CN113567243B - Crack closing stress determination method based on axial stress response - Google Patents
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Abstract
The invention discloses a crack closure stress determination method based on axial stress response, which comprises the steps of establishing a curve graph corresponding to the axial strain-axial stress relation of a rock sample based on a test data point set; selecting an initial point P (epsilon) in a linear elasticity stage of a graph corresponding to the relationship of axial strain to axial stress of a rock samplep,σp) (ii) a Obtaining each test data point (. epsilon.)i,σi) And the initial point P (epsilon)p,σp) The slope of the line between the two points; obtaining an elastic modulus E; acquiring a reference straight line sigma ═ E epsilon corresponding to the axial strain-axial stress; establishing a corresponding curve graph of axial strain-axial stress difference; obtaining a reverse bending point in a curve graph corresponding to the axial strain-axial stress difference, wherein the axial stress corresponding to the reverse bending point is crack closing stress sigmacc. The method effectively solves the problem of determining the compaction point, and remarkably improves the crack closing stress sigmaccThe acquisition accuracy eliminates the influence of artificial subjective assumption on crack closure stress in the prior art.
Description
Technical Field
The invention relates to the technical field of engineering structures, in particular to a crack closure stress determination method based on axial stress response.
Background
Under the influence of complex geological structure action and environmental factors such as excavation disturbance, earthquake, microseism and the like, natural rock materials more or less contain primary microscopic microcracks, and the macroscopic deformation characteristics of the rocks under the compression condition are closely related to the closing, initiation, expansion and penetration action of the microscopic microcracks[1,2]The research on the corresponding characteristics between the microcrack development and the macroscopic stress threshold value has important significance on the stability evaluation of underground engineering such as deep tunnels and underground repositories.
Over the past 60 years, the mechanical properties of rock under compression have been extensively studied[3]. Generally, as shown in fig. 1, there are 4 critical stress thresholds, crack closure stress (σ), during rock compressive failurecc) Crack initiation stress (σ)ci) Damage stress (σ)cd) And peak stress (σ)c) The four stress thresholds divide the rock compression failure process into 5 stages, namely a crack closing stage, an elastic deformation stage, a crack stable growth stage, a crack unstable growth stage and a post-peak stage. The crack closure stress is not considered sufficiently with respect to the initiation stress, damage stress and peak stress, and is considered to be the crack closure stress (σ)cc) Has relatively few researches[4,5]。
However, from a microscopic perspective, the crack closure stress (σ)cc) Under the action of axial stress, the original microcracks in the rock are just completely closed, and the stress threshold value does not change along with the axial stress; macroscopically, crack closure stress (σ)cc) The stress threshold value is corresponding to a turning point of the initial macroscopic deformation of the rock compression process from the nonlinear compaction stage to the quasi-linear stage. Crack closure stress (σ)cc) For objectively describing the macroscopic damage behavior of the rock and evaluating the field strength of the rockDegree has important guiding significance[6]。
Existing Peng et al.[7]The influence of crack closure on the macroscopic mechanical property of rock compressive failure is researched, and a quantitative empirical model for representing the crack closure effect is provided according to an effective medium theory (effective medium theory) and a test result. Martin and Chandler[8]By calculating the crack volume strain, the starting point of the crack volume strain 0 is considered to be the crack closure stress of the rock, i.e. the crack volume strain method. Since the calculation of the crack volume strain requires the use of the elastic modulus E and poisson's ratio of the rock, the accuracy of this method is heavily dependent on the accurate determination of these two elastic parameters. And Eberhardt et al.[9]It is pointed out that the poisson ratio is greatly influenced by microcracks inside the rock sample, i.e. for rocks containing a large number of microcracks inside, the method is no longer applicable. Zhang Xiaoping et al.[10]A uniaxial compression test is carried out on the siliceous siltstone sample, and an improved crack volume strain method based on a moving point regression technology is provided on the basis of the crack volume strain method. Zhang et al.[5]A compression constitutive model capable of reflecting the relation between the initial macroscopic nonlinear deformation and the micro-crack closure of the rock is established, and a method for determining the crack closure stress sigma is provided based on the constitutive modelccThe method of (1).
Determination of crack closure stress (. sigma.) as described abovecc) The method requires the use of the elastic modulus E as the linear elastic phase (σ) in the typical axial stress-axial strain diagram shown in FIG. 1cc-σciSegment), the modulus of elasticity E, the crack closure stress (σ) required for accurate determinationcc) This falls into a self-certified error zone.
At present, stress (σ) to crack closurecc) The International Society for Rock Mechanics (ISRM) has not yet formed a unified approach, and the existing methods are not critical to the reliability of the obtained stress threshold, and there is an urgent need to propose a new objective determination method.
[1]Guéguen Y,Kachanov M.Effective Elastic Properties of Cracked Rocks-An Overview.In:Leroy YM,Lehner FK,editors.Mechanics of Crustal Rocks.Vienna:Springer Vienna；2011.p.73-125.
[2]Han Z,Li D,Zhou T,Zhu Q,Ranjith PG.Experimental study of stress wave propagation and energy characteristics across rock specimens containing cementedmortar joint with various thicknesses.International Journal of Rock Mechanics andMining Sciences.2020；131:104352.doi:https://doi.org/10.1016/j.ijrmms.2020.104352
[3]Li D,Han Z,Sun X,Zhou T,Li X.Dynamic Mechanical Properties andFracturing Behavior of Marble Specimens Containing Single and Double Flaws inSHPB Tests.Rock Mechanics and Rock Engineering.2019；52:1623-43.doi:10.1007/s00603-018-1652-5
[4]Peng J,Rong G,Zhou CB,Peng K.A study of crack closure effect of rocksand its quantitative model.Rock Soil Mech.2016；37:126-32.doi:10.16285/j.rsm.2016.01.015
[5]Zhang C,Cao W-g,Xu Z,He M.Initial macro-deformation simulation anddetermination method of micro-crack closure stress for rock.Rock Soil Mech.2018；39:1281-+.doi:10.16285/j.rsm.2016.0863
[6]Cai M,Kaiser PK.In-situ Rock Spalling Strength near ExcavationBoundaries.Rock Mechanics and Rock Engineering.2014；47:659-75.doi:10.1007/s00603-013-0437-0
[7]Peng J,Rong G,Cai M,Zhou C-B.A model for characterizing crack closureeffect of rocks.Engineering Geology.2015；189:48-57.doi:https://doi.org/10.1016/j.enggeo.2015.02.004
[8]Martin CD,Chandler N.The progressive fracture of Lac du Bonnet Granite.International Journal of Rock Mechanics and Mining Sciences&GeomechanicsAbstracts.1994；31:643-59.doi:10.1016/0148-9062(94)90005-1
[9]Eberhardt E,Stead D,Stimpson B,Read RS.Identifying crack initiation and propagation thresholds in brittle rock.Canadian Geotechnical Journal.1998；35:222-33.doi:10.1139/t97-091
[10] Zhang Xiaoping, Lugen, Zhang Qin, Liuquan Sound, Liwei Weiwei, Schering Ling stress threshold study of silicious siltstone under uniaxial compression condition engineering geology report 2020; 28:441-9.
Disclosure of Invention
Based on the above, the invention aims to provide a crack closure stress determination method based on axial stress response, which ensures the accuracy of crack closure stress determination and is suitable for quantitatively determining the crack closure stress of different types of rocks.
In order to solve the technical problems, the invention adopts the following technical scheme:
the invention provides a crack closure stress determination method based on axial stress response, which comprises the following steps:
performing a compression test for obtaining the relationship between axial strain and axial stress on the rock sample to obtain a test data point set
Establishing a corresponding curve graph of the axial strain-axial stress relation of the rock sample based on the test data point set;
selecting an initial point P (epsilon) in a linear elasticity stage of a graph corresponding to the relationship of axial strain to axial stress of a rock samplep,σp)；
Obtaining each test data point (. epsilon.)i,σi) And the initial point P (epsilon)p,σp) The slope of the line between the two points;
obtaining an elastic modulus E;
based on experimental data points (. epsilon.)i,σi) And elastic modulus E obtaining a second set of data points
Acquiring a reference straight line sigma corresponding to the axial strain-axial stress as E epsilon based on the second data point set;
based on each test data point (. epsilon.)i,σi) Axial stress difference delta sigma with reference line sigma E epsiloni＝E*εi-σiObtaining a third set of data points
Establishing a curve graph corresponding to the axial strain-axial stress difference based on the third data point set;
obtaining a reverse bending point in a curve graph corresponding to the axial strain-axial stress difference, wherein the axial stress corresponding to the reverse bending point is crack closing stress sigmacc。
In one embodiment, the step selects an initial point P (epsilon) in the linear elasticity phase of a graph corresponding to the axial strain-axial stress relationship of the rock samplep,σp) Initial point P (ε)p,σp) The corresponding axial stress value is the peak stress sigmac30-40% of the total.
In one embodiment, the initiation point P (ε)p,σp) The corresponding axial stress value is the peak stress sigma c35% of the total.
In one embodiment, the method for acquiring the elastic modulus E includes:
based on experimental data points (. epsilon.)i,σi) σ of (a)iValue and slope KiObtaining a first set of data points, establishing an axial strain sigma based on the first set of data pointsiSlope KiA corresponding graph;
obtaining axial strain sigmaiSlope KiA plateau in the corresponding graph;
and obtaining the elastic modulus E corresponding to the stable section.
In one embodiment, the elastic modulus E is an axial strain σiSlope KiThe average of the slopes of the first set of data points for the plateau in the corresponding graph.
In one embodiment, the elastic modulus E takes the value of the axial strain σiSlope KiCorresponding K at the mid-point of the plateau in the corresponding graphiThe value is obtained.
In one embodiment, the elastic modulus E takes the value of the axial strain σiSlope KiThe average of the slopes of the first set of data points for the plateau in the corresponding graph.
In one of the embodiments, the axial strain σiSlope KiThe corresponding graph is divided into three phases: a fast rising section, a slow rising section and a stationary section.
In one embodiment, the method further comprises the following steps:
and S8, selecting a plurality of groups of test data of the rocks under the condition of single-axis/three-axis compression, and repeatedly executing the steps S1-S7.
In one embodiment, the inflection point is a coordinate point corresponding to the axial strain-axial stress difference when the axial stress difference in the graph corresponds to the axial strain-axial stress difference for the first time at the maximum value.
In summary, the crack closure stress determination method based on axial stress response provided by the invention establishes a corresponding curve graph of the axial strain-axial stress relationship of the rock sample based on the test data point set, and after the elastic modulus E is obtained, each test data point (epsilon) is usedi,σi) Establishing a curve graph corresponding to the axial strain-axial stress difference with the axial stress difference between the reference straight line sigma ═ E epsilon, and further taking the axial strain corresponding to the reverse bending point in the curve graph corresponding to the axial strain-axial stress difference as the axial strain value of the crack closing stress point, thereby effectively solving the problem of determining the compaction point, and remarkably improving the crack closing stress sigmaccThe acquisition accuracy eliminates the influence of artificial subjective assumption on crack closure stress in the prior art.
Drawings
FIG. 1 is a typical axial stress-axial strain diagram of a prior art rock compression failure process;
fig. 2 is a schematic flowchart of a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
fig. 3 is a graph corresponding to the relationship between axial strain and axial stress in a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
fig. 4 is a schematic diagram illustrating the principle of obtaining an elastic modulus in a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
fig. 5 is a schematic diagram illustrating a principle of obtaining a reference line corresponding to axial strain-axial stress in a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
fig. 7 is a schematic diagram illustrating the principle of obtaining an elastic modulus based on a marble compression test result in a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
fig. 8 is a schematic diagram illustrating a principle that a reference straight line corresponding to axial strain-axial stress is obtained based on a marble compression test result in a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
fig. 9 is a schematic diagram based on the results of a marble compression test in a crack closure stress determination method based on axial stress response according to an embodiment of the present invention;
fig. 10 is a graph comparing a crack closure stress determination method based on axial stress response with other methods for determining crack closure stress according to embodiments of the present invention.
Detailed Description
For a better understanding of the features and technical solutions of the present invention, as well as the specific objects and functions attained by the present invention, reference is made to the accompanying drawings and detailed description of the invention.
Fig. 2 is a schematic flow chart of a crack closure stress determination method based on axial stress response according to an embodiment of the present invention, and as shown in fig. 2, the crack closure stress determination method based on axial stress response specifically includes the following steps:
s1, performing a compression test of the axial strain-axial stress relation on the rock sample to obtain a test data point set
Axial strain-axial stress relation pair of rock sample established based on test data point setThe corresponding graph, as shown in FIG. 3;
step S2, selecting an initial point P (epsilon) in the linear elasticity stage of the graph corresponding to the axial strain-axial stress relation of the rock samplep,σp) The initial point P (epsilon)p,σp) The corresponding axial stress value is the peak stress sigmac30-40%, in this embodiment, the initial point P (ε)p,σp) The corresponding axial stress value may be selected as the peak stress σ c35% of the total.
Wherein, the range of the linear elasticity stage in the curve chart corresponding to the relationship of the axial Strain and the axial Stress is determined to be subjective, while the test data point in the linear elasticity stage is determined to be not so subjective, a data point obviously in the linear elasticity stage is selected, and according to the existing research Wang D, He S, Tannant DD.A line Based Method for Determining the Crack Closure and Initiation Stress in Compression tests, CE Journal of Civil engineering.2019; 23:1819-28.doi:10.1007/s12205-019-0563-7, axial stress is peak stress sigmacThe data points of 30-40% are basically in the range of linear elasticity stage.
Step S3, obtaining each test data point (epsilon)i,σi) And the initial point P (epsilon)p,σp) Slope of the two-point line therebetween
Starting from the origin of the coordinate system corresponding to the relationship between the axial strain and the axial stress, sliding rightwards in the direction of the curve of the axial strain and the axial stress, and further calculating each test data point (epsilon)i,σi) And the initial point P (epsilon)p,σp) Slope K of the line connecting two points therebetweeni。
Step S4, acquiring an elastic modulus E;
as shown in fig. 4, the step S4 of obtaining the elastic modulus E includes the specific operations:
based on experimental data points (. epsilon.)i,σi) Sigma ofiValue and slope KiObtaining a first set of data points, establishing an axial direction based on the first set of data pointsStrain sigmaiSlope KiA corresponding graph;
obtaining axial strain sigmaiSlope KiA plateau in the corresponding graph; wherein the axial strain σiSlope KiThe corresponding graph can be divided into three phases: a rapid rising section, a slow rising section and a stable section;
obtaining an elastic modulus E corresponding to the stable section; at axial strain σiSlope KiThe slope of the first set of data points for the stationary segment in the corresponding graph fluctuates above and below about a stable value, i.e., the modulus of elasticity E, at the axial strain σiSlope KiThe absolute value of the difference value between the slope of the first data point set of the stationary section in the corresponding curve graph and the elastic modulus E is in a preset error range; in this embodiment, the elastic modulus E is taken as the axial strain σiSlope KiThe average of the slopes of the first set of data points of the corresponding plateau in the plot may also be selected as the axial strain σ as desirediSlope KiCorresponding K at corresponding mid-point of stationary section in corresponding graphiThe value, alternatively axial strain σiSlope KiK corresponding to the onset point of the plateau in the corresponding graphiThe value is obtained.
Step S5, based on the test data point (ε)i,σi) And elastic modulus E obtaining a second set of data points
Acquiring a reference straight line σ ═ E ∈ corresponding to the axial strain-axial stress based on the second data point set, as shown in fig. 5;
step S6, based on each test data point (. epsilon.)i,σi) Axial stress difference delta sigma with reference line sigma E epsiloni＝E*εi-σiObtaining a third set of data points
Establishing a graph corresponding to the axial strain-axial stress difference based on the third data point set, as shown in fig. 6;
step S7, obtaining a reverse bending point in a curve graph corresponding to the axial strain-axial stress difference, wherein the axial stress corresponding to the reverse bending point is crack closing stress sigmaccThe axial strain corresponding to the reverse bending point is the axial strain value of the crack closing stress point; and the reverse bending point is a coordinate point corresponding to the axial strain-axial stress difference when the axial stress difference in a curve graph corresponding to the axial strain-axial stress difference is at the maximum value for the first time.
The determination of the inflection point has various implementation manners in the prior art, in this embodiment, a stable segment (last segment) in a graph corresponding to the axial strain-axial stress difference is obtained, a straight line corresponding to the stable segment is obtained according to a third data point set on the stable segment, and in a coordinate system corresponding to the axial strain-axial stress difference relationship, a first intersection point generated by intersection of the straight line corresponding to the stable segment and a curve corresponding to the axial strain-axial stress difference is the inflection point; and obtaining the linear equation corresponding to the stable section through the average value of the axial stress difference values of the third data point set on the stable section.
In one embodiment, step S8 is to select a plurality of sets of test data of the rock under the condition of uniaxial/triaxial compression, and to repeatedly execute steps S1 to S7, so as to verify that the test data of the rock under the condition of uniaxial/triaxial compression is used for the applicability of the method of the invention under the implementation steps S1 to S7.
The method is characterized by establishing a corresponding curve graph of the axial strain-axial stress relation of the rock sample based on the test data point set, acquiring the elastic modulus E and then utilizing each test data point (epsilon)i,σi) Establishing a graph corresponding to the axial strain-axial stress difference with the axial stress difference between the reference straight line sigma and E epsilon, and further establishing an axis corresponding to a reverse bending point in the graph corresponding to the axial strain-axial stress differenceThe axial strain value of the crack closing stress point is changed into the strain direction, so that the determination problem of the compaction point is effectively solved, and the crack closing stress sigma is obviously improvedccThe acquisition accuracy eliminates the influence of artificial subjective assumption on crack closure stress in the prior art.
In order to make the technical solution of the present invention clearer, the following describes a preferred embodiment.
Taking a marble compression test as an example, which is described in Sun's sincere, WangCui, the mechanical introduction of particulate matter; 2009. in the above, the method for determining the crack closure stress based on the axial stress response of the present invention comprises the following specific steps:
step S1, carrying out axial strain-axial stress relation compression test on the marble sample, and obtaining a test data point set
Establishing a corresponding curve graph of the axial strain-axial stress relation of the rock sample based on the test data point set, as shown in FIG. 7;
step S2, selecting an initial point P (epsilon) in the linear elasticity stage of the curve chart corresponding to the axial strain-axial stress relation of the marble samplep,σp) Selecting the value of axial stress to correspond to the peak stress σcIs used as the initial point P, where εp＝1.01％，σp＝35％σc＝13。
Step S3, starting from the coordinate system origin corresponding to the axial strain-axial stress relation, sliding rightwards in the axial strain-axial stress curve direction, and calculating each test data point (epsilon)i,σi) And the initial point P (epsilon)p,σp) Slope of the two-point line therebetween
Step S4, establishing axial strain sigmaiSlope KiCorresponding curve chart to obtain axial strain sigmaiSlope KiCorresponding slope K in the stationary part of the graphiIs stabilized byValue, wherein the axial strain σ can be selectediSlope KiCorresponding K at corresponding mid-point of stationary section in corresponding graphiThe value being a steady value, the axial strain σ being selectableiSlope KiK corresponding to the onset point of the plateau in the corresponding graphiThe value is a stable value, and the axial strain sigma can be selected according to requirementsiSlope KiK corresponding to each point of stationary section in corresponding curve graphiThe average value of the values is a stable value; in the present embodiment, the first and second electrodes are,
namely, the elastic modulus E is 3.23 GPa.
Step S5, based on the test data point (ε)i,σi) And elastic modulus E obtaining a second set of data points
As shown in fig. 8, in the corresponding fig. 8 of this embodiment, since the unit of the axial stress in the coordinate system corresponding to the axial strain-axial stress is MPa, the formula of the reference line obtained by substituting E3.23 GPa into the coordinate system is σ ═ 32.3 ∈, where the reference line σ ═ E ∈ 32.3 ∈ is obtained based on the second data point set.
Step S6, based on each test data point (ε)i,σi) Axial stress difference delta sigma between the reference line sigma and E epsiloni＝E*εi-σiObtaining a third set of data points
A graph of axial strain versus axial stress difference is established based on the third set of data points, as shown in fig. 9.
And step S7, obtaining a bending point in the graph corresponding to the axial strain-axial stress difference, wherein the bending point is a coordinate point corresponding to the axial stress difference in the graph corresponding to the axial strain-axial stress difference when the axial stress difference is at the maximum value for the first time.
As shown in FIG. 10, a crack based on axial stress response used in the present invention was closedThe stress determination method is compared with other methods for determining the crack closing stress, such as an axial strain method, an axial stiffness method, an axial strain response method and a constitutive model method, under the condition that the confining pressure is 0, based on the test result obtained by the marble sample, the corresponding values and the average values of the values of each crack closing stress determination method are shown in table 3, except for the axial stiffness method, the crack closing stress values sigma predicted by other methods areccThe method is relatively approximate, and further the correctness of the crack closure stress determination method based on axial stress response is verified visually.
Wherein, the axial strain method and the axial strain response method are described in Pengjun, Chuamin, Rongguan, etc., evaluation of crack closure stress and rock microcrack damage [ J ] rock mechanics and engineering report, 2015,34(6): 1091-1100;
the axial stiffness method is described in EBERHARDT E, STEAD D, STIMPSON B, et al.identification of the crack initiation and propagation of the crack in the crack rock [ J ]. Canadian Geotechnical Journal, 1998, 35 (2): 222-233. performing the following steps;
the constitutive model method is described in Zhang C, Cao W-g, Xu Z, He M.Initial macro-deformation and determination method of micro-crack closure stress for rock. rock Soil Mech.2018; 39:1281- +. doi: 10.16285/j.rsm.2016.0863.
In addition, as shown in tables 1 to 3, the single-axis/three-axis compression test results of multiple groups of rocks are selected to verify the applicability of the crack closure stress determination method based on axial stress response in the single-axis/three-axis compression condition.
TABLE 1 crack closure stress under uniaxial compression of several rocks
Wherein, the northern mountain granite test data is described in ZHao XG, Cai M, Wang J, Ma LK. Damage stress and environmental impact characteristics of the Beishan granite. International Journal of Rock Mechanics and Mining sciences.2013; 64:258-69.doi: https:// doi.org/10.1016/j.ijrmms.2013.09.003;
the 240LDB granite test data is described in Martin CD, the stretch of massive Lac du Bonnet floor area and floor areas, Canada, University of Manitoba (Canada), 1993;
the 130LDB granite test data is described in Eberhardt E, Stead D, Stimpson B, Read RS.identification crack initiation and propagation thresholds in brittler rock.Canadian Geotechnical journal.1998; 35:222-33.doi:10.1139/t 97-091;
hwangdeung granite and Yoean marble test data are described in Chang SH, Lee CI.estimation of cracking and damage mechanization in Rock under tertiary mechanical compression by motion analysis of environmental impact.
South African Pepper Long Rock test data are described in Pellet FL, Keshavrz M, Amini-Hosseini K. mechanical dam of a crystalline Rock having an experimental high deviatoric stress up to 1.7GPa. International Journal of Rock Mechanics and Mining sciences.2011; 48:1364-8.doi: https:// doi.org/10.1016/j.ijrmms.2011.09.006;
the test data of the siliceous siltstone are recorded in Zhang Xiaoping, Lugegan, Zhang Qin, Liu quan, Liwei Wei and Schering; 28:441-9.
TABLE 2 triaxial compression test data of mountain granite
TABLE 3 Marble triaxial compression test
As can be seen from tables 1-3, the results of the uniaxial and triaxial compression tests based on multiple groups of rocks show that the crack closure stress determined by the method is relatively close to that determined by other methods, the reasonability and correctness of the crack closure stress determination method based on axial stress response are verified, meanwhile, the method is easy to program and operate, and the influence of human factors is removed; compared with the existing crack closure stress determination method, the crack closure stress determination method based on axial stress response obviously improves the crack closure stress sigmaccThe method has the advantages of obtaining accuracy, simple and convenient operation steps, no need of redundant mechanical tests, more convenience in application and more reliable result.
In summary, the crack closure stress determination method based on axial stress response establishes a corresponding curve graph of the axial strain-axial stress relationship of the rock sample based on the test data point set, and after the elastic modulus E is obtained, each test data point (epsilon) is usedi,σi) Establishing a curve graph corresponding to the axial strain-axial stress difference with the axial stress difference between the reference straight line sigma ═ E epsilon, and further taking the axial strain corresponding to the reverse bending point in the curve graph corresponding to the axial strain-axial stress difference as the axial strain value of the crack closing stress point, thereby effectively solving the problem of determining the compaction point, and remarkably improving the crack closing stress sigmaccThe acquisition accuracy eliminates the influence of artificial subjective assumption on crack closure stress in the prior art.
The above examples are merely illustrative of several embodiments of the present invention, and the description thereof is more specific and detailed, but not to be construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.
Claims (8)
1. A crack closure stress determination method based on axial stress response is characterized by comprising the following steps:
carrying out a compression test on the axial strain-axial stress relation of the rock sample to obtain a test data point set
Establishing a corresponding curve graph of the axial strain-axial stress relation of the rock sample based on the test data point set;
selecting an initial point P (epsilon) in a linear elasticity stage of a graph corresponding to the relationship of axial strain to axial stress of a rock samplep,σp) (ii) a Wherein the initial point P (epsilon)p,σp) The corresponding axial stress value is the peak stress sigmac30-40% of the total;
obtaining each test data point (. epsilon.)i,σi) And the initial point P (epsilon)p,σp) The slope of the line between the two points;
obtaining an elastic modulus E;
based on experimental data points (. epsilon.)i,σi) And elastic modulus E obtaining a second set of data points
Acquiring a reference straight line sigma corresponding to the axial strain-axial stress as E epsilon based on the second data point set;
based on each test data point (. epsilon.)i,σi) Axial stress difference delta sigma between the reference line sigma and E epsiloni＝E*εi-σiObtaining a third set of data points
Establishing a curve graph corresponding to the axial strain-axial stress difference based on the third data point set;
obtaining a reverse bending point in a curve graph corresponding to the axial strain-axial stress difference, wherein the axial stress corresponding to the reverse bending point is crack closing stress sigmacc。
2. A shaft-based according to claim 1A method of determining a crack closure stress in response to a stress, characterized by: the initial point P (epsilon)p,σp) The corresponding axial stress value is the peak stress sigmac35% of the total.
3. The method for determining the crack closure stress based on the axial stress response is characterized in that the step of obtaining the elastic modulus E comprises the following specific operations:
based on experimental data points (. epsilon.)i,σi) Sigma ofiValue and slope KiObtaining a first set of data points, establishing an axial strain sigma based on the first set of data pointsiSlope KiA corresponding graph;
obtaining axial strain sigmaiSlope KiA plateau in the corresponding graph;
and obtaining the elastic modulus E corresponding to the stable section.
4. A crack closure stress determination method based on axial stress response according to claim 3, characterized in that: the elastic modulus E takes the value of axial strain sigmaiSlope KiThe average of the slopes of the first set of data points for the plateau in the corresponding graph.
5. A crack closure stress determination method based on axial stress response according to claim 3, characterized in that: the elastic modulus E takes the value of axial strain sigmaiSlope KiCorresponding K at corresponding mid-point of stationary section in corresponding graphiThe value is obtained.
6. A crack closure stress determination method based on axial stress response according to claim 3, characterized in that: the elastic modulus E takes the value of axial strain sigmaiSlope KiThe average of the slopes of the first set of data points for the plateau in the corresponding graph.
7. The method for crack closure stress determination based on axial stress response of claim 1, further comprising:
and S8, selecting a plurality of groups of test data of the rocks under the condition of single-axis/three-axis compression, and repeatedly executing the steps S1-S7.
8. A crack closure stress determination method based on axial stress response according to claim 1, characterized in that: the recurved point is a coordinate point corresponding to the axial stress difference in the curve graph corresponding to the axial strain-axial stress difference when the axial stress difference is at the maximum value for the first time.
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