Anchor cable pretension force calculation method for side slope anchor cable slide-resistant pile

Abstract

The invention discloses an anchor cable pretension calculation method for a side slope anchor cable slide-resistant pile, which is simple and reasonable in concept, capable of quantitatively considering an anchor cable relaxation effect and easy in actual operation, and comprises the following steps: step 10, calculating an anchor cable tension design limit value Fid under the most unfavorable condition of interface damage of an anchor cable hole wall and mortar, interface damage of mortar and an anchor cable and anchor cable snapping damage; step 20, taking a trial value of the pre-tension Ri0 of the anchor cable; representing an anchor cable tension long-term relaxation coefficient xiir by adopting anchor cable pretension Ri0; 30, the anchor cable tension Ri, the pile body maximum bending moment Mp, the pile body maximum shearing force Qp, the pile body built-in section stratum maximum lateral counter-force sigma r and the pile top horizontal displacement up under the designed landslide thrust effect are calculated; step 40, judging whether a calculation control condition is met or not, if not, continuously adjusting the trial calculation value of the anchor cable pretension Ri0 and recalculating from the step 20 until the calculation control condition is met; and step 50, taking the trial calculation value meeting the calculation control condition as the obtained anchor cable pretension force.

Description

Technical Field

[0001] The present invention relates to the technical field of slope and landslide reinforcement engineering, and in particular to a method for calculating the anchor cable pre-tension of a slope anchor cable anti-slide pile. Background Art

[0002] In practice, pre-tension is often applied to anchor cable structures, including slope anchor anti-slide piles, to fully utilize the high strength of the anchor cable structure and its active slope reinforcement function. The magnitude of the applied anchor cable pre-tension has a significant impact on the anchor cable's function, the stress and deformation of the anchor pile, and the stability of the reinforced slope, making it a key concern in related engineering practices.

[0003] Due to the complex interaction between anchor piles and slopes, the application of anchor pretension for slope anchor anti-slide piles is currently not clearly defined in relevant technical specifications. In practice, estimates are generally made based on experience, which is subject to significant subjective uncertainty and blindness. In reality, the total anchor tension is composed of the pretension and the tension generated by the designed landslide thrust. With regard to the former, the pretension gradually decreases over time after tensioning and locking due to the anchor's relaxation characteristics. This factor should be fully considered to ensure the proper application of pretension to better leverage the anchor's active reinforcement and constrain slope and pile deformation. However, in current engineering practice, there is a lack of a method for determining anchor pretension that quantitatively accounts for the relaxation effect of the anchor.

[0004] Generally speaking, numerical simulation methods theoretically have the potential to analyze the long-term relaxation loss of anchor cable pretension in slope anchor piles. However, due to the complexities involved, such as slope creep, anchor cable relaxation, and interaction between the anchor pile and the slope, a constitutive model that can reasonably describe these behaviors is still lacking. Implementing these numerical simulations is both theoretically flawed and practically challenging, including the proper determination of relevant contact parameters. In other words, due to these theoretical limitations, the difficulty of specialized operations, and the extensive and time-consuming computational process, these numerical simulation methods have been difficult to implement on a large scale in practical engineering design. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for calculating the anchor cable pre-tension of slope anchor cable anti-slide piles that is simple and reasonable in concept, can quantitatively consider the anchor cable relaxation effect, and is easy to operate in practice. The technical solution is as follows:

[0006] The method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile includes the following steps:

[0007] Step 10: Take the most unfavorable situation among the damage of the interface between the anchor hole wall and the mortar, the damage of the interface between the mortar and the anchor, and the damage of the anchor breaking, and calculate the anchor tension design limit F of the i-th row anchor id , where i is the row number of anchor cables counted from 1 downward from the top of the pile, i=1~n, and n is the total number of rows of anchor cables on the same pile;

[0008] Step 20: pre-tension R of the anchor cable of row i i0 Take the trial value; use anchor cable pretension R i0 and the actual pulling force R ip Characterizing the long-term relaxation coefficient ξ of anchor cable tension ir ;

[0009] Step 30: Based on the pile-anchor deformation coordination, calculate the anchor cable tension R generated in the i-th row of anchor cables under the design landslide thrust. i , maximum bending moment of pile body M p , maximum shear force of pile Q p , Maximum lateral reaction force of the ground in the pile embedment section σ r and the horizontal displacement of the pile top u p ;

[0010] Step 40: determine whether the calculation control conditions are met. If not, continuously adjust the anchor cable pre-tension R. i0 The trial value is calculated and recalculated from step 20 until the calculation control condition is met;

[0011] The calculation control conditions include: the total tension of the anchor cable R ia Not exceeding the design limit of anchor cable tension F id The ratio of the two is 0.9 to 1, and the maximum bending moment of the pile M p Not exceeding the design limit of bending moment [M], maximum shear force of pile body Q p Does not exceed its shear design limit [Q], pile top horizontal displacement u p Not exceeding its design limit [u], the maximum lateral reaction force of the ground in the pile embedment section σ r Not exceed its horizontal allowable bearing capacity [σ];

[0012] Among them, the total tension of the anchor cable R ia Including the anchor cable pre-tension R after the anchor cable relaxation loss i0 and the anchor cable tension R i ;

[0013] Step 50: Take the anchor cable pretension R that meets the calculation control conditions i0 The calculated value is the required anchor cable pretension.

[0014] As a further improvement to the above-mentioned anchor cable pre-tension calculation method for slope anchor cable anti-slide piles: Step 50 also includes calculating the ratio of the anchor cable pre-tension force of the i-th row on the same pile body to the anchor cable tension design limit as the anchor cable pre-tension rate.

[0015] The outstanding advantages of the method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile of the present invention are:

[0016] First, the calculation method of the present invention reasonably considers the long-term relaxation loss effect of the anchor cable tension, and reasonably quantitatively characterizes the long-term relaxation coefficient of the anchor cable tension, thereby improving the defect that the problem of anchor cable tension loss was not quantitatively considered in the past. Secondly, the calculation method of the present invention includes the anchor cable tension after the anchor cable relaxation loss and the anchor cable tension caused by the designed landslide thrust in the total anchor cable tension, that is, the anchor cable tension required for the long-term loss of the anchor cable pre-tension and the pile-anchor deformation coordination under the action of the designed landslide thrust, which is more in line with the actual force characteristics of the anchor cable in the slope anchor anti-slide pile, and improves the defect of the previous incomplete analysis of the total anchor cable tension. Then, the calculation method of the present invention also takes into account the constraints such as the anchor cable tension, the internal force and displacement of the pile body, and the reaction force of the stratum on the pile side. The calculation control conditions are more comprehensive, and it has the characteristics of clear mechanical concepts and simple principles. Furthermore, the calculation method of the present invention also proposes to express the degree of anchor cable pre-tensioning in terms of pre-tensioning rate, which more intuitively expresses the magnitude of anchor cable pre-tensioning force relative to its designed anchoring force. Compared with the traditional expression of anchor cable pre-tensioning force in absolute value, it is more adaptable to different actual situations.

[0017] In summary, the anchor cable pre-tension calculation method of the slope anchor cable anti-slide pile of the present invention reasonably considers the long-term relaxation loss effect of the anchor cable tension, and at the same time considers comprehensive constraints such as the anchor cable tension, pile body internal force and displacement, pile side stratum reaction force, etc. The calculation principle is clear, the calculation process is simple and easy to operate by computer, and the calculation results are more reasonable and accurate. It avoids the complex modeling and analysis steps and time-consuming calculation process of the numerical simulation method, and provides a convenient, effective and more conceptually reasonable method for the engineering design of slope anchor cable anti-slide piles, taking into account both technical significance and engineering practical value.

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings that constitute part of this invention are intended to assist in understanding the invention. The contents provided in the drawings and their related descriptions in the present invention may be used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0020] Figure 1This is a model diagram of the anchor cable pre-tension calculation method of the slope anchor cable anti-slide pile of the present invention.

[0021] Figure 2 This is a schematic diagram of a slope reinforced with anchor cable anti-slide piles according to an embodiment of the method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide piles of the present invention.

[0022] The relevant marks in the above drawings are:

[0023] 210-slope surface, 220-sliding body, 230-sliding surface, 240-sliding bed, 310-load-bearing section of pile, 320-embedded section of pile, 410-free section of anchor cable, 420-anchor cable anchoring section. DETAILED DESCRIPTION

[0024] The present invention is described clearly and completely below with reference to the accompanying drawings. A person skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention with reference to the accompanying drawings, it should be noted that:

[0025] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other unless there is any conflict.

[0026] In addition, the embodiments of the present invention described below are generally only part of the embodiments of the present invention, rather than all of the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making any creative efforts should fall within the scope of protection of the present invention.

[0027] Regarding the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and the related parts are intended to cover non-exclusive inclusions.

[0028] The specific implementation of the method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile of the present invention includes the following steps:

[0029] Step 10: Take the most unfavorable situation among the damage of the interface between the anchor hole wall and the mortar, the damage of the interface between the mortar and the anchor, and the damage of the anchor breaking, and calculate the design limit value of the anchor tension F of the i-th row of anchors. id .

[0030] Figure 1 This is a model diagram of the anchor cable pre-tension calculation method of the slope anchor cable anti-slide pile of the present invention. Figure 1As shown, i is the row number of anchor cables, counting downward from 1 starting from the apex of the pile, with i ranging from 1 to n, and n being the total number of rows of anchor cables on the same pile. Vertically below the slope surface 210 are the sliding body 220, sliding surface 230, and sliding bed 240. The anti-slide pile includes a pile load-bearing section 310 located above the sliding surface 230 and a pile embedded section 320 located below the sliding surface 230. The anchor cable body includes a free anchor cable section 410 located above the sliding surface 230 and a fixed anchor cable section 420 located below the sliding surface 230.

[0031] The design limit value of the anchor cable tension of the i-th row of anchor cables on the same pile is F id The damage is controlled by three aspects: the interface damage between the anchor hole wall and the mortar, the interface damage between the mortar and the anchor, and the anchor breakage. The most unfavorable situation should be taken, that is, the anchor tension design limit F id Should be taken as:

[0032] (1)

[0033] Where, F id1 、F id2 、F id3 The design anchor tensions for failure of the interface between the anchor hole wall and the mortar, failure of the interface between the mortar and the anchor, and failure of the anchor cable pulling off are calculated as follows:

[0034] (2)

[0035] Where, π is the ratio of circumference to diameter; D is the diameter of the anchor hole; d s L is the outer diameter of the anchor cable; ia is the length of the anchoring section of the i-th row of anchor cables on the pile body; f1, f2, and f3 are the interface strength between the anchor cable hole wall and the mortar, the interface strength between the mortar and the anchor cable, and the breaking strength of the anchor cable, respectively; K s1 , K s2 , K s3 are the pull-out design safety factors for damage to the interface between the anchor hole wall and the mortar, damage to the interface between the mortar and the anchor, and damage to the anchor cable when it is pulled apart; m is the total number of steel strands constituting the anchor cable body in an anchor hole; A is the total number of steel strands constituting the anchor cable body in an anchor hole; and s It is the cross-sectional area of ​​a single bundle of steel strands that constitute the anchor cable body.

[0036] Step 20: pre-tension R of the anchor cable of row i i0 Take the trial value; use the anchor cable pretension R i0 and the actual pulling force R ip Characterizing the long-term relaxation coefficient ξ of anchor cable tension ir .

[0037] Anchor pretension R of the i-th row of anchor cables i0 That is, the tension of the row of anchor cables when they are tensioned and locked. Generally, the anchor cable pre-tension R i0The initial value of the trial value of the anchor cable tension design limit F id 1 / 4~1 / 3 of the anchor cable tension design limit F

[0038] The anchor cable has a long-term relaxation effect, and the long-term relaxation coefficient of the anchor cable tension is ξ ir It can be characterized as:

[0039] (3)

[0040] In the formula, R ip is the actual tension R i (∞) of the anchor cable after long-term relaxation due to the relaxation effect after the i-th row of anchor cables on the same pile body is tensioned and locked i R i (t) is the value of R i (t) at time t, and R (t) is the function of the tension of the i-th row of anchor cables after relaxation with time.

[0041] Wherein, R i (∞) and R i (t) are calculated as follows:

[0042] According to the anchor cable relaxation principle and stress analysis, the calculation expression of the tension R i (t) of the i-th row of anchor cables on the pile body after relaxation at time t is obtained as follows:

[0043] (4)

[0044] Wherein, C i is a constant, and its calculation expression is as follows:

[0045] (5)

[0046] ε i is the initial strain of the anchor cable, which can be determined according to the initial state of the anchor cable, and its calculation expression is as follows:

[0047] (6)

[0048] The calculation index n 1i , n 2i are two real roots of the equation shown in formula (7).

[0049] (7)

[0050] The calculation coefficients k 1i , k 2i , k 3i , k 4i are respectively:

[0051] (8)

[0052] (9)

[0053] (10)

[0054] (11)

[0055] Where, e is a natural constant, e=2.7182818; t a is the typical time after the i-th row of anchor cables on the pile is tensioned and locked, R i (t a ) corresponds to t a The anchor cable tension value at t is taken when there are on-site monitoring conditions. If there are no on-site monitoring conditions, the value is taken based on experience. a =5 days, R i (t a )=0.95R i0 ; A a1 is the equivalent cross-sectional area of ​​the pile body restraining effect of the single hole anchor cable, A a1 =A p S p / b p , where A p is the actual cross-sectional area of ​​the pile, S p is the pile spacing, b p is the cross-sectional width of the pile; A a2 is the cross-sectional area of ​​the anchor cable, A a2 =mA s ; A ri is the effective action range of the i-th row of anchor cables on the pile, which is the rectangular area of ​​the product of the spacing between the upper and lower adjacent rows of anchor cables and the pile spacing, that is, A ri =( a i-1 -a i )S p , where a i is the height of the i-th row anchor cable from the bottom end of the pile body’s load section, and a0=h1, where h1 is the height of the pile body’s load section; E a1 、E a2 are the Hooke elastic modulus that describe the mechanical properties of the pile and anchor cable respectively; E h1 、E h2 are the Hooke elastic modulus in the Hooke-Kelvin body that describes the rheological properties of the free segment sliding body and the surrounding rock of the anchor segment of the anchor body; E k1 、E k2are the Kelvin elastic modulus in the Hooke-Kelvin body that describes the rheological properties of the free section sliding body and the surrounding rock of the anchor section of the anchor body; η1 and η2 are the viscosity coefficients in the Hooke-Kelvin body that describe the rheological properties of the free section sliding body and the surrounding rock of the anchor section of the anchor body; μ is a real number variable.

[0056] Step 30: Based on the pile-anchor deformation coordination, calculate the anchor cable tension R generated in the i-th row of anchor cables under the design landslide thrust. i , maximum bending moment of pile body M p , maximum shear force of pile Q p , Maximum lateral reaction force of the ground in the pile embedment section σ r and the horizontal displacement of the pile top u p .

[0057] The design landslide thrust E acting on the rear side of the pile d , along the height of the pile body, a general triangular distribution pattern with small upper part and large lower part is adopted. The corresponding calculation expression of the linear distribution force q0 acting on the side of the bottom end of the loaded section is:

[0058] (12)

[0059] Under the combined effect of the anchor cable tension and the designed landslide thrust, according to the pile-anchor deformation coordination relationship, the horizontal displacement of the anchor cable and the pile body at the node of each anchor cable and the pile body is the same, that is:

[0060] (13)

[0061] Where u ia 、u ip They represent the horizontal displacements of the anchor cables and pile bodies at the nodes of the i-th row of anchor cables from top to bottom on the same pile body.

[0062] At the node between the i-th row of anchor cables and the pile, the horizontal displacement of the anchor cables can be calculated using the calculation method for axial tension members, namely:

[0063] (14)

[0064] Where R i is the anchor cable tension generated in the i-th row of anchor cables under the design landslide thrust; l fi is the length of the free section of the i-th row of anchor cables; δ i is the horizontal inclination angle of the i-th row of anchor cables; E c is the elastic modulus of the anchor body in a single hole.

[0065] For the horizontal displacement of the pile u ip , the displacement u generated by the load section itself due to the triangular distribution of the landslide thrust ipa and the displacement u caused by the bottom end of the loaded section (the top end of the embedded section) ip b Two parts, namely:

[0066] (15)

[0067] where, according to the cantilever beam model, the displacement u ip a and the displacement u ip b The calculation expressions are respectively:

[0068] (16)

[0069] (17)

[0070] In the formula, the variable j is an integer; EI is the bending stiffness of the pile body; x0, ω0 are the horizontal displacement and rotation angle (uphill side rotation is positive) of the bottom end O point of the pile body, respectively.

[0071] For the general case of the free end of the pile body bottom B point, the calculation expressions of the horizontal displacement x0 and the rotation angle ω0 of the bottom end O point of the pile body are respectively:

[0072] (18)

[0073] In the formula, are the influence coefficient values of the k method, β is the horizontal deformation coefficient of the embedded section of the pile body, Q0, M0 are the shear force and bending moment of the bottom end of the pile body, respectively, and the calculation expressions are respectively:

[0074] (19)

[0075] (20)

[0076] (21)

[0077] In the formula, h2 is the height of the embedded section of the pile body; B p is the calculation width of the pile body, when the cross-sectional width b p of the pile body is ≥1m, take B p =(b p +1) m, otherwise, take B p = (1.5b p +0.5) m (reference 《Railway Subgrade Retaining Structure Design Specification (TB 10025-2019) 》); k is the horizontal elastic resistance coefficient of the embedded section of the pile body.

[0078] Therefore, substituting equations (16) and (17) into equation (15), and then substituting equation (14) into equation (13), we can obtain:

[0079] (twenty two)

[0080] Wherein, j is an integer variable and 1≤j≤n. Different values ​​of j represent the conditions of the rows of anchor cables above and below the i-th row.

[0081] By solving the equations shown in formula (22) simultaneously, we can obtain the anchor cable tension R generated by the i-th row of anchor cables on the same pile under the design landslide thrust: i .

[0082] The obtained anchor cable tension R i Substituting into equation (21), we can obtain the pile shear force Q0 and bending moment M0 at the bottom of the pile body under load. Therefore, according to the differential equation of the pile body under horizontal load, the bending moment M0 of any cross section of the pile body embedded section (the part below the sliding surface) can be obtained by solving it. y , shear force Q y and the lateral reaction force of the formation σ y The calculation expressions are:

[0083] (twenty three)

[0084] Where, are the influence function values ​​of the k method, and their calculation expressions are:

[0085] (twenty four)

[0086] Where y is the depth from point O to the top of the pile embedment section (i.e. the bottom of the loaded section).

[0087] The bending moment M calculated according to formula (23) y , shear force Q y and the lateral reaction force of the formation σ y As a result, the corresponding maximum absolute values ​​are the maximum bending moment of the pile M p , maximum shear force of pile Q p , Maximum lateral reaction force of the ground in the pile embedment section σ r .

[0088] According to the deformation characteristics of the pile body, the horizontal displacement u of the pile top (point A) can be obtained p The calculation expression is:

[0089] (25)

[0090] Step 40: determine whether the calculation control conditions are met. If not, the anchor cable tension design limit F idThe anchor cable pre-tension R is adjusted continuously with a variation range of 1% to 5%. i0 The trial value is calculated and recalculated from step 20 until the calculation control condition is met.

[0091] In the anchor cable pretension R i0 , anchor cable relaxation effect and anchor cable tension R generated by the designed landslide thrust i Under the combined action of ia Including the anchor cable pre-tension R after the anchor cable relaxation loss i0 and the anchor cable tension R i , based on formula (3), the total tension of the anchor cable R ia It can be expressed as:

[0092] (26)

[0093] For the stress of anchor cable anti-slide pile, the calculation control conditions that should be met include: total tension of anchor cable R ia Not exceeding the design limit of anchor cable tension F id The ratio of the two is 0.9 to 1, and the maximum bending moment of the pile M p Not exceeding the design limit of bending moment [M], maximum shear force of pile body Q p Does not exceed its shear design limit [Q], pile top horizontal displacement u p Not exceeding its design limit [u], the maximum lateral reaction force of the ground in the pile embedment section σ r Does not exceed its horizontal allowable bearing capacity [σ], the corresponding expressions are:

[0094] (27)

[0095] Taking formula (27) as the calculation control condition, the anchor cable pretension R i0 The calculated value of the anchor cable meets the calculation control condition. If not, the anchor cable tension design limit F id The anchor cable pre-tension R is adjusted continuously with a variation range of 1% to 5%. i0 The trial value is calculated and recalculated from step 20 until the calculation control condition is met.

[0096] Step 50: Take the anchor cable pretension R that meets the calculation control conditions i0 The trial value is the required anchor cable pretension, and then calculate the anchor cable pretension R of the i-th row on the same pile. i0 The ratio of the anchor cable tension design limit, that is, the anchor cable pre-tensioning rate λ i The calculation expression is:

[0097] (28)

[0098] The beneficial effects of the present invention are described below through specific examples.

[0099] Figure 2 This is a schematic diagram of an embodiment of the method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile of the present invention. Figure 2 As shown in the figure, two rows of anchor cables are set on the pile body, that is, n=2; the diameter of the anchor hole is D=130mm; 6 bundles of steel strands are used to form the anchor cable body in each hole, that is, m=6; the cross-sectional area of ​​a single bundle of steel strands constituting the anchor cable body is A s =140mm 2 ; Anchor body external diameter d s =44.2mm. Take t a =5 days, R i (t a )=0.95R i0 ; Pile bending stiffness EI = 62500000 kN·m 2 , pile cross-sectional area A p =5m 2 , pile cross-sectional width b p =2m; horizontal elastic resistance coefficient of the ground at the pile embedding section k=100000kPa / m; pile load section height h1=16m, embedding section height h2=10m, pile spacing S p =5m; the interface strength between the anchor hole wall and the mortar is f1=300kPa, the interface strength between the mortar and the anchor is f2=1416kPa, and the anchor breaking strength is f3=1320MPa; the pull-out design safety factor K for the interface failure between the anchor hole wall and the mortar is s1 =2, the pull-out design safety factor K for the interface failure between mortar and anchor cable s2 =2, the safety factor K for the pull-out design of anchor cable failure s3 =1.5; horizontal allowable bearing capacity of the ground at the embedded section of the pile [σ] = 2250 kPa, design limit of pile bending moment [M] = 34800 kN·m, design limit of pile shear force [Q] = 6000 kN, design limit of pile top horizontal displacement [u] = 100 mm; Hooke elastic modulus E, which describes the mechanical properties of the pile a1 =24000MPa, Hooke elastic modulus E describing the mechanical properties of the anchor body a2 =195000MPa; Hooke elastic modulus E in the Hooke-Kelvin body that describes the rheological properties of the free segment sliding body of the anchor body h1 =1000MPa, Kelvin modulus E k1 =25MPa, viscosity coefficient η1=200MPa / d; Hooke elastic modulus E in the Hooke-Kelvin body that describes the rheological properties of the surrounding rock in the anchor section of the anchor bodyh2 =12000MPa, Kelvin modulus E k2 =85MPa, viscosity coefficient η2=660MPa / d; design landslide thrust E d =1200kN / m. The rest of the relevant calculation parameters are summarized in Table 1.

[0100] Table 1

[0101]

[0102] Step 10

[0103] From formula (2), we can get: F 1d1 =F 2d1 =612.6kN; F 1d2 =F 2d2 =983.12kN; F 1d3 =F 2d3 =739.2kN.

[0104] According to formula (1), we can get: 1d =F 2d =612.6kN.

[0105] Step 20

[0106] Take the anchor pretension R of the first row of anchor cables 10 The calculated value is 180kN, and the anchor pretension R of the second row of anchor cables is taken as 20 The calculated value is 220kN.

[0107] A a1 =A p S p / b p =5×5 / 2=12.5m 2 ;

[0108] A a2 =mA s =6×140=840mm 2 ;

[0109] A r1 =(a0-a1)S p =(16-14)×5=10 m 2 ;

[0110] A r2 =(a1-a2)S p =(14-12)×5=10 m 2 .

[0111] According to formulas (8) to (11), the calculation coefficient can be obtained:

[0112] k 11 = k 12 =4.9197×10 15 (MN·MPa / d) 2 ;

[0113] k 21 = k 22 =2.51758×10 16 (MN·MPa) 2 / d;

[0114] k 31 = k 32 =3.74996×10 15 (MN·MPa) 2 ;

[0115] k 41 = k 42 =5.14176×10 17 (MN 3 MPa 2 ).

[0116] Then according to formula (7), the calculation index can be obtained as follows: n 11 = n 12 =-0.1535587209 / d;n 21 = n 22 =-4.9637951781 / d.

[0117] Therefore, according to formula (5), the constants are: C1 = -12.009 kN; C2 = -14.678 kN.

[0118] According to formula (4), we can obtain: R1(∞)=152.811kN; R2(∞)=186.769kN.

[0119] According to formula (3), we can get: 1r =ξ 2r =0.151.

[0120] Step 30

[0121] According to formula (12), q0=750kN / m can be calculated.

[0122] Therefore, according to equations (13) to (25), we can obtain:

[0123] R1=431.87kN; R2=405.08kN;

[0124] M p =25874.92kN·m; Q p=5241.47kN;σ r =1388.48kPa;u p =71.51mm.

[0125] Step 40

[0126] According to formula (26), we can get: R 1a =584.69kN; R 2a =591.86kN;

[0127] So we can calculate:

[0128] , , all satisfy Calculation control conditions.

[0129] According to formula (27), it is judged that all relevant calculation control conditions are met.

[0130] Step 50

[0131] Determine the required anchor cable pretension: R 10 =180kN; R 20 =220kN.

[0132] According to formula (28), the corresponding anchor cable pre-tensioning rates are: λ1=29.4%; λ2=35.9%.

[0133] Results test

[0134] For this embodiment, the FLAC3D numerical simulation method is used to calculate the d =1200 kN / m, the tension of the first row of anchor cables, the tension of the second row of anchor cables, the horizontal displacement of the pile top, the maximum bending moment and shear force of the pile body, and the maximum lateral reaction force of the stratum in the pile embedding section are 465 kN, 431 kN, 65.2 mm, 23219 kN·m, 4908 kN, and 1256 kPa, respectively. The absolute values ​​of the relative errors between the calculation method of the present invention and that of the present invention are approximately 7.1%, 6.0%, 9.7%, 11.4%, 6.8%, and 10.5%, respectively.

[0135] It can be seen that the calculation method of the present invention is consistent with the FLAC3D numerical simulation results, and the deviation between the two is within the acceptable error range in engineering, indicating that the calculation method of the present invention is reasonable.

[0136] The above describes the relevant contents of the present invention. Based on this description, a person skilled in the art will be able to implement the present invention. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without making any creative efforts should fall within the scope of protection of the present invention.

Claims

1. The calculation method of anchor cable pre-tension of slope anchor cable anti-slide pile is characterized by: The following steps are involved: Step 10: Take the most unfavorable situation among the damage of the interface between the anchor hole wall and the mortar, the damage of the interface between the mortar and the anchor, and the damage of the anchor breaking, and calculate the anchor tension design limit F of the i-th row anchor id , where i is the row number of anchor cables counted from 1 downward from the top of the pile, i=1~n, and n is the total number of rows of anchor cables on the same pile; Step 20: pre-tension R of the anchor cable of row i i0 Take the trial value; use anchor cable pretension R i0 and the actual pulling force R ip Characterizing the long-term relaxation coefficient ξ of anchor cable tension ir ; Step 30: Based on the pile-anchor deformation coordination, calculate the anchor cable tension R generated in the i-th row of anchor cables under the design landslide thrust. i , maximum bending moment of pile body M p , maximum shear force of pile Q p , Maximum lateral reaction force of the ground in the pile embedment section σ r and the horizontal displacement of the pile top u p ; Step 40: determine whether the calculation control conditions are met. If not, continuously adjust the anchor cable pre-tension R. i0 The trial value is calculated and recalculated from step 20 until the calculation control condition is met; The calculation control conditions include: the total tension of the anchor cable R ia Not exceeding the design limit of anchor cable tension F id The ratio of the two is 0.9 to 1, and the maximum bending moment of the pile M p Not exceeding the design limit of bending moment [M], maximum shear force of pile body Q p Does not exceed its shear design limit [Q], pile top horizontal displacement u p Not exceeding its design limit [u], the maximum lateral reaction force of the ground in the pile embedment section σ r Not exceed its horizontal allowable bearing capacity [σ]; Among them, the total tension of the anchor cable R ia Including the anchor cable pre-tension R after the anchor cable relaxation loss i0 and the anchor cable tension R i ; Step 50: Take the anchor cable pretension R that meets the calculation control conditions i0 The calculated value is the required anchor cable pretension.

2. The method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile according to claim 1, characterized in that: In step 10, the design limit of the anchor cable tension of the i-th row of anchor cables is F id The calculation expression is: ； in, ; Where, F id1 、F id2 、F id3 are the design anchor tension when the interface between the anchor hole wall and the mortar is damaged, the interface between the mortar and the anchor is damaged, and the anchor is broken; π is the pi; D is the diameter of the anchor hole; d s L is the outer diameter of the anchor cable; ia is the length of the anchoring section of the i-th row of anchor cables on the pile body; f1, f2, and f3 are the interface strength between the anchor cable hole wall and the mortar, the interface strength between the mortar and the anchor cable, and the breaking strength of the anchor cable, respectively; K s1 , K s2 , K s3 are the pull-out design safety factors for damage to the interface between the anchor hole wall and the mortar, damage to the interface between the mortar and the anchor, and damage to the anchor cable when it is pulled apart; m is the total number of steel strands constituting the anchor cable body in an anchor hole; A is the total number of steel strands constituting the anchor cable body in an anchor hole; and s It is the cross-sectional area of ​​a single bundle of steel strands that constitute the anchor cable body.

3. The method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile according to claim 2, characterized in that: In step 20, the anchor cable pretension R i0 The initial value of the trial calculation value is the anchor cable tension design limit F id 1 / 4 to 1 / 3 of the anchor cable tension design limit F id Adjust the anchor cable pre-tension R with a variation range of 1% to 5%. i0 The trial value of .

4. The method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile according to claim 2, characterized in that: In step 20, the long-term relaxation coefficient of anchor cable tension ξ ir The calculation expression is: ； Where R ip is the actual tension R after the i-th row of anchor cables are tensioned and locked due to the relaxation effect, which causes the anchor cables to relax for a long time. i (∞), R i (∞) is R i (t) is the value when time t is infinite, R i (t) is the function of the tension of the i-th row of anchor cables after relaxation over time.

5. The method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile according to claim 4, characterized in that: R i The calculation expression of (t) is: ； in, ; ； ； ； ； ； Where, ε i is the initial strain of the anchor cable; C i is a constant; e is a natural constant; calculate the exponent n 1i 、n 2i for The two real roots of the real variable μ; k 1i 、k 2i 、k 3i 、k 4i All are calculation coefficients; t a is the typical time after the i-th row of anchor cables on the pile is tensioned and locked, R i (t a ) corresponds to t a Anchor cable tension value at time A a1 is the equivalent cross-sectional area of ​​the pile body restraining effect of the single hole anchor cable, A a1 =A p S p / b p , where A p is the actual cross-sectional area of ​​the pile, S p is the pile spacing, b p is the cross-sectional width of the pile; A a2 is the cross-sectional area of ​​the anchor cable, A a2 =mA s ; A ri is the effective action range of the i-th row of anchor cables on the pile, which is the rectangular area of ​​the product of the spacing between the upper and lower adjacent rows of anchor cables and the pile spacing, that is, A ri =( a i-1 -a i )S p , where a i is the height of the i-th row anchor cable from the bottom end of the pile body’s load section, and a0=h1, where h1 is the height of the pile body’s load section; E a1 、E a2 are the Hooke elastic modulus in the Hooke-Kelvin body that describes the mechanical properties of the pile and anchor body; E h1 、E h2 are the Hooke elastic modulus in the Hooke-Kelvin body that describes the rheological properties of the free segment sliding body and the surrounding rock of the anchor segment of the anchor body; E k1 、E k2 are the Kelvin elastic modulus in the Hooke-Kelvin body that describes the rheological properties of the free section sliding body and the surrounding rock of the anchor section of the anchor body; η1 and η2 are the viscosity coefficients in the Hooke-Kelvin body that describe the rheological properties of the free section sliding body and the surrounding rock of the anchor section of the anchor body.

6. The method for calculating the anchor cable pre-tension of the slope anchor cable anti-slide pile according to claim 5, characterized in that: In step 30: Anchor cable tension R i The calculation expression is: ； Bending moment M at any cross section of the pile embedded section y , shear force Q y and lateral reaction force of the formation σ y The maximum absolute value of each is the maximum bending moment of the pile M p , maximum shear force of pile Q p , Maximum lateral reaction force of the ground in the pile embedment section σ r , bending moment M y , shear force Q y and lateral reaction force of the formation σ y The calculation expressions are: ； Horizontal displacement of pile top u p The calculation expression is: ； Where, l fi is the length of the free section of the i-th row of anchor cables; E c is the elastic modulus of the anchor cable in a single hole; δ i is the horizontal inclination angle of the i-th row of anchor cables; q0 is the linear distributed force acting on the side of the bottom end of the loaded section; EI is the bending stiffness of the pile; x0 and ω0 are the horizontal displacement and rotation angle of the bottom end of the loaded section of the pile, respectively; β is the horizontal deformation coefficient of the embedded section pile; are the influence function values ​​of the k method; Q0 and M0 are the shear force and bending moment of the pile at the bottom of the loaded section, respectively; k is the horizontal elastic resistance coefficient of the stratum in the pile embedded section; j is an integer variable, and 1≤j≤n.

7. The method for calculating anchor cable pretension of slope anchor cable anti-slide piles according to claim 6, characterized in that: In step 40, the total tension of the anchor cable in the i-th row is R ia The calculation expression is: 。 8. The method for calculating anchor cable pretension of slope anchor cable anti-slide piles according to claim 7, characterized in that: Step 50 also includes calculating the pre-tension force R of the i-th row of anchor cables on the same pile body. i0 and anchor cable tension design limit F id The ratio is the anchor cable pre-tensioning rate λ i .

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