Anisotropic sand constitutive model construction method based on stress heuristic test

Abstract

The invention relates to an anisotropic sandy soil constitutive model construction method based on a stress test. The method comprises the steps that stress increments in different directions are applied to a sandy soil sample through the stress test simulated by discrete elements, corresponding strain increments are measured, and a strain response envelope line is formed; the anisotropy of the sandy soil is quantified through the fabric tensor, and a fabric anisotropy variable is introduced; describing an evolution process of the fabric tensor by adopting a fabric evolution rule; deriving an anisotropic sand constitutive model based on the critical stress state; and verifying the effectiveness of the anisotropic sandy soil constitutive model by comparing a test result with a model prediction result. The method has the beneficial effects that the incremental stress-strain relationship of the anisotropic sandy soil can be accurately obtained through a stress test, and reliable test data is provided for constructing a constitutive model.

Description

Technical Field

[0001] The present invention relates to the field of geotechnical engineering technology, and more specifically, to a method for constructing an anisotropic sand constitutive model based on a stress trial test. Background Art

[0002] Natural sand usually has a significant anisotropic structure, which has a significant impact on its mechanical behavior. Traditional constitutive models often ignore structural anisotropy, resulting in a large deviation between the simulation results and the actual situation. Existing anisotropic constitutive models often ignore the evolution of the structure when considering structural anisotropy, resulting in limitations in the model when simulating the behavior of sand under complex loading conditions. Therefore, the present invention proposes an anisotropic sand constitutive model based on stress probe tests, which can accurately simulate the behavior of anisotropic sand under different initial states and loading conditions. Summary of the Invention

[0003] The purpose of the present invention is to address the deficiencies of the existing technology and propose a method for constructing an anisotropic sand constitutive model based on stress trial tests.

[0004] In the first aspect, a method for constructing an anisotropic sand constitutive model based on a stress test is provided, comprising:

[0005] Step 1, stress test: Through the stress test simulated by discrete element method, stress increments in different directions are applied to the sand sample, the corresponding strain increments are measured, and the strain response envelope is formed;

[0006] Step 2: Introduction of fabric anisotropy variable A: The anisotropy of sand is quantified by the fabric tensor, and the fabric anisotropy variable A is introduced to characterize the relative relationship between structure and loading direction;

[0007] Step 3: Fabric evolution rules: Use fabric evolution rules to describe the evolution process of the fabric tensor;

[0008] Step 4: derive the anisotropic sand constitutive model based on the critical stress state;

[0009] Step 5: Model verification: The validity of the anisotropic sand constitutive model is verified by comparing the test results with the model prediction results.

[0010] Preferably, in step 1, samples with different porosity ratios are prepared by adjusting the inter-particle friction coefficient μ, and the samples are consolidated to different stress states.

[0011] Preferably, step 2 comprises:

[0012] Step 2.1: For a three-dimensional representative volume unit, the fabric tensor is calculated as follows:

[0013]

[0014] Where N is the normalization coefficient, usually taken as N c , N c is the total number of contacts within the RVE, is the component of the unit vector in the direction i that specifies the k-th contact direction, is the component of the unit vector in the j direction that specifies the k-th contact direction;

[0015] Step 2.2: Introduce the structural anisotropy variable A, which is specifically expressed as:

[0016]

[0017] in, is the deviatoric stress unit tensor for a specified loading direction, is the unit direction tensor of structural anisotropy, It is a measure of the relative orientation of the structure and the loading direction.

[0018] Preferably, in step 3, the structure evolution rule is expressed as:

[0019]

[0020] Among them, μ is the model parameter that controls the evolution speed, and L is the loading factor.

[0021] Preferably, in step 4, the anisotropic sand constitutive model includes: elastic relationship of anisotropic sand, shear dilation coefficient of anisotropic sand, anisotropic sand flow direction, anisotropic sand flow direction, anisotropic sand hardening law and anisotropic sand plastic modulus.

[0022] Preferably, in step 5, the model verification includes: prediction verification of anisotropic elastic relationship, prediction verification of anisotropic shear dilatancy coefficient, prediction verification of anisotropic plastic flow direction, prediction verification of anisotropic yield surface, prediction verification of anisotropic plastic model, and verification of the influence of structural anisotropy on stiffness, dilatancy and non-coaxial response.

[0023] In a second aspect, a system for constructing an anisotropic sand constitutive model based on a stress trial test is provided, which is used to execute any of the methods described in the first aspect, including:

[0024] The test module is used to apply stress increments in different directions to the sand sample through discrete element simulation stress test, measure the corresponding strain increments, and form the strain response envelope;

[0025] A module is introduced to quantify the anisotropy of sand through the fabric tensor and introduce the fabric anisotropy variable A to characterize the relative relationship between structure and loading direction;

[0026] A description module is used to describe the evolution process of the fabric tensor using fabric evolution rules;

[0027] Derivation module, used to derive the constitutive model of anisotropic sand based on the critical stress state;

[0028] The verification module is used to verify the validity of the anisotropic sand constitutive model by comparing the test results and the model prediction results.

[0029] 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.

[0030] In a fourth aspect, an electronic device is provided, including:

[0031] Memory, used to store computer programs;

[0032] A processor is used to execute the computer program to implement any method as described in the first aspect.

[0033] The beneficial effects of the present invention are:

[0034] 1. The present invention can accurately obtain the incremental stress-strain relationship of anisotropic sand through stress trial test, providing reliable test data for constructing constitutive model.

[0035] 2. The present invention introduces structural anisotropy variables (FAV) and structural evolution rules, which can effectively reflect the structural anisotropy of sand and its evolution process, thereby improving the applicability of the model.

[0036] 3. The constitutive model proposed in this invention can accurately simulate the behavior of anisotropic sand under different initial states and loading conditions, and is suitable for sand mechanics analysis in geotechnical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of the decomposition direction of anisotropic plastic flow provided by the present invention;

[0038] Figure 2 The present invention provides different deposition angles α F Envelope plot of elastic response of anisotropic specimen;

[0039] Figure 3 The anisotropic dilatancy coefficient model prediction diagram provided by the present invention;

[0040] Figure 4 The anisotropic plastic flow direction prediction diagram provided by the present invention;

[0041] Figure 5 The anisotropic yield surface prediction diagram provided by the present invention;

[0042] Figure 6 The anisotropic plastic flow direction prediction diagram provided by the present invention;

[0043] Figure 7 This is a comparison chart of the test results of the undrained triaxial test provided by the present invention when b=0.5 and the model prediction. DETAILED DESCRIPTION

[0044] 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.

[0045] Example 1:

[0046] Example 1 of the present application provides a method for constructing an anisotropic sand constitutive model based on a stress test, which can accurately simulate the behavior of anisotropic sand under different initial states and loading conditions. Specifically, the method includes:

[0047] Step 1: Stress test: Through the stress test simulated by discrete element method (DEM), stress increments in different directions are applied to the sand sample, and the corresponding strain increments are measured to form the strain response envelope.

[0048] In step 1, use PFC 3D Discrete element method simulations were performed, and specimens with different porosity ratios were prepared by adjusting the inter-particle friction coefficient μ. The specimens were then consolidated to different stress states, including different confining pressures p, stress ratios η = q / p, and intermediate principal stress coefficients b = (σ2-σ3) / (σ1-σ3) (p and q represent the mean stress and shear stress, respectively; σ1, σ2, and σ3 represent the major principal stress, intermediate principal stress, and minor principal stress, respectively). Specimens with different stress states and structural anisotropy were obtained through the above method.

[0049] Step 2: Introduction of fabric anisotropy variable (FAV) A: The anisotropy of sand is quantified by the fabric tensor, and the fabric anisotropy variable A is introduced to characterize the relative relationship between structure and loading direction.

[0050] Step 2 includes:

[0051] Step 2.1: For a three-dimensional representative volume element (RVE), the fabric tensor is calculated using the following formula:

[0052]

[0053] Where N is the normalization coefficient, usually taken as N c , N c is the total number of contacts within the RVE, is the component of the unit vector in the direction i that specifies the k-th contact direction, is the component of the unit vector in the j direction that specifies the k-th contact direction.

[0054] The deviatoric stress tensor is derived from Equation (1):

[0055]

[0056] Among them, F and Represents F ij The norm and unit direction of F' c (θ σ ) represents F before normalization ij The critical norm ensures that no matter the stress Lode angle θ σ How to change the critical value of F to always be 1, δ ij is the Kronecker delta symbol, when i=j, δ ij =1, when i≠j ij =0.

[0057] For a transversely isotropic soil F with the deposition direction being x1 axis, ij It can be expressed as:

[0058]

[0059] Among them, F0 represents the initial structural norm.

[0060] Step 2.2: In order to quantify the relative relationship between the structural direction and the loading direction, the structural anisotropy variable A is introduced, which is specifically expressed as:

[0061]

[0062] in, is the deviatoric stress unit tensor for a specified loading direction, is the unit direction tensor of structural anisotropy, It is a measure of the relative orientation of the structure and the loading direction.

[0063] Step 3: Fabric evolution rules: Use fabric evolution rules to describe the evolution process of the fabric tensor.

[0064] In step 3, the structure evolution rule is expressed as:

[0065]

[0066] Among them, μ is the model parameter that controls the evolution speed, and L is the loading factor.

[0067] Step 4: Derive the anisotropic sand constitutive model based on the critical stress state.

[0068] Step 5: Model verification: The validity of the anisotropic sand constitutive model is verified by comparing the test results with the model prediction results.

[0069] Example 2:

[0070] Based on Example 1, Example 2 of the present application provides a more specific method for constructing an anisotropic sand constitutive model based on a stress test, including:

[0071] Step 1: Stress test: Through the stress test simulated by discrete element method, stress increments in different directions are applied to the sand sample, and the corresponding strain increments are measured to form the strain response envelope.

[0072] Step 2: Introduction of fabric anisotropy variable A: The anisotropy of sand is quantified by the fabric tensor, and the fabric anisotropy variable A is introduced to characterize the relative relationship between structure and loading direction.

[0073] Step 3: Fabric evolution rules: Use fabric evolution rules to describe the evolution process of the fabric tensor.

[0074] Step 4: Derive the anisotropic sand constitutive model based on the critical stress state.

[0075] In step 4, the anisotropic sand constitutive model includes: anisotropic sand elastic relationship, anisotropic sand shear coefficient, anisotropic sand flow direction, anisotropic sand flow direction, anisotropic sand hardening law and anisotropic sand plastic modulus.

[0076] Specifically, step 4 includes:

[0077] (1) The elastic relationship of anisotropic sand is:

[0078]

[0079]

[0080] in, is the deviatoric strain increment, δ ij is the Kronecker delta sign, which is 1 when i=j and 0 otherwise.

[0081] is the volumetric elastic strain increment, ds ij is the deviatoric stress increment, dp is the mean stress increment (hydrostatic pressure increment), G is the shear modulus, G0 is the reference shear modulus, e is the void ratio, P is the mean effective stress, P0 is the atmospheric pressure, K is the bulk modulus, and ν is the Poisson's ratio.

[0082] (2) The shear dilatancy coefficient of anisotropic sand is expressed as:

[0083] The fabric anisotropy variable (FAV) A is introduced to reflect the effect of anisotropy on the dilatancy behavior of sand, and the dilatancy coefficient expression is obtained as follows:

[0084]

[0085] Where ξ is the dilatancy state parameter, e A , d0 and m are model parameters, R is the stress ratio, M c is the critical stress ratio, ψ is the state parameter, and ξ is a function of the porosity e, confining pressure p, and fabric anisotropy A, reflecting the density state of the sand under the combined influence of the porosity, confining pressure, and fabric anisotropy.

[0086] M in formula (7) = M c g(θ) represents the critical stress ratio, which depends on the Lode angle θ σ Interpolation function:

[0087]

[0088] Where c = M e / M c is the model parameter, M e and M c are the critical stress ratios under triaxial tension and compression, θ σ It is Lode corner.

[0089] (3) The flow direction of anisotropic sand is derived as follows:

[0090] Fabric tensor F ij and plastic flow direction n ij is decomposed into The proportional and non-proportional parts are shown in formula (8):

[0091]

[0092] Among them, F ij is the configuration tensor, n ij is the direction of plastic flow, is the isotropic reference direction, and F ijThe proportional and non-proportional parts, and They are n ij The proportional part and non-proportional part; the proportional part (superscript pr): Proportional components are obtained by dot product projection (such as ), non-proportional part (superscript np): the remaining part, that is, the original tensor minus the proportional part (such as ).

[0093] Figure 1 is a schematic diagram of the decomposition. Figure 1 In the equation, φ represents and The angle between the directions is defined as the first joint invariant:

[0094]

[0095] in, is the dot product of the two non-proportional parts, It is the product of the modulus lengths of two vectors, used for normalization, and k1 is the proportional coefficient.

[0096] The plastic flow direction of structural anisotropy is derived from equations (8a) and (9b) as follows:

[0097]

[0098] Will Substituting into formula (10) we get:

[0099]

[0100] Because n ij is a unit norm tensor, we have Substituting into formula (11) we get:

[0101]

[0102] Where, in formulas (9) to (12), k1 to k4 are stress state variables (such as σ ij 、F ij , A, etc.).

[0103] k4=k np (1-A) / R (13)

[0104] Among them, k np is a positive model parameter, A is the degree of anisotropy, and R is the stress state parameter. Formula (13) shows that as A and R increase, the k4 value decreases.

[0105] (4) The yield surface expression of anisotropic sand is:

[0106] f=RH (14)

[0107] Where R is the stress-related quantity and H is the hardening parameter.

[0108] (5) The expression of anisotropic sand hardening law is:

[0109] Hardening Law:

[0110] pm ij dr ij -K p L=0 (15)

[0112] Among them, m ij is the partial unit tensor, indicating that the yield surface is at r ij The normal direction at dr ij is the stress increment tensor, P is the proportionality coefficient, K p is the plastic modulus, and L is the cumulative plastic deformation parameter.

[0113] (6) The expression of the anisotropic plastic modulus of sand is:

[0114]

[0115] Among them, h1, h2, h3, α, θ, β, ξ and n are model parameters, A is the anisotropy, e is the porosity ratio, R is the stress ratio, P is the mean effective stress, P0 is the atmospheric pressure, M c is the critical state stress ratio, and g(θ) is the Lode angle function.

[0116] Step 5: Model verification: The validity of the anisotropic sand constitutive model is verified by comparing the test results with the model prediction results.

[0117] In step 5, the model verification includes: prediction and verification of anisotropic elastic relationship, prediction and verification of anisotropic shear dilatancy coefficient, prediction and verification of anisotropic plastic flow direction, prediction and verification of anisotropic yield surface, prediction and verification of anisotropic plastic model, and verification of the influence of structural anisotropy on stiffness, dilatancy and non-coaxial response.

[0118] Specifically, step 5 includes:

[0119] (1) Prediction and verification of anisotropic elastic relationships

[0120] like Figure 2 The left figure shows the different deposition angles of α F The elastic response envelope of anisotropic specimens is Figure 2 As can be seen from the left figure in , anisotropy has almost no effect on the elastic response of the soil. Figure 2The right figure in is the elastic envelope predicted by formula (6), Figure 2 The model predictions in the right figure agree well with the DEM results, indicating that the elastic relations in Eqs. (6a) and (6b) are sufficient to describe the elastic behavior of anisotropic sand.

[0121] (2) Prediction and verification of anisotropic shear dilation coefficient

[0122] Figure 3 The values ​​of the dilatancy coefficient predicted by Equation (7) are presented. When the loading direction coincides with the sedimentation direction of the soil structure, A increases, causing D calculated by Equation (7) to decrease, which agrees well with the experimental trend. It can be seen that Equation (7) effectively captures the dilatancy behavior of anisotropic sand under different test conditions, verifying the validity of Equation (7).

[0123] (3) Prediction and verification of anisotropic plastic flow direction

[0124] Figure 4 The plastic flow direction predicted by equation (13) is shown. Figure 4 It can be seen that anisotropic soil obeys the associated flow law on the deviatoric plane, and anisotropy will significantly affect the flow direction of the soil on the deviatoric plane, verifying the validity of formula (13).

[0125] (4) Anisotropic yield surface prediction verification

[0126] Figure 5 The relationship between the size of the plastic strain increment and the direction of the stress increment is obtained by performing symmetrical stress test on samples with different deposition angles. Figure 5 It can be seen from the equation (14) that plastic strain will only occur in the specimen when the stress ratio changes, and this characteristic is independent of the specimen deposition angle. Therefore, the yield surface in equation (14) is still valid for anisotropic sand.

[0127] (5) Anisotropic plasticity model prediction and verification

[0128] Figure 6 It shows that under the same conditions, the plasticity model K predicted by formula (16) p The model predictions are in good agreement with the test results, indicating that Equation (16) can reasonably reflect the effect of structural anisotropy on the plastic hardening of sand.

[0129] (6) Effects of structural anisotropy on stiffness, dilatancy, and non-coaxial response

[0130] Figure 7 The comparison between the experimental results of the undrained triaxial test at b = 0.5 and the model prediction is shown. Different principal stress directions α are considered during the test. σThe initial void ratio of the soil samples was e0 = 0.821-0.828. The model accurately predicted the effects of structural anisotropy on stiffness, dilatancy, and non-coaxial response.

[0131] 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.

[0132] Example 3:

[0133] Based on Example 2, Example 3 of the present application provides a system for constructing an anisotropic sand constitutive model based on a stress trial test, comprising:

[0134] The test module is used to apply stress increments in different directions to the sand sample through discrete element simulation stress test, measure the corresponding strain increments, and form the strain response envelope;

[0135] A module is introduced to quantify the anisotropy of sand through the fabric tensor and introduce the fabric anisotropy variable A to characterize the relative relationship between structure and loading direction;

[0136] A description module is used to describe the evolution process of the fabric tensor using fabric evolution rules;

[0137] Derivation module, used to derive the constitutive model of anisotropic sand based on the critical stress state;

[0138] The verification module is used to verify the validity of the anisotropic sand constitutive model by comparing the test results and the model prediction results.

[0139] 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 constructing an anisotropic sand constitutive model based on stress test, characterized in that: include: Step 1, stress test: Through the stress test simulated by discrete element method, stress increments in different directions are applied to the sand sample, the corresponding strain increments are measured, and the strain response envelope is formed; Step 2: Introduction of fabric anisotropy variable A: The anisotropy of sand is quantified by the fabric tensor, and the fabric anisotropy variable A is introduced to characterize the relative relationship between structure and loading direction; Step 3: Fabric evolution rules: Use fabric evolution rules to describe the evolution process of the fabric tensor; Step 4: derive the anisotropic sand constitutive model based on the critical stress state; Step 5: Model verification: The validity of the anisotropic sand constitutive model is verified by comparing the test results with the model prediction results.

2. The method for constructing an anisotropic sand constitutive model based on stress trial test according to claim 1, characterized in that: In step 1, samples with different porosity ratios are prepared by adjusting the inter-particle friction coefficient μ, and the samples are consolidated to different stress states.

3. The method for constructing an anisotropic sand constitutive model based on stress trial test according to claim 2, characterized in that: Step 2 includes: Step 2.1: For a three-dimensional representative volume unit, the fabric tensor is calculated as follows: Where N is the normalization coefficient, usually taken as N c , N c is the total number of contacts within the RVE, is the component of the unit vector in the direction i that specifies the k-th contact direction, is the component of the unit vector in the j direction that specifies the k-th contact direction; Step 2.2: Introduce the structural anisotropy variable A, which is specifically expressed as: in, is the deviatoric stress unit tensor for a specified loading direction, is the unit direction tensor of structural anisotropy, It is a measure of the relative orientation of the structure and the loading direction.

4. The method for constructing an anisotropic sand constitutive model based on stress trial test according to claim 3, characterized in that: In step 3, the structure evolution rule is expressed as: Among them, μ is the model parameter that controls the evolution speed, and L is the loading factor.

5. The method for constructing an anisotropic sand constitutive model based on stress trial test according to claim 4, characterized in that: In step 4, the anisotropic sand constitutive model includes: anisotropic sand elastic relationship, anisotropic sand shear coefficient, anisotropic sand flow direction, anisotropic sand flow direction, anisotropic sand hardening law and anisotropic sand plastic modulus.

6. The method for constructing an anisotropic sand constitutive model based on stress trial test according to claim 5, characterized in that: In step 5, the model verification includes: prediction and verification of anisotropic elastic relationship, prediction and verification of anisotropic shear dilatancy coefficient, prediction and verification of anisotropic plastic flow direction, prediction and verification of anisotropic yield surface, prediction and verification of anisotropic plastic model, and verification of the influence of structural anisotropy on stiffness, dilatancy and non-coaxial response.

7. A system for constructing anisotropic sand constitutive model based on stress trial test, characterized in that: Used to perform the method according to any one of claims 1 to 6, comprising: The test module is used to apply stress increments in different directions to the sand sample through discrete element simulation stress test, measure the corresponding strain increments, and form the strain response envelope; A module is introduced to quantify the anisotropy of sand through the fabric tensor and introduce the fabric anisotropy variable A to characterize the relative relationship between structure and loading direction; A description module is used to describe the evolution process of the fabric tensor using fabric evolution rules; Derivation module, used to derive the constitutive model of anisotropic sand based on the critical stress state; The verification module is used to verify the validity of the anisotropic sand constitutive model by comparing the test results and the model prediction results.

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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