CN114547806B - Self-bearing anchor cable design method considering anchor-rock interaction - Google Patents
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Abstract
The invention discloses a self-bearing anchor cable design method considering anchor-rock interaction, which comprises the following steps: step one, determining a design anchoring force; step two, determining a ground stress parameter; step three, the number of segmented reamers, the aperture of the non-reamers, the aperture of the reamers and the length of the blades are calculated; step four, solving the stress state of the hole wall; step five, calculating the limit contact pressure; step six, calculating the ultimate bearing capacity of the self-bearing anchor cable; step seven, comparing the designed anchoring force with the limit anchoring force; and step eight, adjusting parameters until the requirements are met. According to the method, the distribution of the hole circumferential stress of the drilling hole is obtained based on mechanical theory analysis, and then the relationship between the non-grouting limit bearing capacity and the rock strength parameter of the self-bearing anchor cable is established by utilizing the rock mechanical theory, so that a self-bearing anchor cable design method is formed; the design method has the advantages of full theoretical basis, applicability to various strata, obvious universality and effectiveness compared with the existing design.
Description
Technical Field
The invention relates to the technical field of geological disaster prevention and control, in particular to a self-supporting anchor cable design method considering anchor-rock interaction.
Background
The self-bearing anchor cable structure is a pulling-pressing combined dispersion type quick bearing anchor cable with a sliding mechanism, and can be directly and initially tensioned without depending on grouting bodies, so that the construction period of the anchor cable is greatly shortened, landslide can be actively reinforced in the shortest time, and larger damage caused by further instability of the landslide is avoided.
However, in the existing self-bearing anchor cable design, a set of reasonable, perfect and reliable design method does not exist for selecting key parameters; the existing self-bearing anchor cable design only pays attention to the structure, the research on the interaction of the rock mass and the self-bearing anchor cable is not reported yet, and the research parameter selection is mainly performed in the modes of indoor test, field test and numerical simulation calculation at present, and although more reasonable experience parameters can be obtained, the experimental method has high cost and larger experimental result discreteness; the numerical simulation method has higher requirements on designers and is difficult to widely apply.
Therefore, how to establish a reasonable, perfect and reliable key parameter design method of the self-bearing anchor cable is easy to realize the optimal design of structural parameters, and the key parameter design method becomes a problem to be solved by the self-bearing anchor cable.
Disclosure of Invention
The invention aims to provide a self-bearing anchor cable design method considering anchor-rock interaction, so as to solve the problems in the background art.
To achieve the above objective, the initial tensioning of the self-supporting cable is divided into four stress phases by a large amount of field test data, as shown in fig. 2, wherein, the OA segment: the steel strand is pre-tensioned, the sliding anchor relatively moves in the expanding shell, and the expanding shell blades are gradually opened but are not contacted with the hole wall; AB segment: the shell-expanding blades are gradually opened and squeeze the hole wall to generate friction; the BC section, the expanding shell blade is completely opened and closely attached to the hole wall, the anchor cable is only carried by the friction force of the hole wall, when the tensile force of the anchor cable is larger than the maximum static friction force, slippage is generated, the internal force is reduced, then the hole wall is searched for a point which can provide larger friction force until the friction force is larger than the design value of a single supporting body; CD segment: the upper end of the reaming shell is propped against the locking port of the upper end of the reaming segment, and the locking port of the reaming segment can provide counter force besides friction between the blade and the hole wall; on the basis, the invention provides the following technical scheme: a self-supporting anchor cable design method considering anchor-rock interaction comprises the following steps: step one, determining a design anchoring force; step two, determining a ground stress parameter; step three, the number of segmented reamers, the aperture of the non-reamers, the aperture of the reamers and the length of the blades are calculated; step four, solving the stress state of the hole wall; step five, calculating the limit contact pressure; step six, calculating the ultimate bearing capacity of the self-bearing anchor cable; step seven, comparing the designed anchoring force with the limit anchoring force; step eight, adjusting parameters until the requirements are met;
In the first step, necessary data are obtained through landslide investigation design, and the anchoring force F and the hole depth of a single anchor cable required by landslide treatment are determined according to standard regulations;
In the second step, the horizontal two ground stress sigma h and the horizontal two ground stress ratio lambda are obtained by collecting data, ground stress test and the like;
in the third step, the number n of segmented reaming, the aperture D of the non-reaming section, the aperture D of the reaming section and the length l of the blade are calculated; the pore diameter D of the un-reamed section and the pore diameter D of the reamed section can be determined by a common construction process;
In the fourth step, the stress distribution at the hole wall is solved, and the hole circumferential stress field distribution is calculated by using the elastic mechanics theory:
taking r=r 0, substituting formula (1) to calculate the stress distribution at the hole wall:
In the fifth step, the ultimate contact pressure between the hole wall rock mass and the blade is calculated, and when the hole wall rock mass is in the ultimate tensile state, the corresponding contact pressure P mb between the blade and the hole wall rock mass should satisfy the following formula:
In the sixth step, calculating the non-grouting limit bearing capacity of the self-bearing anchor cable:
1) The friction force F 1 between the hole wall and the shell expansion blade is as follows:
F1＝μπDlPmb (4)；
Wherein F 1 is friction force between the hole wall and the shell expansion blade, mu is friction coefficient between the hole wall and the shell expansion blade, D is hole diameter of the hole expansion section, and l is blade length;
2) Compression bearing capacity at the locking port of the reaming section:
Wherein b is the contact width between the upper end of a single blade of the expanding shell and the locking port of the expanding segment; r c is the compressive strength of the rock, D is the aperture of the reaming section, and D is the aperture of the non-reaming section;
3) Ultimate bearing capacity F of anchor cable without grouting b
Fb＝(F1+F2)*n (6)；
In the seventh step, it is determined that the ultimate bearing capacity F b of the cable is not grouted should satisfy the following formula
kF＜Fb (7)；
In the eighth step, if the formula (7) in the seventh step is satisfied, the design is ended; if the number of the holes cannot be met, returning to the step three, and adjusting the number of the segmented holes to n, the diameter of the non-hole-expanded section to D, the diameter of the hole-expanded section to D and the length of the blade to l until the formula (7) can be met.
Preferably, in the second step, for the region with data missing and not intense structure, the horizontal stress can be approximately 1/2 of the gravity stress, and lambda is approximately 1.
Preferably, in the third step, n is generally 2 or 3, and the length l of the blade is 50cm-80cm.
Preferably, in the fourth step, σ re is radial normal stress of the rock mass around the hole, σ θe is circumferential normal stress, τ rθe is shear stress, P m is average contact pressure of the shell-enlarging blade and the hole wall, r 0 is hole wall radius, r is polar radius of any point, θ is polar angle, σ h is horizontal ground stress, and λ is the ratio of two horizontal ground stresses.
Preferably, in the fifth step, R t is the tensile strength of the rock, and P mb is the contact pressure between the corresponding shell-enlarging blade and the hole wall in the limit stress state of the rock mass.
Preferably, in the seventh step, k is a safety coefficient, and 1.5 is taken when the control engineering grade is first-level; taking 1.25 when the control engineering grade is the second grade; taking 1.1 when the control engineering grade is three-level.
Compared with the prior art, the invention has the beneficial effects that: according to the method, the distribution of the hole circumferential stress of the drilling hole is obtained based on mechanical theory analysis, and then the relationship between the non-grouting limit bearing capacity and the rock strength parameter of the self-bearing anchor cable is established by utilizing the rock mechanical theory, so that a self-bearing anchor cable design method is formed; the design method has the advantages of full theoretical basis, applicability to various strata, obvious universality and effectiveness compared with the existing design.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a tension graph of a casing-expanded anchor cable without grouting;
FIG. 3 is a simplified mechanical calculation of a self-supporting anchor cable blade opening process;
figure 4 is a schematic illustration of the ultimate load bearing capacity of a self-supporting cable;
FIG. 5 is a schematic cross-sectional view of section A-A' of FIG. 4;
fig. 6 is a step diagram of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1-6, the hatched area in fig. 5 is the contact area between the upper end of a single blade and the locking opening of the reaming section, and an embodiment of the present invention is provided: a self-supporting anchor cable design method considering anchor-rock interaction comprises the following steps: step one, determining a design anchoring force; step two, determining a ground stress parameter; step three, the number of segmented reamers, the aperture of the non-reamers, the aperture of the reamers and the length of the blades are calculated; step four, solving the stress state of the hole wall; step five, calculating the limit contact pressure; step six, calculating the ultimate bearing capacity of the self-bearing anchor cable; step seven, comparing the designed anchoring force with the limit anchoring force; step eight, adjusting parameters until the requirements are met;
In the first step, necessary data are obtained through landslide investigation design, and the anchoring force F and the hole depth of a single anchor cable required by landslide treatment are determined according to standard regulations;
In the second step, the horizontal two ground stress sigma h and the horizontal two ground stress ratio lambda are obtained by collecting data, ground stress test and the like; for areas with data missing and not severe in structure, horizontal stress can be approximately 1/2 of the gravity stress, and lambda is approximately 1;
In the third step, the number n of segmented reaming, the aperture D of the non-reaming section, the aperture D of the reaming section and the length l of the blade are calculated; the pore diameter D of the un-reamed section and the pore diameter D of the reamed section can be determined by a common construction process; n is generally 2 or 3, and the length l of the blade is 50cm-80cm;
In the fourth step, the stress distribution at the hole wall is solved, and the hole circumferential stress field distribution is calculated by using the elastic mechanics theory:
wherein, sigma re is radial normal stress of the rock mass around the hole, sigma θe is circumferential normal stress, tau rθe is shear stress, P m is average contact pressure of the shell-expanding blade and the hole wall, r 0 is hole wall radius, r is polar radius of any point, theta is polar angle, sigma h is horizontal ground stress, lambda is the ratio of two horizontal ground stresses;
taking r=r 0, substituting formula (1) to calculate the stress distribution at the hole wall:
In the fifth step, the ultimate contact pressure between the hole wall rock mass and the blade is calculated, and when the hole wall rock mass is in the ultimate tensile state, the corresponding contact pressure P mb between the blade and the hole wall rock mass should satisfy the following formula:
Wherein R t is the tensile strength of the rock, and P mb is the contact pressure of the corresponding shell-enlarging blade and the hole wall in the limit stress state of the rock mass;
In the sixth step, calculating the non-grouting limit bearing capacity of the self-bearing anchor cable:
1) The friction force F 1 between the hole wall and the shell expansion blade is as follows:
F1＝μπDlPmb (4)；
Wherein F 1 is friction force between the hole wall and the shell expansion blade, mu is friction coefficient between the hole wall and the shell expansion blade, D is hole diameter of the hole expansion section, and l is blade length;
2) Compression bearing capacity at the locking port of the reaming section:
Wherein b is the contact width between the upper end of a single blade of the expanding shell and the locking port of the expanding segment; r c is the compressive strength of the rock, D is the aperture of the reaming section, and D is the aperture of the non-reaming section;
3) Ultimate bearing capacity F of anchor cable without grouting b
Fb＝(F1+F2)*n (6)；
In the seventh step, it is determined that the ultimate bearing capacity F b of the cable is not grouted should satisfy the following formula
kF＜Fb (7)；
Wherein k is a safety coefficient, and 1.5 is taken when the control engineering grade is first-level; taking 1.25 when the control engineering grade is the second grade; taking 1.1 when the control engineering grade is three-level;
in the eighth step, if the formula (7) in the seventh step is satisfied, the design is ended; if the number of the holes cannot be met, returning to the step three, and adjusting the number of the segmented holes to n, the diameter of the non-hole-expanded section to D, the diameter of the hole-expanded section to D and the length of the blade to l until the formula (7) can be met.
Examples:
By utilizing the method provided in the embodiment, emergency treatment is carried out on a landslide of a certain rock quality in Chuandon, the landslide is a clay basin series D 2-3 gray black sandstone, and investigation results show that the sandstone has a gravity of 22kN/m 3, a tensile strength of 1.8MPa and a compressive strength of 50MPa; because the threat objects are clear, the potential loss is large, the landslide deformation is obvious, and the landslide deformation stage is in a severe deformation stage, the emergency treatment and prevention are carried out by adopting the segmented reaming self-bearing anchor cable, and the engineering grade is taken as one grade; the method specifically comprises the following steps: step one, determining a design anchoring force; step two, determining a ground stress parameter; step three, the number of segmented reamers, the aperture of the non-reamers, the aperture of the reamers and the length of the blades are calculated; step four, solving the stress state of the hole wall; step five, calculating the limit contact pressure; step six, calculating the ultimate bearing capacity of the self-bearing anchor cable; step seven, comparing the designed anchoring force with the limit anchoring force; step eight, adjusting parameters until the requirements are met:
In the first step, rock physical and mechanical parameters are obtained through landslide investigation design, and the anchoring force F of a single anchor cable required by landslide control is determined to be 500kN, and the hole depth is 25m;
In the second step, since the landslide point ground stress data is missing and the structure is not intense, the horizontal two ground stresses can be approximately taken from 1/2 of the heavy stress, and λ is approximately taken as 1, then:
σh＝22*25/2＝275kPa＝0.275MPa；
In the third step, the number of segmented reamers is calculated, wherein n=2, the diameter of the non-reamed segment is calculated, d=120 mm, d=150 mm, and the length of the blade is calculated, i=50 cm;
In the fourth step, the stress distribution at the hole wall is solved, and the hole circumferential stress field distribution is calculated by using the elastic mechanics theory:
Wherein: σ re is radial normal stress of the rock mass around the hole, σ θe is circumferential normal stress, τ rθe is shear stress, P m is average contact pressure of the shell-expanding blade and the hole wall, r 0 is hole wall radius, r is polar radius of any point, θ is polar angle, σ h is horizontal ground stress, and λ is the ratio of two horizontal ground stresses;
Taking r=r 0, λ=1 substituted into equation (1) to calculate the stress distribution at the hole wall:
In the fifth step, the ultimate contact pressure between the hole wall rock mass and the blade is calculated, and when the hole wall rock mass is in the ultimate tensile state, the corresponding contact pressure P mb between the blade and the hole wall rock mass should satisfy the following formula:
Wherein R t is the tensile strength of the rock, and P mb is the contact pressure of the corresponding shell-enlarging blade and the hole wall in the limit stress state of the rock mass;
Is obtained by the method (3),
Pmb＝1.8+2*0.275＝2.35MPa；
In the sixth step, calculating the non-grouting limit bearing capacity of the self-bearing anchor cable:
1) The friction force F 1 between the hole wall and the shell expansion blade is as follows:
F1＝μπDlPmb (4)；
Wherein F 1 is friction force between the hole wall and the shell expansion blade, mu is friction coefficient between the hole wall and the shell expansion blade, D is hole diameter of the hole expansion section, and l is blade length;
The friction coefficient mu of the pore wall and the expansion shell blade is 0.4, and the friction coefficient mu is obtained by the formula (4):
F1＝0.4*3.14*150*500*2.35＝221370N＝221.37kN
2) Compression bearing capacity at the locking port of the reaming section:
wherein b is the contact width between the upper end of a single blade of the expanding shell and the locking port of the expanding segment, and the example is 5mm; r c is the compressive strength of the rock, D is the aperture of the reaming section, and D is the aperture of the non-reaming section;
Obtained by the formula (5):
3) Ultimate bearing capacity F of anchor cable without grouting b
Fb＝(F1+F2)*n (6)；
Obtained by the formula (6):
Fb＝(221.37+113.825)*2＝670kN；
in the seventh step, it is determined that the ultimate bearing capacity F b of the cable is not grouted should satisfy the following formula
kF＜Fb (7)；
Wherein k is a safety coefficient, and 1.5 is taken;
Obtained by the formula (7):
1.5*500＝650kN＜670kN；
wherein in the above-described step eight, the formula (7) in the step seven is satisfied, and the design is ended.
Based on the above, the invention has the advantages that the invention obtains the distribution of the hole circumferential stress of the drilling hole based on the analysis of the mechanical theory, and then establishes the relation between the non-grouting limit bearing capacity and the rock strength parameter of the self-bearing anchor cable by utilizing the rock mechanical theory, thereby forming the design method of the self-bearing anchor cable; the method enhances the accuracy of the value of the key parameter of the self-bearing anchor cable, and solves the problems that in the prior art, the key parameter of the self-bearing anchor cable is selected without theoretical basis and the initial bearing capacity is not calculated theoretically in practical application.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Claims (2)
1. A self-supporting anchor cable design method considering anchor-rock interaction comprises the following steps: step one, determining a design anchoring force; step two, determining a ground stress parameter; step three, the number of segmented reamers, the aperture of the non-reamers, the aperture of the reamers and the length of the blades are calculated; step four, solving the stress state of the hole wall; step five, calculating the limit contact pressure; step six, calculating the ultimate bearing capacity of the self-bearing anchor cable; step seven, comparing the designed anchoring force with the limit anchoring force; step eight, adjusting parameters until the requirements are met; the method is characterized in that:
In the first step, necessary data are obtained through landslide investigation design, and the anchoring force F and the hole depth of a single anchor cable required by landslide treatment are determined according to standard regulations;
In the second step, through data collection and ground stress test, horizontal two ground stress sigma h and horizontal two ground stress ratio lambda are obtained;
in the third step, the number n of segmented reaming, the aperture D of the non-reaming section, the aperture D of the reaming section and the length l of the blade are calculated; the pore diameter D of the un-reamed section and the pore diameter D of the reamed section can be determined by a common construction process;
In the fourth step, the stress distribution at the hole wall is solved, and the hole circumferential stress field distribution is calculated by using the elastic mechanics theory:
taking r=r 0, substituting formula (1) to calculate the stress distribution at the hole wall:
In the fifth step, the ultimate contact pressure between the hole wall rock mass and the blade is calculated, and when the hole wall rock mass is in the ultimate tensile state, the corresponding contact pressure P mb between the blade and the hole wall rock mass should satisfy the following formula:
In the sixth step, calculating the non-grouting limit bearing capacity of the self-bearing anchor cable:
1) The friction force F 1 between the hole wall and the shell expansion blade is as follows:
F1＝μπDlPmb (4)；
Wherein F 1 is friction force between the hole wall and the shell expansion blade, mu is friction coefficient between the hole wall and the shell expansion blade, D is hole diameter of the hole expansion section, and l is blade length;
2) Compression bearing capacity at the locking port of the reaming section:
Wherein b is the contact width between the upper end of a single blade of the expanding shell and the locking port of the expanding segment; r c is the compressive strength of the rock, D is the aperture of the reaming section, and D is the aperture of the non-reaming section;
3) Ultimate bearing capacity F of anchor cable without grouting b
Fb＝(F1+F2)*n (6)；
In the seventh step, it is determined that the ultimate bearing capacity F b of the cable is not grouted should satisfy the following formula
kF<Fb (7)；
In the eighth step, if the formula (7) in the seventh step is satisfied, the design is ended; if the number of the holes cannot be met, returning to the step three, and adjusting the number of the segmented reamers n, the diameter D of the non-reamed section, the diameter D of the reamed section and the length l of the blade until the formula (7) can be met;
in the third step, n can be 2 or 3, and the length l of the blade is 50cm-80cm;
In the fourth step, σ re is radial normal stress of the rock mass around the hole, σ θe is circumferential normal stress, τ rθe is shear stress, P m is average contact pressure of the shell-expanding blade and the hole wall, r 0 is hole wall radius, r is polar radius of any point, θ is polar angle, σ h is horizontal ground stress, and λ is the ratio of two horizontal ground stresses;
In the fifth step, R t is the tensile strength of the rock, and P mb is the contact pressure of the corresponding shell-expanding blade and the hole wall in the limit stress state of the rock mass;
In the seventh step, k is a safety coefficient, and 1.5 is taken when the control engineering grade is first-level; taking 1.25 when the control engineering grade is the second grade; taking 1.1 when the control engineering grade is three-level.
2. The self-supporting anchor line design method considering anchor-rock interaction according to claim 1, wherein: in the second step, for the region with data missing and not intense structure, the horizontal stress can be approximately 1/2 of the gravity stress, and lambda is approximately 1.
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