Construction method of creep constitutive model of coral sand

Abstract

The invention relates to the technical field of coral sand creep constitutive model construction, and discloses a method for constructing a coral sand creep constitutive model, comprising the following steps: obtaining a dynamic deformation of a coral sand sample that changes with strain and time in a compression creep test; constructing a strain-time relationship curve based on the dynamic deformation, and judging the linear characteristics of the strain-time relationship curve; selecting multiple creep models to form a model set according to the linear characteristics; using a parameter inversion method, substituting required parameters of multiple creep models obtained by inversion calculation into each creep model, and calculating the creep deformation and viscosity coefficient of each creep model under the action of a time and load output program; obtaining a target model by comparison; solving multiple target models to obtain parameter inversion results; using the parameter inversion results to obtain creep curves calculated under multiple target models, and respectively obtaining creep characteristics corresponding to the multiple target models; combining the multiple target models to obtain a creep constitutive model for coral sand.

Description

Technical Field

[0001] The invention relates to the technical field of coral sand creep constitutive model construction, and in particular to a method for constructing a coral sand creep constitutive model. Background Art

[0002] Coral sand is the main material for island and reef construction. Calcareous sand is mainly composed of coral and shell fragments, rich in calcium carbonate, but coral sand has irregular shapes, is rich in pores, has low strength and is easy to break, which is very different from the sand commonly used on land. Under long-term pressure, the coral sand foundation will produce a long-term continuous deformation, which will harm the constructed buildings. Therefore, it is very important to study the long-term creep characteristics of coral sand.

[0003] At present, a series of indoor tests have been carried out on the creep of sand, including one-dimensional and three-dimensional compression tests. A series of triaxial compression tests have been carried out on coral sand to study the creep deformation law under different stresses and analyze the influence of factors such as strain rate on creep. One-dimensional compression tests and creep tests have been carried out on coral sand. The results show that there is a strong correlation between the creep rate coefficient and the compressibility index. The creep properties of coral sand and silica sand have been analyzed by triaxial tests, and the influence of deviatoric stress, confining pressure and relative density on creep properties have been considered. The results show that the volume creep, axial creep and shear creep of coral sand are greater than those of silica sand. However, the research on the creep properties of coral sand mainly focuses on the analysis of appearance, and a relatively complete one-dimensional and three-dimensional creep mathematical model for coral sand has not been established. The creep model of soil often adopts the component model or the empirical model. Among them, the empirical model summarizes the constitutive relationship based on the test results of soil stress deformation, and uses a certain amount of parameters to fit the results. Based on the results of a series of triaxial creep tests, the empirical relationship of soil stress-strain-time and the power function of soil strain development over time are proposed. The power function is used to mathematically describe the creep strain-time of calcareous sand, and the fitting degree is improved compared with the classic Mesri creep model. The stress-strain and strain-time relationships are expressed by hyperbolic functions to establish a creep model, which is compared with the experimental values.

[0004] Although the empirical model is easy to obtain and apply, the physical meaning of each parameter in the formula is unclear and the calculation is mostly dependent on test results, so it has poor universality and is not convenient for numerical application. Compared with the empirical formula, the mechanical element to simulate the creep deformation of soil has the advantages of intuitive concept and clear physical meaning. It can be directly substituted into the numerical value for calculation.

[0005] A uniaxial compression test was carried out on saturated sandy soil, and the identification was carried out through the Merchant model and the Burgers model. Finally, it was verified that the Burgers model can better describe the rheological properties of aquifer sand; a one-dimensional creep test study was carried out on medium and fine sand under high stress state using a high-pressure consolidation instrument, and a generalized Kelvin model suitable for the creep characteristics of medium and fine sand was proposed; one-dimensional creep tests were carried out on sand samples with different fine particle contents, and the generalized Kelvin model was used to describe the creep characteristics of saturated sand with different fine particle contents, which had a high degree of fit with the test results.

[0006] The current research is mainly aimed at the creep model of sand. There are great differences in mechanical properties between coral sand and land sand, and the research on the creep model of coral sand is not in-depth enough. By conducting triaxial creep tests on coral sand under general stress states, a new creep constitutive model was established using different rheological elements, which theoretically described the creep characteristics of calcareous sand. Based on the coral sand creep test data, a new four-parameter mathematical model was proposed, and an element model of the creep characteristics of calcareous coral sand was given. However, most of the existing creep models are combinations of classical elements, and the element model parameters are all constants, which can only represent linear elastic characteristics. The nonlinear characteristics of the attenuation creep stage of coral sand cannot be accurately described, and a three-dimensional model has not been established. Summary of the invention

[0007] In view of this, the main purpose of the present invention is to provide a method for constructing a coral sand creep constitutive model, comprising the following steps:

[0008] Obtain the dynamic deformation of coral sand samples in compression creep tests that varies with strain and time, as well as the test values ​​of creep deformation, viscosity coefficient, and characteristic values ​​on the creep curve;

[0009] Constructing a strain-time relationship curve based on the dynamic deformation amount, and determining the linear characteristics of the strain-time relationship curve;

[0010] Selecting multiple creep models to form a model set according to the linear characteristics, and writing the model set into an inversion program with a programmable controller as a carrier, wherein the inversion program includes an identification module for identifying basic creep characteristics of multiple creep models;

[0011] The inversion program adopts a parameter inversion method to identify the basic creep characteristics of multiple creep models based on the identification module, and substitutes the required parameters of multiple creep models obtained by inversion calculation into multiple creep models to calculate the creep deformation and viscosity coefficient of each creep model under the action of the time and load output program;

[0012] Comparing the creep deformation and viscosity coefficient with test values, and obtaining multiple creep models with creep deformation and viscosity coefficient exceeding a set range as target models;

[0013] The multi-parameter comprehensive inversion program compiled by MATLAB was used to solve multiple target models and obtain parameter inversion results. The creep curves calculated under multiple target models were obtained using the parameter inversion results, and the characteristic values ​​on the creep curves were compared with the experimental values ​​to obtain the creep characteristics corresponding to the multiple target models. The multiple target models were combined according to their corresponding creep characteristics to obtain the creep constitutive model for coral sand.

[0014] Furthermore, before the compression creep test, the obtained coral sand samples were pretreated, and after the pretreatment, the coral sand samples were saturated using the air extraction saturation method.

[0015] Furthermore, during the compression creep test, the time interval of the compression creep test and the vertical stress applied at each time interval are set, and the loading standard of each level of load is set so that the dynamic deformation of the previous level of load within 24 hours is no more than 0.01 mm.

[0016] Furthermore, the strain-time relationship curve is converted into a stress-strain isochronous curve through a conversion module, and the change characteristics of the axial strain rate when the uniaxial compressive stress gradually increases are obtained according to the stress-strain isochronous curve, and the corresponding linear characteristics are divided according to the change characteristics of the axial strain rate.

[0017] Furthermore, the linear characteristics include linear characteristics and nonlinear characteristics.

[0018] Furthermore, the model set is composed of a combination of creep models that characterize decay creep properties, including multiple models of elastic body model, Merchant model, Kelvin model, generalized Kelvin model, Burgers model and Fullerton-Thomson body model.

[0019] Furthermore, the inversion procedure includes:

[0020] Program part I for calling, loading and operating any creep model in the model set based on pointing instructions;

[0021] A program part II for identifying the basic creep characteristics of any creep model in the model set by the identification module when performing parameter inversion based on the inversion program;

[0022] Part III of the program for outputting the creep deformation and viscosity coefficient of each creep model under the action of the time and load output program;

[0023] Part IV of the procedure for receiving and analyzing the creep deformation and viscosity coefficient; and

[0024] The program part V outputs the analysis results.

[0025] Furthermore, the inversion program includes an objective function used for inversion.

[0026] Furthermore, the objective function is derived by the homotopy method, which specifically includes:

[0027] The objective function is established as:

[0028] in, are the inversion values, S and S c are the calculated creep deformation of coral sand and the strain obtained from the test;

[0029] Introducing the homology parameter λ in the objective function, λ∈[1,0], puts a simple problem and the problem to be solved into the same function, as shown in formula (2):

[0030]

[0031] In the formula, is the selected initial value.

[0032] Furthermore, the creep characteristics corresponding to the multiple target models are correlated with each other according to the creep stages of the coral sand, and the multiple target models are combined through their correlation to obtain a creep constitutive model for the coral sand.

[0033] The association relationship is obtained through a judgment model;

[0034] Among them, the judgment model is: ①: used to judge whether the target model can reflect the creep characteristic I with instantaneous elastic strain in the early stage of creep. If so, the creep characteristic I of instantaneous elastic strain is expressed by the elastic body model in the early stage of creep; ②: used to judge whether the creep curve obtained by the target model in the viscoelastic stage is different from the test value obtained by the experiment, and when the characteristic value on the creep curve is lower than the test value obtained by the experiment, the adapted target model is selected to form a series connection with the elastic body model to improve the target model, and an improved target model in the viscoelastic stage is obtained; ③: used to judge whether the improved target model has nonlinear curve characteristics. If so, the viscosity coefficient is corrected by introducing a time function; used to judge whether the creep characteristic II in the late stage of creep is gradually stabilized and the strain and time are approximately linearly related. If so, the creep characteristic II in the late stage of creep is expressed by the Kelvin model.

[0035] The creep constitutive model is improved from a one-dimensional creep constitutive model to a three-dimensional creep constitutive model by setting a conversion program through a programmable controller.

[0036] The conversion program is provided with a conversion equation group, and the creep constitutive model in a one-dimensional state is improved into a creep constitutive model in a three-dimensional state by setting the execution order and execution rules of the conversion equation group.

[0037] The beneficial effects of the present invention are as follows: since the creep characteristics of coral sand have different characteristics at different stages, the creep deformation of coral sand can be divided into two stages, the first stage is the elastic deformation stage, and the second stage is the stable creep deformation stage. In the first stage, the deformation increases significantly with the increase of loading time, but over time, the deformation at the same time interval gradually decreases, and the final deformation tends to a certain value. Therefore, in the first stage, it basically has linear characteristics. At this stage, the isochronous curves of coral sand almost overlap, but with the increase of stress, the isochronous curves gradually separate, and the creep of coral sand has a certain hysteresis. At the same time, the strain shows a nonlinear increase trend with the increase of stress, which also indicates that a nonlinear creep model should be selected when constructing the model later; therefore, the present application integrates the traditional creep model and judges the creep characteristics of different stages through different creep models, so as to find the correlation between different creep models, thereby combining multiple creep models to obtain a model that can describe the creep characteristics of coral sand. The required parameters are obtained by the parameter inversion method, and the creep model is identified. Finally, the one-dimensional creep nonlinear model is derived into a three-dimensional state, and the applicability and accuracy of the one-dimensional and three-dimensional creep models are verified through existing test results. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The following drawings are only used to illustrate and explain the present invention, and are not used to limit the scope of the present invention, wherein:

[0039] Figure 1 is the coral sand grading curve of the present invention;

[0040] Figure 2 The strain-time curve of coral sand under different pressures of the present invention;

[0041] Figure 3 It is a stress-strain isochronal curve diagram of uniaxial compression of coral sand of the present invention;

[0042] Figure 4 The figure is a comparison chart of the Merchant model calculation and test results of the present invention;

[0043] Figure 5 A comparison diagram of the Kelvin model calculation and test results of the present invention;

[0044] Figure 6 This is a comparison chart of the calculation and test results of the generalized Kelvin model of the present invention;

[0045] Figure 7This is a comparison diagram of the Burgers model calculation and test results of the present invention;

[0046] Figure 8 A comparison diagram of the calculation and test results of the Felten-Thomson body model of the present invention;

[0047] Fig. 9 This is a schematic diagram of the improved MHK model of the present invention;

[0048] Fig.10 This is a comparison chart of the calculation and test results of the improved MHK model of the present invention;

[0049] Fig.11 This is a strain-time curve of coral sand under a confining pressure of 100 kPa according to the present invention;

[0050] Fig.12 This is a strain-time curve of coral sand under a confining pressure of 200 kPa according to the present invention;

[0051] Fig.13 This is a strain-time curve of coral sand under a confining pressure of 300 kPa according to the present invention;

[0052] Fig.14 This is a comparison chart of the calculated value of the improved MHK model under 100 kPa confining pressure and the triaxial test result of the present invention;

[0053] Fig.15 This is a comparison chart of the calculated value of the improved MHK model under 200 kPa confining pressure and the triaxial test result of the present invention;

[0054] Fig.16 It is a comparison chart of the calculated value of the improved MHK model under 300kPa confining pressure and the triaxial test result of the present invention;

[0055] Fig.17 It is a comparison chart of the on-site monitoring value and the calculation result of the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution, design method and advantages of the present invention clearer, the present invention is further described in detail by specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0057] Embodiment 1: A method for constructing a creep constitutive model of coral sand, comprising the following steps:

[0058] Obtain the dynamic deformation of coral sand samples in compression creep tests as strain and time change; Obtain the dynamic deformation of coral sand samples in compression creep tests as strain and time change, as well as the test values ​​of creep deformation, viscosity coefficient and characteristic values ​​on the creep curve;

[0059] Constructing a strain-time relationship curve based on the dynamic deformation amount, and determining the linear characteristics of the strain-time relationship curve;

[0060] Selecting multiple creep models to form a model set according to the linear characteristics, and writing the model set into an inversion program with a programmable controller as a carrier, wherein the inversion program includes an identification module for identifying basic creep characteristics of multiple creep models;

[0061] The inversion program adopts a parameter inversion method to identify the basic creep characteristics of multiple creep models based on the identification module, and substitutes the required parameters of multiple creep models obtained by inversion calculation into multiple creep models to calculate the creep deformation and viscosity coefficient of each creep model under the action of the time and load output program;

[0062] Comparing the creep deformation and viscosity coefficient with test values, and obtaining multiple creep models with creep deformation and viscosity coefficient exceeding a set range as target models;

[0063] A multi-parameter comprehensive inversion program compiled by MATLAB (MATrix LABoratary, commercial mathematical software) was used to solve multiple target models and obtain parameter inversion results. The creep curves calculated under multiple target models were obtained using the parameter inversion results, and the characteristic values ​​on the creep curves were compared with the experimental values ​​to obtain the creep characteristics corresponding to the multiple target models. The multiple target models were combined according to the creep characteristics corresponding to the multiple target models to obtain the creep constitutive model for coral sand.

[0064] Furthermore, before the compression creep test, the obtained coral sand samples were pretreated, and after the pretreatment, the coral sand samples were saturated using the air extraction saturation method.

[0065] Furthermore, during the compression creep test, the time interval of the compression creep test and the vertical stress applied at each time interval are set, and the loading standard of each level of load is set so that the dynamic deformation of the previous level of load within 24 hours is no more than 0.01 mm.

[0066] Furthermore, the strain-time relationship curve is converted into a stress-strain isochronous curve through a conversion module, and the change characteristics of the axial strain rate when the uniaxial compressive stress gradually increases are obtained according to the stress-strain isochronous curve, and the corresponding linear characteristics are divided according to the change characteristics of the axial strain rate.

[0067] Furthermore, the linear characteristics include linear characteristics and nonlinear characteristics.

[0068] Furthermore, the model set is composed of a combination of creep models that characterize decay creep properties, including multiple models of elastic body model, Merchant model, Kelvin model, generalized Kelvin model, Burgers model and Fullerton-Thomson body model.

[0069] Furthermore, the inversion procedure includes:

[0070] Program part I for calling, loading and operating any creep model in the model set based on pointing instructions;

[0071] A program part II for identifying the basic creep characteristics of any creep model in the model set by the identification module when performing parameter inversion based on the inversion program;

[0072] Part III of the program for outputting the creep deformation and viscosity coefficient of each creep model under the action of the time and load output program;

[0073] Part IV of the procedure for receiving and analyzing the creep deformation and viscosity coefficient; and

[0074] The program part V outputs the analysis results.

[0075] Furthermore, the inversion program includes an objective function used for inversion.

[0076] Furthermore, the objective function is derived by the homotopy method, which specifically includes:

[0077] The objective function is established as:

[0078] in, are the inversion values, S and S c are the calculated creep deformation of coral sand and the strain obtained from the test;

[0079] By introducing the homology parameter λ, λ∈[1,0], into the objective function, a simple problem and the problem to be solved can be placed in the same function, as shown in formula (2):

[0080]

[0081] In the formula, is the initial value selected. When λ = 0, equation (2) is transformed into the problem to be solved. Therefore, the equation group H satisfies the following conditions:

[0082]

[0083] This deduction process is called the homotopy method, λ is the homotopy parameter, and H(x,λ) is the homotopy equation.

[0084] Furthermore, the creep characteristics corresponding to the multiple target models are interrelated with each other along the creep stage of the coral sand. The multiple target models are combined through their association relationship to obtain the creep constitutive model for the coral sand.

[0085] The association relationship is obtained through a judgment model;

[0086] Among them, the judgment model is: ①: used to judge whether the target model can reflect the creep characteristic I with instantaneous elastic strain in the early stage of creep. If so, the creep characteristic I of instantaneous elastic strain is expressed by the elastic body model in the early stage of creep; ②: used to judge whether the creep curve obtained by the target model in the viscoelastic stage is different from the test value obtained by the experiment, and when the characteristic value on the creep curve is lower than the test value obtained by the experiment, the adapted target model is selected to form a series connection with the elastic body model to improve the target model, and an improved target model in the viscoelastic stage is obtained; ③: used to judge whether the improved target model has nonlinear curve characteristics. If so, the viscosity coefficient is corrected by introducing a time function; used to judge whether the creep characteristic II in the late stage of creep is gradually stabilized and the strain and time are approximately linearly related. If so, the creep characteristic II in the late stage of creep is expressed by the Kelvin model.

[0087] The creep constitutive model is improved from a one-dimensional creep constitutive model to a three-dimensional creep constitutive model by setting a conversion program through a programmable controller.

[0088] The beneficial effects of the present invention are as follows: since the creep characteristics of coral sand have different characteristics at different stages, the creep deformation of coral sand can be divided into two stages, the first stage is the elastic deformation stage, and the second stage is the stable creep deformation stage. In the first stage, the deformation increases significantly with the increase of loading time, but over time, the deformation at the same time interval gradually decreases, and the final deformation tends to a certain value. Therefore, in the first stage, it basically has linear characteristics. At this stage, the isochronous curves of coral sand almost overlap, but with the increase of stress, the isochronous curves gradually separate, and the creep of coral sand has a certain hysteresis. At the same time, the strain shows a nonlinear increase trend with the increase of stress, which also indicates that a nonlinear creep model should be selected when constructing the model later; therefore, the present application integrates the traditional creep model and judges the creep characteristics of different stages through different creep models, so as to find the correlation between different creep models, thereby combining multiple creep models to obtain a model that can describe the creep characteristics of coral sand. The required parameters are obtained by the parameter inversion method, and the creep model is identified. Finally, the one-dimensional creep nonlinear model is derived into a three-dimensional state, and the applicability and accuracy of the one-dimensional and three-dimensional creep models are verified through existing test results.

[0089] Embodiment 2: This embodiment verifies the above-mentioned technical scheme through experiments.

[0090] The surface of the coral sand used in this application is grayish white, uncemented, loose marine debris sediment. The sample is mainly composed of particles with a particle size of 0.3 to 1.2 mm (mass proportion is greater than 50%). The grading curve of the coral sand is as follows: Figure 1 As shown;

[0091] In order to study the creep characteristics of coral sand, a one-dimensional compression creep test was carried out using a single-lever high-pressure consolidation instrument. The diameter of the sample used in the test was 61.8 mm and the height was 20 mm. Since the internal pores of coral sand are difficult to saturate, the coral sand samples were pretreated before the test began. After pretreatment, the coral sand samples were saturated by the method of vacuum saturation. The sample saturation was determined by the B value method, and when the B value was greater than 0.95, it was considered to meet the requirements. The applied vertical stresses were 50kPa, 100kPa, 200kPa, 400kPa, and 800kPa, respectively. Weights were used for graded loading. The loading standard for each level of load was that the deformation of the sample within 24 hours of the previous level of load was not more than 0.01mm.

[0092] Figure 2 The strain-time relationship curve of coral sand under various levels of load. It can be seen from the figure that the creep deformation of coral sand can be divided into two stages. The first stage is the elastic deformation stage, and the second stage is the stable creep deformation stage. In the first stage, the deformation increases significantly with the increase of loading time, but with the passage of time, the deformation at the same time interval gradually decreases, and the final deformation tends to a certain value. It can be seen from the figure that with the increase of vertical load, the initial deformation of coral sand gradually increases. For the original graded coral sand, the initial elastic deformation at 50kPa, 100kPa, 200kPa, 400kPa, and 800kPa is 1.475%, 2.59%, 3.39%, 6.2%, and 9.8%, respectively, accounting for about 90% of the total deformation. Therefore, the creep deformation of coral sand is mainly elastic-plastic deformation.

[0093] Figure 3 The stress-strain isochronal curves in the natural coordinate system show that in the low stress range, the isochronal curves of coral sand almost overlap, but as the stress increases, the isochronal curves gradually separate, and the creep of coral sand has a certain hysteresis. At the same time, the strain increases nonlinearly with the increase of stress, which also indicates that a nonlinear creep model should be selected when constructing the model later.

[0094] Since the creep properties of coral sand have different characteristics at different stages, the creep deformation of coral sand can be divided into two stages, the first stage is the elastic deformation stage, and the second stage is the stable creep deformation stage. In the first stage, the deformation increases significantly with the increase of loading time, but over time, the deformation at the same time interval gradually decreases, and the final deformation tends to a certain value. Therefore, in the first stage, it basically has linear characteristics. At this stage, the isochronous curves of coral sand almost overlap, but with the increase of stress, the isochronous curves gradually separate, and the creep of coral sand has a certain hysteresis. At the same time, the strain shows a nonlinear increase trend with the increase of stress, which also indicates that a nonlinear creep model should be selected when constructing the model later; therefore, when selecting a model set, a creep model that characterizes the attenuated creep property is selected, including the Merchant model, Kelvin model, generalized Kelvin model, Burgers model and multiple models of the Fully-Thomson body. In this way, the characteristics of different stages of coral sand creep deformation can be expressed by different models. Compared with traditional technical means, the present application can provide a standard expression of the characteristics of different stages of creep deformation. Although the creep deformation characteristics of different materials are inconsistent in different test processes, corresponding creep models can be selected under the model set to express them.

[0095] It can be seen from the creep test results of coral sand that the initial stage of creep is mainly the elastic deformation stage, which gradually transitions to the viscoelastic stage and finally to the plastic stage. In order to analyze and predict the creep properties of coral sand, this application uses a variety of creep models with the same components in different connection methods to simulate the complex deformation of coral sand. Considering the viscoelastic creep of coral sand, Hooke's spring is used to simulate its elastic deformation, and Newton's viscosity is used to consider its attenuation creep characteristics. Different models use the same type of components, but the number and combination of components are not the same. This application mainly uses 5 commonly used creep models that can characterize the attenuation creep properties, namely the Merchant model, Kelvin model, generalized Kelvin model, Burgers model and Fuller-Thomson body model.

[0096] In order to compare the applicability of different creep models, the parameter inversion method can be used to identify different models. The required parameters of each model obtained by inversion calculation are substituted into each model to calculate the deformation of each model under different loads at different times.

[0097] In the calculation, the objective function is first established as:

[0098] in, are the inversion values, S and S c are the calculated creep deformation of coral sand and the strain obtained from the test;

[0099] In order to solve the problem of selecting the initial value and ensure the convergence of the result, the homology parameter λ is introduced into the objective function, λ∈[1,0], so that a simple problem and the problem to be solved can be placed in the same function, as shown in formula (2):

[0100]

[0101] In the formula, are the selected initial value and inversion value respectively. When λ = 0, equation (2) is transformed into the problem to be solved. Therefore, the equation group H satisfies the following conditions:

[0102]

[0103] This calculation process is called the homotopy method, λ is the homotopy parameter, and H(x,λ) is the homotopy equation.

[0104] For the coral sand creep problem, the elastic modulus and viscosity coefficient, which have a greater impact on the results, are obtained through the parameter inversion method, and the multi-parameter comprehensive inversion program compiled by MATLAB (MATrix LABoratary, commercial mathematical software) is used to solve it. The parameter inversion results are substituted into different viscoelastic creep models to obtain the creep curves calculated under different models, and the characteristic values ​​on the creep curves are compared with the experimental values. The creep curves under each model are shown in Figure 2. Figures 4 to 8 As shown in the figure, the experimental values ​​are represented by solid lines and the calculated values ​​are represented by scattered points.

[0105] As can be seen from the figure, there is a large gap between the experimental values ​​of the Burgers model and the Kelvin model. The characteristic values ​​of the creep curve of the Burgers model under each load are greater than the experimental values, but they are relatively consistent in the initial stage; the Kelvin model is lower than the experimental value, and it deviates from the experimental value as a whole. The other three models are closer to the experimental values. In order to verify the applicability of each model, the correlation coefficient is used to describe the fit between the calculated value and the experimental value. Table 1 shows the average correlation coefficients of different creep models. Except for the Kelvin model, the correlation coefficients of the other models are all greater than 0.6, which can be considered to be strongly correlated. This proves that the selected model is completely feasible to a certain extent, and also verifies the creep property of coral sand from the side.

[0106] Although the generalized Kelvin model has the highest correlation coefficient, which is close to 0.8 and is a very strong correlation, the initial calculation error is large, and a large deviation occurs under high stress (800kPa). The Merchant model is closest to the test value in the early stage, but the result is slightly lower than the test value in the later stage, which is the main reason for the error. The average correlation coefficients of each model are shown in Table 1.

[0107] Table 1

[0108]

[0109] According to the different characteristics of each stage of coral sand creep, different component combinations are selected to improve the creep model. The sample will produce a large instantaneous elastic strain at the initial loading stage. Since this stage only accounts for a small part of the entire creep process, it can be considered that the elastic deformation is completed instantaneously. This stage can be represented by an elastic body model, and the constitutive equation is:

[0110]

[0111] Where, σ is the stress applied in the test;

[0112] For the viscoelastic stage, in order to solve the problem that the characteristic value on the Kelvin model creep curve is lower than the experimental value, it is improved. By adding an elastic body model in parallel, the HM body model is formed. At the same time, this section of the curve has a more obvious nonlinear characteristic. By introducing the time function to correct the viscosity coefficient, it is assumed that the viscosity coefficient has an exponential function relationship with time during the creep process of coral sand, and a nonlinear MH model is constructed. The constitutive relationship of the MH model is:

[0113]

[0114] Where ε is the strain, To integrate the strain, To integrate the stress applied in the test;

[0115] Introducing the time function into equation (4), its differential constitutive equation satisfies:

[0116]

[0117] Convert equation (5) into a form that can be used to transform constants:

[0118]

[0119] Thus, the general solution of formula (6) is:

[0120]

[0121] Using the initial conditions, at time t = 0, σ is constant at σ0. After substituting the general solution, the creep equation of the nonlinear MH body model can be obtained:

[0122]

[0123] In the later stage of creep, the strain curve gradually becomes stable, and the strain and time are approximately linearly related. The Kelvin model is used to represent it, and its constitutive equation is: After separating the variables, the creep equation is obtained as follows:

[0124]

[0125] The above elastic body model, nonlinear MH body model and Kelvin model are connected in series to obtain an improved MHK creep model that can describe the characteristics of each stage of coral sand creep, such as Fig. 9 shown.

[0126] Combining equations (2), (7) and (8), the equation of the nonlinear creep model of coral sand can be obtained, as shown in equation (10):

[0127]

[0128] In formulas (3)-(10), σ is the stress applied in the test, E1, E2, E3, and E4 are the elastic moduli of different components, η and η2 are different viscosity coefficients, λ is the homotopy parameter, and t is the time parameter;

[0129] Using the improved coral sand creep model, the required physical property parameters are obtained through inversion calculation, and the creep curve is obtained by substituting it into the creep formula. The characteristic values ​​on the creep curve are compared with the experimental values, such as Fig.10 shown.

[0130] As can be seen from the figure, the calculation results of the improved nonlinear MHK model are basically consistent with the test values, and the problem of being lower than the test values ​​in the later stage has been effectively solved. According to calculations, the average correlation coefficient of the improved model is 0.919359, which is a very strong correlation, and the average relative error is 1.150%, which is a great improvement compared to the single model.

[0131] Figures 11 to 13 The curves of axial strain and time in the triaxial creep test of coral sand under different confining pressures are similar to the uniaxial compression creep curve, which is divided into elastic deformation stage and stable creep deformation stage, and basically tends to be stable after 1000-2500 minutes. The elastic deformation increases step by step with the increase of deviator stress. Taking the confining pressure of 100kPa as an example, the initial elastic-plastic deformation generated by deviator stress of 100kPa, 200kPa, 300kPa, 400kPa, and 480kPa are 0.6%, 1.2%, 2.1%, 3.0%, and 4.4%, respectively, accounting for about 80% of the total deformation.

[0132] Most existing creep models are one-dimensional and cannot accurately describe the creep process in three-dimensional state. We use the verified one-dimensional improved nonlinear MHK model and extend it to three-dimensional form to establish a coral sand creep model in three-dimensional state. The stress tensor is decomposed into the deviator stress tensor S ij and the spherical stress tensor δ ij σ m , δ ijis Kronecker, Kronecker tensor; σ m is the mean stress, Similarly, the strain tensor ε ij Decomposed into the deviatoric strain tensor e ij and the spherical strain tensor δ ij ε m ; According to the generalized Hooke's law, we can get:

[0133]

[0134] Where K is the bulk modulus, G is the shear modulus, ε m is the strain, e ij is the deviatoric strain tensor;

[0135] For the elastic body model, its three-dimensional creep equation can be expressed as:

[0136]

[0137] Among them, S ij is the deviatoric stress tensor, δ ij σ m is the spherical stress tensor, δ ij is the Kronecker tensor; σ m is the mean stress;

[0138] The three-dimensional creep equation of the nonlinear MH body model is:

[0139]

[0140] The three-dimensional creep equation of the Kelvin model is:

[0141]

[0142] For triaxial compression creep, where:

[0143]

[0144] Substituting into formulas (10)-(12), we can obtain the creep formula of coral sand in three-dimensional state:

[0145]

[0146] In formulas (11)-(16), H and H2 are different viscosity coefficients in the three-dimensional creep model, K1 is the bulk modulus, G1, G2, G3, and G4 are different shear moduli, σ1, σ2, and σ3 are different stresses, λ is the homotopy parameter, and t is the time parameter;

[0147] like Figures 14 to 16As shown in the figure, the comparison between the calculated values ​​of the improved MHK model and the triaxial test results under different confining pressures is shown. Taking the creep test results with a confining pressure of 300 kPa as an example, they are compared with the calculated values ​​of the three-dimensional nonlinear coral sand creep model compiled by MATLAB (MATrix LABoratary, commercial mathematical software). It can be seen from the figure that the improved coral sand creep model is consistent with the triaxial test values. According to the calculation, the average correlation coefficient of the improved model is 0.9480, which is a very strong correlation, and the average relative error is 1.462%.

[0148] In order to verify the applicability of this application model in actual projects, the Maldives Velana International Airport expansion project was selected, and the on-site monitoring values ​​were compared with the model calculation values. In the calculation, the monitoring point values ​​were used as the original values, and the parameters were obtained through inversion calculation. The settlement values ​​were predicted by the improved MHK creep model. The results are as follows: Fig.17 As shown. As can be seen from the figure, the overall trend of the calculated value and the monitored value is relatively consistent, and can better reflect the various stages of coral sand creep. Through calculation, the correlation coefficients between the monitored values ​​and the calculated results of monitoring point 1 and monitoring point 2 are 0.9803 and 0.9438 respectively, both of which are extremely strongly correlated. The relative errors are 3.273% and 6.1613% respectively. The calculation results of this application are relatively accurate and can well reflect the creep deformation of coral sand in actual engineering. The main reason for the error is the rebound phenomenon produced after the soil is rolled. This part of the deformation accounts for a small proportion, and the time of occurrence is irregular. Therefore, the rebound deformation of this part is ignored in the deformation prediction; at the same time, on-site monitoring will also produce certain errors due to problems such as instrument accuracy and construction personnel operation.

[0149] Through the one-dimensional creep test of coral sand, the characteristics of each creep stage are analyzed. It can be seen from the test curve that the deformation of coral sand under instantaneous loading has obvious staged attenuation creep, and its stress-strain isochronal curve also shows the deformation hysteresis and nonlinearity of coral sand.

[0150] Five traditional models were used to calculate the creep deformation of coral sand. The results showed that there were large deviations between the models and the test values. This application improved the traditional HM body model, constructed a nonlinear MH model, and connected the elastic body model, nonlinear MH model, and Kelvin model in series to obtain the nonlinear improved MHK creep model of coral sand. The inversion calculation was improved by combining the homology method to obtain the parameters required for creep calculation and identify the creep model.

[0151] The nonlinear three-dimensional creep constitutive model is derived through stress and strain tensor decomposition and generalized Hooke's law. The accuracy of the nonlinear improved creep model constructed in this application is verified by using uniaxial compression test data and conventional triaxial compression creep test data of coral sand under different confining pressures and stress levels. The improved model can not only accurately describe the creep stages of coral sand, but also well reflect the nonlinearity of the attenuation creep stage, with high accuracy and strong applicability. Finally, the effectiveness of the model of this application in practical applications is verified through engineering examples.

[0152] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used in this application is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed in this application.

Claims

1. A method for constructing a creep constitutive model of coral sand, characterized in that: The steps include: Obtain the dynamic deformation of coral sand samples in compression creep tests that changes with strain and time, as well as the test values ​​of creep deformation, viscosity coefficient, and characteristic values ​​on the creep curve; Constructing a strain-time relationship curve based on the dynamic deformation amount, and determining the linear characteristics of the strain-time relationship curve; Selecting multiple creep models to form a model set according to the linear characteristics, and writing the model set into an inversion program with a programmable controller as a carrier, wherein the inversion program includes an identification module for identifying basic creep characteristics of multiple creep models; The inversion program adopts a parameter inversion method to identify the basic creep characteristics of multiple creep models based on the identification module, and substitutes the required parameters of multiple creep models obtained by inversion calculation into multiple creep models to calculate the creep deformation and viscosity coefficient of each creep model under the action of the time and load output program; Comparing the creep deformation and viscosity coefficient with test values, and obtaining multiple creep models with creep deformation and viscosity coefficient exceeding a set range as target models; The multi-parameter comprehensive inversion program compiled by MATLAB is used to solve multiple target models and obtain parameter inversion results. The creep curves calculated under multiple target models are obtained using the parameter inversion results, and the characteristic values ​​on the creep curves are compared with the test values ​​to obtain the creep characteristics corresponding to the multiple target models. The multiple target models are combined according to their corresponding creep characteristics to obtain a creep constitutive model for coral sand. The inversion procedure includes: Program part I for calling, loading and operating any creep model in the model set based on pointing instructions; A program part II for identifying the basic creep characteristics of any creep model in the model set by the identification module when performing parameter inversion based on the inversion program; Part III of the program for outputting the creep deformation and viscosity coefficient of each creep model under the action of the time and load output program; Part IV of the program for receiving and analyzing the creep deformation and viscosity coefficient; and a program part V for outputting the analysis results; The inversion program includes an objective function used for inversion; The objective function is derived by the homotopy method, which specifically includes: The objective function is established as: in, are the inversion values, S and S c are the calculated creep deformation of coral sand and the strain obtained from the test; Introducing the homology parameter λ in the objective function, λ∈[1,0], puts a simple problem and the problem to be solved into the same function, as shown in formula (2): In the formula, is the selected initial value.

2. The method for constructing the coral sand creep constitutive model according to claim 1, characterized in that: Before the compression creep test, the obtained coral sand samples were pretreated, and then saturated with the air extraction saturation method.

3. The method for constructing the coral sand creep constitutive model according to claim 1, characterized in that: During the compression creep test, the time interval of the compression creep test and the vertical stress applied at each time interval are set, and the loading standard of each level of load is set so that the dynamic deformation of the previous level of load within 24 hours is not greater than 0.01mm.

4. The method for constructing the coral sand creep constitutive model according to claim 1, characterized in that: The strain-time relationship curve is converted into a stress-strain isochronous curve through a conversion module, and the change characteristics of the axial strain rate when the uniaxial compressive stress gradually increases are obtained according to the stress-strain isochronous curve, and the corresponding linear characteristics are divided according to the change characteristics of the axial strain rate.

5. The method for constructing the coral sand creep constitutive model according to claim 1, characterized in that: The model set is composed of creep models that characterize decay creep properties, including multiple models of elastic body model, Merchant model, Kelvin model, generalized Kelvin model, Burgers model and Fullerton-Thomson body model.

6. The method for constructing a coral sand creep constitutive model according to claim 1, characterized in that: The creep characteristics corresponding to multiple target models are interrelated according to the creep stages of coral sand. Through their association, multiple target models are combined to obtain the creep constitutive model for coral sand.

7. The method for constructing a coral sand creep constitutive model according to claim 6, characterized in that: The association relationship is obtained through a judgment model; Among them, the judgment model is: ①: used to judge whether the target model can reflect the creep characteristic I with instantaneous elastic strain in the early stage of creep. If so, the creep characteristic I of instantaneous elastic strain is expressed by the elastic body model in the early stage of creep; ②: used to judge whether the creep curve obtained by the target model in the viscoelastic stage is different from the test value obtained by the experiment, and when the characteristic value on the creep curve is lower than the test value obtained by the experiment, the adapted target model is selected to form a series connection with the elastic body model to improve the target model, and an improved target model in the viscoelastic stage is obtained; ③: used to judge whether the improved target model has nonlinear curve characteristics. If so, the viscosity coefficient is corrected by introducing a time function; used to judge whether the creep characteristic II in the late stage of creep is gradually stabilized and the strain and time are approximately linearly related. If so, the creep characteristic II in the late stage of creep is expressed by the Kelvin model.

8. The method for constructing a coral sand creep constitutive model according to claim 6, characterized in that: The creep constitutive model is improved from a one-dimensional creep constitutive model to a three-dimensional creep constitutive model by setting a conversion program through a programmable controller.

9. The method for constructing a coral sand creep constitutive model according to claim 8, characterized in that: The conversion program is provided with a conversion equation group, and the creep constitutive model in a one-dimensional state is improved into a creep constitutive model in a three-dimensional state by setting the execution order and execution rules of the conversion equation group.

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