Microbial solidified soil constitutive model parameter identification method

Abstract

The invention discloses a microbial solidified soil constitutive model parameter identification method, and belongs to the field of computational geotechnical engineering and intelligent optimization algorithms. The method comprises the following steps: constructing a microbial solidified soil constitutive model containing a mobile normal consolidation line MNCL, constructing an error objective function, performing parameter inversion by adopting an improved radial movement algorithm, obtaining an optimal to-be-identified parameter vector, and completing identification of to-be-identified parameters. And a greedy selection mechanism is introduced into an improved radial movement algorithm, so that the problem of convergence oscillation caused by easy acceptance of an inferior solution in particle updating is solved, and the optimization stability and precision are remarkably improved. And a parameter identification problem. In addition, a layered decoupling strategy is provided for multi-confining-pressure data, and confining-pressure sensitive parameters and intrinsic parameters of materials are recognized through the recognition method. According to the method, high-precision and automatic identification of the complex mechanical behavior model parameters of the microorganism solidified soil is realized, and the defects of a traditional method are overcome.

Description

Technical Field

[0001] This invention belongs to the field of computational geotechnical engineering and intelligent optimization algorithms, specifically relating to a method for identifying parameters of a constitutive model of microbial solidified soil. Background Technology

[0002] Microbial-induced carbonate precipitation (MICP) is an environmentally friendly soil improvement method that significantly enhances soil strength and stiffness while reducing permeability by generating calcium carbonate cement between soil particles. To accurately predict the mechanical behavior of microbially solidified soil (such as stress-strain relationships, dilatation, and cementation degradation) in numerical analysis, complex constitutive models describing its cementation enhancement and damage mechanisms are needed, such as elastoplastic models incorporating moving normal consolidation lines (MNCLs). These models typically contain multiple physically meaningful but coupled parameters (such as initial degree of cementation, degradation rate, and the coefficient of cementation's influence on stiffness), which are difficult to determine directly through conventional geotechnical tests.

[0003] Traditional model parameter calibration often relies on manual trial and error or experience-based fitting, which suffers from inefficiency, strong subjectivity, and difficulty in finding the global optimum. Automated parameter inversion techniques, especially metaheuristic optimization algorithms (such as genetic algorithms, particle swarm optimization, and radial movement optimization algorithms), provide an effective approach to this problem. The Radial Movement Optimization (RMO) algorithm has attracted attention due to its simple structure, fast convergence, and low memory consumption. However, the standard RMO algorithm has a significant drawback when updating particle positions: regardless of the quality of the newly generated "pre-position," the particle will move to that position (the fitness value is only updated if it is better). This may lead to the overwriting of high-quality solutions and the population oscillating in poor regions, thus affecting the stability of global convergence and the final accuracy. This drawback is particularly prominent when dealing with parameter inversion problems of high-dimensional, nonlinear, and strongly coupled constitutive models.

[0004] Therefore, there is an urgent need for an optimization algorithm that can overcome the above-mentioned defects, has stronger robustness and higher accuracy, and is accompanied by a complete set of procedures and methods applicable to the identification of constitutive model parameters for complex materials such as microbially stabilized soil. Summary of the Invention

[0005] The technical problem to be solved by this invention is the deficiency of the prior art. It aims to provide an improved radial motion optimization algorithm (IRMO) that is convergent, stable, and has high optimization accuracy, and is suitable for the identification of parameters of complex constitutive models. It also aims to establish a complete intelligent identification method for constitutive model parameters of microbial solidified soil. Moreover, this identification method can realize a hierarchical inversion strategy to achieve efficient, automatic, and high-precision parameter inversion.

[0006] To achieve the above objectives, the present invention provides the following technical solution: 1. A method for identifying parameters of a constitutive model of microbially stabilized soil, comprising the following steps: Step 1: Construct a constitutive model of microbial solidified soil containing the moving normal consolidation line MNCL based on the modified Cambridge model; the model parameters are the input parameters of the constitutive model of microbial solidified soil, which are d input parameters, including at least 3 confining pressure sensitive parameters and 6 intrinsic parameters; the output of the constitutive model of microbial solidified soil is two complete datasets: the first dataset is a deviatoric stress-strain dataset, including axial strain sequences and corresponding deviatoric stress sequences; the second dataset is a volumetric strain dataset, including axial strain sequences and corresponding volumetric strain sequences. Step 2, construct the error objective function F( X ) The error is the scalar normalized root mean square error E between the simulated curve obtained by the microbial solidified soil constitutive model and the experimental curve obtained by the confining pressure experiment. This scalar normalized root mean square error E combines the errors caused by deviatoric stress strain and volumetric strain. One or more parameters are arbitrarily selected from d input parameters as parameters to be identified. An error objective function is constructed using the selected parameters to be identified as optimization variables X, with the minimum scalar normalized root mean square error E as the optimization objective. F( X ) ; Step 3, parameter inversion: Specifically, based on physical priors, the upper and lower limits of the parameters to be identified are determined, forming feasible region 1; an improved radial moving algorithm is used to perform a global search within feasible region 1 to obtain a preliminary solution; subsequently, a reduced feasible region 2 is constructed with the preliminary solution as the center, and the improved radial moving algorithm is used to perform a global search within feasible region 2 to obtain the global optimal solution in feasible region 2. This optimal solution is the optimal parameter vector to be identified with the minimum scalar normalized root mean square error E, thus completing the identification of the parameters to be identified. Step 4: Output the optimal vector of parameters to be identified and substitute it into the constitutive model of microbial solidified soil for analysis and prediction.

[0007] Preferably, the confining pressure sensitive parameter in step 1 includes the initial biocementation index. x b0 Initial tensile strength index s 0 and overconsolidation ratio R; the intrinsic parameters include the overconsolidation degradation rate. m Residual structural factor m res Biocement degradation rate k Comprehensive plastic strain proportionality coefficient β The first influencing parameter 'a' and the second influencing parameter 'a' of bio-cementation b。

[0008] Preferably, step 2 is implemented as follows: Step 2.1: Simulation using a microbial solidified soil constitutive model yields a deviatoric stress-strain simulation dataset and a volumetric strain simulation dataset. ， The simulated curves of deviatoric stress-axial strain and volumetric strain-axial strain were plotted on a plane coordinate system; simultaneously, confining pressure experiments were conducted to obtain a deviatoric stress-strain experimental dataset and a volumetric strain experimental dataset. ， The experimental curves of deviatoric stress-axial strain and volumetric strain-axial strain were plotted on a plane coordinate system. Take n data points at equal intervals on two simulated curves and two experimental curves, and record the data corresponding to any one of the data points as the i-th data, i=1,2,…,n; then use interpolation to map the simulated data to the axial strain coordinates of the experimental data to ensure that the comparison is performed at the same axial strain position. Step 2.2, Normalized Root Mean Square Error (NRMSE) of Deviatoric Stress q Calculation For the deviatoric stress-axial strain curve characterizing the shear strength of soil, the normalized root mean square error of deviatoric stress (NRMSE) is... q The calculation process is as follows: Interpolation calculation: Let the i-th data point in the deviatoric stress-axial strain experimental curve be the experimental value of axial strain. The corresponding experimental value of deviatoric stress Let the i-th data point in the deviatoric stress-axial strain simulation curve be the simulated axial strain value. The corresponding simulated deviatoric stress value is Interpolation algorithms were used to obtain the experimental values ​​of axial strain. Corresponding simulated values ​​of deviatoric stress ; Calculate the root mean square error (RMSE) of the deviatoric stress. q The formula for its calculation is:

[0009] Normalized root mean square error of deviatoric stress (NRMSE) q The formula for calculation is:

[0010] Where, max( ) represents the maximum value among n deviatoric stress experimental values ​​in the deviatoric stress-axial strain experimental curve, min( () represents the minimum value among n deviatoric stress experimental values ​​in the deviatoric stress-axial strain experimental curve; Step 2.3, Normalized root mean square error of volumetric strain (NRMSE)v Calculation For the volumetric strain-axial strain curve characterizing the dilatation / contraction properties of soil, the normalized root mean square error of volumetric strain (NRMSE) is... v The calculation process is as follows: Interpolation calculation: Let the i-th data point in the volumetric strain-axial strain experimental curve be the experimental value of axial strain. The corresponding volumetric strain experimental value is Let the i-th data point in the volumetric strain-axial strain simulation curve be the simulated axial strain value. The corresponding simulated volumetric strain value is Interpolation algorithms were used to obtain the experimental values ​​of axial strain. Corresponding volumetric strain simulation values ; Calculate the root mean square error (RMSE) of volumetric strain v The formula for its calculation is:

[0011] Normalized root mean square error of volumetric strain (NRMSE) v The formula for calculation is:

[0012] Where, max( ) represents the maximum value among n volumetric strain experimental values ​​in the volumetric strain-axial strain experimental curve, min( () represents the minimum value among the n volumetric strain experimental values ​​in the volumetric strain-axial strain experimental curve; Step 2.4, calculate the scalar normalized root mean square error E. Introducing the deviatoric stress weighting coefficient and volumetric strain weighting coefficient And satisfy + =1; The formula for calculating the scalar normalized root mean square error E is: .

[0013] Preferably, step 3 is implemented as follows: Step 3.1, determine the feasible region 1 for each parameter to be identified. Based on statistical data, the feasible region 1 for each parameter to be identified is determined to be [X]. min X max ], where X min and X max These are vectors composed of the lower and upper limits of each parameter to be identified; Step 3.2: Perform a global search in feasible region 1 using an improved radial motion optimization algorithm. First, define the parameter dimension, which is the number of parameters to be identified; set the number of particles J in the population; give the number of iterations G, and record any one of the iterations as the g-th iteration. An improved radial motion algorithm is used to perform a global exploration within the feasible region 1 determined in step 3.1, and the region where the optimal solution may exist is located through G iterations. The process is as follows: Step 3.2.1: First, randomly generate an initial population containing N particles, and denote any particle in the initial population as particle X. j-0 0 indicates the initial state, j is the particle number, j=1,...,J; when there is one parameter to be identified, each particle represents one parameter to be identified; when there are two or more parameters to be identified, each particle represents a group of parameters to be identified. Define the fitness function as the scalar normalized root mean square error E described in step 2, and calculate the fitness function values ​​F(X) of the J particles in the initial population. j-0 ), and select the fitness function value F(X) from it. j-0 The position of the smallest particle is taken as the initial global optimal position G. bestloc-0 And the corresponding fitness function value is denoted as F(G). bestloc-0 ); Set the initial global optimum position as the initial survival space center cp0, which will be used to guide the search direction of the population during the first iteration; Step 3.2.2: Perform the 2nd to Gth iterations, where the process of the gth iteration is as follows: Calculate X for each particle in the g-th iteration j-g fitness function value F(X) j-g ); For each particle X in the g-th iteration j-g Generate a trial position Y j-g Its expression is:

[0014] Among them, cp (g-1) W is the center of the survival space obtained in the (g-1)th iteration. g Let w be the iteration weight coefficient for the g-th iteration. g =1.0(g / G)-0.8(g / G), which adaptively changes with the number of iterations: Calculate the trial position Y j-g The corresponding fitness value F(Y) j-g ); The position of the particle is updated through a greedy selection mechanism; specifically, when F(Y) j-g) <F(X j-g When particle X is at time )), j-g Move to new location Y i-j That is, let F(X) j-g )= F(Y j-g Otherwise, particle X i-j It will remain in its original position, i.e., F(X) j-g () Remain unchanged; Once all N particles in the g-th iteration have completed their position updates, proceed to step 3.2.3; Step 3.2.3: Update the global optimal position and the center of the survival space. First, from the updated fitness function values ​​of the G particles in the g-th generation, select the position of the particle with the smallest fitness function value as the pre-selected global optimal position for the g-th iteration, and record the corresponding fitness function value as the pre-selected fitness function value for the g-th iteration. Next, the pre-selected global optimal position in the g-th generation is compared with the global optimal position in the (g-1)-th iteration: specifically, if the pre-selected fitness function value in the g-th iteration is less than the fitness function value corresponding to the global optimal position in the (g-1)-th iteration, then the pre-selected global optimal position in the g-th iteration is taken as the global optimal position in the g-th iteration, and denoted as the global optimal position G in the g-th iteration. bestloc-g The corresponding preselected fitness function value is the fitness function value of the g-th iteration, and is denoted as the fitness function value F(G) of the g-th iteration. bestloc-g Otherwise, take the global optimal position of the (g-1)th iteration as the global optimal position G of the g-th iteration. bestloc-g ; Then, the survival space center is dynamically adjusted. Specifically, the survival space center in the g-th iteration is denoted as cp. g This CP g The optimal position in the g-th iteration is determined by both the globally optimal position in the g-th iteration and the pre-selected optimal position in the g-th iteration. Let the pre-selected optimal position in the g-th iteration be denoted as R. bestloc The calculation formula is:

[0015] Where C1 is the first proportionality coefficient and C2 is the second proportionality coefficient; cp g It will be used to guide the search direction of the population during the (g+1)th iteration; Step 3.2.4: Repeat steps 3.2.2-3 until the maximum number of iterations G is reached, and output the globally optimal position G obtained in the G-th iteration. bestloc-G The globally optimal position G bestloc-G The corresponding one or a set of parameters to be identified is the optimal solution obtained by global search within feasible region 1, and is denoted as the preliminary solution.

[0016] Step 3.3, Local refinement iteration centered on the preliminary solution

[0017] Centered on the preliminary solution obtained in step 3.2, a narrowed feasible region 2 is constructed for each parameter to be identified. Specifically, the value of the preliminary solution for any parameter to be identified is denoted as A, and the feasible region 2 for that parameter is [X]. min2 ,X max2 ], where X min2= AB%A, X max2= A+B%A, where B is the reduction ratio, and B is 7-12; Within this feasible region 2, steps 3.2.2-3.2.4 are run again to obtain the globally optimal position G obtained in the G-th iteration within feasible region 2. bestloc-G2 The globally optimal position G bestloc-G2 The corresponding parameters to be identified are the optimal solution for this identification, that is, the optimal parameter vector to be identified with the smallest scalar normalized root mean square error E, thus completing the identification of the parameters to be identified.

[0018] The beneficial effects of this invention include: (1) Strong convergence stability. The greedy selection mechanism fundamentally avoids population quality degradation and search path oscillation caused by particles accepting inferior solutions, making the improved radial movement algorithm more robust in convergence in high-dimensional parameter space.

[0019] (2) High parameter identification accuracy. The multi-component objective function can comprehensively constrain the model response from multiple physical dimensions. By combining the series strategy of global exploration and local mining, the optimal parameter set with high consistency with experimental data can be obtained.

[0020] (3) Improved computational efficiency. The adaptive shrinking search radius and hierarchical inversion strategy reduce unnecessary search range, enabling the improved radial movement algorithm to locate promising areas more quickly and effectively handle multi-condition data.

[0021] (4) The physical meaning is clear and the applicability is wide. The method closely fits the framework of the microbial solidified soil constitutive model, and the identified parameters have clear physical interpretations. At the same time, the improved radial movement algorithm and objective function construction method are universal and can be transferred to other soil and rock constitutive models and even broader engineering inverse problems.

[0022] (5) Strong interpretability of results: The provided parameter uncertainty and correlation analysis helps to understand the identification degree and mutual influence of model parameters, and enhances the credibility and engineering practical value of parameter identification results. Attached Figure Description

[0023] Figure 1 This is a flowchart of the parameter identification method of the present invention.

[0024] Figure 2 A schematic diagram of the greedy selection mechanism in the improved radial movement algorithm.

[0025] Figure 3 This is a comparison chart of the simulated curves obtained by inversion using the improved radial movement algorithm under single confining pressure and the experimental data.

[0026] Figure 4 This is a comparison chart of simulated curves and experimental data obtained by hierarchical inversion using an improved radial translation algorithm. Detailed Implementation

[0027] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0028] Example 1.

[0029] Figure 1 This is a general flowchart of the parameter identification method of the present invention. Figure 1 Therefore, this invention provides a method for identifying constitutive model parameters of microbially stabilized soil, comprising the following steps: Step 1: Construct a constitutive model of microbial solidified soil containing the moving normal consolidation line MNCL based on the modified Cambridge model; the model parameters are the input parameters of the constitutive model of microbial solidified soil, which are d input parameters, including at least 3 confining pressure sensitive parameters and 6 intrinsic parameters; the output of the constitutive model of microbial solidified soil is two complete datasets: the first dataset is a deviatoric stress-strain dataset, including axial strain sequences and corresponding deviatoric stress sequences; the second dataset is a volumetric strain dataset, including axial strain sequences and corresponding volumetric strain sequences.

[0030] In this embodiment, the confining pressure sensitive parameter in step 1 includes the initial biocementation index. x b0 Initial tensile strength index s 0 and overconsolidation ratio R; the intrinsic parameters include the overconsolidation degradation rate. m Residual structural factor m res Biocement degradation rate k Comprehensive plastic strain α The first influencing parameter 'a' and the second influencing parameter 'a' of bio-cementation b .

[0031] Step 2, construct the error objective function F( X )The error is the scalar normalized root mean square error E between the simulated curve obtained by the microbial solidified soil constitutive model and the experimental curve obtained by the confining pressure experiment. This scalar normalized root mean square error E combines the errors caused by deviatoric stress strain and volumetric strain. One or more parameters are arbitrarily selected from d input parameters as parameters to be identified. An error objective function is constructed using the selected parameters to be identified as optimization variables X, with the minimum scalar normalized root mean square error E as the optimization objective. F( X ) .

[0032] In this embodiment, step 2 is implemented as follows: Step 2.1: Simulation using a microbial solidified soil constitutive model yields a deviatoric stress-strain simulation dataset and a volumetric strain simulation dataset. ， The simulated curves of deviatoric stress-axial strain and volumetric strain-axial strain were plotted on a plane coordinate system; simultaneously, confining pressure experiments were conducted to obtain a deviatoric stress-strain experimental dataset and a volumetric strain experimental dataset. ， The experimental curves of deviatoric stress-axial strain and volumetric strain-axial strain were plotted on a plane coordinate system. Take n data points at equal intervals on two simulated curves and two experimental curves, and record the data corresponding to any one of the data points as the i-th data, i=1,2,…,n; then use interpolation to map the simulated data to the axial strain coordinates of the experimental data to ensure that the comparison is performed at the same axial strain position.

[0033] Step 2.2, Normalized Root Mean Square Error (NRMSE) of Deviatoric Stress q Calculation

[0034] For the deviatoric stress-axial strain curve characterizing the shear strength of soil, the normalized root mean square error of deviatoric stress (NRMSE) is... q The calculation process is as follows: Interpolation calculation: Let the i-th data point in the deviatoric stress-axial strain experimental curve be the experimental value of axial strain. The corresponding experimental value of deviatoric stress Let the i-th data point in the deviatoric stress-axial strain simulation curve be the simulated axial strain value. The corresponding simulated deviatoric stress value is Interpolation algorithms were used to obtain the experimental values ​​of axial strain. Corresponding simulated values ​​of deviatoric stress ; Calculate the root mean square error (RMSE) of the deviatoric stress. q The formula for its calculation is:

[0035] Normalized root mean square error of deviatoric stress (NRMSE) q The formula for calculation is:

[0036] Where, max( ) represents the maximum value among n deviatoric stress experimental values ​​in the deviatoric stress-axial strain experimental curve, min( ) represents the minimum value among the n deviatoric stress experimental values ​​in the deviatoric stress-axial strain experimental curve.

[0037] Step 2.3, Normalized root mean square error of volumetric strain (NRMSE) v Calculation

[0038] For the volumetric strain-axial strain curve characterizing the dilatation / contraction properties of soil, the normalized root mean square error of volumetric strain (NRMSE) is... v The calculation process is as follows: Interpolation calculation: Let the i-th data point in the volumetric strain-axial strain experimental curve be the experimental value of axial strain. The corresponding volumetric strain experimental value is Let the i-th data point in the volumetric strain-axial strain simulation curve be the simulated axial strain value. The corresponding simulated volumetric strain value is Interpolation algorithms were used to obtain the experimental values ​​of axial strain. Corresponding volumetric strain simulation values ; Calculate the root mean square error (RMSE) of volumetric strain v The formula for its calculation is:

[0039] Normalized root mean square error of volumetric strain (NRMSE) v The formula for calculation is:

[0040] Where, max( ) represents the maximum value among n volumetric strain experimental values ​​in the volumetric strain-axial strain experimental curve, min( ) represents the minimum value among the n volumetric strain experimental values ​​in the volumetric strain-axial strain experimental curve.

[0041] Step 2.4, calculate the scalar normalized root mean square error E.

[0042] Introducing the deviatoric stress weighting coefficient and volumetric strain weighting coefficient And satisfy + =1; The formula for calculating the scalar normalized root mean square error E is: .

[0043] Step 3, parameter inversion. Specifically, based on the physical prior to determine the upper and lower limits of the parameters to be identified, a feasible region 1 is formed. An improved radial moving algorithm is used to perform a global search within feasible region 1 to obtain a preliminary solution. Subsequently, with the preliminary solution as the center, a reduced feasible region 2 is constructed. An improved radial moving algorithm is used to perform a global search within feasible region 2 to obtain the global optimal solution in feasible region 2. This optimal solution is the optimal parameter vector to be identified with the minimum scalar normalized root mean square error E, thus completing the identification of the parameters to be identified.

[0044] The implementation process of step 3 is as follows: Step 3.1, determine the feasible region 1 for each parameter to be identified. Based on statistical data, the feasible region 1 for each parameter to be identified is determined to be [X]. min X max ], where X min and X max These are vectors composed of the lower and upper limits of each parameter to be identified.

[0045] Before conducting the optimization search, reasonable upper and lower limits are first set for each parameter to be identified based on the physical meaning of the model parameters, relevant theories, and previous experimental experience, thereby constructing a physically credible search space.

[0046] In this embodiment, the feasible domain 1 for each parameter to be identified is selected as follows: x b0 The range is [0.1, 1.2]. s 0 represents [1, 50]; R represents [0.01, 1]; m The range is [0.1, 20]. m res The range is [0.3, 0.8]. k The range is [0.3, 0.8]. β For [0.01, 1]; a and b The theoretical constraints are set based on a specific yield function (such as the modified Cambridge model, the Duncan-Zhang model, etc.).

[0047] Step 3.2: Perform a global search in feasible region 1 using an improved radial motion optimization algorithm.

[0048] First, set the parameter dimension, which is the number of parameters to be identified; set the number of particles J in the population; give the number of iterations G, and record any one of the iterations as the g-th iteration.

[0049] An improved radial motion algorithm is used to perform a global exploration within the feasible region 1 determined in step 3.1, and the region where the optimal solution may exist is located through G iterations. The process is as follows: Step 3.2.1: First, randomly generate an initial population containing N particles. ， Let any one of the particles in the initial population be denoted as particle X. j-0 0 indicates the initial state, j is the particle number, j=1,...,J; when there is one parameter to be identified, each particle represents one parameter to be identified; when there are two or more parameters to be identified, each particle represents a group of parameters to be identified. Define the fitness function as the scalar normalized root mean square error E described in step 2, and calculate the fitness function values ​​F(J) of the initial population. X j-0 ), and select the fitness function value F( from it. X j-0 The position of the smallest particle is taken as the initial global optimal position G. bestloc-0 And the corresponding fitness function value is denoted as F(G). bestloc-0 ) ; Set the initial global optimum position as the initial survival space center (cp) 0 This center will be used to guide the search direction of the population during the first iteration.

[0050] Step 3.2.2, perform the 2nd iteration - the Gth iteration, where the process of the gth iteration is as follows: Calculate X for each particle in the g-th iteration j-g fitness function value F(X) j-g ); For each particle X in the g-th iteration j-g Generate a trial position Y j-g Its expression is:

[0051] Among them, cp (g-1) W is the center of the survival space obtained in the (g-1)th iteration. g Let w be the iteration weight coefficient for the g-th iteration. g =1.0(g / G)-0.8(g / G), which adaptively changes with the number of iterations.

[0052] In the early stages of the iteration (i.e., when g is small), W g When the value approaches 1.0, particles tend to move significantly towards the center point cp. g Movement facilitates exploration on a global scale; in the later stages of iteration (when g approaches G), W... gThe adaptive reduction in size allows for a smaller step size for the particle to move, which facilitates a fine-grained local search around the region where the optimal solution is most likely to exist.

[0053] Calculate the trial position Y j-g The corresponding fitness value F(Y) j-g ); The position of the particle is updated through a greedy selection mechanism; specifically, when F(Y) j-g ) <F(X j-g When particle X is at time )), j-g Move to new location Y i-j That is, let F(X) j-g )= F(Y j-g Otherwise, particle X i-j It will remain in its original position, i.e., F(X) j-g () Remain unchanged; Once all N particles in the g-th iteration have completed their position updates, proceed to step 3.2.3.

[0054] Figure 2 The diagram illustrates the greedy selection mechanism in the improved radial movement algorithm. As can be seen from the diagram, the greedy selection mechanism ensures that the entire population will only evolve towards a better solution.

[0055] Step 3.2.3: Update the global optimal position and the center of the survival space.

[0056] First, from the updated fitness function values ​​of the G particles in the g-th generation, select the position of the particle with the smallest fitness function value as the pre-selected global optimal position for the g-th iteration, and record the corresponding fitness function value as the pre-selected fitness function value for the g-th iteration. Next, the pre-selected global optimal position in the g-th generation is compared with the global optimal position in the (g-1)-th iteration: specifically, if the pre-selected fitness function value in the g-th iteration is less than the fitness function value corresponding to the global optimal position in the (g-1)-th iteration, then the pre-selected global optimal position in the g-th iteration is taken as the global optimal position in the g-th iteration, and denoted as the global optimal position G in the g-th iteration. bestloc-g The corresponding preselected fitness function value is the fitness function value of the g-th iteration, and is denoted as the fitness function value F(G) of the g-th iteration. bestloc-g Otherwise, take the global optimal position of the (g-1)th iteration as the global optimal position G of the g-th iteration. bestloc-g .

[0057] Then, the survival space center is dynamically adjusted. Specifically, the survival space center in the g-th iteration is denoted as cp. g This CP gThe optimal position in the g-th iteration is determined by both the globally optimal position in the g-th iteration and the pre-selected optimal position in the g-th iteration. Let the pre-selected optimal position in the g-th iteration be denoted as R. bestloc The calculation formula is:

[0058] Where C1 is the first proportionality coefficient and C2 is the second proportionality coefficient; cp g It will be used to guide the search direction of the population during the (g+1)th iteration; Step 3.2.4: Repeat steps 3.2.2-3 until the maximum number of iterations G is reached, and output the globally optimal position G obtained in the G-th iteration. bestloc-G The globally optimal position G bestloc-G The corresponding one or a set of parameters to be identified is the optimal solution obtained by global search within feasible region 1, and is denoted as the preliminary solution.

[0059] Step 3.3, Local refinement iteration centered on the preliminary solution

[0060] Centered on the preliminary solution obtained in step 3.2, a narrowed feasible region 2 is constructed for each parameter to be identified. Specifically, the value of the preliminary solution for any parameter to be identified is denoted as A, and the feasible region 2 for that parameter is [X]. min2 ,X max2 ], where X min2= AB%A, X max2= A+B%A, where B is the reduction ratio, and B is 7-12.

[0061] Within this feasible region 2, steps 3.2.2-3.2.4 are run again to obtain the globally optimal position G obtained in the G-th iteration within feasible region 2. bestloc-G2 The globally optimal position G bestloc-G2 The corresponding parameters to be identified are the optimal solution for this identification, that is, the optimal parameter vector to be identified with the smallest scalar normalized root mean square error E, thus completing the identification of the parameters to be identified.

[0062] In this embodiment, B=10.

[0063] Step 4: Output the optimal vector of parameters to be identified and substitute it into the constitutive model of microbial solidified soil for analysis and prediction.

[0064] Example 2

[0065] This embodiment describes the identification of constitutive model parameters for microbial soil under single confining pressure conditions.

[0066] In this embodiment, microbial induced carbonate precipitation (MICP) was used to treat silt, and triaxial shear tests were conducted at a confining pressure of 100 kPa and an initial void ratio of... e Input parameter recognition is performed under the condition that 0 = 0.60.

[0067] The parameters to be identified are all the input parameters described in step 1, including the initial bio-agglomeration index. x b0 Initial tensile strength index s 0 and the overconsolidation ratio R. The intrinsic parameters include the overconsolidation degradation rate. m Residual structural factor m res Biocement degradation rate k Comprehensive plastic strain proportionality coefficient β The first influencing parameter 'a' and the second influencing parameter 'a' of bio-cementation b .

[0068] Corresponding optimization variables X=(ξ) b0 , s 0, R, m , m res , k , β ,a, b）。 Initialization values ​​are provided based on the test results.

[0069] An improved radial motion optimization algorithm is used, with an initial population of 600 and a maximum number of iterations. G =600. The algorithm uses a greedy selection mechanism to ensure that it only accepts better solutions, thereby improving convergence stability.

[0070] After identification, the optimal solution obtained is: ≈0.495, s 0≈25.069 kPa, R0≈0.118, m ≈25.73, m res ≈0.826, k ≈2.906, β ≈0.566, a ≈0.566, b ≈0.566.

[0071] Figure 3 Figure 3 shows a comparison between the simulated curves obtained by IRMO inversion under a single confining pressure and the experimental data. As can be seen from Figure 3, the model parameters identified by the improved radial motion optimization algorithm are in good agreement with the experimental data, and the peak value and location of the deviatoric stress, as well as the inflection point of the volumetric strain, are accurately predicted.

[0072] Example 3

[0073] This embodiment is a parameter inversion and verification under multiple confining pressure conditions. In this embodiment, treated soil samples under different confining pressure conditions (50 kPa, 100 kPa, 200 kPa) are used, and parameters under multiple working conditions are identified by a hierarchical inversion method. The hierarchical inversion method is to select multiple rounds and use the parameter identification method of this invention to identify the above 9 input parameters.

[0074] (1) Experimental data and stratification settings: Confining pressure settings: 50 kPa, 100 kPa, and 200 kPa.

[0075] In this embodiment, the bio-binding index The overconsolidation ratio R0 and tensile strength index s0 are independently identified for different confining pressures, that is, in step 2, the following is selected: R0 and s0 are used as a set of parameters to be identified and are identified three times independently using the method of the present invention, with one confining pressure selected each time; the other six intrinsic parameters are used as a set of parameters to be identified and are identified once using the method of the present invention.

[0076] (2) Optimization process: Hierarchical inversion: First-level parameters ( m , m res , k , b、a、b (etc.) Each confining pressure is independently identified and its average value is taken, which is the corresponding optimization variable. X=(m) , m res , k , β ,a, b）。 Second layer parameters ( The optimization variables (R0, s0) are obtained through joint inversion of all confining pressure data. X=(ξ) b0 , s 0, R ）。

[0077] (3) Inversion results: The values ​​gradually decreased with increasing confining pressure, and were 0.152 (50 kPa), 0.495 (100 kPa), and 0.475 (200 kPa), respectively.

[0078] The values ​​gradually decreased with increasing confining pressure, and were 28.081 (50 kPa), 25.069 (100 kPa), and 22.069 (200 kPa).

[0079] R0: gradually increases with increasing confining pressure, and is 0.171 (50 kPa), 0.118 (100 kPa), and 0.109 (200 kPa).

[0080] m ≈25.73, m res ≈0.826, k ≈2.906, β ≈0.566, a ≈0.566, b ≈ 0.566.

[0081] Figure 4 This is a comparison chart of simulated curves and experimental data obtained using a layered inversion algorithm with an improved radial translation algorithm. Figure 4 It is evident that the parameter hierarchical inversion method successfully separated the parameters related to confining pressure and ensured the physical consistency of the model, effectively reflecting the cementation and consolidation behavior of soil under different confining pressures.

Claims

1. A method for identifying parameters of a constitutive model of microbially stabilized soil, characterized in that, Includes the following steps: Step 1: Construct a constitutive model of microbial solidified soil containing the moving normal consolidation line MNCL based on the modified Cambridge model; the model parameters are the input parameters of the constitutive model of microbial solidified soil, which are d input parameters, including at least 3 confining pressure sensitive parameters and 6 intrinsic parameters; the output of the constitutive model of microbial solidified soil is two complete datasets: the first dataset is a deviatoric stress-strain dataset, including axial strain sequences and corresponding deviatoric stress sequences; the second dataset is a volumetric strain dataset, including axial strain sequences and corresponding volumetric strain sequences. Step 2, construct the error objective function F( X ) The error is the scalar normalized root mean square error E between the simulated curve obtained by the microbial solidified soil constitutive model and the experimental curve obtained by the confining pressure experiment. This scalar normalized root mean square error E combines the errors caused by deviatoric stress strain and volumetric strain. One or more parameters are arbitrarily selected from d input parameters as parameters to be identified. An error objective function is constructed using the selected parameters to be identified as optimization variables X, with the minimum scalar normalized root mean square error E as the optimization objective. F( X ) ; Step 3, parameter inversion: Specifically, based on physical priors, the upper and lower limits of the parameters to be identified are determined, forming feasible region 1; an improved radial moving algorithm is used to perform a global search within feasible region 1 to obtain a preliminary solution; subsequently, a reduced feasible region 2 is constructed with the preliminary solution as the center, and the improved radial moving algorithm is used to perform a global search within feasible region 2 to obtain the global optimal solution in feasible region 2. This optimal solution is the optimal parameter vector to be identified with the minimum scalar normalized root mean square error E, thus completing the identification of the parameters to be identified. Step 4: Output the optimal vector of parameters to be identified and substitute it into the constitutive model of microbial solidified soil for analysis and prediction.

2. The method for identifying constitutive model parameters of microbial solidified soil according to claim 1, characterized in that, The confining pressure sensitive parameter mentioned in step 1 includes the initial biocementation index. ξ b0 Initial tensile strength index s 0 and overconsolidation ratio R; the intrinsic parameters include the overconsolidation degradation rate. m Residual structural factor μ res Biocement degradation rate k Comprehensive plastic strain proportionality coefficient β The first influencing parameter 'a' and the second influencing parameter 'a' of bio-cementation b .

3. The method for identifying constitutive model parameters of microbial solidified soil according to claim 1, characterized in that, The implementation process of step 2 is as follows: Step 2.1: Simulation using a microbial solidified soil constitutive model yields a deviatoric stress-strain simulation dataset and a volumetric strain simulation dataset. ， The simulated curves of deviatoric stress-axial strain and volumetric strain-axial strain were plotted on a plane coordinate system; simultaneously, confining pressure experiments were conducted to obtain a deviatoric stress-strain experimental dataset and a volumetric strain experimental dataset. ， The experimental curves of deviatoric stress-axial strain and volumetric strain-axial strain were plotted on a plane coordinate system. Take n data points at equal intervals on two simulated curves and two experimental curves, and record the data corresponding to any one of the data points as the i-th data, i=1,2,…,n; then use interpolation to map the simulated data to the axial strain coordinates of the experimental data to ensure that the comparison is performed at the same axial strain position. Step 2.2, Normalized Root Mean Square Error (NRMSE) of Deviatoric Stress q Calculation For the deviatoric stress-axial strain curve characterizing the shear strength of soil, the normalized root mean square error of deviatoric stress (NRMSE) is... q The calculation process is as follows: Interpolation calculation: Let the i-th data point in the deviatoric stress-axial strain experimental curve be the experimental value of axial strain. The corresponding experimental value of deviatoric stress Let the i-th data point in the deviatoric stress-axial strain simulation curve be the simulated axial strain value. The corresponding simulated deviatoric stress value is Interpolation algorithms were used to obtain the experimental values ​​of axial strain. Corresponding simulated values ​​of deviatoric stress ; Calculate the root mean square error (RMSE) of the deviatoric stress. q The formula for its calculation is: Normalized root mean square error of deviatoric stress (NRMSE) q The formula for calculation is: Where, max( ) represents the maximum value among n deviatoric stress experimental values ​​in the deviatoric stress-axial strain experimental curve, min( () represents the minimum value among n deviatoric stress experimental values ​​in the deviatoric stress-axial strain experimental curve; Step 2.3, Normalized root mean square error of volumetric strain (NRMSE) v Calculation For the volumetric strain-axial strain curve characterizing the dilatation / contraction properties of soil, the normalized root mean square error of volumetric strain (NRMSE) is... v The calculation process is as follows: Interpolation calculation: Let the i-th data point in the volumetric strain-axial strain experimental curve be the experimental value of axial strain. The corresponding volumetric strain experimental value is Let the i-th data point in the volumetric strain-axial strain simulation curve be the simulated axial strain value. The corresponding simulated volumetric strain value is Interpolation algorithms were used to obtain the experimental values ​​of axial strain. Corresponding volumetric strain simulation values ; Calculate the root mean square error (RMSE) of volumetric strain v The formula for its calculation is: Normalized root mean square error of volumetric strain (NRMSE) v The formula for calculation is: Where, max( ) represents the maximum value among n volumetric strain experimental values ​​in the volumetric strain-axial strain experimental curve, min( () represents the minimum value among the n volumetric strain experimental values ​​in the volumetric strain-axial strain experimental curve; Step 2.4, calculate the scalar normalized root mean square error E. Introducing the deviatoric stress weighting coefficient and volumetric strain weighting coefficient And satisfy + =1; The formula for calculating the scalar normalized root mean square error E is: 。 4. The method for identifying constitutive model parameters of microbial solidified soil according to claim 1, characterized in that, The implementation process of step 3 is as follows: Step 3.1, determine the feasible region 1 for each parameter to be identified. Based on statistical data, the feasible region 1 for each parameter to be identified is determined to be [X]. min , X max ], where X min and X max These are vectors composed of the lower and upper limits of each parameter to be identified; Step 3.2: Perform a global search in feasible region 1 using an improved radial motion optimization algorithm. First, define the parameter dimension, which is the number of parameters to be identified; set the number of particles J in the population; give the number of iterations G, and record any one of the iterations as the g-th iteration. An improved radial motion algorithm is used to perform a global exploration within the feasible region 1 determined in step 3.1, and the region where the optimal solution may exist is located through G iterations. The process is as follows: Step 3.2.1: First, randomly generate an initial population containing N particles, and denote any particle in the initial population as particle X. j-0 0 indicates the initial state, j is the particle number, j=1,...,J; when there is one parameter to be identified, each particle represents one parameter to be identified; when there are two or more parameters to be identified, each particle represents a group of parameters to be identified. Define the fitness function as the scalar normalized root mean square error E described in step 2, and calculate the fitness function values ​​F(X) of the J particles in the initial population. j-0 ), and select the fitness function value F(X) from it. j-0 The position of the smallest particle is taken as the initial global optimal position G. bestloc-0 And the corresponding fitness function value is denoted as F(G). bestloc-0 ); Set the initial global optimum position as the initial survival space center cp0, which will be used to guide the search direction of the population during the first iteration; Step 3.2.2: Perform the 2nd to Gth iterations, where the process of the gth iteration is as follows: Calculate X for each particle in the g-th iteration j-g fitness function value F(X) j-g ); For each particle X in the g-th iteration j-g Generate a trial position Y j-g Its expression is: Among them, cp (g-1) W is the center of the survival space obtained in the (g-1)th iteration. g Let w be the iteration weight coefficient for the g-th iteration. g =1.0(g / G)-0.8(g / G), which adaptively changes with the number of iterations: Calculate the trial position Y j-g The corresponding fitness value F(Y) j-g ); The position of the particle is updated through a greedy selection mechanism; specifically, when F(Y) j-g ) <F(X j-g When particle X is at time )), j-g Move to new location Y i-j That is, let F(X) j-g )= F(Y j-g Otherwise, particle X i-j It will remain in its original position, i.e., F(X) j-g () Remain unchanged; Once all N particles in the g-th iteration have completed their position updates, proceed to step 3.2.3; Step 3.2.3: Update the global optimal position and the center of the survival space. First, from the updated fitness function values ​​of the G particles in the g-th generation, select the position of the particle with the smallest fitness function value as the pre-selected global optimal position for the g-th iteration, and record the corresponding fitness function value as the pre-selected fitness function value for the g-th iteration. Next, the pre-selected global optimal position in the g-th generation is compared with the global optimal position in the (g-1)-th iteration: specifically, if the pre-selected fitness function value in the g-th iteration is less than the fitness function value corresponding to the global optimal position in the (g-1)-th iteration, then the pre-selected global optimal position in the g-th iteration is taken as the global optimal position in the g-th iteration, and denoted as the global optimal position G in the g-th iteration. bestloc-g The corresponding preselected fitness function value is the fitness function value of the g-th iteration, and is denoted as the fitness function value F(G) of the g-th iteration. bestloc-g Otherwise, take the global optimal position of the (g-1)th iteration as the global optimal position G of the g-th iteration. bestloc-g ; Then, the survival space center is dynamically adjusted. Specifically, the survival space center in the g-th iteration is denoted as cp. g This CP g The optimal position in the g-th iteration is determined by both the globally optimal position in the g-th iteration and the pre-selected optimal position in the g-th iteration. Let the pre-selected optimal position in the g-th iteration be denoted as R. bestloc The calculation formula is: Where C1 is the first proportionality coefficient and C2 is the second proportionality coefficient; cp g It will be used to guide the search direction of the population during the (g+1)th iteration; Step 3.2.4: Repeat steps 3.2.2-3 until the maximum number of iterations G is reached, and output the globally optimal position G obtained in the G-th iteration. bestloc-G The globally optimal position G bestloc-G The corresponding one or one set of parameters to be identified is the optimal solution obtained by global search within feasible region 1, and is denoted as the preliminary solution; Step 3.3, Local refinement iteration centered on the preliminary solution Centered on the preliminary solution obtained in step 3.2, a narrowed feasible region 2 is constructed for each parameter to be identified. Specifically, the value of the preliminary solution for any parameter to be identified is denoted as A, and the feasible region 2 for that parameter is [X]. min2 X max2 ], where X min2= AB%A, X max2= A+B%A, where B is the reduction ratio, and B is 7-12; Within this feasible region 2, steps 3.2.2-3.2.4 are run again to obtain the globally optimal position G obtained in the G-th iteration within feasible region 2. bestloc-G2 The globally optimal position G bestloc-G2 The corresponding parameters to be identified are the optimal solution for this identification, that is, the optimal parameter vector to be identified with the smallest scalar normalized root mean square error E, thus completing the identification of the parameters to be identified.

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