Method for constructing shear constitutive model of discontinuous structural plane

Abstract

The invention discloses a method for constructing a shear constitutive model of a discontinuous structural plane. The method comprises the following steps: acquiring a peak value and a shear strength parameter in a residual stage; obtaining the initial rock mass shear strength tau of the discontinuous structural plane based on a Jennings criterion; introducing coefficients Xij and Xir to respectively adjust the normal stress at the joint and the rock bridge, and meanwhile, introducing a coefficient Omega to adjust the cohesive force of the rock bridge to obtain the rock mass shear strength tau of the adjusted discontinuous structural plane; based on a Lajtai rock bridge failure theory criterion, obtaining failure criteria of three discontinuous structural surfaces of tension, shearing and strength failure; and obtaining a shear constitutive model of the discontinuous structural surface corresponding to the rock bridge under the tension failure condition, the shear failure condition and the strength failure failure condition. According to the method, the shear constitutive model of the discontinuous structural plane is established, the shear behavior characteristics of the discontinuous structural plane can be effectively described, and the practicability of the constitutive model is effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of rock structural surface constitutive models, and in particular to a method for constructing a shear constitutive model of a discontinuous structural surface. Background Art

[0002] In modern geotechnical engineering, anchor rods are one of the important support methods to ensure the long-term stability and safety of engineering rock mass. Since the 1980s, a large number of experts and scholars at home and abroad have paid attention to the fact that anchor rods not only fix loose rock blocks to stable rock formations in the axial direction, but also enhance the shear slip of joint surfaces in the lateral direction. However, in the anchor rock system, the interaction between anchor rods, rock blocks and joints is complex and unclear. In addition, the weak structural surfaces in the rock mass usually have a certain strength and cannot be simply regarded as open joints or faults. In particular, engineering rock mass is often affected by multiple groups of joints, which further increases the complexity of rock mass failure and the difficulty of support regulation.

[0003] like Figure 1 As shown in the figure, under shear action, the rock bridge in the discontinuous joint first undergoes cracking and expansion damage, and the anchor bends after the rock blocks slide against each other, providing shear, tensile or extrusion forces near the joint surface through which it passes, thereby negatively feedbacking the reactionary rock blocks to prevent shear damage and sliding of the rock bridge. Therefore, it is necessary to further understand the mechanical properties of the discontinuous rock mass in this process in detail, but there are problems such as unclear physical and mechanical meanings of parameters and insufficient description of important displacement field evolution laws. In the study of constitutive models, the clarity of the physical and mechanical meanings of model parameters is an important factor in determining the engineering application value of the model. Summary of the invention

[0004] Based on this, the purpose of the present invention is to provide a method for constructing a shear constitutive model of a discontinuous structural surface, which can effectively describe the shear behavior characteristics of the discontinuous structural surface and effectively improve the practicability of the constitutive model.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] The present invention provides a method for constructing a shear constitutive model of a discontinuous structural surface, which comprises the following steps:

[0007] Step S1: Different normal stresses σ n The peak strength τ in the shear stress-strain curve of the discontinuous structural surface during shear failure p and residual strength τ r By fitting respectively, according to the Mohr-Coulomb criterion, the peak and residual stage shear strength parameters can be obtained: cohesion c and internal friction angle

[0008] Step S2, obtaining the initial rock mass shear strength τ of the discontinuous structural surface based on the Jennings criterion;

[0009] Step S3: Introducing coefficient ξ j and r The normal stress at the joints and rock bridges is adjusted respectively, and the coefficient ω is introduced to adjust the cohesion of the rock bridge to obtain the shear strength τ of the rock mass at the discontinuous structural surface after adjustment;

[0010] Step S4, obtaining the failure criteria of three types of discontinuous structural surfaces, namely tension, shear and strength failure, based on the Lajtai rock bridge failure theory;

[0011] Step S5, obtaining the shear constitutive model of the discontinuous structural surface corresponding to the tension failure condition, the shear failure condition and the strength failure failure condition of the rock bridge.

[0012] In one embodiment, the steps of step S2 include:

[0013] Based on the Mohr-Coulomb strength criterion, the shear stress of the discontinuous structural surface is composed of the joint surface and the rock bridge, that is, the rock mass shear strength τ of the discontinuous structural surface is composed of the shear coefficient, cohesion c, and internal friction angle of the joint surface and the rock bridge. Use connectivity k as the coefficient for weighted calculation

[0014]

[0015] in, is the overall equivalent shear coefficient of the structural surface; c j , is the shear coefficient of the joints in the structural plane; c r , is the shear coefficient of the rock bridge in the structural plane.

[0016] In one embodiment, the rock mass shear strength of the discontinuous structural surface in step S3 satisfies

[0017]

[0018] Among them, the coefficient ξ j and ω are both between 0 and 1, and the coefficient ξ j and r The relationship between them and the joint connectivity k is as follows:

[0019]

[0020] In one embodiment, the specific steps of step S4 are as follows:

[0021] Based on the Lajtai rock bridge failure theory, the failure criteria of three discontinuous structural surfaces, namely tension, shear and strength failure, are obtained. The rock mass shear strength τ of the discontinuous structural surface is expressed in sections according to the normal stress value, and satisfies the following formulas in sequence:

[0022] Tensile failure criterion:

[0023]

[0024] Shear failure criterion:

[0025]

[0026] Strength failure criterion:

[0027]

[0028] Where: C is the joint adjustment parameter, ranging from 0 to 1; σ t is the tensile strength of intact rock, MPa; c r is the cohesion of intact rock, MPa; is the internal friction angle of intact rock, °, is the internal friction angle of intact rock, °.

[0029] In one embodiment, the steps of step S5 include:

[0030] Mechanical analysis is performed at different locations of the rock bridge to obtain the normal stress σ of the micro-element a and the tangential stress τ a :

[0031]

[0032] Among them, τ j Characterized by the shear strength of the joint itself;

[0033] Get the normal stress σ of the plane with an angle β to the horizontal direction β and the tangential stress τ β :

[0034]

[0035] The plane normal stress (σ β ) is derived with respect to angle β, that is:

[0036]

[0037] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum stress and minimum stress σ1, σ3 on the principal stress plane:

[0038]

[0039] Among them, σ x Characterized as horizontally acting stress;

[0040] If the rock bridge is initially tensilely damaged, the minimum principal stress is equal to the tensile strength of the rock material, that is:

[0041]

[0042] After calculation, the effective shear stress can be obtained:

[0043]

[0044] The shear constitutive model of the discontinuous structural surface under the condition of tension failure of the rock bridge is obtained as follows:

[0045]

[0046] In one embodiment, the steps of step S5 include:

[0047] Mechanical analysis is performed at different locations of the rock bridge to obtain the normal stress σ of the micro-element a and the tangential stress τ a :

[0048]

[0049] τ a =τ s -kτ j (3-12)

[0050] Among them, τ j Characterized by the shear strength of the joint itself;

[0051] Get the normal stress σ of the plane with an angle β to the horizontal direction β and the tangential stress τ β :

[0052]

[0053] The plane normal stress (σ β ) is derived with respect to angle β, that is:

[0054]

[0055] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum stress and minimum stress σ1, σ3 on the principal stress plane:

[0056]

[0057] Among them, σ x Characterized as horizontally acting stress;

[0058] If the initial strength failure of the rock bridge occurs, the maximum principal stress is equal to the compressive strength of the rock material, that is:

[0059]

[0060] After calculation, the effective shear stress can be obtained:

[0061]

[0062] The shear constitutive model of the discontinuous structural surface under the condition of strength failure of the rock bridge is obtained as follows:

[0063]

[0064] In one embodiment, the steps of step S5 include:

[0065] Mechanical analysis is performed at different locations of the rock bridge to obtain the normal stress σ of the micro-element a and the tangential stress τ a :

[0066]

[0067] τ a =τ s -kτ j (3-12)

[0068] Among them, τ j Characterized by the shear strength of the joint itself;

[0069] Get the normal stress σ of the plane with an angle β to the horizontal direction β and the tangential stress τ β :

[0070]

[0071] The plane normal stress (σ β ) is derived with respect to angle β, that is:

[0072]

[0073] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum stress and minimum stress σ1, σ3 on the principal stress plane:

[0074]

[0075] Among them, σ x Characterized as horizontally acting stress;

[0076] When shear failure occurs in a rock bridge, according to the Coulomb-Navier shear criterion, the effective shear stress Derivation

[0077]

[0078] Available In addition, the shear stress τ β and normal stress σ β According to the Mohr-Coulomb strength criterion, substituting equations 3-8 and 3-9 into equation 3-25, the shear stress of the rock bridge during shear failure can be obtained:

[0079]

[0080] The shear constitutive model of the discontinuous structural surface under the condition of shear failure of the rock bridge is obtained as follows:

[0081]

[0082] In summary, the method for constructing a shear constitutive model of a discontinuous structural surface provided by the present invention establishes a shear constitutive model of a discontinuous structural surface, which can effectively describe the shear behavior characteristics of the discontinuous structural surface and effectively improve the practicability of the constitutive model. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 A three-dimensional non-continuous structural surface of a rock mass in an open-pit landslide provided by an embodiment of the present invention, wherein (a) a schematic diagram of the failure behavior; (b) a geological survey of the structural surface after the failure;

[0084] Figure 2 A schematic diagram of the mechanical analysis of the discontinuous structural surface failure and its crack propagation mode provided by an embodiment of the present invention;

[0085] Figure 3 A diagram of the failure criterion of the Lajtai rock bridge provided by an embodiment of the present invention;

[0086] Figure 4 Mechanical analysis of rock mass failure with non-penetrating structural planes provided by the embodiment of the present invention;

[0087] Figure 5 Comparison of shear stress-strain curves of anchorless specimens with discontinuous joints under different joint connectivity and rock bridge shape conditions provided by the embodiments of the present invention;

[0088] Figure 6 Comparison of shear strength of discontinuous joint specimens with different joint connectivity and rock bridge shapes provided in the embodiments of the present invention, where (a) k = 0.744 τ p (b) τ when k = 0.744 r(c) τ when k = 0.808 p ; (d) τ when k = 0.808 r ; (e) k = 0.872 τ p ; (f) τ when k = 0.872 r ;

[0089] Figure 7 A comparison table of the shear strength test values ​​of rock masses with non-penetrating structural planes and the theoretical prediction values ​​of the Jennings criterion provided in the embodiments of the present invention;

[0090] Figure 8 Comparison between the shear strength test value of the rock mass with non-penetrating structural planes provided in the embodiment of the present invention and the theoretical prediction value of the Lajtai failure criterion;

[0091] Fig. 9 Comparison between the shear strength test value of the rock mass with non-penetrating structural plane provided in the embodiment of the present invention and the theoretical prediction value of the improved Lajtai failure criterion;

[0092] Fig.10 A schematic flow chart of a method for constructing a shear constitutive model of a discontinuous structural surface provided in an embodiment of the present invention;

[0093] Fig.11 A sliding curve corresponding to a typical discontinuous jointed rock mass shear stress-strain curve provided in an embodiment of the present invention;

[0094] Fig.12 A yield curve corresponding to a typical discontinuous jointed rock mass shear stress-strain curve provided in an embodiment of the present invention;

[0095] Fig.13 A shear type curve corresponding to a typical discontinuous jointed rock mass shear stress-strain curve provided in an embodiment of the present invention;

[0096] Fig.14 A brittle fracture curve corresponding to a typical discontinuous jointed rock mass shear stress-strain curve provided in an embodiment of the present invention;

[0097] Fig.15 The shear composite curve corresponding to the shear stress-strain curve of the typical discontinuous jointed rock mass provided in the embodiment of the present invention. DETAILED DESCRIPTION

[0098] In order to further understand the features, technical means, specific objectives and functions of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0099] Fig.10 is a flow chart of a method for constructing a shear constitutive model of a discontinuous structural surface provided by an embodiment of the present invention, such as Fig.10 As shown, the method for constructing the shear constitutive model of the discontinuous structural surface specifically includes the following steps:

[0100] Step S1: Different normal stresses σ n The peak strength τ in the shear stress-strain curve of the discontinuous structural surface during shear failure p and residual strength τ r By fitting separately, according to the Mohr-Coulomb criterion, the peak and residual stage shear strength parameters can be obtained: cohesion c and internal friction angle like Figure 2 As shown;

[0101] Among them, the rock shear stress-strain curve usually has four stages: elastic stage, pre-peak softening stage, post-peak softening stage and residual strength stage. According to the changes in the curve at different stages, the shear stress-strain curve of typical discontinuous jointed rock mass is summarized into five types: sliding type, yield type, shear type, brittle fracture type and shear composite type, as shown in Table 1, which is recorded in the literature "Lin Xingchao. Research on the method of determining the simulation parameters of the failure process of jointed rock mass [D]. Beijing; China Institute of Water Resources and Hydropower Research, 2015." and the literature and "Lin Xingchao, Ling Yongyu, Wang Xiaogang, et al. Indoor direct shear test study of jointed rock mass with typical structural surface distribution type [J]. Journal of China Institute of Water Resources and Hydropower Research, 2021, 19(01): 45-54."

[0102] Table 1 Shear stress-strain curves of typical discontinuous jointed rock mass

[0103]

[0104]

[0105] Step S2: Obtain the rock shear strength τ of the discontinuous structural surface in the initial state based on the Jennings criterion.

[0106] Specifically, the method of step S2 includes the following steps:

[0107] Based on the Mohr-Coulomb strength criterion, the shear stress of the discontinuous structural surface is composed of the joint surface and the rock bridge, that is, the rock mass shear strength τ of the discontinuous structural surface is composed of the shear coefficient, cohesion c, and internal friction angle of the joint surface and the rock bridge. Use connectivity k as the coefficient for weighted calculation

[0108]

[0109] in, is the overall equivalent shear coefficient of the structural surface; c j , is the shear coefficient of the joints in the structural plane; c r , is the shear coefficient of the rock bridge in the structural plane.

[0110] In order to characterize the degree of connectivity of joints, i.e., the connectivity k, the total length of the joints and other structural surfaces (L j ) or total area (A j ) and the total length of the potential failure slip surface (L r +L j ) or total area (A r +A j ) is used as one of the geometric indices to quantitatively describe rock structure.

[0111]

[0112] Among them, L r is the total length of the rock bridge structure, A r is the total structural surface area of ​​the rock bridge.

[0113] Step S3: Introducing coefficient ξ j and r The normal stress at the joints and rock bridges is adjusted respectively, and the coefficient ω is introduced to adjust the cohesion of the rock bridge to obtain the shear strength of the rock mass of the discontinuous structural surface after adjustment.

[0114]

[0115] Among them, the coefficient ξ j and ω are both between 0 and 1, and the coefficient ξ j and r The relationship between them and the joint connectivity k is as follows:

[0116]

[0117] Step S4: Figure 3 As shown in the figure, based on the Lajtai rock bridge failure theory, the failure criteria of three discontinuous structural surfaces, namely tension, shear and strength failure, are obtained. The rock mass shear strength τ of the discontinuous structural surface is expressed in sections according to the normal stress value, and satisfies the following formulas in sequence:

[0118] Tensile failure criterion:

[0119]

[0120] Shear failure criterion:

[0121]

[0122] Strength failure criterion:

[0123]

[0124] Where: C is the joint adjustment parameter, ranging from 0 to 1; σ t is the tensile strength of intact rock, MPa; c r is the cohesion of intact rock, MPa; is the internal friction angle of intact rock, °, is the internal friction angle of intact rock, °.

[0125] Step S5, obtaining the shear constitutive model of the discontinuous structural surface corresponding to the tension failure condition, the shear failure condition and the strength failure failure condition of the rock bridge.

[0126] Specifically, the method of step S5 comprises the following steps:

[0127] like Figure 4 As shown in the figure, mechanical analysis is performed on different positions of the rock bridge to obtain the normal stress σ of the micro-element a and the tangential stress τ a :

[0128]

[0129] τ a =τ s -kτ j (3-12)

[0130] Among them, τ j Characterized by the shear strength of the joint itself.

[0131] Specifically, mechanical analysis of different positions of the rock bridge shows that the forces at the ends (points A and C) and inside (point B) of the rock bridge are different. The micro-units at the ends are mainly subjected to normal stress (σ a ) and tangential stress (τ a ), while the internal unit is affected by the normal stress (σ a ) and tangential stress (τ a ) is also affected by the horizontal stress (σ x )related.

[0132] The stress analysis of any unit on the rock bridge can obtain the normal stress σ of the plane with an angle β to the horizontal direction: β and the tangential stress τ β :

[0133]

[0134] The plane normal stress (σ β ) is derived with respect to angle β, that is:

[0135]

[0136] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum stress and minimum stress σ1, σ3 on the principal stress plane:

[0137]

[0138] If the rock bridge is initially tensilely damaged, the minimum principal stress is equal to the tensile strength of the rock material, that is:

[0139]

[0140] After calculation, the effective shear stress can be obtained:

[0141]

[0142] For point A or point C at the end of the rock bridge, σ x = 0, and the internal point B, σ x >0. Where σ t is a negative value, so from a numerical point of view, the end point A or C τ a Smaller, relatively speaking, it is more likely to have initial tensile failure, that is, the shear stress of the discontinuous structural surface under the tensile failure condition of the rock bridge is:

[0143]

[0144] Similarly, if the initial strength failure of the rock bridge occurs, the maximum principal stress is equal to the compressive strength of the rock material, that is:

[0145]

[0146] After calculation, the effective shear stress can be obtained:

[0147]

[0148] For point A or point C at the end of the rock bridge, σ x = 0, and the internal point B, σ x >0. Where σ c is a positive value, so from a numerical point of view, the end point B τ a Smaller, relatively speaking, it is more likely to have initial strength failure, that is, the shear stress of the discontinuous structural surface under the condition of strength failure of the rock bridge is:

[0149]

[0150] Furthermore, point B can be considered to be the middle of the rock sample, which satisfies Therefore, formula (3-23) can be expressed as:

[0151]

[0152] Similarly, when shear failure occurs in a rock sample, according to the Coulomb-Navier shear criterion, the effective shear stress Derivation, as shown in formula 3-14:

[0153]

[0154] Available In addition, the shear stress τ β and normal stress σ β According to the Mohr-Coulomb strength criterion, substituting equations 3-8 and 3-9 into equation 3-25, the shear stress of the rock bridge during shear failure can be obtained:

[0155]

[0156] For point A or point C at the end of the rock bridge, σ x = 0, and the internal point B, σ x >0. Where σ c is a positive value, so from a numerical point of view, the end point B τ a Smaller, relatively speaking, it is easier to have initial shear failure, that is, the shear stress of the discontinuous structural surface under the shear failure condition of the rock bridge is:

[0157]

[0158] At this point, the construction method of the shear constitutive model based on the discontinuous structural surface has been completely determined, and the physical and mechanical meanings of the constitutive model parameters are clear, which is suitable for the description of the discontinuous structural surface with rock bridges. The feasibility of the construction method of the shear constitutive model of the discontinuous structural surface of the present invention is verified by experimental examples, as follows.

[0159] Sample preparation and testing

[0160] Indoor experiments are one of the most common methods for studying the fracture laws of rocks, and the main research materials are natural rocks and artificial rock-like materials. Although the properties of natural rocks, such as sandstone, granite, and marble, are closest to engineering rock masses, it is difficult to obtain rock samples that meet the experimental size and contain the required complete joint and fissure morphology due to the size effect. Mechanical drilling and cutting, laser engraving, high-pressure water jet and other technical processing not only cause a certain degree of damage to the rock samples, but also limit the processing accuracy (tip opening, length, thickness, etc.). More importantly, it is impossible to process complex joints and fissures. Therefore, artificial rock-like materials have properties very similar to real rock materials, are easy to make, and are cheap. They are the main indoor experimental materials for studying complex jointed rock masses. For example, taking the search results of papers published in Rock Mechanics and Rock Engineering, an international authoritative journal of rock mechanics, as an example, in the past ten years (2013-2023), there are 32 articles with rock-like in the title, and 254 articles with rock-like in the subject, including 10 ESI highly cited articles. Among the many rock-like materials, mortar concrete is one of the most common artificial rock-like substrates because it is simple to make, stable in nature, easy to plasticize and cheap.

[0161] In the present invention, mortar concrete is selected as the experimental substrate, which is composed of national standard 425 white cement as the cementitious material, fine quartz sand as the aggregate to adjust the physical properties such as bonding and friction, and pure water containing 3‰ concentration of defoamer is added as the solvent, and the specific ratio between the three is 100:80:43 by mass. In the present invention, all rock samples are fully mixed by an electric mixer, and 140×70×70mm 3 After 24 hours of solidification in a special stainless steel mold, it was placed in clean water for 7 days after demolding, and finally cured indoors for more than one month. In addition to the experimental group of samples, Ф50×H100 mm 3 Standard cylindrical sample, 70×70×70mm 3 The square specimens were subjected to basic tests such as uniaxial compression, variable angle shear and Brazilian splitting, and the basic mechanical parameters were measured as shown in Table 2:

[0162] Table 2 Basic physical and mechanical parameters of the tested rock substrate

[0163]

[0164]

[0165] All direct shear tests of the present invention use the YSZJ-100 rock direct shear instrument as a loading device. The instrument is produced by Chengdu Donghua Excellence Technology Co., Ltd. and is suitable for testing stress shear test equipment for rocks and other related materials. Through microcomputer automatic control, the loading time, axial load, axial displacement, horizontal load, horizontal displacement and other related parameters can be effectively controlled, stored, measured, displayed and processed. In the test of the present invention, the loading method is force loading, and the rate is 0.5kN / s in the normal direction and 0.1N / s in the horizontal direction.

[0166] Influence of rock bridge morphology

[0167] Figure 5 The results show that the different joint connectivity (k = 0.744, 0.808, 0.872), different rock bridge shapes (a / b = 0.5, 1.0, 2.0) and different normal stresses (σ n =2.5, 5.0, 7.5, 10.0MPa) under other conditions. With the increase of joint connectivity (k), the curve has significant changes, which is mainly reflected in the shortening of the pre-peak softening and post-peak softening stages, the peak strength (τ p ) and residual strength (τ r ) decrease; with the increase of rock bridge shape (a / b), the rock bridge is more concentrated on the shear square axis, and the shear failure curve has obvious differences. In general, the post-peak softening stage is prolonged. At low normal pressure or high joint connectivity, the residual strength (τ r ) and peak intensity (τ p ) gap decreases; as the normal pressure (σ n ) increases, the transition process of the curve before and after the peak is very different. When the normal pressure is low, the curve often drops suddenly when it reaches the peak, while when the normal pressure is high, the curve begins to flatten out and begins to fall slowly and smoothly when it is about to reach the peak. Among them, a / b is characterized by the length ratio in the shear direction.

[0168] As shown in Table 3, from the perspective of the degree of influence on the shear stress-strain curve type, the anchorless discontinuous joint specimen is most significantly affected by the normal stress, which also conforms to the rule that it tends to be brittle fracture or sliding type when the normal force is low, and tends to be yield or shear type when the normal force is high. The influence of rock bridge shape and joint persistence is relatively complex. Generally speaking, it can be considered that with the increase of joint persistence, the probability of sliding type is increasing, and the probability of brittle fracture type is decreasing; with the change of rock bridge shape, when the length-to-width ratio a / b of the rock bridge is closer to 1, the probability of brittle fracture type is increasing, and the probability of sliding or yield type is decreasing.

[0169] Table 3 Influence of rock bridge shape and joint persistence on the shear stress-strain curve type of discontinuous jointed rock mass under anchorless condition

[0170]

[0171] Figure 6 They represent the rock bridge shapes (a / b), normal stress (σ n ) and other conditions. It can be found that as the axial length ratio (a / b) of the elliptical rock bridge in the shear direction increases, the shear peak strength (τ p ) have decreased to varying degrees. Therefore, the results show that the shape of the rock bridge has an important influence on the shear characteristics of non-connected joints. n ) increases, the shear peak strength (τ p ) increase approximately linearly. With the increase of joint connectivity (k), the shear peak strength (τ p ) decreased approximately linearly.

[0172] Comparative analysis of theoretical predictions and experimental results

[0173] like Figure 7 As shown in the figure, the theoretical prediction values ​​of each joint connectivity (k) can be calculated by substituting various parameters, and compared with the peak stress test results of samples with different rock bridge shapes, where the adjustment coefficient ξ j =0.8 and ω=0.9.

[0174] It can be found that: (a) when the normal pressure is small, the smaller the value of a / b is, the larger the peak stress is, and the difference becomes larger with the increase of confining pressure; (b) the original prediction results of the Jennings criterion are smaller under different joint connectivity, rock bridge morphology and normal stress, especially when the normal stress is large; (c) the prediction results of the improved and adjusted Jennings criterion are closer to the experimental results.

[0175] Figure 8 By comparing the calculated values ​​of Lajtai failure criterion with the peak stress experimental results of samples with different rock bridge shapes, we can find that: (a) the calculated results of Lajtai tensile and shear failure criteria are much smaller than the experimental values. The difference gradually increases with the increase of normal stress and decreases with the increase of joint connectivity; (b) the calculated results of Lajtai strength failure criterion are close to the experimental values, and become closer with the increase of joint connectivity. This shows that the fundamental reason for the final failure of the sample is the strength failure of the rock bridge.

[0176] Fig. 9By comparing the calculated values ​​of the improved Lajtai failure criterion with the peak stress experimental results of specimens with different rock bridge shapes, it can be found that: (a) the calculated results of the improved Lajtai tensile and shear failure criteria are closer to the experimental values. Relatively speaking, the shear failure criterion is more accurate when the normal stress is low, and the tensile failure criterion is more accurate when the normal stress is high; (b) the calculated results of the improved Lajtai strength failure criterion are slightly closer to the experimental values ​​at low normal stress, and as the normal stress increases, they exceed the experimental values ​​at all joint connectivity. Overall, the improved Lajtai failure criterion is closer to the experimental value, and the fundamental reason for the final failure of the specimen is the tensile and shear failure at the rock bridge, which is more in line with reality.

[0177] The above-described embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A method for constructing a shear constitutive model of a discontinuous structural surface, characterized in that: The steps include: Step S1: Different normal stresses σ n The peak strength τ in the shear stress-strain curve of the discontinuous structural surface during shear failure p and residual strength τ r By fitting respectively, according to the Mohr-Coulomb criterion, the peak and residual stage shear strength parameters can be obtained: cohesion c and internal friction angle Step S2, obtaining the initial rock mass shear strength τ of the discontinuous structural surface based on the Jennings criterion; Step S3: Introducing coefficient ξ j and r The normal stress at the joints and rock bridges is adjusted respectively, and the coefficient ω is introduced to adjust the cohesion of the rock bridge to obtain the shear strength τ of the rock mass at the discontinuous structural surface after adjustment; Step S4, obtaining the failure criteria of three types of discontinuous structural surfaces, namely tension, shear and strength failure, based on the Lajtai rock bridge failure theory; Step S5, obtaining the shear constitutive model of the discontinuous structural surface corresponding to the tension failure condition, the shear failure condition and the strength failure failure condition of the rock bridge.

2. The method for constructing a shear constitutive model of a discontinuous structural surface according to claim 1, characterized in that: The steps of step S2 include: Based on the Mohr-Coulomb strength criterion, the shear stress of the discontinuous structural surface is composed of the joint surface and the rock bridge, that is, the rock mass shear strength τ of the discontinuous structural surface is composed of the shear coefficient, cohesion c, and internal friction angle of the joint surface and the rock bridge. Use connectivity k as the coefficient for weighted calculation in, is the overall equivalent shear coefficient of the structural surface; c j , is the shear coefficient of the joints in the structural plane; c r , is the shear coefficient of the rock bridge in the structural plane.

3. The method for constructing a shear constitutive model of a discontinuous structural surface according to claim 2, characterized in that: The rock mass shear strength of the discontinuous structural surface in step S3 satisfies Among them, the coefficient ξ j and ω are both between 0 and 1, and the coefficient ξ j and r The relationship between them and the joint connectivity k is as follows:

4. The method for constructing a shear constitutive model of a discontinuous structural surface according to claim 3, characterized in that: The specific steps of step S4 are as follows: Based on the Lajtai rock bridge failure theory, the failure criteria of three discontinuous structural surfaces, namely tension, shear and strength failure, are obtained. The rock mass shear strength τ of the discontinuous structural surface is expressed in sections according to the normal stress value, and satisfies the following formulas in sequence: Tensile failure criterion: Shear failure criterion: Strength failure criterion: Where: C is the joint adjustment parameter, ranging from 0 to 1; σ t is the tensile strength of intact rock, MPa; c r is the cohesion of intact rock, MPa; is the internal friction angle of intact rock, °, is the internal friction angle of intact rock, °.

5. The method for constructing a shear constitutive model of a discontinuous structural surface according to claim 4, characterized in that: The steps of step S5 include: Mechanical analysis is performed at different locations of the rock bridge to obtain the normal stress σ of the micro-element a and the tangential stress τ a : t a =t s -kt j (3-12) Among them, τ j Characterized by the shear strength of the joint itself; Get the normal stress σ of the plane with an angle β to the horizontal direction β and the tangential stress τ β : The plane normal stress (σ β ) is derived with respect to angle β, that is: Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum stress and minimum stress σ1, σ3 on the principal stress plane: Among them, σ x Characterized as horizontally acting stress; If the rock bridge is initially tensilely damaged, the minimum principal stress is equal to the tensile strength of the rock material, that is: After calculation, the effective shear stress can be obtained: The shear constitutive model of the discontinuous structural surface under the condition of tension failure of the rock bridge is obtained as follows:

6. The method for constructing a shear constitutive model of a discontinuous structural surface according to claim 4, characterized in that: The steps of step S5 include: Mechanical analysis is performed at different locations of the rock bridge to obtain the normal stress σ of the micro-element a and the tangential stress τ a : t a =t s -kt j (3-12) Among them, τ j Characterized by the shear strength of the joint itself; Get the normal stress σ of the plane with an angle β to the horizontal direction β and the tangential stress τ β : The plane normal stress (σ β ) is derived with respect to angle β, that is: Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum stress and minimum stress σ1, σ3 on the principal stress plane: Among them, σ x Characterized as horizontally acting stress; If the initial strength failure of the rock bridge occurs, the maximum principal stress is equal to the compressive strength of the rock material, that is: After calculation, the effective shear stress can be obtained: The shear constitutive model of the discontinuous structural surface under the condition of strength failure of the rock bridge is obtained as follows:

7. The method for constructing a shear constitutive model of a discontinuous structural surface according to claim 4, characterized in that: The steps of step S5 include: Mechanical analysis is performed at different locations of the rock bridge to obtain the normal stress σ of the micro-element a and the tangential stress τ a : t a =t s -kt j (3-12) Among them, τ j Characterized by the shear strength of the joint itself; Get the normal stress σ of the plane with an angle β to the horizontal direction β and the tangential stress τ β : The plane normal stress (σ β ) is derived with respect to angle β, that is: Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum stress and minimum stress σ1, σ3 on the principal stress plane: Among them, σ x Characterized as horizontally acting stress; When shear failure occurs in a rock bridge, according to the Coulomb-Navier shear criterion, the effective shear stress Derivation Available In addition, the shear stress τ β and normal stress σ β According to the Mohr-Coulomb strength criterion, substituting equations 3-8 and 3-9 into equation 3-25, the shear stress of the rock bridge during shear failure can be obtained: The shear constitutive model of the discontinuous structural surface under the condition of shear failure of the rock bridge is obtained as follows:

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