A method for establishing an elastic-plastic constitutive model of granular material based on neutral loading

Abstract

The application relates to a kind of methods for establishing elastic-plastic constitutive model based on neutral loading of granular material, comprising: using discrete element stress probing test to analyze the incremental stress-strain response of granular material under neutral loading condition;According to the strain response envelope of different states, under the framework of critical state theory, the plastic flow direction, plastic modulus and shear dilatancy coefficient suitable for the neutral loading condition are derived, and the constitutive model is constructed;The predictive ability of the constitutive model constructed under the neutral loading condition is verified by simulating stress probing test and principal stress axis rotation test.The beneficial effects of the application are that the application can accurately predict the plastic strain, shear dilatancy coefficient and plastic flow direction of granular material under the neutral loading condition, and solve the problem of inaccurate prediction of traditional models under the neutral loading condition.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and more specifically, to a method for establishing an elastoplastic constitutive model of granular materials under neutral loading. Background Technology

[0002] Granular materials (such as sand and gravel) are widely used in geotechnical engineering, and a correct understanding of their mechanical properties is crucial for engineering design and construction. Neutral loading refers to a special stress path where the stress increment is perpendicular to the normal direction of the yield surface. Neutral loading is widespread in practical engineering, for example, in seismic loads, traffic loads, and wave loads, where a considerable proportion of the stress increment borne by the soil is in the neutral loading direction. However, because neutral loading cannot induce the evolution of the yield surface, existing constitutive models often fail to predict plastic strain under this stress path. Furthermore, due to the coaxial assumption, the model cannot simulate the significant non-coaxial response caused by neutral loading. These shortcomings lead to a large deviation between the model's predictions and experimental data.

[0003] The Discrete Element Method (DEM), as a numerical simulation tool, can effectively simulate the macroscopic and microscopic mechanical behavior of particulate materials. However, the application of DEM technology in constitutive model construction, especially in the study of the mechanical properties of particulate materials under neutral loading conditions and related constitutive simulations, remains insufficient. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for establishing an elastoplastic constitutive model of particulate materials under neutral loading.

[0005] Firstly, a method for establishing an elastoplastic constitutive model of particulate materials under neutral loading is provided, including:

[0006] Step 1: Analyze the incremental stress-strain response of granular materials under neutral loading conditions using discrete element stress testing.

[0007] Step 2: Based on the strain response envelope under different states, within the framework of critical state theory, derive the plastic flow direction, plastic modulus, and dilatation coefficient applicable to neutral loading conditions, and construct a constitutive model.

[0008] Step 3: Verify the predictive ability of the constructed constitutive model under neutral loading conditions through simulated stress probing tests and principal stress axis rotation tests.

[0009] Preferably, step 1 includes:

[0010] Step 1.1, Sample preparation: Discrete element numerical simulation experiments were conducted to obtain samples with different initial states by changing the porosity, confining pressure, and stress ratio;

[0011] Step 1.2, Stress test: Apply multiple shear stress increments of the same magnitude but different directions to the specimen.

[0012] Preferably, step 2 includes:

[0013] Step 2.1: Calculate the plastic strain caused by the normal and tangential yield surface stress increments using both conventional and neutral loading mechanisms; the expression for the total strain increment is:

[0014] dε=dε e +dε p1 +dε p2

[0015] Where, dε e It is the elastic strain increment, dε p1 and dε p2 These are the plastic strain increments corresponding to conventional loading and neutral loading mechanisms, respectively;

[0016] Step 2.2: Construct the elastic relationship and conventional loading mechanism of the particulate material;

[0017] Step 2.3: Construct a neutral loading mechanism. Preferably, in step 2.2, the elastic behavior expression of the particulate material is:

[0018]

[0019] Where K and G are the elastic bulk modulus and shear modulus, respectively; I is the second-order unit tensor.

[0020] The yield surface of a conventional loading mechanism is represented as:

[0021] f = R / g(θ) - H = 0

[0022] Where R is the stress ratio invariant, H is the hardening parameter, and g(θ) is the interpolation function, which characterizes the shape of the yield surface.

[0023] Preferably, in step 2.3, the stress ratio increment dr is decomposed into two parts relative to the yield surface normal m:

[0024] dr pr =m(dr:m)

[0025] dr np =dr-m(dr:m)

[0026] Among them, dr pr Proportional to m, i.e., perpendicular to the yield surface; while dr np It contains stress increment components that are not directly proportional to dr and m, and is tangent to the yield surface; therefore, its direction is l = dr. np / ||drnp || represents the loading direction under neutral loading; therefore, the hardening rule of the neutral loading mechanism is expressed as:

[0027] l:dr-K p2 dL2 = 0.

[0028] Preferably, step 2.3 includes:

[0029] 2.3.1 Derivation of the plastic modulus K applicable to neutral loading p2 ;

[0030] 2.3.2. Derive the dilatation coefficient D2 applicable to neutral loading;

[0031] 2.3.3 Derivation of the plastic flow direction n2 applicable to neutral loading.

[0032] Secondly, a system for establishing an elastoplastic constitutive model of particulate materials under neutral loading is provided, for performing any of the methods described in the first aspect, including:

[0033] The analysis module is used to analyze the incremental stress-strain response of particulate materials under neutral loading conditions using discrete element stress probing experiments.

[0034] The derivation module is used to derive the plastic flow direction, plastic modulus, and dilatation coefficient applicable to neutral loading conditions within the framework of critical state theory, based on the strain response envelope under different states, and to construct a constitutive model.

[0035] The verification module is used to verify the predictive ability of the constructed constitutive model under neutral loading conditions through simulated stress probing tests and principal stress axis rotation tests.

[0036] Thirdly, a computer storage medium is provided, wherein a computer program is stored therein; when the computer program is run on a computer, the computer causes the computer to perform any of the methods described in the first aspect.

[0037] Fourthly, an electronic device is provided, comprising:

[0038] Memory, used to store computer programs;

[0039] A processor for executing the computer program to implement the method as described in any of the first aspects.

[0040] The beneficial effects of this invention are: it can accurately predict the plastic strain, dilatation coefficient, and plastic flow direction of granular materials under neutral loading conditions, solving the problem of inaccurate predictions by traditional models under neutral loading conditions. This model is suitable for soil mechanics analysis under complex stress paths such as seismic loads, traffic loads, and wave loads, and has broad application prospects. Attached Figure Description

[0041] Figure 1 Schematic diagram of conventional and neutral loading mechanisms provided by the present invention;

[0042] Figure 2 A schematic diagram of the stress testing scheme provided by the present invention;

[0043] Figure 3 A comparison chart of the results of stress testing under neutral loading and the results predicted by equation (16) provided by the present invention;

[0044] Figure 4 The neutral loading action provided by the present invention and The value;

[0045] Figure 5 The strain response envelope provided by this invention is the result of DEM test and the model prediction.

[0046] Figure 6 A comparison diagram of the DEM drainage principal stress axis rotation test results and model predictions provided by this invention. Detailed Implementation

[0047] The present invention will be further described below with reference to embodiments. The description of the embodiments below is only for the purpose of helping to understand the present invention. It should be noted that those skilled in the art can make several modifications to the present invention without departing from the principle of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0048] Example 1:

[0049] Embodiment 1 of this application provides a method for constructing an elastoplastic constitutive model for granular materials under neutral loading based on stress testing. This method can accurately predict the plastic strain, dilatation coefficient, and plastic flow direction of granular materials under neutral loading, solving the problem of inaccurate predictions by traditional models under neutral loading conditions. Specifically, the method includes:

[0050] Step 1: Discrete element stress testing is used to analyze the incremental stress-strain response of granular materials under neutral loading conditions.

[0051] Step 1 includes:

[0052] Step 1.1, Sample Preparation: Using PFC 3D Discrete element numerical simulation experiments were conducted to obtain samples with different initial states by controlling the porosity, confining pressure, and stress ratio.

[0053] Step 1.2, Stress test: Apply multiple shear stress increments in different directions from the initial stress state.

[0054] In step 1.2, assuming the principal stress direction is consistent with x3, the stress state is: σ 33 >σ 11 =σ 22 .

[0055] use Figure 2 The stress testing scheme shown in (a) is as follows: Starting from the same initial state, multiple shear stress increments of the same magnitude but in different directions are applied, which can be expressed as:

[0056]

[0057] dσ 13 =dσ 31 =dσ r cos(α dσ (1b)

[0058] dσ 23 =dσ 32 =dσ r sin(α dσ (1c)

[0059] dσ r =(σ 11 -σ 33 sin(dθ)cos(dθ)(1d)

[0060] In the formula, dσ r and α dσ These represent the magnitude and direction of the stress increment, respectively.

[0061] Step 2: Based on the strain response envelopes under different states, within the framework of critical state theory, derive the plastic flow direction, plastic modulus, and dilatation coefficient applicable to neutral loading conditions, and construct a constitutive model.

[0062] Step 2 includes:

[0063] Step 2.1, Model Framework: The plastic strain caused by the components of the stress increment in the normal and tangential directions of the yield surface is calculated using both conventional and neutral loading mechanisms; the expression for the total strain increment is:

[0064] dε=dε e +dε p1 +dε p2 (2)

[0065] Where, dε e It is the elastic strain increment, dε p1 and dε p2These represent the plastic strain increments corresponding to conventional loading and neutral loading mechanisms, respectively, and are expressed as follows:

[0066]

[0067] Where dL1=||de p1 ||,dL2=||de p2 || represents the loading factor, which indicates the plastic deviatoric strain increment de. p1 and de p2 Size; n1 = de p1 / ||de p1 ||;n2=de p2 / ||de p2 || represents the unit deviatoric strain tensor indicating its direction; shear dilatation coefficient and The dilatation relationship was quantified; χ1 and χ2 represent dε, respectively. p1 and dε p2 The direction.

[0068] Step 2.2: Construct the model's elastic relationships and conventional loading mechanisms.

[0069] The expression for the elastic stress-strain relationship of granular materials is:

[0070]

[0071] Where K and G are the elastic bulk modulus and shear modulus, respectively; I is the second-order unit tensor.

[0072] The plastic deformation of sand under proportional loading is mainly caused by changes in stress ratio. Therefore, the yield surface of conventional loading mechanism can be expressed as:

[0073] f=R / g(θ)-H=0 (5)

[0074] Where R is the stress ratio invariant, H is the hardening parameter, and g(θ) is the interpolation function, characterizing the shape of the yield surface, and its expression is:

[0075]

[0076] Among them, M e and M c These represent the critical stress ratios under triaxial tension and compression, respectively.

[0077] The loading factor dL1 in equation (2a) can be calculated based on the consistency condition, specifically as follows:

[0078] pm:dr-K p1 dL1=0 (7)

[0079] In the formula, m is the unit deviatoric stress tensor characterizing the normal direction of the yield surface.

[0080] By applying the correlation flow rule on the deviated plane, the plastic strain direction n1 under the conventional loading mechanism can be expressed as:

[0081]

[0082] Step 2.3: Construct a neutral loading mechanism.

[0083] Under a neutral loading path, dr⊥m, therefore m:dr=0, dL1=0. Thus, it can be seen that the conventional loading mechanism in equation (7) cannot simulate plastic strain under neutral loading conditions. Therefore, this invention proposes a neutral loading mechanism as a supplement to the conventional loading mechanism.

[0084] The stress ratio increment dr can be decomposed into two parts about the yield surface normal m:

[0085] dr pr =m(dr:m)(9a)

[0086] dr np =dr-m(dr:m)(9b)

[0087] like Figure 1 As shown, in equation (9), the first part dr pr Proportional to m and perpendicular to the yield surface, while the second part dr np It includes the portion where dr and m are not proportional, and is tangent to the yield surface. Vector l = dr np / ||dr np || represents dr np In the direction of the load path, under a neutral loading path, since m:dr = 0, then dr pr =0 and dr np =dr. Plastic strain is entirely determined by dr. np This is caused by the component of the stress increment in the l direction. Therefore, l can be considered as the loading direction under a neutral loading path, and the hardening rule of the neutral loading mechanism can be expressed as:

[0088] l:dr-K p2 dL2=0 (10)

[0089] Among them, K p2 This represents the plastic modulus under neutral loading conditions.

[0090] Step 3: Verify the predictive ability of the constitutive model under neutral loading conditions through simulated stress testing and principal stress axis rotation testing.

[0091] Example 2:

[0092] Based on Example 1, Example 2 of this application provides a more specific method for constructing an elastoplastic constitutive model for particulate materials suitable for neutral loading based on stress testing, including:

[0093] Step 1: Discrete element stress testing is used to analyze the incremental stress-strain response of granular materials under neutral loading conditions.

[0094] Step 2: Based on the strain response envelopes under different states, within the framework of critical state theory, derive the plastic flow direction, plastic modulus, and dilatation coefficient applicable to neutral loading conditions, and construct a constitutive model.

[0095] The neutral loading mechanism is used to calculate the plastic strain caused by the stress increment perpendicular to the yield surface normal. Specifically, constructing the neutral loading mechanism includes:

[0096] (1) Derive the plastic modulus K applicable to neutral loading p2 .

[0097]

[0098] ψ=ee c

[0099] (11c)

[0100] e c =e-[e Γ -λ c (ppa) ξ (10d)

[0101]

[0102] (2) Derive the dilatation coefficient D2 applicable to neutral loading.

[0103]

[0104] (3) Derive the plastic flow direction n2 applicable to neutral loading.

[0105] In each stress test, n2 can be calculated from the plastic strain increment:

[0106]

[0107] Since neutral loading can induce coaxial and non-coaxial plastic strain, Decomposed into coaxial and non-coaxial parts:

[0108]

[0109] in, and Representing the coaxial and non-coaxial plastic strain increments, respectively. and The direction; and These represent the proportions of coaxial and non-coaxial plastic strain increments in the total plastic strain increment, respectively. Based on the definition of constitutive elements above, their values ​​can be directly determined in stress testing:

[0110]

[0111] In addition, due to It is a unit partial tensor, therefore By fitting Figure 3 From the experimental data, φ can be obtained. co and φ nc The expression for is:

[0112]

[0113] λ=λ1exp(λ2ψ) (17)

[0114] In the formula, λ1 and λ2 are model parameters. When the critical state is reached, R = M. c g(θ), therefore, φ co =1 and φ nc =0 indicates that the non-coaxial response has disappeared. Figure 3 Showing the φ predicted by formula (16) co and φ nc The value of φ. As can be seen from the figure, the value of φ predicted by formula (16) is... co and φ nc The results are highly accurate.

[0115] Introducing coefficients and The relationship between the plastic strain increment and stress ratio for coaxial and non-coaxial plastic strains are described separately, with the specific expressions as follows:

[0116]

[0117] in, Quantified The relationship with r Quantified With dr k The relationship between them.

[0118] Figure 4 Demonstrates stress testing under different conditions and The value of . As can be seen from the graph, the coefficient and It remains almost constant at 1 regardless of the direction of the stress increment, indicating a coaxial plastic strain increment. The plastic strain increment is roughly in the same direction as r, but not coaxial. It is roughly in the same direction as dr. Therefore, we can obtain n. co2 and n nc2 The expression is:

[0119]

[0120] Since all stress tests are conducted under triaxial compressive stress, according to equation (8), we have r / ||r||=n1. Furthermore, since the applied stress increment is always tangential to the yield surface, we have dr pr =0 and dr / ||dr||=dr nc / ||dr nc ||=l. Therefore, in order to make the formula in equation (19) applicable to more general loading conditions, r / ||r|| and dr / ||dr|| in equation (19) are replaced with n1 and l, and the expression for the plastic flow direction applicable to neutral loading is obtained as follows:

[0121] n2=φ co n1+φ nc l (20)

[0122] Step 3: Verify the predictive ability of the constitutive model under neutral loading conditions through simulated stress testing and principal stress axis rotation testing. Specifically:

[0123] Model Validation 1: DEM Trial Experiment Validation

[0124] First, stress testing experiments were simulated under different stress ratios. The strain response envelopes of the DEM test results and the model predictions are as follows: Figure 5 As shown in the figure, the prediction results of the constitutive model proposed in this invention under different initial states are in good agreement with the DEM experimental results.

[0125] Model Validation 2: Rotation Test Validation of Principal Stress Axes in DEM

[0126] To further verify that the constitutive model proposed in this invention can accurately predict the full stress-strain response of particulate materials under neutral loading conditions, the model was further used to simulate the rotation test of the DEM drained principal stress axis under different intermediate principal stress coefficients b, stress ratios η and initial porosity ratios e0. Figure 6 This is a comparison chart of experimental results and model predictions. The non-coaxial response is expressed through the angle α between the principal strain increment direction and the principal stress direction. dε -α σ To quantify. By Figure 6It is known that as the void ratio and stress ratio increase, the non-coaxiality of the soil decreases. The constitutive model proposed in this invention can well simulate this trend, which once again verifies the model's ability to simulate the mechanical behavior of granular materials under neutral loading conditions.

[0127] It should be noted that the parts in this embodiment that are the same as or similar to those in Embodiment 1 can be referred to each other, and will not be repeated in this application.

[0128] Example 3:

[0129] Based on Example 2, Example 3 of this application provides a system for establishing an elastoplastic constitutive model of particulate materials under neutral loading, including:

[0130] The analysis module is used to analyze the incremental stress-strain response of particulate materials under neutral loading conditions using discrete element stress probing experiments.

[0131] The derivation module is used to derive the plastic flow direction, plastic modulus, and dilatation coefficient applicable to neutral loading conditions within the framework of critical state theory, based on the strain response envelope under different states, and to construct a constitutive model.

[0132] The verification module is used to verify the predictive ability of the constructed constitutive model under neutral loading conditions through simulated stress probing tests and principal stress axis rotation tests.

[0133] Specifically, the system provided in this embodiment is the same as the system provided in embodiment 2. Therefore, the parts in this embodiment that are the same as or similar to those in embodiment 2 can be referred to each other and will not be described again in this application.

Claims

1. A method for establishing an elastoplastic constitutive model of particulate materials under neutral loading, characterized in that, include: Step 1: Analyze the incremental stress-strain response of granular materials under neutral loading conditions using discrete element stress testing. Step 2: Based on the strain response envelope under different states, within the framework of critical state theory, derive the plastic flow direction, plastic modulus, and dilatation coefficient applicable to neutral loading conditions, and construct a constitutive model. Step 2 includes: Step 2.1: Calculate the plastic strain caused by the normal and tangential yield surface stress increments using both conventional and neutral loading mechanisms; the expression for the total strain increment is: in, It is the elastic strain increment. and These are the plastic strain increments corresponding to conventional loading and neutral loading mechanisms, respectively; Step 2.2: Construct the elastic relationship and conventional loading mechanism of the particulate material; Step 2.3: Construct a neutral loading mechanism; Step 2.3 includes: Step 2.3.1: Derive the plastic modulus applicable to neutral loading. K p2 ; Step 2.3.2: Derive the dilatation coefficient applicable to neutral loading. D 2; Step 2.3.3: Derive the plastic flow direction applicable to neutral loading. ; Step 3: Verify the predictive ability of the constructed constitutive model under neutral loading conditions through simulated stress probing tests and principal stress axis rotation tests.

2. The method for establishing an elastoplastic constitutive model of particulate materials under neutral loading according to claim 1, characterized in that, Step 1 includes: Step 1.1, Sample preparation: Discrete element numerical simulation experiments were conducted to obtain samples with different initial states by changing the porosity, confining pressure, and stress ratio; Step 1.2, Stress test: Apply multiple shear stress increments of the same magnitude but different directions to the specimen.

3. The method for establishing an elastoplastic constitutive model of particulate materials under neutral loading according to claim 2, characterized in that, In step 2.2, the expression for the elastic behavior of the particulate material is: in, K and G These are the bulk modulus and shear modulus, respectively; is a second-order unit tensor. The yield surface of a conventional loading mechanism is represented as: in, R As the stress ratio invariant, H These are hardening parameters. is the interpolation function, representing the shape of the yield surface.

4. The method for establishing an elastoplastic constitutive model of particulate materials under neutral loading according to claim 3, characterized in that, In step 2.3, the stress ratio increment dr is decomposed into two parts relative to the yield surface normal m: in, Proportional to m, i.e., perpendicular to the yield surface; while It contains stress increment components that are not directly proportional to dr and m, and is tangent to the yield surface, therefore its direction is... As the loading direction under neutral loading; The hardening rule of the neutral loading mechanism is expressed as: in, This is the loading factor.

5. A system for establishing an elastoplastic constitutive model of particulate materials under neutral loading, characterized in that, For performing the method according to any one of claims 1 to 4, comprising: The analysis module is used to analyze the incremental stress-strain response of particulate materials under neutral loading conditions using discrete element stress probing experiments. The derivation module is used to derive the plastic flow direction, plastic modulus, and dilatation coefficient applicable to neutral loading conditions within the framework of critical state theory, based on the strain response envelope under different states, and to construct a constitutive model. The verification module is used to verify the predictive ability of the constructed constitutive model under neutral loading conditions through simulated stress probing tests and principal stress axis rotation tests.

6. A computer storage medium, characterized in that, The computer storage medium stores a computer program; when the computer program is run on the computer, it causes the computer to perform the method described in any one of claims 1 to 4.

7. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method as described in any one of claims 1 to 4.

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