A method for establishing a constitutive model of maximum dilatancy of rock mass joints considering joint material and geometric characteristics

Abstract

The present invention discloses a method for establishing a constitutive model of the maximum dilatancy of rock joints taking into account the material and geometric characteristics of the joints, which is applicable to the fields of geotechnical engineering, geothermal development, energy extraction, and carbon dioxide geological storage technology. The present invention comprises the following steps: S1, obtaining the geometric maximum dilatancy of the joints of the rock sample by three-dimensional scanning, and obtaining the uniaxial compressive strength of the rock by a uniaxial compression test; S2, conducting a shear test on the sample to obtain the maximum dilatancy of the sample. The theoretical model established by the present invention effectively reveals the complex interaction of the material properties of the joint surface, the morphological characteristics of the joint surface, and the magnitude of the applied normal stress on the maximum dilatancy, especially the important influence of the ductility and brittleness of the rock joint surface material on the behavior of the micro-convex body on the joint surface. Specifically, the ductility and brittleness characteristics of the joint surface material determine its ability to store elastic energy and absorb plastic energy, which directly controls the deformation and damage process of the micro-convex body when subjected to force.

Description

Technical Field

[0001] The invention is applicable to the fields of geotechnical engineering, geothermal development, energy extraction, carbon dioxide geological storage, etc., and can be used for rock self-support technology for enhancing permeability by hydraulic shearing. Background Art

[0002] At present, hydraulic shearing (a method of increasing rock joint permeability based on shear expansion) has been widely recognized and used in geological carbon fixation, redevelopment of unconventional oil reservoirs, and geothermal reservoir enhancement. Especially for high-temperature and high-pressure enhanced geothermal systems, the permeability enhanced by hydraulic shearing through shear expansion can be permanently maintained through the self-support of the rock mass, which is more reliable than traditional proppants.

[0003] Hydraulic shear is the increase in joint fissure opening and joint permeability caused by shear expansion (increase in vertical shear displacement between joint surfaces, hereinafter referred to as "shear expansion") caused by micro-convexities on the joint wall when the rock mass slides relatively along the joint surface. Correctly describing the shear expansion behavior of rock joints is the theoretical basis for understanding hydraulic shear and promoting the development of the geothermal energy industry.

[0004] At present, the description of the dilatancy behavior of rock masses mainly focuses on the constitutive models of various peak dilatancy angles. However, other characteristics of dilatancy behavior, such as the kinematic dilatancy angle, the maximum dilatancy and the overall trend of the dilatancy curve, are relatively less studied. In particular, the physical mechanism of how the surface morphology of joints and the material properties of joints determine their dilatancy under different confining pressure conditions (especially normal stress) has not been clarified. The lack of corresponding constitutive models makes it impossible to clearly describe the shear expansion of rock joints, which is not conducive to the optimization of hydraulic shear parameters.

[0005] In view of this, the present invention is proposed. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for establishing a constitutive model of the maximum dilatancy of rock joints taking into account the material and geometric characteristics of the joints, thereby solving the problems raised in the above-mentioned background technology.

[0007] In order to solve the above technical problems, the basic concept of the technical solution adopted by the present invention is:

[0008] A method for establishing a maximum dilatancy constitutive model of rock mass joints considering joint material and geometric characteristics comprises the following steps:

[0009] S1. Obtain the geometric maximum dilatancy of the rock sample joints through three-dimensional scanning, and obtain the uniaxial compressive strength of the rock through uniaxial compression test;

[0010] S2. Carry out shear test on the sample to obtain the maximum shear dilatancy of the sample;

[0011] S3, setting different normal stress levels in the shear test to simulate different geological stress conditions, and adjusting the normal load while keeping the shear load unchanged, and defining the dilatancy suppression rate by the geometric maximum dilatancy and the maximum dilatancy obtained in steps S1-S2;

[0012] S4. Based on tribological theory or material theory, with the surface morphology of joints as the basic parameters, the material properties of joints as the key parameters, the normalized normal stress as the independent variable, and the dilatancy suppression rate as the characterization, a constitutive model of the maximum dilatancy of joints is established.

[0013] Optionally, the normal stress σ applied in step S4 is defined as n is the independent variable, in σ n The maximum dilatancy that can be measured in shear under action is the dependent variable, and the dilatancy under zero normal stress is the geometric maximum dilatancy The maximum dilatancy of the joint under high stress conditions is the maximum dilatancy of the base

[0014] The dilatancy behavior is affected by σ n The strong influence of n increases, the shear strength increases, the compression increases, and the shear expansion effect is suppressed. n The bigger, relatively The smaller the geometric maximum dilatancy is, the smaller the n The impact is suppressed.

[0015] Optionally, step S4 is represented by spring compression and , then the geometric maximum dilatancy is is n The length of the spring in its initial state when it is zero; the normalized applied normal stress is the pressure, and the length of the spring under this pressure is the maximum shear expansion that can be measured The solid length of the spring under full compression is the maximum dilatancy of the base.

[0016] In order to quantify σ n right The degree of influence is the geometric maximum dilatancy when the normal stress is zero. As a benchmark, define and The ratio indicates the normal stress σ n Influence of dilatancy restraint ratio

[0017] The value range is 0 to 1. Represents σ n = 0, dilatancy is not suppressed. Represents σ n → ucs When , dilatancy is completely suppressed. That is, the dilatancy restrained model is obtained.

[0018] Optionally, a method for deriving a maximum dilatancy constitutive model using tribological theory includes the following steps:

[0019] The negative exponential decay model used in tribology to describe the deformation and damage of rough surfaces is used to describe the shear dilatancy inhibition rate. Among them, the attenuation index and the material characteristic parameter C of the joint wall m (ductile and brittle characteristics of the material) and the applied normal stress σ n (The uniaxial compressive strength of the joint wall material σ ucs The shear dilatancy suppression rate can be expressed as:

[0020]

[0021] In rock mechanics, large-scale bulges of certain wavelengths on rough joint surfaces only lead to dilatation without causing damage. Therefore, the maximum dilatation of the base is represents the influence of these bumps, since they are not subject to negative exponential decay components The influence of , formula (1) can be transformed into:

[0022]

[0023] This formula is the mathematical expression of the maximum dilatancy constitutive model based on tribology theory. According to this formula,

[0024] Optionally, based on the maximum dilatancy constitutive model of tribological theory, when stress cannot be applied, there is no contact damage to the micro-asperities, the measured maximum dilatancy is equal to the geometric maximum dilatancy, and when high normal stress is applied, all micro-asperities are deformed / damaged, leaving only indestructible protrusions of a specific wavelength, and the maximum dilatancy is equal to the maximum dilatancy of the substrate.

[0025] Optionally, the logic of deriving the dilatancy constitutive model based on materials theory is:

[0026] Based on the shear dilatancy restraint model represented by spring compression, according to Hooke's law, the applied pressure Dilatancy Restraint There is a linear correlation between them;

[0027] However, considering the brittle-ductile transition of deep rock, in this model, the relationship between the two is non-linear elastic, but includes shear dilatancy suppression caused by elastic deformation, plastic deformation and contact micro-asperity damage;

[0028] Therefore, the definition of pressure Dilatancy Restraint The coefficients between are functions Right now:

[0029]

[0030] In the formula, is the material constant of the joint wall, σ LN is the normal stress when the material dilatancy inhibition rate transitions from linear elastic deformation to nonlinear deformation. is linear elastic, i.e. the dilatancy suppression is contributed by the elastic deformation of the contact bulge;

[0031] on the contrary but is nonlinear, indicating that the dilatancy suppression is contributed by the elastic deformation, plastic deformation and damage of the contact bulge.

[0032] Optionally, the dilatancy suppression in step S4 also has a critical stress threshold, exceeding which the maximum dilatancy is equal to the maximum dilatancy of the base The only remaining dilatancy is provided by the indestructible corrugated protrusions;

[0033] Material parameters of joint wall can be used to represent the threshold, where σ NR is the normal stress at the turning point when the material dilatancy suppression rate changes from nonlinear to close to the base;

[0034] When the normal stress σ n Close to σ NR When the maximum dilatancy Close to the maximum dilatancy of the base Then formula (3) can be transformed into:

[0035]

[0036] In the formula, F R It is a constant after unit conversion.

[0037] By dividing formula (3) by formula (4), we can get:

[0038]

[0039] In the formula, and The simultaneous appearance of σ ucsThe normalization factor has physical significance and cannot be eliminated. Formula (5) can be transformed into:

[0040]

[0041] To obtain the maximum measured dilatancy Transform equation (6) as follows:

[0042]

[0043] Then the formula can be reorganized as:

[0044]

[0045] The independent variable in this equation is the normalized applied normal stress Coefficient term can be unified into a new coefficient function include Dilatancy Restraint Relationship function and the joint wall material constant Therefore, formula (8) can be expressed as:

[0046]

[0047] Using Taylor series expansion e -x , when x is very small, it can be approximated to (1-x); considering the independent variable in formula (9) Small, therefore, Considered to be Therefore, formula (9) can be modified as follows:

[0048]

[0049] Comparing equation (10) with equation (2), it can be seen that the two expressions are the same, which proves that the theoretical derivation formula based on Hooke's law in materials science is consistent with the maximum dilatancy model (equation (2)) derived based on tribology theory.

[0050] Optionally, in formula (10) C m is a material parameter related to the ductility and brittleness of the joint wall material, which controls the transition of dilatancy suppression from linear to nonlinear. The influence of the geometric maximum dilatancy is divided by both sides of formula (10) but:

[0051]

[0052] In the formula, It is named as the base dilatancy suppression rate, and equation (11) is the maximum dilatancy constitutive model of the present invention.

[0053] Optionally, the present application uses shear testing of gypsum cement and rubber with ductile characteristics.

[0054] After adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art. Of course, any product implementing the present invention does not necessarily need to achieve all the advantages described below at the same time:

[0055] The theoretical model established by the present invention effectively reveals the important influence of the ductility and brittleness of the rock joint surface material on the behavior of the micro-asperities on the joint surface. Specifically, the ductility and brittleness characteristics of the joint surface material determine its elastic energy storage and plastic energy absorption capabilities, which directly controls the deformation and damage process of the micro-asperities when subjected to stress.

[0056] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings described below are only some embodiments. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0058] Figure 1 Schematic diagram of dilatancy behavior and its strengthening effect on joint permeability;

[0059] Figure 2 is a schematic diagram of characteristic dilatancy;

[0060] Figure 3 Schematic diagram of the dilatancy suppression model;

[0061] Figure 4 It is a schematic diagram of the maximum dilatancy constitutive model curve;

[0062] Figure 5 The schematic diagram of the model validation using experimental data of brittle cement gypsum samples;

[0063] Figure 6 Schematic diagram of dilatancy curve of joints of ductile material sample;

[0064] Figure 7 Validation of the model with experimental data of ductile material samples;

[0065] Figure 8 For different C m The curve shape of the constitutive model with maximum expansion under the value.

[0066] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but are intended to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0067] The present invention will now be described in further detail with reference to the accompanying drawings.

[0068] See also Figure 1-8 As shown, in this embodiment, a method for establishing a maximum dilatancy constitutive model of rock joints considering joint materials and geometric characteristics is provided, comprising the following steps:

[0069] S1. Obtain the geometric maximum dilatancy of the rock sample joints through three-dimensional scanning, and obtain the uniaxial compressive strength of the rock through uniaxial compression test;

[0070] S2. Carry out shear test on the sample to obtain the maximum shear dilatancy of the sample;

[0071] S3, setting different normal stress levels in the shear test to simulate different geological stress conditions, and adjusting the normal load while keeping the shear load unchanged, and defining the dilatancy suppression rate by the geometric maximum dilatancy and the maximum dilatancy obtained in steps S1-S2;

[0072] S4. Based on tribological theory or material theory, with the surface morphology of joints as the basic parameters, the material properties of joints as the key parameters, the normalized normal stress as the independent variable, and the dilatancy suppression rate as the characterization, a constitutive model of the maximum dilatancy of joints is established.

[0073] In this embodiment, the normal stress σ applied in step S4 is defined as n is the independent variable, in σ n The maximum dilatancy that can be measured in shear under action is the dependent variable, and the dilatancy under zero normal stress is the geometric maximum dilatancy The maximum dilatancy of the joint under high stress conditions is the maximum dilatancy of the base

[0074] The dilatancy behavior is affected by σ n The strong influence of n increases, the shear strength increases, the compression increases, and the shear expansion effect is suppressed. n The bigger, relatively The smaller the geometric maximum dilatancy is, the smaller the n The impact is suppressed.

[0075] In this embodiment, step S4 is represented by spring compression. and , then the geometric maximum dilatancy is is n The length of the spring in its initial state when it is zero; the normalized applied normal stress is the pressure, and the length of the spring under this pressure is the maximum shear expansion that can be measured The solid length of the spring under full compression is the maximum dilatancy of the base.

[0076] In order to quantify σ n right The degree of influence is the geometric maximum dilatancy when the normal stress is zero. As a benchmark, define and The ratio indicates the normal stress σ n Influence of dilatancy restraint ratio

[0077] The value range is 0 to 1. Represents σ n = 0, dilatancy is not suppressed. Represents σ n → ucs When , dilatancy is completely suppressed. That is, the dilatancy restrained model is obtained.

[0078] This application is based on the definition of dilatancy suppression rate, due to the geometric maximum dilatancy It is determined based on the surface morphology of the joints, and research on its determination method has been seen.

[0079] Therefore, the present invention simplifies the problem of quantifying the dilatancy inhibition rate to specifically studying the material properties of the joints and the influence of the normal stress thereon.

[0080] For a pair of contacting micro-convex bodies on a rough joint surface, when the local contact stress is less than the yield strength of the material, sliding occurs along the convex body, and shear expansion increases; when the local contact stress is greater than the yield strength of the material, the convex body is deformed or damaged, and the shear expansion is suppressed ( Figure 3 ), the dilatancy inhibition rate can indicate the joint deformation and damage under different normal stresses. For any moment, the size of the dilatancy increment is determined by the size of all contact asperities at that moment, and the accumulated dilatancy inhibition during the shear process can be obtained by integrating the dilatancy inhibition at each moment during the entire shear process. Therefore, from a mechanical point of view, the dilatancy inhibition rate The quantification problem is a time-space function that is closely related to the strength and deformation characteristics of the rock joint contact micro-asperity material.

[0081] Therefore, the magnitude of the dilatancy inhibition rate is closely related to the energy change accompanying the damage and deformation of the joint asperities during the shear process. The contact asperities during the joint shear process undergo sliding along the asperities, elastic deformation, plastic deformation, and asperity damage, and elastic energy, plastic energy, and thermal energy are generated in this process. Whether a pair of contact asperities tend to slide along the asperities or deform and damage depends on the energy required to overcome the basic friction resistance along the contact interface and the energy required to deform and damage the asperities. If the work done by the contact force acting on the rough asperities reaches the energy required to overcome the basic friction resistance of the contact interface, sliding along the asperities will occur, and dilatancy inhibition will not occur. At this time, the work done by the contact force will be dissipated in the form of frictional heat, and the energy will be converted from mechanical energy to thermal energy. If the work done by the contact force does not reach the energy required to overcome the friction resistance, deformation and damage of the asperities will occur, resulting in dilatancy inhibition. At this time, the work done by the contact force will either be stored in the deformed rough asperities as reversible elastic energy, or absorbed by the deformed / damaged asperities as irreversible dissipated plastic energy.

[0082] As the confining pressure increases in deep rocks, their mechanical properties change from brittle to ductile. The ductility and brittleness of joint materials significantly affect the ability of joint surface micro-asperities to store elastic energy and absorb plastic energy, and play a crucial role in the quantification of shear dilatancy suppression.

[0083] In this embodiment, the derivation method of the maximum dilatancy constitutive model using tribology theory includes the following steps:

[0084] The negative exponential decay model used in tribology to describe the deformation and damage of rough surfaces is used to describe the shear dilatancy inhibition rate. Among them, the attenuation index and the material characteristic parameter C of the joint wall m (ductile and brittle characteristics of the material) and the applied normal stress σ n (The uniaxial compressive strength of the joint wall material σ ucs The shear dilatancy suppression rate can be expressed as:

[0085]

[0086] In rock mechanics, large-scale bulges of certain wavelengths on rough joint surfaces only lead to dilatation without causing damage. Therefore, the maximum dilatation of the base is represents the influence of these bumps, since they are not subject to negative exponential decay components The influence of , formula (1) can be transformed into:

[0087]

[0088] This formula is the mathematical expression of the maximum dilatancy constitutive model based on tribology theory. According to this formula,

[0089] In this embodiment, the maximum dilatancy constitutive model based on tribological theory has no contact damage to the micro-asperities when stress cannot be applied, and the measured maximum dilatancy is equal to the geometric maximum dilatancy. When high normal stress is applied, all micro-asperities are deformed / damaged, leaving only indestructible protrusions of a specific wavelength, and the maximum measured dilatancy is equal to the maximum dilatancy of the substrate.

[0090] In this embodiment, the logic of deriving the dilatancy constitutive model based on material theory is:

[0091] Based on the shear dilatancy restraint model represented by spring compression, according to Hooke's law, the applied pressure Dilatancy Restraint There is a linear correlation between them;

[0092] However, considering the brittle-ductile transition of deep rock, in this model, the relationship between the two is non-linear elastic, but includes shear dilatancy suppression caused by elastic deformation, plastic deformation and contact micro-asperity damage;

[0093] Therefore, the definition of pressure Dilatancy Restraint The coefficients between are functions Right now:

[0094]

[0095] In the formula, is the material constant of the joint wall, σ LN is the normal stress when the material dilatancy inhibition rate transitions from linear elastic deformation to nonlinear deformation. is linear elastic, i.e. the dilatancy suppression is contributed by the elastic deformation of the contact bulge;

[0096] on the contrary but is nonlinear, indicating that the dilatancy suppression is contributed by the elastic deformation, plastic deformation and damage of the contact bulge.

[0097] In this embodiment, the dilatancy suppression in step S4 also has a critical stress threshold. When this threshold is exceeded, the maximum dilatancy is equal to the maximum dilatancy of the base The only remaining dilatancy is provided by the indestructible corrugated protrusions;

[0098] Material parameters of joint wall can be used to represent the threshold, where σ NR is the normal stress at the turning point when the material dilatancy suppression rate changes from nonlinear to close to the base;

[0099] When the normal stress σ n Close to σNR When the maximum dilatancy Close to the maximum dilatancy of the base Then formula (3) can be transformed into:

[0100]

[0101] In the formula, F R is a constant after unit conversion.

[0102] By dividing formula (3) by formula (4), we can get:

[0103]

[0104] In the formula, and The simultaneous appearance of σ ucs The normalization factor has physical significance and cannot be eliminated. Formula (5) can be transformed into:

[0105]

[0106] To obtain the maximum dilatancy Transform equation (6) as follows:

[0107]

[0108] Then the formula can be reorganized as:

[0109]

[0110] The independent variable in this equation is the normalized applied normal stress Coefficient term can be unified into a new coefficient function include Dilatancy Restraint Relationship function and the joint wall material constant Therefore, formula (8) can be expressed as:

[0111]

[0112] Using Taylor series expansion ex, when x is very small, it can be approximated to (1-x); considering the independent variable in formula (9) Small, therefore, Considered to be

[0113] Therefore, formula (9) can be modified as follows:

[0114]

[0115] Comparing equation (10) with equation (2), it can be seen that the two expressions are the same, which proves that the theoretical derivation formula based on Hooke's law in materials science is consistent with the maximum dilatancy model (equation (2)) derived based on tribology theory.

[0116] In this embodiment, in formula (10) C m is a material parameter related to the ductility and brittleness of the joint wall material, which controls the transition of dilatancy suppression from linear to nonlinear. The influence of the geometric maximum dilatancy is divided by both sides of formula (10) but:

[0117]

[0118] In the formula, Named as the base dilatancy suppression rate, equation (11) is the maximum dilatancy constitutive model of the present invention. The visualization curve of the model is described as follows: Figure 4 As shown, the material constants of the two joint walls are and All included in C m In the figure, two key transition points are shown on the curve.

[0119] Figure 4 middle, It is the turning point from linear to nonlinear (LN) of the material, marking the transition of the dilatancy suppression rate from linear elastic deformation to nonlinear deformation. This is the transition threshold of dilatancy suppression. Beyond this threshold, the plastic deformation and damage of the contact micro-convex body will begin to dominate. The LN transition point divides the elastic region and transition region of the constitutive model curve. Under the action of normal stress, if it is in the elastic region The contact asperities only undergo elastic deformation, and the work done by the contact force is stored in the deformed asperities in the form of reversible elastic energy. When all dilatancy restraint occurs, the work done by the contact forces is either stored in the deformed protrusion as reversible elastic energy or absorbed by the deformed / damaged protrusion as irreversible dissipative plastic energy. The greater the material ductility of the joint wall, the larger the transition zone. The transition zone and the base zone are divided to indicate the turning point of the dilatancy suppression rate from nonlinear to base-approaching (NR). All micro-protrusions on the rock mass joint surface are destroyed, leaving only "indestructible" protrusions of a specific wavelength. The resulting base dilatancy makes the dilatancy suppression rate The value is equal to the base dilatancy inhibition rate

[0120] Experimental example

[0121] Gypsum cement with brittle characteristics and rubber with ductile characteristics were used to cast six geometric joints in a mold and subjected to a constant normal load σ n The proposed constitutive model was verified by shear tests under 3000 spherical surfaces. Among them, 10 shear tests were carried out on gypsum cement material samples based on 5 groups of surface morphologies of limestone and granite joints. For rubber materials, due to the ductility of the material, the stress (normalized by There is no linear relationship between the shear expansion and the shear dilatancy, and the overall structure presents nonlinear characteristics. Therefore, only one group of joint forms used in gypsum cement material was used to carry out shear tests for verification.

[0122] (1) The experimental data of gypsum cement samples are shown in Table 1 and are in good agreement with the constitutive model ( Figure 5 , fitting degree 0.9628), its C m The value is 95.15, the base dilatancy inhibition rate It is 0.1534, and the linear-nonlinear transition point (LN) is located close to the vertical axis, which indicates that for gypsum cement materials, the elastic region is limited, which is consistent with the material properties.

[0123] Table 1.Lab test data of gypsum cement jointrepl icas

[0124]

[0125] (2) For the American Smooth-CastTM 310 ductile rubber material (σ ucs =26MPa) were subjected to direct shear tests (6 groups, Table 2, Figure 6 ), the experimental results are in good agreement with the constitutive model ( Figure 7 , goodness of fit 0.9931).

[0126] Table 2 Experimental data of rubber ductility samples

[0127] Table 2.Lab test data of plastic joint replicas

[0128]

[0129] Depend on Figure 6 It can be seen that when joints with the same surface morphology and material are sheared under different normal stresses, the overall trend of the shear expansion curve is similar, the curve smoothness is slightly different, but the overall height and upper limit are different.

[0130] Verification based on replica laboratory data of ductile rubber materials such as Figure 7 shown.

[0131] Depend on Figure 7 It can be seen that the experimental data of the joints made of plastic materials are very consistent with the constitutive model. Compared with gypsum cement materials, their ductility is much more significant. The fitting curve of the plastic material has a very wide transition zone, no obvious LN and NR transition points are observed, and the curve shape is obtuse, which is very different from gypsum cement materials. m The value is 15, the base dilatancy inhibition rate It is 0.3964.

[0132] (3) Material characteristic parameter C m Influence on the shape of dilatancy curve

[0133] According to the above results, it can be seen that the material properties of rock joints have a significant effect on shear dilatancy. C The sensitivity of m value is to assign constants to the other variables in the constitutive model (11) and give different C m value, the shear dilatancy curve is as follows Figure 8 .

[0134] For an ideal ductile material, C The m value is extremely low, and the shape of the constitutive model is close to Figure 8 (a), the transition points of linear-nonlinear (LN) and nonlinear-basal (NR) are located at the two ends of the obtuse curve, which means that the entire curve can be regarded as a transition zone without elastic and basal zones. The results are consistent with the content of materials science: if the joint surface is made of ideal ductile material, no matter under low or high normal stress, the micro-asperities only undergo plastic deformation during shearing, and the work done by the contact force is absorbed by the irreversible plastic deformation of the joint micro-asperities.

[0135] For an ideal brittle material, C The m value is very high, and the constitutive model curve is two straight lines intersecting at one point (approximately Figure 8 (d)). At this time, the LN transition point and the NR transition point overlap at the same position, indicating that the base region appears after the linear elastic region and there is no transition region. That is, no plastic deformation occurs under low or high normal stress.

[0136] For a common brittle material, rock C The m value is close to but higher than the ideal brittle material constitutive model. Figure 8 (c) A transition zone exists, but it is extremely limited.

[0137] It can be seen that the material CThe lower the m value, the stronger the ductility of the material, the larger its transition zone, and the smoother the curve shape.

[0138] Joint material C The higher the m value, the weaker the brittleness of the material, the weaker the material's ability to absorb plasticity, and the more limited the transition zone of the shear dilatancy curve during joint shear. C As the value of m increases, the two turning points of the model curve ( Figure 8 (a) with Figure 8 (b)) to only one connection point ( Figure 8 (d)), the positions of the LN transition point and the NR transition point will be closer. At the same time, the transition zone changes from occupying the entire model curve ( Figure 8 (a), very slow transition) to no transition ( Figure 8 (d), the transition is extremely abrupt), and the transition zone is decreasing.

[0139] Figure 5 and Figure 7 The morphological characteristics of the dilatancy curves of rocks with brittle and ductile material characteristics under different normal stresses are reflected respectively, thus effectively discussing the joint surface material (parameter C m ), joint surface morphology (parameters ) and the applied normal stress (parameter ) jointly affect the maximum dilatancy of rock joints. The derived quantitative description of the maximum dilatancy of rock joints effectively characterizes the complex interaction of joint surface material properties, joint surface morphology and applied normal stress on the maximum dilatancy. The experimental data verification shows the effectiveness of the model. C The influence of the m value on the dilatancy curve is consistent with the brittle-ductile characteristics of the material. The value of each type of rock can be obtained through experiments in the later stage, achieving the expected design goal of quantifying the dilatancy during rock shearing.

[0140] In this model, the brittle material makes the micro-asperities on the joint surface more prone to fragmentation and damage, showing low elastic energy storage and high plastic energy absorption; on the contrary, the ductile material enhances the elastic energy storage capacity of the micro-asperities and slows down the plastic deformation, thus maintaining a large deformation and not easily damaged during the shear process. The interaction between this material property and the micro-asperities significantly affects the response characteristics of the rock joint surface under different load conditions, especially the dilatancy behavior under shear load.

[0141] Introducing the parameter C that characterizes the properties of the joint material m The shape of the constitutive model curve of the maximum shear dilatancy of the joint is very different due to different values. In the process of geothermal development, the deep rock is affected by the material, stress and temperature, and the ductility or brittleness of the material changes significantly. mIt can characterize the brittleness and ductility characteristics of rock materials, C m The value of is between the ideal ductile material and the ideal brittle material (1-1000), and the dilatancy constitutive curve is Figure 8 Between (a) and (d), the dilatancy curve of the brittle material is Figure 8 (b) Approximately, there are elastic zone, transition zone and basement zone. The greater the ductility of the rock material, the wider its transition zone and the smoother the curve shape.

[0142] This application is based on the intrinsic properties of the joints (joint surface morphology characteristics and joint material properties C m ) as a parameter, with external conditions (the magnitude of the applied normal stress ) as independent variables, based on tribology and materials science, the constitutive model formula (11) of the maximum dilatancy that can be measured under different normal stress conditions considering the geometric morphology and material properties of rock joints is established. This model can correctly and quantitatively describe the maximum dilatancy of rock joints.

[0143] In the existing description of the shear dilatancy behavior of rock joints, there is a lack of effective discussion on how the joint surface material, joint surface morphology and applied normal stress jointly affect the maximum dilatancy of rock joints. Therefore, a quantitative description of the maximum dilatancy of rock joints is derived, and the complex interaction of the joint surface material properties, joint surface morphology characteristics and the magnitude of the applied normal stress on the maximum dilatancy is explained. It mainly includes: simplifying the complexity of this interaction from the perspective of energy conversion and achieving quantitative description; based on materials science and tribology theory, a constitutive model of the maximum dilatancy considering the above three factors is established; and the validity of the constitutive model is verified based on experimental data.

[0144] The structural changes made below the illustrations, all the same or similar technical solutions as the present invention, all fall within the protection scope of the present invention. The technology, shape, and structure parts not described in detail in the present invention are all well-known technologies.

Claims

1. A method for establishing a constitutive model of maximum dilatancy of rock mass joints taking into account joint material and geometric characteristics, characterized in that: The following steps are involved: S1. Obtain the geometric maximum dilatancy of the rock sample joints through three-dimensional scanning, and obtain the uniaxial compressive strength of the rock through uniaxial compression test; S2. Carry out shear test on the sample to obtain the maximum shear dilatancy of the sample; S3, setting different normal stress levels in the shear test to simulate different geological stress conditions, and adjusting the normal load while keeping the shear load unchanged, and defining the dilatancy suppression rate by the geometric maximum dilatancy and the maximum dilatancy obtained in steps S1-S2; S4. Based on the tribological theory or material theory, with the surface morphology of the joint as the basic parameter, the material properties of the joint as the key parameter, the normalized normal stress as the independent variable, and the dilatancy suppression rate as the characterization, a constitutive model of the maximum dilatancy of the joint is established; The derivation method of the maximum dilatancy constitutive model using tribological theory includes the following steps: The negative exponential decay model used in tribology to describe the deformation and damage of rough surfaces is used to describe the dilatancy suppression rate. Among them, the attenuation index and the material characteristic parameter C of the joint wall m and the applied normal stress σ n The dilatancy suppression rate can be expressed as: In rock mechanics, certain specific wavelength protrusions on rough joint surfaces only cause shear expansion without damage under high stress conditions. Therefore, the maximum shear expansion of the base is represents the influence of these bumps, since they are not subject to negative exponential decay components The influence of , formula (1) can be transformed into: This formula is the mathematical expression of the maximum dilatancy constitutive model based on tribology theory. According to this formula, in, is the maximum dilatancy, is the geometric maximum dilatancy; The logic of deriving the dilatancy constitutive model based on materials theory is as follows: Based on the shear dilatancy restraint model represented by spring compression, according to Hooke's law, the applied pressure Dilatancy Restraint There is a linear correlation between them; However, considering the brittle-ductile transition of deep rock, in this model, the relationship between the two is nonlinear elastic, but includes elastic deformation, plastic deformation and shear dilatancy suppression caused by contact micro-asperity damage; Therefore, the definition of pressure Dilatancy Restraint The coefficients between are functions Right now: In the formula, is the material constant of the joint wall, σ LN is the normal stress when the material dilatancy inhibition rate transitions from linear elastic deformation to nonlinear deformation. is linear elastic, i.e. the dilatancy suppression is contributed by the elastic deformation of the contact bulge; on the contrary but is nonlinear, indicating that the dilatancy suppression is contributed by the elastic deformation, plastic deformation and damage of the contact bulge.

2. The method for establishing a constitutive model of maximum dilatancy of rock mass joints taking into account joint material and geometric characteristics according to claim 1, characterized in that: The normal stress σ applied in step S4 is defined as n is the independent variable, in σ n The maximum dilatancy that can be measured in shear under action is the dependent variable, and the dilatancy under zero normal stress is the geometric maximum dilatancy The maximum dilatancy under high stress conditions is the maximum dilatancy of the base The dilatancy behavior is affected by σ n The strong influence of n increases, the shear strength is improved, the compression amount is increased, and the shear expansion effect is suppressed. Therefore, σ n The bigger, relatively The smaller the geometric maximum dilatancy is, the smaller the n The impact is suppressed.

3. The method for establishing a maximum dilatancy constitutive model of rock mass joints taking into account joint material and geometric characteristics according to claim 2, characterized in that: Step S4 is represented by spring compression and , then the geometric maximum dilatancy is is n The length of the spring in its initial state when it is zero; normalize the applied normal stress is the pressure, and the length of the spring under this pressure is the maximum shear expansion that can be measured is the geometric maximum dilatancy The solid length of the spring under full compression is the maximum dilatancy of the base. In order to quantify σ n right The degree of influence is the geometric maximum dilatancy when the normal stress is zero. As a benchmark, define and The ratio indicates the normal stress σ n Influence of dilatancy restraint ratio Among them, the normal stress σ n The uniaxial compressive strength of the joint wall material can be ucs Normalize; the value ranges from 0 to 1. Represents σ n = 0, dilatancy is not suppressed. Represents σ n → ucs When , dilatancy is completely suppressed. That is, the dilatancy restrained model is obtained.

4. The method for establishing a constitutive model of maximum dilatancy of rock mass joints taking into account joint material and geometric characteristics according to claim 1, characterized in that: The maximum dilatancy constitutive model based on tribological theory has no contact damage to the micro-asperities when stress cannot be applied, and the maximum measurable dilatancy is equal to the geometric maximum dilatancy. When high normal stress is applied, all micro-asperities are deformed / damaged, leaving only indestructible protrusions of a specific wavelength, and the maximum dilatancy is equal to the maximum dilatancy of the substrate.

5. The method for establishing a constitutive model of maximum dilatancy of rock mass joints taking into account joint material and geometric characteristics according to claim 1, characterized in that: The dilatancy suppression in step S4 also has a critical stress threshold, beyond which the maximum dilatancy is equal to the maximum dilatancy of the base Only the dilatancy provided by the protrusions of a specific wavelength that cannot be damaged remains; Material parameters of joint wall can be used to represent the threshold, where σ NR is the normal stress at the turning point when the material dilatancy suppression rate changes from nonlinear to close to the base; When the normal stress σ n Close to σ NR When the maximum dilatancy Close to the maximum dilatancy of the base Then formula (3) can be transformed into: In the formula, F R is a constant after unit conversion; By dividing formula (3) by formula (4), we can get: In the formula, and The simultaneous appearance of σ ucs The normalization factor has physical significance and cannot be eliminated. Formula (5) can be transformed into: To obtain the maximum dilatancy Transform equation (6) as follows: Then the formula can be reorganized as: The independent variable in this equation is the normalized applied normal stress Coefficient term can be unified into a new coefficient function include Dilatancy Restraint Relationship function and the joint wall material constant Therefore, formula (8) can be expressed as: Using Taylor series expansion e -x , when x is very small, it can be approximated to (1-x); considering the independent variable in formula (9) Small, therefore, Considered to be Therefore, formula (9) can be modified as follows: Comparing equation (10) and equation (2), it can be seen that the two expressions are the same, that is, it can be proved that the theoretical derivation formula obtained from Hooke's law in materials science is consistent with the maximum shear dilatancy model equation (2) derived based on tribology theory, where: is the maximum dilatancy, is the geometric maximum dilatancy, is the maximum dilatancy of the base, σ ucs is the uniaxial compressive strength, σ n is the normal stress.

6. A method for establishing a maximum dilatancy constitutive model of rock mass joints taking into account joint material and geometric characteristics according to claim 5, characterized in that: In formula (10), C m It is a material parameter related to the ductility and brittleness of the joint wall material, which controls the transition of dilatancy suppression from linear to nonlinear. In order to make it clearer about its effect on dilatancy suppression rate The influence of the geometric maximum dilatancy is divided by both sides of formula (10) but: In the formula, It is named as the base dilatancy suppression rate, and equation (11) is the maximum dilatancy constitutive model.

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