CN112800583A - Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof - Google Patents

Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof Download PDF

Info

Publication number
CN112800583A
CN112800583A CN202011634652.2A CN202011634652A CN112800583A CN 112800583 A CN112800583 A CN 112800583A CN 202011634652 A CN202011634652 A CN 202011634652A CN 112800583 A CN112800583 A CN 112800583A
Authority
CN
China
Prior art keywords
damage
rock
strain rate
model
equation
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202011634652.2A
Other languages
Chinese (zh)
Inventor
李二兵
濮仕坤
高磊
段建立
卢辉
潘越
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Army Engineering University of PLA
Original Assignee
Army Engineering University of PLA
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Army Engineering University of PLA filed Critical Army Engineering University of PLA
Priority to CN202011634652.2A priority Critical patent/CN112800583A/en
Publication of CN112800583A publication Critical patent/CN112800583A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/24—Earth materials

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Theoretical Computer Science (AREA)
  • Chemical & Material Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • General Life Sciences & Earth Sciences (AREA)
  • Computer Hardware Design (AREA)
  • Environmental & Geological Engineering (AREA)
  • Geometry (AREA)
  • Geology (AREA)
  • Remote Sensing (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Food Science & Technology (AREA)
  • Medicinal Chemistry (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

A dynamic damage constitutive model with medium and high strain rate suitable for hard rock and an application method thereof comprise the steps of firstly preparing a rock sample by coring in an engineering in-situ rock body, and measuring basic physical parameters including the longitudinal ultrasonic wave velocity of the sample before a test; then carrying out a uniaxial SHPB pressure dynamic mechanical test on the rock sample, and measuring the longitudinal wave velocity of the tested sample again; calculating to obtain a rock sample stress-strain curve according to an SHPB theory, and determining a rock material damage initial strain threshold value based on a corresponding relation between a longitudinal wave velocity and a peak stress; and finally, fitting the SHPB test curve through a medium and high strain rate dynamic damage constitutive model suitable for the hard rock to obtain accurate model parameters. The method effectively overcomes the defects that the damage model suitable for the hard rock established in the prior art breaks away from the result analysis of the material test, the influence rule of the strain rate effect on the damage evolution is not considered, the test damage cannot be actually and objectively reflected, and the like.

Description

Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof
Technical Field
The embodiment of the invention relates to the technical field of hard rock strain, belongs to the technical field of dynamic damage, and particularly relates to a medium and high strain rate dynamic damage constitutive model suitable for hard rock and an application method thereof.
Background
The hard rock is a rock divided according to the compressive strength of the rock, and along with the development of infrastructure construction and underground mining engineering such as hydraulic engineering, tunnel engineering, underground energy storage and the like, the stability and safety of surrounding rock after excavation and excavation are increasingly emphasized, wherein the drilling and blasting method is a main means for excavating hard rock masses. The rock stressed load is obviously different from static loading in the aspects of action time, transient deformation of materials and the like. The traditional constitutive model obtained by a conventional mechanical test without considering the inertia force effect is not suitable for drilling and blasting excavation working conditions. The strain rate index can measure the response state of the material under load, rock dynamics is induced according to the strain rate in the text of rock dynamics foundation and application disclosed in the prior art, and the strain rate is considered to be 10-1～10s-1Belongs to the quasi-dynamic category, 10-103s-1Belongs to the dynamic category and is more than 104s-1Belongs to the category of hyper-dynamic. The surrounding rock strain rate under the drilling and blasting excavation working condition of the hard rock is estimated to be 10-104s-1The test methods mainly used under the conditions include a drop hammer method, a Hopkinson pressure bar, a light gas gun, and the like.
In the underground engineering taking hard rock as a medium, the analysis of rock damage evolution rules has considerable theoretical value on the design construction and stability evaluation of the underground engineering. Generally, rock damage is manifested as phenomena of volume element deterioration, cracks, breakage, etc., which can be interpreted as deterioration of material properties when analyzing mechanical constitutive. Due to the fact that the action time of the dynamic mechanical test is short, damage changes in the loading process cannot be monitored by conventional acoustic emission, electron microscope scanning, CT scanning and the like. The existing rock damage model mainly comprises an HJC model, a K & C model, an RHT model, a CSC model and the like, and a damage constitutive model based on a continuous medium theory is proposed in a text of 'rock elastic brittle damage constitutive model and engineering application' disclosed in documents in the prior art; in the prior art, a rock damage model under the action of unidirectional load and a mechanical property research thereof are disclosed in documents in the prior art, and a rock unidirectional load action damage model is established according to a Weibull statistical distribution theory; in the text of the constitutive model of elastic-plastic damage of rock materials considering high confining pressure and high strain rate disclosed in the literature in the prior art, a rock damage model is established based on Drucker-Prager criterion as a yield function.
The damage model established by the continuous medium theory, the Weibull distribution and other modes disclosed by the prior art documents enriches the physical significance of the constitutive model, but the damage model does not actually and objectively reflect the test damage because the damage model is separated from the result analysis of the material test or the influence rule of the strain rate effect on the damage evolution is not considered.
Disclosure of Invention
In order to solve the above problems, embodiments of the present invention provide a medium and high strain rate dynamic damage constitutive model suitable for hard rock and an application method thereof, which effectively avoid the defects that a damage model suitable for hard rock established in the prior art is separated from the result analysis of a material test, the influence rule of strain rate effect on damage evolution is not considered, and the damage of the test cannot be actually and objectively reflected.
In order to overcome the defects in the prior art, the embodiment of the invention provides a solution for a medium and high strain rate dynamic damage constitutive model suitable for hard rock and an application method thereof, which comprises the following specific steps:
an application method of a medium and high strain rate dynamic damage constitutive model suitable for hard rock comprises the following steps:
step 1: firstly, coring a project in-situ rock mass to prepare a rock sample, and measuring basic physical parameters including the longitudinal ultrasonic wave velocity of the sample before a test;
step 2: then carrying out a uniaxial SHPB pressure dynamic mechanical test on the rock sample, and measuring the longitudinal wave velocity of the tested sample again;
and step 3: calculating to obtain a rock sample stress-strain curve according to an SHPB theory, and determining a rock material damage initial strain threshold value based on a corresponding relation between a longitudinal wave velocity and a peak stress;
and 4, step 4: and finally, fitting the SHPB test curve through a medium and high strain rate dynamic damage constitutive model suitable for the hard rock to obtain accurate model parameters.
A medium and high strain rate dynamic damage constitutive model for hard rock, comprising:
the Zhu-Wang-Tang ZWT model as shown in equation (4) and equation (5):
Figure BDA0002878063000000031
Figure BDA0002878063000000032
wherein σ represents stress and ε represents strain; f. ofe(ε) is a nonlinear spring model consisting of E0The three parameters of alpha and beta are expressed as a cubic function relation of epsilon;
Figure BDA0002878063000000033
represents the strain rate; e1、
Figure BDA0002878063000000034
And E2And
Figure BDA0002878063000000035
the elastic constants and relaxation times of the two Maxwell bodies are provided.
Further, the Maxwell body describing the low strain rate viscoelastic response of the material under the condition of medium and high strain rate is simplified to modulus E1The linear spring model of (2) is simplified as shown in equation (6):
Figure BDA0002878063000000036
the nonlinear spring model is simplified into the elastic modulus E0The linear spring model of (a), as shown in equation (7):
fe(ε)＝E0ε (7)
combining the two simplified linear spring models of formula (6) and formula (7) to obtain EaAs shown in equation (8):
Ea＝E0+E1 (8)
in the formula, EaShowing the modulus of elasticity of the simplified linear spring.
Then, as shown in equation (9):
Figure BDA0002878063000000041
further, it comprises the following
Figure BDA0002878063000000042
The integral term of (a) is simplified again as shown in equation (10):
Figure BDA0002878063000000043
further, the constitutive relation of the hard rock can be expressed as shown in formula (11):
Figure BDA0002878063000000044
in the formula, σ represents an effective stress;
Figure BDA0002878063000000045
representing the true stress; d is a damage parameter, when D is 0, the damage is represented, and when D is 1, the complete damage of the material is represented, and the bearing capacity is lost;
then the constitutive model of hard dynamic damage at constant strain rate is expressed as shown in equation (12):
Figure BDA0002878063000000046
the damage model equation is introduced, i.e. expressed as shown in equation (13):
Figure BDA0002878063000000047
the embodiment of the invention has the beneficial effects that:
the invention improves and simplifies the dynamic mechanical characteristics of the hard rock on the basis of the Z-W-T model, and has better applicability to the elastoplasticity properties and the strain rate effect of the rock dynamics. Impact damage is represented based on longitudinal ultrasonic wave speeds before and after the test, a damage evolution relational expression similar to a thermal activation process is brought in, and accurate and reliable model parameters are obtained by introducing the damage evolution relational expression into a constitutive model to fit an SHPB test stress-strain curve. The method is feasible, and the dynamic damage constitutive model obtained by the method has higher reliability and accuracy due to the combination of the real damage result of the test, thereby effectively avoiding the defects that the damage model which is established in the prior art and is suitable for the hard rock is separated from the result analysis of the material test, the influence rule of the strain rate effect on the damage evolution is not considered, and the test damage can not be actually and objectively reflected.
Drawings
Fig. 1 is a schematic diagram of a vermilion-king-down (ZWT) model according to an embodiment of the present invention.
Fig. 2 is a flowchart of an application method of the medium and high strain rate dynamic damage constitutive model suitable for hard rock according to an embodiment of the present invention.
Figure 3 is an external view of a sampling core according to an embodiment of the present invention.
FIG. 4 is a schematic view of a sampling core and its numbering according to an embodiment of the invention.
FIG. 5 is an external view of a spindle punch loaded in accordance with an embodiment of the present invention.
FIG. 6 is a stress-strain curve of granite according to an embodiment of the present invention.
FIG. 7 is a graph of a logarithmic function according to an embodiment of the present invention.
FIG. 8 is a graph of peak strain versus strain rate for an embodiment of the present invention.
FIG. 9 is a graph of damage versus peak strain for an embodiment of the present invention.
FIG. 10 is a graph showing the fitting of the damage mechanism to the test according to the example of the present invention, FIG. 10(a) is a graph of sample numbers 1-2, FIG. 10(b) is a graph of sample numbers 1-3, FIG. 10(c) is a graph of sample numbers 1-4, FIG. 10(d) is a graph of sample numbers 1-5, FIG. 10(e) is a graph of sample numbers 1-6, FIG. 10(a) is a graph of sample numbers 1-2, FIG. 10(g) is a graph of sample numbers 2-2, FIG. 10(h) is a graph of sample numbers 2-3, FIG. 10(i) is a graph of sample numbers 2-4, FIG. 10(j) is a graph of sample numbers 2-5, FIG. 10(k) is a graph of sample numbers 2-6, and FIG. 10(l) is a graph of sample numbers 3-1, FIG. 10(m) is a graph of sample number 3-2, FIG. 10(n) is a graph of sample number 3-3, FIG. 10(o) is a graph of sample number 3-4, FIG. 10(p) is a graph of sample number 3-5, and FIG. 10(q) is a graph of sample number 3-6.
Fig. 11(a) and 11(b) are graphs fitted to both with an exponential function and a power function, respectively.
Detailed Description
The embodiments of the present invention will be further described with reference to the drawings and the embodiments.
In the document ZWT study and application of nonlinear thermal viscoelastic constitutive relation, it is considered that the damage evolution of hard rock material under dynamic load can be regarded as a stress-promoted thermal activation process D, which is shown in formula (1):
Figure BDA0002878063000000061
in the formula, KDAnd alpha is the dynamic response parameter of the material.
Assuming that a strain threshold ε exists0When the peak value strain is less than the threshold value, no damage is generated, and when the strain is more than or equal to the threshold value, the damage evolution is in a thermal activation process, and then the hard rock dynamic damage evolution equation is expressed as a formula (2)Shown in the figure:
Figure BDA0002878063000000062
because the damage evolution monitoring of the prior art in the rock dynamics test process is difficult, the invention measures the longitudinal ultrasonic wave velocity of the sample through the HS-YS4A type rock sound wave, and represents the impact damage generated by the dynamics test through the change of the ultrasonic wave velocity before and after the test according to the formula (3), thereby obtaining the strain threshold value in the formula (2).
Figure BDA0002878063000000071
In the formula, the longitudinal wave velocity of the complete rock sample before the test is recorded as Vp(ii) a The longitudinal wave velocity of the damaged rock sample after the test is recorded
Figure BDA0002878063000000072
And finally, establishing a proper dynamic damage constitutive model by an element combination constitutive model method and introducing a formula (2) as a damage parameter. And fitting the mechanical test result based on the model function to obtain the damage constitutive model parameters which accurately reflect the working condition of medium and high strain rate.
As shown in fig. 1-2, the application method of the medium and high strain rate dynamic damage constitutive model suitable for hard rock includes the following steps:
step 1: firstly, coring a project in-situ rock mass to prepare a rock sample, and measuring basic physical parameters including the longitudinal ultrasonic wave velocity of the sample before a test;
step 2: then carrying out a uniaxial SHPB pressure dynamic mechanical test on the rock sample, and measuring the longitudinal wave velocity of the tested sample again;
and step 3: calculating to obtain a rock sample stress-strain curve according to an SHPB theory, and determining a rock material damage initial strain threshold value based on a corresponding relation between a longitudinal wave velocity and a peak stress;
and 4, step 4: and finally, fitting an SHPB test curve through the medium and high strain rate dynamic damage constitutive model suitable for the hard rock to obtain accurate model parameters.
A medium and high strain rate dynamic damage constitutive model for hard rock, comprising:
in the literature, the research and application of ZWT nonlinear thermal viscoelastic constitutive relation establishes two Maxwell bodies and a nonlinear elastomer f for nonlinear constitutive problems under the conditions of high strain rate and large deformatione(epsilon) a model formed by connecting the three in parallel, namely a Zhu-wang-Tang (ZWT) model, as shown in figure 1, two Maxwell bodies E1And E2Respectively reflecting the mechanical response and the low strain rate viscoelastic property under the condition of high strain rate.
The expression is as follows, i.e., the Zhu-Wang-Tang ZWT model as shown in formula (4) and formula (5):
Figure BDA0002878063000000081
Figure BDA0002878063000000082
wherein σ represents stress and ε represents strain; f. ofe(ε) is a nonlinear spring model consisting of E0The three parameters of alpha and beta are expressed as a cubic function relation of epsilon;
Figure BDA0002878063000000083
represents the strain rate; e1、
Figure BDA0002878063000000084
And E2And
Figure BDA0002878063000000085
the elastic constants and relaxation times of the two Maxwell bodies are provided.
The Maxwell body, which describes the low strain rate viscoelastic response of a material under conditions of medium and high strain rates, does not have enough time to relax and can be reduced to the modulus E in practice of the invention1Linear spring ofThe model, the expression, is simplified as shown in equation (6):
Figure BDA0002878063000000086
usually, the strain magnitude of the hard rock dynamic test does not exceed 10-2And combining the static test result of the prior granite, the stress-strain curve at the stage basically shows linear behavior. Therefore, the nonlinear spring model can be practically simplified to the elastic modulus E0The linear spring model of (a), as shown in equation (7):
fe(ε)＝E0ε (7)
combining the two simplified linear spring models of formula (6) and formula (7) to obtain EaAs shown in equation (8):
Ea＝E0+E1 (8)
then, as shown in equation (9):
Figure BDA0002878063000000091
control of constant strain rate in the experiments herein, including
Figure BDA0002878063000000092
The integral term of (a) can be simplified again as shown in equation (10):
Figure BDA0002878063000000093
the hard rock is used as a resilient brittle material, and if specific test results show that damage cracks are generated and encrypted along with loading until a sample is damaged, the strength of the material is weakened. According to the strain equivalence assumption of j.lematre, the strain under the effect of real stress is equivalent to the strain under the effect of virtual lossless state effective stress. The constitutive relation of the hard rock can be expressed as shown in formula (11):
Figure BDA0002878063000000094
in the formula, σ represents an effective stress;
Figure BDA0002878063000000095
representing the true stress; d is a damage parameter, when D is 0, the damage is represented, and when D is 1, the complete damage of the material is represented, and the bearing capacity is lost;
the constitutive model of hard dynamic damage at constant strain rate can be expressed as shown in equation (12):
Figure BDA0002878063000000096
the damage model equation of equation (2) is introduced, i.e. can be expressed as shown in equation (13):
Figure BDA0002878063000000097
the invention is explained in detail by taking the underground laboratory engineering of high-level waste in northern mountain of Gansu China as an example. The present invention is described in detail below with reference to the attached drawings. It is to be understood, however, that the drawings are provided solely for the purposes of providing a better understanding of the present invention and are not to be construed as limiting the invention.
Specifically, the main components of the northern mountain new granite and granite amphibole minerals are potash feldspar, quartz and plagioclase, and a small amount of biotite and amphibole. The uniaxial SHPB test core is granite with the depth of 550-552 m and is obtained from a hole site BS06 in a selected area of an underground disposal laboratory in North mountain of Gansu province, and the appearance of the sampling core is silvery white as shown in figure 3, and belongs to fine-grained granite.
The sampling rock cores as samples are divided into two groups, one group is subjected to a pressure dynamic mechanical test, and the total number of the test is 18 under different strain rate loads. The test pieces were prepared into cylindrical test pieces of phi 50mm × 25 mm. The non-defective samples were numbered as shown in fig. 4. The basic parameters of the sample, such as size, mass and ultrasonic wave speed, are measured, and are shown in table 1:
TABLE 1
Figure BDA0002878063000000101
A granite uniaxial SHPB pressure dynamic test is carried out, so that the complexity of parameters is reduced as much as possible in the test process, the derivation difficulty of the constitutive equation is simplified, and the accuracy and precision of the constitutive equation are improved. The fusiform punch shown in figure 5 is used for loading in the test, so that the dynamic load with approximately constant strain rate can be generated, and the load repeatability is good. The test results in a granite stress-strain curve as shown in FIG. 6. Then measuring the longitudinal wave velocity of the complete sample after the test to calculate the impact damage, and summarizing the result as shown in table 2;
TABLE 2
Figure BDA0002878063000000111
Figure BDA0002878063000000121
The rock mechanical characteristics are analyzed, the peak stress of the dynamic pressure test shows obvious rate effect, the dynamic granite strength is approximately linearly increased along with the increase of the strain rate within a certain range, and the strain rate exceeds 130s-1The later increase in dynamic strength is slowed down. The two can be regarded as a logarithmic function relationship as shown in fig. 7, and the fitting relationship is shown as the following formula:
Figure BDA0002878063000000122
the peak strain reflects the damage condition of the sample to a certain extent, fig. 8 shows the relationship of the peak strain with the change of the strain rate, compared with the relationship of the peak stress and the strain rate, the peak strain is more discrete, but the peak strain and the strain rate still have linear correlation in the overall view, and the fitting relationship is shown as the following formula:
Figure BDA0002878063000000123
and (4) representing the impact damage according to the formula and based on the change of the longitudinal wave velocity of the sample before and after the test. FIG. 9 is a graph showing the relationship between the damage parameter D and the peak stress, which is characterized by the velocity of longitudinal waves, by fitting an exponential function to the test results.
Figure BDA0002878063000000131
For the above equation, let D equal 0, in which case σpeak86.12 MPa. Namely the peak stress threshold value of damage generated by dynamic load is 86.12MPa, and the two formulas at the top are substituted to respectively obtain the initial strain rate threshold value of 20.36s of the damage of the granite in the north mountain under the condition of medium and high strain rate-1(ii) a Strain threshold 6.31 x 10-4. And (4) substituting the strain threshold into a hard rock dynamic constitutive model formula.
The test curves were fitted as in fig. 10 using a hard rock dynamic constitutive model function that considers the evolution of the damage. In the embodiment, part of curve fluctuation is mainly related to the punch action, but not reflects the mechanical property of the rock, and can be ignored in the fitting process. The model has better fitting effect in the elastic section and the plastic section. The results obtained are the statistical fit parameters of each sample constitutive according to the law of increasing strain rate as reflected in table 3:
TABLE 3
Figure BDA0002878063000000132
Figure BDA0002878063000000141
Wherein the parameter E2And
Figure BDA0002878063000000142
floating around 200GPa and 10 mus, respectively, while EaThe parameter value is small and unstable, the former reflects the dynamic mechanical properties of most crystals in granite, and the latter reflects that a small part of components can be described as elastic properties under the condition of dynamic load, and the small part of components do not have specific regularity along with the change of strain rate. For northern mountain granite EaCan be 6 x 103To 1X 105Reasonable values are taken within the range. KDAnd alpha is reduced along with the increase of the strain rate, which shows that the granite damage evolution speed is slowed down along with the increase of the strain rate, and an exponential function and a power function are respectively adopted in the graph 11(a) and the graph 11(b) to fit the two to obtain a relation formula shown as the following two formulas:
Figure BDA0002878063000000143
Figure BDA0002878063000000144
the method has practical engineering value and theoretical significance for establishing the high-strain-rate dynamic damage constitutive model in the hard rock aiming at the working conditions of drilling, blasting, excavating and the like in the rock mass. Compared with the conventional rock constitutive model, the method takes the rock material strain rate effect into consideration. However, because the existing damage monitoring method in the traditional dynamic constitutive model is difficult to implement, the damage model is established by adopting a continuous medium theory, Weibull distribution and other modes, the dynamic constitutive model is separated from the dynamic practical test analysis, and the theoretical basis is lacked.
The method is characterized in that the dynamic mechanical characteristics of the hard rock are improved and simplified on the basis of a Z-W-T model, and the method has good applicability to rock dynamics elastoplasticity properties and strain rate effects. Impact damage is represented based on longitudinal ultrasonic wave speeds before and after the test, a damage evolution relational expression similar to a thermal activation process is brought in, and accurate and reliable model parameters are obtained by introducing the damage evolution relational expression into a constitutive model to fit an SHPB test stress-strain curve. The method is feasible, and the dynamic damage constitutive model obtained by the method has higher reliability and accuracy due to the combination of the real damage result of the test.
While the embodiments of the present invention have been described above in terms of procedures illustrated by the embodiments, it will be understood by those skilled in the art that the present disclosure is not limited to the embodiments described above, and that various changes, modifications, and substitutions can be made without departing from the scope of the embodiments of the present invention.

Claims (5)

1. An application method of a medium and high strain rate dynamic damage constitutive model suitable for hard rock is characterized by comprising the following steps:
step 1: firstly, coring a project in-situ rock mass to prepare a rock sample, and measuring basic physical parameters including the longitudinal ultrasonic wave velocity of the sample before a test;
step 2: then carrying out a uniaxial SHPB pressure dynamic mechanical test on the rock sample, and measuring the longitudinal wave velocity of the tested sample again;
and step 3: calculating to obtain a rock sample stress-strain curve according to an SHPB theory, and determining a rock material damage initial strain threshold value based on a corresponding relation between a longitudinal wave velocity and a peak stress;
and 4, step 4: and finally, fitting the SHPB test curve through a medium and high strain rate dynamic damage constitutive model suitable for the hard rock to obtain accurate model parameters.
2. A medium and high strain rate dynamic damage constitutive model for hard rock, comprising:
the Zhu-Wang-Tang ZWT model as shown in equation (4) and equation (5):
Figure FDA0002878062990000011
Figure FDA0002878062990000012
wherein σ represents stress and ε represents strain; f. ofe(ε) is a nonlinear spring model consisting of E0The three parameters of alpha and beta are expressed as a cubic function relation of epsilon;
Figure FDA0002878062990000013
represents the strain rate; e1、
Figure FDA0002878062990000014
And E2And
Figure FDA0002878062990000015
the elastic constants and relaxation times of the two Maxwell bodies are provided.
3. The medium and high strain rate dynamic damage constitutive model for hard rock as claimed in claim 2, wherein the Maxwell body describing the low strain rate viscoelastic response of the material under medium and high strain rate conditions is reduced to modulus E1The linear spring model of (2) is simplified as shown in equation (6):
Figure FDA0002878062990000021
wherein σ represents stress and ε represents strain; f. ofe(epsilon) is a nonlinear spring model; e2And
Figure FDA0002878062990000027
the elastic constant and relaxation time of Maxwell bodies. The nonlinear spring model is simplified into the elastic modulus E0The linear spring model of (a), as shown in equation (7):
fe(ε)＝E0ε (7)
combining the two simplified linear spring models of formula (6) and formula (7) to obtain EaAs shown in equation (8):
Ea＝E0+E1 (8)
then, as shown in equation (9):
Figure FDA0002878062990000022
in the formula (II). EaLinear spring modulus of elasticity.
4. The medium and high strain rate dynamic damage constitutive model for hard rock according to claim 3, comprising
Figure FDA0002878062990000025
The integral term of (a) is simplified again as shown in equation (10):
Figure FDA0002878062990000023
5. the medium and high strain rate dynamic damage constitutive model for hard rock according to claim 3, wherein the constitutive relation of hard rock can be expressed as shown in formula (11):
Figure FDA0002878062990000024
in the formula, σ represents an effective stress;
Figure FDA0002878062990000026
representing the true stress; d is a damage parameter, when D is 0, the damage is represented, and when D is 1, the complete damage of the material is represented, and the bearing capacity is lost;
then the constitutive model of hard dynamic damage at constant strain rate is expressed as shown in equation (12):
Figure FDA0002878062990000031
the damage model equation is introduced, i.e. expressed as shown in equation (13):
Figure FDA0002878062990000032
CN202011634652.2A 2020-12-31 2020-12-31 Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof Pending CN112800583A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011634652.2A CN112800583A (en) 2020-12-31 2020-12-31 Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011634652.2A CN112800583A (en) 2020-12-31 2020-12-31 Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof

Publications (1)

Publication Number Publication Date
CN112800583A true CN112800583A (en) 2021-05-14

Family

ID=75808639

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011634652.2A Pending CN112800583A (en) 2020-12-31 2020-12-31 Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof

Country Status (1)

Country Link
CN (1) CN112800583A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114254423A (en) * 2021-12-21 2022-03-29 中国人民解放军陆军勤务学院 Method for calculating structural effect of porous concrete SHPB test with randomly distributed spherical pores

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104990777A (en) * 2015-07-09 2015-10-21 中国矿业大学 Impact damage rock sample preparation and assay method based on SHPB test
CN110705165A (en) * 2019-10-08 2020-01-17 中国石油大学(华东) Method for constructing elastoplasticity-damage coupling mechanical constitutive model of rock material
CN111554362A (en) * 2020-03-30 2020-08-18 西安建筑科技大学 Method for establishing HBPRC dynamic damage constitutive model

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104990777A (en) * 2015-07-09 2015-10-21 中国矿业大学 Impact damage rock sample preparation and assay method based on SHPB test
CN110705165A (en) * 2019-10-08 2020-01-17 中国石油大学(华东) Method for constructing elastoplasticity-damage coupling mechanical constitutive model of rock material
CN111554362A (en) * 2020-03-30 2020-08-18 西安建筑科技大学 Method for establishing HBPRC dynamic damage constitutive model

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
J. LEMAITRE 等: "《A two scale damage concept applied to fatigue》", 《INTERNATIONAL JOURNAL OF FRACTURE》 *
凌天龙 等: "《花岗岩损伤型黏弹性动态本构模型研究》", 《矿业科学学报》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114254423A (en) * 2021-12-21 2022-03-29 中国人民解放军陆军勤务学院 Method for calculating structural effect of porous concrete SHPB test with randomly distributed spherical pores
CN114254423B (en) * 2021-12-21 2023-06-13 中国人民解放军陆军勤务学院 Structural effect calculation method for porous concrete SHPB test with randomly distributed spherical holes

Similar Documents

Publication Publication Date Title
Xiao et al. Mechanical properties and failure behavior of rock with different flaw inclinations under coupled static and dynamic loads
Dai et al. Numerical assessment of the progressive rock fracture mechanism of cracked chevron notched Brazilian disc specimens
Saadati et al. On the mechanical behavior of granite material with particular emphasis on the influence from pre-existing cracks and defects
Xu et al. Numerical observation of three-dimensional wing cracking of cracked chevron notched Brazilian disc rock specimen subjected to mixed mode loading
Mishra et al. High strain-rate characterization of deccan trap rocks using SHPB device
Yang et al. Experimental investigation of sandstone under cyclic loading: damage assessment using ultrasonic wave velocities and changes in elastic modulus
Wang et al. Effect of heat treatment on dynamic tensile strength and damage behavior of medium-fine-grained huashan granite
CN112800583A (en) Medium and high strain rate dynamic damage constitutive model suitable for hard rock and application method thereof
Li et al. Mechanical responses and fracturing behavior of jointed rock masses with a cavity under different dynamic loads
Fan et al. Study on dynamic loading characteristics and energy evolution of sandstone with double cracks
Wang et al. Mechanical behavior and damage evolution for granite subjected to cyclic loading
Ghazvinian et al. Identification of crack damage thresholds in crystalline rock
Gao et al. Perturbation effect of rock rheology under uniaxial compression
Wang et al. Mechanical Response and Energy Dissipation Analysis of Heat-Treated Granite Under Repeated Impact Loading.
Xu et al. Quantitative damage and fracture mode of sandstone under uniaxial load based on acoustic emission
Koh et al. Numerical and experimental studies of concrete damage under impact
WEN et al. An investigation of the mechanical properties of sandstone under coupled static and dynamic loading
Liu et al. Numerical simulation of the failure process and mechanical behavior of a rock material with nonpersistent cracks under compression
Kegang et al. Damage constitutive model for rock considering cyclic drying-wetting effect and its experimental validation
Iqbal et al. Dynamic tensile strength and mode-I fracture toughness in granitic rocks
Zhang et al. Prefabricated fractured rock under stepwise loading and unloading
Li et al. Experimental research on acoustic wave velocity of frozen soils during the uniaxial loading process
Song et al. Study on the shear creep characteristics of anchored jointed rock masses under creep fatigue loading
Bhave et al. Determination of compressive strength of rocks using ultrasound
Chang et al. Damage and fracture characteristics of Kimachi sandstone in uniaxial compression

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20210514

RJ01 Rejection of invention patent application after publication