A method for measuring the cohesion and internal friction angle of rock mass

Abstract

This invention discloses a method for measuring the cohesion and internal friction angle of fractured rock mass, comprising: Step 1, preparing a rock specimen from the fractured rock mass to be tested, and obtaining the cohesion c0, internal friction angle, and basic friction angle of the intact rock in the rock specimen; Step 2, calculating the damage variable D of the rock specimen; Step 3, obtaining the cohesion and internal friction angle of the fractured rock mass during loading. The calculation parameters in this method are all based on measured data, reducing human error. Furthermore, the measurement is primarily non-destructive testing, requiring less work, and can be performed at high frequency during construction.

Description

Technical Field

[0001] This invention belongs to the field of rock engineering technology, specifically relating to a method for measuring the cohesion and internal friction angle of fractured rock masses. Background Technology

[0002] In rock engineering exploration and construction, indoor rock mechanics tests are usually used to obtain the physical and mechanical parameters of rocks. Then, the physical and mechanical parameters of the rocks are reduced according to the rock mass fracture condition to indirectly obtain the physical and mechanical parameters of the rock mass. This measurement method has two main drawbacks: (1) When reducing the physical and mechanical parameters of rocks, the reduction parameters are usually obtained by looking up tables (such as GSI) according to the rock mass fracture condition, which is highly subjective and relies on personnel experience; (2) As construction progresses, the stress and strain state of the rock mass changes in real time. This measurement method usually has a low measurement frequency and it is difficult to obtain the physical and mechanical parameters of the rock mass in real time. In response to these two problems, this invention proposes a method for measuring the cohesion and internal friction angle of fractured rock mass. The calculated parameters are all based on measured data, which reduces human error. Moreover, the measurement is mainly based on non-destructive testing, which reduces the workload and allows for high-frequency measurement during construction. Summary of the Invention

[0003] The purpose of this invention is to provide a method for measuring the cohesion and internal friction angle of fractured rock masses. The calculation parameters are all based on measured data, which reduces human error. Furthermore, the measurement is mainly based on non-destructive testing, which requires less work and can be performed at high frequency during construction.

[0004] This invention adopts the following technical solution: a method for calculating damage variables in fractured rock mass, the calculation method comprising the following:

[0005] The rock mass is assumed to consist of two parts: intact rock and voids and fissures. Under the action of maximum principal stress and minimum principal stress, the rock mass has a potential shear fracture surface, which consists of intact rock, closed cracks and open cracks.

[0006] Porosity and fractures in rock mass are defined as damage to the rock mass, and represented by the damage variable D:

[0007] (1);

[0008] in: For the longitudinal wave velocity of intact rock, For the transverse wave velocity of intact rock, The longitudinal wave velocity of the rock mass. The transverse wave velocity of the rock mass. For the density of the rock mass, Poisson's ratio of the rock mass; For the longitudinal wave velocity of intact rock, The transverse wave velocity of intact rock.

[0009] This invention also discloses a method for dynamically measuring the cohesion and internal friction angle of fractured rock masses, the method being as follows:

[0010] Take rock specimens and assume that the rock mass consists of two parts: intact rock and voids and fissures. Under the action of the maximum principal stress and the minimum principal stress, the rock mass has a potential shear fracture surface, which consists of intact rock, closed cracks and open cracks. Define the voids and fissures in the rock mass as the damage of the rock mass, and use the damage variable D to represent it.

[0011] Step A: Obtain D:

[0012] (1);

[0013] Step B (85);

[0014] Before the rock yields, the crack length opens. The degree of crack closure is:

[0015] (86);

[0016] By monitoring the wave velocity in real time during the compression process, the loss variable D of the specimen can be obtained in real time.

[0017] Based on the relationship between damage variables and cracks:

[0018] (87);

[0019] Before surrendering:

[0020] (88);

[0021] From formulas (86) and (88) and ;

[0022] Shear strength of rock mass for:

[0023] (14);

[0024] Determine the cohesion of the fractured rock mass and internal friction angle ;

[0025] in: For the longitudinal wave velocity of intact rock, For the transverse wave velocity of intact rock, The longitudinal wave velocity of the rock mass. The transverse wave velocity of the rock mass. For the density of the rock mass, Poisson's ratio of the rock mass;

[0026] The axial strain at the critical point of elastic deformation; The proportionality coefficient at the critical point; The axial stress at the critical point of elastic deformation; This is the maximum principal stress; The elastic modulus of the rock mass; The angle between the shear plane and the plane where the maximum principal stress occurs; The elastic modulus of intact rock; The initial length of the closed crack; The initial length of the crack opening; The length of the shear plane; The initial length of the specimen before loading; For the length of the closed crack, The length of the open crack. Let A be the damage variable during the elastic deformation stage; and let A be the total area of ​​the shear surface. For the complete rock area, The area of ​​the closed crack. This represents the normal stress on the shear plane.

[0027] Furthermore, (61);

[0028] (62);

[0029] in: The diameter is the specimen diameter.

[0030] This invention also discloses a method for dynamically measuring the cohesion and internal friction angle of fractured rock mass. The method employs the aforementioned method for dynamically measuring the cohesion and internal friction angle of fractured rock mass, and includes the following steps:

[0031] Step 1: Take a piece of the fractured rock mass to be tested and prepare a rock specimen to obtain the cohesion of the intact rock within the specimen. and internal friction angle and the basic angle of friction of rocks ;

[0032] Step 2: Calculate the damage variable D of the rock specimen:

[0033] Before loading the rock specimen, the longitudinal wave velocity of the intact rock was measured. transverse wave velocity of intact rock ;

[0034] The rock specimen was subjected to loading and compression, and the wave velocity of the specimen was detected simultaneously during the loading and compression process. Multiple wave velocity values ​​were obtained, and these values ​​were substituted into equation (27) in sequence:

[0035] (1);

[0036] Multiple corresponding damage variable values ​​were calculated;

[0037] Step 3: Obtain the cohesion and internal friction angle of the fractured rock mass during loading:

[0038] Step 3.1, obtain (6);

[0039] Step 3.2, before the rock yields, according to formulas (54) and (56):

[0040] (7);

[0041] (8);

[0042] Find and ;

[0043] From the formula (14)

[0044] Determine the cohesion of fractured rocks and internal friction angle ;

[0045] Step 4: Obtain the damage variables and corresponding cohesion from Steps 2 and 3 using the least squares method. and internal friction angle Its fitting formula is:

[0046] (9);

[0047] (10);

[0048] in: , , and All of these are fitting constants, obtained through fitting, and their values ​​are related to lithology;

[0049] Step 5: Obtain the longitudinal wave velocity and transverse wave velocity of the fractured rock mass on site, calculate the damage variables of the rock mass, and obtain the cohesion and internal friction angle of the rock mass through equations (60) and (61).

[0050] The beneficial effects of this invention are: 1. It directly calculates based on measured data, eliminating the need for manual determination of calculation parameters and reducing human error. 2. It provides a method for obtaining rock mass cohesion and internal friction angle in real time through wave velocity measurement. The measurement method is non-destructive testing and can be performed at high frequency during construction. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of a generalized model of a fractured rock mass;

[0052] Figure 2 This is a schematic diagram of the stress on the lower shear surface of a fractured rock mass under compression.

[0053] Figure 3 This is a schematic diagram of an indoor mechanical testing method for fractured rock;

[0054] Figure 4 It is the stress-strain curve of the specimen during compression;

[0055] Figure 5 This is a schematic diagram of the compression process of a broken rock specimen. Detailed Implementation

[0056] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0057] This invention provides a method for calculating damage variables in fractured rock masses, the method comprising the following steps:

[0058] The rock mass is defined as consisting of two parts: intact rock and porous / fractured rock. Figure 1 As shown, the rock mass has potential shear fracture surfaces under the action of maximum principal stress and minimum principal stress. The shear fracture surfaces consist of intact rock, closed cracks and open cracks.

[0059] The voids and fissures in the rock mass are defined as the damage to the rock mass, and represented by the damage variable D.

[0060] (1);

[0061] in: For the longitudinal wave velocity of intact rock, For the transverse wave velocity of intact rock, The longitudinal wave velocity of the rock mass. The transverse wave velocity of the rock mass. For the density of the rock mass, The value is Poisson's ratio of the rock mass.

[0062] The wave velocity of a rock mass is related to its shear modulus, bulk modulus, and density.

[0063] (11);

[0064] (12);

[0065] Therefore, the Poisson's ratio and elastic modulus of a rock can be related to wave velocity:

[0066] (13);

[0067] (14);

[0068] in: The elastic modulus of the rock mass. The value is Poisson's ratio of the rock mass.

[0069] The present invention also provides a method for dynamically measuring the cohesion and internal friction angle of fractured rock masses, the method being as follows:

[0070] Rock specimens were prepared, and the rock mass was set to consist of two parts: intact rock and voids and fissures. The rock mass also had potential shear fracture surfaces under the action of maximum principal stress and minimum principal stress. The shear fracture surfaces consisted of intact rock, closed cracks and open cracks.

[0071] Basic angle of friction of rocks Shear strength All of these can be obtained directly through indoor testing. The area of ​​the intact rock is... The area of ​​the closed crack is The area of ​​the open crack is Since the discrete nature of rock mass makes it impossible to obtain information directly, we define the voids and fissures in the rock mass as damage, denoted by the damage variable D; D=0 represents no damage (intact rock D=0), and D=1 represents complete damage (which is practically impossible).

[0072] When an intact rock is subjected to compression, the stress-strain relationship is as follows:

[0073] (15);

[0074] In the formula: The elastic modulus of intact rock. For the Poisson's ratio of a complete rock, For the maximum principal stress, The intermediate principal stress, It is the minimum principal stress.

[0075] For rock masses, due to the presence of numerous voids and fissures within them, the stress-strain relationship under compression is as follows:

[0076] (16);

[0077] In the formula, The elastic modulus of the rock mass. Poisson's ratio of the rock mass For the maximum principal stress, The intermediate principal stress, This represents the minimum principal stress. Where:

[0078] (17);

[0079] (18);

[0080] Assume the relationship between damage variables and cracks is as follows:

[0081] (19);

[0082] in: The area of ​​the closed crack. This represents the area of ​​the crack.

[0083] Introducing a coefficient λ to represent the crack closure degree, then:

[0084] (20);

[0085] (twenty one);

[0086] (twenty two);

[0087] Wave velocity can be used to indirectly determine the degree of damage to rock masses. Previous studies have shown that wave velocity in rock masses is related to shear modulus, bulk modulus, and density.

[0088] (twenty three);

[0089]

[0090] Therefore, the Poisson's ratio and elastic modulus of a rock can be related to wave velocity:

[0091]

[0092]

[0093] In the formula: The longitudinal wave velocity of the rock mass. The transverse wave velocity of the rock mass. For the density of the rock mass, The elastic modulus of the rock mass. The rock mass has a Poisson's ratio. The elastic modulus and Poisson's ratio, measured indirectly by wave velocity, are the dynamic elastic modulus and dynamic Poisson's ratio, respectively.

[0094] Damage variables were obtained:

[0095] (1);

[0096] like Figure 2 As shown, the total area of ​​the shear plane is A, and the area of ​​the intact rock is... The area of ​​the closed crack is The area of ​​the open crack is .

[0097] (27);

[0098] According to the Mohr-Coulomb theory, the normal compressive stress and shear stress on the shear plane are:

[0099] (28);

[0100] (29);

[0101] In the formula: The normal stress on the shear plane, The tangential stress on the shear plane, For the maximum principal stress, For the minimum principal stress, The angle between the shear plane and the plane of maximum principal stress is denoted as .

[0102] (30);

[0103] In the formula: This is the internal friction angle within the rock mass (Note: the internal friction angle here is not the same as the internal friction angle of the rock block).

[0104] Thus, the shear force on the rock mass at the shear plane is:

[0105] (31);

[0106] Before shear failure occurs in the rock mass, the rock mass on both sides of the shear plane will not slide along the shear plane; therefore, a resistance force F will be generated on the shear plane to resist the shear force T. Figure 2 We can obtain:

[0107] (32);

[0108] in: The resistance generated by intact rock, The resistance generated by closing the crack, The resistance generated to opening the crack.

[0109] Since there is no cohesive force or frictional force involved in opening the crack, .

[0110] The maximum drag that intact rock can generate depends on its shear strength. Its expression is:

[0111] (33);

[0112] The resistance generated by a closed crack is mainly in the normal stress. The frictional force generated under the action of , therefore:

[0113] (34);

[0114] In the formula: The normal pressure acting on the closed crack. The coefficient of friction on a closed crack. It can be approximated by the basic friction angle:

[0115] (35);

[0116] In the formula: This is the basic friction angle of the rock.

[0117] When the shear force reaches the critical value:

[0118] (36);

[0119] Therefore, the overall shear strength of the rock mass It can be represented as:

[0120] (37);

[0121] According to the Mohr-Coulomb theory, the shear strength of rock is related to cohesion and the angle of internal friction. Therefore, the shear strength of rock mass can be expressed as:

[0122] (38);

[0123] In the formula: The cohesion of the rock mass, The internal friction angle of the rock mass is denoted as .

[0124] For intact rock:

[0125] (39);

[0126] Shear strength of rock mass for:

[0127] (14)

[0128] Determine the cohesion of the fractured rock mass and internal friction angle ;

[0129] in: For the longitudinal wave velocity of intact rock, For the transverse wave velocity of intact rock, The longitudinal wave velocity of the rock mass. The transverse wave velocity of the rock mass. For the density of the rock mass, Poisson's ratio of the rock mass; For the longitudinal wave velocity of intact rock, The transverse wave velocity of intact rock;

[0130] The axial strain at the critical point of elastic deformation; The proportionality coefficient at the critical point; The axial stress at the critical point of elastic deformation; E represents the maximum principal stress; E is the elastic modulus of the rock mass. The angle between the shear plane and the plane where the maximum principal stress occurs; The elastic modulus of intact rock; The initial length of the closed crack; The initial length of the crack opening; The length of the shear plane; The initial length of the specimen before loading; For the length of the closed crack, The length of the open crack. Let A be the damage variable during the elastic deformation stage; and let A be the total area of ​​the shear surface. For the complete rock area, The area of ​​the closed crack. This represents the normal stress on the shear plane.

[0131] For intact rock, its cohesion can be directly obtained through indoor triaxial compression tests. and internal friction angle The basic angle of friction of rocks It can also be obtained through tilt tests or direct shear tests. The method proposed in this invention requires first obtaining the basic friction angle of the rock through conventional indoor mechanical tests. and the cohesion of intact rock. and internal friction angle .

[0132] By carrying out such Figure 3The indoor rock mechanics test shown can simulate the stress on fractured rock mass. The test specimen is a 50×100mm cylindrical specimen, which needs to be pre-compressed until failure to simulate the stress on fractured rock mass. The loading provides axial pressure σ1 and confining pressure σ3. An acoustic wave detection probe is installed on the loading device to simultaneously detect the wave velocity of the specimen during loading.

[0133] For a cylindrical specimen, if the length of the shear plane is... The length of the intact rock in the longitudinal section is The length of the closed crack is The length of the open crack is The diameter of the specimen is ,but

[0134] (40);

[0135] (41);

[0136] (42);

[0137] (43);

[0138] (44);

[0139] The stress-strain curve of the specimen during compression is as follows: Figure 4 As shown. To better analyze the deformation and failure mechanism of the fractured rock specimen under compression, the rock specimen is divided into a porous part and a skeletal part on a macroscopic scale, as shown. Figure 5 As shown.

[0140] Based on this assumption, the initial length of the specimen before loading is defined as... The length of the gap is defined as The length of the solid skeleton is defined as The initial length of a complete rock is defined as The initial length of a closed crack is defined as The initial length of the opening crack is defined as .

[0141] (45);

[0142] (46);

[0143] Specimen under axial stress The axial deformation under the action is ∆l. The deformation of the rock skeleton is expressed as... The deformation of the void portion is represented as Therefore, the strain of the fractured rock can be expressed as:

[0144] (47);

[0145] (48);

[0146] (49);

[0147] Crack closure degree:

[0148] (50);

[0149] Axial strain of rock solid skeleton Axial strain of the void portion They can be represented by equations (51) and (52) respectively. The relationship between them is shown in equation (53).

[0150] In the initial stage of loading, the axial strain of the specimen consists of the axial strain of the rock skeleton and the axial strain of the void portion, and its value is the sum of the two. When the stress reaches the critical point ( Figure 4 At point A in the diagram, the compaction process of micropores and fissures in the rock specimen is essentially complete. At this point, the axial strain of the pore portion reaches its maximum value. And it remains unchanged thereafter.

[0151] (51);

[0152] (52);

[0153] (53);

[0154] To describe the relationship between the strain in the void portion and the total strain, a proportionality coefficient is defined. .

[0155] (54);

[0156] The test results show that during the compaction stage ( Figure 4 In the OA segment (in the diagram), the value of γ decreases monotonically with the increase of axial strain, and there is an approximately linear relationship between axial strain and γ.

[0157] Due to the coefficient in the compaction stage There is a linear relationship between the axial strain of the rock specimen and the strain of the rock specimen, and its coefficient is defined as follows: :

[0158] (55);

[0159] The coefficient k can be calculated based on the geometric relationship of the straight line:

[0160] (56);

[0161] During the compaction stage ( Figure 4 (OA segment in the middle) Relationship with axial strain It can be represented as:

[0162] (57);

[0163] so, The following formula can be used for calculation:

[0164] (58);

[0165] Closed cracks and open cracks are:

[0166] (59);

[0167] (60);

[0168] Crack closure degree:

[0169] (61);

[0170] No new cracks will form before yielding, therefore Nothing will change. It will not change.

[0171] When the stress value reaches the critical point ( Figure 4 At point A in the diagram, the strain in the void portion reaches its maximum value. And it remains unchanged thereafter. Therefore, It can be represented as:

[0172] (62);

[0173] According to the evolution law of elastic strain energy, before rock yields, the deformation of the rock skeleton under load can be regarded as elastic deformation. Assumption:

[0174] (63);

[0175] Based on the above assumptions, it can be calculated using equation (64). Calculated using equation (65) .

[0176] (64);

[0177] (65).

[0178] at this time The degree of crack closure is:

[0179] (86);

[0180] By monitoring the wave velocity in real time during compression, the loss variable D of the specimen can be obtained in real time. Based on the relationship between the damage variable and the crack:

[0181] (87);

[0182] Before loading:

[0183] (88);

[0184] Combining equations (86), (87), and (88) allows for the calculation of... and .at this time, , , , , , All have been obtained through experiments; the unknown quantities are only... and .at this time, , , , , , All have been obtained through experiments; the unknown quantities are only... and This is the solution to a system of two linear equations.

[0185] This invention also discloses a method for dynamically measuring the cohesion and internal friction angle of fractured rock mass. The method employs the aforementioned method for dynamically measuring the cohesion and internal friction angle of fractured rock mass, and includes the following steps:

[0186] Step 1: Take a piece of the fractured rock mass to be tested and prepare a rock specimen to obtain the cohesion of the intact rock within the specimen. and internal friction angle and the basic angle of friction of rocks ;

[0187] Cohesion of intact rock and internal friction angle The maximum principal stress can be obtained indoors through conventional triaxial compression tests. and minimum principal stress And the calculation is performed according to the Mohr-Coulomb theory, that is:

[0188] (69);

[0189] (70);

[0190] (71);

[0191] As long as two or more groups are obtained simultaneously and The above equation can then be solved.

[0192] Step 2: Calculate the damage variable D of the rock specimen:

[0193] Before loading the rock specimen, the longitudinal wave velocity of the intact rock was measured. transverse wave velocity of intact rock ;

[0194] The rock specimen was subjected to loading and compression, and the wave velocity of the specimen was detected simultaneously during the loading and compression process. Multiple wave velocity values ​​were obtained, and these values ​​were substituted into equation (1) in sequence:

[0195] (1);

[0196] Multiple corresponding damage variable values ​​were calculated;

[0197] Step 3: Obtain the cohesion and internal friction angle of the fractured rock mass during loading:

[0198] Step 3.1, obtain (73);

[0199] Step 3.2, before the rock yields, according to formulas (54) and (56):

[0200] (74);

[0201] (75);

[0202] Find and ;

[0203] From the formula (14)

[0204] Determine the cohesion of fractured rocks and internal friction angle ;

[0205] Step 4: Obtain the damage variables and corresponding cohesion from Steps 2 and 3 using the least squares method. and internal friction angle Its fitting formula is:

[0206] (76);

[0207] (77);

[0208] in: , , and These are all fitting constants, obtained through fitting, and their values ​​are related to lithology;

[0209] Step 5: Obtain the longitudinal wave velocity and transverse wave velocity of the fractured rock mass on site, calculate the damage variables of the rock mass, and obtain the cohesion and internal friction angle of the rock mass through equations (76) and (77).

[0210] Taking a type of sandstone as an example, this sandstone has a shear wave velocity of 2500~2800 m / s and a longitudinal wave velocity of 1300~1500 m / s. The corresponding fitting coefficients are: , , , In its complete state, its internal friction angle Therefore , ; , Therefore ; .

[0211] Using the method of this invention, the P-wave velocity of rock mass can be obtained at the construction site via seismic wave analysis. and transverse wave velocity This measurement method is a non-destructive testing method with a small workload, and can be performed at high frequency during construction. By detecting the wave velocity, the damage variable D of the rock mass can be calculated, and then the cohesion of the rock mass can be obtained through equations (60) and (61). and internal friction angle .

Claims

1. A method for dynamically measuring the cohesion and internal friction angle of fractured rock mass, characterized in that, The method includes the following: Step 1: Take a piece of the fractured rock mass to be tested and prepare a rock specimen to obtain the cohesion of the intact rock within the specimen. and internal friction angle and the basic angle of friction of rocks ; Step 2: Calculate the damage variable D of the rock specimen: Before loading the rock specimen, the longitudinal wave velocity of the intact rock was measured. transverse wave velocity of intact rock ; The rock specimen was subjected to loading and compression, and the wave velocity of the specimen was detected simultaneously during the loading and compression process. Multiple wave velocity values ​​were obtained, and these values ​​were substituted into equation (1) in sequence: （1）； in: For the longitudinal wave velocity of intact rock, For the transverse wave velocity of intact rock, The longitudinal wave velocity of the rock mass. E represents the transverse wave velocity of the rock mass, E represents the elastic modulus of the rock mass, and E0 represents the elastic modulus of the intact rock. The damage variable values ​​corresponding to multiple wave velocities were calculated; Step 3: Obtain the cohesion and internal friction angle of the fractured rock mass during loading: Step 3.1, obtain (85); Step 3.2, before the rock yields, according to formulas (86) and (88): （86）； （88）； Find and ; From the formula （14）， Determine the cohesion of fractured rocks and internal friction angle ; in: The axial strain at the critical point of elastic deformation; The proportionality coefficient at the critical point; The axial stress at the critical point of elastic deformation; This is the maximum principal stress; The elastic modulus of the rock mass; The angle between the shear plane and the plane where the maximum principal stress occurs; The elastic modulus of intact rock; The initial length of the closed crack; The initial length of the crack opening; The length of the shear plane; The initial length of the specimen before loading; For the length of the closed crack, The length of the open crack. Let A be the damage variable during the elastic deformation stage; and let A be the total area of ​​the shear surface. For the complete rock area, The area of ​​the closed crack. Normal stress on the shear plane The degree of crack closure. The shear strength of the rock mass; Step 4: Obtain the damage variables and corresponding cohesion from Steps 2 and 3 using the least squares method. and internal friction angle Its fitting formula is: （96）； （97）； in: , , and All of these are fitting constants, obtained through fitting, and their values ​​are related to lithology; Step 5: Obtain the longitudinal wave velocity and transverse wave velocity of the fractured rock mass on site, calculate the damage variables of the rock mass, and obtain the cohesion and internal friction angle of the rock mass through equations (96) and (97).

2. The method for dynamically measuring the cohesion and internal friction angle of fractured rock mass according to claim 1, characterized in that, （61）； （62）； in: The diameter of the specimen. This represents the length of the intact rock in the longitudinal section.

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