Method for calculating anchoring force limit value of directional filling type anchor cable

Abstract

The invention relates to the technical field of anchor cable supporting, and discloses a directional filling type anchor cable anchoring force limit value calculation method which comprises the following steps: step 1, determining the solution gap distribution condition of a karst area by virtue of a drilling television, and then processing a slurry stopping bag directional filling type anchor cable device by adopting canvas according to the solution gap distribution condition; step 2, establishing a coordinate system of an anchoring shear stress section based on the directional filling type anchor cable device; the directional filling type anchor cable device is regarded as an ideal elastic axial stretching rod piece, the shear displacement distribution function of the directional filling type anchor cable device in the solution gap section is calculated, then the coordination balance relation between the solution gap section and the anchoring shear stress section is determined, and finally the function expression of the anchoring force limiting value P of the directional filling type anchor cable is obtained. According to the anchoring force limit calculation method, a theoretical calculation analytic solution of the anchor cable anchoring force of the discontinuous rock stratum in the karst area is provided, and important theoretical support is provided for research on construction safety of a current supporting structure.

Description

Technical Field

[0001] The invention relates to the field of anchor cable support, and in particular to a method for calculating the anchoring force limit of a directional filling type anchor cable. Background Art

[0002] With the increasing number of projects such as construction, water conservancy, transportation and a large number of high slopes, it is essential to control deformation through anchor cable support. Anchor cable support is widely used due to its low cost, safety and stability. The existing anchor cable anchoring force calculation formula also guides the anchor cable anchoring construction work to a certain extent.

[0003] Discontinuous rock formations will not only aggravate the leakage and grouting during drilling backfill grouting, thereby reducing the anchoring effect, but will also make the theoretical calculated value of the existing anchoring force of the anchor cable too high, which is not conducive to the safe construction of the support structure.

[0004] Therefore, how to establish a calculation method for the anchoring force limit of directional filling cave anchor cables based on digital detection of karst distribution to guide the safe construction of anchor cables is an urgent problem to be solved. Summary of the invention

[0005] In order to solve the technical problems raised in the background technology, the present invention provides a method for calculating the anchoring force limit of a directional filling type anchor cable.

[0006] The present invention is implemented by the following technical solution: A method for calculating the anchoring force limit of a directional filling anchor cable comprises the following steps:

[0007] Step 1: Use the drilling television to confirm the distribution of dissolution gaps in the karst area, and then use canvas to process the slurry-stopping bag into a directional filling anchor device according to the distribution of dissolution gaps.

[0008] Step 2: Establish a coordinate system of the anchoring shear stress section based on the directional filling type anchor device; regard the directional filling type anchor device as an ideal elastic axial tensile rod, calculate its shear displacement distribution function in the solution gap section, and then determine the coordinated equilibrium relationship between the solution gap section and the anchoring shear stress section, and finally obtain the function expression of the anchoring force limit P of the directional filling type anchor.

[0009] Specifically, in step 1, the specific operations are as follows:

[0010] Step 101, the panoramic borehole camera probe enters the borehole; the camera light source illuminates the camera area on the borehole wall; the borehole wall image is transformed by a conical reflector to form a panoramic image; the panoramic image and the compass orientation image enter the camera together; the camera transmits the captured image to the video distributor on the ground through a dedicated cable, one way enters the video recorder to record the whole detection process, and the other way enters the capture card in the computer for digitization;

[0011] Step 102: The measuring wheel on the winch measures the position of the probe in real time, and places the depth value in a dedicated port in the computer through the interface board; the capture mode of the capture card is controlled by the depth value; in the continuous capture mode, the panoramic image is quickly restored to a flat unfolded image and displayed in real time; in the static capture mode, the panoramic image is quickly stored for rapid analysis on site and statistical analysis indoors; the probe is lowered until the entire detection is completed;

[0012] Step 103, after drilling, detecting the number, depth and area of ​​geological defects in the borehole;

[0013] Step 104, tie multiple grout-stopping bags on the anchor rod body. The grout-stopping bags should be facing the deep parts of the geological defects. Use canvas to make grout-stopping bags and fix them tightly at various places of the anchor rod. When the slurry is completely filled, a cylindrical string anchor body with a radius of 10 cm and the center of the longitudinal axis of the anchor rod as the origin can be formed. Targeted fixed-point filling can be carried out in actual geological defect sections such as faults, broken zones, and caves, and a grout-stopping bag string with a longitudinal length not exceeding 10 cm can be formed.

[0014] Specifically, a plurality of grout-stopping bags made of canvas grout-stopping bags are arranged at intervals outside the rod body of the directional filling type anchor cable device, and the grout-stopping bags are used to be filled with grout;

[0015] Measuring point anchor points are set between any two adjacent grouting bags, between the grouting bag and the bottom of the borehole, and between the grouting bag and the borehole mouth to fix the two ends of the grouting bag.

[0016] Specifically, in step 2, the specific operations are as follows:

[0017] Step 201, the anchor shear stress section coordinate system is established: the anchoring start end of the anchor cable is taken as the origin, and the length direction of the anchor cable is taken as the x-axis;

[0018] In the coordinate system, is the length of the anchor cable anchoring section, n is the number of dissolution gaps in the anchor cable anchoring section, j is the sequence number of dissolution gaps from the beginning of the anchoring, X j is the jth anchoring rock segment, x j is the length of the jth anchoring rock layer section, W j is the jth exposed crack segment, w j is the thickness of the jth exposed crack section, k i is the anchor shear stiffness of the i-th segment, τ i is the anchor shear stress of the i-th segment, π is the circumference of a circle, Δh j is the height difference between the highest point and the lowest point of the structural surface trace detected by the drilling television, C is the circumference of the hole wall, P is the anchoring force of the anchor cable, and x is the distance from the starting end of the anchor.

[0019] Step 202: Calculate the shear stiffness k of the i-th anchorage by the following formula: i :

[0020]

[0021] In the above formula, G is is the shear modulus of the surrounding rock mass in the i-th section, r im is the maximum shear influence radius of deformation in the i-th rock layer, and D is the diameter of the anchor body.

[0022] Step 203: Calculate the maximum shear influence radius r of the deformation in the i-th rock layer by the following formula: im :

[0023] r im =0.5(1-v i )x i

[0024] In the above formula, v i is the Poisson's ratio of the i-th rock layer.

[0025] Step 204: Calculate the anchor cable shear displacement by the following formula: The distribution function of is:

[0026]

[0027] In the above formula, is the shear displacement on the shear plane between the i-th anchor body and the surrounding rock mass, C 1 and C 2 are the unknown coefficients, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, α i is a constant related to the shear stiffness of the i-th rock layer.

[0028] Step 205: Calculate the constant α related to the shear stiffness of the i-th rock layer by the following formula: i :

[0029]

[0030] In the above formula, k i is the shear stiffness of the i-th rock layer.

[0031] Step 206: Calculate the elastic modulus E by the following formula: P :

[0032]

[0033] In the above formula, E r is the elastic modulus of the grouting body, E s is the elastic modulus of the anchor cable, N is the number of anchor cables, and d is the diameter of the anchor cable.

[0034] Combined with the boundary conditions of the anchor cable, at the end of the anchor section, P|x=L=0, the expression of the anchor cable anchor force limit P is obtained:

[0035]

[0036] In the above formula, C 11 and C 12 is the undetermined coefficient related to the anchoring of the first section.

[0037] The C 11 and C 12 The calculation steps are as follows:

[0038] Considering the continuity of shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of shear displacement can be used, and then: Combined with the equal shear displacement at the intersection of anchor cables, the equation for the shear displacement of anchor cables at the intersection is obtained as follows:

[0039]

[0040] C i2 =C i1 ·g i

[0041] In the above formula, g i is the undetermined parameter related to the anchoring of the i-th segment, g (i+1) is the undetermined parameter related to the anchoring of the i+1th segment, C i1 and C i2 is the undetermined coefficient related to the anchorage of the i-th segment, is less than The maximum integer.

[0042] Combined with the anchor boundary conditions, the anchor section starts with τ|x=0=τ 1 , the distribution expression of the shear stress of the continuous anchor body at the beginning of the anchoring section is obtained as follows:

[0043]

[0044] In the above formula, g 1 is the undetermined parameter related to the anchoring of the first section.

[0045] Considering the continuity of shear stress distribution in the left and right sections of the non-karst cave, the distribution function expression of shear displacement can be used, and then: Combined with the equal axial force at the intersection of the anchor cables, the equation for the axial force of the anchor cables at the intersection is obtained as follows:

[0046]

[0047] In the above formula, C (i+1)1 is the undetermined coefficient related to the anchoring of the i+1th section.

[0048] The combined anchor boundary conditions, the end of the anchor section The distribution expression of the axial force of the continuous anchor cable at the end of the anchoring section is obtained as follows:

[0049] g (2n+1) =cosh(α (2n+1) ·L)+sinh(α (2n+1) ·L)

[0050] In the above formula, g (2n+1) is an undetermined parameter related to the end of the anchoring segment.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] The anchor cable device proposed in the present invention can not only fill the solution gap in a targeted manner during anchoring construction, but also effectively overcome the problems of grout leakage and grout escape occurring during the drilling backfill grouting process under complex geological conditions such as fissures, karst caves, faults and broken zones.

[0053] The anchoring force limitation calculation method proposed in the present invention provides a theoretical calculation analytical solution for the anchoring force of discontinuous rock strata in karst areas, and provides important theoretical support for the current research on the construction safety of supporting structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flowchart of a method for calculating the anchoring force limit of a directional filling anchor cable proposed by the present invention;

[0055] Figure 2 This is an operating principle diagram of the distribution of dissolution gaps in karst areas proposed by the present invention;

[0056] Figure 3 This is a schematic diagram of the structure of a directional filling anchor cable proposed by the present invention;

[0057] Figure 4 The figure is a schematic diagram of the coordinate system of the anchoring shear stress section of a directional filling type anchor cable proposed in the present invention.

[0058] Description of main symbols:

[0059] In the figure: 1. upper structural surface; 2. lower structural surface; 3. hole wall; 4. intersection line between upper structural surface and hole wall; 5. monitoring point; 6. thickness of exposed dissolution crevice section; 7. height difference between the highest point and the lowest point of the structural surface trace detected by drilling television; 8. nut; 9. washer; 10. grout stop plug; 11. grout stop bag; 12. rod body; 13. anchor head. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods. It should be noted that, under the premise of no conflict, the various embodiments or technical features described below can be arbitrarily combined to form a new embodiment.

[0061] Example 1: Reference Figure 1-Figure 4 , a method for calculating the anchoring force limit of a directional filling anchor cable proposed in this scheme includes the following steps:

[0062] Step 1: Use the drilling television to confirm the distribution of dissolution gaps in the karst area, and then use canvas to process the slurry-stopping bag into a directional filling anchor device according to the distribution of dissolution gaps.

[0063] Step 2: Establish a coordinate system of the anchoring shear stress section based on the directional filling type anchor device; regard the directional filling type anchor device as an ideal elastic axial tensile rod, calculate its shear displacement distribution function in the solution gap section, and then determine the coordinated equilibrium relationship between the solution gap section and the anchoring shear stress section, and finally obtain the function expression of the anchoring force limit P of the directional filling type anchor.

[0064] Specifically, in step 1, the specific operations are as follows:

[0065] Step 101, the panoramic drilling camera probe enters the borehole; the camera light source illuminates the camera area on the borehole wall; the borehole wall image is transformed by a conical reflector to form a panoramic image; the panoramic image and the compass orientation image enter the camera together; the camera transmits the captured image via a dedicated cable to a video distributor located on the ground, one path enters the video recorder to record the entire detection process, and the other path enters the capture card in the computer for digitization.

[0066] Step 102, the measuring wheel on the winch measures the position of the probe in real time, and places the depth value in a dedicated port in the computer through the interface board; the depth value controls the capture mode of the capture card; in the continuous capture mode, the panoramic image is quickly restored to a flat unfolded view and displayed in real time; in the static capture mode, the panoramic image is quickly stored for rapid on-site analysis and indoor statistical analysis; the probe is lowered until the entire detection is completed.

[0067] During the specific operation, the measuring wheel on the winch measures the position of the probe in real time (the measuring wheel on the winch records the length of the line in real time, thereby measuring the depth of the probe in real time); and the depth value is placed in the dedicated port in the computer through the interface board; (the computer records the depth of the probe [i.e. the depth x of the dissolution gap], which is convenient for the subsequent automatic processing of the computer) The capture mode of the capture card is controlled by the depth value; (continuous descent is the continuous capture mode; stop descent is the static capture mode); in the continuous capture mode, the panoramic image is quickly restored to a plane expansion diagram and displayed in real time; (referring to Figure 2 The right side plane, where "1 and 2 are the upper and lower structural planes of the dissolution gap", intersects with the "pore wall 3" and is unfolded into a plane to display the "intersection line 4 of the upper structural plane and the pore wall").

[0068] In the static capture mode, the panoramic image is quickly stored for rapid analysis on site and indoor statistical analysis (randomly measure three non-collinear "monitoring points 5", and count the "thickness of the exposed karst section 6, the height difference between the highest and lowest points of the borehole TV detection structure surface trace 7"). The probe is lowered until the entire detection is completed.

[0069] Step 103: After drilling, detect the number, depth and area of ​​geological defects in the borehole.

[0070] Step 104, tie multiple grout-stopping bags 11 on the anchor rod body. The grout-stopping bags 11 should be facing the deep part of the geological defect. Use canvas to make grout-stopping bags and fix them tightly at various places of the anchor rod. When the slurry is completely filled, a cylindrical string anchor body with a radius of 10 cm and the center of the longitudinal axis of the anchor rod as the origin can be formed. Targeted fixed-point filling can be carried out in actual geological defect sections such as faults, broken zones, and caves, and a grout-stopping bag string with a longitudinal length not exceeding 10 cm can be formed.

[0071] Specifically, a plurality of grout-stopping bags 11 made of canvas grout-stopping bags are arranged at intervals outside the rod body of the directional filling type anchor device, and the grout-stopping bags 11 are used to be filled with grout.

[0072] Measuring point anchor points are set between any two adjacent grouting bags, between the grouting bag and the bottom of the borehole, and between the grouting bag and the borehole mouth to fix the two ends of the grouting bag.

[0073] Specifically, in step 2, the specific operations are as follows:

[0074] Step 201, the anchor shear stress section coordinate system is established: the anchoring start end of the anchor cable is taken as the origin, and the length direction of the anchor cable is taken as the x-axis;

[0075] In the coordinate system, refer to Figure 4 , is the length of the anchor cable anchoring section, n is the number of dissolution gaps in the anchor cable anchoring section, j is the sequence number of dissolution gaps from the beginning of the anchoring, X j is the jth anchoring rock segment, x j is the length of the jth anchoring rock layer section, W j is the jth exposed crack segment, w j is the thickness of the jth exposed crack section, k i is the anchor shear stiffness of the i-th segment, τ i is the anchor shear stress of the i-th segment, π is the circumference of a circle, Δh jis the height difference between the highest point and the lowest point of the structural surface trace detected by the drilling television, C is the circumference of the hole wall, P is the anchoring force of the anchor cable, and x is the distance from the starting end of the anchor.

[0076] Step 202: Calculate the shear stiffness k of the i-th anchorage by the following formula: i :

[0077]

[0078] In the above formula, G is is the shear modulus of the surrounding rock mass in the i-th section, r im is the maximum shear influence radius of deformation in the i-th rock layer, and D is the diameter of the anchor body.

[0079] Step 203: Calculate the maximum shear influence radius r of the deformation in the i-th rock layer by the following formula: im :

[0080] r im =0.5(1-v i )x i

[0081] In the above formula, v i is the Poisson's ratio of the i-th rock layer.

[0082] Step 204: Calculate the anchor cable shear displacement by the following formula: The distribution function of is:

[0083]

[0084] In the above formula, is the shear displacement on the shear plane between the i-th anchor body and the surrounding rock mass, C 1 and C 2 are the unknown coefficients, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, α i is a constant related to the shear stiffness of the i-th rock layer.

[0085] Step 205: Calculate the constant α related to the shear stiffness of the i-th rock layer by the following formula: i :

[0086]

[0087] In the above formula, k i is the shear stiffness of the i-th rock layer.

[0088] Step 206: Calculate the elastic modulus E by the following formula: P :

[0089]

[0090] In the above formula, Er is the elastic modulus of the grouting body, E s is the elastic modulus of the anchor cable, N is the number of anchor cables, and d is the diameter of the anchor cable.

[0091] Combined with the boundary conditions of the anchor cable, the end of the anchor section P| x＝L =0, the anchor cable anchoring force limit P expression is obtained:

[0092]

[0093] In the above formula, C 11 and C 12 is the undetermined coefficient related to the anchoring of the first section.

[0094] The C 11 and C 12 The calculation steps are as follows:

[0095] See also Figure 4 , considering the continuity of shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of shear displacement can be used, then: Combined with the equal shear displacement at the intersection of anchor cables, the equation for the shear displacement of anchor cables at the intersection is obtained as:

[0096]

[0097] C i2 =C i1 ·g i

[0098] In the above formula, g i is the undetermined parameter related to the anchoring of the i-th segment, g (i+1) is the undetermined parameter related to the anchoring of the i+1th segment, C i1 and C i2 is the undetermined coefficient related to the anchorage of the i-th segment, is less than The maximum integer.

[0099] Combined with the boundary conditions of the anchor cable, the anchoring section start τ| x＝0 =τ 1 , the distribution expression of the shear stress of the continuous anchor body at the beginning of the anchoring section is obtained as follows:

[0100]

[0101] In the above formula, g 1 is the undetermined parameter related to the anchoring of the first section.

[0102] See also Figure 4 , considering the continuity of shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of shear displacement can be used, then: Combined with the equal axial force at the intersection of anchor cables, the equation for the axial force of the anchor cables at the intersection is obtained as:

[0103]

[0104] In the above formula, C (i+1)1 is the undetermined coefficient related to the anchoring of the i+1th section.

[0105] The combined anchor boundary conditions, the end of the anchor section The distribution expression of the axial force of the continuous anchor cable at the end of the anchoring section is obtained as follows:

[0106] g (2n+1) =cosh(α (2n+1) ·L)+sinh(α (2n+1) ·L)

[0107] In the above formula, g (2n+1) is an undetermined parameter related to the end of the anchoring segment.

[0108] The anchoring force limitation calculation method proposed in the present invention provides a theoretical calculation analytical solution for the anchoring force of discontinuous rock strata in karst areas, and provides important theoretical support for the current research on the construction safety of supporting structures.

[0109] The above-mentioned embodiments are only preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantial changes and substitutions made by technicians in this field on the basis of the present invention shall fall within the scope of protection required by the present invention.

Claims

1. A method for calculating the anchoring force limit of a directional filling anchor cable, characterized in that: The steps include: Step 1: Use drilling television to confirm the distribution of karst crevices in the karst area, and then use canvas to process the slurry-stopping bag into a directional filling anchor device according to the distribution of karst crevices; Step 2: Establish a coordinate system of the anchor shear stress section based on the directional filling type anchor device, regard the directional filling type anchor device as an ideal elastic axial tensile rod, calculate its shear displacement distribution function in the solution gap section, and then determine the coordinated equilibrium relationship between the solution gap section and the anchor shear stress section, and finally obtain the function expression of the anchoring force limit P of the directional filling type anchor.

2. The method for calculating the anchoring force limit of a directional filling anchor cable according to claim 1, characterized in that: In step 1, the specific operations are as follows: Step 101, the panoramic borehole camera probe enters the borehole; the camera light source illuminates the camera area on the borehole wall; the borehole wall image is transformed by a conical reflector to form a panoramic image; the panoramic image and the compass orientation image enter the camera together; the camera transmits the captured image to the video distributor on the ground through a dedicated cable, one way enters the video recorder to record the whole detection process, and the other way enters the capture card in the computer for digitization; Step 102: The measuring wheel on the winch measures the position of the probe in real time, and places the depth value in a dedicated port in the computer through the interface board; the capture mode of the capture card is controlled by the depth value; in the continuous capture mode, the panoramic image is quickly restored to a flat unfolded image and displayed in real time; in the static capture mode, the panoramic image is quickly stored for rapid analysis on site and statistical analysis indoors; the probe is lowered until the entire detection is completed; Step 103, after drilling, detecting the number, depth and area of ​​geological defects in the borehole; Step 104, tie multiple grout-stopping bags on the anchor rod body. The grout-stopping bags should be facing the deep parts of the geological defects. Use canvas to make grout-stopping bags and fix them tightly at various places of the anchor rod. When the slurry is completely filled, a cylindrical string anchor body with a radius of 10 cm and the center of the longitudinal axis of the anchor rod as the origin can be formed. Targeted fixed-point filling can be carried out in actual geological defect sections such as faults, broken zones, and caves, and a grout-stopping bag string with a longitudinal length not exceeding 10 cm can be formed.

3. The method for calculating the anchoring force limit of a directional filling anchor cable according to claim 2, characterized in that: A plurality of grout-stopping bags made of canvas grout-stopping bags are arranged at intervals outside the rod body of the directional filling type anchor cable device, and the grout-stopping bags are used to be filled with grout; Measuring point anchor points are set between any two adjacent grouting bags, between the grouting bag and the bottom of the borehole, and between the grouting bag and the borehole mouth to fix the two ends of the grouting bag.

4. The method for calculating the anchoring force limit of a directional filling anchor cable according to claim 1, characterized in that: In step 2, the specific operations are as follows: Step 201, the anchor shear stress section coordinate system is established: the anchoring start end of the anchor cable is taken as the origin, and the length direction of the anchor cable is taken as the x-axis; In the coordinate system, is the length of the anchor cable anchoring section, n is the number of dissolution gaps in the anchor cable anchoring section, j is the sequence number of dissolution gaps from the beginning of the anchoring, X j is the jth anchoring rock segment, x j is the length of the jth anchoring rock layer section, W j is the jth exposed crack segment, w j is the thickness of the jth exposed crack section, k i is the anchor shear stiffness of the i-th segment, τ i is the anchor shear stress of the i-th segment, π is the circumference of a circle, Δh j is the height difference between the highest point and the lowest point of the structural surface trace detected by the borehole TV, C is the perimeter of the hole wall, P is the anchoring force of the anchor cable, and x is the distance from the starting end of the anchoring; Step 202: Calculate the shear stiffness k of the i-th anchorage by the following formula: i : In the above formula, G is is the shear modulus of the surrounding rock mass in the i-th section, r im is the maximum shear influence radius of deformation in the i-th rock layer, and D is the diameter of the anchor body; Step 203: Calculate the maximum shear influence radius r of the deformation in the i-th rock layer by the following formula: im : r im =0.5(1-v i )x i In the above formula, v i is the Poisson's ratio of the i-th rock layer; Step 204: Calculate the shear displacement of the anchor cable by the following formula: The distribution function of is: In the above formula, is the shear displacement on the shear plane between the i-th anchor body and the surrounding rock mass, C1 and C2 are unknown coefficients, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, α i is a constant related to the shear stiffness of the ith rock layer; Step 205: Calculate the constant α related to the shear stiffness of the i-th rock layer by the following formula: i : In the above formula, k i is the shear stiffness of the i-th rock layer; Step 206: Calculate the elastic modulus E by the following formula: P : In the above formula, E r is the elastic modulus of the grouting body, E s is the elastic modulus of the anchor cable, N is the number of anchor cables, and d is the diameter of the anchor cable; Combined with the boundary conditions of the anchor cable, the end of the anchor section P| x＝L =0, the anchor cable anchoring force limit P expression is obtained: In the above formula, C 11 and C 12 is the undetermined coefficient related to the anchoring of the first section.

5. A method for calculating the anchoring force limit of a directional filling anchor cable as claimed in claim 4, characterized in that: The C 11 and C 12 The calculation steps are as follows: Considering the continuity of shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of shear displacement can be used, and then: Combined with the equal shear displacement at the intersection of anchor cables, the equation for the shear displacement of anchor cables at the intersection is obtained as follows: C i2 =C i1 ·g i In the above formula, g i is the undetermined parameter related to the anchoring of the i-th segment, g (i+1) is the undetermined parameter related to the anchoring of the i+1th segment, C i1 and C i2 is the undetermined coefficient related to the anchorage of the i-th segment, is less than The maximum integer. Combined with the boundary conditions of the anchor cable, the anchoring section start τ| x＝0 =τ1, the distribution expression of the shear stress of the continuous anchor body at the beginning of the anchoring section is obtained as follows: In the above formula, g1 is an undetermined parameter related to the anchoring of the first section. Considering the continuity of shear stress distribution in the left and right sections of the non-karst cave, the distribution function expression of shear displacement can be used, and then: Combined with the equal axial force at the intersection of the anchor cables, the equation for the axial force of the anchor cables at the intersection is obtained as follows: In the above formula, C (i+1)1 is the undetermined coefficient related to the anchorage of the i+1th segment; The combined anchor boundary conditions, the end of the anchor section The distribution expression of the axial force of the continuous anchor cable at the end of the anchoring section is obtained as follows: g (2n+1) =cosh(α (2n+1) ·L)+sinh(α (2n+1) ·L) In the above formula, g (2n+1) is an undetermined parameter related to the end of the anchoring segment.

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