Internal force calculation method of precast slope normal frame anchor structure

Abstract

The present invention discloses a method for calculating the internal forces of a prefabricated slope normal frame anchoring structure that is simple and highly accurate, including the steps: Step 100, calculating the bottom values of the triangular distributed loads borne on the rear side of the rear vertical beam and the front side of the front vertical beam; Step 200, taking the upper structure of half the length and calculating the internal forces of the upper structure when there is no displacement at the bottom; Step 300, taking the bottom beam of half the length to calculate the internal forces of the bottom beam, the cross-section rotation angle, and the bottom rotation angle ω of the current front vertical beam or rear vertical beam j , where j is the number of iterations, j ≥ 1; Step 400, recalculating the additional internal forces of the upper structure caused only by the bottom rotation angle ω j ; Step 500, determining whether the absolute value of the relative error between "the sum of the internal forces and the additional internal forces" and the internal forces meets the calculation accuracy requirement: if it meets the calculation accuracy requirement, the calculation is completed; if it does not meet the calculation accuracy requirement, then replace the internal forces at the bottom of the rear vertical beam or the front vertical beam with "the sum of the internal forces and the additional internal forces" and return to Step 300 to sequentially perform iterative calculations.

Description

Technical Field

[0001] The invention relates to the technical field of engineering protection of buried oil and gas pipelines and shallow surface layers of slopes in mountainous areas, and in particular to an internal force calculation method of a prefabricated slope surface normal frame anchoring structure. Background Art

[0002] In the protection projects of buried oil and gas pipelines and shallow slopes in mountainous areas, traditional retaining structures such as gravity retaining walls, ordinary lattice anchors, and anti-slide piles are currently the main ones. On the one hand, due to the requirements of the action mechanism, gravity retaining walls are often large in size and have high requirements for the bearing capacity of the foundation. They are often limited by the construction environment and foundation conditions in mountainous areas. On the other hand, under the action of strong earthquakes, the sliding displacement of gravity retaining walls is more significant and the wall body is prone to cracking. There are obvious limitations in the protection of gravity retaining walls for oil and gas pipelines in strong earthquake areas. In addition, for the reinforcement of the shallow rock and soil body of the slope where the pipelines are located in mountainous areas, the use of ordinary lattice anchor structures takes a relatively long time to construct due to the cast-in-place frame, and the use of retaining structures such as anti-slide piles and gravity retaining walls often lacks economic rationality.

[0003] Therefore, unlike the traditional frame structure in which a single frame is placed along the slope, the prefabricated slope normal frame anchored seismic protection structure (referred to as the frame anchor structure) is a new type of slope reinforcement structure in which a single frame is placed along the normal direction of the slope. It penetrates the potential sliding surface into a relatively stable stratum through anchor rods, thereby providing sufficient anti-sliding force to reinforce the slope. At the same time, the combined effect of the frame restricts the oil and gas pipeline to a certain range, thereby reducing the permanent displacement of the pipeline under the thrust of the landslide. Therefore, the frame anchor structure can integrate the shallow surface reinforcement of the slope and the protection of the pipeline. It can be used for both shallow surface reinforcement of the slope and the protection of buried pipelines passing through the slope. It is very suitable for protecting long-distance oil and gas pipelines laid across the mountain slope, reducing the risk of damage under adverse working conditions such as earthquakes and heavy rains. Its technical and economic rationality is often better than that of traditional reinforcement structures.

[0004] However, unlike the traditional lattice anchoring structure consisting of longitudinal and transverse beams laid flat on the ground, the longitudinal axes of the top beam and the bottom beam of the frame anchoring structure are both perpendicular to the pipeline axis and are laid flat on the slope and the bottom of the pipeline groove respectively, connected by two vertical beams in the middle. For this new type of structure, there is no suitable internal force calculation and analysis method in the existing specifications and literature. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a simple and highly accurate internal force calculation method suitable for a prefabricated slope normal frame anchoring structure.

[0006] In order to achieve the above object, the present invention provides a method for calculating the internal force of a prefabricated slope normal frame anchor structure, and the technical solution is as follows:

[0007] The internal force calculation method of the prefabricated slope normal frame anchor structure, the frame anchor structure includes anchor rods, bottom beams, rear vertical beams and front vertical beams located on the inner side of the slope and a top beam located on the outer side of the slope, characterized in that the internal force calculation method includes the following steps:

[0008] Step 100, the upper structure composed of the rear vertical beam, the front vertical beam and the top beam is regarded as a plane rigid frame structure with a fixed bottom end, and the local soil force borne by the rear side of the rear vertical beam from the length range thereof and the local soil force borne by the front side of the front vertical beam from the length range thereof are simplified into triangular distributed loads, and the bottom value of the triangular distributed load is calculated;

[0009] Step 200, taking half the length of the upper structure, and using a structural mechanics method to calculate the internal force of the upper structure when the bottom end of the front vertical beam or the rear vertical beam is not displaced;

[0010] Step 300: Take a half-length bottom beam and calculate the internal force, cross-sectional rotation angle, and the bottom end rotation angle ω of the current front vertical beam or rear vertical beam according to the Winkler elastic foundation beam model. j , j is the number of iterations, j ≥ 1;

[0011] Step 400, using structural mechanics method to recalculate the bottom angle ω j The additional internal forces of the superstructure caused;

[0012] Step 500, select the internal force of any one of the rear vertical beam, the front vertical beam and the top beam as the control condition, and judge whether the absolute value of the relative error between the "sum of the internal force and the additional internal force" and the internal force meets the calculation accuracy requirement: if the calculation accuracy requirement is met, the calculation is completed; if the calculation accuracy requirement is not met, the "sum of the internal force and the additional internal force" at the bottom end of the rear vertical beam or the front vertical beam replaces its internal force and then returns to step 300 to perform iterative calculations in sequence.

[0013] It can be seen that the internal force calculation method of the prefabricated slope normal frame anchor structure of the present invention has the following advantages:

[0014] Firstly, according to the stress characteristics of the structure, the present invention divides the frame anchoring structure into two parts, one part is the upper structure composed of the rear vertical beam, the front vertical beam and the top beam, and the other part is the bottom beam. The upper structure is regarded as a plane rigid frame structure, and the bottom beam is regarded as a beam structure on the Winkler elastic foundation. Finally, the stress of the prefabricated slope normal frame anchoring structure is reasonably simplified.

[0015] Secondly, the present invention fully considers the deformation coordination and joint action analysis among the superstructure, bottom beam and foundation soil layer, selects the internal force of any one of the rear vertical beam, the front vertical beam and the top beam as the control condition, and controls the number of iterations by controlling the "sum of the internal force and the additional internal force" and the absolute value of the relative error of the internal force, ultimately forming a more reasonable internal force calculation method with simple calculation and clear concept.

[0016] It can be seen that the internal force calculation method of the prefabricated slope normal frame anchor structure of the present invention is simple, can provide technical support for the reasonable engineering design of the frame anchor structure, can achieve the goal of effective prevention and control of the shallow surface of the slope and saving engineering costs, and has strong practicality.

[0017] The present invention is further described below in conjunction with 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 the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings constituting a part of the present invention are used to assist in understanding the present invention. The contents provided in the drawings and their related descriptions in the present invention can be used to explain the present invention, but do not constitute improper limitations on the present invention. In the drawings:

[0019] Figure 1 It is a structural schematic diagram of the prefabricated slope normal frame anchoring structure of the present invention.

[0020] Figure 2 It is a schematic diagram of the positional relationship between the local sliding body and the most potentially dangerous sliding surface of the present invention.

[0021] Figure 3 It is a schematic diagram of the force analysis of the entire upper structure of the prefabricated slope normal frame anchoring structure of the present invention.

[0022] Figure 4 It is a schematic diagram of the force analysis of the upper structure of half the length in the prefabricated slope normal frame anchoring structure of the present invention.

[0023] Figure 5 It is a schematic diagram of the force analysis of the bottom beam of half the length in the prefabricated slope normal frame anchoring structure of the present invention.

[0024] Figure 6 It is a dimension parameter diagram of the prefabricated slope normal frame anchoring structure in an embodiment of the present invention.

[0025] Figure 7 It is a comparison diagram of the bending moment calculation results and the numerical simulation results of the prefabricated slope normal frame anchoring structure of the present invention.

[0026] Figure 8It is a comparison diagram of the shear force calculation results and the numerical simulation results of the prefabricated slope normal frame anchoring structure of the present invention.

[0027] The relevant marks in the above drawings are:

[0028] 10-anchor rod, 20-bottom beam, 30-rear vertical beam, 40-top beam, 50-front vertical beam, 60-slope, 70-local sliding body, 80-potentially most dangerous sliding surface, 90-pipeline. DETAILED DESCRIPTION

[0029] The present invention is described clearly and completely below in conjunction with 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 in conjunction with the accompanying drawings, it should be particularly noted that:

[0030] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other if there is no conflict.

[0031] In addition, the embodiments of the present invention involved in the following description are generally only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0032] About 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 related parts are intended to cover non-exclusive inclusions.

[0033] Figure 1 Schematic diagram of the structure of the prefabricated slope normal frame anchoring structure of the present invention. Figure 1 As shown, the frame anchoring structure includes an anchor rod 10, a bottom beam 20, a rear vertical beam 30 and a front vertical beam 50 located on the inner side of the slope 60, and a top beam 40 located on the outer side of the slope 60, wherein the longitudinal axes of the top beam 40 and the bottom beam 20 located in the same plane are both perpendicular to the axial direction of the pipeline 90, and are respectively laid flat on the bottom of the grooves of the slope 60 and the pipeline 90, and are connected in the middle by the rear vertical beam 30 and the front vertical beam 50.

[0034] The internal force calculation method for the frame anchoring structure of the present invention includes steps 100-500, which are as follows:

[0035] Step 100, the upper structure composed of the rear vertical beam, the front vertical beam and the top beam is regarded as a plane rigid frame structure with a fixed bottom end, and the local soil force borne by the rear side of the rear vertical beam from the local soil force borne by the front side of the front vertical beam from the local soil force borne by the front side of the front vertical beam from the local soil force borne by the front side of the front vertical beam from the local soil force borne by the front side of the front vertical beam from the local soil force are simplified into triangular distributed loads, and the bottom value of the triangular distributed load is calculated as follows:

[0036] The bottom value of the triangular distributed load is the larger value of the two calculated values ​​calculated by the local landslide thrust and the static earth pressure. The soil force borne by the front side of the front vertical beam is the same as the soil force borne by the rear side of the rear vertical beam.

[0037] Among them, the method for calculating the thrust of local landslide is as follows:

[0038] Figure 2 Schematic diagram of the relationship between the local sliding body and the most potentially dangerous sliding surface of the present invention. Figure 2 As shown in FIG. 1 , after searching for the most potentially dangerous sliding surface 80 in the shallow layer of the slope according to the standard method (Technical Code for Slope Engineering of Buildings (GB50330-2013)), the soil above the intersection of the normal line perpendicular to the longitudinal axis of the bottom beam at the rear end of the bottom beam and the most potentially dangerous sliding surface 80 is taken as the local sliding body 70 directly acting on the rear vertical beam 30, and the residual sliding force E of the local sliding body 70 is calculated by the classic transfer coefficient method (Technical Code for Slope Engineering of Buildings (GB50330-2013)). L n , and then calculate the bottom value q1 of the triangular distributed load, the calculation expression is:

[0039]

[0040] Where: S is the center distance between two adjacent frame anchoring structures along the slope direction; d0 is the vertical distance between the longitudinal axis of the bottom beam 20 and the slope surface 60; d1 is the thickness of the local sliding body 70 at the rear end of the bottom beam 20;

[0041] E L n is the designed landslide thrust at the rear side of the rear vertical beam 30, and its calculation expression is:

[0042]

[0043] Where: E L m is the residual sliding force of the mth soil strip, m=1-n, n is the total number of strips vertically divided from the local sliding body 70 located at the rear side of the rear vertical beam, which is surrounded by the slope surface 60 and the most potentially dangerous sliding surface 80, along the direction from the rear edge of the slope to the front edge; k h k is the horizontal earthquake influence coefficient (positive when pointing to the front edge of the slope);v is the vertical (positive downward) earthquake influence coefficient; W m is the deadweight of the mth soil strip; is the internal friction angle of the sliding surface of the mth soil strip; g m is the cohesion of the sliding surface of the mth soil strip; α m is the horizontal inclination angle of the sliding surface of the mth soil strip; l m is the length of the sliding surface of the mth soil strip; F s Design safety factor for overall slope stability; ξ m-1 is the inter-strip force transfer coefficient between the m-1th and mth soil strips, and its calculation expression is:

[0044]

[0045] In the formula: when m=1, ξ0=0.

[0046] The method for calculating the static earth pressure is as follows:

[0047] The static earth pressure generated by the soil within the depth range of the local sliding body 70 is used as the soil force acting on the rear side of the rear vertical beam 30, and the soil pressure is distributed in a triangular shape and acts on the rear side of the rear vertical beam 30. The calculation expression is:

[0048]

[0049] Where: γ is the soil weight; z s The depth from the slope surface 60 vertically downward from the slope surface 60; is the internal friction angle of the soil behind the rear vertical beam 30; δ is the inclination angle of the slope 60; η is the earthquake angle, and its calculation expression is:

[0050] Step 200, take half the length of the upper structure, and use the structural mechanics method to calculate the internal force of the upper structure when the bottom end of the front vertical beam or the rear vertical beam is not displaced; wherein, when the bottom end is not displaced, the bottom end rotation angle ω0=0, and the corresponding internal force of the upper structure includes the beam bending moment M of the front vertical beam or the rear vertical beam CF0 , the beam shear force Q of the front vertical beam or the rear vertical beam CF0 , beam bending moment M of top beam BC0 , the shear force of the top beam Q BC0 , the bending moment M at the bottom of the front vertical beam or the rear vertical beam F0 .

[0051] Step 300: Take a half-length bottom beam and calculate the internal force, cross-sectional rotation angle, deflection of the bottom beam and the bottom end rotation angle ω of the current front vertical beam or rear vertical beam according to the Winkler elastic foundation beam model. j , j is the number of iterations, j ≥ 1.

[0052] Step 400, using structural mechanics method to recalculate the bottom angle ω j The additional internal force of the superstructure caused by the above mentioned additional internal force includes the additional bending moment M of the front vertical beam or the rear vertical beam. CFj , additional shear force Q of the front vertical beam or rear vertical beam CFj , Additional bending moment of top beam M BCj , additional shear force Q of the top beam BCj , additional bending moment M at the bottom of the front vertical beam or rear vertical beam Fj .

[0053] Step 500, select the internal force of any one of the rear vertical beam, the front vertical beam and the top beam as the control condition, and judge whether the absolute value of the relative error between the "sum of the internal force and the additional internal force" and the internal force meets the calculation accuracy requirement: if the calculation accuracy requirement is met, the calculation is completed; if the calculation accuracy requirement is not met, the "sum of the internal force and the additional internal force" at the bottom end of the rear vertical beam or the front vertical beam replaces its internal force and then returns to step 300 to perform iterative calculations in sequence.

[0054] Figure 3 FIG. 2 is a schematic diagram of the force analysis of the entire upper structure of the prefabricated slope normal frame anchoring structure of the present invention. In step 200 and step 400, as Figure 3 As shown, the upper structure can be regarded as a plane rigid frame subjected to bilaterally symmetrical triangular loads, wherein ABCD is the top beam, the top beam body refers to the area between the longitudinal axes of the front vertical beam and the rear vertical beam (i.e., the BC segment); the node B is the node of the front vertical beam and the top beam; the node C is the node of the rear vertical beam and the top beam; the beam body of the front vertical beam or the rear vertical beam is composed of the area between the bottom beam and the top beam (the CF segment or the BE segment) and the area at half the height of the bottom beam in the height direction of the bottom beam.

[0055] For the convenience of expression, the linear stiffness is introduced here, and its expression is:

[0056]

[0057] In the formula, i1 is the linear stiffness of the front vertical beam or the rear vertical beam; i2 is the linear stiffness of the top beam; I1 is the cross-sectional moment of inertia of the front vertical beam or the rear vertical beam; I2 is the cross-sectional moment of inertia of the top beam; E is the elastic modulus of the beam concrete; L1 is the length of the front vertical beam or the rear vertical beam, which is equal to the sum of the net length of the CF section and half the height of the bottom beam; L2 is the length of the top beam, which is equal to the distance between the longitudinal axes of the front vertical beam and the rear vertical beam.

[0058] Since the upper structure is subjected to symmetrical triangular loads, and the angular displacements at point E at the bottom end of the front vertical beam and point F at the bottom end of the rear vertical beam appear symmetrically, node B and node C have a pair of positively symmetrical angular displacements Δ.

[0059] Figure 4 The figure is a schematic diagram of the force analysis of the upper structure of half the length of the prefabricated slope normal frame anchoring structure of the present invention. Figure 4 As shown, according to the symmetry of the superstructure, taking the half-length superstructure composed of the rear vertical beam and the half-length top beam for calculation, the basic static equilibrium equation can be established as:

[0060] r 11 Δ+R 1C =0 (7)

[0061] In the formula, r 11 is the moment caused at node C when unit angular displacement occurs at node C; R 1C It is the reaction moment generated in the additional rigid arm at the node C under the action of the rotation angle F at the bottom end of the rear vertical beam.

[0062] According to the standard shape constant and load constant table in structural mechanics (Yang Dixiong, ed. Structural Mechanics. Beijing: Science Press, 2019), R 1C and r 11 The expressions are:

[0063] r 11 =-2i2-4i1 (8)

[0064]

[0065] Where ω is the rotation angle of the bottom end F of the rear vertical beam, with clockwise rotation being positive.

[0066] The variable R 1C and r 11 Substituting into equation (7), we can get the angular displacement Δ0 and Δ j The calculation expressions are:

[0067]

[0068] Therefore, the bending moment diagram of the plane frame structure can be drawn by superposition method. For the rear vertical beam, its local coordinate system can take node C as the origin, and the z-axis is the positive direction along the longitudinal axis of the rear vertical beam. The calculation expressions of the internal force and additional internal force of the upper structure are as follows:

[0069] Bending moment of rear vertical beam M CF0 and additional bending moment M CFj The calculation expressions are:

[0070]

[0071] Shear force Q of the rear vertical beam CF0 and additional shear force Q CFj The calculation expressions are:

[0072]

[0073]

[0074] The bending moment of the top beam M BC0 and additional bending moment M BCj The calculation expressions are:

[0075]

[0076] Shear force Q of top beam BC0 and additional shear force Q BCj The calculation expressions are:

[0077] Q BC0 =0 (18)

[0078] Q BCj =0 (19)

[0079] Bending moment M at the bottom end F of the rear vertical beam F0 and additional bending moment M Fj The calculation expressions are:

[0080]

[0081] In the formula, It means that ω0=0 is taken in the expression on its left side; It means that q1=0 is taken in the expression on its left side; q1 is the bottom value of the triangular distributed load; z is the length along the longitudinal axis direction of the front vertical beam or the rear vertical beam, starting from the intersection of the front vertical beam or the rear vertical beam and the top beam.

[0082] Since the CD section of the top beam is not subjected to load and point D is a free end, the static equilibrium theory shows that the internal force of the CD section of the top beam is zero.

[0083] In step 300, the bottom beam is regarded as a beam structure on an elastic foundation, bearing the reaction force of the foundation soil layer, the anchor tension and the moment transmitted from the upper structure through its bottom ends E and F. The internal force and displacement of the bottom beam are calculated according to the Winkler elastic foundation beam model (Long Yuqiu. Calculation of elastic foundation beams. Beijing: People's Education Press, 1981).

[0084] Figure 5 The figure is a schematic diagram of the force analysis of the half-length bottom beam in the prefabricated slope normal frame anchoring structure of the present invention. Considering the force symmetry of the bottom beam, Figure 5The bottom beam of half the length shown is analyzed. The internal forces of the bottom beam include bending moment M and shear force Q. The positive direction of bending moment M is positive when the bottom side is tensile, and the positive direction of shear force Q is positive when it rotates clockwise around the isolation body; the positive direction of the deflection y of the bottom beam is positive vertically downward, and the positive direction of the cross-sectional rotation angle θ is positive when it rotates clockwise.

[0085] Using the initial parameter calculation method, when the bending moment at the bottom end of the rear vertical beam is selected as the control condition, the calculation expression of the bending moment M of the bottom beam is:

[0086]

[0087] The calculation expression of the shear force Q of the bottom beam is:

[0088] Q=4y0EIβ 3 φ2+4θ0EIβ 2 φ3-4M0βφ4+Q0φ1|| c -4M F0 βφ4[β(xc)]|| b -Pφ1[β(xb)](23)

[0089] The calculation expression of the deflection y of the bottom beam is:

[0090]

[0091] The calculation formula for the cross-sectional rotation angle θ of the bottom beam is:

[0092]

[0093] Where β is the characteristic coefficient of the bottom beam, k=k0t, k0 is the elastic resistance coefficient of the soil layer under the bottom beam, t is the cross-sectional width of the bottom beam; EI is the bending stiffness of the bottom beam; x is the horizontal distance from any point on the bottom beam to the midpoint of the bottom beam length; || c It indicates the additional correction term when the right-hand side term is x>c, where c is the horizontal distance from the bottom end of the rear vertical beam or the front vertical beam on the bottom beam to the midpoint of the bottom beam length; || b It represents the additional correction term when the right-hand side term is x>b, where b is the horizontal distance between the design anchor tension action point of a single anchor rod on the bottom beam and the midpoint of the bottom beam length.

[0094] The cross-sectional rotation angle θ of the bottom beam when x=c is the bottom end rotation angle ω of the front vertical beam or the rear vertical beam. j , its calculation expression is:

[0095]

[0096] In the formula, y0, θ0, M0, and Q0 are the initial parameters of the vertical displacement, cross-sectional rotation, bending moment, and shear force of the bottom beam, respectively, which can be determined by the boundary conditions at the end points and midpoints of the bottom beam, namely:

[0097] θ| x＝0 =0Q| x＝0 =0

[0098] M| x＝a =0 Q| x＝a =0 (27)

[0099] Where a is half the length of the bottom beam.

[0100] φ1, φ2, φ3, φ4 are Krylov functions, and their calculation expressions are:

[0101]

[0102] Where e is the natural index.

[0103] P is the design anchor tension of a single anchor rod, and the calculation expression is:

[0104]

[0105] In the formula, is the average internal friction angle of the soil at the most potentially dangerous sliding surface of the slope; r is the horizontal inclination angle of the sliding surface tangent at the intersection of the anchor and the most potentially dangerous sliding surface; ψ is the angle between the anchor and the horizontal plane; λ is the reduction factor, which should be appropriately reduced according to the slope conditions in accordance with the "Code for Design of Railway Roadbed Support Structures (TB 10025-2019)", and can generally be taken as 0.9.

[0106] E 0 N The calculation expression for the overall design landslide thrust of the slope is:

[0107]

[0108] Where: E 0 u is the residual sliding force of the u-th soil strip, u = 1 ~ N, N is the total number of strips vertically divided from the back to the front of the entire potential sliding body surrounded by the slope surface and the most potentially dangerous sliding surface; W u is the deadweight of the u-th soil strip; is the internal friction angle of the sliding surface of the u-th soil strip; g u is the cohesion of the sliding surface of the u-th soil strip; α u is the horizontal inclination angle of the sliding surface of the u-th soil strip; l u is the length of the sliding surface of the u-th soil strip; F s Design safety factor for overall slope stability; ξ u-1is the inter-strip force transfer coefficient between the u-1th and uth soil strips, and its calculation expression is:

[0109]

[0110] In the formula, when u=1, ξ0=0.

[0111] The internal force of any one of the rear vertical beam, the front vertical beam and the top beam is selected as the control condition in step 500. Taking the upper structure having half the length of the rear vertical beam as an example, there are several implementation methods as follows:

[0112] 1. Select the bending moment of the rear vertical beam as the control condition and determine M CFj +M CF0 With M CF0 Whether the absolute value of the relative error meets the calculation accuracy requirements: If it does, the calculation is completed; if the absolute value of the relative error does not meet the calculation accuracy requirements, M Fj +M F0 Replace M F0 Then return to step 300 to perform iterative calculations in sequence.

[0113] 2. Select the shear force of the rear vertical beam as the control condition and determine Q CFj +Q CF0 With Q CF0 Whether the absolute value of the relative error meets the calculation accuracy requirements: If it does, the calculation is completed; if the absolute value of the relative error does not meet the calculation accuracy requirements, M Fj +M F0 Replace M F0 Then return to step 300 to perform iterative calculations in sequence.

[0114] 3. Select the bending moment of the top beam as the control condition and determine M BCj +M BC0 With M BC0 Whether the absolute value of the relative error meets the calculation accuracy requirements: If it does, the calculation is completed; if the absolute value of the relative error does not meet the calculation accuracy requirements, M Fj +M F0 Replace M F0 Then return to step 300 to perform iterative calculations in sequence.

[0115] 4. Select the bending moment at the bottom of the rear vertical beam as the control condition and determine M Fj +M F0 With M F0 Whether the absolute value of the relative error meets the calculation accuracy requirements: If it does, the calculation is completed; if the absolute value of the relative error does not meet the calculation accuracy requirements, M Fj +MF0 Replace M F0 Then return to step 300 to perform iterative calculations in sequence.

[0116] The beneficial effects of the present invention are described below through specific application examples.

[0117] In the embodiment of the present invention, the soil around the pipeline in the slope is a sand layer, and its main physical and mechanical parameters are shown in Table 1. Below the sand layer is sandstone. The slope surface inclination angle δ = 30°. The foundation elastic resistance coefficient of the soil layer below the bottom beam k0 = 80000 kN / m 3 , the horizontal earthquake influence coefficient is taken as k h =0.2, the vertical earthquake influence coefficient is taken as k v =0.1, the overall stability design safety factor of the slope F s Take it as 1.15. The center distance S between two adjacent frame anchor structures along the slope direction is 3m. The frame anchor structure is a reinforced concrete structure, the concrete grade is C30, and the elastic modulus E = 30GPa. The angle between the anchor rod and the horizontal plane is ψ = 60°, and λ = 0.9 is taken. In addition, take n = 10 and N = 20. The calculation accuracy requirement is that the absolute value of the relative error of the calculation result does not exceed 1%.

[0118] Figure 6 : is a dimension parameter diagram of the prefabricated slope normal frame anchoring structure in an embodiment of the present invention. Figure 6 As shown, the dimensions of the top beam and bottom beam in the frame anchoring structure are 60 cm wide × 60 cm high × 300 cm long, the dimensions of the front vertical beam and the rear vertical beam are 30 cm wide × 30 cm high × 90 cm net length, b = 1.1 m, d0 = 0.9 + 0.6 / 2 = 1.2 m, L1 = 1.2 m, L2 = 1.1 m, c = 0.55 m, a = 1.5 m, I1 = 0.000675 m 4 , I2=0.0108m 4 .

[0119] Table 1

[0120]

[0121] According to step 100, the most potentially dangerous sliding surface in the shallow surface of the slope is searched out using the standard method (Technical Code for Building Slope Engineering (GB50330-2013)), and d1 = 2.26 m is obtained.

[0122] Substituting the relevant parameters into equations (1) to (3), we can calculate that the design landslide thrust on the rear side of the rear vertical beam is E L n =53kN / m, corresponding q1=75kN / m.

[0123] Substituting the relevant parameters into formula (4), we can calculate: q1 = 59.2 kN / m.

[0124] Therefore, the larger value of the two, 75kN / m, is taken as the adopted value of q1.

[0125] According to step 200, the relevant parameters are substituted into equations (5), (6), and 10, and we can obtain: i1 = 16.875MN.m 2 / m, i2=294.545MN.m 2 / m, Δ0=-5.48×10 -6 rad.

[0126] Substituting the relevant parameters into equations (10), (12), (14), (16), (18) and (20), the internal forces of the superstructure when ω0 = 0 are obtained as follows:

[0127] M CF0 =-10z 2 +13.962z+3.23(kN·m);

[0128] Q CF0 = -20z + 13.962 (kN);

[0129] M BC0 =-3.23 (kN m);

[0130] Q BC0 =0;

[0131] M F0 =5.590kN·m.

[0132] According to step 300, based on the position of the most dangerous sliding surface, the horizontal inclination angle of the sliding surface tangent at the intersection of the anchor rod and the most dangerous sliding surface is r = 28°. Substituting the relevant parameters into equations (29) and (30), the following can be calculated: the design anchor tension of a single anchor rod P = 123 kN, the overall design landslide thrust E of the slope 0 N =47.2kN / m.

[0133] Substituting the relevant parameters into equations (22) to (25), the bending moment M, shear force Q, deflection y and cross-sectional rotation angle θ of the bottom beam can be calculated and the results are shown in Table 2.

[0134] Table 2

[0135]

[0136]

[0137] When x = c = 0.55m, the cross-sectional rotation angle θ of the bottom beam is the bottom end rotation angle ω of the front vertical beam or the rear vertical beam.j , that is, ω1=5.523×10 -5 .

[0138] According to step 400, the relevant parameters are substituted into equations (11), (13), (15), (17), (19) and (21), and we can obtain ω1 = 5.523 × 10 -5 The additional internal forces of the superstructure at this time are as follows:

[0139] Δ1=2.8419×10 -6 rad;

[0140] M CF1 =4.425z-1.6742(kN·m);

[0141] Q CF1 =4.4251(kN);

[0142] M BC1 =1.6742(kN·m);

[0143] Q BC1 =0;

[0144] M F1 =3.636kN·m.

[0145] By updating the internal force of the superstructure, the sum of the internal force and the additional internal force in the superstructure is as follows:

[0146] M CF0 +M CF1 =-10z 2 +18.387z+1.5558(kN·m);

[0147] Q CF0 +Q CF1 = -20z + 18.387 (kN);

[0148] M BC0 +M BC1 =-1.5558(kN·m);

[0149] Q BC0 +Q BC1 =0;

[0150] M F0 +M F1 =5.590+3.636=9.226kN·m.

[0151] According to step 500, the bending moment at the bottom of the rear vertical beam is selected as the control condition, and M F1 +M F0 =9.226kN.m and the previous calculation result MF0 =5.590 kN.m. The absolute value of the relative error between the two is (9.226-5.590) / 9.226=39%, which exceeds 1% and does not meet the calculation accuracy requirement. Therefore, the iterative calculation is performed as follows:

[0152] Replace M with 9.226 kN.m F0 , calculate again according to step 300 and step 400, and get M F2 +M F0 =8.822 kN.m, compared with the previous calculation result of 9.226 kN.m, the absolute value of the relative error between the two is (9.226-8.822) / 8.822=4.5%, which exceeds 1% and does not meet the calculation accuracy requirement;

[0153] Then replace M with 8.822 kN.m F0 , calculate again according to step 300 and step 400, and get M F3 +M F0 =8.866kN.m, compared with the previous calculation result of 8.822kN.m, the absolute value of the relative error between the two is (8.866-8.822) / 8.866=0.5%, which does not exceed 1%, meeting the calculation accuracy requirement, and the calculation is completed. The sum of the internal force and the additional internal force in the upper structure obtained from the last calculation is the calculated value of the internal force of the upper structure.

[0154] Figure 7 It is a comparison diagram of the bending moment calculation results of the prefabricated slope normal frame anchoring structure of the present invention and the FLAC3D numerical simulation results. Figure 8 It is a comparison diagram of the shear force calculation results of the prefabricated slope normal frame anchoring structure of the present invention and the FLAC3D numerical simulation results.

[0155] like Figure 7-8 As shown in the figure, the calculation results of the present invention and the FLAC3D numerical simulation results show the same distribution characteristics, and the two are relatively close, with a difference of 9.5% in the maximum bending moment and 0.6% in the maximum shear force. It can be seen that the calculation results of the upper structure internal force by the two methods are of the same order of magnitude, and the difference between the two is small, indicating that the theoretical calculation method of the present invention is reasonable.

[0156] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without creative work shall fall within the scope of protection of the present invention.

Claims

1. A method for calculating the internal force of a prefabricated slope normal frame anchor structure, wherein the frame anchor structure comprises anchor rods, bottom beams, rear vertical beams and front vertical beams located on the inner side of the slope and a top beam located on the outer side of the slope, characterized in that: The internal force calculation method includes the following steps: Step 100, the upper structure composed of the rear vertical beam, the front vertical beam and the top beam is regarded as a plane rigid frame structure with a fixed bottom end, and the local soil force borne by the rear side of the rear vertical beam from the length range thereof and the local soil force borne by the front side of the front vertical beam from the length range thereof are simplified into triangular distributed loads, and the bottom value of the triangular distributed load is calculated; Step 200, taking half the length of the upper structure, and using a structural mechanics method to calculate the internal force of the upper structure when the bottom end of the front vertical beam or the rear vertical beam is not displaced; Step 300: Take a half-length bottom beam and calculate the internal force, cross-sectional rotation angle, and the bottom end rotation angle ω of the current front vertical beam or rear vertical beam according to the Winkler elastic foundation beam model. j , j is the number of iterations, j ≥ 1; Step 400, using structural mechanics method to recalculate the bottom angle ω j The additional internal forces of the superstructure caused; Step 500, select the internal force of the rear vertical beam or the front vertical beam as the control condition, and judge whether the absolute value of the relative error between the "sum of the internal force and the additional internal force" and the internal force meets the calculation accuracy requirement: if the calculation accuracy requirement is met, the calculation is completed; if the calculation accuracy requirement is not met, the "sum of the internal force and the additional internal force" at the bottom end of the rear vertical beam or the front vertical beam replaces its internal force and then returns to step 300 to perform iterative calculations in sequence.

2. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 1 is characterized in that: In step 100, the bottom value of the triangular distributed load is taken as the larger value of two calculated values ​​calculated according to the local landslide thrust and the static earth pressure.

3. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 1 is characterized in that: In step 200, when there is no displacement at the bottom, the bottom rotation angle ω0=0 is taken, and the corresponding internal forces of the upper structure include the beam bending moment M of the front vertical beam or the rear vertical beam. CF0 , the beam shear force Q of the front vertical beam or the rear vertical beam CF0 , beam bending moment M of top beam BC0 , the shear force of the top beam Q BC0 , the bending moment M at the bottom of the front vertical beam or the rear vertical beam F0 ; In step 400, the additional internal force of the superstructure includes the additional bending moment M of the front vertical beam or the rear vertical beam. CFj , additional shear force Q of the front vertical beam or rear vertical beam CFj , Additional bending moment of top beam M BCj , additional shear force Q of the top beam BCj , additional bending moment M at the bottom of the front vertical beam or rear vertical beam Fj .

4. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 3 is characterized in that: The beam bending moment M of the front vertical beam or rear vertical beam CF0 and additional bending moment M CFj The calculation expressions are: Shear force Q of the front or rear vertical beam CF0 and additional shear force Q CFj The calculation expressions are: The bending moment of the top beam M BC0 and additional bending moment M BCj The calculation expressions are: Shear force Q of top beam BC0 and additional shear force Q BCj The calculation expressions are: Q BC0 ＝0； Q BCj ＝0； Bending moment M at the bottom end of the front or rear vertical beam F0 and additional bending moment M Fj The calculation expressions are: In the formula, It means that ω0=0 is taken in the expression on its left side; It means that q1=0 is taken in the expression on the left side, q1 is the bottom value of the triangular distributed load; i1 is the beam body linear stiffness of the front vertical beam or the rear vertical beam; i2 is the beam body linear stiffness of the top beam; I1 is the cross-sectional inertia moment of the beam body of the front vertical beam or the rear vertical beam; I2 is the cross-sectional inertia moment of the beam body of the top beam; E is the elastic modulus of the beam body concrete; L1 is the beam body length of the front vertical beam or the rear vertical beam; L2 is the beam body length of the top beam; z is the length along the longitudinal axis direction of the front vertical beam or the rear vertical beam with the intersection of the front vertical beam or the rear vertical beam and the top beam as the starting point; Δ0 and Δ j is the angular displacement at the intersection of the top beam and the rear vertical beam or the front vertical beam, and the calculation expression of Δ0 is: Δ j The calculation expression is: The beam body of the front vertical beam or the rear vertical beam is composed of the area between the bottom beam and the top beam and the area at half the bottom beam height in the bottom beam height direction; the beam body of the top beam refers to the area between the longitudinal axes of the front vertical beam and the rear vertical beam.

5. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 4 is characterized in that: In step 500, the bending moment at the bottom of the front vertical beam or the rear vertical beam is selected as the control condition to determine M Fj +M F0 With M F0 Whether the absolute value of the relative error meets the calculation accuracy requirements: If it does, the calculation is completed; if the absolute value of the relative error does not meet the calculation accuracy requirements, M Fj +M F0 Replace M F0 Then return to step 300 to perform iterative calculations in sequence.

6. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 5 is characterized in that: In step 300, the internal force of the bottom beam includes the bending moment M and shear force Q of the bottom beam; The calculation expression of the bending moment M of the bottom beam is: The calculation expression of the shear force Q of the bottom beam is: Q=4y0EIβ 3 φ2+4θ0EIβ 2 φ3-4M0βφ4+Q0φ1|| c -4M F0 βφ4[β(xc)]|| b -Pφ1[β(xb)]; The calculation formula for the cross-sectional rotation angle θ of the bottom beam is: Where y0, θ0, M0, and Q0 are the initial parameters of the vertical displacement, cross-sectional rotation, bending moment, and shear force of the bottom beam, respectively, which can be determined by the boundary conditions at the end points and midpoints of the bottom beam; β is the characteristic coefficient of the bottom beam, k=k0t, k0 is the elastic resistance coefficient of the soil layer under the bottom beam, t is the cross-sectional width of the bottom beam; EI is the bending stiffness of the bottom beam; x is the horizontal distance from any point on the bottom beam to the midpoint of the bottom beam length; || c It indicates the additional correction term when the right-hand side term is x>c, where c is the horizontal distance from the bottom end of the rear vertical beam or the front vertical beam on the bottom beam to the midpoint of the bottom beam length; || b It represents the additional correction term when the right-hand side term is x>b, b is the horizontal distance between the design anchor tension action point of a single anchor rod on the bottom beam and the midpoint of the bottom beam length; P is the design anchor tension of a single anchor rod; φ1, φ2, φ3, φ4 are Krylov functions; The cross-sectional rotation angle θ of the bottom beam when x=c is the bottom end rotation angle ω of the front vertical beam or the rear vertical beam. j , its calculation expression is:

7. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 6 is characterized in that: Step 300 also includes calculating the deflection y of the bottom beam, and the calculation expression is:

8. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 6 is characterized in that: The calculation expression of the design anchor tension P of a single anchor is: in, is the average internal friction angle of the soil at the most dangerous potential sliding surface of the slope; r is the horizontal inclination angle of the tangent line of the sliding surface at the intersection of the anchor rod and the most dangerous potential sliding surface of the slope; ψ is the angle between the anchor rod and the horizontal plane; λ is the reduction coefficient; E 0 N is the overall designed landslide thrust of the slope; S is the center distance between two adjacent frame anchor structures along the slope.

9. The internal force calculation method of the prefabricated slope normal frame anchor structure according to claim 8, characterized in that: Overall design landslide thrust E 0 N The calculation expression is: Where: E 0 m is the residual sliding force of the mth soil strip, m = 1 ~ N, N is the total number of strips vertically divided from the back to the front of the entire potential sliding body surrounded by the slope surface and the most potentially dangerous sliding surface; k h is the horizontal earthquake influence coefficient; k v is the vertical earthquake influence coefficient; W m is the deadweight of the mth soil strip; is the internal friction angle of the sliding surface of the mth soil strip; g m is the cohesion of the sliding surface of the mth soil strip; α m is the horizontal inclination angle of the sliding surface of the mth soil strip; l m is the length of the sliding surface of the mth soil strip; F s Design safety factor for overall slope stability; ξ m-1 is the inter-strip force transfer coefficient between the m-1th and mth soil strips, and its calculation expression is: And ξ0=0.

Images