Method and device for calculating deflection of foundation pit support pile considering dynamic load effect of vehicle

Abstract

The invention discloses a method and a device for calculating deflection of a foundation pit support pile considering a vehicle dynamic load effect. The method comprises the following steps: constructing an active soil pressure calculation formula of a soil body on the side of the support pile under the vehicle dynamic load effect; constructing a pile body deflection differential equation below an excavation face and a pile body deflection differential equation above the excavation face according to an active soil pressure calculation formula of a soil body on the side of the support pile under the action of a vehicle dynamic load; and according to the pile body deflection differential equation below the excavation face and the pile body deflection differential equation above the excavation face, a segmentation independent coordinate method is adopted to segment the pile body according to the actual working condition, a deformation differential equation of each segment of the pile body is established, and meanwhile, the deformation differential equation of each segment of the pile body is introduced into the pile end boundary condition to calculate the deflection of the pile body. By adopting the technical scheme, the deformation of the support pile of the deep foundation pit close to the road can be calculated more accurately.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering calculation technology, specifically relating to a method and apparatus for calculating the deflection of foundation pit support piles considering the dynamic load of vehicles. Background Technology

[0002] Piles with steel bracing are widely used in deep foundation pit support engineering. The stress-deformation analysis of the support structure is a key focus of stability studies in deep foundation pit support engineering and a crucial issue in the design and construction of foundation pits.

[0003] Especially in urban foundation pit engineering, urban road vehicles continuously apply irregular cyclic loads around the foundation pit, weakening the strength of the support structure and causing damage.

[0004] Currently, national standards do not fully consider the impact of vibration on active earth pressure. They simplify vehicle loads to static loads and use the equivalent soil layer thickness method to convert the load to a soil layer with the same unit weight as the first layer of the roadbed, and then calculate the active earth pressure. However, the vibration characteristics of vehicles during operation vary, and their impact on active earth pressure is a complex issue.

[0005] On the other hand, most current calculation methods simplify the support structure into a rod structure, without considering the constraint effect of the lateral support on the pile deformation during the foundation pit excavation process, that is, without considering the changes in foundation pit support reaction force and structural deformation with the foundation pit excavation process. Summary of the Invention

[0006] To address the problems existing in the prior art, the present invention provides a method and apparatus for calculating the deflection of foundation pit support piles considering the dynamic load of vehicles.

[0007] To achieve the above objectives, the present invention provides the following solution: A method for calculating the deflection of foundation pit support piles considering vehicle dynamic loads, comprising: Construct a formula for calculating the active earth pressure on the side soil of the support pile under vehicle dynamic load; Based on the calculation formula of active earth pressure on the side soil of the support pile under vehicle dynamic load, the differential equation of pile deflection below the excavation surface and the differential equation of pile deflection above the excavation surface are constructed. Based on the differential equations of pile deflection below the excavation surface and above the excavation surface, the pile body is divided into segments according to the actual working conditions using the segmented independent coordinate method. Differential equations of pile deformation for each segment are established, and the pile deflection is calculated by simultaneously applying the differential equations of pile deformation for each segment and substituting them with the boundary conditions at the pile end.

[0008] As a preferred method, the segmented independent coordinate method is defined as follows: the pile body is divided into several units according to the location of the lateral support structure, the soil layer interface and the excavation surface as sub-nodes, and each pile unit establishes its own independent Cartesian coordinate system, and the pile body deflection differential equation is established segment by segment.

[0009] As a preferred option, the pile end boundary conditions are as follows: Fixed end: Simple branch end: Free end: in, x The depth of the pile. y This represents the magnitude of the pile's lateral deformation.

[0010] The present invention also provides a calculation device for the deflection of foundation pit support piles considering the dynamic load of vehicles, comprising: The first processing module is used to construct the calculation formula for the active earth pressure on the side soil of the support pile under the action of vehicle dynamic load. The second processing module is used to construct the pile deflection differential equation below the excavation surface and the pile deflection differential equation above the excavation surface based on the calculation formula of the active earth pressure of the support pile side soil under the action of vehicle dynamic load. The third processing module is used to divide the pile body into segments according to the actual working conditions, based on the differential equations of pile body deflection below the excavation surface and above the excavation surface, using the segmented independent coordinate method, to establish the differential equations of pile body deformation for each segment, and simultaneously calculate the pile body deflection by combining the differential equations of pile body deformation for each segment with the pile end boundary conditions.

[0011] As a preferred method, the segmented independent coordinate method is defined as follows: the pile body is divided into several units according to the location of the lateral support structure, the soil layer interface and the excavation surface as sub-nodes, and each pile unit establishes its own independent Cartesian coordinate system, and the pile body deflection differential equation is established segment by segment.

[0012] As a preferred option, the pile end boundary conditions are as follows: Fixed end: Simple branch end: Free end: in, x The depth of the pile. y This represents the magnitude of the pile's lateral deformation.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention considers the vibration effects of complex urban vehicle dynamic loads on the adjacent foundation pit soil and the nonlinear distribution of other factors. For deep foundation pit strata changes, the soil and rock resistance function is treated as a discontinuous distribution function. The constraint effect of lateral supports on the deformation of the structure during foundation pit excavation is considered; the internal forces and deformations of the pile-support structure continuously change with the progress of the work. The pile body is divided into several pile units according to the actual working conditions, and the pile deflection differential equation is established segment by segment. These improvements more closely approximate actual engineering conditions, reducing errors in the calculation of the stress and deformation of foundation pit support piles, and providing favorable support for the design and construction of support piles in deep foundation pit engineering. Attached Figure Description

[0014] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart illustrating the calculation method for the deflection of foundation pit support piles considering the dynamic load of vehicles, as described in an embodiment of the present invention. Figure 2 A calculation model for active diagram pressure under vehicle dynamic load; Figure 3 This is a schematic diagram of the stress on the pile body below the excavation surface; Figure 4 This is a schematic diagram of the stress on the pile body above the excavation surface; Figure 5 This is a schematic diagram for calculating the deflection of the pile body above the excavation surface; Figure 6 This is a schematic diagram for calculating the pile deflection below the excavation surface; Figure 7 A schematic diagram illustrating the dynamic changes of a vehicle under dynamic load. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] Example 1 like Figure 1 As shown, the present invention provides a method for calculating the deflection of foundation pit support piles considering the dynamic load of vehicles, including: Step 1: Construct the formula for calculating active earth pressure under vehicle dynamic load, and its model diagram is shown below. Figure 2 As shown Assuming that the vibration acceleration decreases as the distance between the vehicle and the pile increases, the horizontal and vertical vibration accelerations on the ground at a distance r from the vibration source center can be calculated using the following formula: in, The horizontal vibration acceleration of the ground at a distance r from the center of the vibration source is mm / s². The vertical vibration acceleration of the ground at a distance r from the center of the vibration source is measured in mm / s². for The horizontal vibration acceleration of the ground at that location is mm / s². for Vertical ground vibration acceleration at the location (mm / s²); The radius of the vibration source (m) is determined according to the standard. Distance from the center of the vibration source (m); The geometric attenuation coefficient, which is related to the vibration source radius, is taken as 0.3; The energy absorption coefficient of soil, s / m, is taken as 1.5 × 10⁻⁶. -4 s / m; Machine disturbance frequency (Hz).

[0019] The formula for the weight of an earth wedge is: in, The unit weight of the soil is kN / m³. 3 , ; ; The thickness of the uniformly distributed soil layer is given in meters.

[0020] Consider a thin element at depth z with thickness dz and mass as follows: The horizontal inertial force acting inside the sliding soil mass Vertical inertial force It can be obtained through integration: Considering the equilibrium of the horizontal forces on the sliding soil wedge, we can obtain: Considering the balance of forces in the vertical direction, we can obtain: Solvable equations The calculation formula is as follows: in, The active earth pressure acting on the retaining piles is expressed in kN. Horizontal inertial force on the soil wedge (kN); Vertical inertial force on the soil wedge (kN); Unit area pile-soil friction force / (kN / m) 3 ); Soil cohesion / (kN / m) 3 ); Failure angle of sliding soil / (°); Pile-soil external friction angle / (°); Angle of internal friction / (°).

[0021] The total active earth pressure can be defined as: in, This refers to the static earth pressure on the pile side caused by gravity. , These are the dynamic earth pressures acting on the pile side caused by horizontal inertial force and vertical inertial force, respectively. This is the reduction in earth pressure due to the effects of pile-soil friction and soil cohesion. Simultaneously, let... Let be the wavelength of a shear wave in a certain soil layer, in meters; , where is the longitudinal wave wavelength of a certain soil layer, in meters.

[0022] Finally, the solvable formula for the distribution of active earth pressure under vehicle dynamic load is as follows: in: Let be the pile-soil external friction angle (°). The rupture angle of the sliding soil mass is (°). It is the internal friction angle. The height of the support piles, The additional static load caused by the weight of pedestrians and vehicles. The acceleration due to gravity (m / s²) The horizontal acceleration vibration coefficient is... It is the vertical vibration acceleration. The radius of the earthquake source is 1. The distance between the vehicle and the pile (m). The wavelength (m) of the shear wave in the soil layer. Density of fill soil for wall thickness (kg / m3) Poisson's ratio, Road surface roughness wavelength (m). Geometric attenuation coefficient related to the vibration source radius The energy absorption coefficient of soil, Soil cohesion (kN·m3), Unit area pile-soil friction force (kN·m3) By using the formula for calculating active earth pressure under vehicle load, and selecting actual working condition parameters, the variation law of active earth pressure is analyzed, such as... Figure 7 As shown, the active earth pressure exhibits a sinusoidal variation.

[0023] Step 2: Construct the differential equation of pile deflection below the excavation surface. like Figure 3 As shown, a stress balance analysis is performed on the pile below the excavation surface, taking a single element as an example. dx We can obtain: in: For shear force, Let be the foundation resistance function. This refers to the external load acting on the unit. According to shear force in mechanics of materials Q With bending moment M The relationship can be obtained as follows: According to relevant knowledge in mechanics of materials, the deflection of a pile differs significantly from its length. Therefore, the bending differential equation can be approximated as follows: Assuming the pile has a uniform cross-section and is straight, then the pile stiffness and moment of inertia are constant. Therefore, the differential equation for pile deflection below the excavation surface is: in, It is the load function of the soil load above the excavation surface acting on the pile body below the excavation surface; This represents the foundation reaction function, and its distribution is related to the pile depth. x and the size of pile deformation y Closely related.

[0024] Step 3: Construct the differential equation for pile deflection above the excavation face. From the formula for the distribution of active earth pressure under vehicle dynamic load, it can be seen that under vehicle load, the pile body above the excavation surface is subjected to nonlinear dynamic active earth pressure, and the distribution of active earth pressure conforms to a sinusoidal variation law, such as... Figure 4 As shown, it is assumed that the load distribution varies with depth. x The change can be represented as: in, m 0 and m This is a proportionality constant, which can be found in the survey report or the "Pile Foundation Engineering Handbook". t The duration of the dynamic load.

[0025] The differential equation for the pile deflection above the excavation surface is then obtained as follows: Step 4: Determine the resistance functions of different strata below the excavation face. p = p(x, y) : in, m It is a proportionality constant. n For about depth x The index, different n The values ​​represent different soil resistance distribution patterns. b 0 The calculated width for pile deformation.

[0026] Step 5: Consider the impact of cross bracing during excavation. During deep foundation pit construction, layered construction with lateral supports is adopted to ensure safety. However, before each support is erected, the pile body has already undergone initial displacement at its corresponding position. At each support erection position, the actual elastic compression deformation of the pile body is the total displacement of the pile body calculated at a certain moment minus the initial displacement of the pile body at that support position.

[0027] Step 6: Using the piecewise independent coordinate method, establish the differential equations of pile deformation for each segment. The segmented independent coordinate method is as follows: the pile body is divided into several units according to the location of the lateral support structure, the soil layer interface and the excavation face. Each pile unit establishes its own independent Cartesian coordinate system, and the pile body deflection differential equation is established segment by segment.

[0028] Above the excavation surface, there are n support points in the foundation pit support structure, such as Figure 5 As shown, the pile body can be divided into n+1 continuous segments, with the segmentation points located at the interfaces between each support point and the soil layer. Selecting the i-th element segment, the corresponding deflection differential equation can be established by analyzing the force balance of that element segment, thus providing a unified expression for the pile element deflection differential equation: Where, in the formula, EI Indicates the pile stiffness; Indicates the intensity of active earth pressure distribution; For Calculate the width; for oi arrive o i+1 The distance between.

[0029] The general solution form of the pile element deflection differential equation can be obtained as follows: Below the excavation surface, the upper pile body has already deformed; therefore, the initial condition for the existence of the pile structure below the excavation surface at the origin is bending moment. M 0 and shear force Q 0 Its computational model is as follows Figure 6 As shown, the pile deflection equation can be obtained as follows: in, P l For The pile side load below the excavation surface of the foundation pit is generated in the soil layer due to the weight of the upper soil layer. x To calculate depth, b s To calculate the width, b 0 The width is calculated for the internal force deformation of the pile. m It is a constant and can be determined according to the actual engineering geological conditions.

[0030] The combined differential equations of pile element deflection and pile deflection ultimately yield the following set of equations for calculating the deflection of the retaining pile: When there are n supports, the pile unit is: n+2 For each segment, the deformation differential equations of each element are solved, corresponding to four undetermined parameters. Based on the pile end boundary conditions (the pile top is the free end and the pile bottom is the fixed end), the deformation continuity at the pile segment, and the static equilibrium conditions, four parametric equations can be obtained for the pile's boundary conditions at the top and bottom ends. n There are a total of road support and soil-rock interface n +2 At each node, by considering the deformation continuity condition and the force equilibrium condition at the node, we can obtain... 4(n+2 A system of equations consisting of ) parametric equations can then yield a total of 4 + 4(n + 2) = 4(n + 3) A parametric equation. Through... 4(n+3) The parametric equation can be solved. 4(n+ 3) By identifying the undetermined parameters, the solution to the differential equation of the pile's overall deflection can be obtained.

[0031] Furthermore, the boundary conditions at the pile tip are as follows: Fixed end: Simple branch end: Free end: in, x The depth of the pile. y This represents the magnitude of pile deformation.

[0032] Example 2 The present invention also provides a calculation device for the deflection of foundation pit support piles considering the dynamic load of vehicles, comprising: The first processing module is used to construct the calculation formula for the active earth pressure on the side soil of the support pile under the action of vehicle dynamic load. The second processing module is used to construct the pile deflection differential equation below the excavation surface and the pile deflection differential equation above the excavation surface based on the calculation formula of the active earth pressure of the support pile side soil under the action of vehicle dynamic load. The third processing module is used to divide the pile body into segments according to the actual working conditions, based on the differential equations of pile body deflection below the excavation surface and above the excavation surface, using the segmented independent coordinate method, to establish the differential equations of pile body deformation for each segment, and simultaneously calculate the pile body deflection by combining the differential equations of pile body deformation for each segment with the pile end boundary conditions.

[0033] As one embodiment of the present invention, the segmented independent coordinate method is defined as follows: the pile body is divided into several units according to the position of the lateral support structure, the soil layer interface and the excavation surface as sub-nodes, and each pile unit establishes its own independent Cartesian coordinate system, and the pile body deflection differential equation is established segment by segment.

[0034] As one embodiment of the present invention, the pile end boundary conditions are as follows: Fixed end: Simple branch end: Free end: in, x The depth of the pile. y This represents the magnitude of the pile's lateral deformation.

[0035] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the deflection of foundation pit support piles considering vehicle dynamic loads, characterized in that, include: Construct a formula for calculating the active earth pressure on the side soil of the support pile under vehicle dynamic load; Based on the calculation formula of active earth pressure on the side soil of the support pile under vehicle dynamic load, the differential equation of pile deflection below the excavation surface and the differential equation of pile deflection above the excavation surface are constructed. Based on the differential equations of pile deflection below the excavation surface and above the excavation surface, the pile body is divided into segments according to the actual working conditions using the segmented independent coordinate method. Differential equations of pile deformation for each segment are established, and the pile deflection is calculated by simultaneously applying the differential equations of pile deformation for each segment and substituting them with the boundary conditions at the pile end.

2. The method for calculating the deflection of foundation pit support piles considering vehicle dynamic loads as described in claim 1, characterized in that, The segmented independent coordinate method is defined as follows: the pile body is divided into several units according to the location of the lateral support structure, the soil layer interface and the excavation face as the sub-nodes. Each pile unit establishes its own independent Cartesian coordinate system, and the pile body deflection differential equation is established segment by segment.

3. The method for calculating the deflection of foundation pit support piles considering vehicle dynamic loads as described in claim 2, characterized in that, The boundary conditions at the pile tip are as follows: Fixed end: Simple branch end: Free end: in, x The depth of the pile. y This represents the magnitude of the pile's lateral deformation.

4. A calculation device for the deflection of foundation pit support piles considering the dynamic load of vehicles, characterized in that, include: The first processing module is used to construct the calculation formula for the active earth pressure on the side soil of the support pile under the action of vehicle dynamic load. The second processing module is used to construct the pile deflection differential equation below the excavation surface and the pile deflection differential equation above the excavation surface based on the calculation formula of the active earth pressure of the support pile side soil under the action of vehicle dynamic load. The third processing module is used to divide the pile body into segments according to the actual working conditions, based on the differential equations of pile body deflection below the excavation surface and above the excavation surface, using the segmented independent coordinate method, to establish the differential equations of pile body deformation for each segment, and simultaneously calculate the pile body deflection by combining the differential equations of pile body deformation for each segment with the pile end boundary conditions.

5. The calculation device for the deflection of foundation pit support piles considering vehicle dynamic loads as described in claim 4, characterized in that, The segmented independent coordinate method is defined as follows: the pile body is divided into several units according to the location of the lateral support structure, the soil layer interface and the excavation face as the sub-nodes. Each pile unit establishes its own independent Cartesian coordinate system, and the pile body deflection differential equation is established segment by segment.

6. The calculation device for the deflection of foundation pit support piles considering vehicle dynamic loads as described in claim 5, characterized in that, The boundary conditions at the pile tip are as follows: Fixed end: Simple branch end: Free end: in, x The depth of the pile. y This represents the magnitude of the pile's lateral deformation.

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