Clay small strain elastic model establishing method considering inherent anisotropy and stress history

Abstract

The invention relates to a method for establishing a clay small strain elastic model by considering inherent anisotropy and stress history, which comprises the following steps of: establishing a mathematical model for describing the degradation of clay rigidity along with strain on the basis of a modified Hardin-Drnevich curve; introducing a stress path rotation angle, and constructing an interpolation function to quantify the influence of the recent stress history on the small strain stiffness of the clay; introducing a fabric tensor to describe the inherent anisotropy of the clay, and establishing an elastic modulus expression to reflect the anisotropy of the clay in an initial state; the effectiveness of the model is verified by comparing various natural clay test data. The method has the beneficial effects that the model provided by the invention can more accurately describe the anisotropic rigidity response of the soil in a small strain range, and particularly, the prediction precision of the model is greatly improved after the influence of the rotation angle of the stress path and the orientation of the laying surface is considered.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical engineering, and more precisely, it relates to a method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history. Background Art

[0002] In geotechnical engineering, the analysis of key issues such as deep foundation pit excavation, filling, and tunnel construction highly depends on the accurate grasp of the small-strain stiffness characteristics of clay. However, existing models are insufficient in capturing the nonlinear small-strain stiffness changes of anisotropic clay, especially when facing clay with different loading histories, it is difficult to accurately reproduce its mechanical behavior. Specifically, traditional models have various deficiencies. For example, they assume that the stiffness is uniformly distributed in space, ignoring the significant directional anisotropy of natural clay due to the deposition process; when modeling, they do not introduce a second-order fabric tensor to quantify the contribution of the microstructure to the macroscopic stiffness, resulting in the inability to accurately describe the structural anisotropy of clay. In addition, traditional models ignore the shear-volume coupling effect, assuming that the shear modulus and bulk modulus are independent, while in fact, there is a significant cross-coupling in anisotropic clay, and the coupling term is not explicitly expressed in the stiffness matrix, leading to errors in predicting the evolution of excess pore pressure or the response of bedding planes. These defects severely restrict the accurate prediction of the mechanical behavior of clay in geotechnical engineering. Therefore, in view of the above problems, a method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history is proposed. Summary of the Invention

[0003] The purpose of the present invention is to address the deficiencies of the prior art and propose a method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history.

[0004] In the first aspect, a method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history is provided, including:

[0005] S1. Based on the modified Hardin-Drnevich curve, establish a mathematical model describing the degradation of clay stiffness with strain;

[0006] S2. Introduce the stress path rotation angle and construct an interpolation function to quantify the influence of the recent stress history on the small-strain stiffness of clay;

[0007] S3. Introduce a fabric tensor to describe the inherent anisotropy of clay and establish an elastic modulus expression to reflect the degree of anisotropy of clay in the initial state;

[0008] S4. Verify the effectiveness of the model by comparing the test data of various natural clays.

[0009] Preferably, in S1, the expression of the mathematical model is:

[0010]

[0011] Among them, G is the current shear modulus, representing the stiffness of the material at a certain strain; G0 is the initial shear modulus, γ is the actual shear strain; γ 0.7 is the reference shear strain;; m is a model parameter used to adjust the rate of degradation of the shear modulus with strain;

[0012] Relate G0 and the confining pressure P using a power function as:

[0013]

[0014] Among them, is the shear modulus specified under the reference mean confining pressure p ref , and m is a model parameter used to reflect the influence of the consolidation confining pressure on the modulus.

[0015] Preferably, in S2, the expression of the interpolation function is:

[0016]

[0017] Among them, m is a dynamically adjusted model parameter used to reflect the influence of different loading paths on the shear modulus; l is a trigonometric function between the change angles of the front and back stress paths, used to quantify the change in the loading direction; m T and m R are the stiffness ratios during vertical loading and reverse loading, respectively.

[0018] Preferably, in S3, the expression of the elastic modulus is:

[0019]

[0020] Among them, E ijkl is the fourth-order elastic modulus, describing the stress-strain relationship of the material in the small strain range, representing the stiffness response between the stress components in the directions i, j and the strain components in the directions k, l, K is the bulk modulus, G is the shear modulus, F ij , F kl , F ki , F li , F lj , F kj respectively represent different components of the fabric tensor; δ ij , δ kl , δ li , δ kj , δ li , δ ki are all Kronecker delta symbols used to simplify the stiffness tensor expression of isotropic materials. For example, δ ij δ kl represents the isotropic volume deformation term.

[0021] Preferably, in S3, the bulk modulus K is calculated by assuming a constant Poisson's ratio, and its expression is:

[0022]

[0023] where ν is Poisson's ratio;

[0024] F ij represents the initial second-order fabric tensor. When the principal direction is the vertical direction, its expression is:

[0025]

[0026] where F ij is the initial second-order fabric tensor, is the fabric strength in the vertical direction (principal direction), is the fabric strength in the horizontal direction. The negative sign indicates the mechanical response opposite to the principal direction, and F0 represents the initial anisotropy degree, which is calculated through the anisotropic stiffness ratio G hh / G hv measured in the bending element or resonant column test. Its formula is as follows:

[0027]

[0028] where G hh is the horizontal-horizontal shear modulus, representing the stiffness of the material when shearing in the horizontal plane, and G hv is the horizontal-vertical shear modulus, representing the stiffness of the material when shearing between the horizontal plane and the vertical direction.

[0029] Preferably, in S3, when F0 = 0, it represents isotropy. Due to the elastic effect, F ij remains unchanged, and the incremental relationship between stress and strain is expressed in the triaxial space as:

[0030]

[0031] where dp is the mean stress increment, dq is the deviator stress increment, is the elastic volumetric strain increment, is the elastic deviator strain increment, and J is the coupling term, which describes the coupling between the volumetric response and the shear response caused by the structural anisotropy.

[0032] Preferably, in S3, for isotropic materials, there is no coupling term J, and the corresponding compliance matrix is expressed as:

[0033]

[0034] where J' pqis the coupling modulus between the mean normal stress and the deviatoric strain, J' qp is the coupling modulus between the deviator stress and the volumetric strain.

[0035] In a second aspect, a system for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history is provided for performing any of the methods described in the first aspect, including:

[0036] An establishment module for establishing a mathematical model describing the degradation of clay stiffness with strain based on a modified Hardin-Drnevich curve;

[0037] A first introduction module for introducing the stress path rotation angle and constructing an interpolation function to quantify the influence of recent stress history on the small-strain stiffness of clay;

[0038] A second introduction module for introducing the fabric tensor to describe the inherent anisotropy of clay and establishing an elastic modulus expression to reflect the anisotropy degree of clay in the initial state;

[0039] A verification module for verifying the effectiveness of the model by comparing a variety of natural clay test data.

[0040] In a third aspect, a computer storage medium is provided, and a computer program is stored in the computer storage medium; when the computer program runs on a computer, the computer is enabled to execute any of the methods described in the first aspect.

[0041] In a fourth aspect, an electronic device is provided, including:

[0042] A memory for storing the computer program;

[0043] A processor for executing the computer program to implement any of the methods described in the first aspect.

[0044] The beneficial effects of the present invention are:

[0045] 1. The present invention has high accuracy: The model proposed by the present invention can more accurately describe the anisotropic stiffness response of soil in the small-strain range. Especially after considering the influence of the stress path rotation angle and the bedding plane orientation, the prediction accuracy of the model is greatly improved.

[0046] 2. The present invention is simple and easy to use: This model only requires four new parameters, which can be directly obtained through experiments and have clear physical meanings.

[0047] 3. The present invention has wide applicability: This model is not only applicable to predicting the soil stiffness in the small-strain range, but also can be combined with any plastic model to predict the behavior of soil in the large-strain range.

[0048] 4. The present invention has strong versatility: the model can be applied to different types of soil and different stress path conditions, with very strong versatility. Description of the Drawings

[0049] Figure 1a and Figure 1b are the test result and simulation result diagrams of the natural Bangkok clay sample provided by the present invention;

[0050] Figure 2 are the test result and simulation result diagrams of the natural London clay sample provided by the present invention;

[0051] Figures 3a - 3c are the test result and simulation result diagrams of the natural Gault clay sample provided by the present invention;

[0052] Figures 4a - 4b are the test result and simulation result diagrams of the natural Chicago clay sample provided by the present invention. Detailed Embodiments

[0053] The present invention will be further described below in conjunction with embodiments. The description of the following embodiments is only for helping to understand the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0054] Embodiment 1:

[0055] As an embodiment, the method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history provided by the present invention includes:

[0056] S1. Based on the modified Hardin-Drnevich curve, establish a mathematical model describing the degradation of clay stiffness with strain.

[0057] In S1, using the modified Hardin-Drnevich relationship, combining parameters such as the initial shear modulus and reference shear strain, a mathematical model describing the degradation of clay stiffness with strain is established, and the expression of the mathematical model is:

[0058]

[0059] where G is the current shear modulus, representing the stiffness of the material at a certain strain; G0 is the initial shear modulus, γ is the actual shear strain; γ 0.7 is the reference shear strain; m is a model parameter used to adjust the rate of degradation of the shear modulus with strain;

[0060] Relate G0 and confining pressure P using a power function as:

[0061]

[0062] Among them, is the shear modulus specified under the reference mean confining pressure p ref where m is a model parameter used to reflect the influence of the consolidation confining pressure on the modulus. To emphasize the role of the recent stress history and anisotropy, the present invention sets m to 1, so that this expression can effectively characterize G0 of different types of clay.

[0063] S2. Introduce the stress path rotation angle, construct an interpolation function to quantify the influence of the recent stress history on the small-strain stiffness of clay, so that the model can more accurately predict the stiffness change of clay under different loading paths.

[0064] In S2, the expression of the interpolation function is:

[0065]

[0066] where m is a dynamically adjusted model parameter used to reflect the influence of different loading paths on the shear modulus; l is a trigonometric function between the change angles of the front and back stress paths, which is used to quantify the change of the loading direction; m T and m R are the stiffness ratios during vertical loading and reverse loading respectively. m T and m R respectively represent the ratios of the initial small-stress modulus to when the stress path rotation angle φ = 90° (vertical loading) and φ = 180° (reverse loading).

[0067] S3. Introduce the fabric tensor to describe the inherent anisotropy of clay and establish an elastic modulus expression to reflect the anisotropy degree of clay in the initial state.

[0068] S4. Verify the effectiveness of the model by comparing the test data of various natural clays.

[0069] Example 2:

[0070] On the basis of Example 1, Example 2 of the present application provides a more specific method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history, including:

[0071] S1. Based on the modified Hardin-Drnevich curve, establish a mathematical model describing the degradation of clay stiffness with strain.

[0072] S2. Introduce the stress path rotation angle, construct an interpolation function to quantify the influence of the recent stress history on the small-strain stiffness of clay.

[0073] S3. Introduce the fabric tensor to describe the inherent anisotropy of clay and establish an elastic modulus expression to reflect the anisotropy degree of clay in the initial state.

[0074] In S3, the elastic modulus expression is:

[0075]

[0076] where E ijkl is the fourth-order elastic modulus, which describes the stress-strain relationship of the material in the small strain range and represents the stiffness response between the stress components in directions i, j and the strain components in directions k, l. K is the bulk modulus, G is the shear modulus, and F ij , F kl , F ki , F li , F lj , F kj represent different components of the fabric tensor respectively; δ ij , δ kl , δ li , δ kj , δ li , δ ki are all Kronecker delta symbols, which are used to simplify the stiffness tensor expression of isotropic materials. For example, δ ij δ kl represents the isotropic volume deformation term.

[0077] The bulk modulus K is calculated by assuming a constant Poisson's ratio, and its expression is:

[0078]

[0079] where ν is Poisson's ratio;

[0080] F ij represents the initial second-order fabric tensor. When the main direction is the vertical direction, its expression is:

[0081]

[0082] where F ij is the initial second-order fabric tensor, is the fabric strength in the vertical direction, is the fabric strength in the horizontal direction. The negative sign represents the mechanical response opposite to the main direction. F0 represents the initial anisotropy degree, which is calculated through the anisotropic stiffness ratio G hh / G hv measured in the bending element or resonant column test, and its formula is as follows:

[0083]

[0084] In the formula, G hh is the horizontal-horizontal shear modulus, representing the stiffness of the material when shearing in the horizontal plane. G hv is the horizontal-vertical shear modulus, representing the stiffness of the material when shearing between the horizontal plane and the vertical direction.

[0085] When the main direction of the structure is horizontal, the expression of F ij should be opposite to the expression when the main direction is vertical. When F0 = 0, it represents isotropy, and at this time the elastic modulus expression simplifies to isotropic elasticity. Due to the elastic effect, F ij remains unchanged, and the incremental relationship between stress and strain is expressed in the three-axis space as:

[0086]

[0087] where dp is the average stress increment, dq is the deviator stress increment, is the elastic volumetric strain increment, is the elastic deviator strain increment, and J is the coupling term, which describes the coupling between the volumetric response and the shear response caused by the structural anisotropy.

[0088] For isotropic materials, there is no coupling term J, and the corresponding compliance matrix is expressed as:

[0089]

[0090] where J' pq is the coupling modulus between the average normal stress and the deviator strain, and J' qp is the coupling modulus between the deviator stress and the volumetric strain. For elastic materials, the compliance matrix must be symmetric, that is, J' qp = J' pq . In fact, these four components K', G', J' qp and J' pq can be obtained from K * , G * and J through the following relationships:

[0091]

[0092] For isotropic materials, there is no coupling term, which means that the reciprocals of 1 / J' qp and 1 / J' pq are infinite. The above incremental relationship formula between stress and strain and the component conversion formula provide the tangent shear modulus, bulk modulus, and coupling modulus considering the initial structural anisotropy.

[0093] S4. By comparing the test data of various natural clays, verify the effectiveness of the model.

[0094] Specifically, four kinds of natural clays were selected for experimental verification. The model parameters G ref0 , m T , m R and γ 0.7 were determined from the experimental data. By comparing the model predictions with the experimental results, it was verified that the elastic model proposed in the present invention has good prediction ability under different stress path rotation angles and bedding plane orientations.

[0095] Exemplarily, tests were conducted on natural Bangkok clay (NBC), natural London clay (NLC), natural Gault clay (NGC) and natural Chicago clay (NCC) respectively, and compared with a small strain elastic model of clay considering inherent anisotropy and recent stress history in the present invention, and the effectiveness of the model was verified.

[0096] Natural Bangkok clay (NBC): Through consolidated undrained and consolidated drained triaxial compression tests, the initial anisotropic stiffness ratio G hh / G hv was measured to be 1.14, and the initial anisotropy degree F0 was calculated to be 0.11 through the formula. By comparing the model predictions with the experimental results in Figure 1a and Figure 1b , it can be seen that the model can accurately capture the stiffness response of samples with different bedding plane orientations.

[0097] Gault clay (NGC): Drained compression tests were carried out on vertically cut and horizontally cut Gault clay NGC samples after consolidation. The comparison between the model predictions and the experimental results is shown in Figures 3a - 3c , and the model can reasonably capture the stiffness degradation response of samples with different deposition orientations.

[0098] London clay (NLC): In order to study the influence of recent history on the stiffness characteristics of natural London clay NLC, undrained triaxial compression tests and triaxial tensile tests were carried out, and the initial anisotropic stiffness ratio G hh / G hv was also measured to be 1.86 and the initial anisotropy degree F0 was 0.55. The comparison between the model predictions and the experimental results is shown in Figure 2 , and the model can accurately capture the stiffness response under different stress path rotation angles.

[0099] Chicago clay (NCC): Tests were carried out for different shear paths and consolidation histories, and the initial anisotropic stiffness ratio G hh / G hv was measured to be 1.2 and the initial anisotropy degree F0 was 0.7. The comparison between the model predictions and the experimental results is shown in Figure 4a and Figure 4b, which once again proves the prediction ability of the model under different stress path rotation angles and initial stress states.

[0100] It should be noted that the same or similar parts in this embodiment and Embodiment 1 can be referred to each other and will not be elaborated in this application.

[0101] Embodiment 3:

[0102] Based on Embodiment 2, Embodiment 3 of the present application provides a system for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history, including:

[0103] A building module for establishing a mathematical model describing the degradation of clay stiffness with strain based on the modified Hardin-Drnevich curve;

[0104] A first introduction module for introducing the stress path rotation angle and constructing an interpolation function to quantify the influence of the recent stress history on the small-strain stiffness of clay;

[0105] A second introduction module for introducing the fabric tensor to describe the inherent anisotropy of clay and establishing an elastic modulus expression to reflect the anisotropy degree of clay in the initial state;

[0106] A verification module for verifying the effectiveness of the model by comparing the test data of various natural clays.

[0107] It should be noted that the system provided in this embodiment is the system corresponding to the method provided in Embodiment 2. Therefore, the same or similar parts in this embodiment and Embodiment 2 can be referred to each other and will not be elaborated in this application.

[0108] In summary, the elastic model proposed by the present invention realizes the accurate prediction of the small-strain stiffness characteristics of clay by introducing the fabric tensor and the stress path rotation angle and combining the modified Hardin-Drnevich curve. This model not only has theoretical innovation but also verifies its effectiveness and accuracy through experiments.

Claims

1. A method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history, characterized in that, Including: S1. Based on the modified Hardin-Drnevich curve, establish a mathematical model to describe the degradation of clay stiffness with strain; S2. Introduce the stress path rotation angle, and construct an interpolation function to quantify the influence of the recent stress history on the small-strain stiffness of clay; S3. Introduce the fabric tensor to describe the inherent anisotropy of clay, and establish an elastic modulus expression to reflect the anisotropy degree of clay in the initial state; S4. Verify the effectiveness of the model by comparing the test data of various natural clays.

2. The method for establishing a clay small strain elastic model considering inherent anisotropy and stress history according to claim 1, characterized in that, In S1, the expression of the mathematical model is: Among them, G is the current shear modulus, representing the stiffness of the material at a certain strain; G0 is the initial shear modulus, γ is the actual shear strain; γ 0.7 is the reference shear strain; m is a model parameter used to adjust the rate of shear modulus degradation with strain; Relate G0 and the confining pressure P using a power function as: Among them, is the shear modulus specified under the reference mean confining pressure, p ref , and m is a model parameter used to reflect the influence of the consolidation confining pressure on the modulus.

3. The method for establishing a clay small-strain elastic model considering inherent anisotropy and stress history according to claim 2, characterized in that, In S2, the expression of the interpolation function is: Among them, m is a dynamically adjusted model parameter used to reflect the influence of different loading paths on the shear modulus; l is a trigonometric function between the angles of the front and back stress path changes, used to quantify the change in the loading direction; m T and m R are the stiffness ratios during vertical loading and reverse loading, respectively.

4. The method for establishing a clay small strain elastic model considering inherent anisotropy and stress history according to claim 3, characterized in that, In S3, the expression of the elastic modulus is: Among them, E ijkl is the fourth-order elastic modulus, which describes the stress-strain relationship of the material within the small strain range and represents the stiffness response between the stress components in directions i, j and the strain components in directions k, l. K is the bulk modulus, G is the shear modulus, F ij , F kl , F ki , F li , F lj , F kj respectively represent different components of the fabric tensor; δ ij , δ kl , δ li , δ kj , δ li , δ ki are all Kronecker delta symbols, which are used to simplify the expression of the stiffness tensor of isotropic materials. For example, δ ij δ kl represents the isotropic volume deformation term.

5. The method for establishing a clay small-strain elastic model considering inherent anisotropy and stress history according to claim 4, characterized in that In S3, the bulk modulus K is calculated by assuming a constant Poisson's ratio, and its expression is: In the formula, ν is Poisson's ratio; F ij represents the initial second-order fabric tensor, and when the principal direction is the vertical direction, its expression is as follows: where F ij is the initial second-order fabric tensor, is the fabric strength in the vertical direction, is the fabric strength in the horizontal direction. The negative sign indicates the mechanical response opposite to the main direction. F0 represents the initial anisotropy degree, which is calculated by the anisotropic stiffness ratio G hh / G hv measured in the bending element or resonant column test. The formula is as follows: where G hh is the horizontal-horizontal shear modulus, representing the stiffness of the material when sheared in the horizontal plane, and G hv is the horizontal-vertical shear modulus, representing the stiffness of the material when sheared between the horizontal plane and the vertical direction.

6. The method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history according to claim 5, characterized in that In S3, when F0 = 0, it indicates isotropy. Due to the elastic effect, F ij remains unchanged, and the incremental relationship between stress and strain is expressed in the three-axis space as: where dp is the average stress increment, dq is the deviator stress increment, is the elastic volumetric strain increment, is the elastic deviator strain increment, and J is the coupling term that describes the coupling between the volumetric response and the shear response caused by the structural anisotropy.

7. The method for establishing a clay small strain elastic model considering inherent anisotropy and stress history according to claim 6, characterized in that, In S3, for an isotropic material, there is no coupling term J, and the corresponding compliance matrix is expressed as: Among them, J′ pq is the coupling modulus between the mean normal stress and the deviatoric strain, and J′ qp is the coupling modulus between the deviatoric stress and the volumetric strain.

8. A system for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history, characterized in that, For performing the method according to any one of claims 1 to 7, including: A building module, configured to establish a mathematical model to describe the degradation of clay stiffness with strain based on the modified Hardin-Drnevich curve; A first introduction module, configured to introduce the stress path rotation angle and construct an interpolation function to quantify the influence of the recent stress history on the small-strain stiffness of clay; A second introduction module, configured to introduce the fabric tensor to describe the inherent anisotropy of clay, and establish an elastic modulus expression to reflect the anisotropy degree of clay in the initial state; A verification module, configured to verify the effectiveness of the model by comparing the test data of various natural clays.

9. A computer storage medium, characterized in that, The computer storage medium stores a computer program; when the computer program runs on a computer, the computer is caused to execute the method according to any one of claims 1 to 7.

10. An electronic device, characterized in that, Including: A memory, configured to store the computer program; A processor, configured to execute the computer program to implement the method according to any one of claims 1 to 7.

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