A calculation method for the anchoring force limit of directional filling anchor cables

Abstract

The present invention relates to the field of anchor cable support technology, and discloses a method for calculating the anchoring force limit of a directional filling anchor cable, comprising the following steps: Step 1, confirming the distribution of dissolution gaps in the karst area with the help of a drilling television, and then using canvas to process a slurry-stopping bag into a directional filling anchor cable device according to the distribution of dissolution gaps. Step 2, establishing a coordinate system of the anchoring shear stress segment based on the directional filling anchor cable device; treating the directional filling anchor cable device as an ideal elastic axial tensile rod, calculating its shear displacement distribution function in the dissolution gap segment, and then determining the coordinated equilibrium relationship between the dissolution gap segment and the anchoring shear stress segment, and finally obtaining a functional expression for the anchoring force limit P of the directional filling anchor cable. The anchoring force limit calculation method proposed in the present invention provides a theoretical calculation analytical solution for the anchoring force of discontinuous rock formations in karst areas, and provides important theoretical support for the current research on the safety of support structure construction.

Description

Technical Field

[0001] The present 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 in construction, water conservancy, transportation, and high-slope construction, anchor cable support is essential for controlling deformation. Anchor cable support is widely used due to its low cost, safety, and stability. Existing anchor cable anchoring force calculation formulas also provide guidance for anchor cable anchoring operations 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, comprising the following steps:

[0007] Step 1: Use 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 based on the distribution of dissolution gaps.

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

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

[0010] Step 101: A panoramic borehole camera probe enters a borehole; a camera light source illuminates a camera area on the borehole wall; an image of the borehole wall is transformed by a conical reflector to form a panoramic image; the panoramic image and a compass orientation image are input into a camera; the camera transmits the captured image via a dedicated cable to a video distributor located on the ground; one path is input to a video recorder to record the entire detection process, and the other path is input to a capture card in a computer for digitization;

[0011] Step 102: The measuring wheel on the winch measures the position of the probe in real time and stores the depth value in a dedicated port in the computer via 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 image 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.

[0012] Step 103: After drilling, detect the number, depth, and area of ​​geological defects in the borehole;

[0013] Step 104: Tie multiple grouting bags on the anchor rod body. The grouting bags should be facing the deep part of the geological defect. Use canvas to make grouting 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. In actual geological defect sections such as faults, fracture zones, and caves, targeted filling can be carried out to form a grouting bag string with a longitudinal length not exceeding 10 cm.

[0014] Specifically, a plurality of grouting bags made of canvas grouting bags are arranged at intervals on the outside of the rod body of the directional filling type anchor device, and the grouting 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 segment coordinate system is established with the anchoring start end of the anchor cable as the origin and the length direction of the anchor cable 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 end, X j is the jth anchoring rock segment, x j is the length of the j-th anchoring rock layer section, W j is the jth exposed crack section, 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, Δh j is the height difference between the highest and lowest points of the structural surface trace detected by borehole television, 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 anchor.

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

[0020]

[0021] In the above formula, G is is the shear modulus of the surrounding rock mass in section i, 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 using the following formula: The distribution function of :

[0026]

[0027] In the above formula, is the shear displacement on the shear plane between the anchor body and the surrounding rock mass in the i-th section, 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 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 anchoring 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 the shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of the shear displacement can be used. Then, considering that the shear displacement at the intersection of the anchor cables is equal, the equation for the shear displacement of the 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+1 segment, C i1 and C i2 is the undetermined coefficient related to the anchoring of the i-th segment, is less than The maximum integer.

[0042] Combined with the boundary conditions of the anchor cable, τ|x=0=τ1 at the beginning of the anchor section, the distribution expression of the shear stress of the continuous anchor body at the beginning of the anchor section is obtained:

[0043]

[0044] In the above formula, g1 is an undetermined parameter related to the anchoring of the first section.

[0045] Considering the continuity of the shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of the 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:

[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 gaps in a targeted manner during anchoring construction, but also effectively overcome the problems of leakage and grouting that occur during the drilling backfill grouting process under complex geological conditions such as cracks, caves, faults and broken zones.

[0053] The anchoring force limitation calculation method proposed in the present invention provides a theoretical calculation and 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 support structures. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0055] Figure 2 This is a diagram showing the operating principle of the karst region dissolution gap distribution proposed by the present invention;

[0056] Figure 3 This is a structural schematic diagram 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 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 will be 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 new embodiments.

[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 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 based on the distribution of dissolution gaps.

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

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

[0065] Step 101: A panoramic drilling camera probe enters the borehole; a 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 are input into the camera together; the camera transmits the captured image via a dedicated cable to a video distributor located on the ground, one path enters a video recorder to record the entire detection process, and the other path enters a capture card in a 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 into 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's descent in real time); and the depth value is placed in a 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 subsequent automatic processing by the computer) The capture mode of the capture card is controlled by the depth value; (continuous descent is continuous capture mode; stopped descent is static capture mode); in continuous capture mode, the panoramic image is quickly restored to a flat unfolded view and displayed in real time; (referring to Figure 2 On the right side, "1 and 2 are the upper and lower structural surfaces of the dissolution gap", which intersect with "pore wall 3" and are unfolded into a plane to display "intersection line 4 of the upper structural surface and pore wall").

[0068] In static capture mode, the panoramic image is quickly stored for rapid on-site analysis and indoor statistical analysis. (Three non-collinear "monitoring points 5" are randomly measured, and the "thickness of the exposed dissolution section 6 and the height difference between the highest and lowest points of the borehole TV detection structural surface trace 7" are calculated.) 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 grouting bags 11 on the anchor rod body. The grouting bags 11 should be facing the deep part of the geological defect. Use canvas to make grouting 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. In actual geological defect sections such as faults, fracture zones, and caves, targeted and fixed-point filling can be carried out to form a grouting bag string with a longitudinal length not exceeding 10 cm.

[0071] Specifically, a plurality of grouting bags 11 made of canvas grouting bags are arranged at intervals on the outside of the rod body of the directional filling type anchor device, and the grouting 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 segment coordinate system is established with the anchoring start end of the anchor cable as the origin and the length direction of the anchor cable 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 end, X j is the jth anchoring rock segment, x j is the length of the j-th anchoring rock layer section, W j is the jth exposed crack section, 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, Δh j is the height difference between the highest and lowest points of the structural surface trace detected by borehole television, 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 anchor.

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

[0077]

[0078] In the above formula, G is is the shear modulus of the surrounding rock mass in section i, 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 using the following formula: The distribution function of :

[0083]

[0084] In the above formula, is the shear displacement on the shear plane between the anchor body and the surrounding rock mass in the i-th section, 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 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, 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.

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

[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+1 segment, C i1 and C i2 is the undetermined coefficient related to the anchoring 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 =τ1, 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, g1 is an undetermined parameter related to the anchoring of the first section.

[0102] See also Figure 4 , considering the continuity of the shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of the shear displacement can be used, 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:

[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 and 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 support structures.

[0109] The above 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 replacements made by technicians in this field on the basis of the present invention 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 borehole television to confirm the distribution of dissolution gaps in the karst area, and then use canvas to process the dissolution gaps into slurry-stopping bag directional filling anchor cable devices according to the distribution of dissolution gaps; Step 2: Establish a coordinate system for the anchoring shear stress section based on the directional filling anchor device, regard the directional filling 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 a functional expression for the anchoring force limit P of the directional filling anchor cable; In step 2, the specific operations are as follows: Step 201: The anchor shear stress segment coordinate system is established with the anchoring start end of the anchor cable as the origin and the length direction of the anchor cable 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 end, X j is the jth anchoring rock segment, is the length of the j-th anchoring rock layer section, W j is the jth exposed dissolution fissure segment, 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, is pi, is the height difference between the highest and lowest points of the structural surface trace detected by borehole television, 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 anchor; Step 202: Calculate the shear stiffness k of the anchorage at segment i by the following formula: i : ； In the above formula is the shear modulus of the surrounding rock mass in section i, 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 of deformation in the i-th rock layer by the following formula: : ； In the above formula is the Poisson's ratio of the i-th rock layer; Step 204: Calculate the anchor cable shear displacement using the following formula: The distribution function of : ； In the above formula, is the shear displacement on the shear plane between the anchor body and the surrounding rock mass in the i-th section, and is the unknown coefficient, is the hyperbolic sine function, is the hyperbolic cosine function, is a constant related to the shear stiffness of the rock layer in the i-th section; Step 205: Calculate the constant related to the shear stiffness of the i-th rock layer by the following formula: : ； In the above formula, is the shear stiffness of the i-th rock layer; Step 206: Calculate the elastic modulus using the following formula: : ； In the above formula, is the elastic modulus of the grouting body, 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 anchor boundary conditions, the anchor end P| x=L =0, the expression of anchor cable anchoring force limit P is obtained: ； In the above formula, and is the undetermined coefficient related to the anchoring of the first section.

2. The method for calculating the anchoring force limit of a directional filling anchor cable according to claim 1, wherein: In step 1, the specific operations are as follows: Step 101: A panoramic borehole camera probe enters a borehole; a camera light source illuminates a camera area on the borehole wall; an image of the borehole wall is transformed by a conical reflector to form a panoramic image; the panoramic image and a compass orientation image are input into a camera; the camera transmits the captured image via a dedicated cable to a video distributor located on the ground; one path is input to a video recorder to record the entire detection process, and the other path is input to a capture card in a computer for digitization; Step 102: The measuring wheel on the winch measures the position of the probe in real time and stores the depth value in a dedicated port in the computer via 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 image 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. Step 103: After drilling, detect the number, depth, and area of ​​geological defects in the borehole; Step 104: Tie multiple grouting bags on the anchor rod body. The grouting bags should be facing the deep part of the geological defect. Use canvas to make grouting 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. In actual geological defect sections such as faults, fracture zones, and caves, targeted filling can be carried out to form a grouting bag string with a longitudinal length not exceeding 10 cm.

3. The method for calculating the anchoring force limit of a directional filling anchor cable according to claim 2, wherein: A plurality of grouting bags made of canvas grouting bags are arranged at intervals on the outside of the rod body of the directional filling type anchor device, and the grouting 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. A method for calculating the anchoring force limit of a directional filling anchor cable according to claim 1, characterized in that: described and The calculation steps are as follows: Considering the continuity of the shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of the shear displacement can be used. Then, considering that the shear displacement at the intersection of the anchor cables is equal, the equation for the shear displacement of the anchor cables at the intersection is obtained as follows: ； ； In the above formula, is the undetermined parameter related to the anchoring of the i-th segment, is the undetermined parameter related to the anchoring of the i+1 segment, and is the undetermined coefficient related to the anchoring of the i-th segment, is less than The largest 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 is the undetermined parameter related to the anchoring of the first section; Considering the continuity of the shear stress distribution in the left and right sections of the non-cavern, the distribution function expression of the 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: ； In the above formula, is the undetermined coefficient related to the anchoring 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: ； In the above formula is an undetermined parameter related to the end of the anchoring segment.

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