Method and device for determining Young's modulus of rock mass based on anchor pull-out experiment

Abstract

The present invention discloses a method and device for determining the Young's modulus of a rock mass based on an anchor pull-out test, comprising: performing an anchor pull-out test on a target area and obtaining corresponding pull-out test results; determining a rock-soil shear modulus formula; determining a rock-soil Young's modulus formula based on the rock-soil shear modulus formula and the relationship between the rock-soil shear modulus and the elastic modulus; and determining the rock-soil Young's modulus in the target area based on the pull-out test results and the rock-soil Young's modulus formula. The present invention determines the rock-soil Young's modulus in the target area based on the pull-out test results and the rock-soil Young's modulus formula, thereby inverting the rock-soil Young's modulus by introducing anchor pull-out test data, thereby achieving rapid and accurate determination of the rock-soil Young's modulus. This simplifies the experimental process, reduces costs, and minimizes sample damage, improving test efficiency and data accuracy, and bringing technological innovation and reliable support for engineering practice to the field of rock mechanics testing.

Description

Technical Field

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

[0002] Testing rock mechanical properties is of great significance in geotechnical engineering. Young's modulus of rock is a key parameter for evaluating its mechanical properties and engineering behavior. Currently, methods for determining the Young's modulus of rock include ultrasonic testing, compression testing, and tensile testing. While these methods can provide quantitative data on rock mechanical properties to a certain extent, they are cumbersome to implement in practical engineering applications, resulting in low measurement efficiency, high costs, and sample loss. Therefore, determining the Young's modulus of rock in a simple and efficient manner is an urgent problem that needs to be addressed. Summary of the Invention

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

[0004] To this end, one purpose of the present invention is to propose a method for determining the Young's modulus of rock mass based on an anchor pull-out test. The method determines the Young's modulus of rock mass in 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 inverted by introducing the anchor pull-out test data, thereby realizing rapid and accurate determination of the Young's modulus of rock mass, simplifying the experimental process, reducing costs and sample damage, improving test efficiency and data accuracy, and bringing reliable support for technological innovation and engineering practice in the field of rock mechanics testing.

[0005] Another object of the present invention is to provide a device for determining the Young's modulus of rock mass based on an anchor pull-out experiment.

[0006] To achieve the above objectives, an embodiment of the present invention provides a method for determining the Young's modulus of a rock mass based on an anchor pull-out test, comprising:

[0007] Conduct anchor pull-out tests on the target area and obtain the corresponding pull-out test results;

[0008] Determine the formula for shear modulus of rock and soil;

[0009] Based on the shear modulus formula of the rock and soil mass, the Young's modulus formula of the rock and soil mass is determined by the relationship between the shear modulus and the elastic modulus of the rock and soil mass;

[0010] Based on the pull-out test results and the Young's modulus formula of the rock and soil, the Young's modulus of the rock mass in the target area is determined.

[0011] 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 may also have the following additional technical features:

[0012] Furthermore, the formula for determining the shear modulus of the rock and soil mass includes:

[0013] Determine the governing equations of the anchor system;

[0014] Determine the equilibrium relationship of micro-element of grouting body or rock and soil body;

[0015] Determine the relationship between shear stress and shear strain within the rock mass;

[0016] Determine the anchor end displacement formula based on the control equation of the anchor system, the equilibrium relationship of the micro-element of the grouting body or rock and soil body, and the relationship between the shear stress and shear strain inside the rock and soil body;

[0017] Based on the anchor rod end displacement formula, the rock and soil shear modulus formula is determined.

[0018] Furthermore, the anchor bolt end displacement formula is determined based on the control equation of the anchor bolt system, the equilibrium relationship of the micro-element of the grouting body or rock and soil body, and the relationship between the shear stress and shear strain inside the rock and soil body, including:

[0019] Determining a first homogeneous linear differential equation of the rock-soil body based on the equilibrium relationship of the micro-element of the grouting body or rock-soil body and the relationship between the shear stress and shear strain inside the rock-soil body;

[0020] Based on the first general solution of the rock-soil displacement of the first homogeneous linear differential equation, a rock-soil displacement formula and a rock-soil internal shear stress distribution formula are obtained;

[0021] Based on the second general solution of the grouting body displacement of the first homogeneous linear differential equation, a grouting body displacement formula and a grouting body internal shear stress distribution formula are obtained;

[0022] At the interface between the grouting body and the rock-soil body, a boundary relationship formula is obtained based on the shear stress distribution formula inside the rock-soil body and the shear stress distribution formula inside the grouting body;

[0023] Based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, the anchor rod end displacement formula is determined.

[0024] Furthermore, the anchor bolt end displacement formula is determined based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, including:

[0025] Based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, a shear stress distribution formula at the interface between the anchor body and the grouting body is obtained;

[0026] Determine the 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 perpendicular to the anchor axis when the anchor body is in the elastic state;

[0027] Determining a second homogeneous linear differential equation based on the shear stress distribution formula at the interface between the anchor body and the grouting body, the linear relationship formula, and the governing equation of the anchor system;

[0028] Based on the general solution of the second homogeneous linear differential equation, a formula for the axial displacement in the anchor body is obtained;

[0029] Based on the axial displacement formula in the anchor rod body, the anchor rod end displacement formula is determined.

[0030] Furthermore, the Young's modulus formula of the rock and soil mass includes:

[0031]

[0032] in, represents the Poisson's ratio of the rock and soil, P0 represents the stress, G g represents the shear modulus of the anchor mortar, d0 represents the anchor influence diameter, d h Indicates the drilling diameter, δ represents displacement, d b Indicates the diameter of the anchor rod during the pull-out test, represents the elastic modulus of the anchor body, It represents the Young's modulus of rock and soil.

[0033] Furthermore, 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 the rock mass includes:

[0034] determining stress and displacement based on a stress-displacement curve corresponding to the pull-out test result;

[0035] Substituting the stress and the displacement into the Young's modulus formula of the rock mass, the Young's modulus of the rock mass in the target area is determined.

[0036] 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 pull-out experiment, the device comprising:

[0037] An acquisition module is used to perform an anchor pull-out test on a target area and obtain corresponding pull-out test results;

[0038] The first determination module is used to determine the shear modulus formula of the rock and soil mass;

[0039] A second determining module is configured to determine a 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;

[0040] The third determination module 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 mass.

[0041] The present invention proposes a method and device for determining the Young's modulus of a rock mass based on an anchor pullout test. The method comprises: conducting an anchor pullout test on a target area and obtaining corresponding pullout test results; determining a formula for the shear modulus of the rock mass; determining a formula for the Young's modulus of the rock mass based on the shear modulus formula and the relationship between the shear modulus and elastic modulus of the rock mass; and determining the Young's modulus of the rock mass in the target area based on the pullout test results and the Young's modulus formula of the rock mass. The present invention determines the Young's modulus of the rock mass in the target area based on the pullout test results and the Young's modulus formula of the rock mass. This allows the Young's modulus of the rock mass to be inverted by introducing anchor pullout test data, enabling rapid and accurate determination of the Young's modulus of the rock mass. This simplifies the experimental process, reduces costs, minimizes sample damage, improves testing efficiency and data accuracy, and brings technological innovation and reliable support for engineering practice to the field of rock mechanics testing.

[0042] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0044] Figure 1 Flowchart of a method for determining Young's modulus of rock mass based on an anchor pull-out experiment according to one embodiment of the present invention;

[0045] Figure 2 is a schematic diagram of the stress-deformation field of the anchoring system in a fully bonded state according to one embodiment of the present invention;

[0046] Figure 3 is a schematic diagram of a stress-displacement curve according to one embodiment of the present invention;

[0047] Figure 4 Schematic diagram of the structure of a device for determining the Young's modulus of a rock mass based on an anchor pull-out experiment according to one embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0049] With the continuous development of geotechnical engineering, anchor pullout testing has gained increasing attention as a common method for inspecting the quality of underground engineering construction. During anchor pullout testing, the anchor is subject to the restraining force of the rock mass. The mechanical properties of the rock mass are assessed by measuring the tension and deformation of the anchor. Inverting the Young's modulus of the rock mass based on anchor pullout test data effectively combines practical engineering applications with rock mechanics theory, providing new perspectives and methods for studying rock mass mechanical properties.

[0050] The use of anchor pull-out test data, combined with mathematical models and derivation methods, can achieve rapid and accurate determination of the Young's modulus of rock masses. This simplifies the experimental process while effectively improving measurement efficiency, providing more reliable data support for technological innovation and engineering practice in the field of rock mechanics testing. By introducing the Young's modulus test of rock masses into anchor pull-out tests, it is expected to bring new ideas and methods to geotechnical engineering practice and promote further development in the field of rock mechanics research.

[0051] Based on the above description, a method and device for determining the Young's modulus of a rock mass based on an anchor pull-out experiment according to an embodiment of the present invention will be described with reference to the accompanying drawings.

[0052] First, a method for determining the Young's modulus of a rock mass based on an anchor pull-out experiment according to an embodiment of the present invention will be described with reference to the accompanying drawings.

[0053] Figure 1 The figure is a flow chart of a method for determining the Young's modulus of a rock mass based on an anchor pull-out experiment according to one embodiment of the present invention.

[0054] like Figure 1 As shown, the method for determining the Young's modulus of rock mass based on the anchor pull-out experiment includes the following steps:

[0055] Step S1: Perform an anchor pull-out test on a target area and obtain corresponding pull-out test results.

[0056] In one embodiment of the present invention, an anchor pull-out test is performed on a target area where the Young's modulus of the rock mass needs to be determined, and corresponding pull-out test results are obtained.

[0057] In one embodiment of the present invention, the pull-out test result may be a corresponding stress-displacement curve, where the abscissa of the stress-displacement curve is displacement and the ordinate is tensile stress.

[0058] Step S2: Determine the shear modulus formula of the rock and soil mass.

[0059] In one embodiment of the present invention, the rock mass is a deformable medium, and its Young's modulus is an inherent property that remains unchanged during the pull-out test. At the same time, the stress load is low at the beginning of the pull-out. At this time, the anchor rod, grouting body and rock mass are fully bonded, the three maintain elasticity, and the displacement is synchronized. The stress-deformation field of the anchor system in the fully bonded state is as follows: Figure 2 shown.

[0060] like Figure 1 As shown, L is the length of the anchor rod; is the anchor radius; Hole radius; is the anchor rod influence radius; is the axial stress acting on the end of the anchor bolt; dx is the infinitesimal length; is the axial stress at position x from the anchor end; is the axial stress change of the anchor rod at the dx position; is the displacement of the anchor end; is the displacement from the anchor end to the x position; is the displacement of the anchor rod at the dx position; is the shear stress at the interface between the anchor body and the grouting body at a position x from the anchor end; is the shear stress at the grouting-rock-soil interface at position x from the anchor end.

[0061] Furthermore, in one embodiment of the present invention, the method for determining the shear modulus formula of rock and soil mass may include the following steps:

[0062] Step S21, determining the control equation of the anchor system;

[0063] Step S22, determining the equilibrium relationship of the micro-element of the grouting body or rock and soil body;

[0064] Step S23, determining the relationship between shear stress and shear strain inside the rock and soil mass;

[0065] Step S24, determining the anchor bolt end displacement formula based on the control equation of the anchor bolt system, the equilibrium relationship of the micro-element of the rock and soil body, and the relationship between the shear stress and shear strain inside the rock and soil body;

[0066] Step S25: Determine the shear modulus formula of the rock and soil based on the anchor end displacement formula.

[0067] In one embodiment of the present invention, when the anchor rod is subjected to an axial load, the control equation of the anchor rod system is obtained by considering the axial stress balance on a small cross section of the anchor rod:

[0068] (1)

[0069] Furthermore, in one embodiment of the present invention, considering that stress exists only in the form of shear stress in the grouting body and the rock-soil body, the following equilibrium relationship exists on the micro-element of the grouting body or the rock-soil body:

[0070] (2)

[0071] Among them, r is the distance from a certain point to the axis of the anchor body, It is the shear stress at a distance r from the axis of the anchor body in the section perpendicular to the axis of the anchor body at position x.

[0072] Furthermore, in one embodiment of the present invention, due to is a high-order small quantity, the above formula (2) can be simplified to:

[0073] (3)

[0074] Furthermore, in one embodiment of the present invention, the above equations are coupled and solved using boundary conditions, and only the pure elastic behavior of the anchor body, the grouting body, and the rock and soil body needs to be considered.

[0075] Among them, considering the constitutive relationship of rock and soil under the elastic state, the relationship between shear stress and shear strain inside the rock and soil is as follows:

[0076] (4)

[0077] in, represents the shear modulus of the rock mass, and Respectively represent the distance between the rock and soil mass and the anchor axis in the direction of the anchor axis Shear stress and displacement at .

[0078] Furthermore, in one embodiment of the present invention, the control equation of the anchor system, the equilibrium relationship of the microelement of the grouting body or rock and soil body, and the relationship between the shear stress and shear strain inside the rock and soil body can be obtained through the above steps to determine the anchor end displacement formula.

[0079] Specifically, in one embodiment of the present invention, the method for determining the anchor bolt end displacement formula based on the governing equation of the anchor bolt system, the equilibrium relationship of the microelement of the grouting body or the rock and soil body, and the relationship between the shear stress and shear strain inside the rock and soil body may include the following steps:

[0080] Step S241, determining the first homogeneous linear differential equation of the rock-soil body based on the equilibrium relationship of the micro-element of the grouting body or the rock-soil body and the relationship between the shear stress and shear strain inside the rock-soil body;

[0081] Step S242, obtaining a formula for the displacement of the rock and soil mass and a formula for the distribution of shear stress inside the rock and soil mass based on a first general solution of the first homogeneous linear differential equation for the displacement of the rock and soil mass;

[0082] Step S243, obtaining a grouting body displacement formula and a grouting body internal shear stress distribution formula based on a second general solution of the first homogeneous linear differential equation;

[0083] Step S244: obtaining a boundary relationship formula at the interface between the grouting body and the rock-soil body based on the shear stress distribution formula inside the rock-soil body and the shear stress distribution formula inside the grouting body;

[0084] Step S245: Determine the anchor bolt end displacement formula based on the shear stress distribution formula inside the grouting body and the boundary relationship formula.

[0085] In one embodiment of the present invention, in a rock mass, formula (3) can be written as , combining it with equation (4) can obtain the following first homogeneous linear differential equation of rock and soil:

[0086] (5)

[0087] And, in one embodiment of the present invention, the first general solution of the rock mass displacement of the first homogeneous linear differential equation is:

[0088] (6)

[0089] in, and is the integration constant, through the boundary conditions:

[0090]

[0091] The constant of integration can be determined as follows:

[0092] ,

[0093] Based on this, the displacement formula of rock and soil mass can be expressed as:

[0094] (7)

[0095] And, combining equation (4) and equation (7), the obtained shear stress distribution formula inside the rock and soil mass can be expressed as:

[0096] (8)

[0097] Furthermore, in one embodiment of the present invention, for the grouting body, the constitutive relation of the grouting body in the elastic state (the same form as equation (4)) can be used to obtain the second general solution of the grouting body displacement of the first homogeneous linear differential equation by the same method as above, that is, the general solution of the grouting body displacement field, as follows:

[0098] (9)

[0099] in, and is the integration constant, Represents the displacement of the grouting body, through the boundary condition

[0100]

[0101] The integral constant that can be determined is as follows:

[0102] ,

[0103] Based on this, the grouting body displacement formula can be expressed as:

[0104] (10)

[0105] And, based on 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 .

[0106] 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 formula (10), and the resulting internal shear stress distribution formula of the grouting body can be expressed as:

[0107] (11)

[0108] in, represents the shear modulus of the grouting body.

[0109] 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 are , from which we can get and The boundary relationship formula between them is as follows:

[0110] (12)

[0111] Furthermore, in one embodiment of the present invention, after obtaining the shear stress distribution formula and boundary relationship formula inside the grouting body through the above steps, the anchor end displacement formula can be determined based on the shear stress distribution formula and boundary relationship formula inside the grouting body.

[0112] Specifically, in one embodiment of the present invention, the method for determining the anchor 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:

[0113] Step 1: Based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, the shear stress distribution formula at the interface between the anchor body and the grouting body is obtained;

[0114] Step 2: determine the 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 body that is perpendicular to the anchor axis when the anchor body is in an elastic state;

[0115] Step 3, determining the second homogeneous linear differential equation by using the shear stress distribution formula, linear relationship formula and the control equation of the anchor system at the interface between the anchor body and the grouting body;

[0116] Step 4, based on the general solution of the second homogeneous linear differential equation, obtain the axial displacement formula in the anchor bolt body;

[0117] Step 5: Based on the axial displacement formula in the anchor body, determine the anchor end displacement formula.

[0118] Among them, 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 at the interface between the anchor body and the grouting body is as follows:

[0119] (13)

[0120] Furthermore, in the elastic state of the anchor body, the linear relationship between the shear stress at the anchor body-grouting body interface and the shear stress at a point inside the anchor body perpendicular to the anchor axis can be considered as follows:

[0121] (14)

[0122] in, It represents the shear stress at a point inside the anchor bolt that is perpendicular to the anchor bolt axis.

[0123] 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:

[0124] (15)

[0125] in, is the elastic modulus of the anchor body.

[0126] 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 anchor body and the grouting body, the linear relationship formula (14) and the control equation (15) of the anchor system are combined to determine the second homogeneous linear differential equation (16) as follows:

[0127] (16)

[0128] in,

[0129]

[0130] The general solution of the above second homogeneous linear differential equation is:

[0131] (17)

[0132] in, and is the integration constant, through the boundary conditions

[0133]

[0134] as well as, , the integration constant can be determined as follows:

[0135] ,

[0136] Based on the above formula, the axial displacement in the anchor body is It can be expressed as:

[0137] (18)

[0138] Also, L in long anchors is significantly greater than , the axial displacement formula can be simplified as:

[0139] (19)

[0140] Furthermore, according to the axial displacement formula (19), the displacement of the anchor end is .

[0141] Among them, the displacement of the anchor end can also be obtained by integrating along the anchor length. The formula is as follows:

[0142] (20)

[0143] And, considering that L is significantly greater than , the displacement formula of the anchor end can be:

[0144] (twenty one)

[0145] in, To apply load at the end of anchor bolt, is the cross-sectional area of ​​the anchor body.

[0146] Furthermore, formula (21) gives the relationship between the end load and the end displacement of the anchor under purely elastic conditions. The above derivation process takes into account the effects of anchor deformation, grouting deformation, and rock and soil deformation on the anchor end displacement through the continuity of displacement. The conclusion obtained is more universal than the rigid rock mass assumption.

[0147] Among them, the above formula (21) can be reversed to get , and square it to get the following expression:

[0148] (twenty two)

[0149] in The shear modulus of the rock mass can be obtained by inversely solving formula (22): , the expression is as follows:

[0150] (twenty three)

[0151] in, is the anchor diameter, is the diameter of the grouting area, The influence range of anchor pullout is generally considered to be .

[0152] Step S3: Based on the shear modulus formula of the rock and soil mass, the Young's modulus formula of the rock and soil mass is determined through the relationship between the shear modulus and the elastic modulus of the rock and soil mass.

[0153] In one embodiment of the present invention, after obtaining the shear modulus formula of the rock and soil through the above steps, the Young's modulus formula of the rock and soil can be determined based on the shear modulus formula of the rock and soil and the relationship between the shear modulus and the elastic modulus of the rock and soil.

[0154] Specifically, in one embodiment of the present invention, the method for determining the Young's modulus formula of the rock and soil based on the shear modulus formula of the rock and soil through the relationship between the shear modulus and the elastic modulus of the rock and soil may include: through the relationship between the shear modulus and the elastic modulus of the rock and soil, the Young's modulus formula of the rock and soil is:

[0155] (twenty four)

[0156] Among them, the relationship between the shear modulus and elastic modulus of rock and soil is: , is the Poisson's ratio of the rock mass, P0 represents the stress, G g represents the shear modulus of the anchor mortar, d0 represents the anchor influence diameter, d h Indicates the drilling diameter, δ represents displacement, d b Indicates the diameter of the anchor rod during the pull-out test, represents the elastic modulus of the anchor body, It represents the Young's modulus of rock and soil.

[0157] 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 the rock mass.

[0158] In one embodiment of the present invention, after obtaining the pull-out test results and the Young's modulus formula of the rock and soil 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 the rock and soil.

[0159] Specifically, in one embodiment of the present invention, the above-mentioned 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 the rock mass may include: determining the stress and displacement based on the stress-displacement curve corresponding to the pull-out test results, substituting the stress and displacement into the Young's modulus formula of the rock mass, and determining the Young's modulus of the rock mass in the target area.

[0160] Based on the above description, the embodiment of the present invention provides an example to illustrate the method for determining the Young's modulus of the rock mass based on the anchor pull-out experiment.

[0161] Assume that the target area is a slope outside a certain underground water-sealed cavern, and conduct an anchor pull-out test on the slope to obtain the stress-displacement curve corresponding to the pull-out test result (e.g. Figure 3 As shown), the surrounding rock of the slope is granite, and the shear modulus G R is 1.22GPa, and the diameter of the anchor rod during the pull-out test d b 15mm, drilling diameter d h 60mm, the anchor rod affects the diameterd 0 is 1200mm, elastic modulus of anchor body The shear modulus of anchor mortar is 180GPa. G g is 0.692GPa, Figure 3 Take any set of stress-displacement data in the elastic stage, stress P 0 is 61.125kN, displacement δ is 0.41 mm, and the Poisson's ratio of rock and soil is Taking 0.33, substituting the above variables into the Young's modulus formula of rock and soil, we get:

[0162]

[0163] In addition, the Young's modulus of the slope surrounding rock calculated from the above-mentioned anchor pull-out test results is 1.14 GPa, which is consistent with the actual situation on site.

[0164] According to an embodiment of the present invention, a method for determining the Young's modulus of a rock mass based on an anchor pull-out test is proposed. The method includes: conducting an anchor pull-out test on a target area and obtaining corresponding pull-out test results; determining a formula for the shear modulus of the rock mass; determining a formula for the Young's modulus of the rock mass based on the shear modulus of the rock mass and the relationship between the shear modulus and the elastic modulus of the rock mass; and 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 the rock mass. 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 Young's modulus formula of the rock mass. Thus, the Young's modulus of the rock mass can be inverted by introducing the anchor pull-out test data, thereby achieving rapid and accurate determination of the Young's modulus of the rock mass. This simplifies the experimental process, reduces costs, and minimizes sample damage, improves test efficiency and data accuracy, and brings technological innovation and reliable support for engineering practice to the field of rock mechanics testing.

[0165] Next, a device for determining the Young's modulus of a rock mass based on an anchor pull-out experiment according to an embodiment of the present invention will be described with reference to the accompanying drawings.

[0166] Figure 4 Schematic diagram of the structure of a device for determining the Young's modulus of a rock mass based on an anchor pull-out experiment according to one embodiment of the present invention.

[0167] like Figure 4 As shown, the rock mass Young's modulus determination device 10 based on the anchor pull-out experiment includes: an acquisition module 201, a first determination module 202, a second determination module 203 and a third determination module 204, wherein:

[0168] The acquisition module 201 is used to perform an anchor pull-out test on a target area and obtain corresponding pull-out test results;

[0169] The first determination module 202 is used to determine the shear modulus formula of the rock and soil mass;

[0170] The second determining module 203 is configured to determine a Young's modulus formula of the rock-soil mass based on the shear modulus formula of the rock-soil mass and the relationship between the shear modulus and the elastic modulus of the rock-soil mass;

[0171] 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 mass.

[0172] Furthermore, the first determining module 201 is specifically configured to:

[0173] Determine the governing equations of the anchor system;

[0174] Determine the equilibrium relationship of micro-element of grouting body or rock and soil body;

[0175] Determine the relationship between shear stress and shear strain within the rock mass;

[0176] Determine the anchor end displacement formula based on the governing equations of the anchor system, the equilibrium relationship of the micro-element of the grouting body or rock and soil body, and the relationship between the shear stress and shear strain inside the rock and soil body;

[0177] Based on the anchor end displacement formula, the shear modulus formula of rock and soil is determined.

[0178] Furthermore, the first determining module 201 is further configured to:

[0179] Based on the equilibrium relationship of the micro-element of the grouting body or rock and soil body and the relationship between the shear stress and shear strain inside the rock and soil body, the first homogeneous linear differential equation of the rock and soil body is determined;

[0180] Based on the first general solution of the first homogeneous linear differential equation of rock and soil displacement, the rock and soil displacement formula and the shear stress distribution formula inside the rock and soil are obtained;

[0181] Based on the second general solution of the first homogeneous linear differential equation for grouting displacement, the formula for grouting displacement and the formula for shear stress distribution inside the grouting body are obtained;

[0182] At the interface between the grouting body and the rock-soil body, the boundary relationship formula is obtained based on the shear stress distribution formula inside the rock-soil body and the shear stress distribution formula inside the grouting body;

[0183] Based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, the anchor end displacement formula is determined.

[0184] Furthermore, the first determining module 201 is further configured to:

[0185] Based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, the shear stress distribution formula at the interface between the anchor body and the grouting body is obtained;

[0186] Determine the 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 perpendicular to the anchor axis when the anchor body is in the elastic state;

[0187] Determine the second homogeneous linear differential equation based on the shear stress distribution formula, linear relationship formula and the control equation of the anchor system at the interface between the anchor body and the grouting body;

[0188] Based on the general solution of the second homogeneous linear differential equation, the formula for the axial displacement in the bolt body is obtained;

[0189] Based on the formula for axial displacement in the anchor body, the formula for anchor end displacement is determined.

[0190] Furthermore, the Young's modulus formula of the rock and soil mass includes:

[0191]

[0192] in, represents the Poisson's ratio of the rock and soil, P0 represents the stress, G g represents the shear modulus of the anchor mortar, d0 represents the anchor influence diameter, d h Indicates the drilling diameter, δ represents displacement, d b Indicates the diameter of the anchor rod during the pull-out test, represents the elastic modulus of the anchor body, It represents the Young's modulus of rock and soil.

[0193] Furthermore, the third determining module 204 is further configured to:

[0194] Determine stress and displacement based on the stress-displacement curve corresponding to the pull-out test results;

[0195] Substitute the stress and displacement into the Young's modulus formula of rock and soil to determine the Young's modulus of the rock mass in the target area.

[0196] According to an embodiment of the present invention, a device for determining the Young's modulus of a rock mass based on an anchor pull-out test is proposed. An anchor pull-out test is performed on a target area and corresponding pull-out test results are obtained. A formula for the shear modulus of the rock mass is determined. Based on the shear modulus formula of the rock mass, the Young's modulus formula of the rock mass is determined by taking into account the relationship between the shear modulus and the elastic modulus of the rock mass. Based on the pull-out test results and the Young's modulus formula of the rock mass, the Young's modulus of the rock mass in the target area is determined. 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 Young's modulus formula of the rock mass. Thus, the Young's modulus of the rock mass can be inverted by introducing the anchor pull-out test data, thereby achieving rapid and accurate determination of the Young's modulus of the rock mass. This simplifies the experimental process, reduces costs and minimizes sample damage, improves test efficiency and data accuracy, and brings technological innovation and reliable support for engineering practice to the field of rock mechanics testing.

[0197] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0198] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features, structures, materials, or characteristics described in conjunction 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 any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0199] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify 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 an anchor pull-out experiment, characterized in that: The method comprises: Conduct anchor pull-out tests on the target area and obtain the corresponding pull-out test results; Determine the formula for shear modulus of rock and soil; Based on the shear modulus formula of the rock and soil mass, the Young's modulus formula of the rock and soil mass is determined by the relationship between the shear modulus and the elastic modulus of the rock and soil mass; 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 the rock mass; The formula for determining the shear modulus of rock and soil includes: Determine the governing equations of the anchor system; Determine the equilibrium relationship of micro-element of grouting body or rock and soil body; Determine the relationship between shear stress and shear strain within the rock mass; Based on the control equation of the anchor system, the equilibrium relationship of the microelement of the grouting body or rock-soil body, and the relationship between the shear stress and shear strain inside the rock-soil body, the anchor end displacement formula is determined, wherein, based on the equilibrium relationship of the microelement of the grouting body or rock-soil body and the relationship between the shear stress and shear strain inside the rock-soil body, the first homogeneous linear differential equation of the rock-soil body is determined; based on the first general solution of the rock-soil body displacement of the first homogeneous linear differential equation, the rock-soil body displacement formula and the rock-soil body internal shear stress distribution formula are obtained; based on the second general solution of the grouting body displacement of the first homogeneous linear differential equation, the grouting body displacement formula and the grouting body internal shear stress distribution formula are obtained; at the interface between the grouting body and the rock-soil body, based on the rock-soil body internal shear stress distribution formula and the grouting body internal shear stress distribution formula, a boundary relationship formula is obtained; based on the grouting body internal shear stress distribution formula and the boundary relationship formula, the anchor end displacement formula is determined; Based on the anchor rod end displacement formula, the rock and soil shear modulus formula is determined.

2. The method according to claim 1, characterized in that The formula for determining the displacement of the anchor end based on the shear stress distribution formula inside the grouting body and the boundary relationship formula includes: Based on the shear stress distribution formula inside the grouting body and the boundary relationship formula, a shear stress distribution formula at the interface between the anchor body and the grouting body is obtained; Determine the 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 perpendicular to the anchor axis when the anchor body is in the elastic state; Determining a second homogeneous linear differential equation based on the shear stress distribution formula at the interface between the anchor body and the grouting body, the linear relationship formula, and the governing equation of the anchor system; Based on the general solution of the second homogeneous linear differential equation, a formula for the axial displacement in the anchor body is obtained; Based on the axial displacement formula in the anchor rod body, the anchor rod end displacement formula is determined.

3. The method according to claim 1, characterized in that The Young's modulus formula of rock and soil includes: in, represents the Poisson's ratio of the rock and soil, P0 represents the stress, G g represents the shear modulus of the anchor mortar, d0 represents the anchor influence diameter, d h Indicates the drilling diameter, δ represents displacement, d b Indicates the diameter of the anchor rod during the pull-out test, represents the elastic modulus of the anchor body, It represents the Young's modulus of rock and soil.

4. The method according to claim 1, wherein The determining of 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 mass comprises: determining stress and displacement based on a stress-displacement curve corresponding to the pull-out test result; Substituting the stress and the displacement into the Young's modulus formula of the rock mass, the Young's modulus of the rock mass in the target area is determined.

5. A device for determining the Young's modulus of rock mass based on an anchor pull-out experiment, characterized in that: The device comprises: An acquisition module is used to perform an anchor pull-out test on a target area and obtain corresponding pull-out test results; The first determination module is used to determine the shear modulus formula of the rock and soil mass; A second determining module is configured to determine a 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; A third determination module 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 mass; The first determining module is specifically configured to: Determine the governing equations of the anchor system; Determine the equilibrium relationship of micro-element of grouting body or rock and soil body; Determine the relationship between shear stress and shear strain within the rock mass; Based on the control equation of the anchor system, the equilibrium relationship of the microelement of the rock and soil body, and the relationship between the shear stress and shear strain inside the rock and soil body, the anchor end displacement formula is determined, wherein, based on the equilibrium relationship of the microelement of the grouting body or rock and soil body and the relationship between the shear stress and shear strain inside the rock and soil body, the first homogeneous linear differential equation of the rock and soil body is determined; based on the first general solution of the rock and soil body displacement of the first homogeneous linear differential equation, the rock and soil body displacement formula and the rock and soil body internal shear stress distribution formula are obtained; based on the second general solution of the grouting body displacement of the first homogeneous linear differential equation, the grouting body displacement formula and the grouting body internal shear stress distribution formula are obtained; at the interface between the grouting body and the rock and soil body, based on the rock and soil body internal shear stress distribution formula and the grouting body internal shear stress distribution formula, a boundary relationship formula is obtained; based on the grouting body internal shear stress distribution formula and the boundary relationship formula, the anchor end displacement formula is determined; Based on the anchor rod end displacement formula, the rock and soil shear modulus formula is determined.

6. An electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed 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 perform the method according to any one of claims 1 to 4.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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