Method for calculating tunnel anchoring bearing capacity based on rock mass quality index BQ

Abstract

This invention provides a method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ, comprising the following steps: S1, obtaining the surface and strata conditions of the anchor site area, as well as the structural types of the main cable and tunnel anchor, and establishing a two-dimensional planar model and a three-dimensional spatial model; S2, statistically analyzing the rock strata composition and proportion on the side of the anchor body through model intersection and segmentation; S3, calculating the rock mass quality index BQ and the corrected index CBQ for each rock stratum on the side of the anchor body according to the strata conditions; S4, calculating the comprehensive rock mass quality index KBQ based on the proportion of each rock stratum on the side of the anchor body and the corrected index CBQ, and calculating the shear strength parameter; S5, calculating the allowable pull-out load on the side of the anchor body without through shear or local shear stress failure based on the shape parameters of the anchor body and the shear strength parameter on the side of the anchor body. This invention proposes a method for calculating the allowable pull-out load of tunnel anchors based on the rock mass quality index BQ, which can accurately evaluate the bearing performance of tunnel anchors.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, specifically a method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ. Background Technology

[0002] Suspension bridges are the main passageways for highways and railways crossing rivers or deep valleys in mountainous areas. The anchoring methods at both ends of the main cable of a suspension bridge are divided into ground anchors and self-anchors. Among the ground anchor methods, gravity anchors and tunnel anchors are used in the vast majority of suspension bridges. The main characteristics of tunnel anchors are: first, a tunnel is excavated in the rock mass, and then a reinforced concrete anchor body is poured. The anchor body and the surrounding rock share the load of the main cable. The unique structure of tunnel anchors determines that the amount of excavation work is relatively small, avoiding disturbance to the ecological environment and damage to the cultural landscape. In addition, due to the small amount of concrete poured, it has a high cost-effectiveness. Engineering practice shows that tunnel anchors can be used not only in hard rock strata, but also in soft rock and even layered strata, and are an anchoring structure with excellent load-bearing capacity.

[0003] The main structure of a tunnel anchor mainly includes: cable saddle, anchor body, rear anchor chamber, etc., among which the anchor body is the main load-bearing structure. The main cable load of a suspension bridge is relatively large, generally between 5,000 and 44,000 tons per cable, corresponding to an anchor body length of generally 35m to 60m. Regarding the calculation model and method for anchor body bearing capacity, the reliability of the trumpet-shaped failure mode along the surrounding rock proposed based on the clamping effect still needs to be verified. In engineering practice, the shear failure mode at the interface between the anchor body and the rock mass is still the only method to calculate the anchor body's pull-out bearing capacity. This mode is further subdivided into through-shear failure and local shear stress failure. The former is represented by the "Design Code for Highway Suspension Bridges," and the latter by the Zhu Yu formula. Due to the complexity of geological conditions, long anchor bodies generally pass through rock strata of different qualities, such as strata with different lithologies or strata with the same lithology but different degrees of integrity. The mechanical properties of these rock strata, such as shear strength parameters, often vary greatly. However, existing anchor body bearing capacity calculation formulas and methods cannot consider this actual working condition. Furthermore, there is a fundamental difference between the calculation methods for through shear failure and local shear stress failure, and there is currently no calculation method for the allowable pull-out load of the anchor body when neither of the above two conditions occurs simultaneously.

[0004] The shortcomings of the aforementioned theoretical calculation methods limit the full utilization of engineering rock mass and the full utilization of the bearing capacity of tunnel anchors, thus restricting the design and engineering application of tunnel anchors. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method for calculating the allowable pull-out load of tunnel anchors based on the rock mass quality index BQ. By constructing and segmenting models of the surface, strata, and anchor body, the distribution and proportion of rock strata on the side of the anchor body are obtained. Combining the rock mass quality index BQ and the modified index CBQ of each rock stratum, the comprehensive rock mass quality index KBQ and shear strength parameters of the side of the anchor body are calculated. Then, the allowable pull-out load on the side of the anchor body without through shear or local shear stress failure is calculated, thereby accurately and reliably evaluating the bearing capacity of the anchor body.

[0006] A method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ includes the following steps:

[0007] S1. Obtain the surface and strata conditions of the anchorage area, as well as the structural types of the main cable and tunnel anchor, and establish a two-dimensional planar model and a three-dimensional spatial model.

[0008] S2. By cross-referencing and segmenting the model, the composition and proportion of rock strata on the side of the anchor body are statistically analyzed.

[0009] S3. Based on the geological conditions, calculate the rock mass quality index BQ and the correction index CBQ of each rock layer on the side of the anchor body;

[0010] S4. Based on the proportion of each rock layer on the side of the anchor body and the correction index CBQ, calculate the comprehensive rock mass quality index KBQ, and calculate the shear strength parameters.

[0011] S5. Based on the shape parameters of the anchor body and the shear strength parameters of the anchor body side, calculate the allowable pull-out load on the anchor body side without through shear or local shear stress failure.

[0012] Furthermore, step S1 specifically includes:

[0013] S11. Conduct geological surveys in the anchorage area, obtain surface contour lines by topographic mapping, and extract rock cores of the strata through borehole exploration. The strata conditions include the saturated uniaxial compressive strength of the rock, the elastic longitudinal wave velocity of the rock, and the elastic longitudinal wave velocity of the rock mass.

[0014] Cores from all rock strata were used to prepare cylindrical rock samples. The elastic longitudinal wave velocity of the rock in all rock strata was tested, and an indoor uniaxial compression test was conducted to obtain the saturated uniaxial compressive strength of the rock in all rock strata.

[0015] Acoustic tests were conducted inside the exploration borehole to obtain the elastic longitudinal wave velocity of the rock mass in all rock layers of the formation.

[0016] Based on different lithological types, weathering degrees, or unloading degrees, the strata are divided into different rock layers, and the rock layer boundaries are obtained.

[0017] Establish a two-dimensional planar model along the longitudinal direction of the bridge, including the surface and strata;

[0018] S12. Conduct bridge structural design and obtain relevant bridge design parameters, including the following design parameters for the main cable: ground surface incident point and incident angle θ1. The following design parameters for the anchorage are obtained: anchorage centerline inclination angle θ2, anchorage side extension angle θ3, front anchorage chamber length L1, anchorage length L2, anchorage side length L3, anchorage front anchorage shape and perimeter L4, and anchorage rear anchorage shape and perimeter L5.

[0019] S13. Establish a three-dimensional spatial model of the surface based on the contour lines of the surface in step S11, establish a three-dimensional spatial model of the strata based on the strata conditions, and establish a three-dimensional spatial model of the anchor body based on the relevant design parameters of the anchor body in step S12.

[0020] Furthermore, step S2 specifically includes:

[0021] S21. In the two-dimensional plane model established in step S1, the rock layer where the anchor body is located is selected according to whether the lines on the side of the anchor body and the lines of the rock layer interface intersect. The lines on the side of the anchor body are divided by the lines of the rock layer interface to obtain different segments. The total length of the segment lines in the intersecting rock layers is counted, and the length ratio is calculated.

[0022] S22. In the three-dimensional spatial model established in step S1, the rock layer where the anchor body is located is selected according to whether the side of the anchor body and the rock layer interface intersect. The side of the anchor body is divided by the rock layer interface to obtain different blocks. The total area of ​​the blocks in the intersecting rock layers is counted and its area ratio is calculated.

[0023] Furthermore, S31, based on the geological conditions in step S1, calculate the rock mass quality index BQ of the stratum where the anchor body is located. i :

[0024] Calculate the rock mass integrity K vi ;

[0025] Based on the integrity of the rock mass K vi The saturated uniaxial compressive strength R of the rock strata ci Calculate the rock mass quality index BQ i The calculation formula is as follows:

[0026] (1)

[0027] When using the above formula, the following restrictions must be observed: 1) When R ci >90K vi At +30, with R ci =90K vi +30 and K vi Substitute into calculation BQ i Value; 2) When K vi>0.04R ci When +0.4, with K vi =0.04R ci +0.4 and R ci Substitute into calculation BQ i value;

[0028] S32. Based on the rock mass quality index BQ of the rock strata. i Calculate the corrected index CBQ i :

[0029] BQ i The threshold for whether to correct is 350, BQ i Values ​​less than this do not require correction; otherwise, a reduction is necessary. (Based on BQ) i Calculate the corrected index CBQ i The calculation formula is as follows:

[0030] (2)

[0031] Following the above calculation process, the rock mass quality index BQ and the correction index CBQ of all rock layers on the side of the anchor body in step S2 are obtained.

[0032] Furthermore, step S4 specifically includes:

[0033] S41. Calculate the comprehensive rock mass quality index KBQ2 on the side of the anchor body in the two-dimensional plane model:

[0034] Using the length proportion of each rock layer on the side of the anchor body in the two-dimensional plane model of step S21 as the weighting coefficient, and based on the rock mass quality index CBQ of each rock layer in step S32, the weighted calculation method is used to calculate the comprehensive rock mass quality index KBQ2 on the side of the anchor body. The calculation formula is as follows:

[0035] (3)

[0036] In the formula: ω i and CBQ i These are the length proportions of each rock layer and the rock mass quality correction index, respectively.

[0037] Step S42: Calculate the comprehensive rock mass quality index KBQ3 on the side of the anchor body in the three-dimensional spatial model:

[0038] Using the area ratio of each rock layer on the side of the anchor body in the three-dimensional spatial model of step S22 as the weighting coefficient, and based on the rock mass quality index CBQ of each rock layer in step S32, the weighted calculation method is used to calculate the comprehensive rock mass quality index KBQ3 on the side of the anchor body. The calculation formula is as follows:

[0039] (4)

[0040] In the formula: η i and CBQ i These are the area proportion of each rock layer and the rock mass quality correction index, respectively.

[0041] Step S43: Based on the rock mass quality comprehensive indices KBQ2 and KBQ3 calculated from the two-dimensional planar model and the three-dimensional spatial model, calculate the rock mass quality comprehensive index KBQ on the side of the anchor body:

[0042] Setting KBQ to the minimum value (KBQ2, KBQ3) ensures project safety.

[0043] Step S44: Calculate the shear strength parameters based on the comprehensive rock mass quality index KBQ on the side of the anchor body.

[0044] The shear strength parameters are represented by two parameters: cohesion c and friction coefficient f. The cohesion c and friction coefficient f are calculated using the comprehensive rock mass quality index KBQ on the side of the anchor body, as follows:

[0045] (5)

[0046] In the formula: c is in kPa and f is a dimensionless parameter.

[0047] Furthermore, step S5 specifically includes:

[0048] Step S51: Calculate the allowable pull-out load P that the anchor body can withstand under the condition that no through shear failure occurs on the side of the anchor body. kp :

[0049] (6)

[0050] In the formula:

[0051] c and f are the cohesion and friction coefficient of the anchor body side in step S3, respectively;

[0052] A is the area of ​​the side of the anchor body;

[0053] W F The component of the anchor weight perpendicular to the side is γVcos(θ2+θ3);

[0054] W L The component of the anchor weight along the centerline of the anchor body is γVsinθ2;

[0055] Where: γ is the unit weight of concrete; V is the volume of the anchor body; θ2 and θ3 are the centerline inclination angle and the side extension angle of the anchor body, respectively;

[0056] Step S52: Calculate the allowable pull-out load P that the anchor body can withstand under the condition that no local shear stress failure occurs on the side of the anchor body. ks The calculation formula is as follows:

[0057] (7)

[0058] In the formula:

[0059] b is a dimensionless parameter, and its calculation formula is 0.14L2 2;

[0060] L m The average perimeter of the anchor body is calculated as (L4+L5) / 2;

[0061] Where: L2, L4 and L5 are the anchor body length, the perimeter of the front anchor face and the perimeter of the rear anchor face, respectively; c is the cohesion of the side of the anchor body in step S4;

[0062] Step S53: Calculate the allowable pull-out load P that the anchor body can withstand under two scenarios: no through shear failure and local shear stress failure. k :

[0063] P k Take the value min(P) kp P ks This ensures the safety of the project.

[0064] Furthermore, the calculation of the rock mass integrity K... vi Specifically, it includes:

[0065] Based on the elastic longitudinal wave velocity V of the rock strata pri and the elastic longitudinal wave velocity V of the rock mass pmi Calculate the rock mass integrity K vi The calculation formula is as follows:

[0066] (8)

[0067] Where: K vi V is a dimensionless parameter. pri and V pmi All units are km / s.

[0068] Furthermore, the calculation of the rock mass integrity K... vi Specifically, it includes:

[0069] K is calculated using the RQD value, a quality index of rock core samples. v Value, taking a certain rock stratum as an example, its RQD i The value is calculated as follows:

[0070] (9)

[0071] RQD of a certain rock stratum i Value calculation K vi The formula for calculating the value is as follows:

[0072] (10).

[0073] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0074] 1. By constructing two-dimensional and three-dimensional models and using model intersection and segmentation, the composition and proportion of rock strata on the side of the anchor body can be accurately obtained, so as to quantitatively evaluate the anchor body's occurrence conditions.

[0075] 2. Based on the rock mass quality index BQ of the rock strata, the corrected index CBQ is obtained, which represents the unfavorable failure surface in the interface between the rock strata and concrete and the internal interface of the rock strata, ensuring the accuracy and objectivity of the calculation results.

[0076] 3. Using the correction index CBQ of the rock strata on the side of the anchor body as the variable value and the proportion as the weighting coefficient, the comprehensive rock mass quality index KBQ of the rock strata on the side of the anchor body is calculated and determined by weighting. In this way, the shear strength parameter that can reflect the actual rock strata conditions on the side of the anchor body is obtained, which improves the reliability of the calculation results.

[0077] 4. The nonlinear function of axial force distribution of the anchor body provided by the present invention conforms to the actual condition that the axial force decreases nonlinearly from the stressed end of the anchor body to the free end, and obtains the shear stress distribution function of the anchor body side under the load of the stressed end of the anchor body, which can fully satisfy the law of force balance and improve the accuracy of the calculation results.

[0078] 5. The allowable pull-out load value of the anchor body in this invention is the smaller value of the calculated value of the anchor body side without through shear failure and local stress failure, so that the safety of the anchor body side as a whole and in a local way can be guaranteed, effectively improving the reliability of the calculation results. Attached Figure Description

[0079] Figure 1 It is a two-dimensional model diagram of the topography, strata, and tunnel anchor of the anchorage area;

[0080] Figure 2 This is a schematic diagram showing the shape and dimensions of a two-dimensional model of a tunnel anchor;

[0081] Figure 3 This is a schematic diagram showing the shape and dimensions of the front and rear anchor faces of the anchor body;

[0082] Figure 4 It is a schematic diagram of a three-dimensional model of the topography, strata and anchor body of the anchorage area;

[0083] Figure 5 This is a schematic diagram of the rock strata dividing the side of the anchor body in a two-dimensional model;

[0084] Figure 6 This is a schematic diagram of the rock strata dividing the side of the anchor body in a 3D model;

[0085] Figure 7 This is a schematic diagram of the forces causing the anchor body to fail under shear along its side.

[0086] Figure 8 This is a schematic diagram showing the relationship between the axial force of the anchor body and its length.

[0087] Figure 9 This is a schematic diagram of the distribution pattern of axial force and lateral shear stress in a micro-segment of the anchor body;

[0088] Figure 10 This is a schematic diagram showing the relationship between the shear stress on the side of the anchor body and its length. Detailed Implementation

[0089] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0090] This invention provides a method for calculating the allowable pull-out load of tunnel anchors based on the rock mass quality index BQ, comprising the following steps:

[0091] S1. Obtain the surface conditions 1 and strata 2 of the anchorage area, as well as the structural types of the main cable 3 and tunnel anchor 4, and establish a two-dimensional planar model and a three-dimensional spatial model.

[0092] Step S1 specifically includes:

[0093] S11. Conduct geological surveys in the anchorage area, obtain contour lines of surface 1 using topographic mapping, and extract rock cores of stratum 2 through borehole exploration.

[0094] All rock strata 21 were used in the geological formation. i Cores (i=1,2,3,⋯,n) were used to prepare cylindrical rock samples. The elastic longitudinal wave velocity Vpri (i=1,2,3,⋯,n) of all rock layers in the formation was tested, and uniaxial compression tests were conducted in the laboratory to obtain the saturated uniaxial compressive strength (R) of all rock layers 21 in formation 2. ci (i=1,2,3,⋯,n).

[0095] Acoustic wave tests were conducted inside the exploration borehole to obtain the elastic longitudinal wave velocity (V2) of all rock layers 21 in stratum 2. pmi (i=1,2,3,⋯,n), as shown in Table 1.

[0096] Table 1. Basic test parameters of different rock strata in the anchorage area

[0097]

[0098] Based on differences in lithology, weathering degree, or unloading degree, stratum 2 is divided into different rock layers 21. i (i=1,2,3,⋯,n), and the rock strata interface 22 is obtained. i (i=1,2,3,⋯,n).

[0099] Establish as Figure 1 The model shown is a two-dimensional planar model along the longitudinal direction of the bridge, containing the surface 1 and the stratum 2.

[0100] S12. Conduct bridge structural design and obtain relevant bridge design parameters. The relevant design parameters for the main cable 3 are as follows: ground surface incident point 31, incident angle θ1, etc. Figure 1 As shown. The relevant design parameters of anchor 4 are as follows: anchor body 42 centerline inclination angle θ2, anchor body side 422 extension angle θ3, front anchor chamber 41 length L1, anchor body 42 length L2, anchor body side 422 length L3, anchor body front anchor face 421 shape and perimeter L4, anchor body rear anchor face 423 shape and perimeter L5, as shown. Figure 2 and Figure 3 As shown.

[0101] S13. Based on the contour lines of surface 1 in step S11, establish a three-dimensional spatial model of surface 1; based on the conditions of stratum 2, establish a three-dimensional spatial model of stratum 2; and based on the relevant design parameters of anchor body 42 in step S12, establish a three-dimensional spatial model of anchor body 42, such as... Figure 4 As shown.

[0102] S2. By cross-referencing and segmenting the model, the composition and proportion of rock strata 21 on the side 422 of the anchor body are statistically analyzed.

[0103] Based on the positional relationship between the anchor body 42 and the rock stratum 21 in the two-dimensional planar model and the three-dimensional spatial model, the composition and distribution of the rock stratum 21 where the anchor body 42 is located are identified by whether the side surface 422 of the anchor body intersects with the rock stratum interface 22. The side surface 422 of the anchor body is divided into different components by the rock stratum interface 22, and the ratio of the sum of each component in the rock stratum 21 to the total sum of all components is its proportion.

[0104] Step S2 specifically includes:

[0105] S21. In the two-dimensional plane model established in step S1, the rock layer 21 where the anchor body 42 is located is selected based on whether the lines of the anchor body side surface 422 and the lines of the rock stratum interface 22 intersect. The lines of the anchor body side surface 422 are divided using the lines of the rock stratum interface 22 to obtain the following... Figure 5 The different segments are shown. The total length of the segment lines within the intersecting rock strata 21 is counted, and their length percentage is calculated.

[0106] The rock stratum 21 where anchor body 42 is located i For example, rock stratum 21 i The total length of the inner segment is L 21i Then the length ratio ω i The calculation formula is as follows:

[0107] (11)

[0108] In the formula: L3 is the length of the side surface 422 of the anchor body in step S1.

[0109] Calculation examples are shown in Table 2:

[0110] Table 2. Length and percentage of different rock strata on the side of the anchor body

[0111]

[0112] S22. In the three-dimensional spatial model established in step S1, the rock stratum 21 where the anchor body 42 is located is selected based on whether the anchor body side surface 422 and the rock stratum interface 22 intersect. The anchor body side surface 422 is divided using the rock stratum interface 22 to obtain the following... Figure 6 For the different blocks shown, the total area of ​​the blocks within the intersecting rock strata 21 is calculated, and their area percentage is also calculated.

[0113] The rock stratum 21 where anchor body 42 is located i For example, rock stratum 21 i The sum of the areas of the inner blocks is A 2i Then the area ratio η i The calculation formula is as follows:

[0114] (12)

[0115] In the formula: A is the area of ​​the side surface 422 of the anchor body, which can be obtained by measuring the area of ​​the side surface 422 of the anchor body in step S1.

[0116] Calculation examples are shown in Table 3.

[0117] Table 3. Area and percentage of different rock strata on the side of the anchor body

[0118]

[0119] S3. Based on the geological conditions of stratum 2, calculate the rock mass quality index BQ and the correction index CBQ of each rock layer 21 on the side of the anchor body 422.

[0120] Step S3 specifically includes:

[0121] The rock stratum 21 where anchor body 42 is located i For example, the rock mass quality index BQ of this rock stratum i and the revised indicator CBQ i The calculation process is as follows:

[0122] S31. Based on the stratum 2 conditions in step S1, calculate the rock stratum 21 where the anchor body 42 is located. i Rock mass quality index BQ i .

[0123] According to rock stratum 21 in step S1 i Rock elastic longitudinal wave velocity V pri and the elastic longitudinal wave velocity V of the rock mass pmi Calculate the rock mass integrity K vi The calculation formula is as follows:

[0124] (8)

[0125] Where: K vi V is a dimensionless parameter. pri and V pmi All units are km / s.

[0126] Based on the integrity of the rock mass K vi And rock strata 21 in step S1 i Rock saturated uniaxial compressive strength R ci Calculate the rock mass quality index BQ i The calculation formula is as follows:

[0127] (1)

[0128] When using the above formula, the following restrictions should be observed: 1) When R ci >90K vi At +30, with R ci =90K vi +30 and K vi Substitute into calculation BQ i Value; 2) When K vi >0.04R ci When +0.4, with K vi =0.04R ci +0.4 and R ci Substitute into calculation BQ i value.

[0129] S32, According to rock strata 21 i Rock mass quality index BQ i Calculate the corrected index CBQ i .

[0130] BQi The threshold for whether to correct is 350, BQ i Values ​​less than this do not require correction; otherwise, a reduction is necessary. (Based on BQ) i Calculate the corrected index CBQ i The calculation formula is as follows:

[0131] (2)

[0132] Following the above calculation process, the rock mass quality index BQ and the corrected index CBQ of all rock layers 21 on the side 422 of the anchor body in step S2 can be obtained. Calculation examples are shown in Table 4.

[0133] Table 4. Rock mass quality (BQ) and correction index (CBQ) of different rock strata on the side of the anchor body

[0134]

[0135] S4. Based on the proportion of each rock layer 21 on the side 422 of the anchor body and the correction index CBQ, calculate the comprehensive rock mass quality index KBQ, and calculate the shear strength parameters.

[0136] Step S4 specifically includes:

[0137] S41. Calculate the comprehensive rock mass quality index KBQ2 of the anchor body side 422 in the two-dimensional plane model.

[0138] Specifically, using the length proportion of each rock layer 21 on the anchor body side 422 in the two-dimensional plane model of step S21 as the weighting coefficient, and based on the rock mass quality index CBQ of each rock layer 21 in step S32, the weighted calculation method is used to calculate the comprehensive rock mass quality index KBQ2 of the anchor body side 422. The calculation formula is as follows:

[0139] (3)

[0140] In the formula: ω i and CBQ i These represent the length percentage of each rock layer 21 and the rock mass quality correction index, respectively.

[0141] Calculation examples are shown in Table 5:

[0142] Table 5. Comprehensive Rock Mass Quality Index (KBQ2) on the Side of the Anchor Body in the Two-Dimensional Plane Model

[0143]

[0144] Step S42: Calculate the comprehensive rock mass quality index KBQ3 of the anchor body side 422 in the three-dimensional spatial model.

[0145] Specifically, using the area proportion of each rock layer 21 on the side of the anchor body 422 in the three-dimensional spatial model of step S22 as the weighting coefficient, and based on the rock mass quality index CBQ of each rock layer 21 in step S32, the weighted calculation method is used to calculate the comprehensive rock mass quality index KBQ3 of the side of the anchor body 422. The calculation formula is as follows:

[0146] (4)

[0147] In the formula: η i and CBQ i These represent the area percentage and rock mass quality correction index of each rock layer 21, respectively.

[0148] Calculation examples are shown in Table 6:

[0149] Table 6. Comprehensive Rock Mass Quality Index (KBQ3) on the Side of the Anchor Body in the Three-Dimensional Spatial Model

[0150]

[0151] Step S43: Calculate the comprehensive rock mass quality index KBQ2 and KBQ3 calculated based on the two-dimensional planar model and the three-dimensional spatial model, and calculate the comprehensive rock mass quality index KBQ on the side of the anchor body 422.

[0152] Specifically, setting KBQ to min(KBQ2, KBQ3) ensures project safety.

[0153] Specifically, KBQ takes the value min(383.25, 384.11) = 383.25.

[0154] Step S44: Calculate the shear strength parameters based on the comprehensive rock mass quality index KBQ on the side 422 of the anchor body.

[0155] According to the Mohr-Coulomb strength theory, the shear strength parameters are represented by two parameters: cohesion *c* and friction coefficient *f*. Based on the national standard "Engineering Rock Mass Classification Standard", the cohesion *c* and friction coefficient *f* are calculated using the comprehensive rock mass quality index KBQ on the anchor body side 422, as follows:

[0156] (5)

[0157] In the formula: c is in kPa and f is a dimensionless parameter.

[0158] The KBQ value is 383.25. According to formula (8), the calculated value of c is 1012.79 kPa and the calculated value of f is 1.00.

[0159] S5. Based on the shape parameters of the anchor body 42 and the shear strength parameters of the anchor body side 422, calculate the allowable pull-out load of the anchor body side 422 without through shear or local shear stress failure.

[0160] Allowable pull-out load P of anchor body 42 k This can be understood as the maximum load that the anchor body side 422 can bear when neither through shear failure nor local shear stress failure occurs simultaneously.

[0161] Step S5 specifically includes:

[0162] Step S51: Calculate the allowable pull-out load P that the anchor body 42 can withstand under the condition that no through shear failure occurs on the side 422 of the anchor body. kp , as Figure 7 The force calculation model of the anchor body 42 shown can be used to obtain the following calculation formula:

[0163] (6)

[0164] In the formula:

[0165] c and f are the cohesion and friction coefficient of the anchor body side 422 in step S3, respectively;

[0166] A is the area of ​​the side surface 422 of the anchor body;

[0167] W F The component of the gravity of anchor body 42 in the direction perpendicular to the side is calculated as γVcos(θ2+θ3);

[0168] W L The component of the gravity of anchor body 42 along the center line of anchor body 42 is calculated as γVsinθ2.

[0169] Where: γ is the unit weight of concrete, with a value of 24 kN / m³. 3 V represents the volume of anchor body 42, which can be obtained by measuring the volume of anchor body 42 in the three-dimensional space model of step S1. θ2 and θ3 are the inclination angle of the centerline of anchor body 42 and the expansion angle of the side surface 422 of anchor body 42 in step S1, respectively.

[0170] Step S52: Calculate the allowable pull-out load P that the anchor body 42 can withstand under the condition that no local shear stress failure occurs on the side 422 of the anchor body. ks The calculation formula is as follows:

[0171] (7)

[0172] In the formula:

[0173] b is a dimensionless parameter, and its calculation formula is 0.14L2 2;

[0174] Lm The average perimeter of the anchor body is 42, and the calculation formula is (L4+L5) / 2;

[0175] Where: L2, L4 and L5 are the length of anchor body 42, the perimeter of front anchor face 421 and the perimeter of rear anchor face 423 in step S1, respectively; c is the cohesion of the side surface 422 of anchor body in step S4;

[0176] Step S53: Calculate the allowable pull-out load P that the anchor body 42 can withstand under two scenarios: no through shear failure and no local shear stress failure. k .

[0177] Specifically, P k Take the value min(P) kp P ks This ensures the safety of the project.

[0178] (6)

[0179] In the formula: c is 1012.79 kPa, f is 1.00, and A is 447.22 m. 2 ;

[0180] W F =γVcos(θ2+θ3)=24×5653.67×cos(40°+4°)=97605.84kN

[0181] W L =γVsinθ2=24×5653.67×sin(40°)=87218.62kN

[0182] P kp =1012.79×1788.87+1.00×97605.84+87218.62=1996174.74kN

[0183] (7)

[0184] In the formula: c is 1012.79 kPa, and f is 1.00.

[0185] b = 0.14L² 2 = 0.14 × 80 2 =896.00;

[0186] L m =(L4+L5) / 2=(17.85+26.78) / 2=22.32;

[0187] P ks =8×22.32×80 2 ×1012.79×8960.5 / (3×3 0.5 ×(896+80 2 = 913378.97kN

[0188] P k Take the value min(P) kp P ks =913378.97kN.

[0189] Due to limitations of actual on-site conditions, unexpected conditions such as the inability to retain water in the borehole often occur, making it impossible to conduct in-hole acoustic testing. Consequently, the rock mass integrity K cannot be calculated using formula (3). v Value. In another embodiment, K is calculated using the quality index RQD value from the core sample of rock layer 21. v The method of value, with rock stratum 21 i For example, its RQD i The value is calculated as follows:

[0190] (9)

[0191] From rock layer 21 i RQD i Value calculation K vi The formula for calculating the value is as follows:

[0192] (10)

[0193] Combined rock strata 21 i Rock saturated uniaxial compressive strength R ci The rock mass quality index BQ can be calculated according to formula (4). i This method can obtain the rock mass quality index BQ of rock layer 21 under the condition of having only drilled rock cores.

[0194] This invention modifies the rock mass quality index BQ of rock layer 21 on the anchor body side 422 because the anchor body side 422 is the interface between the anchor body 42 and rock layer 21, and there are two potential failure modes: one is shear failure along the contact surface between the anchor body 42 concrete and rock layer 21; the other is shear failure along the rock layer 21 near this contact surface. The occurrence of which failure mode occurs depends on the rock mass quality of rock layer 21, because the rock mass quality of rock layer 21 determines not only its shear strength parameter but also the shear strength parameter of the anchor body 42 concrete and its contact surface. When the rock mass quality of rock layer 21 is better, and its shear strength parameter is superior to that of the anchor body 42 concrete and its contact surface, mode one occurs; otherwise, mode two occurs. This invention uses a rock mass quality index BQ of 350 as the boundary value between the two failure modes. When BQ is greater than 350, it is reduced to obtain the modified index CBQ, so that the calculated shear strength parameter is the parameter of the contact surface between the anchor body 42 concrete and rock layer 21. The correction method for the rock mass quality index BQ of rock stratum 21 is shown in formula (5), which makes the calculation result always the result of the unfavorable failure mode.

[0195] The formula for calculating shear strength parameters based on the comprehensive rock mass quality index KBQ provided in this invention originates from two provisions of the national standard "Engineering Rock Mass Classification Standard": Table 4.1.1, which specifies the basic quality classification of rock mass, and Appendix D, which specifies the physical and mechanical parameters of rock mass and structural surfaces. Based on these two provisions, the quality index and peak shear strength range for different rock mass grades are shown in Table 7.

[0196] Table 7 Quality indicators and peak shear strength range for different rock mass grades

[0197]

[0198] According to Table 7, the quality index and peak shear strength at the boundary of different rock mass grades can be obtained as shown in Table 8. With KBQ as the independent variable and c and f as the dependent variables, formula (8) can be obtained by linear fitting.

[0199] Table 8. Quality indicators and peak shear strength at the boundary of different rock mass grades

[0200]

[0201] The calculation process for the shear stress distribution function on the anchor body side 422 is as follows: First, the axial force distribution function of the anchor body 42 is calculated from the external load; then, the shear stress distribution function on the anchor body side 422 is determined by the force system equilibrium. This invention first provides an axial force distribution function for the anchor body 42 that strictly satisfies the conditions at both ends of the anchor body 42. Then, the shear stress distribution function on the anchor body side 422 is calculated. Finally, the maximum shear stress is solved, and the allowable pull-out load is calculated inversely. The specific derivation process is as follows:

[0202] Anchor body 42 has two end faces, the stressed end being under load P ks Under the action, the axial force of anchor body 42 is P ks Under the clamping action of the surrounding rock, the axial force of anchor 42 decreases nonlinearly from the stressed end to the free end, and the magnitude changes from P... ks Reduced to 0, such as Figure 8 As shown. The axial force at any cross-section of anchor body 42 and the length of that cross-section from the force-bearing end are related by a nonlinear function P(x), the expression of which is:

[0203] (13)

[0204] In the formula: a, b and d are dimensionless parameters; P represents the axial force at any cross section of the anchor body 42, x represents the length of the cross section from the force-bearing end, and L2 is the length of the anchor body 42 in step S1.

[0205] Within the range x∈[0, L2], the coordinates of the two endpoints of the curve P(x) are (0, P... ks (L2, 0). Substituting into formula (13), we get the expressions for a and d:

[0206] (14)

[0207] Substituting formula (14) into formula (13) and simplifying it to the following formula:

[0208] (15)

[0209] Differentiating both sides of formula (15), we obtain the expression for the derivative of the function P(x):

[0210] (16)

[0211] Based on the function P(x) and its derivative, neglecting the weight of the anchor body 42, calculate the distribution function of the shear stress τ(x) using the principle of force equilibrium. Figure 9 As shown, within the range x∈[0, L2], taking any micro-segment of anchor body 42 as the analysis object, the length of the micro-segment dx→0, and the perimeter of anchor body 42 changes very little, so it can be approximated as a uniform cross-section. The axial force and shear stress have the following relationship:

[0212] (17)

[0213] In the formula: L m Let L be the average perimeter of the anchor body (42). m The value is (L4+L5) / 2, where L4 and L5 are the perimeters of the front anchor face 421 and the rear anchor face 423 of the anchor body in step S1, respectively.

[0214] According to formulas (16) and (17), the functional expression of τ(x) can be obtained as follows:

[0215] (18)

[0216] It should be noted that the total shear stress on the anchor body side 422 can be calculated using the above formula. =P ks That is, the shear stress on the side of the anchor body 422 is equal to the load at the stressed end, which fully satisfies the force system balance of the anchor body 42, indicating that formula (18) can reflect the shear stress distribution under the load at the stressed end.

[0217] The curve of the function τ(x) first rises and then falls in the interval x∈[0, L2], as shown below. Figure 10 As shown, there exists a maximum value. Taking the derivative of formula (18), when its value is equal to 0, we get... At this point, the function τ(x) is at its maximum value τ. max Its expression is:

[0218] (19)

[0219] From formula (19), it can be seen that as the load P... ks With the increase of τ, the maximum shear stress τ max It also increases. Due to τ max The shear stress cannot exceed the allowable shear stress that the anchor body side 422 can withstand, and the allowable shear stress must be greater than the cohesion c of the anchor body side 422 in step S4, therefore τ max Not greater than the cohesive force c (τ) max Safety is guaranteed when ≤c). Let τ max =c, and substitute into formula (19) and calculate P in reverse. ks The allowable pull-out load P can then be obtained. ks The calculation formula is (7).

[0220] The potential failure modes of the anchor body side 422 are divided into two types: one is through-shear failure occurring along the anchor body side 422, and the other is failure caused by the local shear stress on the anchor body side 422 exceeding its allowable shear stress. This invention calculates the load that the anchor body side 422 can withstand without through-shear failure and local shear stress failure, and takes the smaller value as the allowable pull-out load of the anchor body 42. The anchor body 42 is safe and reliable in bearing the load.

[0221] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ, characterized in that: Includes the following steps: S1. Obtain the surface and strata conditions of the anchorage area, as well as the structural types of the main cable and tunnel anchor, and establish a two-dimensional planar model and a three-dimensional spatial model. S2. By cross-referencing and segmenting the model, the composition and proportion of rock strata on the side of the anchor body are statistically analyzed. S3. Based on the geological conditions, calculate the rock mass quality index BQ and the correction index CBQ of each rock layer on the side of the anchor body; S4. Based on the proportion of each rock layer on the side of the anchor body and the correction index CBQ, calculate the comprehensive rock mass quality index KBQ, and calculate the shear strength parameters. S5. Based on the shape parameters of the anchor body and the shear strength parameters of the side of the anchor body, calculate the allowable pull-out load on the side of the anchor body to prevent through shear and local shear stress failure. Step S2 specifically includes: S21. In the two-dimensional plane model established in step S1, the rock layer where the anchor body is located is selected according to whether the lines on the side of the anchor body and the lines of the rock layer interface intersect. The lines on the side of the anchor body are divided by the lines of the rock layer interface to obtain different segments. The total length of the segment lines in the intersecting rock layers is counted, and the length ratio is calculated. S22. In the three-dimensional spatial model established in step S1, the rock layer where the anchor body is located is selected according to whether the side of the anchor body and the rock layer interface intersect. The side of the anchor body is divided by the rock layer interface to obtain different blocks. The total area of ​​the blocks in the intersecting rock layers is counted and its area ratio is calculated. Step S3 specifically includes: S31. Based on the geological conditions in step S1, calculate the rock mass quality index BQ of the stratum where the anchor body is located. i : Calculate the rock mass integrity K vi ; Based on the integrity of the rock mass K vi The saturated uniaxial compressive strength R of the rock strata ci Calculate the rock mass quality index BQ i The calculation formula is as follows: （1）； When using the above formula, the following restrictions must be observed: 1) When R ci >90K vi At +30, with R ci =90K vi +30 and K vi Substitute into calculation BQ i Value; 2) When K vi >0.04R ci When +0.4, with K vi =0.04R ci +0.4 and R ci Substitute into calculation BQ i value; S32. Based on the rock mass quality index BQ of the rock strata. i Calculate the corrected index CBQ i : BQ i The threshold for whether to correct is 350, BQ i Values ​​less than this do not require correction; otherwise, a reduction is necessary, based on BQ. i Calculate the corrected index CBQ i The calculation formula is as follows: （2）； Following the above calculation process, the rock mass quality index BQ and the correction index CBQ of all rock layers on the side of the anchor body in step S2 are obtained.

2. The method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ as described in claim 1, characterized in that: Step S1 specifically includes: S11. Conduct geological surveys in the anchorage area, obtain surface contour lines by topographic mapping, and extract rock cores of the strata through borehole exploration. The strata conditions include the saturated uniaxial compressive strength of the rock, the elastic longitudinal wave velocity of the rock, and the elastic longitudinal wave velocity of the rock mass. Cores from all rock strata were used to prepare cylindrical rock samples. The elastic longitudinal wave velocity of the rock in all rock strata was tested, and an indoor uniaxial compression test was conducted to obtain the saturated uniaxial compressive strength of the rock in all rock strata. Acoustic tests were conducted inside the exploration borehole to obtain the elastic longitudinal wave velocity of the rock mass in all rock layers of the formation. Based on different lithological types, weathering degrees, or unloading degrees, the strata are divided into different rock layers, and the rock layer boundaries are obtained. Establish a two-dimensional planar model along the longitudinal direction of the bridge, including the surface and strata; S12. Conduct bridge structural design and obtain relevant bridge design parameters, including the following design parameters for the main cable: ground surface incident point and incident angle θ1. The following design parameters for the anchorage are obtained: anchorage centerline inclination angle θ2, anchorage side extension angle θ3, front anchorage chamber length L1, anchorage length L2, anchorage side length L3, anchorage front anchorage shape and perimeter L4, and anchorage rear anchorage shape and perimeter L5. S13. Establish a three-dimensional spatial model of the surface based on the contour lines of the surface in step S11, establish a three-dimensional spatial model of the strata based on the strata conditions, and establish a three-dimensional spatial model of the anchor body based on the relevant design parameters of the anchor body in step S12.

3. The method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ as described in claim 1, characterized in that: Step S4 specifically includes: S41. Calculate the comprehensive rock mass quality index KBQ2 on the side of the anchor body in the two-dimensional plane model: Using the length proportion of each rock layer on the side of the anchor body in the two-dimensional plane model of step S21 as the weighting coefficient, and based on the rock mass quality index CBQ of each rock layer in step S32, the weighted calculation method is used to calculate the comprehensive rock mass quality index KBQ2 on the side of the anchor body. The calculation formula is as follows: （3）； In the formula: ω i and CBQ i These are the length proportions of each rock layer and the rock mass quality correction index, respectively. Step S42: Calculate the comprehensive rock mass quality index KBQ3 on the side of the anchor body in the three-dimensional spatial model: Using the area ratio of each rock layer on the side of the anchor body in the three-dimensional spatial model of step S22 as the weighting coefficient, and based on the rock mass quality index CBQ of each rock layer in step S32, the weighted calculation method is used to calculate the comprehensive rock mass quality index KBQ3 on the side of the anchor body. The calculation formula is as follows: （4）； In the formula: η i and CBQ i These are the area proportion of each rock layer and the rock mass quality correction index, respectively. Step S43: Based on the rock mass quality comprehensive indices KBQ2 and KBQ3 calculated from the two-dimensional planar model and the three-dimensional spatial model, calculate the rock mass quality comprehensive index KBQ on the side of the anchor body: Setting KBQ to the minimum value (KBQ2, KBQ3) ensures project safety. Step S44: Calculate the shear strength parameters based on the comprehensive rock mass quality index KBQ on the side of the anchor body. The shear strength parameters are represented by two parameters: cohesion c and friction coefficient f. The cohesion c and friction coefficient f are calculated using the comprehensive rock mass quality index KBQ on the side of the anchor body, as follows: （5）； In the formula: c is in kPa and f is a dimensionless parameter.

4. The method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ as described in claim 1, characterized in that: Step S5 specifically includes: Step S51: Calculate the allowable pull-out load P that the anchor body can withstand under the condition that no through shear failure occurs on the side of the anchor body. kp : （6）； In the formula: c and f are the cohesion and friction coefficient of the anchor body side in step S3, respectively; A is the area of ​​the side of the anchor body; W F The component of the anchor weight perpendicular to the side is γVcos(θ2+θ3); W L The component of the anchor weight along the centerline of the anchor body is γVsinθ2; Where: γ is the unit weight of concrete; V is the volume of the anchor body; θ2 and θ3 are the centerline inclination angle and the side extension angle of the anchor body, respectively; Step S52: Calculate the allowable pull-out load P that the anchor body can withstand under the condition that no local shear stress failure occurs on the side of the anchor body. ks The calculation formula is as follows: （7）； In the formula: b is a dimensionless parameter, and its calculation formula is 0.14L2 2; L m The average perimeter of the anchor body is calculated as (L4+L5) / 2; Where: L2, L4 and L5 are the anchor body length, the perimeter of the front anchor face and the perimeter of the rear anchor face, respectively; c is the cohesion of the side of the anchor body in step S4; Step S53: Calculate the allowable pull-out load P that the anchor body can withstand under two scenarios: no through shear failure and local shear stress failure. k : P k Take the value min(P) kp P ks This ensures the safety of the project.

5. The method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ as described in claim 1, characterized in that: The calculation of rock mass integrity K vi Specifically, it includes: Based on the elastic longitudinal wave velocity V of the rock strata pri and the elastic longitudinal wave velocity V of the rock mass pmi Calculate the rock mass integrity K vi The calculation formula is as follows: （8）； In the formula: K vi V is a dimensionless parameter. pri and V pmi All units are km / s.

6. The method for calculating the bearing capacity of tunnel anchors based on the rock mass quality index BQ as described in claim 1, characterized in that: The calculation of rock mass integrity K vi Specifically, it includes: K is calculated using the RQD value, a quality index of rock core samples. v Value, taking a certain rock stratum as an example, its RQD i The value is calculated as follows: （9）； RQD of a certain rock stratum i Value calculation K vi The formula for calculating the value is as follows: （10）。

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