A method to characterize and predict crack growth paths in wings under uniaxial compression

Abstract

The present invention discloses a method for characterizing data of stress field at the tip of rock mass cracks under compression and shearing, and its application in rapidly predicting the propagation path of wing cracks under uniaxial compression. When characterizing data of stress field at the tip of rock mass cracks under compression and shearing, the rock mass object data having influence on the terminal output data is pre-expressed in a compatible manner; on this basis, by characterizing data of the wing crack initiation angle and data of the wing crack propagation path under uniaxial compression, rapid prediction of the wing crack propagation path under uniaxial compression is achieved. The present invention can rapidly predict the propagation path of wing cracks under different conditions, and provides strong data support for the analysis and processing of rock mass engineering problems.

Description

Technical Field

[0001] The present invention relates to the technical field of rock mass compression-shear fracture mechanics and its engineering application related thereto, and in particular to a method for characterizing rock mass crack tip stress field data under compression-shear action and its application in rapidly predicting wing crack propagation paths under uniaxial compression. Background Art

[0002] Due to long-term and complex geological processes, natural rock masses often contain a large number of joints, fissures and other structural surfaces. [1,2] It shows that the strength and failure characteristics of rock mass under external forces depend on these natural defects. In different rock mass projects, such as the effect of prestressed anchors on surrounding rocks in mountain tunnels, the compression and shearing effect of shield cutters on rock mass, and the stability analysis of the rock bearing layer under the structure, they are all closely related to the initiation of cracks in the rock mass and their expansion paths.

[0003] There are two main methods for studying the crack propagation paths in different rock masses: indoor experimental method and numerical simulation method. Based on video and acoustic emission technology, Yang et al. [3] The effects of crack inclination and length on crack propagation mechanism in sandstone specimens with a single crack under uniaxial compression were studied, and it was proposed that crack types can be divided into five categories according to the crack propagation mechanism, namely tensile cracks, shear cracks, transverse cracks, far-field cracks and surface peeling cracks. Yuan Yuan et al. [4] The digital image method was used to observe the failure process of marble specimens with prefabricated cracks containing different filling materials under uniaxial compression conditions, and the evolution of the local deformation field on the marble surface during the fracture process was analyzed. The results showed that regardless of whether the specimens were filled or not, the failure type of the marble specimens was mostly a mixed shear-tension type, but for closed cracks filled, the marble specimens were mainly tensile failure dominated by wing cracks on a macroscopic scale. Miao et al. [5] By making sandstone samples with prefabricated cracks of different inclination angles, the effects of filling, gypsum filling, cement filling and resin filling on the crack initiation and crack propagation morphology were studied. [6] , Guo Qifeng [7] et al. prefabricated granite specimens with a single crack and analyzed the relationship between the crack propagation characteristics and the crack inclination. The experimental results showed that the crack initiation angle increased monotonically with the increase of the angle between the crack inclination and the loading direction, and the failure mode of the rock specimen changed from shear failure to tension failure. Using 3D printing technology, Sharafisafa et al. [8,9] Brazilian disk specimens with prefabricated cracks of different inclination angles were fabricated, and the crack initiation and propagation processes under uniaxial compression were analyzed based on digital imaging technology. Zhuang et al.

[10] The rock-like material specimens with prefabricated cracks were made by cement mortar, and the crack initiation and expansion paths of prefabricated cracks with angles of 15°, 30°, 45°, 60° and 75° under uniaxial compression were studied. The results were compared with the simulation results of the extended finite element method. The results show that the expansion trajectory of the wing crack is closely related to the inclination angle of the prefabricated crack, but both show that when the crack starts and expands for a short period, it gradually becomes parallel to the loading direction. Tang Shibin et al.

[11] Using Brazilian disc specimens, the authors studied the effects of physical mechanics such as opening, closing and filling cracks, contact friction, and crack inclination on crack propagation characteristics under compression and shear. They then established a rock fracture simulation method based on the localized fracture theory of quasi-brittle materials, which made up for the current lack of research on closed crack propagation under compression and shear, and achieved a detailed simulation of the fracture path. Lee and Jeon

[12] The propagation process of the wing crack of a PMMA specimen with prefabricated cracks under uniaxial compression was studied by experimental and simulation methods. The results show that the propagation path of the wing crack is closely related to the crack inclination. Due to the advantages of the discrete element method in simulating the failure process of non-continuous medium materials, it is also often used in the analysis of compression and shear failure of fractured rock mass, such as Liu et al.

[13] With Jiang Mingjing

[14] et al. analyzed the stress distribution at the crack tip and the failure morphology of the crack specimen based on the discrete element method and compared and verified it with the experimental results.

[15] Based on the peridynamic method, a numerical simulation study of the uniaxial compression test of rock material specimens with prefabricated cracks was conducted. The results show that the wing crack first occurs near the tip of the prefabricated crack, then gradually expands and penetrates, and its position gradually moves to the two ends of the prefabricated crack as the inclination angle of the prefabricated crack increases.

[16] With Li Pengfei

[17] et al. studied the initiation, propagation and penetration process of prefabricated cracks under uniaxial compression based on the extended finite element method and phase field method.

[0004] Although the above-mentioned indoor experimental method and numerical simulation method are important means of crack initiation and propagation path analysis, both methods have obvious shortcomings. For example, the indoor experimental method requires the preparation of rock samples with prefabricated cracks according to the research object, which has high economic costs and limited crack path samples that can be obtained; although the numerical simulation method has low economic costs, it often has the disadvantage of long calculation time in the analysis of crack propagation path, and cannot quickly give the crack propagation path prediction results. The relevant references are shown below.

[0005] [1]Bieniawski ZT, Denkhaus HG, Vogler UW. Failure of fractured rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1969, 6: 323-341.

[0006] [2]Wang YL,Tang JX,Dai ZY,et al.Experimental study on mechanicalproperties and failure modes of low-strength rock samples containingdifferent fissures under uniaxial compression[J].Engineering FractureMechanics,2018,197:1-20.

[0007] [3]Shengqi Yang,Hongwen Jing.Strength failure and crack coalescencebehavior of brittle sandstone samples containing a single fissure underuniaxial compression[J].International Journal of Fracture,2011,168:227-250.

[0008] [4] Yuan Yuan, Pan Pengzhi, Zhao Shankun, Wang Bin, Song Guihong. Study on the uniaxial compression failure process of marble with filled cracks based on digital image correlation method [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(2): 339-351.

[0009] [5]Shuting Miao, Pengzhi Pan, Zhenhua Wu, Shaojun Li, ShankunZhao. Fracture analysis of sandstone with a single filled flaw under uniaxialcompression[J]. Engineering Fracture Mechanics, 2018, 204: 319-343.

[0010] [6] Zhang Guokai, Li Haibo, Wang Mingyang, Li Xiaofeng. Study on the failure strength and crack propagation characteristics of single-crack granite[J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(s1): 2760-2771.

[0011] [7] Guo Qifeng, Wu Xu, Cai Meifeng, Xi Xun, Ren Fenhua, Miao Shengjun. Strength characteristics and failure mode of prefabricated cracked granite[J]. Journal of Engineering Science, 2019, 41(1): 43-52.

[0012] [8]Mansour Sharafisafa,Luming Shen,Qingfeng Xu.Characterisation ofmechanical behavior of 3D printed rock-like material with digital imagecorrelation[J].International Journal of Rock Mechanics and Mining Sciences,2018,112:122-138.

[0013] [9]Mansour Sharafisafa, Luming Shen, Yonggang Zheng, Jianzhuang Xiao. The effect of flaw filling material on the compressive behavior of 3D printed rock-like discs[J]. International Journal of Rock Mechanics and MiningSciences, 2019, 17: 105-117.

[0014]

[10] Xiaoying Zhuang,Junwei Chun,Hehua Zhu.A comparative study onunfilled and filled crack propagation for rock like brittle material[J].Theoretical and Applied Fracture Mechanics,2014,72:110-120.

[0015]

[11] Tang Shibin, Sun Kang, Zhang Yongliang, Wu Fei. Crack propagation process of Brazilian disk with open / closed cracks[J]. Journal of China Coal Society, 2021, 46(11): 3459-3469.

[0016]

[12] Lee H, Jeon S. An experimental and numerical study of fracturecoalescence in pre-cracked specimens under uniaxial compression[J]. International Journal of Solids and Structures, 2011, 48(6): 979-999.

[0017]

[13] Liwang Liu,Haibo Li,Xiaofeng Li,Renjie Wu.Full-field strainevolution and characteristic stress levels of rocks containing a single pre-existing flaw under uniaxial compression[J].Bulletin of Engineering Geologyand the Environment,2020,79:3145-3161.

[0018]

[14] Jiang Mingjing, Zhang Ning, Shen Zhifu, Chen He. Discrete element analysis of crack propagation mechanism in uniaxial compression of fractured rock mass[J]. Rock and Soil Mechanics, 2015, 36(11): 3293-3300, 3314.

[0019]

[15] Zhu Qizhi, Ni Tao, Zhao Lunyang, Yuan Shuangshuang. Peridynamic simulation of crack propagation and penetration in rock materials[J]. Chinese Journal of Rock Mechanics and Engineering, 2016, 35(S2): 3507-3515.

[0020]

[16] Shi Fang, Gao Feng, Li Xiru, Shen Xiaoming. Propagation finite element method for simulating primary and secondary crack initiation and cracking of rock under compression and shear conditions [J]. Rock and Soil Mechanics, 2014, 35(6): 1809-1817.

[0021]

[17] Li Pengfei, Zhu Qizhi, Gu Shuitao, Ni Tao. Phase field simulation of crack formation and propagation in rock materials[J]. Engineering Mechanics, 2018, 35(3): 41-48. Summary of the invention

[0022] The technical problem to be solved by the present invention is to overcome various deficiencies of the prior art and provide a method for characterizing stress field data at the tip of rock mass cracks under compression and shearing and its application in rapidly predicting the propagation path of wing cracks under uniaxial compression.

[0023] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows.

[0024] A data characterization method for the stress field at the tip of a rock mass fracture under compression and shearing, wherein the method performs a compatibility pre-expression on the rock mass object data having an influence on the terminal output data when performing data characterization on the stress field at the tip of a rock mass fracture; the rock mass object data includes: rock mass properties, rock mass parameters, and others; one or any combination thereof.

[0025] As a preferred technical solution of the present invention, the rock mass parameters include rock mass fracture geometry, rock mass strength, and rock mass deformation; any one of them or any combination thereof.

[0026] As a preferred technical solution of the present invention, the data representation of the stress field at the tip of the compression-shear fracture that is compatible with multiple factors including rock mass mechanical properties, rock mass fracture geometry, rock mass strength and rock mass deformation is as follows:

[0027]

[0028] in, and are the pressure and shear transmission coefficients of the fracture surface, k n and k s are the normal and tangential stiffness of the crack surface, respectively; a is the half length of the crack; α is the angle between the crack and the horizontal direction, with the counterclockwise direction being positive; p is the far-field compression load; and f is the friction coefficient of the crack surface.

[0029] As a preferred technical solution of the present invention, the relevant rock mass object data required for characterizing the stress field data at the tip of the compression-shear fracture is obtained through the following well-known channels: measurement, manuals, credible tangible documents, credible network documents, other credible public data carriers or data channels.

[0030] The application of the stress field data characterization method at the tip of rock cracks under compression and shear in the rapid prediction of the wing crack propagation path under uniaxial compression is realized by characterizing the data of the wing crack initiation angle and the wing crack propagation path under uniaxial compression based on the stress field data characterization at the tip of rock cracks under compression and shear.

[0031] As a preferred technical solution of the present invention, for the data characterization of the wing crack initiation angle, firstly, a stress criterion corresponding to the material is selected, and a data characterization formula for the wing crack initiation angle is constructed based on the data characterization formula (1) of the stress field at the tip of the compression-shear crack that is compatible with multiple factors or its orthogonal coordinate transformation formula and under the selected stress criterion.

[0032] As a preferred technical solution of the present invention, for the data characterization of the wing crack initiation angle, the maximum circumferential stress criterion corresponding to the brittle material is first selected, and the data characterization formula (1) of the stress field at the tip of the compression-shear crack compatible with multiple factors is converted into a polar coordinate form. Then, the data characterization formula of the wing crack initiation angle is obtained under the maximum circumferential stress criterion:

[0033]

[0034] Substituting equation (1) into equation (5) we can obtain the wing crack initiation angle θ0.

[0035] As a preferred technical solution of the present invention, for the data characterization of the wing crack propagation path under uniaxial compression, when establishing the crack path characterization function, the wing crack propagation path under compression and shear is set to satisfy the following logarithmic model:

[0036] y=aln(x-x0)+y0 (12)

[0037] In the formula: x0, y0, a are unknown constants.

[0038] As a preferred technical solution of the present invention, data characterization of the crack propagation path of the wing under uniaxial compression is performed under a logarithmic model:

[0039]

[0040] Finally, the logarithmic model coefficients x0, y0, a and rock object data are substituted into the representation formula (19) to obtain the predicted value of the propagation path of the wing crack.

[0041] An executable carrier for quickly predicting the crack propagation path of a wing under uniaxial compression, wherein the executable carrier is modularly integrated and constructed based on a physical hardware platform or a cloud computing platform, and the executable carrier at least includes:

[0042] Data characterization and processing module for stress field at the tip of rock mass cracks under compression and shear;

[0043] Data characterization and processing module for wing crack initiation angle;

[0044] Data characterization and processing module for wing crack growth path under uniaxial compression;

[0045] The executable vector also allows the following modules to be configured as needed:

[0046] Data storage module;

[0047] Data output module;

[0048] Data transmission module;

[0049] Reminder and / or alarm module;

[0050] Other reserved slots for expansion modules.

[0051] As a preferred technical solution of the present invention, the executable carrier is modularly integrated and constructed based on a physical hardware platform or a cloud computing platform, and the executable carrier at least includes:

[0052] Data characterization and processing module for stress field at the tip of rock mass fracture under compression and shearing; used for pre-expressing compatible rock mass object data that has influence on terminal output data when characterizing the stress field at the tip of rock mass fracture;

[0053] The data representation processing module of the wing crack initiation angle; this module selects the stress criterion corresponding to the material, converts the data representation of the stress field at the tip of the compression-shear crack compatible with multiple factors into the polar coordinate form, and then obtains the data representation of the wing crack initiation angle and the wing crack initiation angle θ0 under the stress criterion;

[0054] A data characterization processing module for the wing crack propagation path under uniaxial compression; used to establish a crack path characterization function under a logarithmic model of the wing crack propagation path under compression and shear, and to obtain data characterization of the wing crack propagation path under uniaxial compression and related terminal parameters.

[0055] The executable vector can set the following modules as required:

[0056] Data storage module; used for data storage;

[0057] Data output module: output data through paper printing, electronic screen display, voice broadcast or other forms;

[0058] Data transmission module; upload and / or download data via fax, email, internal network interface and line, Internet interface and line or other means;

[0059] Reminder and / or alarm module: used for reminders during data output or transmission or alarms after execution obstacles occur;

[0060] Other reserved expandable module positions; subsequent modular construction and expansion will be carried out based on the needs of system functions.

[0061] The beneficial effect of adopting the above technical scheme is that: the present invention proposes a method that can quickly predict the expansion path of wing cracks under uniaxial compression. The method takes into account the physical and mechanical properties of rocks and cracks, and can quickly predict the expansion path of wing cracks under different conditions. It has the advantages of low economic cost and less calculation time. It can quickly provide a reference basis for the analysis of rock engineering problems, and can be used for theoretical analysis and engineering treatment of various types of fractured rock engineering destruction behaviors and fracture mechanisms such as tunnels, underground chambers, mining, rock slopes, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Schematic diagram of the rock mass model containing a single fracture under compression and shear.

[0063] Figure 2 This is the model diagram of the crack propagation path of the wing under uniaxial compression.

[0064] Figure 3 Comparison of experimental and predicted values ​​of wing crack initiation angle under uniaxial compression.

[0065] Figure 4 Comparison diagram of experimental and predicted values ​​of wing crack growth path under uniaxial compression. DETAILED DESCRIPTION

[0066] The following examples describe the present invention in detail. In the description of the following examples, for the purpose of illustration rather than for limitation, the specific details of the technology are proposed, so as to thoroughly understand the present application embodiments. However, it should be clear to those skilled in the art that the present application can also be implemented in other embodiments without these specific details. In other cases, the detailed description of well-known existing methods is omitted to prevent unnecessary details from hindering the description of the present application. It should be understood that when used in the present application specification and the appended claims, the term "comprising" indicates the presence of the described features, integral bodies, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integral bodies, steps, operations, elements, components and / or their collections. It should be understood that the term "and / or" used in the present application specification and the appended claims refers to any combination of one or more of the items listed in association and all possible combinations, and includes these combinations.

[0067] As used in the specification of this application and the appended claims, the term "if" may be interpreted as "when" or "uponce" or "in response to determining" or "in response to detecting" depending on the context. Similarly, the phrase "if it is determined" or "if [the described condition or event] is detected" may be interpreted as meaning "uponce it is determined" or "in response to determining" or "uponce [the described condition or event] is detected" or "in response to detecting [the described condition or event]" depending on the context. In addition, in the description of the specification of this application and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0068] References to "one embodiment" or "some embodiments" etc. described in the specification of this application mean that one or more embodiments of the present application include specific features, structures or characteristics described in conjunction with the embodiment. Therefore, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0069] Example 1: Crack tip stress field model under compression and shear

[0070] In view of the existing literature on the stress field model of the crack tip under compression and shear, rock mechanics parameters and three types of parameters, namely, crack geometry, strength and deformation, are introduced to reflect the influence of material properties of different fractured rock samples. The stress field model of the crack tip under compression and shear given in the present invention is:

[0071]

[0072] Where: p is the far-field compression load, a is the half-length of the crack, α is the angle between the crack and the horizontal direction (counterclockwise is positive), f is the friction coefficient of the crack surface, C n and C s are the pressure and shear transfer coefficients of the fracture surface, which are related to the normal and tangential stiffness of the fracture surface, respectively. The relevant calculation formula is:

[0073]

[0074] Where: E, ν are the rock elastic modulus and Poisson's ratio, respectively, k n and k s are the normal and tangential stiffness of the fracture surface, respectively. Since the stress field model at the fracture tip under compression and shear given by equation (1) introduces rock mechanics parameters and three types of parameters: fracture geometry, strength and deformation, it can theoretically describe different fractured rock samples.

[0075] Example 2: Prediction of Wing Crack Initiation Angle

[0076] First, the stress field expression at the crack tip in the orthogonal rectangular coordinate system of formula (1) is converted into the expression in the polar coordinate system. The result is as follows:

[0077]

[0078] The maximum circumferential stress criterion is often used to predict the crack initiation angle of wing cracks in brittle materials. The criterion expression is as follows:

[0079]

[0080] Substituting equation (3) into equation (4) θ Simplifying, we get:

[0081]

[0082] Substituting equation (2) into equation (5), we can get the wing crack initiation angle θ0.

[0083] Example 3: Establishing a wing crack propagation path model under uniaxial compression

[0084] First, assume that the equivalent shear stress on the crack surface takes the maximum value, that is, the friction force is 0, and the equivalent shear stress on the crack surface is equal to the far-field shear load. At this time, the asymptote of the wing crack propagation path under uniaxial compression is parallel to the loading direction and passes through the center of the crack. Its equation is:

[0085] x min =0 (7)

[0086] Then, assume that the equivalent shear stress on the crack surface takes the minimum value, that is, the far-field shear load is completely offset by the friction force on the crack surface. At this time, under uniaxial compression, the wing crack first starts from the crack tip, and after a short time, it expands along the loading direction after the curve expansion. Its asymptote equation is:

[0087] x max =acosα (8)

[0088] Therefore, the equivalent shear stress on the fracture surface of the single fracture rock mass stress field model under compression and shear in these two cases is:

[0089]

[0090] The friction coefficient f on the crack surface must be between the two extreme cases. According to the linear interpolation method, when the equivalent shear stress on the crack surface is τ, the asymptote equation of the wing crack extension path is:

[0091]

[0092] When the friction coefficient of the crack surface is f, the equivalent shear stress on the crack surface is:

[0093]

[0094] Substituting equations (6) to (9) and (10) into equation (9), the asymptote equation of the wing crack propagation path can be obtained as:

[0095]

[0096] As a preferred technical solution of the present invention, a logarithmic function is used to predict the wing crack propagation path:

[0097] y=aln(x-x0)+y0 (13)

[0098] Where: x0, y0, a are unknown constants, which can be solved by the following method: (1) The starting point of the wing crack is the endpoint of the initial crack (x1, y1):

[0099] x1=acosα,y1=asinα (14)

[0100] (2) The tangent equation at the starting point of the wing crack is:

[0101] y=asinα+(x-acosα)tan(θ0+α) (15)

[0102] Where: θ0 is the crack initiation angle of the wing. Combining equations (11) to (14), we can get:

[0103]

[0104] Substituting the above equation into equation (12), the crack propagation path equation of the upper wing can be obtained as follows:

[0105]

[0106] Similarly, the crack propagation path equation of the lower wing can be obtained as:

[0107]

[0108] Example 4: Characterization and prediction of wing crack propagation paths under uniaxial compression (with accompanying figures)

[0109] (1) The stress field expression near the crack tip under compression and shear is given as

[0110] for Figure 1 The rock mass model with a single fracture under compression and shear is shown in the figure. According to the method described in the present invention, the stress field expression at the fracture tip considering the rock mechanical properties and three types of parameters: fracture geometry, strength and deformation is:

[0111]

[0112] (2) Prediction of wing crack initiation angle

[0113] Transform equation (1) into polar coordinates to obtain the circumferential stress σ at the crack tip: θ The expression is:

[0114]

[0115] Substituting the above equation into the maximum circumferential stress criterion of equation (4) and simplifying it, we can obtain the expression for solving the wing crack initiation angle θ0:

[0116]

[0117] It can be seen from formula (5) that the wing crack initiation angle is related to three parameters: rock mechanical properties and fracture geometry, strength and deformation. Compared with the initiation angle of the classic MTS criterion predicted as a constant value of -70.5°, it is obviously more reasonable and can theoretically reflect the differences in rock properties and fractures.

[0118] (3) Establishment of the crack propagation path model of the wing under uniaxial compression

[0119] for Figure 2 The crack propagation path model of the wing under uniaxial compression is shown, assuming that its path satisfies the logarithmic function relationship:

[0120] y=aln(x-x0)+y0 (9)

[0121] Wherein: x, y are any points on the extension path, x0, y0, a are constants to be determined. According to the method of the present invention, the determination formula is:

[0122]

[0123] Substituting formula (10) into formula (9) we can get Figure 2 The wing crack growth path equation is shown as:

[0124]

[0125] Embodiment 5, application example 1

[0126] Taking the uniaxial compression test of a sandstone specimen with prefabricated cracks as an example, the geometric dimensions of the specimen are: 150mm×150mm×15mm, the crack length is 2a=40mm, and the relevant mechanical parameters are: E=17.67GPa, ν=0.26, σ t =4.67MPa, f=0.26, critical plastic zone size r c =1.296mm, the normal stiffness and tangential stiffness of the crack surface are taken as empirical values, k n =2.0GPa / cm, k s =1.0GPa / cm. Substituting the above parameters into equations (2) and (5), the predicted values ​​of the wing crack initiation angle can be obtained and compared with the classical solution and experimental values, as shown in Figure 3 shown.

[0127] Depend on Figure 3It can be seen that the classical solution is always 70.5°, ignoring the mechanical properties of the rock itself and the influence of the crack strength and deformation parameters, so it cannot correctly predict the crack initiation angle of the wing crack. As a preferred solution, the predicted value of the present invention is well coupled with the experimental results.

[0128] Embodiment 6, Application Example 2

[0129] Taking the uniaxial compression test in reference

[12] as an example, the geometric dimensions of the specimen with a single crack are: 60 mm × 120 mm × 25 mm, the crack length is 2a = 20 mm, and the relevant mechanical parameters are: E = 2.9 GPa, ν = 0.25, σ t =40MPa, other parameters are selected according to experience, namely: f=0.26, k n =2.0GPa / cm, k s =1.0GPa / cm. Substituting the above parameters into equations (2) and (19), the predicted values ​​of the wing crack propagation path can be obtained, and compared with the experimental results, as shown in Figure 4 shown.

[0130] Depend on Figure 4 It can be seen that when the crack inclination angle α is 30°, the wing crack propagation path predicted by the logarithmic model used in the present invention is well coupled in the initial section. When deflection begins, the curvature of the path predicted by the present invention is slightly smaller. When the crack propagation path begins to be parallel to the loading direction, the predicted path of the present invention gradually approaches the experimental path. When the crack inclination angle increases to 45°, 60° and 75° in sequence, the predicted path of the present invention is fully coupled with the experimental path, indicating the rationality and accuracy of the preferred solution of the present invention.

[0131] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0132] From the above implementation cases, it can be seen that the present invention can greatly reduce costs compared with indoor experimental methods. It only needs to measure the physical and mechanical parameters of the rock and the crack-related parameters, and can be used for multiple fracture analysis of the same fractured rock sample; in addition, the theoretical model solution process of the present invention is simple. It only needs to substitute the obtained experimental parameters into the model to draw the change curve of the coordinate xy, and the wing crack propagation path can be obtained, which can greatly save calculation time compared with the numerical simulation method. The present invention provides a method for quickly predicting the wing crack propagation path under uniaxial compression. The method has the advantages of being simple, fast and accurate, and can provide a basis for the fracture analysis of fractured rock mass under compression and shear, and provide practical guidance for the design and construction of related rock mass engineering.

[0133] The embodiments described above are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A data characterization method for the stress field at the tip of a rock mass crack under compression and shear, characterized by: This method uses compatible pre-expression of rock mass object data that has influence on the terminal output data when characterizing the data of the stress field at the tip of the rock mass fracture. The rock mass object data includes: rock mass properties, rock mass parameters; select one or any combination; The data representation of the stress field at the tip of the compression-shear fracture that is compatible with multiple factors including rock mass mechanical properties, rock mass fracture geometry, rock mass strength and rock mass deformation is: in, and are the pressure and shear transmission coefficients of the fracture surface, k n and k s are the normal and tangential stiffness of the crack surface, respectively; a is the half length of the crack; α is the angle between the crack and the horizontal direction, with the counterclockwise direction being positive; p is the far-field compression load; and f is the friction coefficient of the crack surface; exist and In it, E and ν are the elastic modulus and Poisson’s ratio of rock, respectively.

2. The data characterization method for the stress field at the tip of a rock mass crack under compression and shear according to claim 1 is characterized by: The rock mass parameters include rock mass fracture geometry, rock mass strength, and rock mass deformation; any one or any combination thereof may be selected.

3. The data characterization method for the stress field at the tip of a rock mass crack under compression and shear according to claim 2 is characterized by: The relevant rock mass object data required for the characterization of the stress field data at the tip of the compression-shear fracture are obtained through the following well-known channels: measurement, manuals, credible tangible documents, credible network documents, and other credible public data carriers or data channels.

4. Application of the method for characterizing stress field data at the tip of rock mass cracks under compression and shearing according to any one of claims 1 to 3 in rapidly predicting the propagation path of wing cracks under uniaxial compression, characterized in that: This method is based on the data characterization of the stress field at the tip of the rock crack under compression and shear, and through the data characterization of the wing crack initiation angle and the data characterization of the wing crack propagation path under uniaxial compression, to achieve rapid prediction of the wing crack propagation path under uniaxial compression.

5. The application of the method for characterizing the stress field data at the tip of rock mass cracks under compression and shearing according to claim 4 in the rapid prediction of the wing crack propagation path under uniaxial compression is characterized by: For the data characterization of the wing crack initiation angle, the stress criterion corresponding to the material is first selected, and the data characterization of the wing crack initiation angle is constructed based on the data characterization formula (1) of the stress field at the tip of the compression-shear crack that is compatible with multiple factors or its orthogonal coordinate transformation formula and the selected stress criterion.

6. Application of the method for characterizing the stress field data at the tip of rock mass cracks under compression and shearing according to claim 4 in rapidly predicting the propagation path of wing cracks under uniaxial compression, characterized in that: For the data representation of the wing crack initiation angle, the maximum circumferential stress criterion corresponding to the brittle material is first selected, and the data representation formula (1) of the stress field at the tip of the compression-shear crack compatible with multiple factors is converted into polar coordinate form. Then, the data representation formula of the wing crack initiation angle is obtained under the maximum circumferential stress criterion: Substituting equation (1) into equation (5) we can obtain the wing crack initiation angle θ0.

7. Application of the method for characterizing stress field data at the tip of rock mass cracks under compression and shearing according to claim 6 in rapidly predicting the propagation path of wing cracks under uniaxial compression, characterized in that: For the data characterization of the wing crack propagation path under uniaxial compression, the wing crack propagation path under compression and shear is set to satisfy the following logarithmic model when establishing the crack path characterization function: y=aln(x-x0)+y0 (12) In the formula: x0, y0, a are unknown constants.

8. Application of the method for characterizing the stress field data at the tip of rock mass cracks under compression and shearing according to claim 7 in rapidly predicting the propagation path of wing cracks under uniaxial compression, characterized in that: Data characterization of the crack propagation path of the wing under uniaxial compression under the logarithmic model: Finally, the logarithmic model coefficients x0, y0, a and rock object data are substituted into the representation formula (19) to obtain the predicted value of the propagation path of the wing crack.

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