A method for establishing a rock enhancement-damage constitutive model based on the energy principle

Abstract

The present invention relates to the field of rock mechanics and engineering technology, and particularly relates to a method for establishing a rock enhancement-damage constitutive model based on the energy principle. The method includes obtaining the elastic modulus, elastic strain energy, and dissipated energy of soft rock; dividing the deformation and failure process of the soft rock into an enhancement stage and a damage stage; obtaining an enhancement evolution equation and a damage evolution equation; obtaining a constitutive model for the enhancement stage and a constitutive model for the damage stage, and combining the two to obtain an enhancement-damage constitutive model for simulating and obtaining the nonlinear mechanical parameters of soft rock. The present invention can comprehensively consider the internal structure and stress state of rock, providing an important theoretical idea for accurately reflecting the nonlinear mechanical behavior characteristics of soft 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 significant non-linear characteristics in the mechanical behavior of the rocks. 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 rock mechanics theoretical research 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 yield 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 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 of rocks is not only affected by the randomness of internal defects but also by the stress state (such as axial stress) of the rock units themselves. Therefore, although the existing soft rock constitutive models 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 object 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:

[0008] A method for establishing a rock strengthening-damage constitutive model based on the energy principle includes:

[0009] Step S1: Take two batches of soft rocks of the same quality. Conduct a uniaxial compression test on one batch of soft rocks to obtain the average value data of the uniaxial compression strength, denoted as Q; 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 a gradient increasing 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 ;

[0010] Step S2: According to the change trend that the elastic modulus obtained in Step S1 first increases and then decreases, divide the deformation and failure process of the soft rock into a strengthening stage and a damage stage;

[0011] 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;

[0012] 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.

[0013] 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);

[0014] Formula 1);

[0015] in, is the axial stress in the reinforcement stage, and ; 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;

[0016] The elastic strain energy The relationship between and the enhancement factor satisfies a quadratic function, which is expressed by formula 2);

[0017] Formula 2);

[0018] in, is the fitting coefficient, expressed as the elastic strain energy enhancement rate;

[0019] The enhanced evolution equation is obtained by combining Equation 1) and Equation 2), which is expressed by Equation 3);

[0020] Equation 3).

[0021] Optional, ; For the enhancement stage The elastic modulus of the rock at that moment.

[0022] Optionally, in step S3, under the cyclic uniaxial loading and unloading test conditions, the input energy With the elastic strain energy The relationship between them satisfies formula 4); wherein, the input energy Kinetic energy provided for uniaxial loading;

[0023] Formula 4);

[0024] in, is the input energy With the elastic strain energy The linear relationship coefficient between

[0025] Under the cyclic uniaxial loading and unloading test conditions, the elastic strain energy With the dissipated energy The relationship between them satisfies formula 5);

[0026] Equation 5);

[0027] The dissipated energy satisfies the relationship of Equation (6) with the damage factor;

[0028] Equation (6);

[0029] where, is the energy dissipation rate of rock damage; is the damage factor at the moment of the damage stage;

[0030] The elastic strain energy in the damage stage is expressed by Equation (7);

[0031] Equation (7);

[0032] where, is the axial stress in the damage stage, and ; is the maximum value of the elastic modulus of soft rock;

[0033] The damage evolution equation is obtained by combining Equation (5), Equation (6) and Equation (7), and is expressed by Equation (8);

[0034] Equation (8).

[0035] Optionally, ; is the elastic modulus of the rock at the moment of the damage stage.

[0036] 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);

[0037] Equation (9);

[0038] where, is the axial strain, and ,, is changing from to the coefficient of is the yield point strain.

[0039] Optionally, the yield point strain is the strain at the maximum value of the elastic modulus.

[0040] 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);

[0041] Equation (10);

[0042] Among them, is the strain at the peak point of the uniaxial compressive strength.

[0043] Optionally, the average uniaxial compressive strength data includes the data obtained by averaging the uniaxial compression test results of at least three of the soft rocks.

[0044] Optionally, the uniaxial loading force is a force that increases with equal gradients; the increasing gap between two adjacent gradients is 5% - 10%Q.

[0045] Applying the technical solution of the present invention has at least the following beneficial effects:

[0046] 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 rocks into a strengthening stage and a damage stage according to the changing trend of the elastic modulus, which first increases and then decreases, in the cyclic uniaxial loading and unloading test; starting from the energy perspective, a strengthening-damage constitutive model of soft rocks based on the energy principle is established to simulate and obtain the nonlinear mechanical parameters of soft rocks, which can comprehensively consider the internal structure and stress state of rocks and provide an important theoretical idea for accurately reflecting the nonlinear mechanical behavior characteristics of soft rocks.

[0047] In addition to the purposes, features, and advantages described above, the present invention has other purposes, features, and advantages. The following will refer to the drawings to further elaborate on the present invention in detail. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] 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:

[0049] 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;

[0050] Figure 2 [[ID= thirty-one]]is a graph showing the change of the elastic modulus of soft rocks in the cyclic uniaxial loading and unloading test;

[0051] Figure 3 is a graph showing the quadratic function relationship between the elastic strain energy and the strengthening factor;

[0052] Figure 4 is a graph showing the relationship between the theoretical curve and the test curve of soft yellow sandstone;

[0053] Figure 5 is a graph showing the relationship between the theoretical curve and the test curve of soft red sandstone;

[0054] Figure 6It is a relationship diagram between the theoretical curve and the test curve of soft shale. Detailed implementation manners

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying 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. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art shall fall within the protection scope of the present invention.

[0056] Embodiment:

[0057] Refer to Figure 1 , a method for establishing a rock strengthening-damage constitutive model based on the energy principle, including:

[0058] Step S1: Take two batches of soft rocks of the same quality (soft rocks refer to soft rocks, generally referring to 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 equal-gradient increasing variable force, denoted as W; the increasing gap between two adjacent gradients is 5%Q; the W successively adopts 5 times, 10 times, 15 times, 20 times,... of the 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 ;

[0059] 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 rock into a strengthening stage and a damage stage;

[0060] Step S3: Solve the strengthening evolution equation of the strengthening stage according to the relationship between the elastic strain energy and the strengthening factor; according to the elastic strain energy , the dissipated energy and the relationship among the three damage factors, solve the damage evolution equation of the damage stage;

[0061] 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 in 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 in the damage stage; combine the constitutive model in the strengthening stage and the constitutive model in 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.

[0062] In step S3, under the condition of the cyclic uniaxial loading and unloading test, assume that the elastic strain energy of the soft rock is generated by elastic deformation, and the elastic strain energy in the strengthening stage is expressed by Equation (1);

[0063] Equation (1);

[0064] where is the axial stress in the strengthening stage, and ; is the unloading elastic modulus of the first cycle of the cyclic uniaxial loading and unloading test; is the strengthening factor at the th moment in the strengthening stage; where ; is the elastic modulus of the rock at the s th moment in the strengthening stage; is the elastic strain;

[0065] Based on the results of the cyclic uniaxial loading and unloading test, the elastic strain energy and the strengthening factor satisfy a quadratic function relationship, as shown in Figure 3 ( Figure 3 where represents the correlation coefficient), and this quadratic function relationship is expressed by Equation (2);

[0066] Equation (2);

[0067] where is the fitting coefficient, expressed as the elastic strain energy enhancement rate; in Figure 3 where is 0.0297;

[0068] Combining Equation (1) and Equation (2) to obtain the strengthening evolution equation, which is expressed by Equation (3);

[0069] Equation (3).

[0070] In step S3, under the condition of the cyclic uniaxial loading and unloading test, the input energy and the elastic strain energy satisfies the relationship of Equation (4); where the input energy is the kinetic energy provided for uniaxial loading;

[0071] Equation (4);

[0072] where is the input energy and the elastic strain energy is the linear relationship coefficient between them;

[0073] Under the condition of the cyclic uniaxial loading and unloading test, the elastic strain energy and the dissipated energy satisfy the relationship of Equation (5);

[0074] Equation (5);

[0075] The dissipated energy and the damage factor satisfy the relationship of Equation (6);

[0076] Equation (6);

[0077] where is the rock damage energy dissipation rate; is the damage factor at the th moment of the damage stage;

[0078] The elastic strain energy in the damage stage is expressed by Equation (7);

[0079] Equation (7);

[0080] where is the axial stress in the damage stage, and ; where ; is the th moment of the damage stage, and the elastic modulus of the rock; is the maximum value of the elastic modulus of the soft rock;

[0081] The damage evolution equation is obtained by combining Equation (5), Equation (6) and Equation (7), and is expressed by Equation (8);

[0082] Equation (8).

[0083] 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);

[0084] Equation (9);

[0085] Among them, is the axial strain, and , is changing from to the coefficient of is the yield point strain.

[0086] The yield point strain is the strain at the maximum value of the elastic modulus point.

[0087] The constitutive model of the damage stage is obtained by combining the stress-strain relationship of Equation 7) with Equation 8), and it is represented by Equation 10);

[0088] Equation 10);

[0089] Among them, is the strain at the peak point of the uniaxial compressive strength;

[0090] The enhanced-damage constitutive model is obtained by combining the constitutive model of Equation 9) in the enhancement stage and the constitutive model of Equation 10) in the damage stage, and it is represented by Equation 11);

[0091] Equation 11).

[0092] In order to verify whether the enhanced-damage constitutive model in this embodiment can accurately reflect the nonlinear mechanical behavior characteristics of soft rock, the enhanced-damage constitutive model in this embodiment is used to simulate and obtain the theoretical curves of the nonlinear mechanical behavior characteristics of soft yellow sandstone, soft red sandstone and soft shale respectively, as Figures 4 - 6 shown.

[0093] From Figures 4 - 6 it can be seen that the theoretical curves of the nonlinear mechanical behavior characteristics of soft yellow sandstone, soft red sandstone and soft shale obtained by simulating with the enhanced-damage constitutive model 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.

[0094] The above is only the preferred embodiment of the present invention and is not used 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 in the protection scope of the present invention.

Claims

1. A method for establishing a rock enhancement-damage constitutive model based on the energy principle, characterized in that Including: Step S1: Take two batches of soft rocks of the same quality. Conduct a uniaxial compression test on one batch of soft rocks to obtain the average value data of the uniaxial compression strength, denoted as Q; 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 a gradient increasing 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 that the elastic modulus obtained in step S1 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: Calculate the enhancement evolution equation of the enhancement stage according to the relationship between the elastic strain energy and the enhancement factor; calculate 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; The constitutive model of the strengthening stage is expressed by Equation (9): Formula (9); 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; is the axial strain, and , is changing to coefficient; is the elastic strain; is the fitting coefficient, expressed as the elastic strain energy enhancement rate; is the yield point strain; The constitutive model of the damage stage is expressed by Equation (10); Formula 10); Among them, is the axial stress of the damage stage, and ; is the maximum value of the elastic modulus of the weak rock; is the damage factor at the th moment of the damage stage; is the strain at the peak point of the uniaxial compressive strength; is the input energy and the elastic strain energy The linear relationship coefficient between them; is the energy dissipation rate of rock damage; The strengthening-damage constitutive model is obtained by combining the constitutive model of the strengthening stage, Equation (9), and the constitutive model of the damage stage, Equation (10), and is expressed by Equation (11); Formula 11).

2. A method for establishing a rock enhancement-damage constitutive model based on the energy principle according to claim 1, characterized in that In step S3, under the condition of the cyclic uniaxial loading and unloading test, assuming that the elastic strain energy of the soft rock is generated by elastic deformation, the elastic strain energy in the strengthening stage is expressed by Equation (1); Formula 1); The elastic strain energy satisfies a quadratic function relationship with the enhancement factor, which is expressed by Equation (2); Formula 2); The strengthening evolution equation is obtained by simultaneously solving Equation (1) and Equation (2), and is expressed by Equation (3); Formula 3).

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

4. A method for establishing a rock enhancement-damage constitutive model based on the energy principle according to claim 3, characterized in that, In step S3, under the condition of the cyclic uniaxial loading and unloading test, the input energy and the elastic strain energy satisfy the relationship of Equation (4); wherein, the input energy is the kinetic energy provided for uniaxial loading. Formula 4); Under the condition of the cyclic uniaxial loading and unloading test, the elastic strain energy and the dissipated energy satisfy the relationship of Equation (5); Formula 5); The dissipated energy satisfies the relationship of Equation (6) with the damage factor; Formula (6); The elastic strain energy at the damage stage is expressed by Equation (7); Formula 7); The damage evolution equation is obtained by simultaneously solving Equation (5), Equation (6), and Equation (7), and is expressed by Equation (8); Formula 8).

5. A method for establishing a rock strengthening-damage constitutive model based on the energy principle according to claim 4, characterized in that, ; is the elastic modulus of the rock at the th moment of the damage stage.

6. A method for establishing a constitutive model of rock reinforcement-damage based on the energy principle according to claim 5, characterized in that, The constitutive model of the strengthening stage is obtained by combining the stress-strain relationship of Equation (1) and Equation (3).

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

8. A method for establishing a rock enhancement-damage constitutive model based on the energy principle according to claim 6, characterized in that, The constitutive model of the damage stage is obtained by combining the stress-strain relationship of Equation (7) and Equation (8).

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

10. A method for establishing a rock reinforcement-damage constitutive model based on the energy principle according to claim 9, characterized in that The uniaxial loading force is a force that increases in equal gradients; the increasing gap between two adjacent gradients is 5% - 10%Q.

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