Method for constructing constitutive model of sand cemented by micp based on unified hardening theory

Abstract

The present application relates to a MICP cemented sand constitutive model construction method based on unified hardening theory, and belongs to the technical field of simulation of mechanical properties of geotechnical engineering materials. The method takes the unified hardening (UH) model as a basic framework, introduces a cementation additional consolidation pressure correction initial yield surface positively related to the calcium carbonate content, constructs a cementation strength evolution equation coupled with the calcium carbonate content and the confining pressure, modifies the shear dilatancy equation by using the effective deviatoric stress ratio, optimizes the hardening parameters by using the pre-consolidation pressure of cemented sand, and realizes continuous calculation of the stress-strain relationship by solving the consistency condition. The present application can accurately simulate the stress-strain and shear dilatancy characteristics of MICP cemented sand under different cementation degrees and different confining pressures, reduces the simulation error from 25%-33% to within 3%, the model parameters can be determined by conventional soil test, and the present application is suitable for sand ground reinforcement, slope protection, soil site repair and other engineering, and provides reliable support for the mechanical behavior prediction and numerical simulation of MICP solidified soil.

Description

Technical Field

[0001] This invention relates to the field of simulation technology of mechanical properties of geotechnical engineering materials, and in particular to a method for constructing a constitutive model of MICP cemented sand based on the unified hardening theory. Background Technology

[0002] Microbial-induced calcium carbonate precipitation (MICP) is a green and environmentally friendly soil reinforcement technology. It works by using urease-producing bacteria to hydrolyze urea to generate carbonate ions (CO3-). 2- ), and free calcium ions (Ca) in the environment 2+ This process combines sand particles with high-strength calcium carbonate (CaCO3) crystals to form on the surface and at the contact points of the sand particles. These crystals bind the originally loose sand into a cohesive, solidified soil mass by encapsulating the sand particles, filling pores, and forming cementing bonds between particles. This technology shows broad application prospects in geotechnical engineering fields such as sandy soil foundation reinforcement, slope protection, cultural relic restoration, and liquefaction prevention.

[0003] The mechanical properties of MICP-stabilized soils vary significantly with the degree of cementation (calcium carbonate content). Low-cemented soils exhibit mechanical behavior similar to loose sand, while high-cemented soils display typical structural soil characteristics (high strength, significant shear dilatation, and strain softening). These complex mechanical behaviors pose a serious challenge to conducting related engineering numerical simulations and designs.

[0004] Existing constitutive models (such as the Unified Hardening Model UH) perform well in simulating low-cemented soils, but their accuracy in simulating high-cemented soils is limited because they do not fully consider the strengthening effect of the calcium carbonate cementing network and the failure evolution process under load. The simulation error is usually between 25% and 33%, which is insufficient to meet the accuracy requirements of engineering design and numerical simulation. Some improved models for MICP cemented soils, although considering the influence of calcium carbonate content, suffer from inaccurate prediction of shear dilatation characteristics and lack of coupling of the moderating effect of confining pressure on cement strength, thus limiting their engineering applicability.

[0005] Therefore, there is an urgent need to develop a constitutive model that can accurately characterize the mechanical properties of MICP-cemented sand with different degrees of cementation. By quantifying the influence of cementation on the yield surface, dilatation characteristics, and hardening process, the simulation accuracy can be improved, providing reliable support for the engineering application of MICP technology. Summary of the Invention

[0006] The purpose of this invention is to provide a constitutive model construction method for MICP cemented sand based on the unified hardening theory, aiming to solve the technical problems of low accuracy in simulating the mechanical behavior of MICP cemented sand under different cementation degrees and confining pressures, and the inability to accurately characterize the shear dilatation characteristics and cementation failure evolution process of highly cemented soils.

[0007] The constitutive model construction method for MICP cemented sand based on unified hardening theory provided by this invention adopts the following technical solution: The method for constructing a constitutive model of MICP cemented sand based on the unified hardening theory is characterized by the following steps: 1) A unified hardening model is selected as the basic framework; 2) Modify the initial yield surface: Introduce additional consolidation pressure that is positively correlated with calcium carbonate content. The initial consolidation pressure of the original loose sandy soil Corrected to the preconsolidation pressure of cemented sand The corrected formula is as follows: This achieves the expansion of the yield surface; 3) Constructing the equation for the evolution of cementation strength: Establishing the additional consolidation pressure of cementation. With plastic deviatoric strain The evolution equation is a cumulative and decaying equation that couples the calcium carbonate content Cc with the confining pressure. The impact; 4) Modified shear dilatation equation: using effective deviatoric stress ratio Replacement of original deviatoric stress ratio The corrected shear dilatation equation is: ; in, For the plastic volumetric strain increment, is the plastic deviatoric strain increment, and M is the critical state stress ratio; 5) Correct hardening parameters: Replace the baseline parameter in hardening parameter H with the preconsolidation pressure of cemented sand. This allows the hardening parameters to simultaneously reflect the strengthening-damage process of the cemented network and the accumulation of plastic work in the soil matrix; 6) Solving for consistency conditions: Based on the modified yield function, cementation strength evolution equation and hardening parameters, the plastic multiplier is derived, and combined with the generalized Hooke's law and flow rule, the continuous calculation of stress-strain relationship is realized.

[0008] Preferably, the cementation adds consolidation pressure. The introduction is based on the MICP bonding mechanism; The mechanism includes three ways in which calcium carbonate crystals construct a continuous cemented network through surface adhesion, interstitial crystal cluster growth, and contact interface cementation, so that the solidified soil exhibits mechanical properties similar to structured soil.

[0009] Preferably, in step 3), the expression for the bonding strength evolution equation is: , in, For material parameters, For plastic deviatoric strain, This represents the average effective stress.

[0010] Preferably, in step 5), the corrected hardening parameter H is expressed by the overconsolidation parameter R, and the expression for the overconsolidation parameter R is: , in, The initial cementation and early consolidation pressure, , Let the slope of the isotropic compression line of the remolded soil be the e-lnp coordinate. The slope of the rebound line. This represents the initial void ratio.

[0011] Preferably, in step 3), the calcium carbonate content Cc is determined by acid hydrolysis. The specific steps are as follows: the cemented sample is crushed and reacted with excess hydrochloric acid, the generated CO2 is collected and its mass is measured, and the mass fraction of calcium carbonate is calculated based on the stoichiometric relationship of the chemical reaction.

[0012] Preferably, in step 3), the material parameters in the bonding strength evolution equation... The data were obtained by fitting triaxial shear test data of MIP cemented sand under different confining pressures and different calcium carbonate contents.

[0013] Preferably, in step 3), the preconsolidation pressure of the cemented sand is... The maximum value is The relationship between the calcium carbonate content Cc and the content of calcium carbonate follows an exponential function form. , in, , , These are the material constants obtained by fitting experimental data.

[0014] On the other hand, the present invention also provides a MICP cemented sand constitutive model constructed using the above method, employing the following technical solution: The constitutive model of cemented sandy soil using MICP (Micro-Integrated Polymerization) includes the following parameters: physical parameters of the sandy soil, critical state parameters, and cementation characteristic parameters. The bonding characteristic parameters include the material parameters in the bonding strength evolution equation. .

[0015] Furthermore, the present invention also provides the application of the MICP cemented sand constitutive model in the prediction of the mechanical behavior of MICP solidified soil or in finite element numerical simulation. The application is characterized in that the application includes the prediction and numerical analysis of stress-strain behavior in sandy soil foundation reinforcement, slope protection or site restoration projects.

[0016] In summary, the present invention has the following beneficial technical effects: 1. This invention is the first to use calcium carbonate content (Cc) as a quantitative indicator, accurately determined by acid hydrolysis, and incorporated into the initial yield surface correction of the constitutive model, thus establishing the cementation additional consolidation pressure. The quantitative relationship between Cc and Cc. Compared with the existing model which relies solely on empirical parameter adjustments, this invention achieves graded characterization of MIP-solidified soils with different degrees of cementation (low, medium, and high), and can accurately simulate the full range of mechanical behavior from loose sand to highly structured soils.

[0017] 2. The bonding strength evolution equation constructed in this invention The model simultaneously considers the synergistic effects of calcium carbonate content and confining pressure on cementation strength. This equation accurately describes: in the initial state, cementation strength increases exponentially with increasing Cc; during shearing, cementation strength gradually decreases with the accumulation of plastic deviatoric strain; and the cementation failure rate slows down under high confining pressure. This solves the key technical challenge of existing models being unable to simulate the transition from brittle to ductile failure in cemented soils.

[0018] 3. Within a wide range of confining pressures (100-300 kPa) and calcium carbonate content (1.6%-8.1%), the constitutive model constructed in this invention maintains a relative error of less than 3% in simulating the peak strength, maximum volumetric strain (dilatation), and the entire stress-strain curve of MIP-cemented sand. Compared to existing unified hardening (UH) models, the simulation error has been significantly reduced from 25-33% to below 3%, representing an order of magnitude improvement. This breakthrough in accuracy allows the model to directly serve numerical simulation and design in practical engineering projects, overcoming the previous limitation of only being applicable to qualitative analysis.

[0019] 4. The model parameters in this invention can all be determined by conventional triaxial tests or acid hydrolysis, without the need for complex testing methods, which facilitates engineering applications.

[0020] 5. This invention is based on the effective deviatoric stress ratio modified dilatation equation to accurately capture the dilatation characteristics of cemented sand, especially the post-peak dilatation softening phenomenon. Attached Figure Description

[0021] Figure 1 In the middle a, it is a schematic diagram of MIP reinforcement for untreated sandy soil; Figure 1 In the middle b, it is a schematic diagram of MIP reinforcement after microbial solidification; Figure 2 A comparison diagram of the yield surfaces of the cemented model and the UH model; Figure 3 A comparison diagram of the shear dilatation relationship between cemented sand and normally consolidated soil; Figure 4 A comparison of stress-strain curves from cementation model simulation, UH model simulation, and experimental data; Figure 5 This is a comparison chart of shear dilatation curves from cementation model simulation, UH model simulation, and experimental data. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will be described in conjunction with the accompanying drawings. Figure 1-5 The technical solutions of the present invention have been clearly and completely described. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Example Example 1 This embodiment provides a method for constructing a constitutive model of MICP cemented sand based on the unified hardening theory, including the following steps: S1. Analysis of the MICP bonding mechanism Combination Figure 1 , Figure 1 In the middle, a is a schematic diagram of MICP reinforcement of untreated sandy soil. Figure 1 Figure b shows a schematic diagram of MIP reinforcement after microbial solidification. During the MIP cementation process, calcium carbonate crystals act on sand particles in three ways: 1. Directly adhering to the surface of sand particles, increasing interparticle friction; 2. Growing and aggregating in the interparticle gaps to form crystal clusters, achieving indirect particle overlap; 3. Directional deposition at the particle contact interface, forming direct cementation bonds. These three actions synergistically construct a continuous cementation network, giving the solidified soil the mechanical properties of structured soil (high initial stiffness, increased peak strength, significant shear dilatation, and strain softening).

[0024] S2. Select the UH model as the basic framework. The core assumption of the UH model is retained: the total strain of the soil is decomposed into elastic strain and plastic strain, i.e. , in, For total strain, For elastic strain, This is plastic strain.

[0025] The elastic component is calculated using the generalized Hooke's law: , , in, The average effective stress increment, For the deviatoric stress increment, For bulk modulus, For shear modulus, For elastic volumetric strain increment, This represents the elastic deviatoric strain increment.

[0026] The plastic part is solved by coupling the yield surface equation, the flow rule, and the hardening rule. The yield surface equation of the original UH model is: , in, For the average effective stress, It is a deviatoric stress. M represents the initial consolidation pressure of the original loose sand, M represents the critical stress ratio, and H represents the uniform hardening parameter.

[0027] S3, Correcting the initial yield surface Introducing cementation and additional consolidation pressure (Additional consolidation pressure due to cementation, quantifying the increase in pre-consolidation pressure of sand due to calcium carbonate cementation), the pre-consolidation pressure of the original loose sand. Corrected to the preconsolidation pressure of cemented sand The corrected formula is as follows: ; The corrected yield surface equation is: , The cementing effect causes the yield surface to expand, and the degree of expansion increases with increasing calcium carbonate content. Figure 2 The intersection of the yield surface and the p-axis in the low-cementation state is In the highly cemented state, it is ( ).

[0028] S4. Construct the equation for the evolution of bonding strength. By fitting triaxial shear test data, a correlation was established between calcium carbonate content Cc and the preconsolidation pressure of cemented sand. maximum value Quantification relationship: , in, =82.04、 =0.4467、 =497.6, goodness of fit R 2 =0.9783, The maximum value of the preconsolidation pressure of cemented sand is the upper limit of the cementation strength. Considering confining pressure The moderating effect on bond strength (higher confining pressure leads to slower bond failure) is investigated, and a bond strength evolution equation with coupled parameters is constructed: , in, For material parameters, For plastic deviatoric strain, For the average effective stress, this equation achieves: the initial bond strength is determined by Cc and Jointly decided; during the cutting process Follow The cumulative effect decreases exponentially; after the cementation is completely destroyed... →0, the sample degrades into loose sand.

[0029] S5, Modified Dilatation Equation The dilatation ratio of MICP-cemented sand is significantly higher than that of normally consolidated soil, and the original UH model dilatation equation (based on stress history) cannot accurately characterize it. Therefore, the effective deviatoric stress ratio is used instead. Replacement of original deviatoric stress ratio The corrected dilatation equation is: , in, For the plastic volumetric strain increment, The plastic deviatoric strain increment is M, and the critical stress ratio is M. Figure 3 The dilatation relationship of cemented sand differs significantly from that of normal consolidated soil. This equation can accurately capture the "shear contraction-diffraction transition" and post-peak dilatation softening characteristics of cemented sand.

[0030] S6, Modify hardening parameters Replace the baseline parameter H of the hardening parameter with the preconsolidation pressure of the cemented sand. The corrected expression for the overconsolidated parameter R is: , in, The initial cementation and early consolidation pressure, , Let the slope of the isotropic compression line of the remolded soil be the e-lnp coordinate. The slope of the rebound line. The initial void ratio; The expression for the hardening parameter H is: , in, , Let the slope of the isotropic compression line of the remolded soil be the e-lnp coordinate. The slope of the rebound line. For plastic volumetric strain. The modified H simultaneously reflects the strengthening-failure process of the cemented network and the accumulation of plastic work in the soil matrix.

[0031] S7. Solving the consistency condition Based on the modified yield function, the consistency condition is obtained by taking its total differential: , By combining the generalized Hooke's law, the associated flow rule (g=f, where g is the plastic potential function), and the cementation strength evolution equation, the linear equation of the plastic multiplier is derived, and the plastic strain increment is obtained by solving it, thus realizing the continuous calculation of the stress-strain relationship.

[0032] Example 2 The model parameters of this invention include physical parameters of quartz sand, critical state parameters, and cementation characteristic parameters. All of these parameters can be determined through conventional triaxial tests or fitting methods, as detailed below: 1. Physical parameters of quartz sand The specific parameters were determined based on the "Standard for Geotechnical Testing Methods" (GB / T 50123-2019): Specific gravity: The specific gravity bottle method (GB / T 50123-2019 6.2) is used. Dry density: determined by the ring cutter method (GB / T 50123-2019 5.2); initial porosity It is calculated from specific gravity, dry density, and moisture content, using the following formula: , in, For specific gravity, The density of water, Moisture content, Dry density; Poisson's ratio The test was performed using a conventional triaxial compression test (GB / T 50123-2019 16).

[0033] 2. Critical state parameters (M, λ, k) λ, k: The remolded quartz sand was made into a sample and an isotropic consolidation test was conducted. The test data was plotted on an e-lnp semi-logarithmic coordinate system and linearly fitted to obtain the isotropic compression line and the rebound line, with slopes of λ and k, respectively. M: The shear failure stress under different confining pressures was determined by conventional triaxial consolidated undrained test (CU) of remolded sand, and the critical state stress ratio M was obtained by fitting.

[0034] 3. Cementation characteristic parameters (ω, β, C, α, k0, γ) The measurement and fitting process can be broken down into the following operational steps: Sample preparation: MICP cemented sand samples with different cementation levels were prepared, and three parallel samples were set up for each group of samples. Cc determination: The acid hydrolysis method was adopted, and the operation was strictly carried out in accordance with the steps of "crushing the sample, reacting with excess hydrochloric acid, collecting CO2 and weighing it, and calculating Cc based on the stoichiometric relationship of CaCO3+2HCl=CaCl2+H2O+CO2↑". The average value of 3 parallel samples was taken as the final Cc value. Triaxial test: Triaxial consolidated undrained test (CU) was carried out on different Cc specimens under confining pressure of 100-300 kPa to obtain full test data such as stress-strain, plastic deviatoric strain, and shear dilatation ratio; Initial fitting: Substitute the experimental data into... , The nonlinear least squares method was used for fitting to obtain ω, C, and the required goodness of fit R 2 ≥0.9; Global optimization fitting: Substitute the β obtained from the initial fitting into the cementation strength evolution equation. , Using stress-strain data from triaxial tests, α, k0, and γ are obtained through global nonlinear fitting. The goodness of fit R is required. 2 The value must be ≥0.9, and the fitting result must be verified by experimental data from 3 sets of verification samples.

[0035] 4. Basic constant (C), initial consolidation pressure ( , ) An isotropic consolidation test was conducted using unconsolidated loose quartz sand to determine its preconsolidation pressure. The preconsolidation pressure of MICP cemented sand samples in their initial state was determined by isotropic consolidation tests. C: is the experimental fitting constant, obtained by fitting the formula, and is tentatively set to 497.6 kPa under the experimental conditions of this invention.

[0036] Test case Experimental Example 1 Using the model parameter acquisition method as described in Example 2, the following specific measurements were performed: Physical parameters of quartz sand were determined as follows: specific gravity was 2.8 using the hydrometer bottle method, moisture content was 20% using the drying method, and dry density was 1.54 g / cm³ using the ring cutter method. 3 The initial void ratio e = 0.818 and Poisson's ratio ν = 0.3 were calculated. Critical state parameter determination: Through conventional triaxial tests on loose quartz sand, the slope of the compression line λ=0.06, the slope of the rebound line κ=0.015, and the critical state stress ratio M=1.2 were measured. Fitting of cementation characteristic parameters: Nine groups of MIP-cemented sand samples were selected (grouting times of 8, 16, and 24 times, confining pressures of 100 kPa, 200 kPa, and 300 kPa). The calcium carbonate content (Cc) was determined by acid hydrolysis. Triaxial consolidated undrained tests were conducted to obtain stress-strain and dilatation data. The sample strength provided by the cemented structure was calculated using the above data. Finally, the strength was determined using the formula... The fitted cementation parameters yielded α = 89.63. =0.1187, k0=118.4, γ=0.004862. Substitute into the formula. Then, global model optimization and parameter determination are performed.

[0037] Experimental Example 2 Using the parameters determined in Experiment Example 1, stress-strain and shear dilatation characteristics were simulated on 9 groups of specimens. The results show that: Stress-strain curves: The model can accurately predict the initial stiffness, peak strength, and post-peak strain softening characteristics of the specimen, with an average relative error of 2.8%. Dilatation characteristics: The model can accurately capture the "shrinkage-dilatation transition point" and the post-peak dilatation softening phenomenon, with a dilatation ratio simulation error of less than 3%; Adaptability to different degrees of bonding: The simulation results for low bonding (Cc=1.6%), medium bonding (Cc=6.0%), and high bonding (Cc=8.1%) samples were all good, with no obvious distortion.

[0038] Combination Figure 4 , Figure 4 This is a comparison of stress-strain curves from cementation model simulation, UH model simulation, and experimental data (taking Cc=8.1% and σ3=100kPa as an example). Figure 4 It is evident that the model of this invention (cementation model) can accurately predict the initial stiffness, peak strength, and post-peak strain softening characteristics of the specimen, while the traditional UH model has significant deviations in simulating highly cemented soils, especially near the peak strength.

[0039] Combination Figure 5 , Figure 5 This is a comparison of the shear dilatation curves from the cementation model simulation, the UH model simulation, and experimental data (again, using Cc=8.1% and σ3=100kPa as an example). Figure 5 As can be seen, the model of this invention can accurately capture the "shear contraction-shear dilatation transition point" and the post-peak shear dilatation softening phenomenon, while the UH model cannot accurately describe this feature.

[0040] Table 1 shows a comparison of the data simulated by the UH model and the cementation model, covering 18 sets of experimental data under different calcium carbonate contents (1.6%-8.1%) and different confining pressures (100-300kPa).

[0041]

[0042] As shown in Table 1, the absolute values ​​of the relative errors in the simulation of peak intensity by the model of the present invention are all within 4.6%, with most of them being less than 2%; the absolute values ​​of the relative errors in the simulation of maximum volumetric strain (dilatation) are all within 2%.

[0043] In contrast, the UH model exhibits peak strength simulation errors of -35.1%, -30.58%, and -49.82% at high cementation levels (e.g., Cc=6.001%, Cc=7.894%, Cc=8.020%), and the maximum volumetric strain error also increases significantly.

[0044] In summary, this invention reduces the simulation error from 25%-33% in existing UH models to less than 3%, significantly improving simulation accuracy.

[0045] Experimental Example 3 The constitutive model constructed according to this invention was embedded into finite element software to conduct numerical simulations of MICP-reinforced sandy soil foundations. The relative error between the simulation results and the field load test data was 2.5%, significantly better than the traditional UH model (error 28%). This indicates that the model of this invention can provide a reliable basis for foundation bearing capacity assessment and engineering design.

[0046] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for constructing a constitutive model of MICP-cemented sand based on the unified hardening theory, characterized in that, Includes the following steps: 1) A unified hardening model is selected as the basic framework; 2) Modify the initial yield surface: Introduce additional consolidation pressure that is positively correlated with calcium carbonate content. The initial consolidation pressure of the original loose sandy soil Corrected to the preconsolidation pressure of cemented sand The corrected formula is as follows: This achieves the expansion of the yield surface; 3) Constructing the equation for the evolution of cementation strength: Establishing the additional consolidation pressure of cementation. With plastic deviatoric strain The evolution equation is a cumulative and decaying equation that couples the calcium carbonate content Cc with the confining pressure. The impact; 4) Modified shear dilatation equation: using effective deviatoric stress ratio Replacement of original deviatoric stress ratio The corrected shear dilatation equation is: ; in, For the plastic volumetric strain increment, is the plastic deviatoric strain increment, and M is the critical state stress ratio; 5) Correct hardening parameters: Replace the baseline parameter in hardening parameter H with the preconsolidation pressure of cemented sand. This allows the hardening parameters to simultaneously reflect the strengthening-damage process of the cemented network and the accumulation of plastic work in the soil matrix; 6) Solving for consistency conditions: Based on the modified yield function, cementation strength evolution equation and hardening parameters, the plastic multiplier is derived, and combined with the generalized Hooke's law and flow rule, the continuous calculation of stress-strain relationship is realized.

2. The method for constructing a constitutive model of MICP-cemented sand based on unified hardening theory according to claim 1, characterized in that, The cementation additional consolidation pressure The introduction is based on the MICP bonding mechanism; The mechanism includes three ways in which calcium carbonate crystals construct a continuous cemented network through surface adhesion, interstitial crystal cluster growth, and contact interface cementation, so that the solidified soil exhibits mechanical properties similar to structured soil.

3. The method for constructing a constitutive model of MICP-cemented sand based on unified hardening theory according to claim 1, characterized in that, In step 3), the expression for the bonding strength evolution equation is: , in, For material parameters, For plastic deviatoric strain, This represents the average effective stress.

4. The method for constructing a constitutive model of MICP-cemented sand based on unified hardening theory according to claim 1, characterized in that, In step 5), the corrected hardening parameter H is expressed by the overconsolidation parameter R, and the expression for the overconsolidation parameter R is: ， in, The initial cementation and early consolidation pressure, , Let the slope of the isotropic compression line of the remolded soil be the e-lnp coordinate. The slope of the rebound line. This represents the initial void ratio.

5. The method for constructing a constitutive model of MICP-cemented sand based on unified hardening theory according to claim 3, characterized in that, In step 3), the calcium carbonate content Cc is determined by acid hydrolysis. The specific steps are as follows: the cemented sample is crushed and reacted with excess hydrochloric acid, the generated CO2 is collected and its mass is measured, and the mass fraction of calcium carbonate is calculated based on the stoichiometric relationship of the chemical reaction.

6. The method for constructing a constitutive model of MICP-cemented sand based on unified hardening theory according to claim 3, characterized in that, In step 3), the material parameters in the bond strength evolution equation The data were obtained by fitting triaxial shear test data of MIP cemented sand under different confining pressures and different calcium carbonate contents.

7. The method for constructing a constitutive model of MICP-cemented sand based on unified hardening theory according to claim 1, characterized in that, In step 3), the preconsolidation pressure of the cemented sand... The maximum value is The relationship between the calcium carbonate content Cc and the content of calcium carbonate follows an exponential function form. , in, , , These are the material constants obtained by fitting experimental data.

8. A constitutive model of MICP cemented sand constructed by the method described in any one of claims 1-7, characterized in that, The model parameters include: physical parameters of sand, critical state parameters, and cementation characteristic parameters; The bonding characteristic parameters include the material parameters in the bonding strength evolution equation. .

9. The application of the MICP-cemented sand constitutive model as described in claim 8 in the prediction of the mechanical behavior of MICP-solidified soil or in finite element numerical simulation, characterized in that, The applications include stress-strain behavior prediction and numerical analysis in sandy soil foundation reinforcement, slope protection, or site restoration projects.

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