Methods for Establishing Small-Strain Elastic Models of Clay Considering Intrinsic Anisotropy and Stress History

Abstract

This invention relates to a method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history. The method includes: establishing a mathematical model describing the stiffness degradation of clay with strain based on a modified Hardin-Drnevich curve; introducing a stress path rotation angle and constructing an interpolation function to quantify the influence of recent stress history on the small-strain stiffness of clay; introducing a fabric tensor to describe the inherent anisotropy of clay and establishing an expression for the elastic modulus to reflect the degree of anisotropy of clay in its initial state; and verifying the effectiveness of the model by comparing data from various natural clay experiments. The beneficial effects of this invention are: the proposed model can more accurately describe the anisotropic stiffness response of soil within a small strain range, especially after considering the influence of the stress path rotation angle and pavement orientation, which greatly improves the model's prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and more specifically, to a method for establishing a small-strain elastic model of clay that takes into account inherent anisotropy and stress history. Background Technology

[0002] In geotechnical engineering, the analysis of key issues such as deep foundation pit excavation, backfilling, and tunnel construction heavily relies on the accurate understanding of the small-strain stiffness characteristics of clay. However, existing models are insufficient in capturing the nonlinear small-strain stiffness variations of anisotropic clay, especially when dealing with clays that have undergone different loading histories, making it difficult to accurately reproduce their mechanical behavior. Specifically, traditional models have several shortcomings, such as assuming uniform stiffness distribution in space and neglecting the significant anisotropy of natural clay due to deposition; and failing to introduce a second-order fabric tensor to quantify the contribution of microstructure to macroscopic stiffness, resulting in an inability to accurately describe the structural anisotropy of clay. Furthermore, traditional models ignore the shear-volume coupling effect, assuming that the shear modulus and bulk modulus are independent, while in reality, anisotropic clay exhibits significant cross-coupling. The lack of explicit expression of coupling terms in the stiffness matrix leads to errors in predicting the evolution of excess pore pressure or the response of bedding planes. These deficiencies severely restrict the accurate prediction of the mechanical behavior of clay in geotechnical engineering. Therefore, to address the above problems, a method for establishing a small-strain elastic model of clay that considers inherent anisotropy and stress history is proposed. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for establishing a small-strain elastic model of clay that considers inherent anisotropy and stress history.

[0004] Firstly, 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, a mathematical model describing the degradation of clay stiffness with strain is established.

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

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

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

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

[0010]

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

[0012] Using a power function, G0 and the confining pressure P are correlated as follows:

[0013]

[0014] in, Based on the reference mean confining pressure p ref The specified shear modulus is given by m, which is a model parameter used to reflect the effect of consolidation pressure on the modulus.

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

[0016]

[0017] 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 angles of the preceding and following stress paths, used to quantify the change in the loading direction; m T and m R These are the stiffness ratios under vertical loading and reverse loading, respectively.

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

[0019]

[0020] Among them, E ijkl The fourth-order elastic modulus describes the stress-strain relationship of a material within a small strain range. It 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 is the tensile modulus. ij F kl F ki F li F lj F kj These represent different components of the structural tensor; δ ij δ kl δ li δ kj δ li δ ki All are Kronecker delta notations, used to simplify the stiffness tensor expression for isotropic materials, for example, δ ij δ kl This represents the isotropic volume deformation term.

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

[0022]

[0023] In the formula, ν is Poisson's ratio;

[0024] F ij Let the initial second-order configuration tensor, when the principal direction is perpendicular, be expressed as:

[0025]

[0026] In the formula, F ij For the initial second-order structure tensor, The structural strength is in the vertical direction (main direction). The horizontal structural strength is represented by the negative sign, indicating a mechanical response opposite to the principal direction. F0 represents the initial anisotropy, and the anisotropic stiffness ratio G is measured in bending element or resonant column tests. hh / G hv The calculated formula is shown below:

[0027]

[0028] In the formula, G hh G is the horizontal-horizontal shear modulus, representing the stiffness of a material when sheared in a horizontal plane. hv The horizontal-vertical shear modulus represents the stiffness of a material when sheared between a horizontal plane and a vertical direction.

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

[0030]

[0031] Where dp is the average stress increment and dq is the deviatoric stress increment. For elastic volumetric strain increment, For the elastic deviatoric strain increment, 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] Among them, J' pqIt is the coupling modulus between the mean normal stress and the deviatoric strain, J' qp It is the coupling modulus between deviatoric stress and volumetric strain.

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

[0036] A module is established to build a mathematical model describing the degradation of clay stiffness with strain based on the modified Hardin-Drnevich curve;

[0037] The first module is used to introduce the stress path rotation angle and construct an interpolation function to quantify the influence of recent stress history on the small strain stiffness of clay.

[0038] The second introduction module is used to introduce the fabric tensor to describe the inherent anisotropy of clay and to establish the expression for the elastic modulus to reflect the degree of anisotropy of clay in the initial state.

[0039] The validation module is used to verify the effectiveness of the model by comparing test data from various natural clays.

[0040] 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.

[0041] Fourthly, an electronic device is provided, comprising:

[0042] Memory, used to store computer programs;

[0043] A processor for executing the computer program to implement the method as described in any of the first aspects.

[0044] The beneficial effects of this invention are:

[0045] 1. High accuracy of the present invention: The model proposed in this invention can more accurately describe the anisotropic stiffness response of soil in a small strain range. In particular, after considering the influence of stress path rotation angle and pavement orientation, the prediction accuracy of the model is greatly improved.

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

[0047] 3. This invention has wide applicability: This model is not only applicable to soil stiffness prediction in a small strain range, but can also be combined with any plasticity model to predict soil behavior in a large strain range.

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

[0049] Figure 1a and Figure 1b The experimental and simulation results of the natural Bangkok clay sample provided for this invention are shown in the figure.

[0050] Figure 2 Figures showing the experimental and simulation results of natural London clay samples provided for this invention;

[0051] Figures 3a-3c Figures showing the experimental and simulation results of natural Golter clay samples provided for this invention;

[0052] Figures 4a-4b The figures show the experimental and simulation results of the natural Chicago clay sample provided for this invention. Detailed Implementation

[0053] 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.

[0054] Example 1:

[0055] As one 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, a mathematical model is established to describe the degradation of clay stiffness with strain.

[0057] In S1, using the modified Hardin-Drnevich relation and 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. The expression of the mathematical model is as follows:

[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; and γ is the actual shear strain. 0.7 is the reference shear strain; m is a model parameter used to adjust the rate at which the shear modulus degrades with strain;

[0060] Using a power function, G0 and the confining pressure P are related as follows:

[0061]

[0062] in, Based on the reference mean confining pressure p ref The specified shear modulus is given by m, a model parameter used to reflect the effect of consolidation pressure on the modulus. To emphasize the role of recent stress history and anisotropy, this invention sets m to 1, thus making the expression effectively characterize G0 for different types of clay.

[0063] S2. Introduce the stress path rotation angle and construct an interpolation function to quantify the influence of 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 for 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 angles of the preceding and following stress paths, used to quantify the change in the loading direction; m T and m R These represent the stiffness ratios under vertical and reverse loading, respectively. T and m R Express the initial minimum stress modulus and stress path rotation angles φ = 90° (vertical loading) and φ = 180° (reverse loading), respectively. The ratio of .

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

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

[0069] Example 2:

[0070] Based on Example 1, Example 2 of this application provides a more specific method for establishing a small-strain elastic model of clay that considers inherent anisotropy and stress history, including:

[0071] S1. Based on the modified Hardin-Drnevich curve, a mathematical model is established to describe the degradation of clay stiffness with strain.

[0072] S2. Introduce the stress path rotation angle and construct an interpolation function to quantify the influence of 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 expression for the elastic modulus to reflect the degree of anisotropy of clay in the initial state.

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

[0075]

[0076] Among them, E ijkl The fourth-order elastic modulus describes the stress-strain relationship of a material within a small strain range. It 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 is the tensile modulus. ij F kl F ki F li F lj F kj These represent different components of the structural tensor; δ ij δ kl δ li δ kj δ li δ ki All are Kronecker delta notations, used to simplify the stiffness tensor expression for isotropic materials, for example, δ ij δ kl This represents the isotropic volume deformation term.

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

[0078]

[0079] In the formula, ν is Poisson's ratio;

[0080] F ij Let the initial second-order configuration tensor, when the principal direction is perpendicular, be expressed as:

[0081]

[0082] In the formula, F ij For the initial second-order structure tensor, For vertical structural strength, The horizontal structural strength is represented by the negative sign, indicating a mechanical response opposite to the principal direction. F0 represents the initial anisotropy, and the anisotropic stiffness ratio G is measured in bending element or resonant column tests. hh / G hv The calculated formula is shown below:

[0083]

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

[0085] When the main direction of the structure is horizontal, F ij The expression for F0 should be the opposite of the expression when the principal direction is perpendicular. When F0 = 0, it indicates isotropic elasticity, and the expression for the elastic modulus simplifies to isotropic elasticity. Due to the elastic effect, F ij If constant, the incremental relationship between stress and strain in triaxial space is expressed as:

[0086]

[0087] Where dp is the average stress increment and dq is the deviatoric stress increment. For elastic volumetric strain increment, For the elastic deviatoric strain increment, 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] Among them, J' pq It is the coupling modulus between the mean normal stress and the deviatoric strain, J' qp It is the coupling modulus between deviatoric stress and volumetric strain. For elastic materials, the compliance matrix must be symmetric, i.e., J' qp =J' pq In fact, these four components K', G', J' qp and J' pq From K, we can obtain the following relationship * G * The conversion from J yields:

[0091]

[0092] For isotropic materials, there are no coupling terms, meaning 1 / J' qp and 1 / J' pq The reciprocal of is infinite. The above formulas for the incremental relationship between stress and strain and the component conversion formulas provide the tangential shear modulus, bulk modulus, and coupling modulus considering the anisotropy of the initial structure.

[0093] S4. Verify the effectiveness of the model by comparing test data from various natural clays.

[0094] Specifically, four types of natural clay were selected for experimental verification. The model parameter G was determined from the experimental data. ref0 m T m R and γ 0.7 By comparing model predictions with experimental results, the elastic model proposed in this invention has been verified to have good predictive ability under different stress path rotation angles and bedding plane orientations.

[0095] For example, experiments were conducted on natural Bangkok clay (NBC), natural London clay (NLC), natural Galt clay (NGC), and natural Chicago clay (NCC), and the effectiveness of the model was verified by comparing it with a clay small-strain elastic model of the present invention that considers inherent anisotropy and recent stress history.

[0096] Natural Bangkok Clay (NBC): The initial anisotropic stiffness ratio G was measured by consolidated undrained and consolidated drained triaxial compression tests. hh / G hv The initial anisotropy degree F0 is calculated to be 0.11 using the formula, with a value of 1.14. A comparison between model predictions and experimental results is shown below. Figure 1a and Figure 1b It can be seen that the model can accurately capture the stiffness response of samples with different bedding orientations.

[0097] Golter clay (NGC): Drained compression tests were conducted on consolidated vertically and horizontally cut Golter clay NGC samples. A comparison of model predictions and experimental results is shown below. Figures 3a-3c As shown, the model can reasonably capture the stiffness degradation response of samples with different deposition orientations.

[0098] London clay (NLC): To investigate the influence of recent history on the stiffness properties of natural London clay (NLC), undrained triaxial compression and triaxial tensile tests were conducted, and the initial anisotropic stiffness ratio G was also measured. hh / G hv The model prediction is 1.86 and the initial anisotropy degree F0 is 0.55. A comparison between the model prediction and experimental results can be found in [link to data]. Figure 2 As shown, the model can accurately capture the stiffness response under different stress path rotation angles.

[0099] Chicago clay (NCC): Experiments were conducted for different shear paths and consolidation histories, and the initial anisotropic stiffness ratio G was measured. hh / G hv The initial anisotropy value is 1.2 and the initial anisotropy degree F0 is 0.7. A comparison between model predictions and experimental results can be found in [link to data]. Figure 4a and Figure 4bThis further demonstrates the model's predictive ability under different stress path rotation angles and initial stress states.

[0100] 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.

[0101] Example 3:

[0102] Based on Example 2, Example 3 of this application provides a system for establishing a small-strain elastic model of clay that considers inherent anisotropy and stress history, including:

[0103] A module is established to build a mathematical model describing the degradation of clay stiffness with strain based on the modified Hardin-Drnevich curve;

[0104] The first module is used to introduce the stress path rotation angle and construct an interpolation function to quantify the influence of recent stress history on the small strain stiffness of clay.

[0105] The second introduction module is used to introduce the fabric tensor to describe the inherent anisotropy of clay and to establish the expression for the elastic modulus to reflect the degree of anisotropy of clay in the initial state.

[0106] The validation module is used to verify the effectiveness of the model by comparing test data from 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 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.

[0108] In summary, the elastic model proposed in this invention achieves accurate prediction of the small-strain stiffness characteristics of clay by introducing the fabric tensor and stress path rotation angle, and combining it with a modified Hardin-Drnevich curve. This model not only possesses theoretical innovation but also demonstrates 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, include: S1. Based on the modified Hardin-Drnevich curve, a mathematical model describing the degradation of clay stiffness with strain is established. In S1, the expression of the mathematical model is: Where G is the current shear modulus, representing the stiffness of the material at a certain strain; G0 is the initial shear modulus; and γ is the actual shear strain. 0.7 is the reference shear strain; m is a model parameter used to adjust the rate at which the shear modulus degrades with strain; Using a power function, G0 and the confining pressure P are correlated as follows: in, Based on the reference mean confining pressure, p ref The specified shear modulus, where m is a model parameter used to reflect the effect of consolidation pressure on the modulus; S2. Introduce stress path rotation angle and construct interpolation function to quantify the influence of recent stress history on the small strain stiffness of clay. In S2, the expression for the interpolation function is: 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 angles of the preceding and following stress paths, used to quantify the change in the loading direction; m T and m R These are the stiffness ratios under vertical loading and reverse loading, respectively. S3. Introduce the fabric tensor to describe the inherent anisotropy of clay and establish an expression for the elastic modulus to reflect the degree of anisotropy of clay in the initial state. In S3, the expression for the elastic modulus is: Among them, E ijkl The fourth-order elastic modulus describes the stress-strain relationship of a material within a small strain range. It 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 is the tensile modulus. ij F kl F ki F li F lj F kj These represent different components of the structural tensor; δ ij δ kl δ li δ kj δ li δ ki All are Kronecker delta notations, used to simplify the stiffness tensor expression for isotropic materials, δ ij δ kl Represents the isotropic volume deformation term; S4. Verify the effectiveness of the model by comparing test data from various natural clays.

2. The method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history according to claim 1, characterized in that, In S3, the bulk modulus K is calculated by assuming Poisson's ratio is constant, and its expression is: In the formula, ν is Poisson's ratio; F ij Let the initial second-order configuration tensor, when the principal direction is perpendicular, be expressed as: In the formula, F ij For the initial second-order structure tensor, For vertical structural strength, The horizontal structural strength is represented by the negative sign, indicating a mechanical response opposite to the principal direction. F0 represents the initial anisotropy, and the anisotropic stiffness ratio G is measured in bending element or resonant column tests. hh / G hv The calculated formula is shown below: In the formula, G hh G is the horizontal-horizontal shear modulus, representing the stiffness of a material when sheared in a horizontal plane. hv The horizontal-vertical shear modulus represents the stiffness of a material when sheared between a horizontal plane and a vertical direction.

3. The method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history according to claim 2, characterized in that, In S3, when F0 = 0, it indicates isotropy. Due to the elastic effect, F ij If constant, the incremental relationship between stress and strain in triaxial space is expressed as: Where dp is the average stress increment and dq is the deviatoric stress increment. For elastic volumetric strain increment, For the elastic deviatoric strain increment, J is the coupling term, which describes the coupling between the volumetric response and the shear response caused by the structural anisotropy.

4. The method for establishing a small-strain elastic model of clay considering inherent anisotropy and stress history according to claim 3, characterized in that, In S3, for isotropic materials, there is no coupling term J, and the corresponding compliance matrix is ​​expressed as: Among them, J′ pq It is the coupling modulus between the mean normal stress and the deviatoric strain, J′ qp It is the coupling modulus between deviatoric stress and volumetric strain.

5. 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 4, comprising: A module is established to build a mathematical model describing the degradation of clay stiffness with strain based on the modified Hardin-Drnevich curve; The first module is used to introduce the stress path rotation angle and construct an interpolation function to quantify the influence of recent stress history on the small strain stiffness of clay. The second introduction module is used to introduce the fabric tensor to describe the inherent anisotropy of clay and to establish the expression for the elastic modulus to reflect the degree of anisotropy of clay in the initial state. The validation module is used to verify the effectiveness of the model by comparing test data from various natural clays.

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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