A method for constructing a dynamic compression-shear damage constitutive model of fractured rock

Abstract

The application discloses a kind of fissured rock dynamic compression shear damage constitutive model construction methods, belong to geotechnical engineering technical field.The method relies on split Hopkinson pressure bar test, collects the axial stress strain data under the action of dynamic compression shear of fissured rock.Introduce equivalent stress, equivalent strain unified compression shear mechanics parameter, determine microcrack damage variable in combination with Weibull distribution, according to energy equivalence principle, calculate the macroscopic initial damage caused by precrack, then get composite damage variable using strain equivalence principle, establish axial and shear dynamic damage constitutive equation, and complete fitting verification using test data.The application can accurately describe the dynamic mechanical behavior of fissured rock under different shear compression ratio and crack inclination conditions, overcome the shortcomings of existing models that are difficult to apply to compression shear stress state and defective rock mass, and provide theoretical support for deep underground engineering rock mass dynamic stability analysis.

Description

Technical Field

[0001] This invention belongs to the field of rock engineering, specifically relating to a method for constructing a dynamic compressive-shear damage constitutive model for fractured rocks. Background Technology

[0002] In engineering scenarios such as deep underground mining, tunnel excavation, and underground cavern construction, rock masses are generally subjected to dynamic loads such as blasting impacts, rock bursts, and earthquakes. Furthermore, natural rock masses contain numerous macro- and micro-defects such as joints, fissures, and pores, resulting in a complex stress state characterized by the coexistence of compression and shear. Accurately describing the mechanical behavior and damage evolution of defective rocks under dynamic compressive and shear loads is the core theoretical foundation for evaluating the dynamic stability of deep rock masses and preventing disasters.

[0003] Most existing dynamic constitutive models for rocks are designed for intact rocks under uniaxial compressive loading, failing to accurately characterize the rock mechanical response under compressive-shear stress. The few constitutive studies focusing on compressive-shear loading also primarily concentrate on intact rock masses, neglecting the regulatory role of macroscopic and microscopic defects prevalent in natural rock masses on damage evolution. Furthermore, existing damage constitutive models often only consider the damage accumulation of microcracks, failing to simultaneously account for the initial damage effect of macroscopic pre-existing defects and the evolution of microscopic damage during loading. This results in insufficient accuracy in predicting the dynamic compressive-shear mechanical behavior of defective rocks, making it difficult to meet the engineering requirements for rock mass stability analysis in deep underground engineering.

[0004] Therefore, it is necessary to provide a method for constructing a constitutive model of dynamic compression-shear damage in fractured rocks. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, the purpose of this invention is to provide a method for constructing a dynamic compressive-shear damage constitutive model for fractured rocks. This method can simultaneously consider the evolution of microcrack damage and the initial damage effect of macroscopic defects, accurately characterizing the dynamic stress-strain response of fractured rocks under different shear-compression ratios and different defect dip angles.

[0006] To achieve the above-mentioned objectives, this invention provides a method for constructing a dynamic compressive-shear damage constitutive model for fractured rocks, comprising the following steps: A) Impact tests were conducted on fractured inclined prismatic rock specimens using a split Hopkinson bar (SHPB) to obtain axial stress-strain curves, shear stress-strain curves, and strain rate data under different specimen inclination angles and different fracture inclination angles. B) The viscoelastic dynamic mechanical behavior of undamaged rock is described by the standard linear solid (SLS) model, which is composed of Hooke elastic elements and Maxwell viscoelastic elements in parallel. C) Based on the constant strain rate loading condition, the stress-strain constitutive relationship of the undamaged rock is derived; D) Introducing the concepts of equivalent strain and equivalent stress, compressive shear strain and compressive shear stress are unified into a single equivalent variable. Assuming that the strength of rock micro-elements follows a Weibull random distribution, the damage variable corresponding to the initiation and propagation of microcracks is derived. D f ; E) Based on the Griffith crack propagation energy criterion, the elastic strain energy released by the pre-fabricated crack in the compressive-shear stress field is calculated. Combined with the total elastic strain energy of the rock element, the initial damage variable corresponding to the macroscopic crack is derived. D F ; F) Based on Lemaitre's strain equivalence principle, based on microcrack damage variables D f and macroscopic crack damage variables D F Construct composite damage variables D c This characterizes the total degree of damage to the rock during the loading process; G) Combining damage variables D c By introducing the standard linear solid constitutive relation of undamaged rock, dynamic damage constitutive equations are established for the axial compression direction and the shear direction, respectively. H) Using the experimentally measured dynamic stress-strain curve as a benchmark, the model parameters are obtained by fitting using the nonlinear least squares method. The model prediction results are compared with the experimental data to verify the accuracy and reliability of the constitutive model.

[0007] Specifically, the stress relationship of the standard linear solid model described in step B) satisfies the principle of equal strain and superposition of stress in parallel elements, and the total stress of the undamaged medium is the sum of the stress of the Hooke element and the stress of the Maxwell element. More specifically, under the constant strain rate loading condition described in step C), the constitutive expression of the undamaged rock is:

[0008] in, s ( t )for t Dynamic stress at any given moment For a constant strain rate, E 1 represents the elastic modulus of the Hooke element. E 2 represents the elastic modulus of the elastic element in the Maxwell unit. The relaxation time of the Maxwell unit is expressed as follows:

[0009] in, is the viscosity coefficient of the sticky pot.

[0010] More specifically, the steps described in step D) include: a) The equivalent strain e eq Based on the plane strain assumption, a unified characterization of the combined effect of axial compressive strain and shear strain is derived, expressed as follows:

[0011] in, s x For compressive stress, E The elastic modulus of the rock. m Poisson's ratio of the rock i Characterizes the degree of tilt of the sample.

[0012] b) The equivalent stress s eq The calculation expression is:

[0013] c) Microscopic damage variables based on the Weibull distribution D f The percentage of micro-elements destroyed during the loading process is obtained by statistically analyzing the proportion of micro-elements destroyed. The specific expression is:

[0014]

[0015] in, F 0 and m For the Weibull distribution parameters, A It is a constant.

[0016] More specifically, the macroscopic crack damage variables described in step E) D F The calculation is based on the equivalent relationship between the elastic strain energy released by crack propagation and the total elastic strain energy of the element, expressed as:

[0017]

[0018] in, a The length of the macroscopic crack. α The angle of inclination of the macroscopic fracture. t f For the sample thickness, V This represents the sample volume.

[0019] More specifically, the composite damage variable described in step F). D cBased on Lemaitre's strain equivalence principle, the expression is as follows:

[0020] More specifically, in step G), the viscoelastic parameters for the axial compression direction and the shear direction are respectively used to obtain the dynamic damage constitutive equations for the two directions:

[0021]

[0022] Among them, subscript x Material parameters indicating the axial compression direction, subscript xyz Material parameters indicating the shear direction; For axial strain rate, is the shear strain rate.

[0023] More specifically, in step H), the constitutive model parameters are obtained by fitting using the nonlinear least squares method.

[0024] By adopting the above technical solution, the beneficial effects of the present invention are as follows: 1. This invention simultaneously considers the initial damage of primary macroscopic fractures and the damage of micro-cracks generated by dynamic loads, constructing a composite damage variable to truly reflect the damage evolution law of natural fractured rock masses, overcoming the shortcomings of existing models that only consider micro-damage; 2. Equivalent stress and equivalent strain are introduced to describe the stress state of compression-shear coupling, and dynamic damage constitutive models in both axial and shear directions are established to solve the problem that traditional uniaxial compression constitutive models cannot characterize the mechanical response under the condition of coexistence of compression and shear. 3. A basic constitutive model based on the standard linear solid viscoelastic model is built, which can accurately reflect the strain rate effect and viscoelastic deformation characteristics of rock under dynamic loading; 4. Experimental data can be obtained by relying on SHPB dynamic compression-shear tests. The model parameters are quickly calibrated by nonlinear least square fitting. The theoretical curves and experimental results have a high degree of matching and reliable calculation accuracy. 5. The model can quantitatively analyze the influence of geometric parameters such as fracture dip angle, fracture length, and sample dip angle on the dynamic mechanical properties of rocks, and can directly serve the dynamic stability analysis and disaster prevention of rock masses in deep underground engineering. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating an example of the method for constructing a constitutive model of dynamic compression-shear damage in fractured rock according to the present invention; Figure 2 This is a schematic diagram of the experimental setup in an embodiment of the method for constructing a constitutive model of dynamic compression-shear damage in fractured rock according to the present invention; Figure 3This is a schematic diagram of a sample in an embodiment of the constitutive model construction method for dynamic compression-shear damage in fractured rock of the present invention; Appendix Figure 4 This is a schematic diagram of a standard linear solid (SLS) model in an embodiment of the constitutive model construction method for dynamic compression-shear damage in fractured rock according to the present invention; Figure 5 This is a schematic diagram of the stress state around a prefabricated macroscopic fracture in an embodiment of the constitutive model construction method for dynamic compression-shear damage in fractured rock of the present invention; Figure 6 The dynamic damage constitutive equation in the axial compression direction is an example of the method for constructing a dynamic compression-shear damage constitutive model for fractured rocks in this invention. Figure 7 The dynamic damage constitutive equation in the shear direction is an example of the method for constructing a dynamic compressive-shear damage constitutive model for fractured rock in this invention. The labels in the figure are as follows: 1-Strain gauge, 2-Transmission rod, 3-Incident rod, 4-Sample, 5-Spindle-shaped impact rod, 6-Oscilloscope, 7-Computer. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation steps. It should be understood that the specific embodiments described herein are only for illustrating and explaining the embodiments of the present invention and are not intended to limit the embodiments of the present invention.

[0027] like Figure 1 As shown, the present invention provides a method for constructing a dynamic compressive-shear damage constitutive model for fractured rock, comprising the following steps: A) Impact tests were conducted on fractured inclined prismatic rock specimens using a split Hopkinson bar (SHPB) to obtain axial stress-strain curves, shear stress-strain curves, and strain rate data under different specimen inclination angles and different fracture inclination angles. B) The viscoelastic dynamic mechanical behavior of undamaged rock is described by the standard linear solid (SLS) model, which is composed of Hooke elastic elements and Maxwell viscoelastic elements in parallel. C) Based on the constant strain rate loading condition, the stress-strain constitutive relationship of the undamaged rock is derived; D) Introducing the concepts of equivalent strain and equivalent stress, compressive shear strain and compressive shear stress are unified into a single equivalent variable. Assuming that the strength of rock micro-elements follows a Weibull random distribution, the damage variable corresponding to the initiation and propagation of microcracks is derived. D f ; E) Based on the Griffith crack propagation energy criterion, the elastic strain energy released by the pre-fabricated crack in the compressive-shear stress field is calculated. Combined with the total elastic strain energy of the rock element, the initial damage variable corresponding to the macroscopic crack is derived.D F ; F) Based on Lemaitre's strain equivalence principle, based on microcrack damage variables D f and macroscopic crack damage variables D F Construct composite damage variables D c This characterizes the total degree of damage to the rock during the loading process; G) Combining damage variables D c By introducing the standard linear solid constitutive relation of undamaged rock, dynamic damage constitutive equations are established for the axial compression direction and the shear direction, respectively. H) Using the experimentally measured dynamic stress-strain curve as a benchmark, the model parameters are obtained by fitting using the nonlinear least squares method. The model prediction results are compared with the experimental data to verify the accuracy and reliability of the constitutive model.

[0028] like Figure 2 As shown, in one embodiment of the constitutive model construction method for dynamic compression-shear damage in fractured rock provided by the present invention, the dynamic compression-shear experiment on the sample is conducted based on a Hopkinson pressure bar device. Specifically, the Hopkinson pressure bar device includes a spindle-shaped impact bar, an incident bar, and a transmission bar. The sample is clamped between the incident bar and the transmission bar. The spindle-shaped impact bar strikes the incident bar to apply an impact load to the sample, ensuring that the sample reaches dynamic stress equilibrium and constant strain rate loading. An incident bar strain gauge is provided on the incident bar, and the incident bar strain gauge is connected to a waveform acquisition and display device to measure loading parameters, including the incident strain. e I ( t ), reflection strain e R ( t The transmission rod is equipped with a transmission rod strain gauge, which is connected to a waveform acquisition and display device to include the transmission strain. e T ( t ).

[0029] like Figure 3 As shown, in one embodiment of the constitutive model construction method for dynamic compression-shear damage of fractured rock provided by the present invention, the sample can be set as a fractured inclined prismatic rock sample, and the pre-fabricated fracture is preferably located in the middle of the upper plane of the sample and penetrates the sample along the thickness direction.

[0030] like Figure 4 As shown, in one embodiment of the constitutive model construction method for dynamic compression-shear damage in fractured rock provided by the present invention, the standard linear solid model is composed of Hooke elements and Maxwell elements connected in parallel, and the stress of the Hooke elements is... s 1 and Maxwell element stress s 2. Calculate according to the following formulas respectively:

[0031]

[0032]

[0033] in, For a constant strain rate, E 1 represents the elastic modulus of the Hooke element. E 2 represents the elastic modulus of the elastic element in the Maxwell unit. For the relaxation time of the Maxwell unit, t For loading time, s For reference time.

[0034] Based on the principle that the strain of parallel elements is equal and the stress is superimposed, the total stress of the undamaged medium is... s ( t The sum of the stresses in the Hooke element and the Maxwell element is given.

[0035] Introducing equivalent strain e eq The concept of represents the combined effect of axial compressive strain and shear strain, and is derived based on the plane strain assumption. The expression is:

[0036] in, s x For compressive stress, E The elastic modulus of the rock. m Poisson's ratio of the rock i Characterizes the degree of tilt of the sample.

[0037] Introducing equivalent stress s eq The concept of represents the combined effect of axial compressive stress and shear stress, and its calculation expression is:

[0038] Equivalent stress s eq Equivalent variation e eq The following relationship exists:

[0039]

[0040] in, A It is a constant.

[0041] Microscopic damage variables based on Weibull distribution D f The percentage of micro-elements destroyed during the loading process is obtained by statistically analyzing the proportion of micro-elements destroyed. The specific expression is:

[0042] in, F 0 and m These are the parameters of the Weibull distribution.

[0043] Substituting the equivalent strain into the micro-damage variable D f This yields the following expression:

[0044] The stress state around the precast crack is as follows Figure 5 As shown, the far-field compressive stress is decomposed into normal stress perpendicular to the crack surface. s n Shear stress parallel to crack surface t s Based on the Griffith energy criterion, the elastic strain energy released during crack propagation U 1 is:

[0045]

[0046]

[0047] in, t f For the sample thickness, a The length of the macroscopic crack. α The angle of inclination of the macroscopic fracture. K I , K II These are type I and type II stress intensity factors, respectively. t xy This represents the shear stress at the boundary of the specimen.

[0048] Total elastic strain energy of rock element U 2 includes both compression and shearing, and can be calculated using the following formula:

[0049] in, G This is the shear modulus.

[0050] Based on the elastic strain energy released during crack propagation U1 and the total elastic strain energy of the rock element U The equivalent relationship of 2, the initial damage variable corresponding to the macroscopic crack. D F It can be calculated using the following formula:

[0051]

[0052]

[0053] Constructed based on Lemaitre's strain equivalence principle, combined with microcrack damage variables. D f and macroscopic crack damage variables D F Construct composite damage variables D c The expression is:

[0054] By introducing the equivalent damage variable into the standard linear solid model and considering the parameter differences in the axial and shear directions, constitutive equations for the two directions are obtained:

[0055]

[0056] Among them, subscript x Material parameters indicating the axial compression direction, subscript xyz Material parameters indicating the shear direction; For axial strain rate, is the shear strain rate.

[0057] The nonlinear least squares method was used to fit the model parameters based on the experimentally measured stress-strain curves. Comparisons between the model prediction curves and experimental curves for each group of specimens are shown below. Figure 6 and Figure 7 As shown, the two agree well, verifying the accuracy and reliability of the model constructed in this invention. It can effectively describe the dynamic compression-shear mechanical behavior of defective rocks under different shear-compression ratios and different fracture angles.

[0058] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

[0059] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for constructing a constitutive model of dynamic compressive-shear damage in fractured rock, characterized in that, Includes the following steps: A) Obtain the axial stress-strain curves and shear stress-strain curves of a fractured inclined prism rock specimen under dynamic compression and shear loading by using the split Hopkinson bar (SHPB) test. B) Based on the standard linear solid model, the viscoelastic constitutive relation of undamaged rock under constant strain rate loading is established. The standard linear solid model is composed of Hooke elements and Maxwell elements connected in parallel. C) By introducing equivalent strain and equivalent stress, and characterizing the intensity distribution of rock micro-elements based on the Weibull random distribution, the damage variables corresponding to microcracks are derived. D f ; D) Based on the Griffith crack propagation energy criterion, and combining crack geometry parameters, specimen tilt angle, and compressive-shear stress state, the damage variables corresponding to macroscopic cracks are derived. D F ; E) Based on Lemaitre's equivalent strain principle, a composite damage variable is constructed based on microcrack damage variables and macrocrack damage variables. D c ; F) Introduce the composite damage variable into the standard linear solid constitutive relation of the undamaged rock, and derive the dynamic damage constitutive equations for the axial compression direction and the shear direction respectively; G) The model parameters were obtained by nonlinear least square fitting using experimentally measured stress-strain curves to verify the accuracy of the constitutive model.

2. The method for constructing a constitutive model of dynamic compression-shear damage in fractured rock according to claim 1, characterized in that, The expression for the viscoelastic constitutive relation of the undamaged rock under constant strain rate loading is as follows: in, σ ( t )for t Dynamic stress at any given moment For a constant strain rate, E 1 represents the elastic modulus of the Hooke element. E 2 represents the elastic modulus of the elastic element in the Maxwell unit. The relaxation time of the Maxwell unit is expressed as follows: in, is the viscosity coefficient of the sticky pot.

3. The method for constructing a dynamic compressive-shear damage constitutive model for fractured rock according to claim 2, characterized in that, The equivalent strain The calculation expression is: in, σ x For compressive stress, E The elastic modulus of the rock. μ Poisson's ratio of the rock θ is Characterizes the degree of tilt of the sample.

4. The method for constructing a constitutive model of dynamic compression-shear damage in fractured rock according to claim 3, characterized in that, The equivalent stress σ eq The calculation expression is: 。 5. The method for constructing a constitutive model of dynamic compression-shear damage in fractured rock according to claim 4, characterized in that, The microcrack damage variable D f The calculation expression is: in, F 0 and m For the Weibull distribution parameters, A It is a constant.

6. The method for constructing a constitutive model of dynamic compression-shear damage in fractured rock according to claim 5, characterized in that, The macroscopic crack damage variable D F The calculation is based on the equivalent relationship between the elastic strain energy released by crack propagation and the total elastic strain energy of the element, expressed as: in, a The length of the macroscopic crack. α The angle of inclination of the macroscopic fracture. t f For the sample thickness, V This represents the sample volume.

7. The method for constructing a constitutive model of dynamic compression-shear damage in fractured rock according to claim 6, characterized in that, The composite damage variable D c The expression is: 。 8. The method for constructing a dynamic compressive-shear damage constitutive model for fractured rock according to claim 7, characterized in that, The dynamic damage constitutive equations for the axial compression direction and the shear direction are respectively: Among them, subscript x Material parameters indicating the axial compression direction, subscript xy Material parameters indicating the shear direction; For axial strain rate, is the shear strain rate.

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