Method for predicting mechanical parameters of discontinuous jointed rock mass based on hoek-brown criterion

Abstract

The application discloses a kind of intermittent joint rock mass mechanical parameter prediction method based on Hoek-Brown criterion, by introducing the damage D caused by joint to rock mass, and the parabolic variation law of joint rock mass GSI with joint dip angle is established, and then the quantitative calculation method of s, a and m b Parameter is presented, which avoids the artificial error caused by the commonly used empirical value method. The above method is introduced into the calculation of uniaxial compressive strength, cohesion and internal friction angle and other mechanical parameters of jointed rock mass. Finally, the intermittent joint rock mass mechanical parameter prediction method based on H-B criterion is proposed, and it is successfully applied to the stability analysis of intermittent joint rock slope, providing a new idea for the research of this kind of problem.

Description

Technical Field

[0001] This invention belongs to the field of rock mechanics technology, specifically relating to a method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion. Background Technology

[0002] Accurately obtaining mechanical parameters such as compressive strength and deformation modulus in actual rock mass engineering projects such as tunnels and slopes is the prerequisite and foundation for reasonable rock mass engineering design and stability evaluation. Therefore, how to quickly and accurately obtain rock mass mechanical parameters has always been a major challenge for the academic and engineering communities of rock mechanics. In-situ testing methods suffer from high costs, implementation difficulties, and large result dispersion. Therefore, the commonly used method is to drill in the field to collect samples, process them into standard specimens, and conduct laboratory tests. The laboratory test results are then reasonably reduced based on the field geological conditions, especially the development and characteristics of structural surfaces such as joints and fissures. However, although various reduction methods have been proposed, due to the varying field geological conditions, current methods often only consider one factor. For example, Yin Jinghan et al. focused on the influence of joint roughness, thereby deriving a method for calculating the equivalent elastic compliance matrix of the rock mass. Therefore, current methods mainly suffer from large result errors and poor method universality.

[0003] The Hoek-Brown (HB) criterion, first proposed in 1980, is a rock mass strength failure criterion developed by fully considering the geological characteristics of actual rock masses, such as joints and fissures. After years of development and improvement, it has gradually matured. In particular, by introducing the geological strength index GSI and the damage variable (or disturbance coefficient) D, it better considers the specific conditions of actual rock masses, including geological features and the impact of construction disturbances. However, accurately determining these two parameters has become a new challenge. Initially, the methods for determining these parameters were based on a comprehensive selection of rock mass structural characteristics, the state of structural planes, and the damage caused by construction disturbances. These methods were relatively crude, highly subjective, and failed to adequately reflect the anisotropy caused by joints to the mechanical properties of the rock mass. Therefore, many scholars have conducted in-depth research and, drawing on the functional relationship between the rock mass disturbance parameter D and GSI proposed by predecessors, quantified the calculation method of D. Finally, the HB criterion was applied to determine the rock mass mechanical parameters of a mine roadway. The above research has greatly helped in the accurate selection of GSI and D, but it still has a certain degree of subjectivity and lacks corresponding quantitative methods. Li Guoxiao et al., based on triaxial compression test data of rock masses at different bedding dip angles, obtained the variation law of GSI with bedding dip angle, and established a quantitative relationship between GSI and bedding dip angle using a Gaussian function, further improving the accuracy of GSI value determination. This provides a good approach for accurate GSI value determination.

[0004] Therefore, based on previous research, this study aims to address the shortcomings of the current HB criterion, such as the strong subjectivity in the selection of key parameters GSI and D and the failure to adequately consider the influence of joint dip angle. By introducing a calculation method for GSI and D that considers joint dip angle, a method for predicting the mechanical parameters of discontinuous jointed rock masses based on the HB criterion will be proposed. This method will then be applied to the stability calculation of discontinuous jointed rock slopes to explore the influence of joint dip angle on slope stability. Summary of the Invention

[0005] To address the aforementioned problems, embodiments of the present invention propose a method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion.

[0006] The method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion of the present invention includes the following steps:

[0007] S1. Establish the calculation formula for the deformation modulus of jointed rock mass;

[0008] S2. Establish the calculation formula for the uniaxial compressive strength of jointed rock mass;

[0009] S3. Establish the calculation formula for damage variables in jointed rock masses;

[0010] S4. Establish the calculation formula for the geological strength index of jointed rock mass;

[0011] S5. Substitute the jointed rock mass damage variables and jointed rock mass geological strength indices into the calculation formula for the jointed rock mass deformation modulus to obtain the jointed rock mass deformation modulus;

[0012] S6. Substitute the jointed rock mass damage variables and jointed rock mass geological strength indices into the calculation formula for the uniaxial compressive strength of the jointed rock mass to obtain the uniaxial compressive strength of the jointed rock mass.

[0013] The formula for calculating the damage variable of the jointed rock mass is as follows:

[0014]

[0015] In the formula, D j For jointed rock masses, that is, the damage variable caused by a single set of multiple rows of discontinuous joints to the rock mass in the vertical direction; J V Joint density in a plane, strips / m 2 ; α and denoted as joint dip angle (°) and friction angle (°); a, b, and d represent joint half-length (m), center-to-center distance (m), and row spacing (m), respectively; f(a,b,d) is a coefficient reflecting the mutual influence of joints.

[0016] The formula for calculating the geological strength index of the jointed rock mass is as follows:

[0017]

[0018] In the formula, GSI j GSI is the geological strength index of jointed rock mass; α is the joint dip angle (°); max (Corresponding to rock masses with joint dip angles of 0° and 90°) and GSI min (Corresponding to rock masses with a joint dip angle of 45°) are GSI j The minimum and maximum values.

[0019] The formula for calculating the deformation modulus of the jointed rock mass is:

[0020]

[0021] In the formula, E rm E i Here, GSI and D represent the deformation modulus of jointed rock mass and intact rock mass, respectively, in MPa; GSI is the geological strength index of intact rock mass, and D is the damage variable of intact rock mass. When intact rock mass undergoes complex geological processes or engineering disturbances, GSI and D change from 100 and 0 for intact rock mass to GSI for jointed rock mass, respectively. j and D j .

[0022] The formula for calculating the uniaxial compressive strength of the jointed rock mass is as follows:

[0023]

[0024] In the formula, σ rc σ1 is the uniaxial compressive strength of the jointed rock mass; σ1 is the maximum principal stress; σ2 is the uniaxial compressive strength of the jointed rock mass. c For the uniaxial compressive strength of intact rock; s and All of these are rock mass material strength parameters.

[0025] The formula for calculating the strength parameters of the rock mass material is as follows:

[0026]

[0027] In the formula, D j For jointed rock masses, the damage variable is GSI. j This is a geological strength index for jointed rock masses.

[0028] The beneficial effects of this invention are that, in view of the shortcomings of existing methods for determining the values ​​of rock mass GSI and D in the HB criterion, such as strong human subjectivity and large errors, a method for calculating the rock mass damage variable D caused by joints is introduced, and a parabolic GSI calculation model is established to improve the prediction accuracy of GSI and D. On this basis, a method for predicting joint rock mass mechanical parameters such as uniaxial compressive strength based on the HB criterion is proposed. This method reflects well the influence of joint dip angle on rock mass mechanical parameters. Attached Figure Description

[0029] Figure 1 It is a jointed rock mass in an open-pit mine.

[0030] Figure 2 This is a schematic diagram of the method for predicting the uniaxial compressive strength of jointed rock mass according to the present invention.

[0031] Figure 3 This invention relates to a cylindrical specimen containing a single set of joints.

[0032] Figure 4 This is a comparison between the predicted and measured values ​​of the jointed specimen strength of the present invention.

[0033] Figure 5 This invention relates to a rock slope containing a single set of discontinuous joints.

[0034] Figure 6 These are the calculation results of the potential slip surface and stability coefficient of the slope in this invention.

[0035] Figure 7 This invention describes the variation law of slope stability coefficient with joint dip angle. Detailed Implementation

[0036] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0037] The method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion of the present invention includes the following steps:

[0038] S1. Establish the formula for calculating the deformation modulus of jointed rock mass.

[0039] Based on the Griffith fracture criterion and extensive statistical analysis of triaxial test results of intact rocks, Hoek and Brown first proposed the HB empirical strength criterion, namely:

[0040] (1)

[0041] In the formula: σ1 and σ3 are the maximum and minimum principal stresses, respectively; σc The uniaxial compressive strength of intact rock; m i is a constant for complete rock material.

[0042] If we let σ3 = 0, then we get: σ1 = σ c The maximum principal stress is the uniaxial compressive strength of the rock. However, this formula cannot reflect the influence of the rock mass structure on the compressive strength, and therefore it is only applicable to intact rocks.

[0043] To better apply this concept to actual jointed rock masses, a disturbance coefficient D is introduced to account for the damage to the rock mass caused by construction disturbances such as blasting and excavation, i.e.:

[0044] (2)

[0045] Where: m b s and All are rock mass material strength parameters; GSI is the rock mass geological strength index, and its value is determined as shown in Table 1; D is the damage to the rock mass caused by construction disturbances such as blasting and excavation, and its empirical value is determined as shown in Table 2.

[0046] Table 1. Method for determining the GSI value of rock mass

[0047]

[0048] Table 2 Method for determining the D value of rock mass damage

[0049]

[0050] Formula (2) is applicable to rock mass conditions such as Figure 1 This means that the rock mass is cut by multiple sets of joints, forming interlocking polygonal blocks. Under low to moderate confining pressure, the failure of the rock mass is mainly controlled by structural planes, manifested as block sliding and rotation, while the failure of intact rock blocks is less common.

[0051] The methods for determining the values ​​of GSI and D in the criteria were improved, and an expression for the rock mass deformation modulus was established for the characteristics of geotechnical engineering in China, namely:

[0052] (3)

[0053] In the formula: E rm E i , respectively, are the deformation moduli of jointed rock mass and intact rock mass, in MPa.

[0054] The deformation modulus of jointed rock mass can be calculated from the deformation modulus of intact rock and the GSI and D values ​​of the rock mass in the field using equation (3).

[0055] S2. Establish the calculation formula for the uniaxial compressive strength of jointed rock mass.

[0056] From the first equation of (2), we can see that when σ3=0, we can obtain σ1, i.e., the uniaxial compressive strength σ of the rock mass at the point of rock mass failure. rc for:

[0057] (4)

[0058] In the formula, σ rc σ1 is the uniaxial compressive strength of the jointed rock mass; σ1 is the maximum principal stress; σ2 is the uniaxial compressive strength of the jointed rock mass. c For the uniaxial compressive strength of intact rock; s and All of these are rock mass material strength parameters.

[0059] Due to σ c It can be measured by uniaxial compressive strength tests on intact indoor rock, so the key is how to determine s and From the second equation of equation (2), we can see that GSI and D can be obtained by referring to Tables 1 and 2, and from this, s and can be calculated. The above prediction method is illustrated in the diagram below. Figure 2 That is, assuming Figure 2 (a) is a complete rock, and its uniaxial compressive strength σ can be measured by laboratory tests. c After undergoing complex geological processes or engineering disturbances, it forms... Figure 2 (b) shows a jointed rock mass, where the GSI and D of the rock mass change from 100 and 0 for intact rock, respectively, to GSI. j and D j Therefore, how to accurately determine GSI j and D j This is an important aspect of the present invention.

[0060] The commonly used method is to obtain the GSI of jointed rock masses by referring to Tables 1 and 2. j and D j However, this method has three problems: ① The value selection principles given in the two tables above are all qualitative descriptions, thus inevitably containing strong subjective bias; ② The value selection conditions given in the two tables above are very limited. For example, Table 2 only gives five rock mass damage conditions: 0, 0.5, 0.7, 0.8, and 1.0, while the actual rock mass damage can be any value between 0 and 1; similarly, Table 1 only gives 20 cases where GSI is an integer multiple of 5 between 0 and 100, while the actual rock mass GIS may take any value between 0 and 100, thus human estimation will produce a large error; ③ The D and GSI values ​​given in the two tables above are not related to the joint dip angle, thus failing to reflect the influence of the joint dip angle on D, that is, failing to reflect the rock mass strength anisotropy problem caused by the presence of joints. Therefore, this invention intends to study the above three problems and firstly proposes a rock mass GSI considering the characteristics of joint distribution. j and Dj The calculation method is then used to predict the rock mass strength using equation (4).

[0061] S3. Establish the calculation formula for damage variables in jointed rock masses.

[0062] The following is based on Figure 2 (b) Taking the rock mass containing a single set of discontinuous joints as an example, we introduce its damage variable D. j The calculation method.

[0063] like Figure 2 (b) shows the damage variable D caused by a single set of multiple rows of discontinuous joints to the rock mass in the vertical direction (i.e., the uniaxial vertical compression direction). j For (for plane stress problems and neglecting joint surface cohesion):

[0064] (5)

[0065] In the formula, D j For jointed rock masses, the damage variable is J; V Joint density in a plane, strips / m 2 ; α and These are the joint dip angle (°) and the friction angle (°), respectively. b and d are the joint half length (m), center spacing (m), and row spacing (m), respectively. To reflect the coefficients that reflect the mutual influence of joints, if we assume that the upper and lower rows of joints are aligned, their values ​​are shown in Table 3.

[0066] Table 3 value

[0067]

[0068] The jointed rock mass damage variables obtained by this method can not only well take into account the influence of joint dip angle, but also the influence of other geometric parameters such as joint length and number of groups, as well as mechanical parameters such as friction angle, and therefore are more consistent with the mechanical characteristics of actual rock masses.

[0069] S4. Establish a calculation formula for the geological strength index of jointed rock mass.

[0070] The following discussion explores GSI (Glass Intake) of Jointed Rock Mass. j The calculation method currently mainly relies on the rock mass structural characteristics and structural plane conditions, as determined by Table 1. However, this method has two significant shortcomings: firstly, the rock mass conditions given in Table 1 are limited, and the values ​​are subject to considerable subjective judgment. Therefore, Hoek et al. established the GSI... j The relationship between the mass correction value Q' of the Barton rock mass and the mass correction value is as follows:

[0071] (6)

[0072] In the formula: RQD is the rock quality index, %; J n J r and These are the number of joint groups, the joint roughness coefficient, and the joint surface alteration coefficient, respectively.

[0073] Another important shortcoming is that it does not consider the influence of joint dip angle, as shown in equation (6), GSI j It is directly related to RQD, and the RQD value is the percentage of the cumulative length of core samples with a length of 10cm to the total length of the borehole core. For example... Figure 2 As shown in (b), when the borehole direction is fixed and vertically downward, the length of the intact core changes with the joint dip angle. For example, when the borehole direction is perpendicular to the joint strike, the length of the intact core is the shortest. Then, as the joint dip angle changes, the length of the intact core will increase. Therefore, according to equation (6), the GSI of the rock mass... j The GSI value will also vary with the joint dip angle. However, the GSI value method given in Table 1 does not consider the influence of the joint dip angle and therefore needs improvement. Meanwhile, Wang Keyi et al.'s research found that the rock mass GSI and its integrity coefficient K... v Proportional, K v The GSI is the square of the ratio of the P-wave velocity of the rock mass to the P-wave velocity of the rock block. Studies by Yan Xianzheng et al. have found that the joint dip angle affects the P-wave velocity of the rock mass, and thus the GSI of the rock mass can also be determined. j The GSI value is related to the joint dip angle. Li Guoxiao et al. also found that when the bedding dip angle increases from 0° to 90°, the GSI value of sandstone first decreases and then increases, exhibiting a distinct U-shape. Therefore, based on this finding, this invention assumes that the GSI of jointed rock masses... j The value is a function of the joint dip angle and forms a quadratic standard parabola opening upwards. That is, when the joint dip angle is considered to be 45°, the GSI of the rock mass is... j Minimum. Extensive research shows that when the joint dip angle is 0° and 90°, the effect of joints on the uniaxial compressive strength of the rock mass is minimal, and the uniaxial compressive strength of the rock mass is maximum at these angles. Therefore, the corresponding GSI of the rock mass is... j Maximum. Furthermore, based on the rock mass structure type and structural plane condition, Table 1 shows that when the joint dip angle varies from 0° to 90°, the GSI of the rock mass... j The relationship with the joint dip angle α can be expressed as:

[0074] (7)

[0075] In the formula, GSI j GSI is the geological strength index of jointed rock mass; α is the joint dip angle, °; max (Corresponding to rock masses with joint dip angles of 0° and 90°) and GSI min(Corresponding to rock masses with a joint dip angle of 45°) are GSI j The minimum and maximum values.

[0076] S5. Substitute the jointed rock mass damage variables and jointed rock mass geological strength indices into the calculation formula for the jointed rock mass deformation modulus to obtain the jointed rock mass deformation modulus.

[0077] S6. Substitute the jointed rock mass damage variables and jointed rock mass geological strength indices into the calculation formula for the uniaxial compressive strength of the jointed rock mass to obtain the uniaxial compressive strength of the jointed rock mass.

[0078] That is: the jointed rock mass damage variable D obtained from equations (5) and (7) respectively j and GSI j Substituting into equations (3) and (4) respectively, the deformation modulus E of the jointed rock mass can be obtained. rm and uniaxial compressive strength σ rc This method is a prediction method for the mechanical parameters of jointed rock masses based on the HB criterion.

[0079] It should also be noted that the uniaxial compressive strength and deformation modulus of rock are usually obtained by uniaxial compression tests on standard specimens (cylindrical specimens with a diameter of 50 mm and a length of 100 mm). However, current research suggests that even for intact rock specimens, there is still a significant size effect in their uniaxial compressive strength and deformation modulus. The fundamental reason for the size effect is the end-face friction effect at both ends of the specimen. When a special device is used to reduce the friction effect at both ends of the specimen, the size effect on the rock material strength can be ignored. Based on this, the influence of the size effect on the rock strength, i.e., σ, will not be considered here. rc This is taken as the uniaxial compressive strength of the standard rock specimen. It is also assumed that the joints in the rock mass are uniformly distributed; therefore, J... V、 b and d are all taken as the average values ​​of the entire study area.

[0080] Model Validation

[0081] To verify the rationality of this method, the experimental results of Zhao Xiucheng et al. are cited below for further study. The experiment adopted the following... Figure 3 The cylindrical specimen shown has a diameter of 100 mm, a height of 200 mm, and a joint length of 2 mm. =20mm, joint center spacing b=40mm, and row spacing d=90mm. Joint density J of the specimen in a two-dimensional plane. V =500 items / m 2The specimens were made from a mixture of gypsum and water at a mass ratio of 1:0.6. Joints were created using pre-cast steel sheets within a mold. After demolding, the specimens were cured indoors for 28 days. The physical and mechanical parameters of the intact specimens, measured using a uniaxial compression test, were: density 1179.86 kg / m³. 3 The uniaxial compressive strength was 3.19 MPa, the uniaxial tensile strength was 0.53 MPa, the elastic modulus was 1.75 GPa, and the Poisson's ratio was 0.181. The uniaxial compressive strength of specimens with different joint inclination angles is shown in Table 4. The joint friction angle is estimated to be 10º.

[0082] Table 4 Uniaxial compressive strength of specimens

[0083]

[0084] The damage variable D of rock masses with different joint dip angles is calculated below. j and GSI j First, by substituting the above parameters into equation (5), the damage variables of each specimen can be calculated as shown in Table 4. Second, the GSI of each specimen is calculated using equation (7). j Value, by Figure 3 It can be seen that the specimen was only cut by 2-3 sets of large-spacing and discontinuous joints, and the specimen was freshly processed. Therefore, the joint surface can be considered fresh and rough. Thus, as shown in Table 1, when the joint dip angle varies between 0° and 90°, GSI j The minimum value is approximately 80, and the maximum value can be taken as 100. That is, when the joint dip angle is 0°, its uniaxial compressive strength is based on being equal to the uniaxial compressive strength of intact rock. Therefore, according to equation (7), the rock mass GSI at different joint dip angles can be obtained. j for:

[0085] (8)

[0086] When the joint dip angle varies from 15° to 75°, its GSI j The calculated values ​​are shown in Table 4. Then, D in Table 4... j and GSI j Substituting into equation (4) yields the uniaxial compressive strength of the corresponding specimen. The predicted results are shown in Table 4 and... Figure 4 It can be seen that the predicted and measured values ​​of the uniaxial compressive strength of the specimens agree very well, with a significant deviation only occurring at α=45°. Analysis suggests two possible reasons: ① The experimental results may exhibit some dispersion. Numerous experimental studies have shown that the minimum uniaxial compressive strength of rock mass typically occurs within the range of joint dip angles of 30~60°, and many experimental results also show that the uniaxial compressive strength of rock mass is minimum when α=45°. Simultaneously, theoretical studies also indicate that when α=45°+ When α = 2, the uniaxial compressive strength of the rock mass is at its minimum. Therefore, when α is small or even 0°, the uniaxial compressive strength of the rock mass reaches its minimum value at α = 45°, which is consistent with the experimental results. ② This invention assumes that the GSI value of the rock mass is a symmetrical parabola in the range of 0~90°. Although the overall pattern is consistent, there may still be some errors.

[0087] In summary, the above prediction results demonstrate that the proposed method for predicting the mechanical parameters of jointed rock masses based on the HB criterion is feasible.

[0088] Example

[0089] This study takes the stability calculation of rock slopes containing single sets of discontinuous joints, as studied by Zhou Yu et al., as an example (e.g.) Figure 5 This slope is a mining slope in an open-pit mine in Zambia. It contains a set of discontinuous bedding joints, the rock mass is relatively broken, and the lithology is mainly argillaceous quartzite. Its physical and mechanical parameters are: density 2560 kg / m³. 3 The elastic modulus is 5.96 GPa, Poisson's ratio is 0.15, and uniaxial compressive strength is 34.5 MPa. Joint surface parameters are: length 3 m, dip angle 25°, cohesion 149.33 kPa, and friction angle 12.35°. The single-step design slope height is 15 m and the slope angle is 65°. However, its tensile strength is not given. Based on experience, the direct tensile strength of dry, intact rock blocks is 4-7 MPa; here, an average value of 5.5 MPa is taken. Zhou Yu et al. believe that after slope excavation and unloading, the stress state of the slope surface approximately exhibits a uniaxial loading state. Therefore, the damage calculation method proposed in this invention can be used to solve the damage caused by natural joints to the slope. Figure 5 It can be seen that the joint density of this slope is 0.083 joints / m². 2 Substituting the above parameters into equation (5), we can obtain that the natural damage caused by joints to the rock slope is 0.269. Meanwhile, as shown in Table 1, the rock mass structure of this slope is either intact or monolithic. Therefore, when the joint dip angle varies between 0° and 90°, the GSI... j The minimum value is about 80, and the maximum value can be 100. Therefore, by substituting the above calculation parameters into equation (8), the GSI value of the slope rock mass is 83.95.

[0090] The following calculation uses the limit equilibrium method to determine the slope stability under its own weight. Currently, the strength criterion for the limit equilibrium method mainly adopts the MC criterion, thus requiring parameters such as the slope rock mass density, equivalent cohesion, and internal friction angle. Since joints have a negligible effect on rock mass density, it is assumed here that the rock mass density remains constant at 2560 kg / m³. 3 The following discussion focuses on the shear strength parameters of jointed rock masses, namely the equivalent cohesion c and the internal friction angle. The calculation method.

[0091] Hoek et al. proposed shear strength parameters based on the HB and MC criteria. The parameter conversion relationship between c and :

[0092] (9)

[0093] In the formula: σ c The uniaxial compressive strength of intact rock;

[0094] ;

[0095] γ is the rock mass density, H is the slope height; the other parameters are the same as before.

[0096] Furthermore, as can be seen from equation (2), if we want to obtain m b Then m needs to be determined. i It is the material constant of intact rock. Hoek et al., based on indoor test results and practical engineering experience, gave m i The chosen empirical method is prone to significant subjectivity and error. Therefore, we adopt the method proposed by Colak et al., which uses the uniaxial compressive strength σ of the rock as the criterion. c and direct tensile strength σ t Calculate the m of the rock i Value, that is:

[0097] (10)

[0098] In the formula, strength is defined as positive for tensile stress and negative for compressive stress.

[0099] The rock mechanical parameters mentioned above can be used to calculate... Figure 5 The corresponding complete rock m shown i =6.11, which is consistent with the empirical value.

[0100] Then m i Substituting =6.11, GSI=83.95, and D=0.269 into equation (2), we can obtain: m b =3.15, s=0.329, =0.50, and then substitute it into equation (9) to calculate the equivalent frictional strength parameter of the rock mass: c=4.89MPa, =44.2°. (By...) Figure 5 Based on the slope model shown and the above calculation parameters, using the Morgenstern-Price limit equilibrium method in the slope module of Geostudio software, the stability coefficient of the slope under natural self-weight is 1.705, and the slip surface is as follows. Figure 6 .

[0101] The following section focuses on the variation of the slope stability coefficient with the joint dip angle. Here, the joint dip angle is taken as 15°~75°, with a step size of 15°, while all other parameters remain constant. From this, the variation of the slope stability coefficient with the joint dip angle can be obtained as follows: Figure 7 It can be seen that as the joint dip angle changes, the slope stability coefficient varies from 1.63 to 1.749, and basically follows a parabolic pattern with the joint opening upward. The minimum value of 1.63 is obtained when the joint dip angle is 45°, which is consistent with the current research conclusions.

[0102] Although the above embodiments have been shown and described, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Any changes, modifications, substitutions and variations made to the above embodiments by those skilled in the art are within the protection scope of the present invention.

Claims

1. A method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion, characterized in that, Includes the following steps: S1. Establish the calculation formula for the deformation modulus of jointed rock mass; S2. Establish the calculation formula for the uniaxial compressive strength of jointed rock mass; S3. Establish the calculation formula for damage variables in jointed rock masses; S4. Establish the calculation formula for the geological strength index of jointed rock mass; S5. Substitute the jointed rock mass damage variables and jointed rock mass geological strength indices into the calculation formula for the jointed rock mass deformation modulus to obtain the jointed rock mass deformation modulus; S6. Substitute the jointed rock mass damage variables and jointed rock mass geological strength indices into the calculation formula for the uniaxial compressive strength of the jointed rock mass to obtain the uniaxial compressive strength of the jointed rock mass.

2. The method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion according to claim 1, characterized in that, The formula for calculating the damage variable of the jointed rock mass is as follows: ； In the formula, D j For jointed rock masses, the damage variable is J; V The joint density on the plane; α and denoted as joint dip angle and friction angle, respectively; a, b, and d represent joint half-length, center-to-center distance, and row spacing, respectively; f(a,b,d) is a coefficient reflecting the mutual influence of joints.

3. The method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion according to claim 2, characterized in that, The formula for calculating the geological strength index of the jointed rock mass is as follows: ； In the formula, GSI j GSI is the geological strength index of jointed rock mass; α is the joint dip angle; max and GSI min GSI j The minimum and maximum values.

4. The method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion according to claim 3, characterized in that, The formula for calculating the deformation modulus of the jointed rock mass is: ； In the formula, E rm E i Here, GSI and D represent the deformation modulus of jointed rock mass and intact rock mass, respectively, in MPa; GSI is the geological strength index of intact rock mass, and D is the damage variable of intact rock mass. When intact rock mass undergoes complex geological processes or engineering disturbances, GSI and D change from 100 and 0 for intact rock mass to GSI for jointed rock mass, respectively. j and D j .

5. The method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion according to claim 4, characterized in that, The formula for calculating the uniaxial compressive strength of the jointed rock mass is as follows: ； In the formula, σ rc σ1 is the uniaxial compressive strength of the jointed rock mass; σ1 is the maximum principal stress; σ2 is the uniaxial compressive strength of the jointed rock mass. c For the uniaxial compressive strength of intact rock; s and All of these are rock mass material strength parameters.

6. The method for predicting mechanical parameters of discontinuous jointed rock masses based on the Hoek-Brown criterion according to claim 5, characterized in that, The formula for calculating the strength parameters of the rock mass material is as follows: ； In the formula, D j For jointed rock masses, the damage variable is GSI. j This is a geological strength index for jointed rock masses.

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