A slope protection chair type anchor pile combination structure and its calculation method

Abstract

The present invention proposes a slope protection chair-type anchor cable pile combination structure and its calculation method, which solves the problem that anti-slip piles are difficult to excavate when buried deep, and cannot maintain long-term stability in front of the piles when buried shallowly on easily weathered rock slopes; the combination structure includes chair-type piles, prestressed anchor cables and hanging plates; the chair-type piles include front piles, rear piles and inclined beams, the top elevation of the front piles is lower than the bottom elevation of the rear piles, and the front piles penetrate deep into the weathered rock layer; the rear piles are in a cantilever state, and hanging plates are provided between adjacent front piles; the front piles and rear piles are connected by an inclined beam, the two ends of the inclined beam are rigidly connected to the top end of the front pile and the bottom end of the rear pile respectively, the inclined beam is close to the ground and two rows of prestressed anchor cables are arranged on the inclined beam, one end of the prestressed anchor cable is fixed on the inclined beam, and the other end of the prestressed anchor cable is fixed in the rock and soil body with stable slope, and the two rows of prestressed anchor cables are close to the two ends of the inclined beam respectively. The present invention derives the calculation formula for the internal force of the chair-type anchor cable pile, which realizes the support of high and steep easily weathered rock embankment slopes.

Description

Technical Field

[0001] The present invention relates to the technical field of embankment slope protection and management, in particular to a slope protection chair-type anchor pile combination structure and a calculation method thereof. Background Art

[0002] At present, the protection of high and steep slopes mainly adopts prestressed anchor cable frames, reinforced concrete lattices, anti-slide piles and other structures, which have the following main problems: 1. Reinforced concrete lattices cannot bear large slope top loads; 2. Prestressed anchor cable frame structures cannot support fill embankments beyond the scope of the protection structure; 3. Anti-slide pile structures are expensive and cannot guarantee the stability of the soil in front of the piles in shallow and easily weathered rocks; 4. The effect of gravity is not considered in the calculation of the longitudinal beam structure of the prestressed anchor cable frame, resulting in a small internal force of the structure and increased structural risk; 5. The demand for widening the platform at the top of the slope cannot be met; 6. The anti-slide pile structure causes great disturbance to the easily weathered rock slope, which is not conducive to the long-term stable protection of the slope. Summary of the Invention

[0003] In view of the deficiencies in the above-mentioned background technology, the present invention proposes a slope protection chair-type anchor pile combination structure and a calculation method thereof, which can support the high, steep and easily weathered rock embankment slopes.

[0004] The technical solution of the present invention is achieved as follows:

[0005] A slope protection chair-type anchor pile combination structure includes a chair-type pile, a prestressed anchor cable and a hanging plate; the chair-type pile includes a front pile, a rear pile and an inclined beam, the top elevation of the front pile is lower than the bottom elevation of the rear pile, and the front pile penetrates deep into the weathered rock layer; the rear pile is in a cantilever state, and a hanging plate is provided between adjacent front piles; the front pile and the rear pile are connected by an inclined beam, one end of the inclined beam is rigidly connected to the top end of the front pile, and the other end of the inclined beam is rigidly connected to the bottom end of the rear pile, the inclined beam is close to the ground and two rows of prestressed anchor cables are arranged on the inclined beam, one end of the prestressed anchor cable is fixed on the inclined beam, and the other end of the prestressed anchor cable is fixed in the stable rock and soil of the slope, and the two rows of prestressed anchor cables are respectively close to the two ends of the inclined beam.

[0006] A calculation method for a slope protection chair type anchor pile combination structure, the steps of which are as follows:

[0007] Build a calculation model for chair-type anti-slip piles and calculate the internal forces of the front and rear piles of the chair-type piles;

[0008] The inclined beam bears the tension of the anchor cable, the reaction force of the foundation, and the forces of the front and rear piles. Based on the gravity load of the rear pile and the inclined beam, and the friction between the slope and the inclined beam, under the assumption of the Winkel model, the differential equation of the deflection curve of the inclined beam is established according to the forces borne by the inclined beam, and the internal force of the inclined beam is calculated.

[0009] The calculation method of the internal force of the inclined beam is:

[0010] Set the length of the rear pile to h1, the length of the inclined beam to h2, and the length of the front pile to h3;

[0011] The bending moment M of the inclined beam at point B where the inclined beam connects to the bottom of the rear pile B and shear force Q B The calculation of is as follows:

[0012]

[0013] M B =M;

[0014] Wherein, M is the bending moment at point B of the rear pile bottom caused by the horizontal thrust of the fill, and Q is the shear force at point B of the rear pile bottom caused by the horizontal thrust of the fill; is the slope gradient; G1 is the weight of the rear pile; and G1 = γabh1g, γ is the bulk density of the pile, a is the length of the anti-sliding pile section, b is the width of the anti-sliding pile section, and g is the acceleration of gravity;

[0015] According to the elastic foundation beam theory, the deflection curve differential equation of the inclined beam is established:

[0016]

[0017] Where E is the elastic modulus of the inclined beam, I is the moment of inertia of the inclined beam, k is the base coefficient, and q(x) is the load on the beam;

[0018] By mathematically solving the differential equation of the deflection curve of the inclined beam, the calculation formula for the internal force and displacement at point C of the inclined beam is obtained:

[0019]

[0020]

[0021]

[0022]

[0023] Among them, y c is the displacement of the inclined beam at point C, y B is the displacement of the inclined beam at point B, θ B is the angle of the inclined beam at point B, α is the characteristic coefficient, P is the anchor cable tension, is the anchor angle of the anchor cable, x is the distance between the inclined beam calculation point and the origin, and x c is the distance between the calculation point C and the origin of the inclined beam, x1 is the distance between the first row of anchor cables and the origin of the inclined beam, x2 is the distance between the second row of anchor cables and the origin of the inclined beam, and θ c is the angle of the inclined beam at point C, M c is the bending moment of the inclined beam at point C, Qc is the shear force of the inclined beam at point C;

[0024] Calculate the horizontal displacement x of the front pile top by the foundation coefficient method cd and the rotation angle θ cd :

[0025]

[0026]

[0027] Among them, M1 is the bending moment at the top of the front pile, Q1 is the shear force at the top of the front pile, β is the deformation coefficient of the front pile, φ1, φ2, φ3, φ4 are the influence value functions of the foundation coefficient method, and

[0028]

[0029] M c =M cb ;

[0030]

[0031]

[0032] Among them, N cb is the axial force of the inclined beam, Q cb is the shear force of the inclined beam at point C, G2 is the gravity of the inclined beam, and F s is the friction force on the inclined beam, and G2=γabgh2, μ is the friction coefficient between the inclined beam and the slope;

[0033] make

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] According to the displacement continuity at point C, the horizontal displacement at point C of the inclined beam is equal to the horizontal displacement of the top of the front pile, and the rotation angle is equal, so we can get: θ c =θ cd ;

[0040] Displacement y at the connection between the inclined beam and the bottom end of the rear pile B and the rotation angle θ B The calculation method is:

[0041]

[0042]

[0043] According to the position of the anchor cable on the inclined beam, the calculation of the internal force of the inclined beam is divided into the internal force of the inclined beam in the xBx1 section, the internal force of the inclined beam in the x1x2 section, and the internal force of the inclined beam in the x2xc section;

[0044] When x B ≤x≤x1, that is, the shear force Q at any section of the inclined beam xBx1 segment x and bending moment M x The calculation formula is as follows:

[0045]

[0046]

[0047] When x1≤x≤x2, the shear force Q at any section of the inclined beam x1x2 is x and bending moment M x The calculation formula is as follows:

[0048]

[0049]

[0050] When x2≤x≤x c When the shear force Q at any section of the inclined beam x2xc is x and bending moment M x The calculation formula is as follows:

[0051]

[0052]

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] 1) Considering the gravity effect of the structure, a calculation formula for the internal force of the chair-type anchor pile was derived. The maximum shear force of the inclined beam increased by 37.5%, and the maximum bending moment at the bottom of the inclined beam increased by 32.8%. The design of the slope protection structure using the calculation results of the chair-type anchor pile internal force calculation formula is safer;

[0055] 2) The cantilevered rear piles above the inclined beam solved the problem of slope protection of fill embankment;

[0056] 3) The overall use of chair-type anchor piles enables the structure to bear greater vertical and lateral loads on the slope top;

[0057] 4) The new structure solves the problem of difficult excavation of deep-buried anti-slide piles on easily weathered rock slopes, and the inability to maintain long-term stability in front of the piles when buried shallowly;

[0058] 5) The use of new structural slope protection can expand the embankment area at the top of the slope, meeting the need for road widening;

[0059] 6) It reduces the disturbance of slope excavation, which is beneficial to the protection of easily weathered rock slopes;

[0060] 7) Compared with ordinary anti-slide piles with a cross-section of 1.6m×2.4m, the chair pile reduces the cross-sectional area by 5.4 times, thus reducing the construction cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0062] Figure 1 This is a cross-sectional view of the chair-type slope protection anchor pile combined structure of the present invention.

[0063] Figure 2 This is a vertical view of the chair-type slope protection anchor pile combined structure of the present invention.

[0064] Figure 3 This is the calculation model of each section of the chair-type slope protection anchor pile of the present invention; among them, (a) is the calculation schematic diagram of the chair-type slope protection anchor pile, and (b) is the calculation schematic diagram of the inclined beam.

[0065] Figure 4 This is the internal force diagram of the chair-type anchor pile of the present invention; among them, (a) is the shear force of the pile body, and (b) is the bending moment of the pile body. DETAILED DESCRIPTION

[0066] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0067] Example 1, as Figure 1 and Figure 2As shown, a slope protection chair anchor pile combination structure includes chair piles, prestressed anchor cables and hanging plates; the chair piles include front piles, rear piles and inclined beams, the top elevation of the front piles is lower than the bottom elevation of the rear piles, and the front piles penetrate deep into the weathered rock layer to play the role of anchoring and supporting structures; the rear piles are in a cantilever state and mainly play the role of bearing the embankment load, and hanging plates are provided between adjacent front piles to support the fill and transfer the soil pressure to the chair piles; the front piles and the rear piles are connected by an inclined beam, one end of the inclined beam is rigidly connected to the top of the front pile, and the other end of the inclined beam is rigidly connected to the bottom of the rear pile, the inclined beam is close to the ground and two rows of prestressed anchor cables are arranged on the inclined beam to maintain the stability of the slope, one end of the prestressed anchor cable is fixed on the inclined beam, and the other end of the prestressed anchor cable is fixed in the stable rock and soil of the slope, and the two rows of prestressed anchor cables are close to the two ends of the inclined beam.

[0068] Example 2, a calculation method for a slope protection chair type anchor pile combination structure, the steps are as follows:

[0069] Build a calculation model for chair-type anti-slip piles and calculate the internal forces of the front and rear piles of the chair-type piles;

[0070] Shear force Q at any section of the rear pile y and bending moment M y The calculation formula is as follows:

[0071]

[0072]

[0073] Among them, q1 is the strength distribution of the fill thrust at the top of the rear pile, and q2 is the strength distribution of the fill thrust at the bottom of the rear pile.

[0074] The calculation formula of the internal force of the front pile is as follows:

[0075] The differential equation for the deflection of the front pile top under horizontal load is:

[0076]

[0077] Through mathematical solution, the shear force Q at any section of the pile body is obtained y and bending moment M y The calculation formula is as follows:

[0078]

[0079]

[0080] Among them, y cd is the displacement of the top of the front pile, θ cd is the rotation angle at the top of the front pile, M1 is the bending moment at the top of the front pile, Q1 is the shear force at the top of the front pile, β is the deformation coefficient of the front pile, B pis the calculated width of the front pile, φ1, φ2, φ3, φ4 are the influence value functions of the foundation coefficient method, and

[0081] The inclined beam bears the tension of the anchor cable, the reaction force of the foundation, and the forces of the front and rear piles. Based on the gravity load of the rear pile and the inclined beam, and the friction between the slope and the inclined beam, under the assumption of the Winkel model, the differential equation of the deflection curve of the inclined beam is established according to the forces borne by the inclined beam, and the internal force of the inclined beam is calculated.

[0082] The calculation model of chair-type anti-slide pile is as follows Figure 3 As shown, the length of the rear pile is set to h1, the length of the inclined beam is set to h2, and the length of the front pile is set to h3; the bending moment M of the inclined beam at point B where the inclined beam connects to the bottom of the rear pile is B and shear force Q B The calculation of is as follows:

[0083]

[0084] M B =M;

[0085] Wherein, M is the bending moment at point B of the rear pile bottom caused by the horizontal thrust of the fill, and Q is the shear force at point B of the rear pile bottom caused by the horizontal thrust of the fill; is the slope gradient; G1 is the weight of the rear pile; and G1 = γabh1g, γ is the bulk density of the pile, a is the length of the anti-sliding pile section, b is the width of the anti-sliding pile section, and g is the acceleration of gravity;

[0086] According to the elastic foundation beam theory, the deflection curve differential equation of the inclined beam is established:

[0087]

[0088] Where E is the elastic modulus of the inclined beam, I is the moment of inertia of the inclined beam, k is the base coefficient, and q(x) is the load on the beam;

[0089] By mathematically solving the differential equation of the deflection curve of the inclined beam, the calculation formula for the internal force and displacement at point C of the inclined beam is obtained:

[0090]

[0091]

[0092]

[0093]

[0094] Among them, y c is the displacement of the inclined beam at point C, y B is the displacement of the inclined beam at point B, θ Bis the angle of the inclined beam at point B, α is the characteristic coefficient, P is the anchor cable tension, is the anchor angle of the anchor cable, x is the distance between the inclined beam calculation point and the origin, and x c is the distance between the calculation point C and the origin of the inclined beam, x1 is the distance between the first row of anchor cables and the origin of the inclined beam, x2 is the distance between the second row of anchor cables and the origin of the inclined beam, and θ c is the angle of the inclined beam at point C, M c is the bending moment of the inclined beam at point C, Q c is the shear force of the inclined beam at point C;

[0095] Calculate the horizontal displacement x of the front pile top by the foundation coefficient method (K method) cd and the rotation angle θ cd :

[0096]

[0097]

[0098] Where M1 is the bending moment at the top of the front pile, Q1 is the shear force at the top of the front pile, β is the deformation coefficient of the front pile, φ1, φ2, φ3, φ4 are the influence value functions of the foundation coefficient method, and

[0099]

[0100] M c =M cb ;

[0101]

[0102]

[0103] Among them, N cb is the axial force of the inclined beam, Q cb is the shear force of the inclined beam at point C, G2 is the gravity of the inclined beam, and F s is the friction force on the inclined beam, and G2=γabgh2, μ is the friction coefficient between the inclined beam and the slope;

[0104] make

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] According to the displacement continuity at point C, the horizontal displacement at point C of the inclined beam is equal to the horizontal displacement of the top of the front pile, and the rotation angle is equal, so we can get:

[0111] θ c =θ cd ;

[0112] Displacement y at the connection between the inclined beam and the bottom end of the rear pile B and the rotation angle θ B The calculation method is:

[0113]

[0114]

[0115] According to the position of the anchor cable on the inclined beam, Figure 3 As shown, the calculation of the internal force of the inclined beam is divided into the internal force of the inclined beam in the xBx1 segment, the internal force of the inclined beam in the x1x2 segment, and the internal force of the inclined beam in the x2xc segment;

[0116] When x B ≤x≤x1, that is, the shear force Q at any section of the inclined beam xBx1 segment x and bending moment M x The calculation formula is as follows:

[0117]

[0118]

[0119] When x1≤x≤x2, the shear force Q at any section of the inclined beam x1x2 is x and bending moment M x The calculation formula is as follows:

[0120]

[0121]

[0122] When x2≤x≤x c When the shear force Q at any section of the inclined beam x2xc is x and bending moment M x The calculation formula is as follows:

[0123]

[0124]

[0125] Specific examples

[0126] A slope at the eastern entrance of Erlang Mountain in Ya'an City, Sichuan Province, features steep terrain and a 50° slope. The interior of the slope is primarily composed of calcareous mudstone with internal joints and fissures, while the surface is composed of weathered granular mudstone. Construction of the Sichuan-Tibet Highway necessitated the expansion of the roadbed platform by filling the middle of the slope. The roadbed is located at an elevation of 2,080 meters above sea level, and the fill height is 5 meters. This slope support utilizes a combination of chair-type anchor piles.

[0127] The front pile section width of the chair-type anchor pile composite structure is 0.8m×1m, and it is 3m long and penetrates into the rock; the rear pile section width is 0.8m×1m, the cantilever height is 5m, the inclined beam section width is 0.8m×1m, and the length is 6m. Two anchor holes are set on the inclined beam, 1m each from the upper and lower ends of the inclined beam, the anchor cable is 30m long, and the anchoring section is 10m long. The chair piles are spaced 4m apart, and prefabricated reinforced concrete retaining plates are placed between the piles. The length is 3.6m and the thickness is 0.2m. The overlap length between the plates and the piles exceeds 0.2m. According to the fill load, the thrust acting on the rear pile is 800kN. According to the rectangular distribution, the gravity of the structure is considered according to the calculation method proposed in the present invention, and the maximum shear force of the chair pile is calculated to be 1242.77kN. Figure 4 (a) shows that the maximum bending moment at the lower part of the inclined beam is 343.88 kN·m. Figure 4 (b) If the structural gravity is not considered, the maximum shear force of the pile body is 904.00 kN. Figure 4 (a) shows that the maximum bending moment at the lower part of the inclined beam is calculated to be 258.91 kN·m. Figure 4 (b) As shown in FIG. Using the calculation results of the method of the present invention to arrange reinforcement can make the slope safer and is beneficial to the long-term stability of the slope.

[0128] The construction process of the chair-type anchor pile composite structure is as follows: first, clean the slope surface, excavate the front pile casting hole, and after reaching the design elevation, put in the steel cage, support the concrete casting formwork, and reserve the hole position for the prestressed anchor cable on the inclined beam, and then pour the concrete; secondly, when the chair-type pile reaches the design strength, start the construction of the prestressed anchor cable, and complete the anchor cable tensioning that exceeds the design stress by 5%; finally, hang a retaining plate at the rear of the rear pile, fill the soil and compact it in layers to form an embankment platform.

[0129] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A calculation method for a slope protection chair type anchor pile combination structure, characterized in that: The combined structure of the chair-type anchor pile for slope protection includes a chair-type pile, a prestressed anchor cable, and a hanging plate. The chair-type pile includes a front pile, a rear pile, and an inclined beam. The top elevation of the front pile is lower than the bottom elevation of the rear pile, and the front pile is deep into the weathered rock layer. The rear pile is in a cantilever state, and a hanging plate is provided between adjacent front piles. The front and rear piles are connected by an inclined beam. One end of the inclined beam is rigidly connected to the top of the front pile, and the other end of the inclined beam is rigidly connected to the bottom of the rear pile. The inclined beam is close to the ground and two rows of prestressed anchor cables are arranged on the inclined beam. One end of the prestressed anchor cable is fixed to the inclined beam, and the other end of the prestressed anchor cable is fixed to the stable rock and soil of the slope. The two rows of prestressed anchor cables are respectively close to the two ends of the inclined beam. The calculation steps are as follows: Build a calculation model for chair-type anti-slip piles and calculate the internal forces of the front and rear piles of the chair-type piles; The inclined beam bears the tension of the anchor cables, the reaction force of the foundation, and the forces acting on the front and rear piles. Based on the gravity loads of the rear piles and the inclined beam, as well as the friction between the slope and the inclined beam, and assuming the Winkel model, a differential equation for the deflection curve of the inclined beam is established based on the forces acting on the inclined beam, and the internal forces of the inclined beam are calculated. The calculation method of the internal force of the inclined beam is: Set the length of the rear pile to h1, the length of the inclined beam to h2, and the length of the front pile to h3; The bending moment M of the inclined beam at point B where the inclined beam connects to the bottom of the rear pile B and shear force Q B The calculation of is as follows: M B =M; Wherein, M is the bending moment at point B of the rear pile bottom caused by the horizontal thrust of the fill, and Q is the shear force at point B of the rear pile bottom caused by the horizontal thrust of the fill; is the slope gradient; G1 is the weight of the rear pile; and G1 = γabh1g, γ is the bulk density of the pile, a is the length of the anti-sliding pile section, b is the width of the anti-sliding pile section, and g is the acceleration of gravity; According to the elastic foundation beam theory, the deflection curve differential equation of the inclined beam is established: Where E is the elastic modulus of the inclined beam, I is the moment of inertia of the inclined beam, k is the base coefficient, and q(x) is the load on the beam; By mathematically solving the differential equation of the deflection curve of the inclined beam, the calculation formula for the internal force and displacement at point C of the inclined beam is obtained, where point C is the connection between the inclined beam and the top of the front pile: Among them, y c is the displacement of the inclined beam at point C, y B is the displacement of the inclined beam at point B, θ B is the angle of the inclined beam at point B, α is the characteristic coefficient, P is the anchor cable tension, is the anchor angle of the anchor cable, x is the distance between the inclined beam calculation point and the origin, and x c is the distance between the calculation point C and the origin of the inclined beam, x1 is the distance between the first row of anchor cables and the origin of the inclined beam, x2 is the distance between the second row of anchor cables and the origin of the inclined beam, and θ c is the angle of the inclined beam at point C, M c is the bending moment of the inclined beam at point C, Q c is the shear force of the inclined beam at point C; Calculate the horizontal displacement x of the front pile top by the foundation coefficient method cd and the rotation angle θ cd : Where M1 is the bending moment at the top of the front pile, Q1 is the shear force at the top of the front pile, β is the deformation coefficient of the front pile, φ1, φ2, φ3, φ4 are the influence value functions of the foundation coefficient method, and Among them, N cb is the axial force of the inclined beam, G2 is the gravity of the inclined beam, F s is the friction force on the inclined beam, and G2=γabgh2, μ is the friction coefficient between the inclined beam and the slope; make According to the displacement continuity at point C, the horizontal displacement at point C of the inclined beam is equal to the horizontal displacement of the top of the front pile, and the rotation angle is equal, so we can get: θ c =θ cd ; Displacement y at the connection between the inclined beam and the bottom end of the rear pile B and the rotation angle θ B The calculation method is: According to the position of the anchor cable on the inclined beam, the calculation of the internal force of the inclined beam is divided into the internal force of the inclined beam in the xBx1 section, the internal force of the inclined beam in the x1x2 section, and the internal force of the inclined beam in the x2xc section; When x B ≤x≤x1, that is, the shear force Q at any section of the inclined beam xBx1 segment x and bending moment M x The calculation formula is as follows: When x1≤x≤x2, the shear force Q at any section of the inclined beam x1x2 is x and bending moment M x The calculation formula is as follows: When x2≤x≤x c When the shear force Q at any section of the inclined beam x2xc is x and bending moment M x The calculation formula is as follows:

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