CN113569416A - Method for calculating limit bearing capacity of multi-section hole expanding type anchor rod in soil body - Google Patents
Method for calculating limit bearing capacity of multi-section hole expanding type anchor rod in soil body Download PDFInfo
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Abstract
The invention discloses a method for calculating the ultimate bearing capacity of a multi-section hole expanding type anchor rod in a soil body, which comprises the following steps: (1) determining the geometric dimension and rock-soil strength parameters of the multi-section hole expanding type anchor rod; (2) calculating the side resistance bearing capacity and the end resistance bearing capacity in the arch transfer mode, and then calculating the limit bearing capacity of the multi-section hole expanding type anchor rod in the arch transfer mode; (3) calculating the side resistance bearing capacity and the end resistance bearing capacity in the cylindrical transmission mode, and then calculating the limit bearing capacity of the multi-section hole expanding type anchor rod in the cylindrical transmission mode; (4) the limit bearing capacity of the multi-section hole expanding type anchor rod arch-shaped transfer mode and the limit bearing capacity of the multi-section hole expanding type anchor rod cylindrical transfer mode are small values, and the small values are the limit bearing capacity of the anchor rod. The invention solves the problem of calculation of the ultimate bearing capacity of the multi-section hole-expanding anchor rod commonly used in the fields of foundation engineering and geotechnical engineering, and comprises a mechanical transmission mode of the multi-section hole-expanding anchor rod, the ultimate bearing capacity composition of the multi-section hole-expanding anchor rod, ultimate bearing capacity calculation under different transmission mechanisms and the ultimate bearing capacity value of the multi-section hole-expanding anchor rod.
Description
Technical Field
The invention relates to a method for calculating the ultimate bearing capacity of a multi-section hole expanding type anchor rod in a soil body, and belongs to the field of foundation engineering and geotechnical engineering.
Background
The anchoring length of a non-counterbored bolt is generally less than 10m, and when the length of the bolt exceeds the effective anchoring length, the bearing capacity is not improved remarkably even if the length of the bolt is increased. In order to improve the bearing capacity of the anchor rod and solve the problem of insufficient bearing capacity of soil bodies in soft soil areas, some researchers develop reaming anchor rods. In recent decades, the development of reaming anchor rods has been great and the types of anchor rods tend to be diversified, such as self-bearing anchors, bulbous anchors, recoverable enlarged head anchors, inflatable anchors, umbrella-shaped anchors, high-pressure jet enlarged head anchors, etc., and these types of reaming anchor rods have been widely used in the engineering fields of civil engineering, construction, traffic, water conservancy, oceans, disasters, etc.
The bearing capacity of the reaming type anchor rod is provided by side resistance and end resistance, in the load transmission process of the anchor rod, the bearing capacity of the reaming anchor is mainly provided by friction at the initial stage of load transmission, and after the reaming anchor reaches a certain displacement value, the bearing capacity of the reaming anchor is converted into end resistance. The mechanical transfer mechanism of the reaming type anchor rod is complex, and the mechanical process can be divided into 3 stages: the first stage is a static soil pressure stage; the second stage is a transition stage and is characterized in that an inflection point exists on the displacement curve; the third stage is a plastic region compaction-expansion stage, and is characterized in that the anchoring force of the expansion head is improved along with the compaction and the reinforcement of the soil body. Although prior engineering practices describe the mechanical transfer mechanism of multi-segment reamed bolts, the ultimate bearing capacity calculation method of multi-segment reamed bolts has not been established.
A calculation method for predicting the ultimate bearing capacity of an anchor rod based on a mathematical model is disclosed in chinese patent publication No. CN104794365A, which is published as 5, 6 and 2015. The method mainly comprises the following steps: (1) establishing an anchoring interface shearing slip model; (2) determining the limit uplift load of the anchor rod; (3) determining the influence coefficient of the anchoring length on the bonding strength, determining the influence coefficient of the fracture length of the rock mass on the bonding strength, and determining the fracture opening of the rock mass and the influence coefficient of the filler on the bonding strength; (4) and determining a mathematical model for predicting the ultimate bearing capacity of the anchoring rod. The main problems of the existing method are as follows: (1) the prediction model is only suitable for rock masses and is not suitable for soil masses; (2) the anchoring interface model of the model is a shear slip model, is better applied to the full-length bonding type anchor rod, but cannot reflect the mechanical effect of the reaming anchor rod on the reaming anchor rod; (3) the prediction model only gives the shear failure mode of the full-length bonding type anchor rod, and the failure mode of the multi-section hole expanding anchor rod is not related. Therefore, the predicted results tend to deviate greatly from the actual engineering.
Disclosure of Invention
The invention aims to overcome the problems in the prior art and provides a method for calculating the ultimate bearing capacity of a multi-section hole expanding type anchor rod in a soil body. The invention solves the problem of calculation of the ultimate bearing capacity of the multi-section hole-expanding anchor rod commonly used in the fields of foundation engineering and geotechnical engineering, and comprises a mechanical transmission mode of the multi-section hole-expanding anchor rod, the ultimate bearing capacity composition of the multi-section hole-expanding anchor rod, ultimate bearing capacity calculation under different transmission mechanisms and the ultimate bearing capacity value of the multi-section hole-expanding anchor rod.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for calculating the limit bearing capacity of a multi-section hole expanding type anchor rod in a soil body is characterized by comprising the following steps:
(1) determining the geometric dimension and rock-soil strength parameters of the multi-section hole expanding type anchor rod;
(2) calculating the lateral resistance bearing capacity Q under the arch-shaped transmission mode according to the determined geometric dimension and rock-soil strength parametersskAnd end resistance bearing capacity QpkThen obtaining the side resistance bearing capacity Q according to the calculationskAnd end resistance bearing capacity QpkUltimate bearing capacity Q of multi-section hole expanding type anchor rod for calculating arch transfer modeuk-ar；
(3) According to determined geometrical dimensions and rockCalculation of lateral resistance bearing capacity Q under cylindrical transmission mode by soil strength parametersskAnd end resistance bearing capacity QpkThen obtaining the side resistance bearing capacity Q according to the calculationskAnd end resistance bearing capacity QpkCalculating the ultimate bearing capacity Q of the multi-section hole expanding anchor rod in the cylindrical transmission modeuk-cy；
(4) The limit bearing capacity of the multi-section hole expanding type anchor rod arch transfer mode and the limit bearing capacity of the multi-section hole expanding type anchor rod column transfer mode are small values, namely the limit bearing capacity Q of the anchor roduk。
In the step (1), the parameters for determining the geometric dimension and the rock-soil strength of the multi-section hole expanding type anchor rod comprise hole expanding number n, anchor rod length L, anchor rod diameter D, reinforcing steel bar diameter D, hole expanding coefficient lambda and hole expanding length LeNon-reaming length LrHole expansion distance LsAnchor-soil interface side resistance qeSoil body shear strength tau forming axial cracksrInternal friction angle and cohesion of anchor-soil interface
And ceInternal friction angle and cohesion of soil
cs。
The side resistance bearing capacity Q in the arch-shaped transmission mode in the step (2)skThe calculation method is as follows:
side drag bearing capacity QskFrom the side resistance q of the anchor-soil interfaceeAnd shear force τ to form axial cracksrIs provided with as
Qsk＝nπλDLeqe+πSLrτr
Wherein, the side resistance q of the anchor rod-soil body interfaceeAnd shear force τ to form axial cracksrSatisfy Mohr-Coulomb strength theory, then
In the formula, n is the reaming number; λ is the hole expansion coefficient; sigmaeIs the compressive stress at the anchor-soil interface; sigmarFor compressive stress perpendicular to the axial crack, σ is the depth of penetration at the anchor locatione≈σrAnd gamma is the weight of the soil body covered on the anchor rod, and h is the average thickness of the soil body covered on the anchor rod.
The end resistance bearing capacity Q in the arch-shaped transmission mode in the step (2)pkThe calculation method is as follows:
end resistance bearing capacity QpkShear force tau for forming arch-shaped crack from reaming turning end positionsAnd τs1Is provided with as
Wherein the content of the first and second substances,
in the above formula, τsThe shear strength of the soil body for forming the arch-shaped crack; tau iss1Forming the soil body shear strength of a deflection crack for the first section of reaming; s is the arc length of the arch; y(s) is the height of the corresponding arc segment s; delta is a reaming angle; sigmasIs the compressive stress acting on the arch shaft; sigmas1The fracture is deflected in order to ream the compressive stress acting on the first section.
The limit bearing capacity Q of the multi-section hole expanding type anchor rod in the arch-shaped transmission mode in the step (2)uk-arThe calculation method is as follows:
ultimate bearing capacity Q of multi-section hole expanding type anchor rod in arch transfer modeuk-arBearing the force Q by side resistanceskAnd end resistance bearing capacity QpkThe composition is as follows:
Quk-ar＝Qsk+Qpk
the lateral resistance bearing capacity Q in the arch transfer modeskCalculation formula and end resistance bearing capacity QpkSubstituting the calculation formula into the formula to obtain:
the lateral resistance bearing capacity Q in the cylindrical transmission mode in the step (3)skThe calculation method is as follows:
side drag bearing capacity QskFrom the side resistance q of the anchor-soil interfaceeAnd shear force τ to form axial cracksrIs provided with as
The end resistance bearing capacity Q in the column transmission mode in the step (3)pkThe calculation method is as follows:
end resistance bearing capacity QpkShear force tau for forming cylindrical crack from reaming turning end positionsIs provided with as
In the step (3), the limit bearing capacity Q of the multi-section hole expanding type anchor rod in the cylindrical transmission modeuk-cyThe calculation method is as follows:
ultimate bearing capacity Q of cylindrical transmission mode multi-section hole expanding type anchor roduk-cyBearing the force Q by side resistanceskAnd end resistance bearing capacity QpkThe composition is as follows:
Quk-cy＝Qsk+Qpk
the lateral resistance bearing capacity Q in the columnar transmission modeskCalculation formula and end resistance bearing capacity QpkSubstituting the calculation formula into the formula to obtain:
the invention has the advantages that:
1. the invention solves the problem of the commonly used method for calculating the ultimate bearing capacity of a multi-section hole-expanding type anchor rod in the fields of foundation engineering and geotechnical engineering, and comprises a mechanical transmission mode of the multi-section hole-expanding type anchor rod, the ultimate bearing capacity of the multi-section hole-expanding type anchor rod, a calculation method for the ultimate bearing capacity of the multi-section hole-expanding type anchor rod under different transmission mechanisms and a dereferencing method for the ultimate bearing capacity of the multi-section hole-expanding type anchor rod.
2. The invention breaks through the shear landslide model in the existing anchor rod limit bearing prediction and provides a cylindrical transfer model and an arched transfer mode.
3. The invention has clear mechanical mechanism and simple and convenient calculation method, and can be applied to the design of multi-section hole expanding type anchor rod engineering.
4. The method for calculating the ultimate bearing capacity of the multi-section hole-expanding anchor rod in the soil body is the basis of engineering design, the calculation method is not established at present, and the design of the multi-section hole-expanding anchor rod engineering lacks theoretical basis.
Drawings
FIG. 1 is a schematic view of a multi-segment reamed anchor arch delivery pattern;
FIG. 2 is a schematic view of a cylindrical transfer mode of a multi-segment reamer anchor;
FIG. 3 is a schematic view of a mechanical model of a special-shaped arch;
FIG. 4 is a schematic view of a mechanical model of a special-shaped arch;
FIG. 5a is a graph of ultimate bearing capacity for two failure modes as a function of number of reaming stages;
FIG. 5b is a graph of the ultimate bearing capacity for two failure modes as a function of reaming angle;
FIG. 5c is a graph of ultimate bearing capacity for two failure modes as a function of soil layer thickness;
FIG. 5d is a graph of ultimate bearing capacity for two failure modes as a function of hole expansion coefficient;
FIG. 5e is a graph of the ultimate bearing capacity of two failure modes as a function of the bolt shank diameter;
FIG. 5f is a graph of ultimate bearing capacity for two failure modes as a function of counterbore length;
FIG. 5g is a graph of ultimate bearing capacity for two failure modes as a function of counterbore spacing;
figure 5h is a graph of the ultimate bearing capacity of the two failure modes as a function of the non-counterbore length.
Detailed Description
Example 1
The present embodiment will be described in detail with reference to the accompanying drawings.
The mechanical transmission mode of the multi-section hole expanding type anchor rod in the soil body is divided into 2 types: an arcuate transfer mode and a cylindrical transfer mode (fig. 1, 2). The multistage hole expanding type anchor rod resists pulling damage and undergoes 3 stages of crack initiation, crack deflection and crack communication, and crack initiation angles
In the final stage of crack deflection or the initial stage of crack penetration, the uplift load of the multi-section hole expanding type anchor rod is maximized, and the corresponding peak load is the ultimate bearing capacity; the ultimate bearing capacity of the multi-section hole expanding type anchor rod consists of side resistance bearing capacity and end resistance bearing capacity; in the multi-section hole-expanding type anchor rod arch destruction mode, the arch crack at the hole-expanding turning end part conforms to the soil arch destruction theory; the multi-section hole expanding anchor rod is damaged according to Mohr-Coulomb strength criterion.
The uplift bearing capacity of the multi-section hole expanding type anchor rod in the arch transfer mode and the column transfer mode is a small value, namely the limit bearing capacity Q of the anchor roduk。
The ultimate bearing capacity calculation method of the arch transfer mode comprises the following steps:
ultimate bearing capacity Q of multi-section hole expanding type anchor rod in arch transfer modeuk-arBearing the force Q by side resistanceskAnd end resistance bearing capacity QpkThe structure of the utility model is that the material,
Quk-ar＝Qsk+Qpk (1)
side drag bearing capacity QskFrom the side resistance q of the anchor-soil interfaceeAnd shears for forming axial cracksShear force taurIs provided with as
Qsk＝nπλDLeqe+πSLrτr (2)
Wherein, the side resistance q of the anchor rod-soil body interfaceeAnd shear force τ to form axial cracksrSatisfy Mohr-Coulomb strength theory, then
In the formula, n is the reaming number; λ is the hole expansion coefficient; l iseIs the reaming length; l issThe hole expansion distance is set; q. q.seThe resistance of the anchor rod-soil body interface side is obtained; tau isrThe shear strength of the soil body for forming axial cracks;
cethe internal friction angle and the cohesive force of the anchor rod-soil body interface are respectively;
csthe internal friction angle and cohesive force of the soil body are respectively; sigmaeIs the compressive stress at the anchor-soil interface; sigmarFor compressive stress perpendicular to the axial crack, σ is the depth of penetration at the anchor locatione≈σrGamma is the weight of the overlying soil body of the anchor rod, and h is the average thickness of the overlying soil body; the other physical meanings are the same as above.
End resistance bearing capacity QpkShear force tau for forming arch-shaped crack from reaming turning end positionsAnd τs1Is provided with as
Wherein the content of the first and second substances,
in the above formula, τsThe shear strength of the soil body for forming the arch-shaped crack; tau iss1Forming the soil body shear strength of a deflection crack for the first section of reaming; s is the arc length of the arch; y(s) is the height of the corresponding arc segment s; delta is a reaming angle; sigmasIs the compressive stress acting on the arch shaft; sigmas1Reaming the deflection crack for the first section; the other physical meanings are the same as above.
As can be seen from FIG. 1, LsSegment and Ls1The fracture initiation angle and the through length of the segment reaming turning end are the same, and the stress states of the segment reaming turning end and the fracture initiation angle are considered to be the same according to the geometric similarity, namely sigmas＝σs1And τs＝τs1。
To solve for the positive stress σ acting on the arch axissA mechanical model is established, as shown in fig. 3, of a special arch shaft, the arch being subjected to the action of gravity uniformly distributed along the axis and the action of oblique forces uniformly distributed on the nodes. Setting the calculation span of the special-shaped arch to be LsThe calculated loss is f. The special-shaped arch is loaded by vertical downward loads which are uniformly distributed along the arch axis by the self weight of the arch ring, the load per unit length is gamma h, and the load is also loaded by the load which is uniformly distributed along the span and has an inclination angle of beta, and the load per unit length is p. The arch crown O is taken as the origin of coordinates, a horizontal line and a lead straight line in the arch plane are taken as an x axis and a y axis, the length of a section of arc OM originally adjusted to any point M on the arch is taken as an arc coordinate s, and the s is taken as positive along the counterclockwise direction of the curve.
As shown in fig. 4, a special-shaped arch section OM is cut, the force acting on the arch section OM is a distributed load P with a length of x + ycot β, and the resultant force is P ═ P (x + ycot β); the resultant force of the distributed load γ h over the length s is G ═ γ hs; pressure H at point O, in the horizontal direction; pressure N at point M, in the tangential direction of the arch at point M. Because the arch segment is P, G, H, N fourBalance is maintained under a single force, 4 forces meet the balance condition, and then the sum of sigma xiThe product can be obtained when the yield is 0,
Ncosθ＝H-Pcosα (8)
namely, it is
Ncosθ＝H-p(x+ycotβ)cosβ (9)
By Σ yiThe product can be obtained when the yield is 0,
Nsinθ＝G+Psinβ (10)
namely, it is
Nsinθ＝γhs+p(x+ycotβ)sinβ (11)
Wherein theta is the included angle between the tangent of the arch at the point M and the x axis, and is
By substituting formula (9) and formula (11) for formula (12)
The formula (14) is divided by the formula (15) to obtain H
For a downwardly concave arc, there are
Substituting formula (15) for formula (13), substituting formula (13) for formula (15), and obtaining the derivative
This is the second order differential equation for the profile arch axis.
The initial conditions are
From the formula (19) it is possible to deduce the uniform load p acting on the arch shaft, of
Therefore, once the arch axis is determined, the uniform load p on the arch axis is a fixed value.
From the mechanical geometry of fig. 3 and 4, the load σ perpendicular to the arch axis can be derivedsIs a
σs＝γhcosθ+psin(θ+β) (19)
The formula (19) is substituted for the formula (11), and the formula (11) is substituted for the formula (10) to calculate the end resistance bearing capacity Qpk。
Therefore, by substituting the formula (2) and the formula (5) into the formula (1), the limit bearing capacity Q of the multi-segment hole-expanding anchor rod in the arch transmission mode can be obtaineduk-arIs composed of
The ultimate bearing capacity calculation method of the cylindrical transmission mode comprises the following steps:
as shown in fig. 2, the ultimate bearing capacity Q of the cylindrical transmission mode multi-segment reamer shank is alsouk-cyBearing the force Q by side resistanceskAnd end resistance bearing capacity QpkThe structure of the utility model is that the material,
Quk-cy＝Qsk+Qpk (21)
side drag bearing capacity QskFrom the side resistance q of the anchor-soil interfaceeAnd shear force τ to form axial cracksrIs provided with as
End resistance bearing capacity QpkShear force tau for forming cylindrical crack from reaming turning end positionsIs provided with as
The ultimate bearing capacity Q of a multi-stage hole-expanding anchor rod in a cylindrical transmission mode can be obtained by substituting the formula (22) and the formula (23) into the formula (21)uk-cyIs composed of
The implementation steps of the invention are as follows:
(1) aiming at a multi-section hole expanding type anchor rod in foundation engineering or geotechnical engineering, firstly, the geometric dimension and the geotechnical strength parameters of the multi-section hole expanding type anchor rod are determined, wherein the parameters comprise hole expanding number n, anchor rod length L, anchor rod diameter D (unit m), hole expanding coefficient lambda and hole expanding length LeHole expansion distance LsNon-reaming length LrAnchor-soil interface side resistance qeSoil body shear strength tau forming axial cracksrSteel bar diameter d (unit m), anchor-soil interface internal friction angle and cohesion
And ceInternal friction angle and cohesion of soil
cs。
(2) Calculating the lateral resistance bearing capacity Q in the arch-shaped transmission mode according to the formula (2)skCalculating the end resistance bearing capacity Q in the arch transfer mode according to the formula (5)pkThen, the ultimate bearing capacity Q of the multi-segment hole expanding anchor rod in the arch transmission mode is calculated according to the calculation result (20)uk-ar。
(3) Calculating the side drag bearing capacity Q in the columnar transfer mode according to equation (22)skCalculating the end resistance bearing capacity Q in the columnar and shape transfer mode according to the formula (23)pkThen calculate the cylinder from (24)Ultimate bearing capacity Q of multi-section hole expanding anchor rod in transmission modeuk-cy。
(4) The uplift bearing capacity of the multi-section hole expanding type anchor rod in the arch transfer mode and the column transfer mode is a small value, namely the limit bearing capacity Q of the anchor roduk。
The calculation principle of the invention is as follows:
(1) the mechanical transmission mode of the multi-section hole expanding type anchor rod is divided into 2 types: an arcuate transfer mode and a cylindrical transfer mode. The multistage hole expanding type anchor rod resists pulling damage and undergoes 3 stages of crack initiation, crack deflection and crack communication, and crack initiation angles
In the final stage of crack deflection or the initial stage of crack penetration, the uplift load of the multi-section hole expanding type anchor rod is maximized, and the corresponding peak load is the ultimate bearing capacity;
(2) the uplift bearing capacity of the multi-section hole expanding type anchor rod in the arch transfer mode and the column transfer mode is a small value, namely the limit bearing capacity Q of the anchor roduk。
Example 2
This example illustrates the effect of using the present invention to predict the ultimate bearing capacity of a multi-segment reamed anchor.
The invention is used for testing the engineering example, the calculation error range is small, and the accuracy of the prediction result is high, thereby demonstrating that the reliability of the invention applied to the actual engineering is high; the method can be widely applied to actual engineering in the future, and is used for more accurately predicting the bearing capacity of the multi-section hole expansion anchor rod in the actual engineering, improving the safety and reliability of the engineering and promoting the technical progress of the engineering.
In order to verify the correctness of the method for calculating the ultimate bearing capacity of the multi-section hole expanding type anchor rod, the ultimate bearing capacity of the anchor rod obtained by the method is compared with the ultimate bearing capacity of the anchor rod obtained by the model test of the two-section hole expanding anchor rod and the three-section hole expanding anchor rod, and the number n of hole expanding sections, the hole expanding angle delta, the soil layer thickness h, the hole expanding coefficient lambda, the diameter D of the anchor rod body and the hole expanding length L are analyzed simultaneouslyeHole expansion distance LsNon-reaming length LrEqual parameter pairThe limit bearing capacity influence rule of the arch damage and the column damage of the multi-section hole expanding type anchor rod.
FIGS. 5a-h show the ultimate load curves (Q) for two failure modes under different parametersuk-arFor the ultimate bearing capacity of arch-shaped damage, Q, obtained by the calculation methoduk-cyFor the column-like damage limit bearing capacity, Q, obtained by the calculation methoduk-Tset is the ultimate bearing capacity obtained by the model test; a. the number of reaming sections n; b. a reaming angle δ; c. the thickness of the soil layer is h; d. a hole expansion coefficient lambda; e. the diameter D of the anchor rod body; f. reaming length Le(ii) a g. Hole expansion distance Ls(ii) a h. Non-reaming length Lr) The ultimate bearing capacity value obtained by the model test is more consistent with the ultimate bearing capacity value of the anchor rod obtained by the calculation method provided by the invention, the ultimate bearing capacity value is basically between the ultimate bearing capacity values of the arch-shaped damage and the columnar damage, and the error is within 5 percent.
Figure 5a shows the ultimate bearing capacity Q of the arch failure of a multi-segment reamed anchor with increasing number of reaming segmentsuk-arUltimate bearing capacity value Q against column failureuk-cyLinearly increase, and Quk-arHas a growth rate greater than Quk-cyAnd the increase of the number of the reaming sections can obviously improve the ultimate bearing capacity of the multi-section reaming type anchor rod.
FIG. 5b shows the ultimate bearing capacity Q of the multi-segmented hole-expanding anchor for arch failure with increasing hole expansion angleuk-arUltimate bearing capacity value Q of curve nonlinear reduction and column destructionuk-cyThe curve of the multi-section hole-expanding anchor rod is gradually close to the same stable value, which shows that the larger the hole-expanding angle is, the smaller the bearing capacity of the multi-section hole-expanding anchor rod for arch damage is, and the bearing capacity of the multi-section hole-expanding anchor rod for arch damage is gradually close to the bearing capacity of the cylindrical damage, and the foreseeable that when the hole-expanding angle is 90 degrees, the arch formed by the multi-section hole-expanding anchor rod damage is basically parallel to the axial direction of the anchor rod and is approximately cylindrical damage.
FIG. 5c shows the ultimate bearing capacity Q of the multi-segment reamed anchor for arch failure with increasing soil burial thicknessuk-arUltimate bearing capacity value Q against column failureuk-cyThe linear increase shows that the increase of the number of the reaming sections can obviously improve the ultimate bearing capacity of the multi-section reaming type anchor rod.
FIG. 5d shows the ultimate bearing capacity Q of the multi-segment reamed anchor for arch collapse with increasing reaming factoruk-arUltimate bearing capacity value Q against column failureuk-cyNon-linearly increases, and Quk-cyThe curve increases at a rate greater than Quk-arCurve, at the same time, Quk-cyValue less than Quk-arThe anchor rod mainly generates column-shaped damage, and gradually develops to arch-shaped damage along with the increase of the hole expansion coefficient. The increase of reaming coefficient is representing the increase of reaming section stock diameter, and the increase of reaming diameter has increased the bearing area of the soil body around the stock, and the soil body volume that drives when the stock atress simultaneously increases to show the bearing capacity that has improved the stock.
Fig. 5e shows the ultimate bearing capacity Q of the arch failure of a multi-segment reamed anchor with increasing anchor diameteruk-arUltimate bearing capacity value Q against column failureuk-cyIncrease in non-linearity, Q when the diameter of the anchor rod is smalluk-arGreater than Quk-cyThe anchor rod has a tendency to cause cylindrical damage, and when the diameter of the anchor rod is larger, Q isuk-arLess than Quk-cyThe anchor has a tendency to arch failure. Therefore, the cylindrical damage and the arch damage of the anchor rod have the phenomenon of mutual transformation along with the change of the diameter of the anchor rod.
FIG. 5f shows the ultimate bearing capacity Q of the multi-segment reamed anchor for arch collapse with increasing reamed lengthuk-arUltimate bearing capacity value Q against column failureuk-cyLinear increase, Q when the anchor diameter is smalluk-arGreater than Quk-cyThe anchor rod has a tendency to cause cylindrical damage, and when the diameter of the anchor rod is larger, Q isuk-arLess than Quk-cyThe anchor has a tendency to arch failure. At the same time, Quk-cyThe slope of the curve being greater than Quk-arSlope of the curve, indicating ultimate bearing capacity Q of column failureuk-arIs sensitive to the length of the counterbore.
FIG. 5g shows the ultimate bearing capacity Q of the multi-segment reamed anchor for arch collapse as the reaming spacing increasesuk-arNon-linearly increasing, and column-like failure ultimate bearing capacity Quk-cyCurve basically has no change, tableClear limit bearing capacity Quk-arIs sensitive to the reaming distance, and Quk-cyInsensitive to reaming spacing.
FIG. 5h shows the ultimate bearing capacity Q of a multi-segment reamed anchor for arch failure with increased non-reamed lengthuk-arUltimate bearing capacity value Q against column failureuk-cyLinearly increasing with the same slope, it can be seen that the increase in non-counterbore length merely increases the ultimate bearing capacity of the non-counterbore segment provided by the side resistance, and the ultimate bearing capacity of the non-end resistance.
The above detailed description is specific to possible embodiments of the invention, and the embodiments are not intended to limit the scope of the invention, and all equivalent implementations or modifications that do not depart from the scope of the invention should be construed as being included within the scope of the invention.
In addition, various modifications, additions and substitutions in other forms and details may occur to those skilled in the art within the scope and spirit of the invention as disclosed in the claims. It is to be understood that various modifications, additions, substitutions and the like can be made without departing from the spirit of the invention as disclosed in the accompanying claims.
Claims (8)
1. A method for calculating the limit bearing capacity of a multi-section hole expanding type anchor rod in a soil body is characterized by comprising the following steps:
(1) determining the geometric dimension and rock-soil strength parameters of the multi-section hole expanding type anchor rod;
(2) calculating the lateral resistance bearing capacity Q under the arch-shaped transmission mode according to the determined geometric dimension and rock-soil strength parametersskAnd end resistance bearing capacity QpkThen obtaining the side resistance bearing capacity Q according to the calculationskAnd end resistance bearing capacity QpkUltimate bearing capacity Q of multi-section hole expanding type anchor rod for calculating arch transfer modeuk-ar；
(3) Calculating the lateral resistance bearing capacity Q under the cylindrical transmission mode according to the determined geometric dimension and rock-soil strength parametersskAnd end resistance bearing capacity QpkThen obtaining the side resistance bearing capacity Q according to the calculationskAnd end resistance bearing capacity QpkLimit bearing of multi-section hole expanding type anchor rod for calculating cylindrical transmission modeForce of load Quk-cy；
(4) The limit bearing capacity of the multi-section hole expanding type anchor rod arch transfer mode and the limit bearing capacity of the multi-section hole expanding type anchor rod column transfer mode are small values, namely the limit bearing capacity Q of the anchor roduk。
2. The method for calculating the limit bearing capacity of the multi-section reaming type anchor rod in the soil body according to claim 1, wherein the method comprises the following steps: in the step (1), the parameters for determining the geometric dimension and the rock-soil strength of the multi-section hole expanding type anchor rod comprise hole expanding number n, anchor rod length L, anchor rod diameter D, reinforcing steel bar diameter D, hole expanding coefficient lambda and hole expanding length LeNon-reaming length LrHole expansion distance LsAnchor-soil interface side resistance qeSoil body shear strength tau forming axial cracksrInternal friction angle and cohesion of anchor-soil interface
And ceInternal friction angle and cohesion of soil
cs。
3. The method for calculating the limit bearing capacity of the multi-section reaming type anchor rod in the soil body according to claim 2, wherein the method comprises the following steps: the side resistance bearing capacity Q in the arch-shaped transmission mode in the step (2)skThe calculation method is as follows:
side drag bearing capacity QskFrom the side resistance q of the anchor-soil interfaceeAnd shear force τ to form axial cracksrIs provided with as
Qsk＝nπλDLeqe+πSLrτr
Wherein, the side resistance q of the anchor rod-soil body interfaceeAnd shear force τ to form axial cracksrSatisfy Mohr-Coulomb strength theory, then
In the formula, n is the reaming number; λ is the hole expansion coefficient; sigmaeIs the compressive stress at the anchor-soil interface; sigmarFor compressive stress perpendicular to the axial crack, σ is the depth of penetration at the anchor locatione≈σrAnd gamma is the weight of the soil body covered on the anchor rod, and h is the average thickness of the soil body covered on the anchor rod.
4. The method for calculating the limit bearing capacity of the multi-section reaming type anchor rod in the soil body according to claim 3, wherein the method comprises the following steps: the end resistance bearing capacity Q in the arch-shaped transmission mode in the step (2)pkThe calculation method is as follows:
end resistance bearing capacity QpkShear force tau for forming arch-shaped crack from reaming turning end positionsAnd τs1Is provided with as
Wherein the content of the first and second substances,
in the above formula, τsThe shear strength of the soil body for forming the arch-shaped crack; tau iss1Forming the soil body shear strength of a deflection crack for the first section of reaming; s is the arc length of the arch; y(s) is the height of the corresponding arc segment s; delta is a reaming angle; sigmasIs the compressive stress acting on the arch shaft; sigmas1Reaming a deflection crack for acting on a first sectionCompressive stress of (a).
5. The method for calculating the limit bearing capacity of the multi-section reaming type anchor rod in the soil body according to claim 4, wherein the method comprises the following steps: the limit bearing capacity Q of the multi-section hole expanding type anchor rod in the arch-shaped transmission mode in the step (2)uk-arThe calculation method is as follows:
ultimate bearing capacity Q of multi-section hole expanding type anchor rod in arch transfer modeuk-arBearing the force Q by side resistanceskAnd end resistance bearing capacity QpkThe composition is as follows:
Quk-ar＝Qsk+Qpk
the lateral resistance bearing capacity Q in the arch transfer modeskCalculation formula and end resistance bearing capacity QpkSubstituting the calculation formula into the formula to obtain:
6. the method for calculating the limit bearing capacity of the multi-section reaming type anchor rod in the soil body according to claim 5, wherein the method comprises the following steps: the lateral resistance bearing capacity Q in the cylindrical transmission mode in the step (3)skThe calculation method is as follows:
side drag bearing capacity QskFrom the side resistance q of the anchor-soil interfaceeAnd shear force τ to form axial cracksrIs provided with as
7. The method for calculating the limit bearing capacity of the multi-section reaming type anchor rod in the soil body according to claim 6, wherein the method comprises the following steps: the end resistance bearing capacity Q in the column transmission mode in the step (3)pkThe calculation method is as follows:
end resistance bearing capacity QpkShear force tau for forming cylindrical crack from reaming turning end positionsIs provided with as
8. The method for calculating the limit bearing capacity of the multi-section reaming type anchor rod in the soil body according to claim 7, wherein the method comprises the following steps: in the step (3), the limit bearing capacity Q of the multi-section hole expanding type anchor rod in the cylindrical transmission modeuk-cyThe calculation method is as follows:
ultimate bearing capacity Q of cylindrical transmission mode multi-section hole expanding type anchor roduk-cyBearing the force Q by side resistanceskAnd end resistance bearing capacity QpkThe composition is as follows:
Quk-cy＝Qsk+Qpk
the lateral resistance bearing capacity Q in the columnar transmission modeskCalculation formula and end resistance bearing capacity QpkSubstituting the calculation formula into the formula to obtain:
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