A method for obtaining high-reliability critical cracking load of rock mass under compression and shear

Abstract

The present invention discloses a method for obtaining a high-confidence critical cracking load of a rock mass under compression and shear. Based on the actual stress state of a rock mass with compression and shear fractures and the stress boundary conditions of the rock mass fracture surface, and compatible with the multi-dimensional parameter attributes of the rock mass fractures and the stress component combination at the rock mass fracture tips, a data characterization method for the critical cracking load of a rock mass under compression and shear is obtained, which can provide basic value data for rock mass engineering design and its operation and construction. The present invention combines the compression and shear stress characteristics of fractured rock masses, starting from the stress boundary conditions of the fracture surface, and uses a complex variable function method to conduct an in-depth analysis of the stress field distribution of the compression and shear fractured rock mass. It also considers three types of parameters: fracture geometry, strength, and deformation. This method can more accurately predict the critical cracking load of a fractured rock mass, and has important theoretical and application value for various rock mass compression and shear fracture mechanics application scenarios such as tunnels, underground chambers, mining, slopes, and dam foundations.

Description

Technical Field

[0001] The present invention relates to the technical field of rock mass compression-shear fracture mechanics and its engineering application, and specifically to a method for obtaining the critical cracking load of rock mass under the action of compression-shear load by considering multiple influencing parameters of cracks in the application of compression-shear fracture mechanics models of various rock masses such as tunnels, underground chambers, mining, slopes, and dam foundations. Background Art

[0002] Natural rock masses often contain defects such as cracks, joints and micropores, and are often under compressive shear stress conditions, such as the deadweight effect of the rock mass, the compressive stress of the shield cutter on the rock mass in soft and hard uneven strata, the effect of prestressed anchor rods on the surrounding rock in mountain tunnels, the hydrostatic pressure of underground water-sealed oil depots on the surrounding rock, and the effect of buildings or dams on the rock bearing layer. Therefore, rock mass engineering inevitably involves the initiation and arrest of cracks in fractured rock masses. Accurately characterizing the critical initiation load of fractured rock masses under compression and shear has attracted the attention of many researchers.

[0003] Classical fracture mechanics [1] It cannot be directly used to analyze the compression-shear fracture of fractured rock mass[2,3]. However, many scholars often directly quote the modified results of classical fracture mechanics when analyzing compression-shear failure. [4-7] , or simplify the rock mass into an elastic medium during derivation [8,9] , ignoring the influence of fracture surface strength or deformation parameters on the stress field of rock mass, so its theoretical prediction results are often irrelevant to the physical and mechanical properties of fractured rock mass, which is obviously unreasonable.

[0004] The compression-shear failure mechanism of fractured rock mass can be explained from both internal and external aspects. From the internal cause, the biggest difference between the compression-shear fracture and the tension-shear fracture of fractured rock mass is that the former is closed due to compression of the fracture surface, which in turn generates friction to hinder the relative slip between the fracture surfaces. Therefore, the properties of the fracture will have a significant impact on the compression-shear fracture of the rock mass. In order to evaluate the influence of fractures on the mechanical properties of rock mass, three types of fracture parameters are introduced to describe them, namely: (1) geometric parameters, such as fracture length and inclination; (2) strength parameters, namely fracture surface friction coefficient and cohesion; (3) deformation parameters, namely fracture surface normal and tangential stiffness. Prudencio and Jan

[10] Compression experiments on fractured rock masses and Xia et al.

[11] Direct shear tests on fractured rock masses show that the peak strength of the rock mass increases with the increase of fracture deformation parameters, which indicates that fracture deformation parameters also have an important influence on the mechanical properties of the rock mass. However, in the current research on the compression and shear failure of fractured rock masses, only the influence of fracture geometry parameters and strength parameters is often considered, while the influence of deformation parameters is not considered from a theoretical perspective. [12-14]From an external perspective, the crack surface tends to close during compression, and due to the intrusion of the material, the stress boundary conditions of the crack surface will change. This change in stress boundary conditions is the fundamental reason why classical fracture mechanics cannot be directly applied to analyze the compression and shear failure of fractured rock masses.

[0005] Although there are relatively rich research results on the critical cracking load of fractured rock mass under compression and shear, there are still certain problems, such as directly making corrections based on the classical fracture mechanics model and failing to consider the influence of fracture deformation parameters, which leads to the theoretical characterization results being inconsistent with the actual situation, or even far from it.

[0006] Related references are listed below.

[0007] [1]Griffith A A.The phenomena of rupture and flow in solids[J].Philosophical Transactions of the Royal Society of London A,1921,221:163-198.

[0008] [2]Zhu ZM,Wang L,Mohanty B,et al.Stress intensity factor for cracked specimen under compression[J].Engineering Fracture Mechanics,2006,73(4):482-489.

[0009] [3]Ji PQ, Zhang XP, Zhang QA new method to model the non-linearcrack closure behavior of rocks under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences, 2018, 112: 171-183.

[0010] [4]Sih G C.Strain-energy-density factor applied to mixed mode crackproblems[J].International Journal of Fracture,1974,10(3):305-321.

[0011] [5]Zhou Z H,Cao P,Ye Z Y.Crack propagation mechanism of compression-shear rock under static-dynamic loading and seepage water pressure[J].Journalof Central South University,2014,21(4):1565-1570.

[0012] [6]Alneasan M,Behnia M,Bagherpour R.Applicability of the classicalfracture mechanics criteria to predict the crack propagation path in rockunder compression[J].European Journal of Environmental and Civil Engineering,2020,24(11):1761-1784.

[0013] [7]Bahrami B,Nejati M,Ayatollahi M R,et al.Theory and experiment ontrue mode II fracturing of rocks[J].Engineering Fracture Mechanics,2020,240:107314.

[0014] [8]Zheng T,Zhu Z M,Wang B,et al.Stress intensity factor for aninfinite plane containing three collinear cracks under compression[J].ZAMM-Journal of Applied Mathematics and Mechanics,2014,94(10):853-861.

[0015] [9]Fan Y,Zhu Z M,Zhao Y L,et al.Analytical solution of T-stresses foran inclined crack in compression[J].International Journal of Rock Mechanicsand Mining Sciences,2021,138:104433.

[0016]

[10] Prudencio M,Jan M V S.Strength and failure modes of rock massmodels with non-persistent joints[J].International Journal of Rock Mechanicsand Mining Sciences,2007,44(6):890-902.

[0017]

[11] Xia C C,Yu Q F,Xin Q,et al.Experimental study on shear-seepagebehaviour of rock joints under constant normal stiffness[J].Rock and SoilMechanics,2020,41(1):57.

[0018]

[12] Li N,Chen W,Zhang P,et al.The mechanical properties and afatigue-damage model for jointed rock masses subjected to dynamic cyclicalloading[J].International Journal of Rock Mechanics and Mining Sciences,2001,7(38):1071-1079.

[0019]

[13] Alneasan M, Behnia M, Bagherpour R. Frictional crack initiation and propagation in rocks under compressive loading[J]. Theoretical and AppliedFracture Mechanics, 2018,97:189-203.

[0020]

[14] Zhao YL, Wang YX, Wang WJ, et al. Modeling of rheological fracturebehavior of rock cracks subjected to hydraulic pressure and far fieldstresses[J]. Theoretical and Applied Fracture Mechanics, 2019,101:59-66. Summary of the Invention

[0021] The technical problem to be solved by the present invention is to overcome various deficiencies of the prior art and provide a method for obtaining a highly reliable critical cracking load of a rock mass under compression and shearing.

[0022] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows.

[0023] A method for obtaining the critical cracking load of rock mass under compression and shear is based on the actual stress state of the compression-shear fractured rock mass and the stress boundary conditions of the rock mass fracture surface. At the same time, it is compatible with the multi-dimensional parameter attributes of the rock mass fracture and the stress component combination at the rock mass fracture tip. The method obtains a data characterization method for the critical cracking load of rock mass under compression and shear, which can provide basic value data for rock mass engineering design and its operation construction.

[0024] As a preferred technical solution of the present invention, this method first obtains the stress intensity factor data and related stress data at the tip of the rock crack by constructing the compressive shear stress field data of the fractured rock mass, and further obtains the crack initiation angle data of the wing of the compressive shear crack tip based on the setting of the rock compressive shear crack initiation data specification, and finally realizes the high-confidence acquisition of the critical compressive shear initiation load data of the fractured rock.

[0025] As a preferred technical solution of the present invention, the data processing process for constructing the data-oriented compressive and shear stress field of fractured rock mass is as follows: based on the stress distribution characteristics of the fracture surface of the rock mass, the full-field stress function of the fractured rock mass is derived from the stress boundary conditions of the fracture surface, and then the stress intensity factor K at the tip of the rock mass fracture is obtained. I , KII and T-stress data characterization algorithms;

[0026] As a preferred technical solution of the present invention, the data processing process of the rock mass compression shear crack initiation data specification is as follows: for the maximum circumferential stress (MTS) criterion, first introduce the three components of T-stress, namely T x , T y and T xy , establish the modified maximum circumferential stress (MMTS) criterion considering T-stress, thereby obtaining a data characterization algorithm for the crack initiation angle of the tip wing of the rock mass compression-shear crack; for other applicable criteria that are optional in parallel, use the corresponding data process as needed;

[0027] As a preferred technical solution of the present invention, the data processing process for obtaining the critical compressive shear cracking load data of fractured rock with high reliability is as follows: first, the tensile strength σ of the intact rock is introduced. t , in order to establish a data characterization algorithm for the critical cracking load of rock mass under compression and shear that is compatible with the multi-dimensional parameter attributes of cracks, and to achieve high-reliability acquisition of the critical compression and shear cracking load of fractured rock.

[0028] As a preferred technical solution of the present invention, the crack tip stress intensity factor K I , K II The data characterization algorithm of and T-stress is:

[0029]

[0030] 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 crack inclination; p is the far-field compression load; and f is the friction coefficient of the crack surface.

[0031] As a preferred technical solution of the present invention, the data characterization algorithm corresponding to the modified maximum circumferential stress (MMTS) criterion considering T-stress is:

[0032]

[0033] As a preferred technical solution of the present invention, the data characterization algorithm of the crack initiation angle of the tip wing of the rock mass compression shear crack is: the stress intensity factor K of the crack tip is I , K II Substitute the data characterization formula (12) of T-stress into the data characterization formula (15) corresponding to the modified maximum circumferential stress (MMTS) criterion to obtain the wing crack initiation angle θ0.

[0034] As a preferred technical solution of the present invention, the rock mass critical cracking load data characterization algorithm compatible with the multi-dimensional parameter attributes of the crack under compression and shear is:

[0035]

[0036] The data representation algorithm of function g is:

[0037]

[0038] in, is the relative plastic zone size of the material, r c is the critical plastic zone size of the material.

[0039] As a preferred technical solution of the present invention, the physical and mechanical parameters of rock and crack are substituted into the data representation formulas (16) and (17) to obtain the high confidence critical cracking load value p of rock mass under compression and shear c ; The methods for obtaining the physical and mechanical parameters of rocks and fractures include: measurement, manuals, credible tangible documents, credible online documents, and other credible public data carriers or data channels.

[0040] As a preferred technical solution of the present invention, the multi-dimensional parameter attributes of the rock mass fracture include: fracture geometry parameters, fracture strength parameters, fracture deformation parameters, other fracture parameters, any one or any combination thereof.

[0041] As a preferred technical solution of the present invention, the combination of stress components at the tip of the rock fracture includes: T-stress at the tip of the rock fracture along any orthogonal spatial direction and any combination thereof.

[0042] An executable carrier for obtaining the critical cracking load of rock mass under compression and shear is constructed through modular integration based on a physical hardware platform or a cloud computing platform. The executable carrier includes at least:

[0043] Construct a data processing module guided by the data of compression and shear stress field of fractured rock mass;

[0044] Data processing module for rock mass compression and shear crack initiation data specification setting;

[0045] A data processing module for obtaining high-reliability data on critical compressive shear initiation loads of fractured rock;

[0046] The executable also allows the following modules to be configured as needed:

[0047] Data storage module;

[0048] Data output module;

[0049] Data transmission module;

[0050] Reminder and / or alarm module;

[0051] Other reserved slots are for expansion modules.

[0052] 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:

[0053] Construct a data processing module for compressive and shear stress field data of fractured rock mass; this module is used to: derive the full-field stress function of fractured rock mass based on the stress distribution characteristics of fracture surface of rock mass and the stress boundary conditions of fracture surface, and then obtain the stress intensity factor K at the tip of fracture of rock mass I , K II and T-stress data characterization algorithms;

[0054] The data processing module for the rock mass compression shear crack initiation data specification is used to: for the maximum circumferential stress (MTS) criterion, introduce the three components of T-stress, namely T x , T y and T xy , establish the modified maximum circumferential stress (MMTS) criterion considering T-stress, thereby obtaining a data characterization algorithm for the crack initiation angle of the tip wing of the rock mass compression-shear crack; for other applicable criteria that are optional in parallel, use the corresponding data process as needed;

[0055] A data processing module for obtaining high-confidence data on the critical compressive shear initiation load of fractured rock; this module is used to: introduce the tensile strength σ of intact rock t , in order to establish a data characterization algorithm for the critical cracking load of rock mass under compression and shear that is compatible with the multi-dimensional parameter attributes of fractures, and to achieve high-reliability acquisition of the critical compression and shear cracking load of fractured rock;

[0056] The executable loads the following modules as needed:

[0057] Data storage module; used for data storage;

[0058] Data output module; output data through paper printing, electronic screen display, voice broadcast or other forms;

[0059] Data transmission module; uploading and / or downloading data via fax, email, internal network interface and line, Internet interface and line or other means;

[0060] Reminder and / or alarm module: used for reminders during data output or transmission or alarms when execution obstacles occur;

[0061] Other reserved expandable module positions; subsequent modular construction and expansion will be carried out based on the need for system functions.

[0062] The beneficial effects of adopting the above-mentioned technical solution are as follows: the present invention specifically and comprehensively addresses many of the shortcomings of the existing technology. Based on a new data model and data processing process, a method for characterizing the critical cracking load of rock masses under compression and shear is obtained, taking into account three types of fracture parameters. This invention combines the compressive and shear stress characteristics of fractured rock masses, starting from the stress boundary conditions of the fracture surface, and uses a complex variable function method to conduct an in-depth analysis of the stress field distribution of compression and shear fractured rock masses. It also considers three types of parameters: fracture geometry, strength, and deformation. This method can more accurately predict the critical cracking load of fractured rock masses, thereby providing a reference for the design of related rock mass engineering projects. The specific beneficial effects are detailed below.

[0063] (1) Most of the stress intensity factors K at the crack tip under compression and shear have been I , K II The T-stress characterization model is based on the modification of classical fracture mechanics. However, classical fracture mechanics does not meet the stress boundary conditions of the compression-shear fracture surface, which is fundamentally inconsistent with the true stress state of the compression-shear fractured rock mass. Therefore, the stress intensity factor K at the crack tip under compression-shear action has been I , K II The T-stress characterization results are inconsistent with the actual results, or even wrong. To this end, the present invention starts from the stress boundary conditions of the crack surface and considers the three types of crack geometry, strength and deformation.

[0064] K proposed by previous scholars I , K II The characterization method will inevitably lead to the influence of the crack initiation angle and parameters of the wing crack, and the full-field stress function of the compression-shear fractured rock mass is derived, and then the stress intensity factor K at the crack tip under compression-shear action is obtained. I , K II and T-stress characterization methods, which makes K I , K II The characterization of the stress and T-stress is more accurate and can reflect the effects of the physical and mechanical characteristics of different rocks and fractures.

[0065] (2) The existing crack initiation criteria under compression and shear usually do not consider the influence of the three T-stress components at the crack tip. At the same time, the stress intensity factor in the stress component is also used in practice, which has a large error. Based on this, this patent proposes a method that considers the three T-stress components at the crack tip and the K I , K II A new characterization method is used to characterize the crack initiation angle of wing cracks under compression and shear, which will make the estimation of crack initiation angle more consistent with the actual situation.

[0066] (3) The critical cracking load of the fractured rock mass under compression and shear is divided by the rock tensile strength σ tThe method proposed in this paper is able to reflect the influence of different rocks and fractures, thereby making the prediction of the critical cracking load of fractured rock mass under compression and shear more accurate, thus providing a basis for the design of related rock mass engineering.

[0067] In summary, the research results of this invention can provide basic value data for rock engineering design and its operation and construction, and have important theoretical and application value for various rock compression-shear fracture mechanics application scenarios such as tunnels, underground chambers, mining, slopes, and dam foundations. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 Schematic diagram of the fractured rock mass model under compression and shear.

[0069] Figure 2 Schematic diagram of the stress state of the crack surface under compression and shear.

[0070] Figure 3 This is a diagram showing the friction force distribution of a 45° inclined crack surface under compression and shear.

[0071] Figure 4 This is a diagram showing the friction force distribution of a 30° inclination crack surface under compression and shear.

[0072] Figure 5 This is a diagram showing the influence of crack geometric parameters on the circumferential stress at the crack tip.

[0073] Figure 6 This is a diagram showing the influence of crack strength parameters on the circumferential stress at the crack tip.

[0074] Figure 7 This is a diagram showing the influence of the crack normal stiffness on the circumferential stress at the crack tip.

[0075] Figure 8 This is a diagram showing the influence of the crack tangential stiffness on the circumferential stress at the crack tip.

[0076] Figure 9 This is the relationship curve between the wing crack initiation angle θ0 and the crack inclination angle α.

[0077] Figure 10 is the critical load for crack initiation p c The relationship curve between the crack inclination angle α. DETAILED DESCRIPTION

[0078] The following examples illustrate the present invention in detail. In the description of the following examples, for the purpose of illustration and not for limitation, the specific details of the technology are proposed so that the embodiments of the present application are thoroughly understood. However, it will 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, detailed descriptions of well-known existing methods are omitted to avoid unnecessary details that hinder the description of the present application. It should be understood that when used in this specification and the appended claims, the term "comprising" indicates the presence of described features, wholes, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their collections. It should be understood that the term "and / or" used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0079] As used in the specification of this application and the appended claims, the term "if" can be interpreted as "when..." or "upon..." 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" can be interpreted as meaning "upon determination," "in response to determining," or "upon detection of [the described condition or event]," 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 used merely to distinguish descriptions and are not to be understood as indicating or implying relative importance.

[0080] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0081] Example 1: Characterization of the critical cracking load of rock mass under compression and shear considering three types of crack parameters

[0082] (1) Establishing a compressive shear stress field model for fractured rock mass

[0083] The stress diagram of the compression-shear fracture rock mass model is as follows Figure 1At this time, the compressive stress on the crack surface is the internal force transferred to the crack surface by the far-field compression load. No real compressive stress is applied to the outer surfaces of the upper and lower crack surfaces. Instead, the external load is transferred to the inner surface of the crack and causes the crack to close. The load that really acts on the outer surfaces of the upper and lower cracks is only the friction force caused by relative sliding, as shown in Figure 2 As shown. The far-field compressive load is transferred from the inner surface of the crack to the outer surface of the crack through the crack surface. Combined with the normal stiffness k of the crack surface, n Definition of (normal stress increment required for crack surface closure at effective stress level), virtual compressive stress σ caused by friction on the outer surface of the crack n It can be defined as:

[0084] σ n =(1-C n )σ α =-(1-C n )pcos 2 α (1)

[0085] Where: is the fracture surface pressure transmission coefficient, a is the fracture half length, E is the rock elastic modulus, and v is the rock Poisson's ratio; σ α is the compressive stress on the inner surface of the crack; α is the crack inclination; and p is the far-field compressive load.

[0086] Similarly, combined with the fracture surface tangential stiffness k s The definition of (the shear stress increment required for the shear displacement increment) and the distribution of friction along the crack surface (such as Figure 3 and Figure 4 ), the actual friction force τ acting on the outer surface of the crack due to the relative sliding tendency α (t) can be defined as:

[0087]

[0088] Where: is the shear transfer coefficient of the crack surface; τ f (t) is the ideal friction force distribution function; f is the friction coefficient of the crack surface; t is any point on the crack surface that does not include the endpoints, -a <t<a。

[0089] therefore, Figure 1 The stress boundary condition of the crack surface can be written as:

[0090]

[0091] Where: L + , L - Represent the upper and lower surfaces of the crack respectively. And because the stress component (σ x ,σ y ,τxy ) and the two complex analytic functions Φ(z) and Ω(z) are related as follows:

[0092]

[0093] Where: z=x+iy is an arbitrary complex variable, is the conjugate complex variable of z. When z→t, according to formula (4):

[0094]

[0095] Combining equations (3) and (5) we can get:

[0096]

[0097] Where p(t) and q(t) are functions of the fracture L with respect to t. The fractured rock mass problem can be transformed into a Riemann-Hilbert boundary value problem, and the general solution of the problem can be obtained according to the Plemeli-Sokhozki formula:

[0098]

[0099] Where: P n (z) = C0z n +C1z n-1 +...+C n , n represents the number of cracks, polynomial P n The coefficient of (z) can be given by the following formula:

[0100]

[0101] Where: is the conjugate form of Γ′ and is a complex variable related to the far-field load. For this problem, the far-field load is 0, so:

[0102]

[0103] When the number of cracks is 1, that is, n = 1, let a1 = a, b1 = -a, and simplify Equations (6) to (9), the full-field stress function of the cracked rock mass under compression and shear can be obtained as follows:

[0104]

[0105] Combining equations (4) and (10) and performing Taylor expansion at the crack tip, we can obtain the stress field expression at the crack tip as follows:

[0106]

[0107] in:

[0108]

[0109] Equations (10) to (12) are the stress field model of a single fracture rock mass under compression and shear, which considers three types of fracture parameters, and the stress field model at the fracture tip, which considers T-stress and fracture deformation parameters. This model can always satisfy the absence of type I singularity at the fracture tip, that is, mathematically guaranteeing the compression-shear closed fracture tip K I = 0, ensuring that the two sides of the crack do not physically invade each other. From formula (12), it can be seen that the crack deformation parameter has an influence on the stress intensity factor K at the crack tip. II It has an impact, and also has an impact on the third T-stress component

[0110] (2) Select the compression-shear crack initiation criterion and predict the crack initiation angle

[0111] Converting formula (11) into polar coordinate form, we have:

[0112]

[0113] The maximum circumferential stress (MTS) criterion is introduced to predict the wing crack initiation angle, which is defined as follows:

[0114]

[0115] Combining equations (13) and (14) yields the modified maximum circumferential stress (MMST) criterion, which is expressed as follows:

[0116]

[0117] Substituting equation (12) into equation (15) we can obtain the wing crack initiation angle θ0.

[0118] (3) Characterization of critical cracking load of compression-shear fractured rock mass

[0119] Assume that the tensile strength of rock is σ t , combining equations (14) and (15) to obtain the critical cracking load p of rock mass considering three types of crack parameters under compression and shear c Characterization formula:

[0120]

[0121] The expression of function g is:

[0122]

[0123] Where: is the relative plastic zone size of the material, r c is the critical plastic zone size of the material.

[0124] In summary, by substituting the physical and mechanical parameters of rock and crack into formulas (16) and (17), the critical cracking load value p of the fractured rock mass under compression and shear can be obtained. c , this value can provide a reference for the design of relevant rock mass engineering.

[0125] Example 2: Application Example

[0126] The geometric dimensions of a rock sample with a single crack under compression and shear are: 60mm×120mm×25mm, the crack length 2a=20mm, and the relevant mechanical parameters are: E=2.9GPa, ν=0.25, σ t =40MPa, and other parameters are based on experience, namely: f=0.26, k n =2.0GPa / cm,k s =1.0 GPa / cm. Substituting the above parameters into equations (11) and (12) yields the stress distribution at the crack tip under compression and shear, substituting them into equation (15) yields the wing crack initiation angle θ0, and substituting them into equations (16) and (17) yields the critical initiation load for compression and shear in fractured rock mass. The following discussion discusses the effects of three parameters—fracture geometry, strength, and deformation—on the stress field at the crack tip, and the relationship between the wing crack initiation angle and critical initiation load and the crack inclination angle under different critical plastic zone sizes.

[0127] (1) Influence of crack geometric parameters on circumferential stress at the crack tip

[0128] Here, the crack inclination angle α is taken as 45°, the crack half length a is taken as 10mm, 15mm, 20mm, 25mm and 30mm respectively, and the other parameters are the same as before. The circumferential stress σ at the crack tip is plotted. θ Then the crack half-length a is taken as 20 mm, the crack inclination angle α is taken as 15°, 30°, 45°, 60° and 75° respectively, and other parameters remain unchanged. The circumferential stress σ at the crack tip is plotted. θ The distribution curve of Figure 5 As shown. When the circumferential stress σ θ When in a compressive stress state, cracks will not initiate. Figure 5 (a) It can be seen that the circumferential stress σ at the crack tip θ As the crack half-length a increases, the range of the crack in the tensile stress state also increases, that is, the range of the potential tensile failure zone increases. θ When it takes the maximum value and is positive, the corresponding angle is the optimal crack initiation angle at the crack tip. Figure 5 It can also be seen that the optimal crack initiation angle does not change with the change of crack length, but changes with the change of crack inclination angle α. Figure 5 (b) It can be seen that the optimal crack initiation angle decreases with the increase of the crack inclination angle.

[0129] (2) Influence of crack strength parameters on circumferential stress at the crack tip

[0130] Here, the crack inclination angle α is taken as 20°, 40°, 60° and 80° respectively, the crack half-length a is taken as 20 mm, the crack surface friction coefficient f is taken as 0, 0.2, 0.4, 0.6 and 0.8 respectively, and other parameters remain unchanged. The circumferential stress σ at the crack tip is plotted. θ The distribution curve of Figure 6 It can be seen that when the crack inclination angle α = 20°, the crack surface friction coefficient significantly changes the circumferential stress σ near the crack tip. θ The distribution of friction coefficient f increases, σ θ The range of the tensile stress zone is reduced, and the corresponding optimal crack initiation angle of the wing crack is also reduced. When the crack inclination angle α increases to 40°, the crack surface friction coefficient f has an influence on the circumferential stress σ θ The distribution of Figure 6 (c) and 6(d) show that when the crack inclination angle is large, the friction coefficient f has an influence on the circumferential stress σ. θ The impact will not be obvious. Figure 6 In (d), although f increases from 0 to 0.8, the curves almost overlap, which means that the circumferential stress σ at the crack tip is θ The sensitivity to the friction coefficient f is greatly reduced. From the above results, it can be seen that the effect of the crack surface strength parameter, that is, the friction coefficient f, on the stress field at the crack tip is also controlled by the crack geometric parameters.

[0131] (3) Influence of crack deformation parameters on circumferential stress at the crack tip

[0132] Here the normal stiffness of the crack surface k n The crack tip circumferential stress σ is plotted by taking 0.02 GPa / cm, 0.2 GPa / cm, 2 GPa / cm, 20 GPa / cm and 200 GPa / cm in sequence, the crack inclination angle α is taken as 10°, 15°, 30° and 60° respectively, the crack half-length a is taken as 20 mm, and other parameters remain unchanged. θ The distribution curve of Figure 7 As shown. Then, similarly, the tangential stiffness k of the crack surface s Take 0.01GPa / cm, 0.1GPa / cm, 1GPa / cm, 10GPa / cm and 100GPa / cm in turn, and keep other parameters unchanged to plot the circumferential stress σ at the crack tip θ The distribution curve of Figure 8 As shown. Figure 7 and 8 It can be seen that the normal stiffness k of the crack surface n and tangential stiffness k s The circumferential stress at the crack tip σ θThe influence of the distribution is almost the same, which can be seen from the k n and k s The meaning of and the mechanism of friction are explained. First, the generation of friction on the crack surface requires two conditions: first, under the action of compressive stress, the upper and lower surfaces of the crack are in contact with each other, that is, the crack surface must be closed; second, under the action of shear stress, the upper and lower surfaces of the crack after contact must have a relative sliding tendency. And k n The size of k reflects the difficulty of closing the crack surface. s The size of reflects the difficulty of the sliding trend of the upper and lower surfaces of the crack, so these two crack deformation parameters have a significant impact on the circumferential stress σ at the crack tip. θ The impact of the distribution should be the same.

[0133] Comparison of the effects of normal stiffness and tangential stiffness on the circumferential stress σ at the crack tip under different crack inclination angles α θ From the influence of the distribution, it can be seen that when the crack inclination angle α is small, the effect of the crack deformation parameters on the stress field at the crack tip is more significant. For example, when α = 10° or 15°, the tensile stress area at the crack tip increases with the increase of the normal stiffness or tangential stiffness, and the intensity of the singular stress field becomes larger; when α = 30°, this influence will be significantly weakened, and when α = 60°, the influence is almost negligible. In addition, according to Figure 7 (a), 7(b), 8(a) and 8(b) show that as the crack surface stiffness parameter increases, the corresponding wing crack initiation angle increases slightly, and this phenomenon is consistent with the results observed in the experiment.

[0134] (4) Relationship between the crack initiation angle and crack inclination angle of the wing crack

[0135] The above rock and crack mechanical parameters remain unchanged, and the wing crack initiation angle θ0 can be obtained by substituting them into formula (15). The result is as follows: Figure 9 As shown in the figure, it can be seen that when the crack inclination angle α is large, the wing crack initiation angle predicted by this paper is smaller than the experimental result; when the crack inclination angle α is small, the predicted result is larger. This may be related to the experimental error caused by the crack thickness (1 mm) in the original paper, but it is generally consistent with its distribution law. When the crack inclination angle α is 45° and 60°, the predicted value is consistent with the experimental value.

[0136] (5) Critical cracking load of rock mass considering three types of crack parameters under compression and shear

[0137] The above rock and fracture mechanical parameters remain unchanged, and substituting them into equations (16) and (17) yields the critical cracking load p of fractured rock mass under compression and shear: c , the results are as follows Figure 10 As shown. It can be seen that when the critical plastic zone size r c = 0.4 mm, the critical load p for wing crack initiation predicted in this paper isc The results agree well with the experimental results. The curves show that when the crack inclination angle α increases from 15° to 30° and 45°, the compressive strength of the cracked specimen gradually decreases, indicating that the damage caused by the crack to the specimen is significantly enhanced at this stage. When the crack inclination angle α increases from 45° to 60° and 75°, the compressive strength of the cracked specimen gradually increases, indicating that the damage caused by the crack to the specimen is decreasing at this stage. It can also be seen that when the crack inclination angle α approaches horizontal or vertical, the compressive strength of the cracked specimen approaches that of the intact specimen. This result is consistent with the experiments of many previous scholars.

[0138] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0139] 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 they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. A method for obtaining the critical cracking load of a rock mass under compression and shear, characterized by: This method first obtains the stress intensity factor data and related stress data at the rock mass crack tip by constructing the compressive shear stress field data of the fractured rock mass. Then, based on the setting of the rock mass compressive shear crack initiation data specification, the crack initiation angle data of the wing at the compressive shear crack tip is obtained. Finally, the critical compressive shear initiation load data of the fractured rock is obtained with high confidence. The data processing process for constructing the data-oriented compressive and shear stress field of fractured rock mass is as follows: based on the stress distribution characteristics of the fracture surface of the rock mass, the full-field stress function of the fractured rock mass is derived from the stress boundary conditions of the fracture surface, and then the stress intensity factor K at the tip of the rock mass fracture is obtained. I , K II and T-stress data characterization algorithms; The data processing process of the rock mass compression shear crack initiation data specification is as follows: For the maximum circumferential stress criterion, first introduce the three components of T-stress, namely T x , T y and T xy , establish a modified maximum circumferential stress criterion considering T-stress, thereby obtaining a data characterization algorithm for the crack initiation angle of the tip wing of the rock mass compression-shear crack; for other applicable criteria that are optional in parallel, use the corresponding data process as needed; The data processing process for obtaining the critical compressive shear cracking load data of fractured rock with high reliability is as follows: first, the tensile strength σ of the intact rock is introduced. t , in order to establish a data characterization algorithm for the critical cracking load of rock mass under compression and shear that is compatible with the multi-dimensional parameter attributes of cracks, and to achieve high-reliability acquisition of the critical compression and shear cracking load of fractured rock.

2. The method for obtaining the critical cracking load of rock mass under compression and shear according to claim 1, characterized in that: The crack tip stress intensity factor K I , K II The data characterization algorithm of and T-stress 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 crack inclination; p is the far-field compression load; and f is the friction coefficient of the crack surface.

3. The method for obtaining the critical cracking load of rock mass under compression and shear according to claim 2, characterized in that: The data characterization algorithm corresponding to the modified maximum circumferential stress criterion considering T-stress is:

4. The method for obtaining the critical cracking load of rock mass under compression and shear according to claim 3, characterized in that: The data characterization algorithm for the crack initiation angle of the tip wing of the rock mass compression shear crack is: the stress intensity factor K of the crack tip is I , K II Substitute the data characterization formula (12) of T-stress into the data characterization formula (15) corresponding to the modified maximum circumferential stress criterion to obtain the wing crack initiation angle θ0.

5. The method for obtaining the critical cracking load of rock mass under compression and shear according to claim 4, characterized in that: The characterization algorithm of rock mass critical cracking load data under compression and shear is compatible with the multi-dimensional parameter attributes of cracks: The data representation algorithm of function g is: in, is the relative plastic zone size of the material, r c is the critical plastic zone size of the material.

6. The method for obtaining the critical cracking load of rock mass under compression and shear according to claim 5, characterized in that: Substituting the physical and mechanical parameters of rock and crack into the data representation equations (16) and (17), the critical cracking load value p of rock mass under compression and shear with high confidence is obtained. c ; The methods for obtaining the physical and mechanical parameters of rocks and fractures include: measurement, manuals, credible tangible documents, credible online documents, and other credible public data carriers or data channels.

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