Method and device for determining Young modulus of rock mass based on anchor rod drawing experiment

Abstract

The invention discloses a rock mass Young modulus determination method and device based on an anchor rod drawing experiment, and the method comprises the steps: carrying out the anchor rod drawing experiment on a target area, and obtaining a corresponding drawing experiment result; determining a rock-soil body shear modulus formula; based on a rock-soil body shear modulus formula, a rock-soil body Young modulus formula is determined through the relation between the rock-soil body shear modulus and the elastic modulus; and determining the rock mass Young modulus of the target area based on a pull-out test result and a rock-soil mass Young modulus formula. The rock mass Young modulus of the target area is determined on the basis of the pull-out test result and the rock-soil body Young modulus formula, so that the Young modulus of the rock mass is inversed by introducing anchor rod pull-out test data, rapid and accurate measurement of the Young modulus of the rock mass is achieved, the experimental process is simplified, the cost is reduced, sample damage is reduced, and the method is suitable for large-scale popularization and application. The testing efficiency and the data accuracy are improved, and reliable support is brought to technical innovation and engineering practice in the field of rock mechanics testing.

Description

Technical Field

[0001] The present invention relates to the technical field of rock mechanics testing, and particularly to a method and device for determining the Young's modulus of rock mass based on bolt pull-out tests. Background Art

[0002] The testing of rock mechanical properties is of great significance in the field of geotechnical engineering. Among them, the Young's modulus of rock mass is one of the key parameters for evaluating rock mechanical properties and engineering behavior. At present, the methods for determining the Young's modulus of rock mass include ultrasonic testing, compression tests, and tensile tests, etc. Among them, the above methods can provide quantitative data for rock mechanical properties to a certain extent, but in practical engineering applications, the above methods are cumbersome to operate, resulting in low determination efficiency, high cost, and sample loss. Therefore, how to simply and efficiently determine the Young's modulus of rock mass is an urgent problem to be solved. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems in the related art to some extent.

[0004] To this end, an object of the present invention is to propose a method for determining the Young's modulus of rock mass based on bolt pull-out tests. The method determines the Young's modulus of the target area based on the pull-out test results and the Young's modulus formula of rock and soil mass, so that the Young's modulus of rock mass can be inversely calculated by introducing bolt pull-out test data, realizing the rapid and accurate determination of the Young's modulus of rock mass, simplifying the experimental process, reducing the cost, reducing sample damage, improving the test efficiency and data accuracy, and bringing technical innovation and reliable support for engineering practice to the field of rock mechanics testing.

[0005] Another object of the present invention is to propose a device for determining the Young's modulus of rock mass based on bolt pull-out tests.

[0006] To achieve the above object, an embodiment of one aspect of the present invention proposes a method for determining the Young's modulus of rock mass based on bolt pull-out tests, including: Conduct a bolt pull-out test on the target area and obtain the corresponding pull-out test results; Determine the shear modulus formula of rock and soil mass; Based on the shear modulus formula of rock and soil mass, determine the Young's modulus formula of rock and soil mass through the relationship between the shear modulus and elastic modulus of rock and soil mass; Based on the pull-out test results and the Young's modulus formula of rock and soil mass, determine the Young's modulus of the rock mass in the target area.

[0007] The method for determining the Young's modulus of rock mass based on bolt pull-out tests according to the embodiment of the present invention may further have the following additional technical features: Further, the determining the shear modulus formula of rock and soil mass includes: Determine the control equation of the anchor rod system; Determine the equilibrium relationship of the micro-elements of the grout body or the rock and soil mass; Determine the relationship between the shear stress and shear strain inside the rock and soil mass; Based on the control equation of the anchor rod system, the equilibrium relationship of the micro-elements of the grout body or the rock and soil mass, and the relationship between the shear stress and shear strain inside the rock and soil mass, determine the displacement formula of the anchor rod end; Based on the displacement formula of the anchor rod end, determine the shear modulus formula of the rock and soil mass.

[0008] Further, the step of determining the displacement formula of the anchor rod end based on the control equation of the anchor rod system, the equilibrium relationship of the micro-elements of the grout body or the rock and soil mass, and the relationship between the shear stress and shear strain inside the rock and soil mass includes: Based on the equilibrium relationship of the micro-elements of the grout body or the rock and soil mass and the relationship between the shear stress and shear strain inside the rock and soil mass, determine the first homogeneous linear differential equation of the rock and soil mass; Based on the first general solution of the displacement of the rock and soil mass of the first homogeneous linear differential equation, obtain the displacement formula of the rock and soil mass and the shear stress distribution formula inside the rock and soil mass; Based on the second general solution of the displacement of the grout body of the first homogeneous linear differential equation, obtain the displacement formula of the grout body and the shear stress distribution formula inside the grout body; At the interface between the grout body and the rock and soil mass, based on the shear stress distribution formula inside the rock and soil mass and the shear stress distribution formula inside the grout body, obtain the boundary relationship formula; Based on the shear stress distribution formula inside the grout body and the boundary relationship formula, determine the displacement formula of the anchor rod end.

[0009] Further, the step of determining the displacement formula of the anchor rod end based on the shear stress distribution formula inside the grout body and the boundary relationship formula includes: Based on the shear stress distribution formula inside the grout body and the boundary relationship formula, obtain the shear stress distribution formula at the interface between the anchor rod body and the grout body; Determine the linear relationship formula between the shear stress at the interface between the anchor rod body and the grout body and the shear stress at a point on the vertical axis of the anchor rod inside the anchor rod in the elastic state of the anchor rod body; Based on the shear stress distribution formula at the interface between the anchor rod body and the grout body, the linear relationship formula, and the control equation of the anchor rod system, determine the second homogeneous linear differential equation; Based on the general solution of the second homogeneous linear differential equation, obtain the axial displacement formula in the anchor rod body; Based on the axial displacement formula in the anchor rod body, determine the displacement formula of the anchor rod end.

[0010] Furthermore, the Young's modulus formula of the rock and soil mass includes:

[0011] Wherein, represents the Poisson's ratio of the rock and soil mass, P0 represents the stress, and G g represents the shear modulus of the anchor rod mortar, d0 represents the influence diameter of the anchor rod, and d h represents the borehole diameter, δ represents the displacement, d b represents the diameter of the anchor rod during the pull-out test, represents the elastic modulus of the anchor rod body, represents the Young's modulus of the rock and soil mass.

[0012] Furthermore, based on the pull-out test results and the Young's modulus formula of the rock and soil mass, determining the Young's modulus of the rock mass in the target area includes: Determining the stress and displacement based on the stress-displacement curve corresponding to the pull-out test results; Substituting the stress and the displacement into the Young's modulus formula of the rock and soil mass to determine the Young's modulus of the rock mass in the target area.

[0013] To achieve the above object, another embodiment of the present invention provides a device for determining the Young's modulus of a rock mass based on an anchor rod pull-out test. The device includes: An acquisition module, configured to perform an anchor rod pull-out test on a target area and acquire the corresponding pull-out test results; A first determination module, configured to determine the shear modulus formula of the rock and soil mass; A second determination module, configured to determine the Young's modulus formula of the rock and soil mass based on the shear modulus formula of the rock and soil mass through the relationship between the shear modulus and the elastic modulus of the rock and soil mass; A third determination module, configured to determine the Young's modulus of the rock mass in the target area based on the pull-out test results and the Young's modulus formula of the rock and soil mass.

[0014] The method and device for determining the Young's modulus of rock mass based on the bolt pull-out test proposed by the present invention include: conducting a bolt pull-out test on the target area and obtaining the corresponding pull-out test results; determining the formula for the shear modulus of rock and soil; based on the formula for the shear modulus of rock and soil, determining the formula for the Young's modulus of rock and soil through the relationship between the shear modulus and the elastic modulus of rock and soil; and determining the Young's modulus of the rock mass in the target area based on the pull-out test results and the formula for the Young's modulus of rock and soil. The present invention determines the Young's modulus of the rock mass in the target area based on the pull-out test results and the formula for the Young's modulus of rock and soil, so that the Young's modulus of the rock mass can be inversely calculated by introducing the bolt pull-out test data, realizing the rapid and accurate determination of the Young's modulus of the rock mass, simplifying the experimental process, reducing the cost and sample damage, improving the test efficiency and data accuracy, and bringing technical innovation and reliable support for engineering practice to the field of rock mechanics testing.

[0015] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present invention. Description of the Drawings

[0016] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of the embodiments in conjunction with the drawings, in which: Figure 1 It is a flowchart of the method for determining the Young's modulus of rock mass based on the bolt pull-out test according to an embodiment of the present invention; Figure 2 It is a schematic diagram of the stress and deformation field of the anchoring system in the fully bonded state according to an embodiment of the present invention; Figure 3 It is a schematic diagram of the stress-displacement curve according to an embodiment of the present invention; Figure 4 It is a schematic structural diagram of the device for determining the Young's modulus of rock mass based on the bolt pull-out test according to an embodiment of the present invention. Detailed Description of the Embodiments

[0017] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals denote the same or similar elements or elements with the same or similar functions throughout. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0018] With the continuous development of the geotechnical engineering field, the anchor pull-out test, as a commonly used means for detecting the construction quality of underground engineering, has gradually attracted attention. In the anchor pull-out test, the anchor is subjected to the restraint force of the rock mass, and the mechanical properties of the rock mass are evaluated by measuring the tension and deformation of the anchor. Inverting the Young's modulus of the rock mass based on the anchor pull-out test data can effectively combine practical engineering applications and rock mechanics theories, providing a new perspective and method for the study of the mechanical properties of rock masses.

[0019] Among them, the anchor pull-out test data can be used, combined with mathematical models and derivation methods, to achieve the rapid and accurate determination of the Young's modulus of the rock mass. Thus, while simplifying the experimental process, the determination efficiency can be effectively improved, providing more reliable data support for technological innovation and engineering practice in the field of rock mechanics testing. By introducing the test of the Young's modulus of the rock mass in the anchor pull-out test, it is expected to bring new ideas and methods to geotechnical engineering practice and promote the further development of the field of rock mechanics research.

[0020] Based on the above description, with reference to the accompanying drawings, the method and device for determining the Young's modulus of a rock mass based on an anchor pull-out test according to an embodiment of the present invention will be described.

[0021] First, the method for determining the Young's modulus of a rock mass based on an anchor pull-out test according to an embodiment of the present invention will be described with reference to the accompanying drawings.

[0022] Figure 1 FIG. is a flowchart of a method for determining the Young's modulus of a rock mass based on an anchor pull-out test according to an embodiment of the present invention.

[0023] As Figure 1 shown, the method for determining the Young's modulus of a rock mass based on an anchor pull-out test includes the following steps: Step S1, conduct an anchor pull-out test on the target area and obtain the corresponding pull-out test results.

[0024] In an embodiment of the present invention, an anchor pull-out test is conducted on the target area where the Young's modulus of the rock mass needs to be determined, and the corresponding pull-out test results are obtained.

[0025] Among them, in an embodiment of the present invention, the above pull-out test results may be the corresponding stress-displacement curve, where the abscissa of the stress-displacement curve is displacement and the ordinate is tensile stress.

[0026] Step S2, determine the formula for the shear modulus of the rock and soil mass.

[0027] Among them, in an embodiment of the present invention, as a deformable medium, the Young's modulus of the rock and soil mass is an inherent property and remains unchanged during the pulling test. At the same time, in the initial stage of pulling, the stress load is relatively low. At this time, the anchor rod body, the grouting body and the rock and soil mass are completely bonded, and the three maintain elasticity and the displacements are synchronous. The stress and deformation field of the anchoring system in the completely bonded state is as Figure 2 shown.

[0028] As Figure 1 shown, L is the length of the anchor rod; is the radius of the anchor rod; hole radius; is the influence radius of the anchor rod; is the axial stress acting on the end of the anchor rod; dx is an infinitesimal length; is the axial stress at the position x from the end of the anchor rod; is the change in the axial stress of the anchor rod at the dx position; is the displacement of the end of the anchor rod; is the displacement at the position x from the end of the anchor rod; is the displacement of the anchor rod body - grouting body interface at the dx position; is the shear stress of the anchor rod body - grouting body interface at the position x from the end of the anchor rod; is the shear stress of the grouting body - rock and soil mass interface at the position x from the end of the anchor rod.

[0029] In addition, in an embodiment of the present invention, the method for determining the shear modulus formula of the rock and soil mass may include the following steps: Step S21, determining the control equation of the anchor rod system; Step S22, determining the equilibrium relationship of the micro - element of the grouting body or the rock and soil mass; Step S23, determining the relationship between the shear stress and shear strain inside the rock and soil mass; Step S24, based on the control equation of the anchor rod system, the equilibrium relationship of the micro - element of the rock and soil mass, and the relationship between the shear stress and shear strain inside the rock and soil mass, determining the displacement formula of the end of the anchor rod; Step S25, based on the displacement formula of the end of the anchor rod, determining the shear modulus formula of the rock and soil mass.

[0030] Among them, in an embodiment of the present invention, when the anchor rod is subjected to an axial load, considering the axial stress balance of the anchor rod on a tiny cross - section, the control equation of the anchor rod system is obtained as: (1) In addition, in an embodiment of the present invention, considering that the stress exists only in the form of shear stress in the grouting body and the rock and soil mass, there is the following equilibrium relationship on the micro - element of the grouting body or the rock and soil mass: (2) where r is the distance from a certain point to the axis of the anchor rod body, is the shear stress at a distance r from the axis of the anchor rod body in the cross-section perpendicular to the axis of the anchor rod body at the x position.

[0031] Furthermore, in an embodiment of the present invention, since is a higher-order small quantity, the above formula (2) can be simplified as: (3) Moreover, in an embodiment of the present invention, by using the boundary conditions to solve the above equations by coupling, only the pure elastic behavior of the anchor rod body, the grouting body and the rock and soil mass needs to be considered.

[0032] Among them, considering the constitutive relationship of the rock and soil mass in the elastic state, the relationship between the internal shear stress and shear strain of the rock and soil mass is as follows: (4) where represents the shear modulus of the rock and soil mass, and respectively represent the shear stress and displacement of the rock and soil mass at a distance from the axis of the anchor rod in the direction of the axis of the anchor rod.

[0033] Furthermore, in an embodiment of the present invention, the control equation of the anchor rod system, the equilibrium relationship of the micro-elements of the grouting body or the rock and soil mass, and the relationship between the internal shear stress and shear strain of the rock and soil mass can be obtained through the above steps, and the displacement formula of the anchor rod end can be determined.

[0034] Specifically, in an embodiment of the present invention, the method for determining the displacement formula of the anchor rod end based on the control equation of the anchor rod system, the equilibrium relationship of the micro-elements of the grouting body or the rock and soil mass, and the relationship between the internal shear stress and shear strain of the rock and soil mass may include the following steps: Step S241, based on the equilibrium relationship of the micro-elements of the grouting body or the rock and soil mass and the relationship between the internal shear stress and shear strain of the rock and soil mass, determine the first homogeneous linear differential equation of the rock and soil mass; Step S242, based on the first general solution of the displacement of the rock and soil mass of the first homogeneous linear differential equation, obtain the displacement formula of the rock and soil mass and the distribution formula of the internal shear stress of the rock and soil mass; Step S243, based on the second general solution of the displacement of the grouting body of the first homogeneous linear differential equation, obtain the displacement formula of the grouting body and the distribution formula of the internal shear stress of the grouting body; Step S244, at the interface between the grouting body and the rock and soil mass, based on the distribution formula of the internal shear stress of the rock and soil mass and the distribution formula of the internal shear stress of the grouting body, obtain the boundary relationship formula; Step S245: Determine the bolt end displacement formula based on the internal shear stress distribution formula and the boundary relation formula of the grouting body.

[0035] Among them, in an embodiment of the present invention, in the rock and soil mass, formula (3) can be written as , and by combining it with formula (4), the following first homogeneous linear differential equation of the rock and soil mass can be obtained: (5) And, in an embodiment of the present invention, the first general solution of the displacement of the rock and soil mass of the above first homogeneous linear differential equation is: (6) Among them, and are integration constants. Through the boundary conditions:

[0036] the integration constants can be determined as follows: ,

[0037] Based on this, the rock and soil mass displacement formula can be expressed as: (7) And, by combining formula (4) with formula (7), the internal shear stress distribution formula of the rock and soil mass obtained can be expressed as: (8) Furthermore, in an embodiment of the present invention, for the grouting body, from the constitutive relation in the elastic state of the grouting body (in the same form as formula (4)), through the same method as above, the second general solution of the displacement of the grouting body of the first homogeneous linear differential equation can be obtained, that is, the general solution of the grouting body displacement field, as follows: (9) Among them, and are integration constants, represents the displacement of the grouting body. Through the boundary conditions

[0038] the integration constants that can be determined are as follows: ,

[0039] Based on this, the grouting body displacement formula can be expressed as: (10) And, according to the relationship between shear stress and shear strain inside the rock and soil mass, the relationship between shear stress and shear strain inside the grouting mass can be obtained: ,in, represents the shear modulus of the rock mass, and Respectively represent the distance of the grouting body from the anchor axis to the anchor axis. Shear stress and displacement at .

[0040] Furthermore, in one embodiment of the present invention, the relationship between the internal shear stress and shear strain of the grouting body is combined with equation (10), and the internal shear stress distribution formula of the grouting body can be expressed as: (11) in, Represents the shear modulus of the grouting body.

[0041] And, in one embodiment of the present invention, at the grouting body-rock body interface, according to the continuity of shear stress, that is, when Sometimes, there is , from which we can get and The boundary relationship formula between is as follows: (12) Furthermore, in one embodiment of the present invention, after obtaining the internal shear stress distribution formula and the boundary relationship formula of the grouting body through the above steps, the anchor end displacement formula can be determined based on the internal shear stress distribution formula and the boundary relationship formula of the grouting body.

[0042] Specifically, in one embodiment of the present invention, the method for determining the bolt end displacement formula based on the internal shear stress distribution formula of the grouting body and the boundary relationship formula may include the following steps: Step 1, based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, obtain the shear stress distribution formula at the interface between the anchor body and the grouting body; Step 2, determining a linear relationship formula between the shear stress at the interface between the anchor body and the grouting body and the shear stress at a point inside the anchor that is perpendicular to the anchor axis when the anchor body is in an elastic state; Step 3, determining the second homogeneous linear differential equation by using the shear stress distribution formula of the interface between the anchor body and the grouting body, the linear relationship formula and the control equation of the anchor system; Step 4, based on the general solution of the second homogeneous linear differential equation, obtain the axial displacement formula in the anchor bolt body; Step 5: Determine the displacement formula of the anchor end based on the axial displacement formula in the anchor body.

[0043] In one embodiment of the present invention, the above-mentioned shear stress distribution formula (11) inside the grouting body and the boundary relationship formula (12) are combined to obtain the anchor body-grouting body interface. When , the shear stress distribution formula of the interface between the anchor body and the grouting body is as follows: (13) And, in the elastic state of the anchor body, the linear relationship formula between the shear stress at the anchor body-grouting body interface and the shear stress at a point inside the anchor perpendicular to the anchor axis can be considered as follows: (14) in, It represents the shear stress at a point inside the anchor bolt that is perpendicular to the anchor bolt axis.

[0044] Furthermore, considering the stress-strain of the elastic anchor ( ) and strain-displacement ( ) relationship, the control equation (1) of the anchor system can be expressed as: (15) in, is the elastic modulus of the anchor body.

[0045] And, at the interface between the bolt body and the grouting body ( ), according to the continuity of shear stress, we have Based on this, the shear stress distribution formula (13) at the interface between the bolt body and the grouting body, the linear relationship formula (14) and the control equation (15) of the bolt system are combined to determine the second homogeneous linear differential equation (16) as follows: (16) in,

[0046] The general solution of the above second homogeneous linear differential equation is: (17) in, and is the integration constant, through the boundary conditions

[0047] as well as, , the integration constant can be determined as follows: ,

[0048] Based on the above formula, the axial displacement in the anchor body is It can be expressed as: (18) And, in the long bolt, L is significantly greater than , the axial displacement formula can be simplified to: (19) Furthermore, according to the axial displacement formula (19), the displacement at the bolt end is .

[0049] Among them, by integrating along the bolt length, the displacement at the bolt end can also be obtained, and the formula is as follows: (20) And, considering that L is significantly greater than , the bolt end displacement formula can be: (21) Among them, is the load applied at the bolt end position, is the cross-sectional area of the bolt body.

[0050] Furthermore, formula (21) gives the relationship between the end load and the end displacement of the bolt under pure elastic conditions. Among them, in the above derivation process, through the continuity of displacement, the influences of the bolt body deformation, the grout body deformation and the rock and soil body deformation on the bolt end displacement are considered, and the obtained conclusion is more universal than the rigid rock mass assumption.

[0051] Among them, can be solved inversely through the above formula (21), and after squaring it, the following expression can be obtained: (22) Among them , the shear modulus of the rock and soil body can be solved inversely through formula (22) , and the expression is as follows: (23) Among them, is the bolt diameter, is the diameter of the grout body area, is the influence range of bolt pulling, and it is usually considered that .

[0052] Step S3, based on the rock and soil body shear modulus formula, determine the rock and soil body Young's modulus formula through the relationship between the rock and soil body shear modulus and the elastic modulus.

[0053] In an embodiment of the present invention, after obtaining the rock and soil body shear modulus formula through the above steps, the rock and soil body Young's modulus formula can be determined based on the rock and soil body shear modulus formula through the relationship between the rock and soil body shear modulus and the elastic modulus.

[0054] Specifically, in one embodiment of the present invention, the method for determining the Young's modulus formula of rock and soil mass based on the shear modulus formula of rock and soil mass through the relationship between the shear modulus and the elastic modulus of rock and soil mass may include: through the relationship between the shear modulus and the elastic modulus of rock and soil mass, the Young's modulus formula of rock and soil mass is: (24) Wherein, the relationship between the shear modulus and the elastic modulus of rock and soil mass is , is the Poisson's ratio of rock and soil mass, P0 represents stress, G g represents the shear modulus of anchor rod mortar, d0 represents the influence diameter of the anchor rod, d h represents the borehole diameter, δ represents displacement, d b represents the anchor rod diameter during the pull-out test, represents the elastic modulus of the anchor rod body, represents the Young's modulus of rock and soil mass.

[0055] Step S4: Determine the Young's modulus of the rock mass in the target area based on the pull-out test results and the Young's modulus formula of rock and soil mass.

[0056] In one embodiment of the present invention, after obtaining the pull-out test results and the Young's modulus formula of rock and soil mass through the above steps, the Young's modulus of the rock mass in the target area can be determined based on the pull-out test results and the Young's modulus formula of rock and soil mass.

[0057] Specifically, in one embodiment of the present invention, the method for determining the Young's modulus of the rock mass in the target area based on the pull-out test results and the Young's modulus formula of rock and soil mass may include: determining stress and displacement based on the stress-displacement curve corresponding to the pull-out test results, and substituting the stress and displacement into the Young's modulus formula of rock and soil mass to determine the Young's modulus of the rock mass in the target area.

[0058] Based on the above description, an embodiment of the present invention exemplifies the method for determining the Young's modulus of rock mass based on the anchor rod pull-out test.

[0059] Suppose the target area is a slope outside a certain groundwater-sealed cavern, and a pull-out test is conducted on the slope to obtain the stress-displacement curve corresponding to the pull-out test results (as Figure 3 shown), the surrounding rock of the slope is granite, and the shear modulus G R is 1.22 GPa, the anchor rod diameter d b during the pull-out test is 15 mm, the borehole diameter d h is 60 mm, and the influence diameter of the anchor rod d0 is 1200 mm, and the elastic modulus of the bolt body is 180 GPa, and the shear modulus of the bolt mortar G g is 0.692 GPa. In Figure 3 any set of stress-displacement data in its elastic stage is taken, and the stress P 0 is 61.125 kN, and the displacement δ is 0.41 mm. The Poisson's ratio of the rock and soil mass is taken as 0.33. Substituting the above variables into the formula for the Young's modulus of the rock and soil mass, we get:

[0060] Moreover, through the back analysis of the Young's modulus of the slope surrounding rock from the results of the above bolt pull-out test, it is 1.14 GPa, which is consistent with the actual on-site situation.

[0061] According to the method for determining the Young's modulus of rock mass based on bolt pull-out test proposed in the embodiment of the present invention, the method includes: conducting a bolt pull-out test on the target area and obtaining the corresponding pull-out test results; determining the formula for the shear modulus of the rock and soil mass; based on the formula for the shear modulus of the rock and soil mass, determining the formula for the Young's modulus of the rock and soil mass through the relationship between the shear modulus and the elastic modulus of the rock and soil mass; and determining the Young's modulus of the rock mass in the target area based on the pull-out test results and the formula for the Young's modulus of the rock and soil mass. Based on the pull-out test results and the formula for the Young's modulus of the rock and soil mass, the present invention determines the Young's modulus of the rock mass in the target area, so that the Young's modulus of the rock mass can be inversely calculated by introducing the bolt pull-out test data, realizing the rapid and accurate determination of the Young's modulus of the rock mass, simplifying the experimental process, reducing the cost and sample damage, improving the test efficiency and data accuracy, and bringing technical innovation and reliable support for engineering practice to the field of rock mechanics testing.

[0062] Secondly, a device for determining the Young's modulus of rock mass based on bolt pull-out test proposed in the embodiment of the present invention is described with reference to the accompanying drawings.

[0063] Figure 4 It is a schematic structural diagram of a device for determining the Young's modulus of rock mass based on bolt pull-out test according to an embodiment of the present invention.

[0064] As Figure 4 shown, the device 10 for determining the Young's modulus of rock mass based on bolt pull-out test includes: an acquisition module 201, a first determination module 202, a second determination module 203, and a third determination module 204, where The acquisition module 201 is used to conduct a bolt pull-out test on the target area and obtain the corresponding pull-out test results; The first determination module 202 is used to determine the formula for the shear modulus of the rock and soil mass; The second determination module 203 is configured to determine the Young's modulus formula of the rock and soil mass based on the shear modulus formula of the rock and soil mass and the relationship between the shear modulus and the elastic modulus of the rock and soil mass; The third determination module 204 determines the Young's modulus of the rock mass in the target area based on the pull-out test results and the Young's modulus formula of the rock and soil mass.

[0065] Further, the first determination module 201 is specifically configured to: Determine the control equation of the anchor rod system; Determine the equilibrium relationship of the micro-elements of the grout or the rock and soil mass; Determine the relationship between the internal shear stress and the shear strain of the rock and soil mass; Based on the control equation of the anchor rod system, the equilibrium relationship of the micro-elements of the grout or the rock and soil mass, and the relationship between the internal shear stress and the shear strain of the rock and soil mass, determine the anchor rod end displacement formula; Based on the anchor rod end displacement formula, determine the shear modulus formula of the rock and soil mass.

[0066] Further, the first determination module 201 is further configured to: Based on the equilibrium relationship of the micro-elements of the grout or the rock and soil mass and the relationship between the internal shear stress and the shear strain of the rock and soil mass, determine the first homogeneous linear differential equation of the rock and soil mass; Based on the first general solution of the displacement of the rock and soil mass of the first homogeneous linear differential equation, obtain the rock and soil mass displacement formula and the internal shear stress distribution formula of the rock and soil mass; Based on the second general solution of the displacement of the grout of the first homogeneous linear differential equation, obtain the grout displacement formula and the internal shear stress distribution formula of the grout; At the interface between the grout and the rock and soil mass, based on the internal shear stress distribution formula of the rock and soil mass and the internal shear stress distribution formula of the grout, obtain the boundary relationship formula; Based on the internal shear stress distribution formula of the grout and the boundary relationship formula, determine the anchor rod end displacement formula.

[0067] Further, the first determination module 201 is further configured to: Based on the internal shear stress distribution formula of the grout and the boundary relationship formula, obtain the shear stress distribution formula at the interface between the anchor rod body and the grout; Determine the linear relationship formula between the shear stress at the interface between the anchor rod body and the grout and the shear stress at a point on the vertical axis of the anchor rod inside the anchor rod in the elastic state of the anchor rod body; Based on the shear stress distribution formula at the interface between the anchor rod body and the grout, the linear relationship formula, and the control equation of the anchor rod system, determine the second homogeneous linear differential equation; Based on the general solution of the second homogeneous linear differential equation, obtain the axial displacement formula in the anchor rod body; Based on the axial displacement formula in the anchor rod body, determine the displacement formula of the anchor rod end.

[0068] Further, the above-mentioned Young's modulus formula of the rock and soil mass includes:

[0069] Among them, represents the Poisson's ratio of the rock and soil mass, P0 represents the stress, and G g represents the shear modulus of the anchor rod mortar, d0 represents the influence diameter of the anchor rod, and d h represents the borehole diameter, δ represents the displacement, d b represents the anchor rod diameter during the pull-out test, represents the elastic modulus of the anchor rod body, represents the Young's modulus of the rock and soil mass.

[0070] Further, the above-mentioned third determination module 204 is further configured to: Based on the stress-displacement curve corresponding to the pull-out test result, determine the stress and displacement; Substitute the stress and displacement into the Young's modulus formula of the rock and soil mass to determine the Young's modulus of the rock mass in the target area.

[0071] According to the device for determining the Young's modulus of the rock mass based on the anchor rod pull-out test proposed in the embodiment of the present invention, perform an anchor rod pull-out test on the target area and obtain the corresponding pull-out test result; determine the shear modulus formula of the rock and soil mass; based on the shear modulus formula of the rock and soil mass, determine the Young's modulus formula of the rock and soil mass through the relationship between the shear modulus and the elastic modulus of the rock and soil mass; based on the pull-out test result and the Young's modulus formula of the rock and soil mass, determine the Young's modulus of the rock mass in the target area. The present invention determines the Young's modulus of the rock mass in the target area based on the pull-out test result and the Young's modulus formula of the rock and soil mass, so that the Young's modulus of the rock mass can be inversely calculated by introducing the anchor rod pull-out test data, realizing the rapid and accurate determination of the Young's modulus of the rock mass, simplifying the experimental process, reducing the cost and sample damage, improving the test efficiency and data accuracy, and bringing technical innovation and reliable support for engineering practice to the field of rock mechanics testing.

[0072] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of these features. In the description of the present invention, "a plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0073] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples", etc., mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0074] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for determining the Young's modulus of rock mass based on bolt pull-out test, characterized in that, The method includes: Conduct a pull-out test on the target area and obtain the corresponding pull-out test results; Determine the formula for the shear modulus of the rock and soil mass; Based on the formula for the shear modulus of the rock and soil mass, determine the formula for Young's modulus of the rock and soil mass through the relationship between the shear modulus and Young's modulus of the rock and soil mass; Based on the pull-out test results and the formula for Young's modulus of the rock and soil mass, determine the Young's modulus of the rock mass in the target area.

2. The method according to claim 1, wherein The determination of the formula for the shear modulus of the rock and soil mass includes: Determine the control equation of the anchor rod system; Determine the equilibrium relationship of the micro-elements of the grout or the rock and soil mass; Determine the relationship between the shear stress and shear strain inside the rock and soil mass; Based on the control equation of the anchor rod system, the equilibrium relationship of the micro-elements of the grout or the rock and soil mass, and the relationship between the shear stress and shear strain inside the rock and soil mass, determine the formula for the displacement of the anchor rod end; Based on the formula for the displacement of the anchor rod end, determine the formula for the shear modulus of the rock and soil mass.

3. The method according to claim 2, characterized in that The determination of the formula for the displacement of the anchor rod end based on the control equation of the anchor rod system, the equilibrium relationship of the micro-elements of the grout or the rock and soil mass, and the relationship between the shear stress and shear strain inside the rock and soil mass includes: Based on the equilibrium relationship of the micro-elements of the grout or the rock and soil mass and the relationship between the shear stress and shear strain inside the rock and soil mass, determine the first homogeneous linear differential equation of the rock and soil mass; Based on the first general solution of the displacement of the rock and soil mass of the first homogeneous linear differential equation, obtain the formula for the displacement of the rock and soil mass and the formula for the distribution of shear stress inside the rock and soil mass; Based on the second general solution of the displacement of the grout of the first homogeneous linear differential equation, obtain the formula for the displacement of the grout and the formula for the distribution of shear stress inside the grout; At the interface between the grout and the rock and soil mass, based on the formula for the distribution of shear stress inside the rock and soil mass and the formula for the distribution of shear stress inside the grout, obtain the boundary relationship formula; Based on the formula for the distribution of shear stress inside the grout and the boundary relationship formula, determine the formula for the displacement of the anchor rod end.

4. The method according to claim 3, characterized in that The determination of the formula for the displacement of the anchor rod end based on the formula for the distribution of shear stress inside the grout and the boundary relationship formula includes: Based on the formula for the distribution of shear stress inside the grout and the boundary relationship formula, obtain the formula for the distribution of shear stress at the interface between the anchor rod body and the grout; Determine the linear relationship formula between the shear stress at the interface between the anchor rod body and the grout and the shear stress at a point on the vertical axis of the anchor rod inside the anchor rod body in the elastic state of the anchor rod body; Based on the formula for the distribution of shear stress at the interface between the anchor rod body and the grout, the linear relationship formula, and the control equation of the anchor rod system, determine the second homogeneous linear differential equation; Based on the general solution of the second homogeneous linear differential equation, obtain the formula for the axial displacement in the anchor rod body; Based on the formula for the axial displacement in the anchor rod body, determine the formula for the displacement of the anchor rod end.

5. The method according to claim 1, wherein The formula for Young's modulus of the rock and soil mass includes: Among them, represents the Poisson's ratio of rock and soil mass, P0 represents stress, G g represents the shear modulus of anchor rod mortar, d0 represents the influence diameter of the anchor rod, d h represents the borehole diameter, δ represents displacement, d b represents the diameter of the anchor rod during the pull-out test, represents the elastic modulus of the anchor rod body, represents the Young's modulus of rock and soil mass.

6. The method according to claim 1, wherein The determination of the Young's modulus of the rock mass in the target area based on the pull-out test results and the formula for Young's modulus of the rock and soil mass includes: Based on the stress-displacement curve corresponding to the pull-out test results, determine the stress and displacement; Substitute the stress and the displacement into the formula for Young's modulus of the rock and soil mass to determine the Young's modulus of the rock mass in the target area.

7. A device for determining the Young's modulus of a rock mass based on a bolt pull-out test, characterized in that, The method includes: An acquisition module for conducting a bolt pull-out test on a target area and acquiring corresponding pull-out test results; A first determination module for determining a formula for the shear modulus of a rock and soil mass; A second determination module for determining a formula for the Young's modulus of a rock and soil mass based on the relationship between the shear modulus and the elastic modulus of the rock and soil mass according to the formula for the shear modulus of the rock and soil mass; A third determination module for determining the Young's modulus of the rock mass in the target area based on the pull-out test results and the formula for the Young's modulus of the rock and soil mass; 8. The device according to claim 7, characterized in that, The first determination module is specifically configured to: Determine the control equation of the bolt system; Determine the equilibrium relationship of the micro-elements of the rock and soil mass; Determine the relationship between the shear stress and the shear strain inside the rock and soil mass; Based on the control equation of the bolt system, the equilibrium relationship of the micro-elements of the rock and soil mass, and the relationship between the shear stress and the shear strain inside the rock and soil mass, determine the formula for the displacement of the bolt end; Based on the formula for the displacement of the bolt end, determine the formula for the shear modulus of the rock and soil mass; 9. An electronic device, comprising: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method according to any one of claims 1-6; 10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program, when executed by a processor, implements the method according to any one of claims 1-6.

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