Method for establishing elastic-plastic constitutive model of granular material based on neutral loading

Abstract

The invention relates to a method for establishing an elastic-plastic constitutive model of a granular material based on neutral loading. The method comprises the following steps: analyzing an incremental stress-strain response of the granular material under a neutral loading condition by adopting a discrete element stress test; deducing a plastic flow direction, a plastic modulus and a shear expansion coefficient suitable for a neutral loading condition under a framework of a critical state theory according to strain response envelopes in different states, and constructing a constitutive model; the prediction capability of the constructed constitutive model under a neutral loading condition is verified by simulating a stress tentative test and a principal stress axis rotation test. The method has the beneficial effects that the plastic strain, the shear expansion coefficient and the plastic flow direction of the granular material under the neutral loading condition can be accurately predicted, and the problem that a traditional model is inaccurate in prediction under the neutral loading condition is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical engineering, and more specifically, to a method for establishing an elastic-plastic constitutive model of granular materials under neutral loading. Background Art

[0002] Granular materials (such as sand, gravel, etc.) are widely used in geotechnical engineering, and a correct understanding of their mechanical properties is crucial to the design and construction of projects. Neutral loading refers to a special stress path in which the stress increment is perpendicular to the normal direction of the yield surface. Neutral loading is widely present in actual engineering. For example, in earthquake loads, traffic loads, and wave loads, the stress increment borne by the soil has a considerable component in the neutral loading direction. However, since neutral loading cannot cause the evolution of the yield surface, existing constitutive models often cannot predict plastic strain under this stress path. In addition, due to the use of the coaxial assumption, the model cannot simulate the significant non-coaxial response caused by neutral loading. The above defects lead to large deviations between the model's prediction results and the experimental data.

[0003] The discrete element method (DEM), as a numerical simulation tool, can effectively simulate the macroscopic and microscopic mechanical behaviors of granular materials. However, the application of DEM technology in constitutive model construction, especially in the study of the mechanical properties of granular materials under neutral loading conditions and related constitutive simulations, is still insufficient. Summary of the Invention

[0004] The purpose of the present invention is to address the deficiencies of the prior art and to propose a method for establishing an elastic-plastic constitutive model of granular materials under neutral loading.

[0005] In a first aspect, a method for establishing an elastic-plastic constitutive model of granular materials under neutral loading is provided, comprising:

[0006] Step 1: Using discrete element stress test to analyze the incremental stress-strain response of granular materials under neutral loading conditions;

[0007] Step 2: Based on the strain response envelopes of different states, the plastic flow direction, plastic modulus, and dilatancy coefficient applicable to neutral loading conditions are derived within the framework of critical state theory, and a constitutive model is constructed.

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

[0009] Preferably, step 1 comprises:

[0010] Step 1.1, sample preparation: discrete element numerical simulation test is carried out to obtain samples with different initial states by changing the porosity ratio, 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 comprises:

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

[0014] dε=dε e +dε p1 +dε p2

[0015] Among them, dε e is the elastic strain increment, dε p1 and dε p2 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 granular material;

[0017] Step 2.3: Construct a neutral loading mechanism. Preferably, in step 2.2, the elastic behavior expression of the granular 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 for the conventional loading mechanism is expressed 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 that characterizes the shape of the yield surface.

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

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

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

[0026] Among them, dr pr is proportional to m, i.e. perpendicular to the yield surface; and dr np Contains the stress increment component that is not proportional to dr and m, and is tangent to the yield surface, so its direction l = dr np / ||drnp || is used as the loading direction under neutral loading; therefore, the hardening law for 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 for neutral loading p2 ;

[0030] 2.3.2. Derive the dilatancy coefficient D2 for neutral loading;

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

[0032] In a second aspect, a system for establishing an elastic-plastic constitutive model of granular materials under neutral loading is provided, which is used to execute any of the methods described in the first aspect, including:

[0033] An analysis module for analyzing the incremental stress-strain response of granular materials under neutral loading conditions using discrete element stress exploratory tests;

[0034] A derivation module is used to derive the plastic flow direction, plastic modulus, and dilatancy coefficient applicable to neutral loading conditions based on the strain response envelopes of different states within the framework of critical state theory, 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 trial tests and principal stress axis rotation tests.

[0036] According to a third aspect, a computer storage medium is provided, wherein a computer program is stored in the computer storage medium; when the computer program is executed on a computer, the computer executes any one of the methods described in the first aspect.

[0037] In a fourth aspect, an electronic device is provided, including:

[0038] Memory, used to store computer programs;

[0039] A processor is used to execute the computer program to implement any method as described in the first aspect.

[0040] The present invention accurately predicts the plastic strain, dilatancy coefficient, and plastic flow direction of granular materials under neutral loading conditions, resolving the inaccurate predictions of conventional models under neutral loading conditions. This model is suitable for soil mechanics analysis under complex stress paths, such as earthquake loads, traffic loads, and wave loads, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

[0044] Figure 4 Under the neutral loading provided by the present invention and The value of

[0045] Figure 5 The strain response envelope of the DEM test results and model prediction provided by the present invention;

[0046] Figure 6 A comparison chart of the DEM drainage principal stress axis rotation test results and model predictions provided by the present invention. DETAILED DESCRIPTION

[0047] The present invention will be further described below with reference to the following examples. The following examples are provided only to facilitate understanding of the present invention. It should be noted that, without departing from the principles of the present invention, it is possible for a person skilled in the art to make various modifications to the present invention, and such improvements and modifications fall within the scope of the claims of the present invention.

[0048] Example 1:

[0049] Example 1 of the present application provides a method for constructing an elastic-plastic constitutive model of granular materials suitable for neutral loading based on a stress trial test, which can accurately predict the plastic strain, shear dilatancy coefficient, and plastic flow direction of the granular materials under neutral loading, thereby solving the problem of inaccurate predictions of traditional models under neutral loading conditions. Specifically, the method includes:

[0050] Step 1: Use discrete element stress exploration test 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 carried out to obtain samples with different initial states by controlling the porosity ratio, confining pressure and stress ratio.

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

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

[0055] use Figure 2 The stress trial scheme shown in (a) is as follows. Starting from the same initial state, multiple shear stress increments with different directions but the same magnitude 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] Where dσ r and α dσ represent the magnitude and direction of the stress increment respectively.

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

[0062] Step 2 includes:

[0063] Step 2.1, model framework: Use conventional loading mechanism and neutral loading mechanism to calculate the plastic strain caused by the stress increment in the normal and tangential directions of the yield surface respectively; the total strain increment expression is:

[0064] dε=dε e +dε p1 +dε p2 (2)

[0065] Among them, dε e is the elastic strain increment, dε p1 and dε p2are the plastic strain increments corresponding to conventional loading and neutral loading mechanisms, respectively, and are expressed as:

[0066]

[0067] Where, dL1=||de p1 ||,dL2=||de p2 || is the loading factor, and represents the plastic deviatoric strain increment de p1 and de p2 The size of n1 = de p1 / ||de p1 ||; n2 = de p2 / ||de p2 || is the unit deviatoric strain tensor indicating its direction; the dilatancy coefficient and The dilatancy relationship is quantified; χ1 and χ2 represent dε p1 and dε p2 direction.

[0068] Step 2.2: Construct the elastic relationship and general loading mechanism of the model.

[0069] The elastic stress-strain relationship of granular materials is expressed as:

[0070]

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

[0072] The plastic deformation of sand under proportional loading conditions is mainly caused by the change of stress ratio. Therefore, the yield surface of the 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 that characterizes the shape of the yield surface. Its expression is:

[0075]

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

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

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

[0079] Where m is the unit deviatoric stress tensor representing the normal direction of the yield surface.

[0080] By applying the associated flow law on the deviatoric 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 the neutral loading path, dr⊥m, so m:dr=0, dL1=0. It can be seen from this that the conventional loading mechanism in Equation (7) cannot simulate plastic strain under neutral loading conditions. Therefore, the present 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 with respect to 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, the first part dr in formula (9) pr is proportional to m and perpendicular to the yield surface, while the second part dr np Contains the non-proportional part of dr and m and is tangent to the yield surface. Vector l = dr np / ||dr np ||, means dr np In the neutral loading path, since m:dr=0, dr pr =0 and dr np =dr. Plastic strain is completely determined by dr np induced, that is, the component of the stress increment in the l direction. Therefore, l can be used as the loading direction under the neutral loading path, and the hardening law of the neutral loading mechanism can be expressed as:

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

[0089] Among them, K p2 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 test and principal stress axis rotation test.

[0091] Example 2:

[0092] Based on Example 1, Example 2 of the present application provides a more specific method for constructing an elastic-plastic constitutive model of granular materials suitable for neutral loading based on a stress trial test, including:

[0093] Step 1: Use discrete element stress exploration test to analyze the incremental stress-strain response of granular materials under neutral loading conditions.

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

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

[0096] (1) Derivation of 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 dilatancy 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 strains, Decomposed into coaxial and non-coaxial parts:

[0108]

[0109] in, and denote the coaxial and non-coaxial plastic strain increments respectively and direction; and They represent the proportion of the coaxial and non-coaxial plastic strain increments in the entire plastic strain increment. According to the above definitions of constitutive elements, their values ​​can be directly determined in stress test:

[0110]

[0111] In addition, due to is the unit partial tensor, so By fitting Figure 3 The experimental data in φ can be obtained co and φ nc The expression is:

[0112]

[0113] λ=λ1exp(λ2ψ) (17)

[0114] Where λ1 and λ2 are model parameters. When the critical state is reached, R=M c g(θ), so φ co =1 and φ nc =0, indicating that the non-coaxial response disappears. Figure 3 Show the φ predicted by formula (16) co and φ nc As can be seen from the figure, the φ predicted by formula (16) co and φ nc The results are highly accurate.

[0115] Introduction coefficient and The relationship between the coaxial and non-coaxial plastic strain increments and stress ratios is described respectively. The specific expressions are as follows:

[0116]

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

[0118] Figure 4 Shows the stress test under different conditions and The value of . As can be seen from the figure, the coefficient and It hardly changes with the direction of stress increment and always remains at 1, indicating that the coaxial plastic strain increment Roughly consistent with the r direction, rather than the coaxial plastic strain increment The direction is roughly consistent with dr. Therefore, we can get n co2 and n nc2 The expression is:

[0119]

[0120] Since all stress probe tests are carried out under triaxial compressive stress state, according to formula (8), r / ||r||=n1. In addition, since the applied stress increment is always tangential to the yield surface, 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 by n1 and l, and the expression of 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 capability of the constitutive model under neutral loading conditions through simulated stress test and principal stress axis rotation test.

[0123] Model Validation 1: DEM Trial Test Validation

[0124] First, stress test under different stress ratios was simulated. The DEM test results and the strain response envelope predicted by the model are shown in Figure 2. Figure 5 As shown in the figure, the prediction results of the constitutive model proposed in the present invention are in good agreement with the DEM test results under different initial conditions.

[0125] Model Verification 2: DEM principal stress axis rotation test verification

[0126] In order to further verify that the constitutive model proposed in this invention can accurately predict the full stress-strain response of granular materials under neutral loading conditions, the model was further used to simulate the DEM drainage principal stress axis rotation test under different intermediate principal stress coefficients b, stress ratios η and initial porosity ratios e0. Figure 6 The non-coaxial response is expressed by the angle α between the principal strain increment direction and the principal stress direction. dε -α σ To quantify. Figure 6It can be seen that with the increase of porosity ratio and stress ratio, the non-coaxiality of the soil decreases, and the constitutive model proposed in this invention can simulate this trend well, which once again verifies the ability of this model 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 or similar to those in Example 1 can be referenced to each other and will not be described in detail in this application.

[0128] Example 3:

[0129] Based on Example 2, Example 3 of the present application provides a system for establishing an elastic-plastic constitutive model of granular materials under neutral loading, including:

[0130] An analysis module for analyzing the incremental stress-strain response of granular materials under neutral loading conditions using discrete element stress exploratory tests;

[0131] A derivation module is used to derive the plastic flow direction, plastic modulus, and dilatancy coefficient applicable to neutral loading conditions based on the strain response envelopes of different states within the framework of critical state theory, 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 trial tests and principal stress axis rotation tests.

[0133] Specifically, the system provided in this embodiment is a system corresponding to the method provided in Example 2. Therefore, the parts in this embodiment that are the same or similar to those in Example 2 can be referenced to each other and will not be repeated in this application.

Claims

1. A method for establishing an elastic-plastic constitutive model of granular materials under neutral loading, characterized in that: include: Step 1: Using discrete element stress test to analyze the incremental stress-strain response of granular materials under neutral loading conditions; Step 2: Based on the strain response envelopes of different states, the plastic flow direction, plastic modulus, and dilatancy coefficient applicable to neutral loading conditions are derived within the framework of critical state theory, and a constitutive model is constructed. Step 3: Verify the predictive ability of the constructed constitutive model under neutral loading conditions through simulated stress test and principal stress axis rotation test.

2. The method for establishing an elastic-plastic constitutive model of granular materials under neutral loading according to claim 1, characterized in that: Step 1 includes: Step 1.1, sample preparation: discrete element numerical simulation test is carried out to obtain samples with different initial states by changing the porosity ratio, 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 elastic-plastic constitutive model of granular materials under neutral loading according to claim 2, characterized in that: Step 2 includes: Step 2.1: Calculate the plastic strain caused by the normal and tangential yield surface stress increments using the conventional loading mechanism and the neutral loading mechanism respectively; the total strain increment expression is: dε=dε e +dε p1 +dε p2 Among them, dε e is the elastic strain increment, dε p1 and dε p2 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 granular material. Step 2.3: Construct the neutral loading mechanism.

4. The method for establishing an elastic-plastic constitutive model of granular materials under neutral loading according to claim 3, characterized in that: In step 2.2, the elastic behavior expression of the granular material is: Where K and G are the elastic bulk modulus and shear modulus respectively; I is the second-order unit tensor; The yield surface for the conventional loading mechanism is expressed as: f=R / g(θ)-H=0 Where R is the stress ratio invariant, H is the hardening parameter, and g(θ) is the interpolation function that characterizes the shape of the yield surface.

5. The method for establishing an elastic-plastic constitutive model of granular materials under neutral loading according to claim 4, characterized in that: In step 2.3, the stress ratio increment dr relative to the yield surface normal m is decomposed into two parts: dr pr =m(dr:m) dr np =dr-m(dr:m) Among them, dr pr is proportional to m, i.e. perpendicular to the yield surface; and dr np Contains the stress increment component that is not proportional to dr and m, and is tangent to the yield surface, so its direction l = dr np / ||dr np || is the loading direction under neutral loading; The hardening law for the neutral loading mechanism is expressed as: l:dr-K p2 dL2=0。 6. The method for establishing an elastic-plastic constitutive model of granular materials under neutral loading according to claim 5, characterized in that: Step 2.3 includes: Step 2.3.

1. Derive the plastic modulus K for neutral loading p2 ; Step 2.3.2: Derive the dilatancy coefficient D2 for neutral loading. Step 2.3.

3. Derive the plastic flow direction n2 for neutral loading.

7. A system for establishing an elastic-plastic constitutive model of granular materials under neutral loading, characterized in that: Used to perform the method according to any one of claims 1 to 6, comprising: An analysis module for analyzing the incremental stress-strain response of granular materials under neutral loading conditions using discrete element stress exploratory tests; A derivation module is used to derive the plastic flow direction, plastic modulus, and dilatancy coefficient applicable to neutral loading conditions based on the strain response envelopes of different states within the framework of critical state theory, 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 trial tests and principal stress axis rotation tests.

8. A computer storage medium, characterized in that The computer storage medium stores a computer program; when the computer program is run on a computer, the computer executes the method according to any one of claims 1 to 6.

9. An electronic device, characterized in that: include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the method according to any one of claims 1 to 6.

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