Shear fractional order constitutive model construction method considering structural surface disturbance damage

Abstract

The invention discloses a shear creep model construction method considering a rock nonlinear strain rate, and the construction process comprises the following steps: S1, determining shear characteristic stress of a rock entering start viscoplastic deformation and accelerated viscoplastic deformation, and representing rock viscoplastic deformation and plastic deformation unstable expansion; s2, determining a rock elastic modulus damage equation D, and constructing expression functions of a rock damage elastic element ue (t) and a fractional order viscoelastic element uve (t); s3, constructing a fractional order viscoplastic element uvp (t) expression function; s4, constructing a nonlinear viscoplastic element up (t) expression function; s5, constructing a rock shear creep element model u (t) which is formed by connecting a damaged elastic element ue, a fractional order viscoelastic element uve, a fractional order viscoplastic element uvp and a nonlinear viscoplastic element up in series; and S6, carrying out a shear test on the rock sample, and verifying the rock shear creep element model in the step S5.

Description

Technical Field

[0001] The invention relates to the field of rock mass structural surface engineering, and is used for simulating and analyzing the micro-dynamic disturbance damage degradation behavior and shear disturbance characteristics of rock mass under action. Background Art

[0002] In rock mass structural surface engineering, the damage and shear characteristics of rock mass are crucial for the study of micro-dynamic disturbance shear deformation of rock mass structural surface and engineering stability. A large number of studies have shown that the disturbance deformation of rock mass structural surface is similar to creep behavior, and is divided into three stages according to the deformation characteristics of rock mass structural surface: deceleration stage, constant velocity stage and acceleration stage. Certain conditions are required for the deceleration stage to enter the constant velocity stage. When this condition is met, the micro-dynamic disturbance deformation of the rock mass structural surface enters the stable crack expansion stage; certain conditions are also required for the constant velocity stage to enter the acceleration stage. When this condition is not met, the disturbance deformation of the rock mass structural surface tends to be stable and no disturbance damage occurs; when this condition is met, the rock mass structural surface disturbance enters the acceleration stage from the constant velocity stage, the internal crack expansion of the rock mass structural surface intensifies, and finally the rock mass structural surface is disturbed and damaged. However, traditional rock shear models often ignore the internal degradation damage of the rock mass structural surface caused by disturbance factors and ignore the nonlinear influence of strain rate and shear stress, resulting in deviations between the simulation results of the acceleration disturbance process and the actual engineering situation.

[0003] Fractional calculus is the extension of integer-order derivative operators to arbitrary real-order calculus. Compared with traditional elements such as springs and Newtonian viscous pots, fractional-order elements have the advantages of fewer parameters, clearer physical meanings, and the ability to describe nonlinear deformations. Therefore, a method for constructing a shear fractional-order constitutive model that considers the disturbance damage of rock mass structural surfaces is developed to provide a theoretical basis for the prediction of disasters caused by surrounding rock disturbance shear failure in rock mass structural surface engineering and long-term stability analysis. Summary of the invention

[0004] The purpose of the present invention is to provide a method for constructing a shear fractional-order constitutive model taking into account the disturbance damage of rock mass structural surfaces. After tunnel excavation, the model can accurately simulate and analyze the damage behavior and shear characteristics of the rock mass under micro-dynamic disturbance.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] S1. Determine the shear disturbance viscoplastic starting stress and shear disturbance viscoplastic critical stress corresponding to the moment when the rock structure surface enters the disturbance viscoplastic deformation and the disturbance accelerated viscoplastic deformation respectively under true three-dimensional stress, and characterize the starting of the disturbance viscoelastic-plastic deformation and the disturbance unstable plastic deformation of the rock structure surface;

[0007] S2. Construct rock mass structural surface elastic element u e (t) and the fractional damage viscoelastic element uve (t) expression function;

[0008] S3, determine the viscosity coefficient damage equation D of the rock mass structural surface, and construct the damage fractional viscoplastic element u based on the viscoplastic deformation starting point of the rock mass structural surface in step S1 vp (t) expression function;

[0009] S4, based on the starting point of the unstable extension of the plastic deformation of the rock mass structure surface in step S1, construct a nonlinear viscoplastic element u p (t) expression function;

[0010] S5. Construct a system consisting of elastic elements u e , fractional damage viscoelastic element u ve and the fractional viscoplastic element u vp and the nonlinear viscoplastic element u p A series of shear fractional constitutive models u(t) that characterize the disturbance damage of rock mass structural surfaces;

[0011] S6. Carry out shear tests on rock mass structural surface samples to verify the shear fractional-order constitutive model of rock mass structural surface disturbance damage in step S5.

[0012] In the step S1, the shear disturbance stress corresponding to the rock structure surface entering plastic deformation in the shear disturbance stress-strain curve of the rock structure surface is used as the shear disturbance viscoplastic starting stress τ0 for starting viscoplastic deformation, and the corresponding shear strain is u0; the shear stress corresponding to the ratio of the product of the strain and the unit stress in the nth (n>1) unit time to the product of the strain and the unit stress in the n-1th unit time in the shear disturbance stress-strain curve of the rock structure surface is greater than 1.2 is used as the shear disturbance viscoplastic critical stress τ for characterizing accelerated viscoplastic deformation p , the corresponding shear strain is u p ;

[0013] In step S2, the rock mass structural surface elastic element u is constructed. e (N) Expression function: Where G1 is the elastic shear modulus, τ is the stress on the rock mass structure test block;

[0014] Construct fractional damage viscoelastic element u ve (N) Expression function:

[0015] In formula (2), the left and right sides are integrated and combined with formula (3) and the relationship N = tf is used to determine the fractional-order viscoelastic element u of the rock mass structural surface by Laplace transformation and inverse transformation. ve The expression of (t) is: Where G2 is the elastic shear modulus, τ is the shear stress on the rock mass structure test block, is the fractional viscosity coefficient, and α is the fractional order.

[0016] In step S3, the viscosity coefficient damage equation D of the rock mass structural surface is determined, and the damage fractional viscoplastic element u is constructed. vp (N) The method of expressing the function is:

[0017] A1. Based on the physical and mechanical parameters of the rock mass structure surface under different amplitudes and frequencies obtained from the micro-dynamic disturbance experiment on the rock mass structure surface in step S1, the law between the strain rate and time of a certain rock mass structure surface under micro-dynamic disturbance is obtained, and the deformation of the rock mass structure surface is divided into elastic deformation ε e and micro-dynamic perturbation plastic deformation ε p : ε=ε e +ε p (5)

[0018] A2. Obtaining micro-dynamic perturbation plastic deformation ε p Relationship between amplitude, time and material properties of rock mass structural surface: Among them, E K represents the structural surface modulus of the rock mass under micro-dynamic disturbance; A represents the disturbance amplitude; n represents the hardening index under micro-dynamic disturbance;

[0019] A3. Calculate the unit increment of plastic strain due to micro-dynamic disturbance: Among them, Δt is the unit time;

[0020] A4. The damage caused by micro-dynamic disturbance inside the rock mass structure surface is D, which causes the modulus under the micro-dynamic disturbance to be damaged; the modulus after damage is constructed expression:

[0021] A5. According to E K The relationship between the mineral composition of the rock mass structure, the amplitude of the micro-disturbance and the loading time is as follows: K Equation with amplitude and loading time: E K =ρ·Aα ·t β (9) If the final damage equation expression is consistent with the actual rock mass structural surface damage curve, then the assumption is valid;

[0022] A6. Construct the unit increment of disturbance damage:

[0023] A7. Introducing the influence of micro-dynamic disturbance on the damage of rock mass structure surface, a constitutive model of rock mass structure surface damage considering micro-dynamic disturbance is constructed:

[0024] According to the Manson-Coffin empirical formula, the relationship function between plastic strain and micro-dynamic disturbance amplitude under micro-dynamic disturbance is constructed: Where c represents the material parameter;

[0025] And using the relationship N = tf, the damage constitutive model of rock mass structural surface under micro-dynamic disturbance is obtained:

[0026] A8. Construct the yield function F(τ) based on the perturbation shear strength criterion under three-dimensional stress:

[0027] A9. Carry out a preliminary experiment on shear disturbance of rock mass structural surface, determine the shear disturbance viscoplastic starting stress τ0 based on the method described in step S1, introduce the flow law of Perzyna overstress theory according to the value of τ0 and the yield function F(τ) in step A8, determine the disturbance shear viscoplastic starting yield function F1, and construct the fractional-order viscoplastic element constitutive equation: in And take F0 = 1;

[0028] A10. Integrate the left and right sides of equation (17) in step A9, and use the relationship N = tf and the Laplace transform and inverse transform method to determine the fractional-order viscoplastic shear perturbation constitutive equation:

[0029] Where τ is the shear stress on the rock mass structure test block, η β 2 is the fractional viscosity coefficient, β is the fractional order;

[0030] In step S4, based on the starting point of the unstable extension of the plastic deformation of the rock mass structure surface in step S1, a nonlinear viscoplastic element u is constructed. p (N) The method of expressing the function is:

[0031] B1. Carry out preliminary experiments on shear disturbance of rock mass structure surface, and determine the critical stress τ of shear disturbance viscoplasticity based on the method described in step S1. p , according to τ p The value of and the yield function F(τ) in step A8 are used to determine the yield critical function F2 of the rock mass structural surface entering accelerated viscoplastic deformation under the action of three-dimensional perturbation shear;

[0032] B2. Based on the relationship between strain and time, and between stress and strain of the rock structure surface obtained in the shear disturbance test in step B1, the relationship between stress rate and time of the rock structure surface under different shear stresses is clarified, and the relationship between shear strain rate and stress of the rock structure surface is constructed:

[0033] B3. Integrate equation (19) in step B2, introduce the flow law of Perzyna overstress theory, and determine the nonlinear viscoplastic element u of the rock mass structural surface. p The expression of (t) is: Where η3 is the fractional viscosity coefficient, N is the number of perturbations, δ is the material coefficient, And take F0=1.

[0034] In step S5, based on the starting point of the viscoplastic deformation and the unstable extension of the plastic deformation of the rock mass structure surface in step S1, a damage elastic element u is constructed. e (N), fractional viscoelastic element u ve (N) and the fractional viscoplastic element u vp (N) and the nonlinear viscoplastic element u p (N) The series shear fractional constitutive model u(N) that characterizes the disturbance damage of rock mass structural surface:

[0035] In step S6, a shear test is carried out on the rock mass structural surface sample to verify the shear fractional-order constitutive model of the rock mass structural surface disturbance damage in step S5 as follows:

[0036] C1. Determine the strength failure criterion of the rock mass structural surface, and determine the corresponding strength threshold of the shear disturbance element model of the rock mass structural surface according to the criterion;

[0037] C2. Carry out shear disturbance test on the rock mass structure surface to obtain the shear disturbance test data of the rock mass structure surface: stress, strain, and test time;

[0038] C3. Based on the test data obtained in step C2: stress, strain, test time, the shear disturbance element model u(t) of the rock mass structural surface in step S5 is fitted to obtain fitting parameters and correlation results.

[0039] The beneficial effects of the present invention are:

[0040] 1. The present invention introduces new nonlinear disturbance elements and the damage caused by disturbance degradation to describe the nonlinear disturbance deformation of the rock structure surface after the disturbance shear action, especially the rock structure surface entering the accelerated disturbance stage. Based on this, a nonlinear shear constitutive element model that can reflect the disturbance degradation of the rock structure surface is established, with simple model parameters and clear physical meaning.

[0041] 2. Based on damage theory, the present invention introduces damage variables to describe the change of elastic modulus of rock structure surface caused by loading of rock structure surface. The damage variables and elastic elements form a damaged elastic element with gradually decreasing elastic modulus.

[0042] 3. Based on the strength criterion, the present invention proposes a method for constructing a shear disturbance model that takes into account the nonlinear strain rate of the rock structure surface. It completely characterizes the three stages of attenuation disturbance stage, constant speed disturbance stage and accelerated disturbance stage in the rock structure surface disturbance process under true triaxiality, and can accurately simulate and analyze the damage behavior and shear characteristics of the rock under the action of time.

[0043] 4. After secondary development, the model constructed by the present invention can be used to improve the accuracy of rock mass structural surface engineering design and analysis and provide strong support for the safety and stability assessment of rock mass engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flow chart is provided for the method for constructing a shear disturbance model taking into account the nonlinear strain rate of the rock mass structural surface of the present invention;

[0045] Figure 2 is the starting stress of limestone shear disturbance viscoplasticity τ0 and the critical stress of rock mass structural surface viscoplasticity shear disturbance τ p Definition diagram of

[0046] Figure 3 This is a comparison chart between the theoretical prediction results and the test results of limestone damage;

[0047] Figure 4 A model to characterize the initiation and acceleration of shear disturbance in limestone under true triaxial conditions;

[0048] Figure 5This is a comparison chart between the theoretical prediction results and the experimental results of the model under true triaxial conditions. DETAILED DESCRIPTION

[0049] The specific implementation of the present invention is described below in conjunction with the accompanying drawings, but the present invention is not limited to the scope of the specific implementation. It should be noted that all creations based on or dependent on the present invention are within the protection scope of the present invention.

[0050] Embodiment 1:

[0051] This embodiment provides a model for constructing and verifying the accuracy and rationality of a model for characterizing the initiation and acceleration of shear disturbance of a rock mass structural surface under true triaxial conditions using limestone as a rock mass structural surface sample.

[0052] Figure 1 A flow chart of a method for constructing a shear fractional-order constitutive model considering disturbance damage of rock mass structural surfaces is shown. The method includes steps S1 to S6.

[0053] In step S1, a true triaxial shear disturbance test is performed on the limestone to determine the shear characteristic stress of the limestone in the real three-dimensional stress field, and the shear disturbance stress corresponding to the limestone entering plastic deformation in the shear disturbance stress-strain curve that characterizes the viscoelastic-plastic deformation and unstable plastic deformation of the limestone is used as the shear disturbance viscoplastic starting stress τ0 for starting viscoplastic deformation, and the corresponding shear strain is u0; the shear stress corresponding to the ratio of the product of the strain and the unit stress in the nth (n>1) unit time to the product of the strain and the unit stress in the n-1th unit time in the shear disturbance stress-strain curve of the limestone is greater than 1.2 as the shear disturbance viscoplastic critical stress τ for characterizing accelerated viscoplastic deformation p , the corresponding shear strain is u p , see Figure 2 ;

[0054] In step S2, construct the elastic element u of the limestone e (t) Expression function: Where G1 is the elastic shear modulus, τ is the stress on the limestone specimen;

[0055] Construct fractional damage viscoelastic element u ve (t) Expression function:

[0056] Using the relationship N = tf, the fractional viscoelastic element u of limestone is determined ve The expression of (t) is: Where G2 is the elastic shear modulus, τ is the shear stress on the limestone specimen, is the fractional viscosity coefficient, and α is the fractional order.

[0057] In step S3, the damage equation D of the limestone viscosity coefficient is determined, and it is fitted with the test results to determine the availability of the damage equation, and the damage fractional viscoplastic element u is constructed. vp (t) Expression function:

[0058] Based on the degradation of limestone deformation caused by disturbances of different amplitudes and frequencies, the damage equation D of the viscosity coefficient is constructed:

[0059] Where n represents the hardening index of limestone under microdynamic disturbance, b, c, k, and m are material parameters, which are fitted with the test results as follows: Figure 3 shown.

[0060] A limestone shear disturbance pre-experiment with a normal stress of 10 MPa, a lateral stress of 15 MPa, a disturbance amplitude of 0.5 MPa, and a disturbance frequency of 4 Hz was carried out. Based on the method described in step S1, the shear disturbance viscoplastic starting stress τ0 = 12.4 MPa was determined, and the yield function F1 was constructed:

[0061] According to the value of τ0 and the yield function F(τ) in step B2, the shear creep viscoplastic initiation yield function F1 is determined, and the constitutive equation of the fractional viscoplastic element is constructed: in And take F0 = 1;

[0062] The shear perturbation constitutive equation of fractional viscoplastic body is determined by Laplace transform and inverse transform: Where τ is the shear stress on the limestone specimen, is the fractional viscosity coefficient, and β is the fractional order.

[0063] In step S4, based on the starting point of the unstable extension of the plastic deformation of the rock mass structure surface in step S1, a nonlinear viscoplastic element u is constructed. p (t) Expression function:

[0064] Carry out limestone shear disturbance experiment and determine the shear disturbance viscoplastic critical stress τ based on the method described in step S1 p =24.8MPa, construct the yield function F2:

[0065] In addition, the relationship between limestone strain and time, stress and strain obtained in the shear disturbance test is used to clarify the relationship between stress rate and time of limestone under different shear stresses, and to construct the relationship between limestone shear strain rate and stress:

[0066] Using the relationship N = tf, the nonlinear viscoplastic element u of limestone is determined p The expression of (t) is: Where η3 is the fractional viscosity coefficient, t is the time, and δ is the material coefficient.

[0067] In step S5, Figure 4 As shown in the figure, based on the starting point of the unstable extension of the viscoplastic deformation and plastic deformation of the limestone in step S1, based on the relationship between time, frequency and the number of disturbances: t·f=N, a damage elastic element u is constructed. e (N), fractional viscoelastic element u ve (N) and the fractional viscoplastic element u vp (N) and the nonlinear viscoplastic element u p (N) The series shear fractional constitutive model u(N) that characterizes the disturbance damage of rock mass structural surface: In step S6, a shear test is carried out on the limestone sample to verify the shear fractional-order constitutive model of disturbance damage of granite in step S5:

[0068] The shear disturbance test was carried out on the limestone to obtain the limestone shear disturbance test data: stress, strain, test time, and true triaxial shear test was carried out on the limestone at different stress levels. The amplitude was determined to determine the shear fractional constitutive model parameters of disturbance damage under different stress states: G1, G2, α, β, δ, as shown in Table 1;

[0069] The limestone shear disturbance element model u(t) in step S5 is fitted to obtain fitting parameters and correlation results, such as Figure 5 shown. Table 1 Parameters of perturbation shear fractional constitutive model under different stress states

Claims

1. A method for constructing a shear fractional constitutive model considering structural surface disturbance damage, comprising the following steps: S1. Determine the shear disturbance viscoplastic starting stress and shear disturbance viscoplastic critical stress corresponding to the moment when the rock structure surface enters the disturbance viscoplastic deformation and the disturbance accelerated viscoplastic deformation respectively under true three-dimensional stress, and characterize the starting of the disturbance viscoelastic-plastic deformation and the disturbance unstable plastic deformation of the rock structure surface; S2. Construct rock mass structural surface elastic element u e (N) and the fractional damage viscoelastic element u ve (N) Expression function: Where G2 is the elastic shear modulus, τ is the shear stress on the rock mass structure test block, ηα1 is the fractional viscosity coefficient, and α is the fractional order; S3, establish the viscosity coefficient damage equation D of the rock mass structural surface, and construct the damage fractional viscoplastic element u based on the viscoplastic deformation starting point of the rock mass structural surface in step S1 vp (t) The expression function method is: A1. Based on the physical and mechanical parameters of the rock at different amplitudes and frequencies obtained from the micro-dynamic perturbation experiment on the rock in step S1, the law between the strain rate and time of a certain rock under micro-dynamic perturbation is obtained and the deformation of the rock is divided into elastic deformation ε e and micro-dynamic perturbation plastic deformation ε p : e=e e +e p A2. Obtaining micro-dynamic perturbation plastic deformation ε p Relationship between amplitude, time and rock material properties: Among them, E K represents the rock modulus under micro-dynamic disturbance; A represents the disturbance amplitude; n represents the hardening index under micro-dynamic disturbance; A3. Calculate the unit increment of plastic strain due to micro-dynamic disturbance: Among them, Δt is the unit time; A4. The damage caused to the rock by micro-dynamic disturbance is D, which causes the modulus under micro-dynamic disturbance to be damaged; construct the modulus after damage expression: A5. According to E K Relationship with rock mineral composition, perturbation amplitude and loading time, assuming E K Equation with amplitude and loading time: E K =ρ·A α ·t β If the final damage equation expression is consistent with the actual rock damage curve, the assumption is valid; A6. Based on steps B2 and B3, construct the unit increment of disturbance damage: A7. Introduce the influence of micro-dynamic disturbance on rock damage and construct a rock damage constitutive model considering micro-dynamic disturbance: According to the Manson-Coffin empirical formula, the relationship function between plastic strain and micro-dynamic disturbance amplitude under micro-dynamic disturbance is constructed: Where c represents the material parameter; And using the relationship N = tf, the rock damage constitutive model under micro-dynamic disturbance is obtained: A8. Construct the yield function F(τ) based on the perturbation shear strength criterion under three-dimensional stress: A9. Carry out a preliminary experiment of shear disturbance on the rock mass structure surface, determine the shear disturbance viscoplastic starting stress τ0 based on the method described in step S1, introduce the flow law of Perzyna overstress theory according to the value of τ0 and the yield function F(τ) in step A8, determine the disturbance shear viscoplastic starting yield function F1, and construct the constitutive equation of fractional-order viscoplastic element: in And take F0 = 1; A10. Using the relationship N = tf and the Laplace transform and inverse transform method, the shear perturbation constitutive equation of fractional viscoplastic body is determined: Where τ is the shear stress on the rock mass structure test block, η β 2 is the fractional viscosity coefficient, β is the fractional order; S4, based on the starting point of the unstable extension of the plastic deformation of the rock mass structure surface in step S1, construct a nonlinear viscoplastic element u p (N) Expression function, the method is: B1. Carry out preliminary experiments on shear disturbance of rock mass structure surface, and determine the critical stress τ of shear disturbance viscoplasticity based on the method described in step S1. p According to τ p The value of and the yield function F(τ) in step A8 are used to determine the yield critical function F2 of the rock mass structural surface entering accelerated viscoplastic deformation under the action of three-dimensional perturbation shear; B2. Based on the relationship between strain and time, and between stress and strain of the rock mass structural surface obtained in the shear disturbance test in step B1, the relationship between stress rate and time of the rock mass structural surface under different shear stresses is clarified, and the relationship between shear strain rate and stress of the rock mass structural surface is constructed; B3. According to the value of τ0 and the yield function F2 in step B1, the flow law of Perzyna overstress theory is introduced to determine the shear creep viscoplastic starting yield function F1, and the nonlinear viscoplastic element u of the rock mass structural surface is determined by using the relationship N = tf. p The expression of (N) is: Where η3 is the fractional viscosity coefficient, N is the number of perturbations, δ is the material coefficient, And take F0 = 1; S5. Construct a damaged elastic element u e (N), fractional viscoelastic element u ve (N) and the fractional viscoplastic element u vp (N) and the nonlinear viscoplastic element u p (N) Series shear fractional constitutive model u(N) for characterizing rock disturbance damage: S6. Conduct a perturbation shear test on the rock mass structural surface under true three-dimensional stress to verify the shear fractional-order constitutive model of perturbation damage on the rock mass structural surface in step S5.

2. The method for constructing a shear fractional-order constitutive model considering structural surface disturbance damage according to claim 1, characterized in that: In the step S1, the shear disturbance stress corresponding to the rock mass structural surface entering plastic deformation in the shear disturbance stress-strain curve is used as the shear disturbance viscoplastic starting stress τ0 for starting viscoplastic deformation, and the corresponding shear strain is u0; the shear stress corresponding to the ratio of the product of the strain and the unit stress in the nth (n>1) unit time to the product of the strain and the unit stress in the n-1th unit time in the shear disturbance stress-strain curve of the rock mass structural surface is greater than 1.2 as the shear disturbance viscoplastic critical stress τ for characterizing accelerated viscoplastic deformation p , the corresponding shear strain is u p .

3. The method for constructing a shear fractional-order constitutive model considering structural surface disturbance damage according to claim 1, characterized in that: In step S6, a rock mass structural surface disturbance shear test under true three-dimensional stress is carried out to verify the shear fractional-order constitutive model of rock mass structural surface disturbance damage in step S5 as follows: C1. Determine the strength failure criterion of the rock mass structural surface, and determine the corresponding strength threshold of the shear disturbance element model of the rock mass structural surface according to the criterion; C2. Carry out shear disturbance test on the rock mass structure surface to obtain the shear disturbance test data of the rock mass structure surface: stress, strain, and test time; C3. Based on the test data obtained in step C2: stress, strain, test time, the shear disturbance element model u(t) of the rock mass structural surface in step S5 is fitted to obtain fitting parameters and correlation results.

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