Construction method of high stress boundary surface constitutive model of sand considering particle crushing
By introducing particle breakage variables and decomposing plastic strain rates, a new constitutive model for high-stress sand is established, which solves the shortcomings of existing models in describing particle breakage under high-stress conditions, and realizes accurate simulation of particle breakage process and precise description of sand mechanical behavior.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- OCEAN UNIV OF CHINA
- Filing Date
- 2026-06-16
- Publication Date
- 2026-07-21
AI Technical Summary
Existing constitutive models for sand and soil are insufficient to accurately describe the irreversible characteristics of particle breakage, the dual breakage mechanism of shear-induced and compression-induced breakage, and the breakage evolution process under complex loading paths under high stress conditions.
A single narrow conical closed yield surface is used as the constitutive model carrier. Particle breakage variables are introduced, and critical state lines and reference compression curves are incorporated. The plastic strain rate is decomposed into two parts: non-breakage induced and breakage induced. The particle breakage evolution equation is established, and a complete high-stress constitutive model is formed by combining boundary surface plasticity theory.
It accurately captures the irreversible historical dependence behavior of particle breakage, uniformly describes the evolution of particle breakage under shear and compression, and successfully reproduces the characteristics of stiffness degradation and shear enhancement in sandy soil.
Smart Images
Figure CN122433449A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of geotechnical mechanics and numerical calculation, and in particular to a method for constructing a constitutive model of a high-stress boundary surface of sand considering particle fragmentation. Background Technology
[0002] High stress conditions are widely present in geotechnical engineering projects such as deep foundations, high earth-rock dams, deep mines, and deep oil-bearing strata. For example, the pressure at the bottom of a high earth-rock dam can reach approximately 7 MPa, and the pressure at the tip of a deep pile can reach up to 350 MPa. Under such high stress conditions, sand particles undergo significant fragmentation, leading to soil stiffness degradation and increased compressibility. Accurately simulating the mechanical behavior of sand with particle fragmentation effects is crucial for engineering design.
[0003] To account for the impact of particle breakage in sandy soil, researchers have developed various constitutive models, mainly divided into implicit and explicit models. Implicit models indirectly incorporate particle breakage effects by modifying hardening laws and stress-dilatation relationships. These models have relatively simple formulas and are easy to calibrate parameters, but they cannot reveal the spatial distribution and extent of particle breakage, and they are difficult to preserve the irreversible nature of particle breakage history, exhibiting significant shortcomings when simulating cyclic loading and unloading paths.
[0004] Explicit models incorporate evolving fragmentation indices into their constitutive equations. However, key challenges remain in the evolution of particle fragmentation indices in existing explicit models: some models directly correlate fragmentation indices with current stress components, failing to capture the irreversible nature of particle fragmentation; while evolution methods based on cumulative plastic work are widely used (e.g., Lade et al., 1996; Einav, 2007; Xiao and Liu, 2017), studies have shown that this method incorrectly predicts volumetric dilatation under isotropic compression conditions. Furthermore, existing models struggle to simultaneously consider both shear-induced and compression-induced particle fragmentation mechanisms, resulting in limited accuracy in describing particle fragmentation evolution under complex loading paths. Summary of the Invention
[0005] The purpose of this invention is to provide a method for constructing a constitutive model of high-stress boundary surface of sand that considers particle breakage, in order to solve the problem that the particle breakage evolution law in existing constitutive models of sand cannot simultaneously and accurately describe irreversible breakage characteristics, shear-induced and compression-induced dual breakage mechanisms, and the breakage evolution process under complex loading paths.
[0006] The above-mentioned objective of this application is achieved through the following technical solution: S1: Establish the constitutive model framework for sandy soil, using a single narrow conical closed yield surface as the carrier of the constitutive model; S2: In the constitutive model framework, a particle breakage variable is introduced to characterize the degree of particle breakage in sand. The particle breakage variable is simultaneously incorporated into the critical state line expression and the reference compression curve expression, so that the critical state line and the reference compression curve shift downward as particle breakage evolves. S3: Using the non-associated flow rule, the plastic strain rate is decomposed into two parts: non-fracture-induced plastic strain rate and fracture-induced plastic strain rate. S4: Using non-fracture-induced plastic strain rate as the driving variable, establish the particle breakage evolution equation and express the evolution rate of particle breakage variable as a function of non-fracture-induced plastic strain rate; S5: Based on the boundary surface plasticity theory and combined with the fracture-induced plastic strain rate, the evolution equations of isotropic hardening variables and back stress ratios are established to form a complete constitutive model of high-stress sand.
[0007] Optional, S1: Establish the constitutive model framework for sandy soil, using a single narrow conical closed yield surface as the carrier of the constitutive model; S2: In the constitutive model framework, a particle breakage variable is introduced to characterize the degree of particle breakage in sand. The particle breakage variable is simultaneously incorporated into the critical state line expression and the reference compression curve expression, so that the critical state line and the reference compression curve shift downward as particle breakage evolves. S3: Using the non-associated flow rule, the plastic strain rate is decomposed into two parts: non-fracture-induced plastic strain rate and fracture-induced plastic strain rate. S4: Using non-fracture-induced plastic strain rate as the driving variable, establish the particle breakage evolution equation and express the evolution rate of particle breakage variable as a function of non-fracture-induced plastic strain rate; S5: Based on the boundary surface plasticity theory and combined with the fracture-induced plastic strain rate, the evolution equations of isotropic hardening variables and back stress ratios are established to form a complete constitutive model of high-stress sand.
[0008] Optionally, step S1 includes: The single narrow conical closed yield surface simultaneously obeys both rotational hardening and isotropic hardening rules, and its yield function is expressed as:
[0009] in, For the deviatoric stress tensor, For the average effective stress, The back stress ratio, For isotropic hardening variables, To control the dimensionless parameters of the wedge-shaped opening of the yield surface, For exponential parameters.
[0010] Optionally, step S2 includes: Consider particle breakage variables The expression for the critical state line is:
[0011]
[0012] in, The critical porosity. For reference porosity, The initial limiting void ratio, The limiting void ratio decreases as particles break down. This is the slope parameter of the critical state line. Atmospheric pressure, For exponential parameters, For particle breakage variables The limiting porosity at that time; Consider particle breakage variables The reference compression curve expression is:
[0013]
[0014] in, For reference, the porosity on the compression curve, The compression slope related to the back stress ratio, For reference compression slope, , , For model parameters, Lode's angle functions The critical stress ratio under triaxial compression conditions; Represents the back stress ratio tensor The double dot product.
[0015] Optionally, step S3 includes: The plastic strain rate decomposition is applicable to both the plastic strain rate caused by changes in stress ratio and the plastic strain rate caused by changes in average effective stress under a fixed stress ratio. The expression for the decomposition of plastic strain rate is:
[0016]
[0017]
[0018]
[0019] in, Represents the plastic deviatoric strain rate tensor; Represents the tensor of the plastic flow direction; Represents the relative stress ratio tensor; Indicates the strain rate of a plastic body; Represents normalized or cumulative strain in plastic bodies; This represents the plastic strain rate caused by the change in stress ratio. Represents the plastic strain rate caused by the change in average effective stress at a fixed stress ratio, indicated by the superscript. Indicates the non-fragmentation induced portion, superscript Indicates the fragmentation-induced portion. As a plastic multiplier, Represents plastic multipliers The non-negative values of ; It is a stress-to-distance function. and These are model constants. The dilatation coefficient is denoted by . It is a function related to the back stress ratio. These are the model parameters.
[0020] Optionally, step S4 includes: The particle breakage evolution equation considers both shear-induced and compression-induced particle breakage mechanisms, and uses Macaulay brackets to ensure the irreversibility of the breakage process. The particle breakage evolution equation in multiaxial stress space is expressed as: Fracture variable evolution rate under variable stress ratio loading conditions ,as follows:
[0021] Fragmentation Variable Evolution Rate under Constant Stress Ratio Loading Conditions ,as follows:
[0022] in, and To control the non-negative model constants of particle crushing rate, For Heaviside step function, Let be the deviatoric stress ratio direction tensor. This is the tensor in the direction of plastic flow; This represents the normalized evolution rate of particle breakage variables; The strain rate of the plastic body induced by particle breakage is calculated using the following expression: Under varying stress ratio loading conditions:
[0023] Under constant stress ratio loading conditions:
[0024] in, This represents the current porosity. Indicates the limiting void ratio Rate of change over time.
[0025] Optionally, step S5 includes: Total strain rate It consists of two parts: the volumetric strain rate caused by particle breakage. and the volumetric strain rate caused by non-particle fragmentation ;
[0026] The non-particle breakage portion includes both recoverable elastic strain and irrecoverable plastic strain caused by particle sliding, rolling and rearrangement; Elastomer strain rate on reference compression curve Should be smaller Defined as:
[0027] Where k are non-negative model parameters; Indicates the reference compression curve at - Slope parameter on the plane; Indicates the reference void ratio; Mean effective stress The first derivative with respect to time; The strain rate of the plastic body caused by non-granular fragmentation on the reference compression curve It is through the total strain rate Subtract What was obtained:
[0028] Based on boundary surface technology, the second contribution of plastic body strain caused by non-particle fragmentation is... Defined as:
[0029]
[0030] in Indicates back stress ratio Related functions; Representation and state parameters Related boundary scaling functions; This represents the shape control parameters of the boundary surface scaling function; Isotropic hardening variables The evolution equation is:
[0031] in, For the boundary surface scaling function, These are state parameters; Back stress ratio The evolution equation is:
[0032]
[0033]
[0034] in, Indicates the back stress ratio evolution plastic modulus; The image back stress ratio on the boundary surface, For non-negative model parameters, This represents the initial value of the back stress ratio; This represents the projection of the back stress ratio increment onto the loading direction; For the subelastic model variables, The influence function of the overconsolidation ratio, This is the porosity influence function.
[0035] An electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform a constitutive model construction method for a high-stress boundary surface of sand considering particle fragmentation.
[0036] A computer-readable storage medium storing instructions that, when executed, perform a method for constructing a constitutive model of a high-stress boundary surface of sandy soil that takes into account particle fragmentation.
[0037] The beneficial effects of the technical solution provided in this application are: 1. The original implicit model for handling particle breakage is changed to an explicit expression, introducing a breakage variable that evolves with the loading history, and using Macaulay brackets to ensure the irreversibility of the breakage process. This accurately captures the irreversible historical dependency behavior of particle breakage under cyclic loading and unloading.
[0038] 2. The proposed particle breakage evolution law is the first to simultaneously consider both shear-induced and compression-induced breakage mechanisms, with non-breakage plastic strain rate as the driving variable. It provides a unified description of particle breakage evolution under both shear and compression pathways; 3. By incorporating the fracturing variable into both the critical state line and the reference compression curve, and shifting both downwards with the degree of fracturing, the stiffness degradation and shear enhancement characteristics of sandy soil under high pressure were successfully reproduced.
[0039] 2. The plastic strain is first decomposed according to the loading mechanism (stress ratio change / constant stress ratio), and then further subdivided into four parts according to whether it is non-fractured or fractured. Attached Figure Description
[0040] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a constitutive model framework diagram in the embodiments of this application; Figure 2 This is a schematic diagram of CSL and RCC under different particle breakage degrees in the embodiments of this application; Figure 3 This is a schematic diagram of CSL and RCC under different particle breakage degrees in the embodiments of this application; Figure 4 These are the parameters in the embodiments of this application. Figure showing the influence of conventional drainage triaxial test results under confining pressure of 40 MPa; Figure 5 This is a comparison diagram of simulation and experiment in the constant stress ratio compression test of Fujian sand in the embodiments of this application; Figure 6 This is a comparison diagram of simulation and experiment in the conventional drainage triaxial test of Fujian sand in the embodiments of this application; Figure 7 This is a schematic diagram of the electronic device structure in the embodiments of this application. Detailed Implementation
[0041] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.
[0042] The embodiments of this application provide a method for constructing a constitutive model of a high-stress boundary surface of sand that takes into account particle fragmentation.
[0043] Please refer to Figure 1 , Figure 1 This is a constitutive model framework diagram of a constitutive model construction method for high-stress boundary surfaces of sand considering particle fragmentation, as described in an embodiment of this application, including: S1: Establish the constitutive model framework for sandy soil, using a single narrow conical closed yield surface as the carrier of the constitutive model; S2: In the constitutive model framework, a particle breakage variable is introduced to characterize the degree of particle breakage in sand. The particle breakage variable is simultaneously incorporated into the critical state line expression and the reference compression curve expression, so that the critical state line and the reference compression curve shift downward as particle breakage evolves. S3: Using the non-associated flow rule, the plastic strain rate is decomposed into two parts: non-fracture-induced plastic strain rate and fracture-induced plastic strain rate. S4: Using non-fracture-induced plastic strain rate as the driving variable, establish the particle breakage evolution equation and express the evolution rate of particle breakage variable as a function of non-fracture-induced plastic strain rate; S5: Based on the boundary surface plasticity theory and combined with the fracture-induced plastic strain rate, the evolution equations of isotropic hardening variables and back stress ratios are established to form a complete constitutive model of high-stress sand.
[0044] This application provides an embodiment as follows, which makes three key improvements to the SANISAND-H model: (1) a particle breakage variable is introduced to quantify the degree of particle breakage and is simultaneously incorporated into the definition of the critical state line and the reference compression curve, so that these two curves evolve with particle breakage; (2) the plastic strain is reasonably decomposed into non-breakage-induced plastic strain and breakage-induced plastic strain; (3) a new particle breakage variable evolution equation is established, which simultaneously considers the particle breakage mechanism induced by shear and compression.
[0045] As an example, under high stress conditions, the particle breakage effect of sand becomes significant, and accurate simulation of its mechanical behavior is crucial for geotechnical engineering applications such as deep foundations, high earth-rock dams, and impact loading. This paper proposes a novel boundary surface model, an extension of the SANISAND-H model, employing a single narrow conical closed yield surface that simultaneously undergoes rotational hardening and isotropic hardening. The model replaces the implicit treatment of particle breakage in the SANISAND-H model with an explicit expression by introducing an evolving breakage variable, which is simultaneously incorporated into the expressions of the critical state line and the reference compression curve. The plastic strain rate is decomposed into two parts: breakage-induced and non-breakage-induced. A novel particle breakage evolution law is proposed, which can simultaneously consider shear-induced and compression-induced particle breakage. The breakage rate is defined as a function of the non-breakage plastic strain rate. The model is validated using laboratory tests on sand under different pressure ranges and loading paths. The results show that the model can accurately capture the evolution process of particle breakage and its influence on the mechanical behavior of sand.
[0046] Step S1 includes: The single narrow conical closed yield surface simultaneously obeys both rotational hardening and isotropic hardening rules, and its yield function is expressed as:
[0047] in, For the deviatoric stress tensor, For the average effective stress, The back stress ratio, For isotropic hardening variables, To control the dimensionless parameters of the wedge-shaped opening of the yield surface, For exponential parameters.
[0048] This application provides an embodiment as follows: the back stress ratio tensor reflects the kinematic hardening of the yield surface; the isotropic hardening variable controls the size of the yield surface. The exponent n takes a large default value of 20. For clarity, Figure 1 (a) The yield surface was plotted in triaxial stress space. As shown in the figure, when much smaller At this point, the yield surface tends to be wedge-shaped in the region outside its tip. The wedge opening is controlled by a dimensionless parameter m, with a default constant value of 0.05 to ensure that the sand has an elastic range close to zero. In the stress ratio π plane ( Figure 1 b) On the yield surface, the yield surface exhibits a ratio of back stress to back stress. A small circle centered on the center.
[0049] For by Isotropic hardening under change control is proposed, with a reference compression curve (RCC) as the boundary surface in the e-lnp space. Figure 2 This curve depends on the back stress ratio α and is used to calculate the strain of a plastic body under constant stress ratio loading, and then derive... The evolution rate. Specifically, the strain rate of the plastic body in the current state is calculated by scaling the rate of change on the RCC as a function of the porosity ratio "distance," which measures the difference between the current e and the corresponding p on the RCC. The difference between them.
[0050] For by Isotropic hardening under change control is proposed, with a reference compression curve (RCC) as the boundary surface in the e-lnp space. Figure 2 This curve depends on the back stress ratio α and is used to calculate the strain of a plastic body under constant stress ratio loading, and then derive... The evolution rate. Specifically, the strain rate of the plastic body in the current state is calculated by scaling the rate of change on the RCC as a function of the porosity ratio "distance," which measures the difference between the current e and the corresponding p on the RCC. The difference between them.
[0051] Step S2 includes: Consider particle breakage variables The expression for the critical state line is:
[0052]
[0053] in, The critical porosity. For reference porosity, The initial limiting void ratio, The limiting void ratio decreases as particles break down. This is the slope parameter of the critical state line. Atmospheric pressure, For exponential parameters, For particle breakage variables The limiting porosity at that time; Consider particle breakage variables The reference compression curve expression is:
[0054]
[0055] in, For reference, the porosity on the compression curve, The compression slope related to the back stress ratio, For reference compression slope, , , For model parameters, Lode's angle functions The critical stress ratio under triaxial compression conditions; Represents the back stress ratio tensor The double dot product.
[0056] As one example, numerous studies on breakable soils have shown that increased particle breakage leads to a downward shift of the critical state line (CSL) in e-lnp space, with the gradient remaining constant. However, there are exceptions; triaxial tests on pre-broken sand have also shown a counter-clockwise rotation of the CSL. To simplify the model, this application assumes that particle breakage only causes a downward shift of the CSL. Similar to the CSL, the reference compression curve (RCC) is also assumed to shift downward with increasing particle breakage. Figure 3 ) Figure 3 The RCC was demonstrated The case of downward translation, and CSL following Translational changes.
[0057] Step S3 includes: The plastic strain rate decomposition is applicable to both the plastic strain rate caused by changes in stress ratio and the plastic strain rate caused by changes in average effective stress under a fixed stress ratio. The expression for the decomposition of plastic strain rate is:
[0058]
[0059]
[0060]
[0061] in, Represents the plastic deviatoric strain rate tensor; Represents the tensor of the plastic flow direction; Represents the relative stress ratio tensor; Indicates the strain rate of a plastic body; Represents normalized or cumulative strain in plastic bodies; This represents the plastic strain rate caused by the change in stress ratio. Represents the plastic strain rate caused by the change in average effective stress at a fixed stress ratio, indicated by the superscript. Indicates the non-fragmentation induced portion, superscript Indicates the fragmentation-induced portion. As a plastic multiplier, Represents plastic multipliers The non-negative values of ; It is a stress-to-distance function. and These are model constants. The dilatation coefficient is denoted by . It is a function related to the back stress ratio. These are the model parameters.
[0062] As one embodiment, the SANISAND-H model decomposes the plastic strain rate into two parts: the first part is caused by changes in the stress ratio, and the second part is caused by changes in stress at a fixed stress ratio. To better capture the influence of particle breakage on sand deformation, the new model further subdivides these two plastic strain rate components into two parts each: one part is induced by particle breakage, and the other part is independent of particle breakage. The model constant X is used to scale the breakage-induced biased plastic strain component caused by changes in the stress ratio (i.e., the contribution of the first part). For the biased plastic strain rate caused by constant stress ratio loading (i.e., the contribution of the second part), the model constant X acts as a uniform scaling factor, affecting both the non-breakage-induced and breakage-induced components.
[0063] Step S4 includes: The particle breakage evolution equation considers both shear-induced and compression-induced particle breakage mechanisms, and uses Macaulay brackets to ensure the irreversibility of the breakage process. The particle breakage evolution equation in multiaxial stress space is expressed as: Fracture variable evolution rate under variable stress ratio loading conditions ,as follows:
[0064] Fragmentation Variable Evolution Rate under Constant Stress Ratio Loading Conditions ,as follows:
[0065] in, and To control the non-negative model constants of particle crushing rate, For Heaviside step function, Let be the deviatoric stress ratio direction tensor. This is the tensor in the direction of plastic flow; This represents the normalized evolution rate of particle breakage variables; The strain rate of the plastic body induced by particle breakage is calculated using the following expression: Under varying stress ratio loading conditions:
[0066] Under constant stress ratio loading conditions:
[0067] in, This represents the current porosity. Indicates the limiting void ratio Rate of change over time.
[0068] As one example, during the shearing process with varying stress ratio, the void ratio tends to approach the critical state line (CSL), while the CSL itself shifts downward due to particle breakage.
[0069] Step S5 includes: As one embodiment, the evolution of the isotropic hardening variable is controlled solely by the second contribution term of the plastic strain rate induced by constant stress ratio loading. A reference compression curve (RCC) evolving with particle breakage is used as the boundary surface in ep space to determine... If the current state point ep is located on RCC, the total strain rate is... The time derivative is obtained by referring to the relevant expression of the compression curve.
[0070] Total strain rate It consists of two parts: the volumetric strain rate caused by particle breakage. and the volumetric strain rate caused by non-particle fragmentation ;
[0071] The non-particle breakage portion includes both recoverable elastic strain and irrecoverable plastic strain caused by particle sliding, rolling and rearrangement; Elastomer strain rate on reference compression curve Should be smaller Defined as:
[0072] Where k are non-negative model parameters; Indicates the reference compression curve at - Slope parameter on the plane; Indicates the reference void ratio; Mean effective stress The first derivative with respect to time; The strain rate of the plastic body caused by non-granular fragmentation on the reference compression curve It is through the total strain rate Subtract What was obtained:
[0073] Based on boundary surface technology, the second contribution of plastic body strain caused by non-particle fragmentation is... Defined as:
[0074]
[0075] in Indicates back stress ratio Related functions; Representation and state parameters Related boundary scaling functions; This represents the shape control parameters of the boundary surface scaling function; Isotropic hardening variables The evolution equation is:
[0076] in, For the boundary surface scaling function, These are state parameters.
[0077] Back stress ratio The evolution equation is:
[0078]
[0079]
[0080] in, Indicates the back stress ratio evolution plastic modulus; The image back stress ratio on the boundary surface, For non-negative model parameters, This represents the initial value of the back stress ratio; This represents the projection of the back stress ratio increment onto the loading direction; For the subelastic model variables, The influence function of the overconsolidation ratio, This is the porosity influence function.
[0081] As one example, the metaelastic model variables allow the effective plastic modulus to exhibit a dependence on the mean effective stress p similar to that of the elastic shear modulus G. (Function) This reflects the increased stiffness with increasing overconsolidation ratio and serves as an effective constitutive component for improving the simulation of undrained response under high pressure conditions. (Function) The effect of the porosity e on the reduction of h was introduced.
[0082] As one example, the SANISAND-HB model requires calibration of 19 material constants, including 4 new parameters that take into account particle breakage. , , and ,in The determination was performed by compressing the sand sample to a sufficiently high pressure to achieve complete particle breakage. and Calibration was performed using crushing index test data. The model was determined using conventional triaxial shear test data under high confining pressure through a trial-and-error method. The model is applicable to the simulation and prediction of the mechanical behavior of sand under high stress conditions, including pressures of up to 350 MPa at the pile tip of deep driven pile foundations, pressures of up to 7 MPa at the bottom of high earth-rock dams, and high-stress geotechnical engineering scenarios such as deep oil-bearing strata and deep mines.
[0083] As one example, constant stress ratio compression and drained triaxial shear tests were conducted on Fujian quartz sand. The comparison between model predictions and experimental results (hollow symbols) is shown below. Figure 5 and Figure 6 .like Figure 5 As shown, the proposed model successfully captures the compressibility behavior of Fujian sand, with its compressibility increasing with increasing stress ratio. This increase in compressibility is attributed to more significant particle breakage, such as... Figure 5 As shown by the dashed line in (a). Figure 5(b) The relationship between the measured relative fragmentation index and total input power at p = 10, 20, 30, 40, and 50 MPa was plotted. It can be seen that, under the same mean effective pressure p, specimens compressed at higher stress ratios exhibit larger relative fragmentation index values. However, the relationship between the relative fragmentation index and total input power appears to be relatively less affected by the stress ratio. The proposed model reproduces this trend well, indicating that the proposed compression-induced particle fragmentation evolution law is effective.
[0084] Figure 6 The model predictions (solid line) were further compared with the results of drained triaxial shear tests (hollow symbols) conducted on Fujian sand within a wide confining pressure range of 1 to 40 MPa. The void ratio and relative fragmentation index after consolidation under different confining pressures were obtained from... Figure 5 Simulation of a medium-compression test. Figure 6 (c) The relationship between the measured relative fracture index and the total input work w under different axial strains is plotted. In the legend, for example, "T2-20" represents the relative fracture index measured at a confining pressure of 2 MPa and an axial strain of 20%. The solid line represents the simulated evolution of the relative fracture index from 0 to 20% axial strain. Figure 6 As shown, the predicted response accurately captures the stress-strain relationship and volumetric response. Furthermore, particle breakage was also well predicted, further validating the effectiveness of the particle breakage evolution law proposed in this study.
[0085] A novel boundary surface model, SANISAND-HB, is proposed to simulate the shear and compressive stress response of sand over a wide pressure range, explicitly considering the particle breakage effect. This model is an extension of the SANISAND-H model, replacing the implicit treatment in the original model that failed to adequately reflect the irreversible nature of particle breakage with explicit treatment. The new model retains two fundamental features of its predecessor: the use of a single narrow closed conical yield surface subject to rotational hardening and isotropic hardening, and the decomposition of plastic strain into a portion caused by stress ratio variation and a portion caused by stress variation at a fixed stress ratio. Both the critical state line and the reference compression curve shift downwards in the e-logp plane as particle breakage intensifies. The plastic strain rate is subdivided into non-breakage-induced and breakage-induced components. A new equation for the particle breakage rate related to the non-breakage plastic strain rate is proposed. Validation through laboratory tests on sand demonstrates that the proposed equation accurately describes the particle breakage evolution under various loading paths, including constant stress ratio loading and triaxial compression. Furthermore, the model reproduces well the stiffness reduction and shear-intensification behavior of sand caused by particle breakage.
[0086] The proposed particle breakage rate equation can also be incorporated into other constitutive frameworks, provided that the plastic strain is properly decomposed into breakage-induced and non-breakage-induced components. Currently, the reliability of this equation has only been verified under monotonic loading paths. Nevertheless, based on its formulation, the equation also has potential applications under cyclic loading. Furthermore, since this model is developed within a boundary-surface plastic framework, it has an inherent advantage in capturing cyclic behavior compared to other models. However, to achieve more accurate simulations under cyclic loading, additional constitutive features can be introduced.
[0087] This application also discloses an electronic device. (See reference...) Figure 7 , Figure 7 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application. The electronic device 500 may include: at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.
[0088] The communication bus 502 is used to enable communication between these components.
[0089] The user interface 503 may include a display screen, and optionally, the user interface 503 may also include a standard wired interface or a wireless interface.
[0090] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).
[0091] This application also discloses a computer-readable storage medium storing multiple instructions adapted for loading by a processor to execute the above-described method for constructing a constitutive model of a high-stress boundary surface of sand considering particle fragmentation.
[0092] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure.
[0093] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.
Claims
1. A method for constructing a constitutive model of a high-stress boundary surface of sandy soil considering particle fragmentation, characterized in that, The method includes the following steps: S1: Establish the constitutive model framework for sandy soil, using a single narrow conical closed yield surface as the carrier of the constitutive model; S2: In the constitutive model framework, a particle breakage variable is introduced to characterize the degree of particle breakage in sand. The particle breakage variable is simultaneously incorporated into the critical state line expression and the reference compression curve expression, so that the critical state line and the reference compression curve shift downward as particle breakage evolves. S3: Using the non-associated flow rule, the plastic strain rate is decomposed into two parts: non-fracture-induced plastic strain rate and fracture-induced plastic strain rate. S4: Using non-fracture-induced plastic strain rate as the driving variable, establish the particle breakage evolution equation and express the evolution rate of particle breakage variable as a function of non-fracture-induced plastic strain rate; S5: Based on the boundary surface plasticity theory and combined with the fracture-induced plastic strain rate, the evolution equations of isotropic hardening variables and back stress ratios are established to form a complete constitutive model of high-stress sand.
2. The method for constructing a constitutive model of a high-stress boundary surface of sand considering particle fragmentation as described in claim 1, characterized in that, Step S1 includes: The single narrow conical closed yield surface simultaneously obeys both rotational hardening and isotropic hardening rules, and its yield function is expressed as: in, For the deviatoric stress tensor, For the average effective stress, The back stress ratio, For isotropic hardening variables, To control the dimensionless parameters of the wedge-shaped opening of the yield surface, For exponential parameters.
3. The method for constructing a constitutive model of a high-stress boundary surface of sand considering particle fragmentation as described in claim 2, characterized in that, Step S2 includes: Consider particle breakage variables The expression for the critical state line is: in, The critical porosity. For reference porosity, The initial limiting void ratio, The limiting void ratio decreases as particles break down. This is the slope parameter of the critical state line. Atmospheric pressure, For exponential parameters, For particle breakage variables The limiting porosity at that time; Consider particle breakage variables The reference compression curve expression is: in, For reference, the porosity on the compression curve, The compression slope related to the back stress ratio, For reference compression slope, , , For model parameters, Lode's angle functions The critical stress ratio under triaxial compression conditions; Represents the back stress ratio tensor The double dot product.
4. The method for constructing a constitutive model of a high-stress boundary surface of sand considering particle fragmentation as described in claim 3, characterized in that, Step S3 includes: The plastic strain rate decomposition is applicable to both the plastic strain rate caused by changes in stress ratio and the plastic strain rate caused by changes in average effective stress under a fixed stress ratio. The expression for the decomposition of plastic strain rate is: in, Represents the plastic deviatoric strain rate tensor; Represents the tensor of the plastic flow direction; Represents the relative stress ratio tensor; Indicates the strain rate of a plastic body; Represents normalized or cumulative strain in plastic bodies; This represents the plastic strain rate caused by the change in stress ratio. Represents the plastic strain rate caused by the change in average effective stress at a fixed stress ratio, indicated by the superscript. Indicates the non-fragmentation induced portion, superscript Indicates the fragmentation-induced portion. As a plastic multiplier, Represents plastic multipliers The non-negative values of ; It is a stress-to-distance function. and These are model constants. The dilatation coefficient is denoted by . It is a function related to the back stress ratio. These are the model parameters.
5. The method for constructing a constitutive model of a high-stress boundary surface of sand considering particle fragmentation as described in claim 4, characterized in that, Step S4 includes: The particle breakage evolution equation considers both shear-induced and compression-induced particle breakage mechanisms, and uses Macaulay brackets to ensure the irreversibility of the breakage process. The particle breakage evolution equation in multiaxial stress space is expressed as: Fracture variable evolution rate under variable stress ratio loading conditions ,as follows: Fragmentation Variable Evolution Rate under Constant Stress Ratio Loading Conditions ,as follows: in, and To control the non-negative model constants of particle crushing rate, For Heaviside step function, Let be the deviatoric stress ratio direction tensor. This is the tensor in the direction of plastic flow; This represents the normalized evolution rate of particle breakage variables; The strain rate of the plastic body induced by particle breakage is calculated using the following expression: Under varying stress ratio loading conditions: Under constant stress ratio loading conditions: in, This represents the current porosity. Indicates the limiting void ratio Rate of change over time.
6. The method for constructing a constitutive model of a high-stress boundary surface of sand considering particle fragmentation as described in claim 5, characterized in that, Step S5 includes: Total strain rate It consists of two parts: the volumetric strain rate caused by particle breakage. and the volumetric strain rate caused by non-particle fragmentation ; The non-particle breakage portion includes both recoverable elastic strain and irrecoverable plastic strain caused by particle sliding, rolling and rearrangement; Elastomer strain rate on reference compression curve Should be smaller Defined as: Where k are non-negative model parameters; Indicates the reference compression curve at - Slope parameter on the plane; Indicates the reference void ratio; Mean effective stress The first derivative with respect to time; The strain rate of the plastic body caused by non-granular fragmentation on the reference compression curve It is through the total strain rate Subtract What was obtained: Based on boundary surface technology, the second contribution of plastic body strain caused by non-particle fragmentation is... Defined as: in Indicates back stress ratio Related functions; Representation and state parameters Related boundary scaling functions; This represents the shape control parameters of the boundary surface scaling function; Isotropic hardening variables The evolution equation is: in, For the boundary surface scaling function, These are state parameters; Back stress ratio The evolution equation is: in, Indicates the back stress ratio evolution plastic modulus; The image back stress ratio on the boundary surface, For non-negative model parameters, This represents the initial value of the back stress ratio; This represents the projection of the back stress ratio increment onto the loading direction; For the subelastic model variables, The influence function of the overconsolidation ratio, This is the porosity influence function.
7. An electronic device, characterized in that, The device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform the constitutive model construction method for high-stress boundary surfaces of sand considering particle fragmentation as described in any one of claims 1-6.
8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a computer, perform the constitutive model construction method for high-stress boundary surfaces of sandy soil considering particle fragmentation as described in any one of claims 1-6.