A method for calculating the anchoring force limit of adaptive filling type anchor cable

Abstract

The present invention relates to the field of anchor cable support technology, and discloses a method for calculating the anchoring force limit of an adaptive filling type anchor cable, comprising the following steps: step 1, preparing an adaptive filling type anchor cable device, and installing the adaptive filling type anchor cable device; step 2, establishing an anchor shear stress segment coordinate system based on the adaptive filling type anchor cable device; step 3, calculating the distribution function of the shear displacement of the anchor cable device in the dissolution gap segment, determining the coordinated balance relationship between the dissolution gap segment and the anchor shear stress segment passed by the anchor cable device, and finally obtaining a function expression of the anchoring force limit P of the adaptive filling type anchor cable device. The anchoring force calculation method proposed in the present invention provides a theoretical calculation analytical solution for the anchoring force of discontinuous rock formations in karst areas, provides theoretical support for the current field of support structure construction safety, and makes up for the problem of inaccurate theoretical calculation of the anchoring force of discontinuous rock formations in karst areas.

Description

Technical Field

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

[0002] In the context of the rapid development of my country's industrial construction, anchor cable support is widely used in construction, water conservancy, transportation, land and a large number of high slope projects as a low-cost, safe and stable technical application method. The existing anchor cable anchoring force calculation formula also guides the anchor cable anchoring construction work to a certain extent.

[0003] In southern my country, especially in the karst landform areas in the southwest, the karst development in the hydrogeological areas of limestone depressions is relatively significant, and they often face complex geological conditions such as fissures, caves, faults and broken zones. These discontinuous rock layers will not only aggravate the problems of grout leakage and grouting during the backfill grouting process, reduce the anchoring effect, but also make the theoretical calculated value of the anchoring force of the existing anchor cable too high, thus affecting the safe construction of the support structure.

[0004] Therefore, how to establish a self-filling anchor device suitable for karst areas and a calculation method for its anchoring force limit to guide the safe construction of anchor cables will be a key issue that needs to be solved urgently. 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 an adaptive filling type anchor cable.

[0006] The present invention is implemented by the following technical solutions: A method for calculating the anchoring force limit of an adaptive filling type anchor cable comprises the following steps:

[0007] Step 1, preparing an adaptive filling type anchor cable device, and installing the adaptive filling type anchor cable device;

[0008] Step 2: establishing an anchor shear stress segment coordinate system based on the adaptive filling anchor cable device;

[0009] Step 3: The adaptive filling type anchor device passing through the dissolution gap section is regarded as an ideal elastic axial tensile rod, and the distribution function of the shear displacement of the anchor device in the dissolution gap section is calculated to determine the coordinated equilibrium relationship between the dissolution gap section passed by the anchor device and the anchoring shear stress section, and finally the function expression of the anchoring force limit P of the adaptive filling type anchor device is obtained.

[0010] Specifically, in step 1, the adaptive filling type anchor cable device uses a canvas grout-stopping bag to wrap the outer side of the anchor cable rod body, and a closed space for filling grout is formed between the canvas grout-stopping bag and the rod body.

[0011] Specifically, the functional expression of the anchoring force limit value P is:

[0012]

[0013] In the above formula is a constant related to the shear stiffness of the first rock layer, is the shear stress of the first anchorage, is the elastic modulus, is the undetermined parameter related to the anchoring of the first section, is the maximum shear influence radius of deformation in the first rock layer, is the shear modulus of the first section of the surrounding rock mass, and D is the diameter of the anchor body.

[0014] Combined with the anchor cable boundary conditions, the anchor section starts , the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section is obtained as follows:

[0015]

[0016] Specifically, the operation steps of step 2 are as follows:

[0017] The relative position relationship between the dissolution crevice section and the anchor shear stress section through which the adaptive filling anchor cable passes and its related parameters are clarified, and then the anchor shear stress section coordinate system is established. The anchor shear stress section coordinate system takes the anchoring start end of the anchor cable as the origin and the length direction of the anchor cable as the x-axis.

[0018] Construct a static equilibrium analysis model of anchor cable micro-segment.

[0019] In the anchor shear stress segment coordinate system, is the total length of the anchor cable anchoring section, n is the number of dissolution gaps in the anchor cable anchoring section, i is the sequence number of anchoring from the beginning of the anchoring end, is the length of the i-th anchorage, Xi is the i-th anchorage, ki is the shear stiffness of the i-th anchorage, τi is the shear stress of the i-th anchorage, P is the anchoring force of the anchor cable, and x is the distance from the starting end of the anchorage.

[0020] Shear stiffness k of the i-th anchorage i The calculation method is as follows:

[0021]

[0022] In the above formula is the circumference of a circle, is the shear modulus of the surrounding rock mass in the i-th section, is the maximum shear influence radius of deformation in the i-th rock layer, and D is the diameter of the anchor body.

[0023] The maximum shear influence radius of deformation in the i-th rock layer The calculation method is as follows:

[0024]

[0025] In the above formula is the Poisson's ratio of the i-th rock layer.

[0026] The micro-segment static equilibrium equation is established as follows:

[0027]

[0028] In the above formula is the tension of the anchor micro-segment, C is the perimeter of the anchor, is the micro-segment shear stress, is the length of the anchor micro-segment, is the micro-segment shear displacement, A is the micro-segment interface area of ​​the anchor body, is the composite elastic modulus.

[0029] Composite elastic modulus The calculation method is as follows:

[0030]

[0031] 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, d is the diameter of the anchor cable, and D is the diameter of the anchor body.

[0032] Specifically, the steps for determining the functional expression of the anchoring force limit value P in step 3 are as follows:

[0033] Step S31: The micro segment in step 2 , determine the distribution function of the shear displacement.

[0034]

[0035] In the above formula, is the shear displacement on the shear plane between the i-th anchor body and the surrounding rock mass, and is the coefficient to be determined, is the hyperbolic sine function, is the hyperbolic cosine function, is a constant related to the shear stiffness of the i-th rock layer; is a constant related to the shear stiffness of the i-th rock layer The calculation method is as follows:

[0036]

[0037] In the above formula, is the shear stiffness of the i-th rock layer.

[0038] Step S32, considering the continuity of the shear stress distribution in the left and right sections at the interface between the dissolution crevice and the rock formation, the expression of the distribution function of the shear displacement obtained in step S31 is adopted, and then: Combined with the equal shear displacement at the intersection of the anchor cables, the equation for the shear displacement of the anchor cables at the intersection is obtained as follows:

[0039]

[0040] In the above formula, and is the undetermined coefficient related to the anchorage of the i-th segment, and is the undetermined coefficient related to the anchoring of the i+1th section.

[0041] Step S33, considering the continuity of the shear stress distribution of the left and right sections of the non-dissolution gap section, the expression of the distribution function of the shear displacement obtained in step S31 is adopted, 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:

[0042]

[0043] Step S34: using the shear displacement expression equation of the anchor cable at the intersection obtained in step S32, the equation is:

[0044]

[0045]

[0046] 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+1th segment.

[0047] Step S34.1: Combine the anchor cable boundary conditions and the anchor section start , the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section is obtained as follows:

[0048]

[0049] Step S34.2: Using the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section obtained in step S4.1, the equation is:

[0050]

[0051] Step S35, combined with the anchor cable boundary conditions, 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:

[0052]

[0053] Step S36: Combine the anchor cable boundary conditions and anchor 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:

[0054]

[0055] Step S37: Using the distribution expression of the axial force of the continuous anchor cable at the end of the anchoring section obtained in step S35, the equation is:

[0056]

[0057] In the above formula is an undetermined parameter related to the end of the anchoring segment.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The adaptive anchor cable device proposed in the present invention does not need to detect the specific distribution of the karst crevices in the borehole. During the anchor cable anchoring construction, it can not only adaptively fill the karst crevices, but also overcome the problems of leakage and grouting during backfill grouting in boreholes under complex geological conditions such as cracks, karst caves, faults, and broken zones, thereby ensuring the density requirements and anchoring effect of the grouting in the borehole.

[0060] The anchoring force calculation method proposed in the present invention provides a theoretical calculation analytical solution for the anchoring force of anchor cables in discontinuous rock formations in karst areas, provides theoretical support for the current field of support structure construction safety, and makes up for the inaccurate theoretical calculation of the anchoring force of anchor cables in discontinuous rock formations in karst areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A flowchart of a method for calculating the anchoring force limit of an adaptive filling type anchor cable proposed by the present invention;

[0062] Figure 2 This is a schematic structural diagram of an adaptive filling type anchor cable device proposed by the present invention;

[0063] Figure 3 This is a schematic structural diagram of the installation of the adaptive filling type anchor cable device proposed by the present invention;

[0064] Figure 4 It is the anchor shear stress section coordinate system of the adaptive filling type anchor cable proposed by the present invention;

[0065] Figure 5 This is a schematic diagram of the structure of the static equilibrium analysis model of the anchor body micro-segment proposed in the present invention.

[0066] Description of main symbols:

[0067] In the figure: 1. nut; 2. washer; 3. grouting plug; 4. rod body; 5. canvas grouting bag; 6. anchor head; 7. grouting device; 8. pedestal; 9. anchor; 10. supporting structure; 11. solution gap; 12. grouting body. DETAILED DESCRIPTION

[0068] 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.

[0069] Example: Refer to Figure 1-Figure 5 The present invention proposes a method for calculating the anchoring force limit of an adaptive filling type anchor cable, comprising the following steps:

[0070] Step 1: Prepare an adaptive filling type anchor cable device and install the adaptive filling type anchor cable device. When installing the anchor cable, a retaining structure 10 is set at the end of the anchor cable. The retaining structure 10 has a pedestal 8 for the end of the anchor cable to pass through. Figure 3 A grout stopper 7 is mounted on the outer side of the middle part of the anchor cable, and the two sides of the grout stopper 7 are a free section and an anchoring section after grouting, respectively, and the anchoring section passes through the dissolution crevice 11 in the rock mass.

[0071] Step 2: Based on the adaptive filling type anchor device, the anchor shear stress coordinate system of the dissolution section and the anchoring section is established, and the adaptive filling type anchor device passing through the dissolution section is regarded as an ideal elastic axial tensile rod; the distribution function of the shear displacement of the anchor device in the dissolution section is calculated, and the coordinated equilibrium relationship between the dissolution section and the anchoring shear stress section passed by the adaptive filling type anchor device is determined, and finally the function expression of the anchoring force limit P of the adaptive filling type anchor device is obtained.

[0072] Reference Figure 2 In step 1, the adaptive filling type anchor device includes a nut 1, a washer 2, a grouting plug 3, a rod body 4 and a canvas grouting bag 5. The adaptive filling type anchor device uses a canvas grouting bag to wrap the outside of the anchor rod body, and a closed space for filling slurry is formed between the canvas grouting bag 5 and the rod body 4 to form a grouting body 12.

[0073] Specifically, the functional expression of the anchoring force limit value P is:

[0074]

[0075] In the above formula is a constant related to the shear stiffness of the first rock layer, is the shear stress of the first anchorage, is the elastic modulus, is the undetermined parameter related to the anchoring of the first section, is the maximum shear influence radius of deformation in the first rock layer, is the shear modulus of the first section of the surrounding rock mass, and D is the diameter of the anchor body.

[0076] Combined with the anchor cable boundary conditions, the anchor section starts , the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section is obtained as follows:

[0077]

[0078] Specifically, the operation steps of step 2 are as follows:

[0079] Reference Figure 3 , Figure 4 , clarify the relative position relationship and related parameters between the dissolution crevice section and the anchor shear stress section through which the adaptive filling anchor cable passes, and then establish the anchor shear stress section coordinate system, wherein the anchor shear stress section coordinate system takes the anchoring start end of the anchor cable as the origin and the length direction of the anchor cable as the x-axis;

[0080] Construct the static balance analysis model of anchor cable micro-segment, refer to Figure 5 ;

[0081] In the anchor shear stress segment coordinate system, is the total length of the anchor cable anchoring section, n is the number of dissolution gaps in the anchor cable anchoring section, i is the sequence number of anchoring from the beginning of the anchoring end, is the length of the i-th anchorage, Xi is the i-th anchorage, ki is the shear stiffness of the i-th anchorage, τi is the shear stress of the i-th anchorage, P is the anchoring force of the anchor cable, and x is the distance from the starting end of the anchorage;

[0082] Shear stiffness k of the i-th anchorage i The calculation method is as follows:

[0083]

[0084] In the above formula is the circumference of a circle, is the shear modulus of the surrounding rock mass in the i-th section, is the maximum shear influence radius of deformation in the i-th rock layer, and D is the diameter of the anchor body;

[0085] The maximum shear influence radius of deformation in the i-th rock layer The calculation method is as follows:

[0086]

[0087] In the above formula is the Poisson's ratio of the i-th rock layer

[0088] The micro-segment static equilibrium equation is established as follows:

[0089]

[0090] Reference Figure 5 , in the above formula is the tension of the anchor micro-segment, C is the perimeter of the anchor, is the microsegment shear stress, is the length of the anchor micro-segment, is the micro-segment shear displacement, A is the micro-segment interface area of ​​the anchor body, is the composite elastic modulus;

[0091] Composite elastic modulus The calculation method is as follows:

[0092]

[0093] 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.

[0094] Specifically, the steps for determining the functional expression of the anchoring force limit value P in step 3 are as follows:

[0095] Step S31: The micro segment in step 2 , determine the distribution function of the shear displacement:

[0096]

[0097] In the above formula, is the shear displacement on the shear plane between the i-th anchor body and the surrounding rock mass, and is the coefficient to be determined, is the hyperbolic sine function, is the hyperbolic cosine function, is a constant related to the shear stiffness of the i-th rock layer; is a constant related to the shear stiffness of the i-th rock layer The calculation method is as follows:

[0098]

[0099] In the above formula, is the shear stiffness of the i-th rock layer.

[0100] Step S32, considering the continuity of the shear stress distribution in the left and right sections at the interface between the dissolution crevice and the rock formation, the expression of the distribution function of the shear displacement obtained in step S31 is adopted, and then: Combined with the equal shear displacement at the intersection of the anchor cables, the equation for the shear displacement of the anchor cables at the intersection is obtained as follows:

[0101]

[0102] In the above formula, and is the undetermined coefficient related to the anchorage of the i-th segment, and is the undetermined coefficient related to the anchoring of the i+1th section.

[0103] Step S33, considering the continuity of the shear stress distribution of the left and right sections of the non-dissolution gap section, the expression of the distribution function of the shear displacement obtained in step S31 is adopted, 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:

[0104]

[0105] Step S34: using the shear displacement expression equation of the anchor cable at the intersection obtained in step S32, the equation is:

[0106]

[0107]

[0108] 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+1th segment.

[0109] Step S34.1: Combine the anchor cable boundary conditions and the anchor section start , the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section is obtained as follows:

[0110]

[0111] Step S34.2: Using the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section obtained in step S4.1, the equation is:

[0112]

[0113] Step S35, combined with the anchor cable boundary conditions, 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:

[0114]

[0115] Step S36: Combine the anchor cable boundary conditions and anchor 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:

[0116]

[0117] Step S37: Using the distribution expression of the axial force of the continuous anchor cable at the end of the anchoring section obtained in step S35, the equation is:

[0118]

[0119] In the above formula is an undetermined parameter related to the end of the anchoring segment.

[0120] The anchoring force calculation method proposed in the present invention provides a theoretical calculation analytical solution for the anchoring force of anchor cables in discontinuous rock formations in karst areas, provides theoretical support for the current field of support structure construction safety, and makes up for the inaccurate theoretical calculation of the anchoring force of anchor cables in discontinuous rock formations in karst areas.

[0121] 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 an adaptive filling type anchor cable, characterized in that: The steps include: Step 1: preparing an adaptive filling type anchor cable device and installing the adaptive filling type anchor cable device; Step 2: establishing an anchor shear stress segment coordinate system based on the adaptive filling anchor cable device; Step 3, the adaptive filling type anchor device passing through the dissolution gap section is regarded as an ideal elastic axial tensile rod, and the distribution function of the shear displacement of the anchor device in the dissolution gap section is calculated to determine the coordinated equilibrium relationship between the dissolution gap section passed by the anchor device and the anchor shear stress section, and finally obtain the function expression of the anchoring force limit value P of the adaptive filling type anchor device; The functional expression of the anchoring force limit value P is: In the above formula, α1 is a constant related to the shear stiffness of the first section of rock formation, τ1 is the shear stress of the first section of anchoring, and E P is the elastic modulus, g1 is the undetermined parameter related to the anchoring of the first section, r 1m is the maximum shear influence radius of deformation in the first rock layer, G 1s is the shear modulus of the first section of the surrounding rock mass, and D is the diameter of the anchor body; Combined with the boundary conditions of the anchor cable, the anchoring section start P| x＝0 =P, the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section is obtained as follows: Among them: C 11 and C 12 is the undetermined coefficient related to the anchorage of the first section; The specific operation steps of step 2 are as follows: The relative position relationship between the dissolution gap section and the anchor shear stress section through which the adaptive filling anchor cable passes and the related parameters are clarified, and then the anchor shear stress section coordinate system is established, wherein the anchor shear stress section coordinate system takes the anchoring start end of the anchor cable as the origin and the length direction of the anchor cable as the x-axis; Construct the static equilibrium analysis model of anchor cable micro-segment; In the anchor shear stress segment coordinate system, is the total length of the anchor cable anchoring section, n is the number of dissolution gaps in the anchor cable anchoring section, i is the sequence number of anchoring from the beginning of the anchoring end, x i is the anchorage length of the i-th segment, k i is the shear stiffness of the i-th anchorage, τ i is the shear stress of the i-th anchorage, P is the anchoring force of the anchor cable, and x is the distance from the starting end of the anchorage; Shear stiffness k of the i-th anchorage i The calculation method is as follows: In the above formula, π is the circumference of a circle, 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; The maximum shear influence radius r of the deformation in the i-th rock layer im The calculation method is as follows: 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 The micro-segment static equilibrium equation is established as follows: dP(x)=-Cτ(x)dx In the above formula, dP(x) is the tension of the anchor micro-segment, C is the perimeter of the anchor, τ(x) is the micro-segment shear stress, dx is the length of the anchor micro-segment, ds(x) is the micro-segment shear displacement, A is the interface area of ​​the anchor micro-segment, and E is P is the composite elastic modulus; Composite elastic modulus E P The calculation method is as follows: 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, d is the diameter of the anchor cable, and D is the diameter of the anchor body.

2. A method for calculating the anchoring force limit of an adaptive filling type anchor cable as claimed in claim 1, characterized in that: In step 1, the adaptive filling type anchor cable device uses a canvas grout-stopping bag to wrap the outer side of the anchor cable rod body, and a closed space for filling grout is formed between the canvas grout-stopping bag and the rod body.

3. The method for calculating the anchoring force limit of an adaptive filling type anchor cable according to claim 1, characterized in that: The steps for determining the functional expression of the anchoring force limit value P in step 3 are as follows: Step S31: Determine the distribution function of shear displacement based on the micro-segment static equilibrium equation in step 2: 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 i-th rock layer; a constant related to the shear stiffness of the i-th rock layer i The calculation method is as follows: In the above formula, k i is the shear stiffness of the i-th rock layer; Step S32, considering the continuity of the shear stress distribution in the left and right sections at the interface between the dissolution crevice and the rock formation, the expression of the distribution function of the shear displacement obtained in step S31 is adopted, and then: Combined with the equal shear displacement at the intersection of the anchor cables, the equation for the shear displacement of the anchor cables at the intersection is obtained as follows: In the above formula, C i1 and C i2 is the unknown coefficient related to the anchorage of the i-th section, C (i+1)1 and C (i+1)2 is the unknown coefficient related to the anchoring of the i+1th segment, j is an arbitrary number, x j is the jth anchorage length, and 1≤j≤i; Step S33, considering the continuity of the shear stress distribution of the left and right sections of the non-dissolution gap section, the expression of the distribution function of the shear displacement obtained in step S31 is adopted, 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: Step S34: using the shear displacement expression equation of the anchor cable at the intersection obtained in step S32, the equation is: 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; Step S34.1, combined with the anchor cable boundary conditions, the anchor section start P| x＝0 =P, the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section is obtained as follows: Step S34.2: Using the distribution expression of the axial force of the continuous anchor cable at the beginning of the anchoring section obtained in step S34.1, the equation is: Step S35, combined with the anchor cable boundary conditions, 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: Step S36: Combine the anchor cable boundary conditions and anchor 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: Step S37: Using the distribution expression of the axial force of the continuous anchor cable at the end of the anchoring section obtained in step S35, the equation is: 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 section.

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