in Step 3.1 regularly to establish a uniaxial compression model of discrete element sea ice. The model size is 200 mm × 200 mm × 500 mm (a × a × l), as Figure 2 shown.

[0099] Step 3.3: Select the elastic modulus of the spherical particles as E, and E = E c0 = 1200 MPa; select the Poisson's ratio of the spherical particles as u, and the value is 0.3; select the normal stiffness coefficient of the particles as N k and the value is 0.01.

[0100] Step 3.4: Determine that the number of particles in unilateral contact between the discrete element sea ice model and the structure during uniaxial compression is 126.

[0101] Step 3.5: Select the expected average overlap x between the discrete element sea ice model and the structure, and the value is 0.05Δl, where Δl is the compression displacement value.

[0102] Step 3.6: Calculate the contact stiffness proportionality factor SFP according to the uniaxial compression strain formula, stress-strain relationship, pressure-stress relationship, and discrete element theory formula:

[0103]

[0104] Step 3.7: Introduce SPH particles with fluid properties into each particle element in the discrete element uniaxial compression sea ice model to establish a co-node DEM-SPH uniaxial compression model of sea ice, as Figure 3 shown.

[0105] Step 3.8: Set the SPH particle parameters.

[0106] Step 3.9: Set the cement normal bonding strength pb_n and the cement tangential bonding strength pb_s to 100 MPa so that the cement in the discrete element sea ice model does not fail during compression.

[0107] Step 3.10: Estimate the normal stiffness of cementation pb_k according to the target value E in Step 1.2 c0 = 1200 MPa n The value of is as follows:

[0108]

[0109] Step 3.11: Take the ratio of the tangential stiffness to the normal stiffness of cementation pb_k s / pb_k n = 0.3, and conduct uniaxial compression numerical simulations on the discrete element models with different normal stiffnesses of cementation. The results of the compression elastic modulus of the discrete element models are as Figure 4 shown.

[0110] Step 3.12: Analyze the data obtained in Step 3.11 to obtain the relationship between the compression elastic modulus E of the discrete element model c and the normal stiffness of cementation pb_k n as E c = 1.6pb_k n , let E c = 1.6pb_k n = E c0 , and obtain pb_k n = 750 N / mm.

[0111] Step 3.13: Take the normal stiffness of cementation pb_k n = 750 N / mm, and conduct uniaxial compression numerical simulations on the discrete element models with different ratios of tangential stiffness to normal stiffness of cementation. The results of the compression elastic modulus of the discrete element models are as Figure 5 shown.

[0112] Step 3.14: Analyze the data obtained in Step 3.13 to obtain the relationship between the compression elastic modulus E of the discrete element model c and the ratio of tangential stiffness to normal stiffness of cementation pb_k s / pb_k n as E c = 996 + 672pb_k s / pb_k n .

[0113] Step 3.15: Finally, obtain the relationship between the compression elastic modulus E of the discrete element model c and the normal stiffness of cementation pb_k n , and the ratio of tangential stiffness to normal stiffness of cementation pb_k s / pb_k n as E c = F(pb_k n , pb_k s / pb_k n ) is as follows:

[0114] E c = 1328pb_k n + 896pb_k n (pb_k s / pb_k n );

[0115] Step 3.16: Determine the values of multiple groups of cementation normal stiffness and the ratio of cementation tangential stiffness to legal system stiffness. Let the relational expression obtained in Step 3.15 be equal to E c0 , pb_k s / pb_k n Take 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 respectively, and obtain the values of pb_k n as 846.5 N / mm, 796.2 N / mm, 751.5 N / mm, 711.6 N / mm, 675.7 N / mm, 643.2 N / mm respectively.

[0116] Step 4: Three-point bending discrete element numerical simulation:

[0117] Step 4.1: Arrange the selected spherical particles regularly, and introduce SPH particles into each particle element to establish a co-node DEM-SPH sea ice three-point bending model. The model size is 150 mm × 150 mm × 1400 mm (h × h × b), as Figure 6 shown.

[0118] Here, it should be noted that in Step 4.1, during the process of solving the structure to be simulated by means of the discrete element parameter calibration method of the co-node DEM-SPH sea ice model, based on the potential physical connection between the macro and micro strength parameters of sea ice, the matching error of the uniaxial compressive strength and the three-point bending flexural strength parameters is converged to a small range, making the results obtained by discrete element parameter calibration more accurate.

[0119] Step 4.2: Select the particle elastic modulus E, particle Poisson's ratio u, and particle normal stiffness coefficient Nk, and take the same values as those in Step 3.3.

[0120] Step 4.3: Select the contact stiffness proportionality factor SFP, and take the same value as that in Step 3.6.

[0121] Step 4.4: Set the values of the cementation normal bond strength pb_n and the cementation tangential bond strength pb_s. Their preliminary estimated values are pb_n = pb_s = σ b0 / 2 = 0.7 MPa.

[0122] Step 4.5: Select a group of ratios of cementation tangential stiffness to legal system stiffness pb_k s / pb_k nAnd the normal stiffness of cementation pb_k n The value of, take pb_k s / pb_k n = 0.1, pb_k n = 846.5 N / mm.

[0123] Step 4.6: Conduct numerical simulation to obtain the flexural strength σ of the discrete element sea ice model b Is 1.303 MPa.

[0124] Step 4.7: According to the flexural strength σ obtained in Step 4.6 b , adjust the values of the normal bonding strength pb_n and the tangential bonding strength pb_s of the cementation to 0.752 MPa.

[0125] Step 4.8: Repeat Steps 4.5 to 4.7.

[0126] Step 4.9: Establish the relationship pb_n = G(pb_k s / pb_k n ) between the normal bonding strength pb_n of the cementation obtained in Step 4.7 and the ratio of the tangential bonding to the legal system stiffness pb_k s / pb_k n ) selected in Step 4.5 as:

[0127] pb_n = 1.281(pb_k s / pb_k n ) 2 -1.483pb_k s / pb_k n + 0.924;

[0128] Step 5: Secondary uniaxial compression discrete element numerical simulation:

[0129] Step 5.1: Adopt the same co - node DEM - SPH sea ice uniaxial compression model as in Step 3.

[0130] Step 5.2: Select a set of values of the normal stiffness of cementation pb_k n and the ratio of the tangential bonding to the legal system stiffness pb_k s / pb_k n The value of, take pb_k s / pb_k n = 0.1, pb_k n = 846.5 N / mm, and obtain the corresponding value of the normal stiffness of cementation pb_n as 0.788 MPa from Step 4.9.

[0131] Step 5.3: Take different tangential bonding strengths pb_s of the cementation, and the ratios of the tangential bonding strength pb_s to the normal bonding strength pb_n of the cementation are 1, 1.5, 2, 2.5, ……

[0132] Step 5.4: Conduct uniaxial compression numerical simulations on the discrete element models with different ratios of tangential to normal stiffness of the cementation to obtain the uniaxial compression strength of the discrete element sea ice model.

[0133] Step 5.5: Repeat Steps 5.2 to 5.4, and the results are as Figure 7 shown.

[0134] Step 5.6: For the compression strength σ c obtained in Step 5.4, its maximum compression strength is denoted as (σ c )max, and the corresponding minimum ratio of tangential to normal bonding strength of the cementation is denoted as (pb_s / pb_n)min.

[0135] Step 5.7: The ratio e of the maximum compression strength (σ c )max obtained in Step 5.6 to the flexural strength σ b0 is e = (σ c )max / 1.4.

[0136] Step 5.8: Establish the relationship pb_k Figure 7 / pb_k s / pb_k n between the ratio of tangential to normal stiffness of the cementation pb_k s / pb_k n selected in Step 5.2 and the ratio e obtained in Step 5.7 as pb_k

[0137] pb_k s / pb_k n = 0.31e - 0.39;

[0138] Step 5.9: Establish the relationship (pb_s / pb_n)min = I(pb_k Figure 7 / pb_k s / pb_k n ) between the minimum ratio of tangential to normal bonding strength of the cementation (pb_s / pb_n)min obtained in Step 5.6 and the ratio of tangential to normal stiffness of the cementation pb_k s / pb_k n selected in Step 5.2 as:

[0139] (pb_s / pb_n) min = 6pb_k s / pb_k n - 0.3;

[0140] Step 6: Calibrate the discrete element parameters of the sea ice specimen in Step 1.1, which includes the following sub-steps:

[0141] Step 6.1: Calculate the ratio e0 = 3 of the uniaxial compressive strength σ c0 = 4.2 MPa obtained in Step 1.1 to the flexural strength σ b0 = 1.4 MPa.

[0142] Step 6.2: Determine the value of the ratio of the cemented tangential stiffness to the normal stiffness as pb_k s / pb_k n = 0.54 from the relationship pb_k s0 / pb_k n0 = H(e) obtained in Step 5.8 and the ratio e0 obtained in Step 6.1.

[0143] Step 6.3: Determine the value of the cemented normal stiffness as pb_k c0 = 662.3 N / mm from the compressive elastic modulus E c = 1200 MPa obtained in Step 1.1, the relationship E n = F(pb_k s ,pb_k n ) obtained in Step 3.15, and the ratio of the cemented tangential stiffness to the normal stiffness pb_k s0 / pb_k n0 obtained in Step 6.2. n0 = 662.3 N / mm.

[0144] Step 6.4: Determine the value of the cemented normal bonding strength as pb_n0 = 0.497 MPa from the relationship pb_n = G(pb_k s / pb_k n ) obtained in Step 4.9 and the ratio of the cemented tangential stiffness to the normal stiffness pb_k s0 / pb_k n0 obtained in Step 6.2.

[0145] Step 6.5: Determine the value of the cemented tangential bonding strength as pb_s0 = 1.461 MPa from the relationship (pb_s / pb_n)min = I(pb_k s / pb_k n ) obtained in Step 5.9, the ratio of the cemented tangential stiffness to the normal stiffness pb_k s0 / pb_k n0 obtained in Step 6.2, and the cemented normal bonding strength pb_n0 obtained in Step 6.4.

[0146] The final results are as follows: pb_k n0 = 662.3 N / mm, pb_k s0 / pb_k n0= 0.54, pb_n0 = 0.497 MPa, pb_s0 = 1.461 MPa.

[0147] In the technical solution disclosed by the present invention, through the combination of theoretical analysis and numerical simulation, the influencing factors of the macroscopic strength of the structure to be simulated are comprehensively and fully considered, and the functional relationship between the microscopic parameters and the macroscopic parameters is established, so as to quickly determine the discrete element parameters of sea ice with different strengths, making the results obtained by the calibration of the discrete element parameters more comprehensive and efficient.

[0148] In addition, it should be noted here that the above method is also applicable to the parameter calibration of other sea ice (not the sea ice specimen set in step 1.1). Steps 1, 2, 3, 4, and 5 can be executed with reference to the above content. The difference is that the sub-steps included in step 6 need to be rewritten correspondingly as:

[0149] Step 6.1': Through uniaxial compression test and three-point bending test, determine the compression elastic modulus E c1 = 1000 MPa, uniaxial compression strength σ c1 = 3 MPa, and bending strength σ b1 = 1.2 MPa.

[0150] Step 6.2': Calculate the ratio e1 = 2.5 of the uniaxial compression strength σ c1 obtained in step 6.1' to the bending strength σ b1 .

[0151] Step 6.3': Determine the value of the ratio of the cementation tangential stiffness to the normal stiffness as pb_k s / pb_k n = 0.385 according to the ratio e1 obtained in step 6.2' and the relationship pb_k s1 / pb_k n1 = H(e) obtained in step 5.8.

[0152] Step 6.4': Determine the value of the cementation normal stiffness as pb_k c1 = 597.7 N / mm according to the compression elastic modulus E c obtained in step 6.1', the relationship E n = F(pb_k s , pb_k n / pb_k s1 / pb_k n1 obtained in step 3.15, and the ratio of the cementation tangential stiffness to the normal stiffness pb_k n1 .

[0153] Step 6.5': According to the relationship pb_n = G(pb_k s / pb_kn ) The ratio of the tangential to normal stiffness of the cementation pb_k obtained in step 6.3' s1 / pb_k n1 and the flexural strength σ b1 and σ b0 to determine the value of the normal bonding strength of the cementation as pb_n1 = 0.388 MPa.

[0154] Step 6.6': From the relationship (pb_s / pb_n)min = I(pb_k s / pb_k n ) obtained in step 5.9, the ratio of the tangential to normal stiffness of the cementation pb_k s1 / pb_k n1 obtained in step 6.3', and the normal bonding strength of the cementation pb_n1 obtained in step 6.5' to determine the value of the tangential bonding strength of the cementation as pb_ s1 = 0.78 MPa.

[0155] The final results are as follows: pb_k n1 = 597.7 N / mm, pb_k s1 / pb_k n1 = 0.385, pb_n1 = 0.388 MPa, pb_s1 = 0.78 MPa.

[0156] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. Discrete element parameter calibration method for co - nodal DEM - SPH sea ice model, characterized in that, It includes the following steps: S1. Selection of macroscopic mechanical parameters of sea ice; the specific method is as follows: S11: Determine the compressive elastic modulus E, uniaxial compressive strength σ c0 , and flexural strength σ b0 of the sea ice specimen to be simulated through uniaxial compression tests and three-point bending tests; c0 and uniaxial compressive strength σ c0 and flexural strength σ b0 ; S12: Take the compressive elastic modulus E obtained in step S11 c0 , the uniaxial compressive strength σ c0 and the flexural strength σ b0 as the target values of the discrete element sea ice model; S2. Selection of the friction coefficient between sea ice and structure; S3. Uniaxial compression discrete element numerical simulation; S4. Three-point bending discrete element numerical simulation; S5. Secondary uniaxial compression discrete element numerical simulation; S6. Calibration of discrete element parameters of sea ice specimens; the specific method is as follows: S61: Calculate the uniaxial compressive strength σ obtained from sub-step S11 c0 and the flexural strength σ b0 to obtain the ratio e0; S62: Establish the ratio pb_k of the cementation tangential stiffness to the normal stiffness s / pb_k n The relationship with the ratio e of the maximum compressive strength (σc)max to the flexural strength σ b0 : pb_k s / pb_k n = H(e); and determine the value of the ratio pb_k of the cementation tangential stiffness to the normal stiffness with the ratio e0 obtained in sub-step S61 as pb_k s0 / pb_kn0 = H(e0); S63: The compressive elastic modulus E obtained from sub-step S11 c0 , the compressive elastic modulus E of the discrete element model c and the cementation normal stiffness pb_k n , the ratio of the cementation tangential stiffness to the normal stiffness pb_k s / pb_k n to determine the relationship of E c = F(pb_k n , pb_k s / pb_k n ) and the ratio of the cementation tangential stiffness to the normal stiffness pb_k s0 / pb_k n0 obtained from sub-step S62 to determine the value of the cementation normal stiffness pb_k n0 such that E c0 = F(pb_k n0 , pb_k s0 / pb_k n0 ); S64: Establish the relationship between the normal bonding strength pb_n of the cementation and the ratio pb_ks / pb_kn of the tangential to normal stiffness of the cementation pb_n = G(pb_k s / pb_k n ) and the ratio pb_k s0 / pb_k n0 of the tangential to normal stiffness of the cementation obtained in sub-step S62 to determine that the value of the normal bonding strength of the cementation is pb_n0 = G(pb_k s0 / pb_k n0 ); S65: Establish the relationship between the minimum ratio of the tangential to the normal bond strength (pb_s / pb_n)min and the ratio of the tangential to the normal bond stiffness pb_k s / pb_k n such that (pb_s / pb_n)min = I(pb_k s / pb_k n ), the ratio of the tangential to the normal bond stiffness pb_k s0 / pb_k n0 obtained in sub-step S62, and the normal bond strength pb_n0 obtained in sub-step S64 to determine the value of the tangential bond strength as pb_s0 = pb_n0I(pb_k s0 / pb_k n0 ).

2. The calibration method of discrete element parameters of the co - node DEM - SPH sea ice model according to claim 1, wherein, Step S2 includes the following sub-steps: S21: Determine the friction coefficient between sea ice and structure in the research or actual project; S22: Use the result in step S21 as the friction coefficient μ between sea ice and structure in the discrete element simulation.

3. The calibration method for the discrete element parameters of the co - nodal DEM - SPH sea ice model according to claim 2, characterized in that, Step S3 includes the following sub-steps: S31: Select the particle radius r for constructing the discrete element sea ice model; S32: Regularly arrange the spherical particles selected in step S31 to establish a discrete element sea ice uniaxial compression model with the model size of a×a×l; S33: Select the elastic modulus of the particles as E, and the value is the target value E in step S12 c0 ; Select the Poisson's ratio of the particles as u; Select the normal stiffness coefficient of the particles as N k ; S34: Determine the number of particles n in unilateral contact between the discrete element sea ice model and the structure during uniaxial compression; S35: Select the expected average overlap x between the discrete element sea ice model and the structure, where Δl is the compression displacement value; S36: Calculate the contact stiffness proportionality factor SFP according to the uniaxial compression strain formula, stress-strain relationship, pressure-stress relationship and discrete element theory formula, and its formula is: S37: Introduce SPH particles with fluid properties into each particle unit in the discrete element uniaxial compression sea ice model to establish a co-nodal DEM-SPH sea ice uniaxial compression model; S38: Set the SPH particle parameters; S39: Set the normal bonding strength pb_n and tangential bonding strength pb_s of the cementation method; S310: Estimate the normal stiffness value pb_k of cementation according to the target value Ec0 in step S11 n , and its estimation formula is: S311: Set the ratio pb_k of the cementation tangential stiffness to the normal stiffness s / pb_k n = Ω, and 0.29 < Ω < 0.32; Conduct uniaxial compression numerical simulations on discrete element models with different cementation normal stiffnesses. And set the acting force at the compression displacement of Δl to be F. Then the results of the compression elastic modulus of the discrete element models are as follows: S312: Analyze the data obtained in step S311 to obtain the compressive elastic modulus E of the discrete element model c and the cementation normal stiffness pb_k n relationship E c = k1pb_k n , and let E c = k1pb_k n = E c0 , to obtain pb_k n = E c0 / k1; S313: Obtain the normal stiffness of cementation pb_k n = E c0 / k1, conduct uniaxial compression numerical simulations on discrete element models with different ratios of tangential to normal stiffness of cementation, and obtain the results of the compression elastic modulus of the discrete element models; S314: Analyze the data obtained in step S313 to obtain the compressive elastic modulus Ec of the discrete element model and the ratio pb_k of the cemented tangential stiffness to the normal stiffness s / pb_k n The relationship of E c = a + k2pb_k s / pb_k n ; S315: Obtain the compressive elastic modulus E of the discrete element model c and the cementation normal stiffness pb_k n , the ratio of the cementation tangential stiffness to the normal stiffness pb_k s / pb_k n and the relationship of E c = F(pb_k n , pb_k s / pb_k n ), and its formula is as follows: S316: Determine the values of multiple groups of normal bond stiffness and the ratio of tangential bond stiffness to normal bond stiffness, and make the relational expression obtained in step S315 equal to E c0 , pb_k s / pb_k n Take 0.1, 0.2, 0.3, 0.4... respectively to obtain the value of pb_k n .

4. The discrete element parameter calibration method of the co - node DEM - SPH sea ice model according to claim 3, characterized in that, Step S4 includes the following sub-steps: S41: Regularly arrange the spherical particles selected in step S31 and introduce SPH particles into each particle unit to establish a co-nodal DEM-SPH sea ice three-point bending model with the model size of h×h×b; S42: Select the particle elastic modulus E, particle Poisson's ratio u, and particle normal stiffness coefficient Nk, and their values are the same as those in sub-step S33; S43: Select the contact stiffness proportionality factor SFP, and its value is the same as that in sub-step S36; S44: Set the values of the normal bonding strength pb_n and the tangential bonding strength pb_s of the cementation, and initially estimate the values as pb_n = pb_s = σ b0 / 2; S45: Select a set of values of the normal stiffness pb_k of the cementation method in sub-step S316 n and the ratio pb_k of the tangential stiffness to the normal stiffness of the cementation method s / pb_k n ; S46: Conduct numerical simulation. If the acting force when the discrete element sea ice model breaks is F b , then the bending strength result of the discrete element sea ice model is obtained as follows: S47: The bending strength result of the discrete element sea ice model is linearly related to the cementation bonding strength. According to the bending strength σb obtained in sub-step S46, adjust the values of the normal bonding strength pb_n and tangential bonding strength pb_s of the cementation method, and its calculation formula is: S48: Repeat sub-steps S45 - S47; S49: Establish the relationship between the normal bonding strength pb_n obtained in step S47 and the ratio pb_ks / pb_kn of tangential to legal system stiffness selected in step S45 as pb_n = G(pb_ks / pb_kn).

5. The calibration method for discrete element parameters of the co - node DEM - SPH sea ice model according to claim 4, characterized in that Step S5 includes the following sub-steps: S51: Adopt the same co-nodal DEM-SPH sea ice uniaxial compression model as in step S3; S52: Select a set of values of the normal stiffness pb_kn of the cementation method and the ratio pb_ks / pb_kn of tangential to legal system stiffness in sub-step S316, and obtain the corresponding value of the normal stiffness pb_n of the cementation method from step S47; S53: Take different tangential bonding strengths pb_s of cementation, and the ratios of them to the normal bonding strength pb_n of cementation are 1, 1.5, 2, 2.5...; S54: Uniaxial compression numerical simulations are carried out on discrete element models with different ratios of tangential to normal stiffness of cementation. If the acting force at the failure of the discrete element sea ice model is F c , then the uniaxial compression strength of the discrete element sea ice model is obtained as follows: S55: Repeat sub-steps S52 - S54; S56: For the compressive strength σc obtained in sub-step S54, its maximum compressive strength is denoted as (σc)max, and the corresponding minimum tangential to normal bonding strength of cementation is denoted as (pb_s / pb_n)min; S57: Let the ratio of the maximum compressive strength (σc)max obtained in sub-step S56 to the flexural strength σ b0 be e; S58: Establish the relationship between the ratio pb_k of the selected cementation tangential stiffness to the normal stiffness in sub-step S52 s / pb_k n and the ratio e obtained in sub-step S57 as pb_k s / pb_k n = H(e); S59: Establish the relationship between the minimum bond tangential and normal bond strength (pb_s / pb_n)min obtained in sub-step S56 and the bond tangential and normal stiffness ratio pb_k selected in sub-step S52 s / pb_k n as (pb_s / pb_n)min = I(pb_k s / pb_k n ).

6. The discrete element parameter calibration method of the co - nodal DEM - SPH sea ice model according to claim 1, characterized in that When performing the discrete element parameter calibration operation on other sea ice specimens to be simulated, step S6 includes the following sub-steps: S61’: Determine the compressive elastic modulus E c1 , uniaxial compressive strength σ c1 and flexural strength σ b1 ; S62’: Calculate the uniaxial compressive strength σ obtained from the previous step S61’ c1 and the flexural strength σ b1 to obtain the ratio e1; S63’: The relationship pb_k obtained from sub-step S58 s / pb_k n = The value of the ratio of the bonding tangential stiffness to the normal stiffness is determined as pb_k by the ratio H(e) obtained from sub-step S62’ s1 / pb_k n1 = H(e1); S64’: The compressive elastic modulus E obtained from the grandson step S61’ c1 , the relationship E obtained from the sub-step S315 c = F(pb_k n , pb_k s / pb_k n ), and the ratio pb_k of the cementation tangential stiffness to the normal stiffness obtained from the grandson step S63’ s1 / pb_k n1 to determine that the value of the cementation normal stiffness pb_k n1 satisfies E c1 = F(pb_k n1 , pb_k s1 / pb_k n1 ); S65’: The value of the normal bonding strength of the cementation pb_n1 is determined by the relationship pb_n = G(pb_k s / pb_k n ) obtained from the sub-step S49, the ratio of the tangential to normal stiffness of the cementation pb_k s1 / pb_k n1 obtained from the grandchild-step S63’, and the ratio of the bending strength σ b1 to σ b0 , i.e., pb_n1 = (σb1 / σb0)G(pb_k s1 / pb_k n1 ); S66’: The value of the bond tangential bond strength pb_s1 is determined to be pb_s1 = pb_n1I(pb_k s / pb_k n ) from the relationship (pb_s / pb_n)min = I(pb_k s1 / pb_ kn1 ) obtained in sub-step S59, the ratio of the bond tangential stiffness to the normal stiffness pb_k s1 / pb_k n1 ) obtained in grand-sub-step S63’, and the bond normal bond strength pb_n1 obtained in grand-sub-step S65’.

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