CN115017592B - Calculation method of pushing type landslide prestressed anchor cable rigid pile - Google Patents
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Abstract
The invention provides a calculation method of a pushing type landslide pre-stressed anchor rope rigid pile, which comprises an anchor rope pile, an anchor rope and an anchor block, wherein the anchor rope is arranged at the pile top of the anchor rope pile, the anchor rope pile is fixedly connected with the anchor rope, one end of the anchor rope is fixed on the anchor block, and the other end of the anchor rope is fixed in a stable rock-soil body of a side slope; the calculation method comprises the following steps: firstly, the anchor cable pile and the anchor cable are regarded as a whole; secondly, calculating the pile front soil resistance of the pushing type landslide at the pile setting position according to the movement form of the landslide; finally, establishing a balance equation according to displacement deformation coordination at the anchor pull point; and calculating the pile body corner, the actual tension of the anchor cable, the pile side elastic resistance of the anchoring section and the pile body section shear force, bending moment and displacement according to the balance equation and the pile front soil resistance. According to the invention, the pile-anchor deformation coordination of the prestressed anchor rope rigid pile is considered, the actual tension of the anchor rope, the position of the pile body rotation point and the pile body displacement are calculated, the calculation result is more practical, and the calculation method is simple and convenient.
Description
Technical Field
The invention relates to a calculation method of anchor cable slide pile internal force in the technical field of landslide hazard prevention and control, in particular to a calculation method of pushing type landslide pre-stress anchor cable rigid piles.
Background
The prestressed anchor cable slide-resistant pile is widely applied to landslide control due to the advantages of simple construction, more reasonable stress than the slide-resistant pile, lower engineering cost, obvious treatment effect and the like; however, the design and calculation theory is still immature and is far behind engineering application, and particularly, the rigid pile of the prestressed anchor cable lacks a definite calculation method. The existing method for calculating the rigid pile of the prestressed anchor cable mainly comprises the following steps: 1. the actual tension of the anchor cable is valued according to an empirical value, the valued method is not clear enough, and the anchor cable is in and out of the actual stress; 2. the pile top displacement value of the existing anchor cable pile elastic pile calculation method is larger, and especially the pile top displacement calculation of the anchor cable pile with a large section is inconsistent with the actual calculation; 3. the calculation formula of the shear force and the bending moment of the pile body of the rigid pile of the deformation coordination prestressed anchor cable is not considered; 4. the calculation formula of the neutral point position of the pile body is coordinated by considering the deformation of the anchor cable and the pile; 5. the landslide movement state is not considered in the calculation of the anchor cable anti-slide pile, so that the calculated value of the internal force of the pile body is larger, the design cost of the pile body is increased, and the pile body is not economical; 6. the calculation process is complicated and not convenient enough.
Disclosure of Invention
Aiming at the defects in the background art, the invention provides a pushing type landslide prestressed anchor cable rigid pile calculating method, which aims at calculating the pile body internal force and displacement of the prestressed anchor cable rigid pile under the pushing type landslide; predicting the stress state of the prestressed anchor cable rigid pile; checking whether the prestressed anchor cable rigid pile is safe under the action of landslide thrust; providing basis for the structural design of the prestressed anchor cable pile.
The technical scheme of the invention is realized as follows:
A calculation method of a pushing type landslide pre-stressed anchor rope rigid pile comprises the steps of anchor rope piles, anchor ropes and anchor piers; an anchor rope is arranged at the pile top of the anchor rope pile, the anchor rope pile is fixedly connected with the anchor rope, one end of the anchor rope is fixed on the anchor pier, and the other end of the anchor rope is fixed in a rock-soil body of the side slope;
The calculation method of the pushing type landslide prestressed anchor cable rigid pile comprises the following steps: firstly, an anchor cable pile and an anchor cable are regarded as a whole, the pile length of the pile above a sliding surface is set to be h 1, the pile length below the sliding surface is set to be h 2, the soil resistance height before the pile is set to be h k, and the calculated width of the pile is set to be B p; secondly, calculating the pile front soil resistance of the pushing type landslide at the pile setting position according to the movement form of the landslide; finally, according to the displacement deformation coordination at the anchor pull point, a displacement deformation coordination balance equation is established; and calculating the pile body corner, the actual tension of the anchor cable, the pile side elastic resistance of the anchoring section, the pile body section shearing force, the bending moment and the displacement according to a displacement deformation coordination balance equation, landslide thrust and balance conditions of pile front soil resistance.
Preferably, the method for calculating the pile front soil resistance of the pushing type landslide at the pile setting position according to the movement form of the landslide comprises the following steps: the front edge of the pushing type landslide is provided with radial cracks, the cracks are parallel to the sliding direction, at the moment, an anti-sliding pile arranged at the lower part of the landslide is subjected to the action of pile front soil resistance, the pile front soil resistance is related to the inclination angle of the pile front sliding surface, when the inclination angle is positive, the action of pile front soil resistance is ignored, and when the inclination angle is negative, the pile front soil resistance is calculated;
The strength distribution of the pile front soil resistance E K at the ground surface is q 3, and the strength distribution of the pile front soil resistance E K at the sliding surface is q 4; the calculation formulas are respectively as follows:
Wherein S is the unit calculated area of soil before the pile, b is the pile width, m 1 is the distribution coefficient of resistance of soil before the pile, alpha is the slip angle before the pile, gamma is the soil weight, Is the internal friction angle of the soil.
Preferably, the displacement deformation coordination equation of the anchor point is:
δ(P-P0)＝△φ(y0+d)；
Wherein, P 0 is the initial prestress of the anchor cable, P is the actual tension of the anchor cable, delta is the flexibility coefficient of the anchor cable, delta phi is the rotation angle of the pile, y 0 is the distance between the rotation point of the pile and the top end of the anchoring section, and d is the distance between the anchor tension point and the sliding surface; and delta i＝△φ(y0+d),fi＝d(P-P0), L i is the length of the free section of the anchor cable, A s is the sectional area of each bundle of anchor cable, E g is the elastic modulus of the anchor cable, and N is the bundle number of the anchor cable in each hole;
the displacement deformation coordination balance equation comprises a shear balance equation and a bending moment balance equation at the pile bottom, which are respectively expressed as follows:
Wherein A is the foundation coefficient at the sliding surface, M is the foundation proportionality coefficient, Q 0 is the shearing force of the pile at the sliding surface, M 0 is the bending moment, and
Q 1 is the intensity distribution of landslide thrust at the pile top, q 2 is the intensity distribution of landslide thrust at the slip plane, q 3 is the intensity distribution of soil resistance before the pile at the ground, and q 4 is the intensity distribution of soil resistance before the pile at the slip plane.
Preferably, the calculation method of the rotation angle delta phi of the pile is as follows:
Preferably, the calculation method of the distance y 0 between the rotation point of the pile and the top end of the anchoring section is as follows:
Wherein Q 1 is the shear force generated by the pile at the sliding surface under the action of landslide thrust, M 1 is the bending moment generated by the pile at the sliding surface under the action of landslide thrust, Q 2 is the shear force generated by the pile at the sliding surface under the action of soil resistance before the pile, and M 2 is the bending moment generated by the pile at the sliding surface under the action of soil resistance before the pile.
Preferably, the calculation method of the actual tension of the anchor cable comprises the following steps:
Preferably, the calculation method of the pile side elastic resistance of the anchoring section comprises the following steps:
σi＝(A+my)(y0-y)△φ；
wherein y is the distance from the calculated point to the sliding surface, and sigma i is the pile side elastic resistance of the anchoring section.
Preferably, the calculation of the pile body section shear force, bending moment and displacement is divided into four sections;
The calculation method of the pile body section shear force, bending moment and displacement in the first section, when d is less than or equal to y and less than or equal to h 1, comprises the following steps:
Xi＝△φ(y0+y)；
The second section, the calculation method of pile section shearing force, bending moment and displacement when h k < y is less than or equal to d is as follows:
Xi＝△φ(y0+y)；
The calculation method of pile body section shear force, bending moment and displacement in the third section, when y is more than 0 and less than or equal to h k, comprises the following steps:
Xi＝△φ(y0+y)；
The calculation method of pile section shear force, bending moment and displacement in the fourth section, wherein y is more than or equal to 0 and less than or equal to h 2, comprises the following steps:
Xi＝△φ(y0+y)；
Wherein Q i is pile section shear force, M i is bending moment, and X i is displacement.
Compared with the prior art, the invention has the beneficial effects that:
1) According to the invention, the pile-anchor deformation coordination of the prestressed anchor rope rigid pile is considered, the actual tension of the anchor rope, the position of the rotation point of the pile body and the displacement of the pile body can be calculated, and the calculation result of the internal force of the pile body is more practical; especially, the calculation result of the displacement of the large-section anchor cable pile accords with the actual condition within 50 mm;
2) When the sliding surface in front of the pile is minus 5 degrees and the internal friction angle of the soil body of the sliding surface is 15 degrees, the calculated bending moment of the pile body is 26.48 percent smaller than that calculated according to the existing cantilever pile, and the shearing force is 25.2 percent smaller, so that the structural reinforcement design is reduced, and the construction cost is reduced;
3) The method is simple and convenient to calculate, shortens the calculation process and improves the calculation efficiency.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a computational model of the present invention.
FIG. 2 is a coordinated calculation model of pile-anchor deformation according to the present invention.
FIG. 3 is a graph showing the comparison of pile side elastic resistance calculated by the conventional cantilever method and the method according to the present invention.
FIG. 4 is a graph showing the shear force versus shear force calculated by the conventional cantilever method and the method of the present invention.
FIG. 5 is a graph showing the comparison of bending moments calculated by the conventional cantilever method and the method of the present invention.
FIG. 6 is a graph showing the displacement contrast curve calculated by the conventional cantilever method and the method according to 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 any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention provides a calculation method of a pushing type landslide pre-stressed anchor cable rigid pile, which comprises a large-section reinforced concrete pile, namely an anchor cable pile (the length of the general section is not less than 3 m), an anchor cable and an anchor pier. And the pile top of the anchor rope pile is provided with an anchor rope, the anchor rope pile is fixedly connected with the anchor rope, one end of the anchor rope is fixed on the anchor pier, and the other end of the anchor rope is fixed in a rock-soil body with stable side slope.
The calculation model of the pushing type landslide rigid anchor cable pile is shown in fig. 1, and the pile length of the pile above the sliding surface is set to be h 1, the pile length below the sliding surface is set to be h 2, the soil resistance height before the pile is set to be h k, and the calculated width of the pile is set to be B p. The calculation method of the pushing type landslide prestressed anchor cable rigid pile comprises the following steps: firstly, assuming that a prestressed anchor cable rigid pile bears landslide thrust, pile front soil resistance, anchor cable tension and pile surrounding soil acting force of an anchoring section; the anchor cable pile and the anchor cable are regarded as a whole, and the displacement of the anchor pull point pile is equal to the elongation of the anchor cable; secondly, calculating the pile front soil resistance of the pushing type landslide at the pile setting position according to the movement form of the landslide; finally, according to the displacement deformation coordination at the anchor pull point, a displacement deformation coordination balance equation is established; and calculating the pile body corner, the actual tension of the anchor cable, the pile side elastic resistance of the anchoring section, the pile body section shearing force, the bending moment and the displacement according to a displacement deformation coordination balance equation, the landslide thrust and the pile front soil resistance balance condition.
The front edge of the pushing type landslide is provided with radial cracks, the cracks are parallel to the sliding direction, at the moment, an anti-sliding pile arranged at the lower part of the landslide is subjected to the action of pile front soil resistance, the pile front soil resistance is related to the inclination angle of the pile front sliding surface, when the inclination angle is positive, the action of pile front soil resistance is ignored, and when the inclination angle is negative, the pile front soil resistance is calculated;
The strength distribution of the pile front soil resistance E K at the ground surface is q 3, and the strength distribution of the pile front soil resistance E K at the sliding surface is q 4; the calculation formulas are respectively as follows:
Wherein S is the unit calculated area of soil before the pile, b is the pile width, m 1 is the distribution coefficient of resistance of soil before the pile, alpha is the slip angle before the pile, gamma is the soil weight, Is the internal friction angle of the soil.
Fig. 2 shows a pile-anchor deformation coordination calculation model, and the displacement deformation coordination equation of the anchor pull point obtained by fig. 2 is as follows:
δ(P-P0)＝△φ(y0+d)；
Wherein, P 0 is the initial prestress of the anchor cable, P is the actual tension of the anchor cable, delta is the flexibility coefficient of the anchor cable, delta phi is the rotation angle of the pile, y 0 is the distance between the rotation point of the pile and the top end of the anchoring section, and d is the distance between the anchor tension point and the sliding surface; and delta i＝△φ(y0+d),fi＝d(P-P0), L i is the length of the free section of the anchor cable, A s is the sectional area of each bundle of anchor cable, E g is the elastic modulus of the anchor cable, and N is the bundle number of the anchor cable in each hole;
the displacement deformation coordination balance equation comprises a shear balance equation and a bending moment balance equation at the pile bottom, which are respectively expressed as follows:
Wherein A is the foundation coefficient at the sliding surface, M is the foundation proportionality coefficient, Q 0 is the shearing force of the pile at the sliding surface, M 0 is the bending moment, and
Q 1 is the intensity distribution of landslide thrust at the pile top, q 2 is the intensity distribution of landslide thrust at the slip plane, q 3 is the intensity distribution of soil resistance before the pile at the ground, and q 4 is the intensity distribution of soil resistance before the pile at the slip plane.
The calculation method of the rotation angle delta phi of the pile comprises the following steps:
the calculation method of the distance y 0 between the rotation point of the pile and the top end of the anchoring section comprises the following steps:
Wherein Q 1 is the shear force generated by the pile at the sliding surface under the action of landslide thrust, M 1 is the bending moment generated by the pile at the sliding surface under the action of landslide thrust, Q 2 is the shear force generated by the pile at the sliding surface under the action of soil resistance before the pile, and M 2 is the bending moment generated by the pile at the sliding surface under the action of soil resistance before the pile.
The calculation method of the actual tension of the anchor cable comprises the following steps:
The calculation method of the pile side elastic resistance of the anchoring section comprises the following steps:
σi＝(A+my)(y0-y)△φ；
wherein y is the distance from the calculated point to the sliding surface, and sigma i is the pile side elastic resistance of the anchoring section.
The calculation of the pile body section shear force, bending moment and displacement is divided into four sections;
the calculation method of the shear force, bending moment and displacement of the pile body section when d < y is less than or equal to h 1 from the pile top to the anchor point in the first section is as follows:
Xi＝△φ(y0+y)；
The second section, namely the calculation method of pile body section shearing force, bending moment and displacement from the anchor pull point to the resistance soil height, namely h k < y is less than or equal to d, comprises the following steps:
Xi＝△φ(y0+y)；
The third section, namely the calculation method of pile body section shearing force, bending moment and displacement when the resistance soil is up to the sliding surface, namely 0< y is less than or equal to h k, comprises the following steps:
Xi＝△φ(y0+y)；
The fourth section, namely the calculation method of pile body section shearing force, bending moment and displacement under the sliding surface, namely when y is more than or equal to 0 and less than or equal to h 2, is as follows:
Xi＝△φ(y0+y)；
Wherein Q i is pile section shear force, M i is bending moment, and X i is displacement.
Examples of the invention
A landslide of the Sichuan-Tibetan highway is positioned at the western side of the Erlangshan in Sichuan province, and the landslide is revived and slides due to the piling load of engineering construction. The scale is large, the occurrence and development mechanism is very complex, and the method is representative in landslide groups near the tunnel of the Erlang mountain. The landslide features are steep, the average gradient is about 43 degrees, and the landform zones belong to the middle and high mountain areas of the gantry. The landslide area has the lowest elevation 1840m, the highest elevation 2135m, the front-rear elevation difference of approximately 200m, the length of approximately 250m, the width of approximately 500m along the line and the thickness of approximately 40m. The landslide control engineering adopts comprehensive control engineering measures, and the prestressed anchor cable slide-resistant pile.
And calculating the thrust of the C-C section of the main sliding section of the landslide by adopting an unbalanced thrust coefficient method in engineering design and construction technical specification of landslide prevention. The design parameters of the prestressed anchor cable rigid piles are shown in the following table 1.
TABLE 1 calculation parameter table for prestressed anchor cable rigid piles
According to the theoretical calculation model provided by the invention, the main sliding section is calculated. The actual tension P of the anchor cable is 2161KN, the distance y 0 between the pile rotation point and the sliding surface is 6.125m, the pile rotation angle is 0.000223rad, and the internal force and displacement of the pile body structure are shown in figures 3,4,5 and 6. As shown in fig. 5, the prestress of the anchor cable from the pile top to the anchor pull point is positive bending moment, the hogging moment increases with depth from the anchor pull point and decreases, the hogging moment decreases after decreasing to 0, the hogging moment continues to increase along the opposite direction, the maximum bending moment is 2m below the sliding surface, the maximum bending moment is 20852 KN.m, and the bending moment starts to decrease after reaching the maximum value and approaches to the pile bottom; as shown in fig. 4, the shearing force at the pile top is 0, positive value is first increased along with the depth, then negative value is reduced, the shearing force at the anchor-passing point is gradually reduced along with the depth, the shearing force continues to increase along the reverse direction after the shearing force is reduced to 0, the maximum shearing force is 4156KN, and the shearing force is located at the position 6m below the sliding surface. The shearing force and bending moment of the pile bottom are all close to 0. As shown in fig. 6, the displacement of the pile body at the pile top is 7.17mm at the maximum, gradually decreases with increasing depth, becomes 0 at the pile rotation point, and increases in the opposite direction. As shown in FIG. 3, the pile-side elastic resistance at the top end of the pile anchoring section is the maximum, 820KN/m, gradually decreases with increasing depth, and continues to increase in the opposite direction after decreasing to 0. The maximum shearing force and bending moment of the pile body are 5196KN and 28362 KN.m respectively without considering the action of the pile front soil resistance, and the method is smaller than the pile body bending moment calculated without considering the pile front soil resistance by 26.48 percent and smaller than the shearing force by 25.2 percent.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (6)
1. A calculation method of a pushing type landslide pre-stressed anchor cable rigid pile is characterized in that the pushing type landslide pre-stressed anchor cable rigid pile comprises an anchor cable pile, an anchor cable and an anchor pier; an anchor rope is arranged at the pile top of the anchor rope pile, the anchor rope pile is fixedly connected with the anchor rope, one end of the anchor rope is fixed on the anchor pier, and the other end of the anchor rope is fixed in a rock-soil body of the side slope;
The calculation method of the pushing type landslide prestressed anchor cable rigid pile comprises the following steps: firstly, an anchor cable pile and an anchor cable are regarded as a whole, the pile length of the pile above a sliding surface is set to be h 1, the pile length below the sliding surface is set to be h 2, the soil resistance height before the pile is set to be h k, and the calculated width of the pile is set to be B p; secondly, calculating the pile front soil resistance of the pushing type landslide at the pile setting position according to the movement form of the landslide; finally, according to the displacement deformation coordination at the anchor pull point, a displacement deformation coordination balance equation is established; calculating the pile body corner, the actual tension of the anchor cable, the pile side elastic resistance of the anchoring section, the pile body section shear force, the bending moment and the displacement according to a displacement deformation coordination balance equation, landslide thrust and balance conditions of pile front soil resistance;
the displacement deformation coordination equation of the anchor point is as follows:
δ(P-P0)＝△φ(y0+d)；
Wherein, P 0 is the initial prestress of the anchor cable, P is the actual tension of the anchor cable, delta is the flexibility coefficient of the anchor cable, delta phi is the rotation angle of the pile, y 0 is the distance between the rotation point of the pile and the top end of the anchoring section, and d is the distance between the anchor tension point and the sliding surface; and delta i＝△φ(y0+d),fi＝d(P-P0), L i is the length of the free section of the anchor cable, A s is the sectional area of each bundle of anchor cable, E g is the elastic modulus of the anchor cable, and N is the bundle number of the anchor cable in each hole;
the displacement deformation coordination balance equation comprises a shear balance equation and a bending moment balance equation at the pile bottom, which are respectively expressed as follows:
Wherein A is the foundation coefficient at the sliding surface, M is the foundation proportionality coefficient, Q 0 is the shearing force of the pile at the sliding surface, M 0 is the bending moment, and
Q 1 is the intensity distribution of landslide thrust at the pile top, q 2 is the intensity distribution of landslide thrust at the sliding surface, q 3 is the intensity distribution of soil resistance before the pile at the ground, and q 4 is the intensity distribution of soil resistance before the pile at the sliding surface;
The calculation of the pile body section shear force, bending moment and displacement is divided into four sections;
The calculation method of the pile body section shear force, bending moment and displacement in the first section, when d is less than or equal to y and less than or equal to h 1, comprises the following steps:
The second section, the calculation method of pile section shearing force, bending moment and displacement when h k < y is less than or equal to d is as follows:
The calculation method of pile body section shear force, bending moment and displacement in the third section, when y is more than 0 and less than or equal to h k, comprises the following steps:
Xi＝△φ(y0+y)；
The calculation method of pile section shear force, bending moment and displacement in the fourth section, wherein y is more than or equal to 0 and less than or equal to h 2, comprises the following steps:
Xi＝△φ(y0+y)；
Wherein Q i is pile section shear force, M i is bending moment, and X i is displacement.
2. The method for calculating the pre-stressed anchor cable rigid pile of the push-type landslide according to claim 1, wherein the method for calculating the pile front soil resistance of the push-type landslide at the pile-setting position according to the movement form of the landslide is as follows: the front edge of the pushing type landslide is provided with radial cracks, the cracks are parallel to the sliding direction, at the moment, an anti-sliding pile arranged at the lower part of the landslide is subjected to the action of pile front soil resistance, the pile front soil resistance is related to the inclination angle of the pile front sliding surface, when the inclination angle is positive, the action of pile front soil resistance is ignored, and when the inclination angle is negative, the pile front soil resistance is calculated;
The strength distribution of the pile front soil resistance E K at the ground surface is q 3, and the strength distribution of the pile front soil resistance E K at the sliding surface is q 4; the calculation formulas are respectively as follows:
Wherein S is the unit calculated area of soil before the pile, b is the pile width, m 1 is the distribution coefficient of resistance of soil before the pile, alpha is the slip angle before the pile, gamma is the soil weight, Is the internal friction angle of the soil.
3. The method for calculating the pushing type landslide pre-stressed anchor cable rigid pile according to claim 1, wherein the method for calculating the rotation angle delta phi of the pile is as follows:
4. the calculation method of the pushing type landslide pre-stressed anchor cable rigid pile according to claim 1, wherein the calculation method of the distance y 0 between the rotation point of the pile and the top end of the anchoring section is as follows:
Wherein Q 1 is the shear force generated by the pile at the sliding surface under the action of landslide thrust, M 1 is the bending moment generated by the pile at the sliding surface under the action of landslide thrust, Q 2 is the shear force generated by the pile at the sliding surface under the action of soil resistance before the pile, and M 2 is the bending moment generated by the pile at the sliding surface under the action of soil resistance before the pile.
5. The method for calculating the pushing type landslide pre-stressed anchor cable rigid pile according to claim 1, wherein the method for calculating the actual tension of the anchor cable is as follows:
6. The method for calculating the pushing type landslide pre-stressed anchor cable rigid pile according to claim 1, wherein the method for calculating the pile side elastic resistance of the anchoring section is as follows:
σi＝(A+my)(y0-y)△φ；
wherein y is the distance from the calculated point to the sliding surface, and sigma i is the pile side elastic resistance of the anchoring section.
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