A method for constructing a weakly cemented soft rock fractional order creep damage constitutive model

Abstract

The application provides a construction method of a creep damage constitutive model suitable for weakly cemented soft rock under staged confining pressure, and the method comprises the following steps: carrying out a creep test of weakly cemented soft rock under staged confining pressure, and obtaining creep test data; based on the creep test data, drawing a creep variable-time relationship curve and a creep rate-time relationship curve, and analyzing the creep characteristics of weakly cemented soft rock under staged confining pressure; introducing a Riemann-Liouville fractional integral operator and a negative time index damage evolution variable, defining a nonlinear damage Abel sticky pot, and constructing a creep damage constitutive model suitable for weakly cemented soft rock under staged confining pressure; based on the creep test results under staged confining pressure, using a Levenberg-Marquardt algorithm to preliminarily identify model parameters, and then using an ant colony algorithm to optimize the model parameters, and finally determining optimal model parameters. The model established according to the method can be used to describe the whole process creep damage characteristics of weakly cemented soft rock under excavation unloading conditions, and has important significance for the long-term stability prediction of surrounding rock of underground engineering.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock. Background Technology

[0002] Rock materials exhibit instantaneous deformation and creep characteristics under long-term loading. The total strain under long-term static loading includes instantaneous strain and creep, with creep comprising three stages: decaying creep, constant-rate creep, and accelerated creep. The creep performance of rock materials is a crucial factor for the long-term stability of rock engineering projects such as foundations, slopes, and chambers. Creep models of rock materials reflect the mechanical essence of rock material creep and are fundamental for long-term stability analysis in rock engineering, promoting mine construction and safe, efficient mining, and improving mine engineering design. Weakly cemented soft rock contains numerous microcracks, cavities, and other defects. The longer the soft rock is subjected to loading, the more internal damage accumulates, and the more severe the crack development, ultimately leading to the failure of the soft rock. Therefore, studying the creep damage characteristics of weakly cemented soft rock under unloading pressure has significant engineering implications.

[0003] The mechanical properties of rock masses under excavation unloading conditions differ significantly from those under loading conditions. Scholars both domestically and internationally have conducted a series of tests on rock mass mechanical parameters under unloading confining pressure conditions. For example, the literature “Xue Y, Ranjith P, Gao F, et al. Mechanical behaviour and permeability evolution of gas-containing coal from unloading confining pressure tests[J]. Journal of Natural Gas Science and Engineering, 2017,40.” quantitatively studied the influence of unloading rate on the mechanical behavior and permeability evolution (including energy evolution and fractal dimension) of coal and rock. The literature “Chen Xiutong, Li Lu. Experimental study on the mechanical properties of rock under high confining pressure and high water pressure[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, (S1):2694-2699.” studied the weakening law and failure types of rock mechanical properties under unloading. The literature “Cheng Jianlong, Yang Shengqi, Yin Pengfei, et al. Study on deformation and strength characteristics of composite rock strata under unloading pressure test [J]. Journal of China University of Mining and Technology, 2018, 47(06): 1233-1242” studied the influence of unloading pressure rate on the ultimate bearing strength and real-time confining pressure of composite rock strata samples. It can be seen that scholars at home and abroad have made fruitful results in the study of strength deterioration, energy evolution law and deformation failure mode of unloading confining pressure rock masses. However, after the excavation of underground chambers, the surrounding rock is in a state of single-sided unloading for a long time. Under the long-term single-sided unloading state, the strength damage of weakly cemented soft rock is particularly significant. The problem of large rheological deformation of soft rock caused by underground chamber excavation is still a key technical problem faced by soft rock underground engineering.

[0004] Currently, significant progress has been made in the research of creep models for geotechnical materials, especially nonlinear creep models. For example, the literature "Liu Quansheng, Luo Ciyou, Peng Xingxin, et al. Field rheological test and nonlinear fractional creep model of soft rock [J]. Journal of Coal Science and Technology, 2020, 45(04): 1348-1356." established a nonlinear fractional creep model for weak rock masses through field graded loading compression creep tests. The literature "Liu Jiashun, Jing Hongwen, Meng Bo, et al. Creep characteristics and fractional creep model of weakly cemented soft rock under water-bearing conditions [J]. Rock and Soil Mechanics, 2020, 41(08): 2609-2618." established a four-element fractional creep model for weakly cemented soft rock that can describe accelerated creep by replacing the sticking pot element in the Kelvin model with an Abel sticking pot and the elastic element with a plastic element. The literature “Liu Wenbo, Zhang Shuguang, Chen Lei. Rock time-dependent creep model based on unsteady fractional order [J]. Journal of Mining and Safety Engineering, 2021, 38(02):388-395” constructs an unsteady Abel pot by unsteadying the viscosity coefficient of the pot, and then unsteadies the fractional order based on it to establish a constitutive model of sandstone time-dependent creep based on unsteady fractional order.

[0005] Based on fractional-order creep constitutive models, some scholars have begun to study constitutive models that couple rock damage and creep. For example, the literature “Yang Juntao, Song Yanqi, Ma Hongfa, et al. Study on salt rock creep constitutive model considering hardening and damage effects [J]. Rock and Soil Mechanics, 2023, 44(10):2953-2966” establishes a salt rock creep constitutive model considering damage and hardening effects based on the component combination model and combined with fractional-order calculus theory. The literature “Hao K, Chuan H, Wenbo Y, et al. A Fractional Nonlinear Creep Damage Model for Transversely Isotropic Rock [J]. Rock Mechanics and Rock Engineering, 2022, 56(2):831-846” assumes that Poisson's ratio is constant, extends the creep equation of isotropic rocks to transversely isotropic rocks, and establishes a nonlinear damage creep model for transversely isotropic rocks. The literature “Yu Bingbing, Li Qing, Zhao Tongde, et al. A nonlinear creep damage model for rock based on stress and time dual thresholds [J]. Chinese Journal of Rock Mechanics and Engineering, 2023, 42(08):1928-1944” uses a combination of nonlinear elements and damage mechanics to construct a nonlinear creep damage model for rock in all time. It can be seen that introducing fractional calculus theory and damage theory into the rheological constitutive model of rock mass can better describe the creep characteristics of soft rock. It can be seen that scholars at home and abroad have achieved fruitful results in the coupled constitutive model of rock damage and creep. However, after the excavation of underground chambers, the surrounding rock is in a long-term unloaded state. Under the long-term unloaded state, the strength damage of weakly cemented soft rock is particularly significant. The problem of large rheological deformation of soft rock caused by the excavation of underground chambers is still a key technical problem faced by soft rock underground engineering. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock. This model can describe the decaying creep stage, the constant-rate creep stage, and the accelerated creep stage, providing a basis for long-term stability analysis of rock mass engineering, promoting mine construction and safe and efficient mining, and improving the level of mine engineering design.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock, specifically including: S1: Conduct graded unloading creep tests on weakly cemented soft rock to obtain creep data of weakly cemented soft rock; S2: Based on creep data, plot creep-time curves and creep rate-time curves, and use the inflection point method of the steady-state creep rate reciprocal-stress relationship curve to determine the long-term strength of weakly cemented soft rock. S3: Introducing the Riemann-Liouville fractional integral operator and negative time exponential damage evolution variables, defining the nonlinear damage Abel sticky pot, and constructing a six-element fractional creep damage constitutive model including elastic elements, fractional Kelvin viscoelastic damage elements, viscous damage elements, and nonlinear viscoplastic damage elements; S4: Based on the results of the unloading confining pressure test, the Levenberg-Marquardt algorithm is used to identify the parameters of the six-element fractional creep damage constitutive model, and the improved ant colony algorithm is used to optimize the model parameters. S5: Substitute the model parameters into the six-element fractional-order creep damage constitutive model, obtain the calculation results of the six-element fractional-order creep damage constitutive model, and compare the calculation results with the experimental data to verify the reliability of the model.

[0008] Preferably, a method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock is built based on the Riemann-Liouville fractional-order integral operator theory and damage mechanics theory, specifically including: Step S3 involves establishing a fractional-order Kelvin viscoelastic damage model and a nonlinear viscoplastic damage element based on the Riemann-Liouville fractional-order integral operator theory and damage mechanics theory. The fractional-order Kelvin viscoelastic damage model and the nonlinear viscoplastic damage element are then connected in series with an elastic element and a viscous damage element. The elastic element is used to characterize the instantaneous deformation characteristics of weakly cemented soft rock, the fractional-order Kelvin viscoelastic damage element is used to characterize the decay creep characteristics of weakly cemented soft rock, the viscous damage element is used to characterize the iso-rate creep characteristics of weakly cemented soft rock, and the nonlinear viscoplastic damage element is used to characterize the accelerated creep characteristics of weakly cemented soft rock.

[0009] Based on the creep equation of the elastic element, the creep equation of the fractional Kelvin viscoelastic damage model, the creep equation of the viscous damage element, and the creep equation of the nonlinear viscoplastic damage element, a six-element fractional creep damage constitutive model is established.

[0010] Preferably, the creep equation of the elastic element is:

[0011] In the formula: For the strain of the elastic element, For the stress of the elastic element, This refers to the elastic modulus of an elastic element; Preferably, the fractional-order Kelvin viscoelastic damage element is composed of a nonlinear damage Abel and a spring connected in parallel, and the constitutive equation is:

[0012] make When t=0, =0, then the above expression can be written as:

[0013] Applying the Laplace transform to the above equation yields:

[0014] Summarized as follows:

[0015] Performing an inverse Laplace transform on the above equation yields:

[0016] In the formula: Solving the above equation and substituting a and b, we get:

[0017] Introducing the damage variable D1 for the decay creep stage, and assuming that the damage evolution of weakly cemented soft rock in the decay creep stage has a negative exponential relationship with time, the damage evolution equation for the decay creep stage is:

[0018] The damage viscosity coefficient η of the viscous body ve1,D for:

[0019] The creep equation for the fractional-order Kelvin viscoelastic damage element is then:

[0020] In the formula: η1 is the viscosity coefficient of the fractional-order Kelvin viscoelastic element, η ve1.D β1 is the viscosity coefficient of the fractional-order Kelvin viscoelastic damage element, α1 is the order of the fractional-order Kelvin viscoelastic damage element, t is the loading time, and E1 is the elastic modulus of the fractional-order Kelvin viscoelastic damage element.

[0021] Preferably, the constitutive equation of the viscous damage element is:

[0022] Introducing the damage variable D2 during the constant-rate creep stage, and assuming that the evolution of soft rock creep damage follows a negative exponential function with respect to time, the damage evolution equation for the constant-rate creep stage is:

[0023] The damage viscosity coefficient η of the viscous body ve2,D for:

[0024] The creep equation for the viscous damage element is:

[0025] In the formula: η2 is the viscosity coefficient of the viscous element, η ve2,D α is the viscosity coefficient of the viscous damage element, α2 is the correlation coefficient of the rock mass material, and t is the loading time.

[0026] Preferably, the constitutive equation of the Abel pot in the nonlinear viscoplastic element is:

[0027] The creep equation for the Abel sticky pot in the nonlinear viscoplastic element is:

[0028] Introducing the damage variable D3 for the accelerated creep stage, and assuming that the evolution of soft rock creep damage follows a negative exponential function with time, the damage evolution equation for the accelerated creep stage is:

[0029] The damage viscosity coefficient η of the nonlinear viscoplastic body vp,D for:

[0030] The creep equation of the nonlinear viscoplastic damage element is:

[0031] In the formula: η3 is the viscosity coefficient of the nonlinear viscoplastic element, η vp,D β1 is the viscosity coefficient of the nonlinear viscoplastic damage element, β2 is the order of the fractional order of the nonlinear viscoplastic damage element, α3 is the correlation coefficient of the rock mass material, t is the loading time, and σ is the viscosity coefficient of the rock mass material. s To accelerate creep stress, this value can be taken as the long-term strength σ of weakly cemented soft rock. ∞ .

[0032] Preferably, the nonlinear viscoplastic damage element refers to an element in which the friction plate is rigid and inactive when the deviatoric stress level is less than the long-term strength; and when the deviatoric stress level is greater than the long-term strength, the friction plate is triggered and begins to function. The creep-time relationship of the nonlinear viscoplastic damage element is as follows:

[0033] Preferably, the fractional-order creep damage constitutive equation for weakly cemented soft rock is established based on the creep equation of the elastic element, the creep equation of the fractional-order Kelvin viscoelastic damage element, the creep equation of the viscous damage element, and the creep equation of the nonlinear viscoplastic damage element, as shown in the following equation. In step S4, based on the creep variable-time relationship curve, the Levenberg-Marquardt algorithm in Matlab is used to identify the parameters of the fractional creep damage model, thereby obtaining the parameters of the fractional creep damage model, and the improved ant colony algorithm is used to optimize the model parameters. Step S5 involves substituting the model parameters obtained from parameter identification into the fractional-order damage model for weakly cemented soft rock, obtaining the calculation results of the fractional-order creep damage model, and comparing the model calculation results with the experimental data to verify the reliability of the model.

[0034] The beneficial effects of this invention are as follows: The method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock can accurately describe the characteristics of the entire process of instantaneous deformation, decaying creep, isochronous creep, and accelerated creep in weakly cemented soft rock, and accurately judge and predict the entire creep deformation process of weakly cemented soft rock. It is more accurate for predicting the creep damage characteristics of weakly cemented soft rock under excavation and unloading conditions in underground engineering, as well as the long-term stability of underground engineering projects. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the method for constructing the constitutive model of creep damage in weakly cemented soft rock according to the present invention. Figure 2 The indoor creep test curves for weakly cemented soft rock are from an embodiment of the present invention. Figure 3 This invention provides a single-stage loading creep test curve for weakly cemented soft rock obtained based on the Boltzmann linear superposition principle. Figure 4 This is the creep rate-time curve for the first stage obtained by the present invention based on the creep rate-time curve; Figure 5 This invention provides the second-stage creep rate-time curve obtained based on the creep rate-time curve. Figure 6 This invention provides the third-level creep rate-time curve obtained based on the creep rate-time curve. Figure 7 This invention provides the fourth-level creep rate-time curve obtained based on the creep rate-time curve. Figure 8 This invention provides the creep rate-time curve for the fifth stage, obtained based on the creep rate-time curve. Figure 9 This is a constitutive model diagram of fractional-order creep damage in weakly cemented soft rock according to an embodiment of the present invention. Figure 10 This is a flowchart of the improved ant colony algorithm optimization model parameters proposed in this invention; Figure 11 This is a comparison chart of the model calculation results and experimental results of Embodiment 2 of the present invention. Detailed Implementation

[0036] The present invention will be further illustrated below with specific embodiments. The examples given are for illustrative purposes only and are not intended to limit the scope of the invention.

[0037] Example 1

[0038] This invention provides a method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock. The construction process is as follows: Figure 1 As shown. The method for constructing the fractional-order creep damage constitutive model specifically includes: In step S1, a graded unloading creep test of weakly cemented soft rock is conducted to obtain creep data of the weakly cemented soft rock. In step S2, creep-time curves and creep rate-time curves are plotted based on creep data. The long-term strength of weakly cemented soft rock is determined by using the inflection point method of the steady-state creep rate reciprocal-stress relationship curve. In step S3, the Riemann-Liouville fractional integral operator and negative time exponential damage evolution variables are introduced, and the nonlinear damage Abel sticky pot is defined to construct a six-element fractional creep damage constitutive model that includes elastic elements, fractional Kelvin viscoelastic damage elements, viscous damage elements and nonlinear viscoplastic damage elements. In implementation, this scheme preferably uses step S3, where the six-element fractional-order creep damage constitutive model is constructed based on the Riemann-Liouville fractional-order integral operator theory and damage mechanics theory, to build a method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock. Specifically, this method includes: Fractional Kelvin viscoelastic damage elements and nonlinear viscoplastic damage elements are established based on the Riemann-Liouville fractional integral operator theory and damage mechanics theory. Fractional Kelvin viscoelastic damage elements and nonlinear viscoplastic damage elements are connected in series with an elastic element and a viscous damage element. The elastic element is used to characterize the instantaneous deformation characteristics of weakly cemented soft rock, the fractional Kelvin viscoelastic damage element is used to characterize the decay creep characteristics of weakly cemented soft rock, the viscous damage element is used to characterize the iso-rate creep characteristics of weakly cemented soft rock, and the nonlinear viscoplastic damage element is used to characterize the accelerated creep characteristics of weakly cemented soft rock. Based on the creep equations of the elastic element, the fractional-order Kelvin viscoelastic damage element, the viscous damage element, and the nonlinear viscoplastic damage element, a six-element fractional-order creep damage constitutive model is established, namely, the fractional-order creep damage constitutive model of weakly cemented soft rock.

[0039] Preferably, the creep equation of the elastic element is: (1) In the formula: For the strain of the elastic element, For the stress of the elastic element, This refers to the elastic modulus of an elastic element; Preferably, the fractional-order Kelvin viscoelastic damage element is composed of a nonlinear damage Abel and a spring connected in parallel, and its constitutive equation is: (2) In the formula, E1 is the elastic modulus of the spring in the fractional-order Kelvin viscoelastic damage element; t is the loading time; η ve1,D The viscosity coefficient of the fractional-order Kelvin viscoelastic damage element; make When t=0, =0, then equation (2) can be written as: (3) Applying the Laplace transform to equation (3) yields: (4) Simplifying equation (4), we get: (5) Performing an inverse Laplace transform on equation (5) yields: (6) In the formula: ; Solving equation (6) and substituting a and b, we get: (7) Introducing the damage variable D1 for the decay creep stage, and assuming that the damage evolution of weakly cemented soft rock in the decay creep stage has a negative exponential relationship with time, the damage evolution equation for the decay creep stage is: (8) Viscosity coefficient η of fractional-order Kelvin viscoelastic damage element ve1,D for: (9) The creep equation for the fractional-order Kelvin viscoelastic damage element is then: (10) In the formula: η1 is the viscosity coefficient of the fractional-order Kelvin viscoelastic element, η ve1.D β1 is the viscosity coefficient of the fractional-order Kelvin viscoelastic damage element, α1 is the order of the fractional-order Kelvin viscoelastic damage element, t is the loading time, and E1 is the elastic modulus of the fractional-order Kelvin viscoelastic damage element.

[0040] Preferably, the constitutive equation of the viscous damage element is: (11) Introducing the damage variable D2 during the constant-rate creep stage, and assuming that the evolution of soft rock creep damage follows a negative exponential function with respect to time, the damage evolution equation for the constant-rate creep stage is: (12) The viscosity coefficient η of the viscous damage element ve2,D for: (13) The creep equation for the viscous damage element is: (14) In the formula: η2 is the viscosity coefficient of the viscous element, η ve2,D α is the viscosity coefficient of the viscous damage element, α2 is the correlation coefficient of the rock mass material, and t is the loading time.

[0041] Preferably, the constitutive equation of the Abel pot in the nonlinear viscoplastic element is: (15) The creep equation for the Abel sticky pot in the nonlinear viscoplastic element is: (16) Introducing the damage variable D3 for the accelerated creep stage, and assuming that the evolution of soft rock creep damage follows a negative exponential function with time, the damage evolution equation for the accelerated creep stage is: (17) The viscosity coefficient η of the nonlinear viscoplastic damage element vp,D for: (18) The creep equation of the nonlinear viscoplastic damage element is: (19) In the formula: η3 is the viscosity coefficient of the nonlinear viscoplastic element, η vp,D β1 is the viscosity coefficient of the nonlinear viscoplastic damage element, β2 is the order of the fractional order of the nonlinear viscoplastic damage element, α3 is the correlation coefficient of the rock mass material, t is the loading time, and σ is the viscosity coefficient of the rock mass material. s To accelerate creep stress, this value can be taken as the long-term strength σ of weakly cemented soft rock. ∞ .

[0042] Preferably, the nonlinear viscoplastic damage element refers to an element in which the friction plate is rigid and inactive when the deviatoric stress level is less than the long-term strength; and when the deviatoric stress level is greater than the long-term strength, the friction plate is triggered and begins to function. The creep-time relationship of the nonlinear viscoplastic damage element is as follows: (20) Preferably, the creep equation (1) of the elastic element, the creep equation (10) of the fractional Kelvin viscoelastic damage element, the creep equation (14) of the viscous damage element and the creep equation (20) of the nonlinear viscoplastic damage element are used to establish the fractional creep damage constitutive equation of weakly cemented soft rock as shown in equation (21).

[0043] (twenty one) In step S4, based on the results of the unloading confining pressure test, the Levenberg-Marquardt algorithm is used to identify the parameters of the six-element fractional creep damage constitutive model, and the improved ant colony algorithm is used to optimize the model parameters. In step S5, the model parameters are substituted into the six-element fractional-order creep damage constitutive model to obtain the calculation results of the six-element fractional-order creep damage constitutive model. The calculation results are then compared with the experimental data to verify the reliability of the model.

[0044] Example 2

[0045] (1) Conduct graded unloading creep tests on weakly cemented soft rock. The unloading creep test used the stress control module in the GDSLAB advanced loading module to load the specimen to σ at a loading rate of 0.1 MPa / min. 10 = σ 30 The initial stress state is maintained and kept constant. Subsequently, the axial compression σ is maintained. 10 The confining pressure was kept constant at a rate of 0.05 MPa / s until it reached a predetermined value. The specimen was then kept under constant stress for approximately 50 hours before proceeding to the next stage of confining pressure release. The confining pressure was released in five stages. The deviatoric stress after each stage of release was determined based on 30%, 40%, 50%, 55%, and 60% of the uniaxial compressive strength of the rock. The staged confining pressure release test scheme is shown in Table 1.

[0046] Table 1. Staged Unloading Confining Pressure Test Scheme

[0047] (2) Obtain creep data of weakly cemented soft rock, and plot the creep-time relationship curve based on the creep data, such as... Figure 2 As shown.

[0048] (3) Based on the principle of linear superposition, the creep test data under graded loading are processed, and creep length-time curves and creep rate-time curves under different stress levels are plotted, such as... Figure 3-8 As shown.

[0049] (4) Based on the Riemann-Liouville fractional integral operator theory and damage mechanics theory, an elastic element is connected in series with a fractional Kelvin viscoelastic damage element, a viscous damage element, and a nonlinear viscoplastic damage element to construct a six-element fractional creep damage model for weakly cemented soft rock, such as... Figure 9 As shown.

[0050] (5) Based on the creep equation of the elastic element, the creep equation of the fractional Kelvin viscoelastic damage element, the creep equation of the viscous damage element and the creep equation of the nonlinear viscoplastic damage element, a fractional creep damage constitutive equation for weakly cemented soft rock is established.

[0051]

[0052] (6) Based on the creep variable-time relationship curve, the parameters of the fractional creep damage model are identified to obtain the creep model parameters. The initial values ​​of the fractional creep damage model parameters E0, E1, β1, β2, η1, η2, η3, α1, α2, α3, t1, and t2 of the weakly cemented soft rock fractional creep damage model are identified using the Trust-Region algorithm in Matlab.

[0053] (7) The improved ant colony algorithm is used to optimize the model parameters. The optimization process is as follows: Figure 10 As shown in Table 2, the optimized model parameters are presented.

[0054] Table 2. Parameter optimization results of the fractional-order creep damage constitutive model

[0055] (8) Substitute the optimized model parameters into the fractional-order creep damage constitutive model of weakly cemented soft rock (Equation (21)), and compare the model calculation results with the experimental data, such as Figure 11 As shown.

[0056] The comparative analysis of the model calculation results and experimental data shows that the fractional-order creep damage constitutive model for weakly cemented soft rock provided by this invention can accurately describe the characteristics of the entire process of instantaneous deformation, decay creep, isochronous creep and accelerated creep of weakly cemented soft rock, and accurately reflect the creep damage characteristics of weakly cemented soft rock under excavation and unloading conditions, which is of great significance for ensuring the long-term stability of underground engineering.

[0057] This invention has used specific examples to illustrate its principles and implementation methods. The above descriptions of the embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock, characterized in that, The steps include the following: S1: Conduct graded unloading creep tests on weakly cemented soft rock to obtain creep data of weakly cemented soft rock; S2: Based on creep data, plot creep-time curves and creep rate-time curves, and use the inflection point method of steady-state creep rate reciprocal-stress relationship curve to determine the long-term strength of weakly cemented soft rock. S3: Introducing the Riemann-Liouville fractional integral operator and negative time exponential damage evolution variables, defining the nonlinear damage Abel sticky pot, and constructing a six-element fractional creep damage constitutive model including elastic elements, fractional Kelvin viscoelastic damage elements, viscous damage elements, and nonlinear viscoplastic damage elements; S4: Based on the results of the unloading confining pressure test, the Levenberg-Marquardt algorithm is used to identify the parameters of the six-element fractional creep damage constitutive model, and the improved ant colony algorithm is used to optimize the model parameters. S5: Substitute the model parameters into the six-element fractional-order creep damage constitutive model, obtain the calculation results of the six-element fractional-order creep damage constitutive model, and compare the calculation results with the experimental data to verify the reliability of the model. In step S3, constructing the six-element fractional-order creep damage constitutive model specifically includes: Based on the Riemann-Liouville fractional integral operator theory and damage mechanics theory, fractional Kelvin viscoelastic damage elements and nonlinear viscoplastic damage elements are established and connected in series with an elastic element and a viscous damage element, respectively. Based on the creep-time relationship curves under different stress levels, creep equations for elastic elements, fractional-order Kelvin viscoelastic damage elements, viscous damage elements, and nonlinear viscoplastic damage elements are established. Based on the creep equation of the elastic element, the creep equation of the fractional Kelvin viscoelastic damage element, the creep equation of the viscous damage element, and the creep equation of the nonlinear viscoplastic damage element, a six-element fractional creep damage constitutive model is established. The constitutive equations for the elastic element, viscous damage element, fractional-order Kelvin viscoelastic damage element, and nonlinear viscoplastic damage element are specifically as follows: The constitutive equation of the elastic element is: (1) In the formula: For the strain of the elastic element, For the stress of the elastic element, This refers to the elastic modulus of an elastic element; The fractional-order Kelvin viscoelastic damage element consists of a nonlinear damage Abel and a spring connected in parallel, and its constitutive equation is: (2) In the formula, E1 is the elastic modulus of the spring in the fractional-order Kelvin viscoelastic damage element; t is the loading time; η ve1,D The viscosity coefficient of the fractional-order Kelvin viscoelastic damage element; make ; When t=0, =0, then equation (2) can be written as: (3) In the formula, β1 is the order of the fractional order Kelvin viscoelastic damage element; Applying the Laplace transform to equation (3) yields: (4) Simplifying equation (4), we get: (5) Performing an inverse Laplace transform on equation (5) yields: (6) In the formula: Solving the above equation and substituting a and b, we get: (7) Introducing the damage variable D1 for the decay creep stage, and assuming that the damage evolution of weakly cemented soft rock in the decay creep stage has a negative exponential relationship with time, the damage evolution equation for the decay creep stage is: (8) Viscosity coefficient η of fractional-order Kelvin viscoelastic damage element ve1,D for: (9) In the formula, η1 is the viscosity coefficient of the fractional-order Kelvin viscoelastic loss element; The creep equation for the fractional-order Kelvin viscoelastic damage element is then: (10) In the formula: α1 is the correlation coefficient of the rock mass material; The constitutive equation of the viscous damage element is: (11) Introducing the damage variable D2 during the constant-rate creep stage, and assuming that the evolution of soft rock creep damage follows a negative exponential function with respect to time, the damage evolution equation for the constant-rate creep stage is: (12) In the formula, α2 is the correlation coefficient of the rock mass material. The viscosity coefficient η of the viscous damage element ve2,D for: (13) In the formula, η2 is the viscosity coefficient of the viscous element. The creep equation for the viscous damage element is: (14) In the formula: η ve2,D The viscosity coefficient of the viscous damage element. The constitutive equation for Abel's sticky pot in a nonlinear viscoplastic element is: (15) In the formula, σ s To accelerate the creep stress threshold, this value is taken as the long-term strength σ of weakly cemented soft rock. ∞ ; The creep equation for Abel's sticky pot in a nonlinear viscoplastic element is: (16) In the formula, β2 is the order of the fractional order of the nonlinear viscoplastic damage element; Introducing the damage variable D3 for the accelerated creep stage, and assuming that the evolution of soft rock creep damage follows a negative exponential function with time, the damage evolution equation for the accelerated creep stage is: (17) In the formula, α3 is the correlation coefficient of the rock mass material. The viscosity coefficient η of the nonlinear viscoplastic damage element vp,D for: (18) In the formula, η3 is the viscosity coefficient of the nonlinear viscoplastic element. The creep equation for a nonlinear viscoplastic damage element is: ； (19) The fractional-order creep damage constitutive equation for weakly cemented soft rock is established as shown in the following equation. (20) 。 2. The method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock according to claim 1, characterized in that, In step S1, the creep data includes the creep-time relationship curve and the creep rate-time relationship curve.

3. The method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock according to claim 1, characterized in that, The nonlinear viscoplastic damage element refers to an element in which the friction plate is rigid and inactive when the deviatoric stress level is less than the long-term strength; when the deviatoric stress level is greater than the long-term strength, the friction plate is triggered and begins to function. The creep-time relationship of the nonlinear viscoplastic damage element is as follows: (21) 。 4. The method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock according to claim 1, characterized in that, In step S3, a six-element fractional-order creep damage constitutive model is established based on the creep equations of elastic elements, fractional-order Kelvin viscoelastic damage elements, viscous damage elements, and nonlinear viscoplastic damage elements. Specifically, this includes: Elastic elements are used to describe the instantaneous deformation characteristics of creep in weakly cemented soft rock; Fractional-order Kelvin viscoelastic damage elements are used to describe the decay creep characteristics of weakly cemented soft rock. Viscous damage elements are used to describe the isoresistive creep characteristics of weakly cemented soft rock. Nonlinear viscoplastic damage elements are used to describe accelerated creep characteristics.

5. The method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock according to claim 2, characterized in that, In step S4, the Levenberg-Marquardt algorithm in Matlab is used to identify the parameters of the six-element fractional-order creep damage constitutive model based on the creep variable-time relationship curve, and the improved ant colony algorithm is used to optimize the model parameters.

6. The method for constructing a fractional-order creep damage constitutive model for weakly cemented soft rock according to claim 1, characterized in that, In step S5, the 10 model parameters E0, E1, β1, β2, η1, η2, η3, α1, α2 and α3 obtained from parameter identification are substituted into the six-element fractional-order creep damage constitutive model described in step S3 to calculate the calculation result of the six-element fractional-order creep damage constitutive model. The calculation result is compared with the experimental data to verify the reliability of the model.

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