A modified Duncan-Chang model considering gradation and internal erosion and a determination method thereof

Abstract

This application provides a modified Duncan-Chang model and its determination method that considers gradation and internal erosion. The determination method includes: S2, introducing a modified erosion degree; S3, constructing a shear-dominated linear elastic-non-correlated elastoplastic framework based on the traditional Duncan-Chang model, and explicitly setting key mechanical parameters as functions of , thus obtaining the modified Duncan-Chang model considering gradation and internal erosion. The modified Duncan-Chang model of this application, by introducing a modified erosion degree, solves the problem of traditional models neglecting gradation differences. Its prediction errors for the elastic stiffness and peak strength of eroded clay gravel are far superior to existing models, and it can be directly used for stability assessment of eroded clay gravel subgrade engineering, providing a theoretical basis for engineering reinforcement scheme formulation and reducing the risk of erosion disasters.

Description

Technical Field

[0001] This application relates to the field of roadbed engineering technology, and in particular to a modified Duncan-Chang model and its determination method that takes into account gradation and internal erosion. Background Technology

[0002] Clay gravel, characterized by high strength and good permeability, is widely used in highway subgrades. Its mechanical properties and stability directly impact the long-term service safety of transportation infrastructure structures. However, during long-term operation, water seepage can easily induce the migration and loss of fine particles (≤2mm in diameter) within the clay gravel, a phenomenon known as "internal erosion." This directly disrupts the continuity of the original particle skeleton of the clay gravel, leading to a significant reduction in soil elastic stiffness, a continuous decline in peak strength, and a marked weakening of shear dilatation characteristics. This can ultimately result in severe accidents such as excessive deformation, increased leakage, and even instability and collapse of the engineering structure.

[0003] However, current research on the simulation of the mechanical behavior of clay gravel and its erosion effects faces key technological bottlenecks, making it difficult to meet the needs of precise engineering design. Firstly, traditional elastoplastic constitutive models, such as the Mohr-Coulomb model and the Duncan-Chang model, neglect the deterioration effect of internal erosion. Both models focus on uneroded clay gravel and fail to consider the impact of fine particle loss on soil mechanical properties. Secondly, while some recent studies have attempted to construct constitutive models that consider internal erosion—for example, Zhang and Chen established a quantitative relationship between model parameters and particle loss within the Duncan-Chang EB model framework based on triaxial test results (Zhang, Y.; Chen, Y. A Constitutive Relationship for Gravelly Soil Considering Fine Particle Suffusion[J]. Materials 2017)—these models often use a single index to quantify the degree of erosion, neglecting the fractal characteristics of gradation. The fractal dimension of gradation is a core parameter determining the continuity of the particle skeleton and the strength of intergranular bonding. Third, existing erosion constitutive models often require the introduction of parameters such as erosion threshold, erosion rate coefficient, and porosity evolution / mass exchange to model erosion. For example, Bonelli et al. pointed out in their modeling of piping erosion that pitting tests are often used to quantify erosion rates and establish models accordingly. Scheperboer et al. proposed a hydraulic-mechanical coupled erosion model that explicitly introduces erosion kinetics and porosity / cavitation evolution mechanisms to analyze the formation process of piping and cavities in soil (Bonelli S, Brivois O, Borghi R, Benahmed N. On the Modellingof Piping Erosion[J]. Comptes Rendus. Mécanique, 2006). However, these parameters usually rely on specialized erosion tests (such as pitting tests) or hydraulic-mechanical coupled tests for calibration and inversion. They are difficult to obtain directly through conventional triaxial, consolidation, and other mechanical tests, resulting in poor operability and difficulty in generalization of the model.

[0004] In summary, existing technologies are insufficient for accurately predicting the mechanical behavior of clay gravel after internal erosion. There is an urgent need to construct an elastoplastic constitutive model for clay gravel that integrates the "internal erosion effect" with the fractal characteristics of clay gravel gradation, and to establish a standardized parameter determination method based on conventional geotechnical tests, so as to meet the needs of accurate evaluation of the mechanical behavior of eroded clay gravel and provide a theoretical basis for engineering safety design and stability assessment. Summary of the Invention

[0005] The purpose of this application is to provide a modified Duncan-Chang model that considers gradation and internal erosion, and a method for determining it, which solves the problems existing in the prior art.

[0006] The technical solution adopted in this invention is that this application provides a method for determining a modified Duncan-Chang model that considers gradation and internal erosion, comprising the following steps: S1, Introducing a correction for erosion level ; ; ; In the above formula, the degree of erosion is corrected. This represents the relative decay rate of the gradation fractal dimension caused by erosion; The dimension of the gradational fractal is represented by the Tyler fractal model. For particles smaller than The percentage of particle mass; The maximum particle size of the sample; This represents the volume fraction of fine particles lost. , To reduce the volume of fine particles, For the initial fine particle volume; when When the sample is in a non-bleeding state, its fractal characteristics remain unchanged, and its fractal dimension is denoted as . , satisfying 2≤ ≤3; when 0 < When ≤1, Characterizes the gradation fractal features under the corresponding erosion state; S2. Based on the traditional Duncan-Chang model, a shear-dominated linear elastic-unrelated elastoplastic framework is constructed, and the key mechanical parameters are explicitly set as follows: The function is used to obtain the modified Duncan-Chang model that takes into account gradation and internal erosion.

[0007] Furthermore, in step S2, the modified Duncan-Chang model considering gradation and internal erosion includes: During the elastic phase, consider This leads to stiffness degradation and secant modulus reduction. Take as Functions: ; ; In the formula, For confining pressure, for The initial secant modulus of the uneroded clay gravel was obtained from the stress-strain curves of the triaxial test. The elastic modulus attenuation coefficient is a fractal correlation used to characterize the coupling law of "gradation morphology-normal constraint-stiffness attenuation rate", consisting of multiple sets of... The results were obtained by fitting the triaxial test results; During the plastic stage, the following steps are introduced: and hardening / softening index The Mohr-Coulomb criterion has been revised as follows: ; In the formula, For peak deviatoric stress, For average stress, For hardening / softening indicators, Peak stress ratio; plastic hardening modulus The method employs linear softening combined with superimposed erosion-gradation degradation terms: ; ; In the formula, For confining pressure, The initial plastic hardening modulus of uneroded clay gravel is given by... The slope of the triaxial pre-peak stress-strain curve is obtained; The softening rate coefficient (1 / strain) is obtained by linear fitting of the post-peak stress-strain curve; The erosion of fractal correlations exacerbates the softening coefficient, which is composed of multiple groups The results were obtained by fitting the triaxial test results; The minimum plastic hardening modulus to ensure numerical stability.

[0008] Furthermore, in step S2, the peak stress ratio Follow Approximate linear decay, expressed as: ; ; In the formula, For confining pressure, for Peak stress ratio before erosion The peak stress ratio attenuation coefficient is composed of multiple sets. The results were obtained by fitting the triaxial test results.

[0009] Furthermore, adopt Invariants focus on characterizing the shear response, mean stress eccentric stress , Principal stress, For confining pressure; in the elastic stage, under axisymmetric stress state, the increment of deviatoric stress With elastic shear strain increment satisfy .

[0010] Furthermore, in engineering applications, the modified Duncan-Chang model considering gradation and internal erosion requires incremental iterative stress calculation; based on the Sloan incremental elastoplastic algorithm, in each step of the calculation, according to the current... Moment State With strain increment The stress increment, confining pressure constant condition, and yield function are updated; plastic correction is performed through consistency conditions, and plastic shear strain, deviatoric stress, and hardening / softening index are updated to achieve a complete simulation of the stress-strain response of eroded clay gravel.

[0011] Furthermore, the step of incrementally iteratively calculating stress includes: Assuming the strain increment is entirely elastic, the stress increment can be calculated using the elastic constitutive model, yielding the following formula: Under constant confining pressure, the following equation is satisfied: Then the yield function is calculated as follows: ; Among them, if ≤0, then and order =0; if If the value is greater than 0, then plastic correction is initiated, including the following steps: By consistency conditions Derivative ; The plastic shear strain is updated to: ; The deviatoric stress is updated to: ; The hardening / softening index has been updated to: ; In the above formula, The calculated deviatoric stress is obtained from the elastic calculation. To correct the degree of erosion The corresponding secant modulus, For strain increment; The trial mean stress is calculated under constant confining pressure. For confining pressure; To test the yield function; , , , The first Peak deviatoric stress, hardening / softening index, plastic shear strain, and plastic hardening modulus at time t. ; To correct the degree of erosion The corresponding peak stress ratio; This represents the increment of plastic shear strain.

[0012] Furthermore, the volume fraction of fine particles lost. Obtained from sieving tests before and after the erosion test; , , From different The results were obtained by conducting consolidated undrained triaxial shear tests on clay gravel samples.

[0013] Furthermore, in the triaxial shear test, the confining pressure For loads of 30 kPa, 60 kPa, and 100 kPa, axial strain control loading was used, with an axial strain rate of 0.5% / min.

[0014] This application also proposes a modified Duncan-Chang model that considers gradation and internal erosion, which is constructed using the aforementioned method for determining the modified Duncan-Chang model that considers gradation and internal erosion.

[0015] To facilitate reference to the meaning of each symbol, the main symbols and their meanings are summarized in Table 1.

[0016] Table 1 Summary of main symbols and their meanings

[0017] The technical solution of this application has the following beneficial effects: The modified Duncan-Chang model in this application introduces a correction for the degree of erosion. It solves the problem of traditional models ignoring gradation differences. Its prediction error for the elastic stiffness and peak strength of eroded clay gravel is much better than that of existing models. It can be directly used for the stability assessment of eroded clay gravel subgrade engineering, providing a theoretical basis for the formulation of engineering reinforcement schemes and reducing the risk of erosion disasters. The parameters required for constructing the modified Duncan-Chang model in this application are all obtained through conventional geotechnical tests such as sieve tests and triaxial tests, without the need for special equipment, and engineers can quickly master the calibration process. Attached Figure Description

[0018] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. Wherein: Figure 1The images show the sample forming and samples under different erosion conditions in the triaxial test, which is a verification example of the present invention; where (a) is the prepared sample and (b) is a height comparison of samples with different degrees of erosion.

[0019] Figure 2 Different triaxial tests were used as verification examples for this invention. and The deviatoric stress-axial strain curves of the specimen are shown below; where (a), (b), and (c) are respectively... The deviatoric stress-axial strain curves of the specimens at 30 kPa, 60 kPa, and 100 kPa are shown.

[0020] Figure 3 In the triaxial test of the verification example of this invention, different and Destructive strength of the lower specimen .

[0021] Figure 4 In the triaxial test of the verification example of this invention, different Cohesion of the lower sample and internal friction angle .

[0022] Figure 5 In the triaxial test of the verification example of this invention, different and secant modulus The evolution of.

[0023] Figure 6 In the triaxial test of the verification example of this invention, different and Lower peak stress ratio The evolution of.

[0024] Figure 7 The test results of the triaxial test in the verification examples of this invention, the traditional Duncan-Chang model and the model of this application are compared. =30kPa and different The stress-strain response under the given conditions; where (a), (b), (c), and (d) are... The deviatoric stress-axial strain curves are 0%, 0.4%, 1.4%, and 4.2%, respectively.

[0025] Figure 8 The test results of the triaxial test in the verification examples of this invention, the traditional Duncan-Chang model and the model of this application are compared. =60kPa and different The stress-strain response under the given conditions; where (a), (b), (c), and (d) are... The deviatoric stress-axial strain curves are 0%, 0.4%, 1.4%, and 4.2%, respectively.

[0026] Figure 9 The test results of the triaxial test in the verification examples of this invention, the traditional Duncan-Chang model and the model of this application are compared. =100kPa and different The stress-strain response under the given conditions; where (a), (b), (c), and (d) are... The deviatoric stress-axial strain curves are 0%, 0.4%, 1.4%, and 4.2%, respectively. Detailed Implementation

[0027] This application will now be described in detail with reference to the accompanying drawings and embodiments. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used herein is for the purpose of describing embodiments of this disclosure only and is not intended to limit this disclosure.

[0028] The problem with the existing technology is: (1) Traditional constitutive models are only constructed for uneroded clay gravel and cannot reflect the reduction in elastic stiffness, peak strength decay and shear dilatation caused by the loss of fine particles. In engineering applications, the bearing capacity and deformation resistance of eroded soil are easily overestimated. (2) A few constitutive models that consider erosion rely solely on the volume ratio of lost fine particles. The degree of erosion is described by the ratio of the volume of lost fine particles to the initial volume of leached fine particles, without considering the fractal dimension of the gradation. The influence on the continuity of the particle skeleton and interlocking. However, in actual engineering, under the same conditions... Down, The smaller the clay gravel (the less uniform the gradation), the faster its mechanical properties degrade after erosion, resulting in existing models often having prediction errors exceeding 15%, limiting their applicability to specific gradations of soil.

[0029] To address the aforementioned issues, this application proposes a method for determining a modified Duncan-Chang model (hereinafter referred to as "this model") that considers gradation and internal erosion, comprising the following steps: S1. To quantitatively characterize the loss of fine particles caused by internal erosion and the resulting gradation remodeling effect, and to ensure the comparability of samples under different erosion conditions, this model introduces a correction for the degree of erosion. : First, the volume fraction of fine particles lost. Defined as: (1); In the formula, To reduce the volume of fine particles, This represents the initial volume of the fine particles; Fine particle loss volume fraction While it can be used to measure the amount of fine particles lost due to erosion, it is difficult to distinguish the differences in structural deterioration caused by different degrees of gradation remodeling under the same amount of loss. Therefore, this model utilizes cumulative passing rate data obtained from sieve tests and employs the Tyler (1992) fractal model to characterize the fractal features of the gradation under erosion, with the gradation fractal dimension... Defined as in equation (2): (2); In the formula, For particles smaller than The percentage of particle mass; The maximum particle size of the sample; when When the sample is in a non-bleeding state, its fractal characteristics remain unchanged, and its fractal dimension is denoted as . , usually satisfying 2≤ ≤3; when 0 < When ≤1, Characterizes the gradation fractal features under the corresponding erosion state; To simultaneously reflect the coupling effect of "fine particle loss" and "gradation reconstruction degree", this model introduces a modified erosion degree. Specifically, as shown in equation (3): (3); In the formula, The physical meaning is the relative decay rate of the gradation fractal dimension caused by erosion; Corresponding to the un-eroded state The fractal characteristics remain unchanged; as erosion intensifies, Gradually decrease, The monotonically increasing gradient reflects the degree of gradation refinement or coarsening caused by internal erosion. Taking this model as an example, in this prototype... =2.82 and When =2.81, =0.4%, which means the fractal dimension decreases by approximately 0.4%; When =2.78, =1.4%, indicating that the fractal dimension decreases by approximately 1.4%; When =2.70, =4.2%, indicating that the fractal dimension decreases by approximately 4.2%. This is compared to using only volume fraction. Compared to traditional methods for characterizing fine particle loss, introducing It can distinguish the differences in structural degradation caused by different initial gradation conditions under the same loss volume, thus overcoming the limitation that a single volume fraction index is difficult to describe the "gradation remodeling effect".

[0030] S2. To describe the gradation degradation and load-bearing capacity deterioration caused by internal erosion within a unified framework, this model, based on the stress-dependent stiffness concept of the Duncan-Chang model, introduces a shear-dominated linear elastic-non-associated elastoplastic framework, and explicitly sets the key mechanical parameters as follows: The function is used to reflect the coupling effect of erosion and gradation fractal; since the total volumetric strain under undrained conditions in the consolidated undrained triaxial test (CU, referred to as the triaxial test in this paper) is approximately zero, this paper adopts... The invariants are characterized with an emphasis on the shear response, as shown in equation (4): , (4); In the formula, For average stress, It is a deviatoric stress. Principal stress, For confining pressure; In the elastic stage, under axisymmetric stress state, the increment of deviatoric stress With elastic shear strain increment Satisfying equation (5): (5); consider This leads to stiffness degradation and secant modulus reduction. Take as The function is shown in equation (6): (6); , ; In the formula, For confining pressure, It is short for the natural exponential function in mathematics. for The initial secant modulus of the uneroded clay gravel was obtained from the stress-strain curves of the triaxial test. The elastic modulus attenuation coefficient is a fractal correlation used to characterize the coupling law of "gradation morphology-normal constraint-stiffness attenuation rate", consisting of multiple sets of... The results were obtained by fitting the triaxial test results; plastic stage, yield function The traditional Mohr-Coulomb criterion, which describes the stress threshold at which clay gravel transitions from the elastic to the plastic stage, cannot accurately reflect the yield function. The impact; to maintain consistency with subsequent consistency condition derivations, this model introduces and hardening / softening index The Mohr-Coulomb criterion has been revised as follows: (7); In the formula, For peak deviatoric stress, For average stress, For hardening / softening indicators, Peak stress ratio; Triaxial tests show peak stress Compare The approximate linear decay can be expressed as equation (8): (8); , ; In the formula, For confining pressure, for The peak stress ratio before erosion, where , The initial peak deviatoric stress, This represents the average stress corresponding to the initial peak deviatoric stress. The peak stress ratio attenuation coefficient is composed of multiple sets. The results were obtained by fitting the triaxial test results; The smaller, The larger the value, the faster the friction angle decays, which conforms to macroscopic laws; Under a one-dimensional shear-dominated framework (where the volumetric strain is approximately zero under undrained conditions, and the stress-strain relationship can be simplified to a one-dimensional shear problem), the plastic potential... Pick Therefore Plastic shear strain increment Satisfying equation (9): (9); It is the engineering shear strain increment (the shear angle that can be directly measured experimentally). Introducing hardening / softening indicators Its variation with plastic shear strain Evolutionary satisfaction formula (10): , (10); Among them, plastic hardening modulus The linear softening and superimposed erosion-gradation degradation terms are adopted, as shown in equation (11): (11); , ; In the formula, For confining pressure, The initial plastic hardening modulus of uneroded clay gravel is given by... The slope of the triaxial pre-peak stress-strain curve is obtained; The softening rate coefficient (1 / strain) is obtained by linear fitting of the post-peak stress-strain curve. absolute slope / peak intensity; The erosion of fractal correlations exacerbates the softening coefficient, which is composed of multiple groups The results were obtained by fitting the triaxial test results; To ensure numerical stability, the minimum plastic hardening modulus, Given, where The range is 0.01 to 0.05, and the value is determined through a comprehensive check of fitting error and numerical convergence. (This paper...) The value is 0.01. This type of lower limit truncation idea is consistent with the cut-off treatment introduced in the soil constitutive model to avoid excessively low stiffness.

[0031] In engineering applications, this model requires incremental iterative stress calculation, based on Sloan's (1987) incremental elastoplastic algorithm, and according to current... Moment State With strain increment The following updates will be made: Assuming the strain increment is entirely elastic, the stress increment calculated from the elastic constitutive model yields equation (12): (12); Under constant confining pressure, equation (13) must be satisfied: (13); The yield function is then calculated as equation (14): (14); Among them, if ≤0, then and order =0; if If the value is greater than 0, then plasticity correction is initiated, as follows: By consistency conditions Equation (15): (15); The plastic shear strain is updated to Equation (16): (16); The deviatoric stress is updated to equation (17): (17); The hardening / softening index is updated to Equation (18): ; In the above formula, The calculated deviatoric stress is obtained from the elastic calculation. To correct the degree of erosion The corresponding secant modulus, For strain increment; The trial mean stress is calculated under constant confining pressure. For confining pressure; To test the yield function; The first Peak deviatoric stress, hardening / softening index, plastic shear strain, and plastic hardening modulus at time t. ; To correct the degree of erosion The corresponding peak stress ratio; This represents the increment of shear strain in engineering.

[0032] Verification Example The verification example compares the results of triaxial tests, the traditional Duncan-Chang model (hereinafter referred to as the DC model), and the modified Duncan-Chang model of this application that considers gradation and internal erosion (hereinafter referred to as this model).

[0033] (1) Triaxial test: Research results indicate that after approximately 20 years of service, the dry density of roadbed fill material may decrease to about 86% of its maximum dry density under long-term cyclic loading and seepage. Therefore, to reasonably reflect the density reduction and moisture content fluctuations at the engineering site in triaxial tests, while maintaining the integrity of the samples, the initial dry density and initial moisture content of the clay gravel samples were controlled at 1.89 g / cm³. 3 and 7.8%.

[0034] The internal erosion process was simulated using soluble glucose particles to migratable fine particles: First, the fine particles were replaced with glucose particles by an equal mass according to the target gradation, and the mixture was compacted in layers in a 100mm × 200mm (diameter × height) mold. Then, under constant water head conditions, the sample was immersed in a water tank for over 48 hours, allowing the glucose particles to gradually dissolve and migrate out, simulating the random loss of fine particles. Simultaneously, the pore pressure coefficient B was measured to ensure saturation met the requirement of B > 0.95. After saturation, the sample was dried in a 40℃ forced convection oven, and the sample mass was recorded using an electronic balance every 10–30 minutes until the difference between the measured moisture content and the optimum moisture content was controlled within ±1%.

[0035] Preliminary trial results show that when the designed erosion volume fraction When the erosion values ​​are 0, 0.1, 0.2, and 0.3, the resulting sample heights are approximately 201 mm, 199 mm, 195 mm, and 182 mm, respectively, with errors relative to the standard height of 200 mm of approximately 0.5%, 0.5%, 2.5%, and 9.0%, respectively. Considering that the sample height decreases significantly when the erosion degree is too high, which can easily cause triaxial sample shape deviation and stress boundary condition distortion, and taking into account both geometric integrity and the identifiability of the erosion effect, the final selection was... Using 0, 0.05, 0.1, and 0.2 as representative erosion conditions, the corresponding fractal-corrected erosion degrees are approximately... =0%, 0.4%, 1.4%, 4.2%. Figure 1 The image visually demonstrates the comparison of sample formation and sample height under different erosion conditions; (a) shows the completed sample, and (b) shows the height comparison of samples with different erosion levels. Figure 1 It can be seen that with As the sample height increases, the apparent structure becomes more porous, providing a basis for subsequent mechanical property degradation analysis.

[0036] According to the "JTG 3430-2020 Highway Geotechnical Testing Procedures", this study investigated different... Consolidated undrained (CU) triaxial shear tests were conducted on clay gravel samples. A Dynatriax 100 / 14 servo-controlled triaxial system manufactured by Wykeham Farrance, Italy, was used. The system consists of a computer, main control unit, confining pressure control system, loading frame, and triaxial pressure chamber, and can realize closed-loop control of confining pressure and axial load and automatic data acquisition throughout the process.

[0037] Considering that the principal stress level of typical roadbed fill material under long-term service conditions is usually between 30 and 100 kPa, the confining pressure is selected. =30, 60, 100 kPa to cover common stress ranges. The shear stage adopts axial strain controlled loading method, and the axial strain rate is 0.5% / min; the specific test plan is shown in Table 2.

[0038] Table 2 Triaxial Test Scheme

[0039] Figure 2 Showing different (0, 0.4%, 1.4%, 4.2%) and Deviatoric stress-axial strain curves of specimens at (30kPa, 60kPa, 100kPa); Figure 3 Different (0%, 0.4%, 1.4%, 4.2%) and Destructive strength of specimens at (30 kPa, 60 kPa, 100 kPa) , Figure 4 Different Cohesion of samples at (0%, 0.4%, 1.4%, 4.2%) and internal friction angle ; Figure 5 Different (0, 0.4%, 1.4%, 4.2%) and Evolution of the secant modulus at (30kPa, 60kPa, 100kPa) Figure 6 Different (0, 0.4%, 1.4%, 4.2%) and Evolution of peak stress ratio at (30kPa, 60kPa, 100kPa).

[0040] According to JTG 3430-2020 Highway Geotechnical Testing Procedures, the failure strength of a specimen depends on the shape of its stress-strain curve: when the curve exhibits obvious strain softening characteristics, the deviatoric stress... -Axial strain The peak deviatoric stress of the curve is taken as the failure strength; when the curve exhibits strain hardening without a significant peak, the stress at 15% axial strain is taken as the failure strength. As the intensity of damage. Based on this, based on each Mohr circles were plotted based on the failure strength, and the cohesion was inverted using the Mohr-Coulomb strength criterion. and internal friction angle At the same time, for quantification The resulting stiffness degradation is addressed by selecting the secant modulus (defined as the modulus corresponding to 50% of the failure strength). place, and The ratio of peak stress to peak deviatoric stress is used as a stiffness index. The peak stress ratio is defined as the ratio of peak deviatoric stress to peak deviatoric stress. With average stress The ratio. The above indicators are used to reveal the same... and The study investigates the strength-stiffness evolution of clay gravel under certain conditions, providing a unified experimental basis for subsequent constitutive parameter calibration and microscopic numerical simulation comparison.

[0041] (2) Traditional Duncan-Chang model: The traditional Duncan-Chang model used in this application is a nonlinear elastic stress-strain model based on the hyperbolic relationship of triaxial tests proposed by Duncan and Chang (Duncan JM, Chang CY. Nonlinear Analysis of Stress and Strain in Soils[J]. Journal of the Soil Mechanics and Foundations Division, ASCE, 1970), whose deviatoric stress and axial strain can be characterized by the following hyperbolic form: ; in, Principal stress (axial strain). For confining pressure, For axial strain, These are the fitting parameters.

[0042] (3) Construction of this model: The model is constructed in accordance with the previous text, where... , , These three coefficients were also obtained through the "(1) triaxial test" in the verification example. The specific fitting steps are as follows: Fitting steps: 1) For the same gradation The raw materials are produced under the same confining pressure. At different degrees of erosion A consolidated undrained triaxial test (referred to as the triaxial test) was conducted to obtain the corresponding secant modulus. For each experiment, right For linear regression, the slope is... 2) Change the raw material gradation and confining pressure After conducting multiple triaxial tests, the results were obtained. and The corresponding multiple sets of data were used to perform multiple regression to obtain... formula: .

[0043] Fitting steps: 1) For the same gradation The raw materials are produced under the same confining pressure. At different degrees of erosion Triaxial tests were conducted to obtain the corresponding peak stress ratio. For each experiment, right For linear regression, the slope is... 2) Change the raw material gradation and confining pressure After conducting multiple triaxial tests, the results were obtained. and The corresponding multiple sets of data were used to perform multiple regression to obtain... formula: .

[0044] Fitting steps: 1) For the same gradation The raw materials are produced under the same confining pressure. At different degrees of erosion The plastic hardening modulus was obtained by inverting the stress-strain curves from triaxial tests. For each experiment, under the same plastic strain, right For linear regression, the slope is... 2) Change the raw material gradation and confining pressure After conducting multiple triaxial tests, the results were obtained. and The corresponding multiple sets of data were used to perform multiple regression to obtain... formula: .

[0045] (4) Experimental results and analysis; Figure 7 , Figure 8 , Figure 9 The system compared experimental results and the traditional Duncan-Chang model (DC model) with the modified DC model (this model) under different conditions. (30kPa, 60kPa, 100kPa) and Stress-strain response at (0%, 0.4%, 1.4%, 4.2%). Figure 7 (a), (b), (c), and (d) in the text represent the three items respectively. =30kPa, =0%, 0.4%, 1.4%, 4.2% deviatoric stress-axial strain curves. Figure 8 (a), (b), (c), and (d) in the text represent the three items respectively. =60kPa, =0%, 0.4%, 1.4%, 4.2% deviatoric stress-axial strain curves. Figure 9 (a), (b), (c), and (d) in the text represent the three items respectively. =100kPa, The deviatoric stress-axial strain curves are shown for 0%, 0.4%, 1.4%, and 4.2%. Solid lines represent the model in question, dashed lines represent the traditional Duncan-Chang model (DC model), and hollow circles represent experimental results.

[0046] As can be seen from the figure, the main biases of the traditional DC model are consistent and directional: it tends to provide predicted curves for strong or weak hardening across all operating conditions, making it difficult to simultaneously reproduce the peak appearance, rapid post-peak decay, and residual plateau of the experimental curve. This results in a general overestimation of the deviatoric stress level in the post-peak segment and a weakening of the load-bearing degradation caused by erosion. This bias is particularly pronounced under conditions of low confining pressure or more significant softening: when the confining pressure is lower... (0%~0.4%) and when the experimental curve shows a clear peak and rapid softening, traditional models can maintain a certain trend in the pre-peak segment, but often cannot provide a reasonable post-peak decay slope; when the peak is higher... (4.2%) and when the test shows weak softening, the traditional model may still maintain a high level of hardening, thus systematically smoothing out the characteristics of "high erosion and low load".

[0047] In comparison, this model in Figures 7 to 9 The given 12 groups ( In all operating conditions, it can simultaneously approximate (i) the initial loading slope (stiffness level), (ii) the peak amplitude and peak strain location, and (iii) the post-peak attenuation rate and residual trend. Especially in low erosion conditions... =0%~0.4%) strong softening chemical conditions and high corrosion ( Even under weakly soft chemical conditions (e.g., 4.2%), this model maintains a consistent fit quality. This is because the model's fitting accuracy is directly related to its construction: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Introduction This enables the model to reflect erosion-induced stiffness decay in the peak region; Incorporating yield conditions reduces peak mobilization capacity with erosion; and through Erosion exacerbates the project By controlling the post-peak softening intensity, the three segments of "pre-peak, peak, and post-peak" characteristics can evolve in a coordinated manner under the same state variable.

[0048] In conclusion, Figures 7 to 9 The results demonstrate that this model can significantly improve the predictability of the stress-strain response under erosion conditions, providing usable constitutive support for subsequent parameter inversion, engineering numerical analysis, and performance degradation assessment under service conditions.

[0049] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for determining a modified Duncan-Chang model considering gradation and internal erosion, characterized in that, Includes the following steps: S1, Introducing a correction for erosion level ; ； ； In the above formula, the degree of erosion is corrected. This represents the relative decay rate of the gradation fractal dimension caused by erosion; The dimension of the gradational fractal is represented by the Tyler fractal model. For particles smaller than The percentage of particle mass; The maximum particle size of the sample; This represents the volume fraction of fine particles lost. , To reduce the volume of fine particles, For the initial fine particle volume; when When the sample is in a non-bleeding state, its fractal characteristics remain unchanged, and its fractal dimension is denoted as . , satisfying 2≤ ≤3; when 0 < When ≤1, Characterizes the gradation fractal features under the corresponding erosion state; S2. Based on the traditional Duncan-Chang model, a shear-dominated linear elastic-unrelated elastoplastic framework is constructed, and the key mechanical parameters are explicitly set as follows: The function is used to obtain the modified Duncan-Chang model that takes into account gradation and internal erosion.

2. The method for determining the modified Duncan-Chang model considering gradation and internal erosion according to claim 1, characterized in that, In step S2, the modified Duncan-Chang model considering gradation and internal erosion includes: During the elastic phase, consider This leads to stiffness degradation and secant modulus reduction. Take as Functions: ； ； In the formula, For confining pressure, for The initial secant modulus of the uneroded clay gravel was obtained from the stress-strain curves of the triaxial test. The elastic modulus attenuation coefficient is a fractal correlation used to characterize the coupling relationship between "gradation morphology - normal constraint - stiffness attenuation rate", consisting of multiple sets of... The results were obtained by fitting the triaxial test results; During the plastic stage, the following steps are introduced: and hardening / softening index The Mohr-Coulomb criterion has been revised as follows: ； In the formula, For peak deviatoric stress, For average stress, For hardening / softening indicators, Peak stress ratio; plastic hardening modulus The method employs linear softening combined with superimposed erosion-gradation degradation terms: ； ； In the formula, For confining pressure, The initial plastic hardening modulus of uneroded clay gravel is given by... The slope of the triaxial pre-peak stress-strain curve is obtained; The softening rate coefficient (1 / strain) is obtained by linear fitting of the post-peak stress-strain curve; The erosion of fractal correlations exacerbates the softening coefficient, which is composed of multiple groups The results were obtained by fitting the triaxial test results; The minimum plastic hardening modulus to ensure numerical stability.

3. The method for determining the modified Duncan-Chang model considering gradation and internal erosion according to claim 2, characterized in that, In step S2, the peak stress ratio Follow Approximate linear decay, expressed as: ； ； In the formula, For confining pressure, for Peak stress ratio before erosion The peak stress ratio attenuation coefficient is composed of multiple sets. The results were obtained by fitting the triaxial test results.

4. The method for determining the modified Duncan-Chang model considering gradation and internal erosion according to claim 2, characterized in that, use Invariants focus on characterizing the shear response, mean stress eccentric stress , Principal stress, For confining pressure; in the elastic stage, under axisymmetric stress state, the increment of deviatoric stress With elastic shear strain increment satisfy .

5. The method for determining the modified Duncan-Chang model considering gradation and internal erosion according to claim 2, characterized in that, In engineering applications, the modified Duncan-Chang model considering gradation and internal erosion requires incremental iterative stress calculation. Based on the Sloan incremental elastoplastic algorithm, in each step of the calculation, the stress is calculated according to the current... Moment State With strain increment The stress increment, confining pressure constant condition, and yield function are updated; plastic correction is performed through consistency conditions, and plastic shear strain, deviatoric stress, and hardening / softening index are updated to achieve a complete simulation of the stress-strain response of eroded clay gravel.

6. The method for determining the modified Duncan-Chang model considering gradation and internal erosion according to claim 5, characterized in that, The steps for incremental iterative stress calculation include: Assuming the strain increment is entirely elastic, the stress increment can be calculated using the elastic constitutive model, yielding the following formula: Under constant confining pressure, the following equation is satisfied: Then the yield function is calculated as follows: ； Among them, if ≤0, then and order =0; if If the value is greater than 0, then plastic correction is initiated, including the following steps: By consistency conditions Derivative ; The plastic shear strain is updated to: ; The deviatoric stress is updated to: ; The hardening / softening index has been updated to: ; In the above formula, The calculated deviatoric stress is obtained from the elastic calculation. To correct the degree of erosion The corresponding secant modulus, For strain increment; The trial mean stress is calculated under constant confining pressure. For confining pressure; To test the yield function; , , , The first Peak deviatoric stress, hardening / softening index, plastic shear strain, and plastic hardening modulus at time t. ; To correct the degree of erosion The corresponding peak stress ratio; This represents the increment of plastic shear strain.

7. The method for determining the modified Duncan-Chang model considering gradation and internal erosion according to claim 3, characterized in that, Fine particle loss volume fraction Obtained from sieving tests before and after the erosion test; , , From different The results were obtained by conducting consolidated undrained triaxial shear tests on clay gravel samples.

8. The method for determining the modified Duncan-Chang model considering gradation and internal erosion according to claim 7, characterized in that, confining pressure in triaxial shear test For loads of 30 kPa, 60 kPa, and 100 kPa, axial strain control loading was used, with an axial strain rate of 0.5% / min.

9. A modified Duncan-Chang model considering gradation and internal erosion, characterized in that, The modified Duncan-Chang model, which considers gradation and internal erosion, as described in any one of claims 1-8, is constructed using this method.

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