Method for establishing rock reinforcement-damage constitutive model based on energy principle

Abstract

The invention relates to the technical field of rock mechanics and engineering, in particular to a method for establishing a rock reinforcement-damage constitutive model based on an energy principle. The method comprises the following steps: acquiring the elastic modulus, the elastic strain energy and the dissipation energy of the weak rock; dividing the deformation failure process of the weak rock into an enhancement stage and a damage stage; obtaining an enhanced evolution equation and a damage evolution equation; and obtaining a constitutive model of an enhancement stage and a constitutive model of a damage stage, and combining the constitutive model of the enhancement stage and the constitutive model of the damage stage to obtain an enhancement-damage constitutive model for simulating to obtain nonlinear mechanical parameters of the weak rock. According to the method, the internal structure and the stress state of the rock can be comprehensively considered, and an important theoretical thought is provided for accurately reflecting the nonlinear mechanical behavior characteristics of the weak rock.

Description

Technical Field

[0001] The present invention relates to the technical field of rock mechanics and engineering, and particularly relates to a method for establishing a rock enhancement-damage constitutive model based on the energy principle. Background Art

[0002] Rock materials are the main materials encountered in underground engineering construction projects. Under the long-term action of tectonic stress, defects such as joints, fissures, and pores inside the rock materials gradually develop, resulting in the mechanical behavior characteristics of the rock showing significant non-linear characteristics. Many underground engineering construction projects show that accurately evaluating the mechanical behavior characteristics of rocks is the key to ensuring the safe construction of the project. Among them, the constitutive model is an important method for reflecting and predicting the mechanical behavior characteristics of rocks. Therefore, constructing a suitable rock constitutive model is not only the basis of the theoretical research on rock mechanics but also one of the core theories for the design basis of underground engineering construction.

[0003] Currently, in the research on rock constitutive models, the mechanical behavior of rocks before yielding is usually simplified as linear elasticity, and then the elastoplastic damage constitutive model is used to reflect the mechanical behavior characteristics of rocks. Although such a simplification can make the calculation simpler, a large number of rock tests show that even for very dense hard rocks, their mechanical behavior characteristics before yielding are not linear, and for soft rocks with lower strength (i.e., soft rocks, generally referring to rocks with a uniaxial compressive strength lower than 25 MPa), the non-linear characteristics of their mechanical behavior are more significant. The deformation process of soft rocks generally includes four stages: compaction stage, linear elastic stage, plastic yielding stage, and failure stage. If the existing elastoplastic damage constitutive model is used to reflect the mechanical behavior characteristics of soft rocks while ignoring the compaction stage, its accuracy may be far from sufficient, thus affecting the construction design of underground engineering.

[0004] In view of the non-linear characteristics of the mechanical behavior of soft rocks, some scholars have introduced the principle of statistics, considered the influence of the pore structure on rocks in the compaction stage, and then modified the elastoplastic damage constitutive model, improving the accuracy of the existing rock constitutive model. However, the mechanical behavior characteristics of rocks are not only affected by the randomness of internal defects but also by the stress (such as axial stress) state of the rock element itself. Therefore, although the existing constitutive models of soft rocks consider the influence of the pore structure on rocks in the compaction stage, it is difficult to accurately reflect the non-linear mechanical behavior characteristics of soft rocks.

[0005] As is well known, the deformation and failure process of rocks is essentially driven by energy, accompanied by the input, accumulation, and release of energy. Within the framework of thermodynamics, studying the non-linear mechanical behavior characteristics of soft rocks from the energy perspective can comprehensively consider the internal structure and stress state of rocks and better reflect the non-linear mechanical behavior characteristics of soft rocks.

[0006] In summary, it is necessary to develop a method for establishing a rock strengthening-damage constitutive model based on the energy principle from the energy perspective, which provides an important theoretical idea for accurately reflecting the nonlinear mechanical behavior characteristics of soft rocks. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for establishing a rock strengthening-damage constitutive model based on the energy principle. The specific technical solution is as follows: A method for establishing a rock strengthening-damage constitutive model based on the energy principle includes: Step S1: Take two batches of soft rocks of the same quality. Conduct uniaxial compression tests on one batch of soft rocks to obtain the average uniaxial compression strength data, denoted as Q; conduct cyclic uniaxial loading and unloading tests on the other batch of soft rocks until the soft rocks are deformed and damaged; the uniaxial loading force used in the cyclic uniaxial loading and unloading test is a gradient-increasing variable force, denoted as W; W is 5% - 100% times of Q; in the cyclic uniaxial loading and unloading test, obtain the elastic modulus, elastic strain energy and dissipated energy ; Step S2: According to the change trend of the elastic modulus obtained in Step S1, which first increases and then decreases, divide the deformation and failure process of the soft rock into a strengthening stage and a damage stage; Step S3: Solve the strengthening evolution equation of the strengthening stage according to the relationship between the elastic strain energy and the strengthening factor; solve the damage evolution equation of the damage stage according to the relationship among the elastic strain energy , the dissipated energy and the damage factor; Step S4: Substitute the stress-strain relationship of the soft rock in the strengthening stage into the strengthening evolution equation to obtain the constitutive model of the strengthening stage; substitute the stress-strain relationship of the soft rock in the damage stage into the damage evolution equation to obtain the constitutive model of the damage stage; combine the constitutive model of the strengthening stage and the constitutive model of the damage stage to obtain a strengthening-damage constitutive model, which is used to simulate and obtain the nonlinear mechanical parameters of the soft rock.

[0008] Optionally, in Step S3, under the conditions of the cyclic uniaxial loading and unloading test, assume that the elastic strain energy of the soft rock is generated by elastic deformation, then the elastic strain energy in the strengthening stage is expressed by Equation (1); Equation (1); where is the axial stress in the strengthening stage, and ; It is the unloading elastic modulus of the first cycle of the cyclic uniaxial loading and unloading test; For the enhancement stage The enhancement factor of the moment; is the elastic strain; The elastic strain energy and the enhancement factor satisfy a quadratic function relationship, which is expressed by formula 2); Formula 2); in, is the fitting coefficient, expressed as the elastic strain energy enhancement rate; The enhanced evolution equation is obtained by combining equation 1) and equation 2), which is expressed by equation 3); Formula 3).

[0009] Optional, ; For the enhancement stage Elastic modulus of rock at moment.

[0010] Optionally, in step S3, under the cyclic uniaxial loading and unloading test conditions, the energy input With the elastic strain energy The relationship between them satisfies equation 4); wherein the input energy Kinetic energy provided for uniaxial loading; Formula 4); in, is the input energy With the elastic strain energy The linear relationship coefficient between Under the cyclic uniaxial loading and unloading test conditions, the elastic strain energy With the dissipated energy The relationship between them satisfies formula 5); Formula 5); The dissipated energy The relationship between the damage factor and formula (6) is satisfied; Formula 6); in, is the energy consumption rate of rock damage; The injury stage Damage factor at the moment; The elastic strain energy at the damage stage It is expressed by formula 7); Formula 7); in, is the axial stress at the damage stage, and ; is the maximum value of the elastic modulus of the weak rock; The damage evolution equation is obtained by combining Equation (5), Equation (6) and Equation (7), and is expressed by Equation (8); Equation (8).

[0011] Optionally, ; is the elastic modulus of the rock at the th moment of the damage stage.

[0012] Optionally, the constitutive model of the strengthening stage is obtained by combining the stress-strain relationship of Equation (1) with Equation (3), and is expressed by Equation (9); Equation (9); wherein, is the axial strain, and , is changing to coefficient; is the yield point strain.

[0013] Optionally, the yield point strain is the strain at the maximum value of the elastic modulus point.

[0014] Optionally, the constitutive model of the damage stage is obtained by combining the stress-strain relationship of Equation (7) with Equation (8), and is expressed by Equation (10); Equation (10); wherein, is the strain at the peak point of the uniaxial compressive strength.

[0015] Optionally, the average uniaxial compressive strength data includes the data obtained by averaging the uniaxial compression test results of at least three of the weak rocks.

[0016] Optionally, the uniaxial loading force is a force that increases in an equal gradient; the increasing gap between two adjacent gradients is 5% - 10%Q.

[0017] Applying the technical solution of the present invention has at least the following beneficial effects: A method for establishing a rock strengthening-damage constitutive model based on the energy principle provided by the present invention divides the deformation and failure process of soft rock into a strengthening stage and a damage stage according to the change trend of the elastic modulus that first increases and then decreases in the cyclic uniaxial loading and unloading test; a strengthening-damage constitutive model of soft rock based on the energy principle is established from the energy perspective to simulate and obtain the non-linear mechanical parameters of soft rock, which can comprehensively consider the internal structure and stress state of the rock and provide an important theoretical idea for accurately reflecting the non-linear mechanical behavior characteristics of soft rock.

[0018] In addition to the purposes, features, and advantages described above, the present invention has other purposes, features, and advantages. The present invention will be further described in detail below with reference to the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a schematic flow chart of a method for establishing a rock strengthening-damage constitutive model based on the energy principle in an embodiment; Figure 2 is a graph showing the change of the elastic modulus of soft rock in the cyclic uniaxial loading and unloading test; Figure 3 is a graph showing the quadratic function relationship between the elastic strain energy and the strengthening factor; Figure 4 is a graph showing the relationship between the theoretical curve and the test curve of soft yellow sandstone; Figure 5 is a graph showing the relationship between the theoretical curve and the test curve of soft red sandstone; Figure 6 is a graph showing the relationship between the theoretical curve and the test curve of soft shale. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention belong to the scope of protection of the present invention. Embodiment:

[0021] See Figure 1 , a method for establishing a rock strengthening-damage constitutive model based on the energy principle, including: Step S1: Take two batches of soft rocks of the same quality (soft rocks refer to soft rocks, generally rocks with a uniaxial compressive strength lower than 25 MPa). Conduct a uniaxial compression test on one batch of soft rocks to obtain the average value data of the uniaxial compressive strength, denoted as Q; the average value data of the uniaxial compressive strength comes from the average value of the uniaxial compression test results of three of the soft rocks; conduct a cyclic uniaxial loading and unloading test on the other batch of soft rocks until the soft rocks are deformed and damaged; the uniaxial loading force used in the cyclic uniaxial loading and unloading test is an equally gradient increasing force, denoted as W; the increasing gap between two adjacent gradients is 5%Q; W successively adopts 5 times, 10 times, 15 times, 20 times,... of Q until the soft rocks are deformed and damaged; in the cyclic uniaxial loading and unloading test, obtain the elastic modulus, elastic strain energy and dissipated energy ; Step S2: Refer to Figure 2 , according to the change trend that the elastic modulus obtained in Step S1 first increases and then decreases, divide the deformation and damage process of the soft rocks into an enhancement stage and a damage stage; Step S3: Solve the enhancement evolution equation of the enhancement stage according to the relationship between the elastic strain energy and the enhancement factor; solve the damage evolution equation of the damage stage according to the relationship among the elastic strain energy , the dissipated energy and the damage factor; Step S4: Substitute the stress-strain relationship of the soft rocks in the enhancement stage into the enhancement evolution equation to obtain the constitutive model of the enhancement stage; substitute the stress-strain relationship of the soft rocks in the damage stage into the damage evolution equation to obtain the constitutive model of the damage stage; combine the constitutive model of the enhancement stage and the constitutive model of the damage stage to obtain an enhancement-damage constitutive model, which is used to simulate and obtain the nonlinear mechanical parameters of the soft rocks.

[0022] In Step S3, under the conditions of the cyclic uniaxial loading and unloading test, assume that the elastic strain energy of the soft rocks is generated by elastic deformation, then the elastic strain energy in the enhancement stage is expressed by Equation 1); Equation 1); Wherein, is the axial stress in the enhancement stage, and ; is the unloading elastic modulus of the first cycle of the cyclic uniaxial loading and unloading test; is the enhancement factor at the th moment in the enhancement stage; wherein, ; For the enhancement stage The elastic modulus of the rock at that moment; is the elastic strain; Based on the results of the cyclic uniaxial loading and unloading tests, the elastic strain energy and the enhancement factor satisfy a quadratic function relationship, such as Figure 3 As shown ( Figure 3 middle represents the correlation coefficient), and the quadratic function relationship is expressed by formula 2); Formula 2); in, is the fitting coefficient, expressed as the elastic strain energy enhancement rate; Figure 3 middle is 0.0297; The enhanced evolution equation is obtained by combining equation 1) and equation 2), which is expressed by equation 3); Formula 3).

[0023] In step S3, under the cyclic uniaxial loading and unloading test conditions, the energy With the elastic strain energy The relationship between them satisfies equation 4); wherein the input energy Kinetic energy provided for uniaxial loading; Formula 4); in, is the input energy With the elastic strain energy The linear relationship coefficient between Under the cyclic uniaxial loading and unloading test conditions, the elastic strain energy With the dissipated energy The relationship between them satisfies formula 5); Formula 5); The dissipated energy The relationship between the damage factor and formula (6) is satisfied; Formula 6); in, is the energy consumption rate of rock damage; The injury stage Damage factor at the moment; The elastic strain energy at the damage stage It is expressed by formula 7); Formula 7); in, is the axial stress at the damage stage, and ; where ; is the elastic modulus of the rock at the th moment of the damage stage; is the maximum value of the elastic modulus of the weak rock; The damage evolution equation is obtained by combining Equations (5), (6) and (7), and is expressed by Equation (8); Equation (8).

[0024] The constitutive model of the strengthening stage is obtained by combining the stress-strain relationship of Equation (1) with Equation (3), and is expressed by Equation (9); Equation (9); where is the axial strain, and , is changing to coefficient; is the yield point strain.

[0025] The yield point strain is the strain at the maximum value of the elastic modulus point.

[0026] The constitutive model of the damage stage is obtained by combining the stress-strain relationship of Equation (7) with Equation (8), and is expressed by Equation (10); Equation (10); where is the strain at the peak point of the uniaxial compressive strength; The strengthening-damage constitutive model is obtained by combining the constitutive model Equation (9) of the strengthening stage and the constitutive model Equation (10) of the damage stage, and is expressed by Equation (11); Equation (11).

[0027] In order to verify whether the strengthening-damage constitutive model in this embodiment can accurately reflect the nonlinear mechanical behavior characteristics of weak rock, the nonlinear mechanical behavior characteristic theoretical curves of weak yellow sandstone, weak red sandstone and weak shale are respectively simulated and obtained by using the strengthening-damage constitutive model in this embodiment, as Figures 4 - 6 shown.

[0028] From Figures 4 - 6It can be seen that the theoretical curves of the nonlinear mechanical behavior characteristics of soft yellow sandstone, soft red sandstone, and soft shale respectively simulated by using the enhanced-damage constitutive model described in this embodiment can well describe the stress-strain process (i.e., the test curve) of the corresponding soft rock under cyclic uniaxial loading and unloading from the trend of change, thus proving that the enhanced-damage constitutive model established based on the energy principle can well reflect the nonlinear mechanical behavior characteristics of soft rock.

[0029] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for establishing a rock enhancement-damage constitutive model based on energy principle, characterized in that: include: Step S1, take two batches of weak rocks of the same quality, perform a uniaxial compression test on one batch of the weak rocks, and obtain the average value of the uniaxial compression strength, which is recorded as Q; perform a cyclic uniaxial loading and unloading test on the other batch of weak rocks until the weak rocks are deformed and damaged; the uniaxial loading force used in the cyclic uniaxial loading and unloading test is a gradient increasing force, which is recorded as W; W is 5% to 100% of Q; in the cyclic uniaxial loading and unloading test, the elastic modulus and elastic strain energy of the weak rocks are obtained. and dissipated energy ; Step S2, according to the elastic modulus obtained in step S1, which shows a trend of first increasing and then decreasing, the deformation and failure process of the soft rock is divided into an enhancement stage and a damage stage; Step S3: According to the elastic strain energy The relationship between the enhancement factor and the enhancement factor is solved to obtain the enhancement evolution equation of the enhancement stage; according to the elastic strain energy , the dissipated energy The relationship between the three and the damage factor is solved to obtain the damage evolution equation of the damage stage; Step S4, substituting the stress-strain relationship of the weak rock in the enhancement stage into the enhancement evolution equation to obtain the constitutive model of the enhancement stage; substituting the stress-strain relationship of the weak rock in the damage stage into the damage evolution equation to obtain the constitutive model of the damage stage; and combining the constitutive model of the enhancement stage and the constitutive model of the damage stage to obtain an enhancement-damage constitutive model for simulating the nonlinear mechanical parameters of the weak rock.

2. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 1 is characterized in that: In step S3, under the cyclic uniaxial loading and unloading test conditions, it is assumed that the elastic strain energy of the soft rock is Produced by elastic deformation, the elastic strain energy in the enhancement stage is It is expressed by formula 1); Formula 1); in, is the axial stress in the reinforcement stage, and ; It is the unloading elastic modulus of the first cycle of the cyclic uniaxial loading and unloading test; For the enhancement stage The enhancement factor of the moment; is the elastic strain; The elastic strain energy and the enhancement factor satisfy a quadratic function relationship, which is expressed by formula 2); Formula 2); in, is the fitting coefficient, expressed as the elastic strain energy enhancement rate; The enhanced evolution equation is obtained by combining equation 1) and equation 2), which is expressed by equation 3); Formula 3).

3. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 2 is characterized in that: ; For the enhancement stage The elastic modulus of the rock at that moment.

4. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 3 is characterized in that: In step S3, under the cyclic uniaxial loading and unloading test conditions, the energy With the elastic strain energy The relationship between them satisfies equation 4); wherein the input energy Kinetic energy provided for uniaxial loading; Formula 4); in, is the input energy With the elastic strain energy The linear relationship coefficient between Under the cyclic uniaxial loading and unloading test conditions, the elastic strain energy With the dissipated energy The relationship between them satisfies formula 5); Formula 5); The dissipated energy The relationship between the damage factor and formula (6) is satisfied; Formula 6); in, is the rock damage energy consumption rate; The injury stage Damage factor at the moment; The elastic strain energy at the damage stage It is expressed by formula 7); Formula 7); in, is the axial stress at the damage stage, and ; is the maximum value of the elastic modulus of weak rock; The damage evolution equation is obtained by combining equations 5), 6) and 7), which is expressed by equation 8); Equation 8).

5. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 4 is characterized in that: ; The injury stage The elastic modulus of the rock at that moment.

6. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 5 is characterized in that: The constitutive model of the enhancement stage is obtained by combining the stress-strain relationship of formula 1) with formula 3), which is expressed by formula 9); Formula 9); in, is the axial strain, and , for Change to The coefficient of is the yield point strain.

7. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 6 is characterized in that: The yield point strain The maximum value of elastic modulus The strain at the point.

8. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 6 is characterized in that: The constitutive model of the damage stage is obtained by combining the stress-strain relationship of formula 7) with formula 8), which is expressed by formula 10); Formula 10); in, is the peak strain of uniaxial compressive strength.

9. A method for establishing a rock enhancement-damage constitutive model based on energy principle according to any one of claims 1 to 8, characterized in that: The average uniaxial compression strength data includes data of the average value of at least three uniaxial compression test results of the soft rock.

10. The method for establishing a rock enhancement-damage constitutive model based on energy principle according to claim 9, characterized in that: The uniaxial loading force is a force with an equal gradient and an increasing difference between two adjacent gradients is 5% to 10%Q.

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