Analytic calculation method for retaining-overhanging-supporting special roadbed structure

Abstract

The invention discloses an analytic calculation method for a retaining-overhanging-supporting special roadbed structure, the structure generally comprises four parts, namely an inner-side sheet-pile wall, a cross beam, an outer-side supporting column and a pavement slab, and the method comprises the following specific steps: firstly, solving an internal force value acting on a node of a pile and the beam according to a load distribution form; and then constructing a structural static equilibrium equation set at the special node. Separating the equation set according to parameter categories to obtain a corresponding matrix equation; and further solving a to-be-solved parameter (namely a structure initial parameter matrix) by adopting a matrix method. And finally, substituting the to-be-solved parameters into the analytical formula to obtain an internal force and deformation formula of the structure. According to the supporting-retaining-overhanging structure analytical calculation method, the situation that the structure lacks a reasonable calculation method at present is made up, and the method has a clear mathematical mechanics concept and a definite structure stress and deformation mechanism, has higher calculation efficiency compared with a numerical solution, and is suitable for large-scale popularization and application. The method is more suitable for engineering calculation and design parameter optimization analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of geotechnical engineering and structural engineering, and particularly relates to a special "retaining-cantilever-support" roadbed structure used for a semi-filled and semi-cut section in road route design. The present invention aims to provide an analytical calculation method for the structure under complex geological conditions. Background Art

[0002] In view of the engineering problems of half-filled and half-cut sections in road route design, the traditional single retaining roadbed structure is often difficult to cope with complex geological conditions and engineering requirements due to its design limitations. In this context, the "retaining-cantilever-support" special roadbed structure, as a new type of combined structure, has shown more superior mechanical properties, economic benefits and terrain adaptability due to its comprehensive bending resistance of piles and beams, as well as the function of beams to widen the roadbed.

[0003] The special roadbed structure of "retaining-cantilevering-supporting" is mainly composed of four parts: inner pile-sheet wall, crossbeam, outer support column and road slab. The inner pile-sheet wall is used to resist soil pressure and ensure structural stability; the crossbeam plays the role of distributing load and increasing the width of the roadbed; the outer support column is used to support the crossbeam, reduce the length of the cantilever end and thus ensure the driving safety of the road surface; the road slab is laid on the top of the structure to form a complete driving surface. The special roadbed structure of "retaining-cantilevering-supporting" is complex. How to consider the deformation coordination of the crossbeam and the pile body under the overall force effect of the combined structure, and the interaction between the pile body and the deep soil, and the crossbeam and the surface soil is a key issue.

[0004] At present, this structure has shown good economic and environmental benefits in actual engineering, but there are still deficiencies in theoretical calculation and a lack of systematic calculation methods. Therefore, it is urgent to develop an analytical calculation method that can accurately reflect the characteristics of the "retaining-cantilever-support" special roadbed structure to guide engineering practice and ensure the safety and reliability of structural design. Summary of the invention

[0005] The purpose of the present invention is to propose an analytical calculation method for a special roadbed structure of "retaining-cantilever-support".

[0006] In order to achieve the above objectives and ideas, the present invention adopts the following technical solutions: S1, the load acting on the inner pile wall is calculated according to the geomechanical model. For slopes with obvious sliding surfaces, the landslide thrust is used for calculation. For homogeneous and granular rock and soil, the Coulomb active earth pressure theory is used for calculation. In the case of cohesive-free soil, the Rankine earth pressure theory is used for calculation. For field measured data, the measured data are used. S2, calculate the total bending moment, shear force and axial force of the above loads acting on the pile and beam nodes; S3, at the pile-beam node (point O), the boundary between the beam and the rock and soil (point A), the intersection of the beam and the supporting column (point B), and the boundary of the anchor section stratum (point C), a group of structural static equilibrium equations are established based on the assumptions of internal force continuity and deformation coordination. S4, using the matrix method to solve the above equations, separating the parameters to be solved from the known parameters in the equations, forming a stiffness matrix, a structural initial parameter matrix and an external load matrix equation similar to the form of [K][V]=[P], and using the matrix inversion method to inversely solve the parameters to be solved; S5, substitute the initial parameters of the structure into the analytical formulas of structural displacement, rotation, bending moment and shear force, and finally obtain the formulas of internal force and deformation at any cross section of the structure.

[0007] Further, the structural static equilibrium equations constructed according to internal force continuity and deformation coordination at the pile-beam node (point O), the boundary between the beam and the rock and soil (point A), the intersection of the beam and the support column (point B), and the boundary of the anchoring section stratum (point C) described in step S3 are specifically composed of: (1) At the pile-beam node (point O), the bending moment is distributed based on the assumption that the beam and pile have the same rotation angle. (2) In the local coordinate system of the beam, the bending moment and shear force of the beam are continuous at x = L1 (point A); and the vertical displacement is coordinated with the bottom of the supporting column at x = L1 + l2 (point B). (3) In the local coordinate system of the pile, the bending moment and shear force are continuous, and the horizontal displacement and rotation are coordinated at the ground interface of the anchoring section at x = H1 (point C); and the bending moment and shear force at the bottom of the pile are zero at x = H1 + H2 (point D). Let the bending moment be positive in the clockwise direction and the shear force be positive when the cross section rotates clockwise, and the following static equilibrium equations can be obtained: in: Where: M, M0, M 0b 、M i It is the total bending moment at point O, the distributed bending moment of the pile body, the distributed bending moment at the beam end, and the bending moment at the i-th section of the pile body, in kN·m. 0b , Q i The shear force of the pile at point O, the shear force at the beam end, and the shear force at the i-th section of the pile, unit: kN. 0b ,y i θ is the vertical displacement of the beam end at point O in the local coordinates and the vertical displacement of the pile at the i-th section, unit: m. 0b ,θ i It is the beam end rotation angle at point O in the local coordinates and the rotation angle at the i-th section of the pile body, unit: rad. G p , P ay ,q G ,q vIt is the deadweight of the pile, the vertical component of the soil pressure behind the pile, the uniformly distributed load superimposed on the beam and the road slab, and the uniformly distributed load of the vehicle, unit: kN. K B , K D It is the equivalent spring coefficient of the foundation reaction force at the bottom of the support column, the equivalent spring coefficient of the resultant force of the foundation reaction force at the bottom of the pile and the friction resistance on the side of the pile, unit: kN / m. B 、F D E is the foundation reaction force at the bottom of the supporting column and pile, unit: kN. c I b 、E c I p 、E c A p is the bending stiffness of beams, bending stiffness of piles, and compressive stiffness, unit: kN·m 2 . k v , k hi is the vertical foundation resistance coefficient per unit width at the bottom of the beam and the horizontal foundation resistance coefficient per unit width of the i-th layer of soil, unit: kN / m 3 . H, H0, H i is the length of the pile, the length of the pile cantilever section, and the length of the pile anchoring section in different soil layers. i is the characteristic coefficient of beams and piles, Among them, B b , B p is the calculated width of the beam and pile (based on the actual width of the pile b+1). φ1(x)=chβxcosβx, is the Krylov function.

[0008] It is worth noting that in actual engineering applications, pile-sheet walls are often interspersed between 2-3 strata. Therefore, in the description, the static equilibrium equations under double strata conditions are selected as the preferred embodiment, and the number of stratum boundaries is one. If the number of strata increases, four additional equations should be added at each newly added stratum boundary to ensure that the assumption of continuity of the internal force of the structure at the stratum boundary is met.

[0009] Further, the separation of the parameters of the system of equations to form a matrix equation in step S4 is specifically described as follows: In the parameter separation step, the relevant structural size parameters, material parameters, cross-sectional property parameters, and foundation resistance coefficient items are refined to form the left stiffness matrix [K]; the initial parameters (displacement, rotation, shear force, bending moment) of the starting and ending points of the structural segments are refined to form the structural initial parameter matrix [V]; and the external load items, including the bending moment and shear force acting on the retaining structure and various forces caused by vehicle loads, are refined to form the load matrix [P] on the right. The specific form still selects the double-stratum condition as the preferred embodiment, and the expansion calculation for other soil layers is also very convenient, that is, for each additional soil layer, the stiffness matrix [K] is expanded from 10×10 to 14×14, and the initial parameter matrix [V] is expanded from 10×1 to 14×1. For a single-layer soil foundation, the stiffness matrix in formula (5) is simplified to 6×6, and the initial parameter matrix is ​​simplified to 6×1. The specific matrix equations for the double-stratum condition are as follows: in:

[0010] Further, the analytical formula for substituting the initial structural parameters into the structural displacement, rotation angle, bending moment and shear force in step S5 is specifically described:

[0011] In terms of specific form, the double-layer condition and the vehicle load as a uniformly distributed load are used as the preferred implementation cases. For the layer conditions with more than two layers, it can be handled in the form of an extended pile body function. When dealing with external and internal distributed loads, if the outer load is considered, the length of the inner load is set to zero; on the contrary, if the inner load is concerned, the vehicle load arranged on the outer side is regarded as zero. The displacement, rotation, bending moment, and shear force functions of any cross section of the beam in the local coordinate system are:

[0012] The displacement, rotation, bending moment and shear force functions of any section of the pile in the local coordinate system are: BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of the analytical calculation method of the "retaining-cantilever-support" roadbed structure.

[0014] Figure 2 It is a schematic diagram of the "retaining-cantilever-support" roadbed structure.

[0015] Figure 3 It is a schematic diagram of calculation parameters of the “retaining-cantilever-support” roadbed structure.

[0013] Figure 4It is a schematic diagram of an implementation example of the present invention.

[0014] Figure 5 It is a bending moment diagram of pile body of implementation example.

[0015] Figure 6 It is a shear force diagram of the pile body of the implementation example.

[0016] Figure 7 It is a diagram of the horizontal rotation angle of the pile body of the implementation example.

[0017] Figure 8 It is the horizontal displacement diagram of the pile body of the implementation example.

[0018] Fig. 9 is an example beam bending moment diagram for implementation.

[0019] Fig.10 is an implementation example beam shear diagram.

[0020] Fig.11 is an example beam angle diagram of implementation.

[0021] Fig.12 is a diagram of the vertical displacement of a beam according to an implementation example. Fig.13 It is a comparison chart of pile bending moment. Fig.14 It is a comparison diagram of beam bending moment. DETAILED DESCRIPTION

[0022] The present invention is further described below in conjunction with an implementation example, but the present invention is not limited to this embodiment.

[0023] The present invention is used in a specific implementation example of a multi-lane highway subgrade design in a mountainous steep slope terrain. Figure 4 As shown in the figure, the surface of the mountain slope in the example is 2-3m thick slope soil, below which is 7-10m strongly weathered sandstone, and the deep part is weakly weathered sandstone. The joints and fissures are relatively developed, and no potential sliding surface is found in the slope. The cross section of the pile body is 2m×1.5m, the pile spacing is 5m, and the soil pressure of the mountain behind the pile-sheet wall is calculated according to the Coulomb active earth pressure formula. The dimensions of the structural section are: cross beam section 1.5m×1.5m, support column section 0.6m×0.6m, and expanded foundation bottom surface 1.2m×1.2m. The basic parameters such as materials, strata, and external loads are shown in Table 1. Table 1 Basic parameters of the example model

[0023] Figures 5 to 11The distribution characteristics of the structure in terms of bending moment, shear force, rotation angle and displacement are respectively shown. By carefully analyzing these internal forces and deformation modes, we can clearly understand the stress-deformation characteristics of the structure: the crossbeam and the pile body work together to effectively resist the soil pressure from behind the pile, resulting in a specific distribution pattern of the bending moment, which reduces the maximum bending moment value at the bottom of the pile body. At the same time, due to the different resistance provided by rock strata with different degrees of weathering to the pile side, this causes a significant change in the shear force of the pile body. In addition, the external support column not only effectively alleviates the sinking problem caused by the excessive length of the cantilever part, but also successfully reduces the maximum bending moment value at the top of the crossbeam, further optimizing the overall performance of the structure.

[0024] In order to verify the feasibility and correctness of the above theoretical calculation method, Figure 4 As an example, the structural internal forces are solved by analytical method, and the numerical solution of Midas GTS NX finite difference method is used for comparison and verification. The comparison of structural internal force deformation parameters at some key positions is shown in Table 2, and the comparison of pile body bending moment and beam bending moment is shown in Table 2. Fig.13 , 14 The structural internal force distribution obtained by the analytical method and the Midas GTS NX finite difference method is basically consistent, and the amplitude difference is less than 1‰. In this case, it takes about half an hour to model and solve using Midas software, while the analytical method implemented by programming can get very close results in less than one second. Therefore, the analytical solution has clear mathematical mechanics concepts, clear structural force and deformation mechanisms, high calculation efficiency and accuracy, and is more suitable for engineering calculation applications and design parameter optimization analysis than the numerical solution. Table 2 Comparison of analytical solution and numerical solution

Claims

1. A "retaining-cantilever-support" special roadbed structure analytical calculation method, characterized in that: The following steps are involved: S1, the load acting on the inner pile-sheet wall is calculated according to the geological-mechanical behavior model. For slopes with obvious sliding surfaces, the landslide thrust is used for calculation, while for homogeneous and granular rock and soil, the Coulomb active earth pressure theory is used for calculation. In the case of cohesive-free soil, the Rankine earth pressure theory is used for calculation. For field measured data, the measured data are used; S2, calculate the total bending moment, shear force and axial force acting on the pile and beam nodes; S3, establish the structural static equilibrium equations; S4, using a matrix method to solve the parameters to be solved in the above equations; S5, substituting the initial parameters of the structure into the analytical formulas of structural displacement, rotation, bending moment and shear force, the internal force and deformation values ​​at any cross section of the structure can be obtained.

2. The analytical calculation method of the "retaining-cantilever-support" special roadbed structure according to claim 1 is characterized by: The structural static equilibrium equation group described in step 3 is obtained based on the assumptions of internal force continuity and deformation coordination at the pile-beam node, i.e. point O, the boundary between the beam and the rock and soil, i.e. point A, the intersection of the beam and the supporting column, i.e. point B, and the boundary of the anchoring section, i.e. point C. The static equilibrium equation group is related to the number of strata interspersed by the pile-sheet wall. As the number of strata increases, four additional equations are added at each newly added stratum boundary.

3. The analytical calculation method of the "retaining-cantilever-support" special roadbed structure according to claim 1 is characterized by: The matrix method described in step 4 solves the parameters to be solved. First, the parameters to be solved in the equation group obtained in step 3 are separated from the known parameters to form a matrix equation form of [K][V]=[P], where [K] is the stiffness coefficient matrix, which reflects the overall stiffness of the structure and foundation, and its various equations are calculated based on the structural size, material parameters and soil layer parameters; the intermediate matrix [V] includes the initial parameters to be solved on the pile body section at the pile-beam node and the soil layer boundary; the right side of the equation is the external load matrix [P], which is related to the soil pressure, structural deadweight, and vehicle load; the matrix inversion method [V]=[K] -1 [P] Inversely solve the parameters to be solved, that is, the initial parameter matrix of the structure.

4. The analytical calculation method of the "retaining-cantilever-support" special roadbed structure according to claim 1 is characterized by: The analytical formulas for structural displacement, rotation, bending moment and shear force described in step 5 are derived based on the theory of elastic foundation beams under load and the principles of structural mechanics.

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