Vibration pile hammer driven by multiple two-dimensional power units in cooperation

Abstract

The present application belongs to the technical field of vibration pile driving (pulling), and discloses a vibration pile hammer driven by multiple two-dimensional power units. The vibration pile hammer comprises multiple two-dimensional power driving units. When the number of two-dimensional power driving units is odd, the units are arranged at equal intervals on a circle, the circle has the axis of the vibration hammer body and the pile body as the center, and the plane of the circle is perpendicular to the axis direction of the vibration hammer body and the pile body. When the number of two-dimensional power driving units is even, the units are arranged in pairs in a central symmetrical manner. The multiple two-dimensional power driving units are cooperatively driven to provide linkage linear vibration exciting force and linkage torsional vibration exciting force, and the linkage linear vibration exciting force and the linkage torsional vibration exciting force are arranged in a decoupled manner. The present application significantly improves the penetration rate of large piles, meets the requirements of ocean large pile foundation depth engineering, significantly improves the overall pile driving and pulling efficiency of large piles, significantly reduces the cost of large pile foundation engineering, effectively realizes the driving and pulling function of large piles in hard soil conditions, saves energy consumption, and prevents the deformation or damage of piles.

Description

Technical Field

[0001] This invention relates to the field of vibratory pile driving (extraction) technology, and in particular to a vibratory pile hammer driven by multiple two-dimensional power units in a coordinated manner. Background Technology

[0002] The application of pile foundations in various construction projects is becoming increasingly widespread, and vibratory pile hammers (including vibratory pile driving and vibratory pile extraction functions), as an indispensable pile foundation construction equipment, are bound to be used more and more extensively. Especially for wind power and photovoltaic projects in deserts, tidal flats, or mountains, as well as infrastructure construction projects such as buildings, roads, bridges, and airports, and construction projects such as offshore wind power or offshore operation platforms, the first step in the construction of these projects is the pile driving process, and the subsequent dismantling process requires the pile extraction process.

[0003] As the core equipment in vibratory pile driving / extraction technology, the performance of the vibratory pile hammer directly affects the efficiency and quality of pile driving / extraction. Existing conventional pile driving procedures are generally divided into hydraulically driven static pressure pile driving, impact pile driving, and vibratory pile driving. Among these, vibratory pile driving is the most common. The basic principle of most traditional vibratory pile driving or extraction methods involving vibratory pile hammers is: to generate a single-direction excitation force through a single exciter (i.e., an eccentric rotor driven by a power source such as a motor / hydraulic / pneumatic power source) or multiple exciters, thereby driving the vibratory pile hammer and pile to achieve linear vibration in a single direction. In other words, traditional pile driving and extraction methods all use one-dimensional power, achieving the vibratory pile driving and extraction function solely through a single-direction linear vibration trajectory. Research and practice have shown that this driving method has the following shortcomings:

[0004] 1) The pile depth cannot meet the project requirements;

[0005] 2) The overall efficiency of the piling process is low (i.e., the pile penetration rate is too low).

[0006] 3) Piles driven using conventional vibratory piling technology are difficult to extract later;

[0007] 4) High piling costs (e.g., most photovoltaic piles in the desert must be filled with water before they can be driven to the required depth).

[0008] 5) Piling is more difficult in hard soil conditions;

[0009] 6) High power consumption;

[0010] 7) The pile itself is prone to deformation / damage;

[0011] 8) The dynamic load and noise transmitted to the surrounding environment of the pile are large (for onshore pile driving, it affects the health of surrounding residents or the safety of surrounding buildings or operating equipment; for offshore pile driving, it affects the health and reproduction of marine life).

[0012] To address the shortcomings of existing technologies, this invention proposes a vibratory pile hammer driven by multiple two-dimensional power units. This invention aims to achieve efficient, high-quality, environmentally friendly, noise-reducing, pile-protecting, energy-saving, and easy-to-extract pile foundation operations through innovative technologies such as innovative vibration modes (using two-dimensional power drive), redistribution of the coupled frictional force vector between the pile and soil, and improved vibration reduction and noise reduction effects. This provides a completely new solution for pile foundation engineering. Summary of the Invention

[0013] To address the shortcomings of existing technologies, this invention proposes a vibratory pile hammer driven collaboratively by multiple two-dimensional power units.

[0014] The technical solution of the present invention is as follows: a vibratory pile hammer driven by multiple two-dimensional power units, comprising multiple two-dimensional power drive units; when the number of two-dimensional power drive units is odd, they are evenly distributed circumferentially, with the center line of the vibratory hammer body and the pile body as the center, and the plane of the circumference is perpendicular to the direction of the center line of the vibratory hammer body and the pile body; when the number of two-dimensional power drive units is even, they are arranged in pairs symmetrically at the center; the multiple two-dimensional power drive units drive in concert, providing a linked linear vibration excitation force and a linked torsional vibration excitation force, and the linked linear vibration excitation force and the linked torsional vibration excitation force are decoupled.

[0015] Each two-dimensional power drive unit includes a linear vibration exciter group and a torsional vibration exciter group; the linear vibration exciter group and the torsional vibration exciter group are decoupled; the linear vibration exciter group of each two-dimensional power drive unit provides linear vibration excitation force, and all linear vibration excitation forces are arranged on a circumference with the axis of the vibrating hammer and the pile as the center, and the plane of the circumference is perpendicular to the axis of the vibrating hammer and the pile; all linear vibration excitation forces are evenly or symmetrically distributed on the circumference; each linear vibration exciter group operates synchronously, with the same amplitude, frequency and phase; each torsional vibration exciter group of each two-dimensional power drive unit operates synchronously, providing local torsional vibration excitation force; when the number of two-dimensional power drive units is odd, the direction of the local torsional vibration excitation force is arranged clockwise or counterclockwise, with the same amplitude, frequency and phase; when the number of two-dimensional power drive units is even, the local torsional vibration excitation forces are arranged in pairs with the axis of symmetry of the vibrating hammer and the pile as the axis of symmetry, and are centrally symmetrical, with the same amplitude, frequency and phase.

[0016] All local torsional vibration excitation forces work synchronously and collaboratively to form a periodic torsional couple, which serves as the periodic torsional couple of the entire vibratory hammer and pile body around their axis of rotation for the coordinated torsional vibration excitation force.

[0017] Each of the two-dimensional power drive units is equipped with a torsional vibration exciter group. The torsional vibration exciter group includes multiple rotating shafts with eccentric rotors arranged sequentially vertically or horizontally. The rotating shafts are coupled together by a strong coupling mechanism to achieve synchronous operation. When the rotating shafts are arranged vertically, the center lines of all rotating shafts and the overall axis of symmetry of all rotating shafts are parallel to the radial plane of the pile body. When the eccentric rotors on all rotating shafts run to the direction of the axis of the vibrating hammer, the phase difference between two adjacent eccentric rotors is 180 degrees. When the number of rotating shafts is even, the eccentric rotors on adjacent rotating shafts have the same mass moment, the phase is symmetrical about the radial direction of the vibrating hammer, and they rotate in opposite directions. When the number of rotating shafts is odd, the phase between the eccentric rotors on each adjacent rotating shaft is symmetrical about the radial direction of the vibrating hammer, and they rotate in opposite directions. The sum of the mass moments of the eccentric rotors in the clockwise rotation direction is equal to the sum of the mass moments of the eccentric rotors in the counterclockwise rotation direction.

[0018] When the shafts are arranged laterally, the centerlines of all shafts and the overall axis of symmetry of all shafts are perpendicular to the radial plane of the pile. When the resultant force of the excitation force generated by the eccentric rotors on all shafts is perpendicular to the line connecting the center of mass of the torsional vibration exciter group to the axis of the vibrating hammer, the phase difference between two adjacent eccentric rotors is 180 degrees. When the number of shafts is even, the eccentric rotors on adjacent shafts have the same moment of mass, the phase is symmetrical about the axial direction of the vibrating hammer, and they rotate in opposite directions. When the number of shafts is odd, the phase between the eccentric rotors on each adjacent shaft is symmetrical about the axial direction of the vibrating hammer, and they rotate in opposite directions. The sum of the moment of mass of the eccentric rotors in the clockwise direction is equal to the sum of the moment of mass of the eccentric rotors in the counterclockwise direction.

[0019] Each of the two-dimensional power drive units is provided with a linear vibration exciter group, which includes at least two strongly coupled vibration exciters; each vibration exciter is equipped with an eccentric rotor; the vibration exciters in the linear vibration exciter groups of all two-dimensional power drive units are symmetrical about the axis of the vibrating hammer body, or are evenly distributed on the circumference of a circle with the axis of the axis as the center and perpendicular to the plane containing the axis of the axis; the eccentric rotors of the linear vibration exciter groups of each two-dimensional power drive unit are symmetrically arranged about the axial direction of the vibrating hammer body; when all vibration exciters are eccentric... When the eccentric rotor moves to the direction perpendicular to the axis of the vibrating hammer, the phase difference between two adjacent eccentric rotors is 180 degrees. When the number of vibrating exciters in the linear vibration exciter group is even, the mass moments of each eccentric rotor are the same, and the phase between each adjacent eccentric rotor is symmetrical about the axial direction of the vibrating hammer and rotates in the opposite direction. When the number of vibrating exciters in the linear vibration exciter group is odd, the phase between each adjacent eccentric rotor is symmetrical about the axial direction of the vibrating hammer and rotates in the opposite direction. The sum of the mass moments of the eccentric rotors in the clockwise rotation direction is equal to the sum of the mass moments of the eccentric rotors in the counterclockwise rotation direction.

[0020] Each two-dimensional power drive unit's linear vibration exciter group consists of a single piston exciter or multiple piston exciters. For a linear vibration exciter group composed of multiple piston exciters, multiple piston exciters are driven to perform reciprocating motion with the same amplitude, frequency, and phase through synchronous control. The piston exciters of multiple two-dimensional power drive units are arranged symmetrically about the axis of the vibrating hammer or are evenly distributed on the circumference of a circle with the axis as the center and perpendicular to the plane where the axis is located.

[0021] Each two-dimensional power drive unit's torsional vibration exciter group consists of a single piston exciter or multiple piston exciters. For a torsional vibration exciter group composed of multiple piston exciters, multiple piston exciters are driven to perform reciprocating motion with the same amplitude, frequency, and phase through synchronous control. The piston exciters of multiple two-dimensional power drive units are arranged symmetrically about the radial direction of the vibrating hammer, or are evenly distributed on the circumference of a circle with the axis as the center and perpendicular to the plane where the axis is located.

[0022] The linear vibration exciter groups of adjacent two-dimensional power drive units achieve synchronous operation through a strong coupling mechanism and a coupling; the two ends of the coupling are respectively connected to the strong coupling mechanism connected to the linear vibration exciter groups of adjacent two-dimensional power drive units.

[0023] The torsional vibration exciter groups of adjacent two-dimensional power drive units achieve synchronous operation through a strong coupling mechanism and a coupling; the two ends of the coupling are respectively connected to the strong coupling mechanism connected to the torsional vibration exciter groups of adjacent two-dimensional power drive units.

[0024] The excitation force for linear vibration is either low-frequency large amplitude or high-frequency small amplitude, and the excitation force for torsional vibration is either low-frequency large amplitude or high-frequency small amplitude.

[0025] When the vibration exciter of the linear vibration exciter group is an eccentric rotor, and the torsional vibration exciter group is a rotating shaft with an eccentric rotor, the angle between the rotation plane of the eccentric rotor of the linear vibration exciter group and the rotation plane of the eccentric rotor of the torsional vibration exciter group in each two-dimensional power drive unit is 0-90 degrees.

[0026] The beneficial effects of this invention are as follows: the penetration rate of large piles is significantly improved, meeting the requirements of deep marine pile foundation engineering; the overall driving and pulling efficiency of large piles is significantly improved; the cost of large pile foundation engineering is significantly reduced; the driving and pulling function of large piles can be effectively realized even in hard soil conditions; energy consumption is saved; the piles are not easily deformed or damaged; due to the flexible vibration driving and pulling function of large pile foundations, the dynamic load and noise transmitted to the foundation during the driving and pulling of large piles are very small, avoiding the impact on the surrounding environment; for the driving and pulling of marine large piles, the two-dimensional dynamic flexible drive scheme can effectively protect marine life from the impact, avoid the adverse effects on the marine ecological environment during the vibration driving and pulling process, and protect the environment. Attached Figure Description

[0027] Figure 1 A structural principle and dynamic model of a vibratory pile hammer driven by multiple two-dimensional dynamic units;

[0028] Figure 2 A schematic diagram of a vibratory pile hammer driven by multiple two-dimensional power units in a coordinated manner;

[0029] Figure 3 This is a schematic diagram of a single two-dimensional power drive unit structure after rotation in direction A.

[0030] Figure 4 The mechanical model of a vibratory pile hammer driven by multiple two-dimensional dynamic units is shown in (a) as a front view, (b) as a top view of section AA in (a), (c) as an overall mechanical analysis, and (d) as a partial schematic diagram of the pile tip-soil contact part.

[0031] Figure 5 A calculation framework diagram for the mechanical model of a vibratory pile hammer driven by multiple two-dimensional dynamic units;

[0032] Figure 6 A schematic diagram of the frictional redistribution mechanism at the pile-soil contact surface; (a) shows the application of vertical harmonic load, and (b) shows the application of both vertical and torsional harmonic loads.

[0033] Figure 7 The stress-strain relationship of the soil in cylindrical coordinates;

[0034] Figure 8 The vertical displacement and velocity of the pile;

[0035] Figure 9 Let (a) be the rotation angle and angular velocity of the vibratory hammer; (b) is the angle and (a) is the angular velocity.

[0036] Figure 10 These are the pile top rotation angle, pile bottom rotation angle, and pile body deformation angle.

[0037] Figure 11 The shear stress of the pile at different locations is shown in (a) as a three-dimensional schematic diagram and (b) as a two-dimensional schematic diagram.

[0038] Figure 12 The amplitude-frequency characteristic curve of the soil when it is excited at r=0.5m and z=2m;

[0039] Figure 13 For torsional load ( Circumferential displacement of soil at z=2m with radial r (Hz = 48Hz);

[0040] Figure 14 For vertical load ( Vertical displacement of soil at z=2m as radial r changes (24Hz);

[0041] Figure 15 For torsional load ( Circumferential displacement of soil at depth z of r=0.3m (Hz = 48Hz);

[0042] Figure 16 For vertical load ( Radial displacement of soil at depth z of r=0.3m (24Hz) as r=0.3m.

[0043] Figure 17 For vertical load ( Vertical displacement of soil at depth z with r=0.3m (24Hz) as r=0.3m.

[0044] Figure 18 The ratio of vibration frequency The effect on friction distribution;

[0045] Figure 19 The ratio of vibration frequency The impact on the vertical displacement of the pile.

[0046] In the figure: 1. Vibratory hammer body; 2. Pile body; 3. Two-dimensional power drive unit; 4. Linear vibration exciter group; 5. Gear meshing strong coupling mechanism a; 6. Torsional vibration exciter group; 7. Gear meshing strong coupling mechanism b; 8. Coupling gear meshing strong coupling mechanism a; 9. Coupling gear meshing strong coupling mechanism b. Detailed Implementation

[0047] exist Figure 1 Based on this, one of the structural working principle dynamic models of a vibratory pile hammer driven by multiple two-dimensional dynamic units is as follows: Figure 2 and Figure 3 As shown.

[0048] The invention provides a two-dimensional power source. The two-dimensional power source acts together on the vibratory hammer 1, and the pile 2 is rigidly fixed to the vibratory hammer 1. A strong coupling mechanism, including a coupling and gear meshing, is used to ensure the synchronous operation of the linear vibration exciter group and the torsional vibration exciter group. The two-dimensional power source acting on the large vibratory hammer 1 includes a linear vibration excitation force along the axial direction of the vibratory hammer 1 and the pile 2, i.e., the first-dimensional power source. F ( t The torsional vibration excitation force, which is circumferentially directed around the axis of the vibratory hammer 1 and the pile 2 (i.e., around the center line of the cross section of the pile 2), serves as the second-dimensional power source. M ( t All linear vibration exciter groups together generate the first-dimensional power source. F (t All torsional vibration exciter groups together generate a second-dimensional power source. M ( t ).

[0049] In this embodiment, the vibratory hammer 1 and the pile 2 are driven by eight two-dimensional power drive units 3. The linear vibration exciter group 4 and the torsional vibration exciter group 6 of each two-dimensional power drive unit 3 are decoupled. The total linear vibration exciter group and the total torsional vibration exciter group driven by these two-dimensional power drive units 3 are also decoupled and symmetrical about the axis of the vibratory hammer 1 and the pile 2 in the axial direction.

[0050] Linear vibration exciter group 4 uses two vibration exciters and achieves strong coupling through a strong coupling mechanism a5 such as gear meshing. The mass moment of the eccentric rotor of the vibration exciter is... m s r s The resultant force of the excitation force perpendicular to the axial direction of the vibratory hammer 1 and the pile 2 is 0, while the excitation force along the axial direction of the vibratory hammer 1 and the pile 2 is positively superimposed, thereby realizing the linear vibration function of the two-dimensional drive unit 3 along the axial direction of the vibratory hammer 1 and the pile 2; the linear vibration exciter group 4 of the eight two-dimensional power drive units 3 achieves strong coupling through the strong coupling mechanism a8 of the coupling gear meshing, thereby realizing the linear vibration function of the linkage drive of the eight two-dimensional power drive units 3.

[0051] The torsional vibration exciter group 6 of the two-dimensional power drive unit 3 uses two torsional vibration exciters, which are strongly coupled through a gear meshing and other strong coupling mechanism b7. The mass torque of the torsional vibration exciter is... m 0 rThe resultant excitation force along the axial direction of the vibratory hammer 1 and the pile 2 is zero, while the excitation force perpendicular to the axial direction of the vibratory hammer 1 and the pile 2 is positively superimposed, thereby realizing the unit local torsional vibration function of each two-dimensional power drive unit 3 for the vibratory hammer 1 and the pile 2; the torsional vibration exciter groups of the eight two-dimensional power drive units 3 are strongly coupled through a coupling gear meshing equal strong coupling mechanism b9, thereby realizing the torsional vibration function of the linkage drive of the eight two-dimensional power drive units 3. The linear vibration exciter group 4 of each two-dimensional power drive unit 3 can be multiple, and strong coupling is achieved through a gear meshing equal strong coupling mechanism a5. The torsional vibration exciter group 6 of each two-dimensional power drive unit can be multiple, and strong coupling is achieved through a gear meshing equal strong coupling mechanism b7. The number of two-dimensional power drive units 3 is not limited to 8; any number, including 2 or more, can be used. When the number of two-dimensional power drive units is odd, they are evenly distributed circumferentially on a circle perpendicular to the axes of the vibrating hammer 1 and the pile 2, with the center lines of the axes of the vibrating hammer 1 and the pile 2 as the center. Simultaneously, the number of corresponding strong coupling mechanisms, such as coupling gear meshing, that realize linear and torsional vibrations, also increases or decreases accordingly. When the number of two-dimensional power drive units is even, they are arranged in pairs with central symmetry.

[0052] The positions of the linear vibration exciter group 4 and the torsional vibration exciter group 6 in the multiple two-dimensional power drive units 3 can be interchanged simultaneously. The angle between the eccentric rotor rotation plane of the linear vibration exciter group and the eccentric rotor rotation plane of the torsional vibration exciter group in each two-dimensional power drive unit is 0-90 degrees.

[0053] Furthermore, in one specific embodiment, the linear vibration exciter group of each two-dimensional power drive unit is a single piston exciter or includes multiple piston exciters; for the linear vibration exciter group composed of multiple piston exciters, the multiple piston exciters are driven to perform reciprocating motion with the same amplitude, frequency and phase through synchronous control, and the multiple piston exciters are symmetrically arranged about the axial direction of the vibrating hammer 1.

[0054] Furthermore, in one specific embodiment, the torsional vibration exciter group of each two-dimensional power drive unit is a single piston exciter or includes multiple piston exciters; for the torsional vibration exciter group composed of multiple piston exciters, the multiple piston exciters are driven to perform reciprocating motion with the same amplitude, frequency and phase through synchronous control, and the multiple piston exciters are symmetrically arranged about the radial direction of the vibrating hammer 1.

[0055] A method for determining the parameters of a vibratory pile hammer driven collaboratively by multiple two-dimensional dynamic units includes the following steps:

[0056] Step 1: Establish a pile-soil mechanical model;

[0057] Based on the two-dimensional dynamic driving model, the magnitudes of the vertical and torsional excitations of the vibratory hammer are calculated using the following formulas:

[0058] (1)

[0059] in, It is the excitation force for linear vibration; It is vertical static pressure; This represents the vertical harmonic load generated by the eccentric rotor. It is the excitation eccentricity of the vertical eccentric rotor. , It is the vertical excitation frequency; It is torsional torque. The circumferentially eccentric rotor generates torsional excitation. To the vertical axis of the vibratory hammer body distance, i These refer to the directions of the resultant force generated by the left and right eccentric rotors, respectively. i= 1 and 4 represent the clockwise resultant force generated by a pair of eccentric rotors on the left and right sides, respectively. i= 2 and 3 represent the counterclockwise resultant force generated by a pair of eccentric rotors on the left and right sides, respectively. It is the circumferential excitation eccentricity. , It is the torsional excitation frequency;

[0060] In vertical Direction, based on the excitation force of linear vibration This causes the vibrating hammer to vibrate up and down; in the circumferential direction Direction, through torsional excitation generated by two or more pairs of eccentric rotors. By controlling the phase angle, the centrifugal forces at the top and bottom are canceled out, causing the vibrating hammer to generate a total torsional torque. A cylindrical coordinate system is established, with the bottom of the vibratory hammer and the top of the pile connected by a fixed constraint. The motion and excitation of the vibratory hammer are transmitted through the coupling part, enabling two-dimensional dynamic drive between the pile and the vibratory hammer to achieve two types of vibration, transmitting linear vibration excitation force. and torsional moment , This represents the torsional moment transmitted at the connection between the vibratory hammer and the pile;

[0061] Step 2: Establish the preconditions for the pile-soil elastoplastic dynamics equations;

[0062] 1. Under small strain conditions, the stress-strain relationship of soil is represented by a linear elastic model;

[0063] 2. Non-cohesive soil is considered a linear elastic material;

[0064] Based on the above assumptions, the solution for a two-dimensional dynamic-driven vibratory pile driving method based on the pile-soil friction redistribution mechanism is given: the torsional moment and vertical harmonic load are generated by the vibratory hammer and act on the pile together. According to the analysis of the pile's torsional vibration force and vertical vibration force, the torsional vibration and vertical vibration of the pile are solved separately. The vertical vibration of the pile is solved using the separation of variables method based on the boundary conditions at both ends of the pile. The vertical vibration of the pile is solved using the R-K45 method. Based on the frictional interaction between the pile and the soil, the pile is subjected to a torsional excitation and a vertical excitation. The soil response is solved using the integral transform method based on the soil boundary conditions. Based on the mechanism of friction redistribution between the pile and the soil and the difference between the torsional and vertical responses between the pile and the soil, the circumferential friction force and the vertical friction force are calculated separately.

[0065] Step 3: Establish the dynamic equations of the vibratory pile hammer driven by multiple two-dimensional dynamic units in a coordinated manner;

[0066] In the process of establishing the pile-soil elastoplastic dynamic equation: Under periodic load, the stress-strain relationship of the soil has two major characteristics: nonlinearity and hysteresis. The power function nonlinear dynamic model is used as the skeleton equation to reflect the nonlinear relationship of the soil under dynamic load. On this basis, according to the Masing double method, the skeleton equation is constructed into a nonlinear hysteresis curve.

[0067] When establishing a vertical drive model for a vibratory pile hammer driven by multiple two-dimensional dynamic units, the vibratory hammer body is directly connected to the pile, resulting in the vibratory hammer-pile system having the same motion trajectory. Based on the dynamics of pile-soil interaction, and considering the elastoplastic properties of the soil, a cubic nonlinear hyperbolic hysteresis model of the pile's vertical motion is established, with the soil restoring force-displacement relationship taken as follows:

[0068] (2)

[0069] in, It is the linear elastic stiffness coefficient of the soil at the bottom of the pile. It is the maximum amplitude of the vertical displacement of the pile. It is the nonlinear coefficient of the soil reaction at the pile bottom. It is the maximum restoring force; It is a sign function, where z represents the vertical direction;

[0070] (3)

[0071] The dynamic equation for the vertical vibration of the pile is:

[0072] (4)

[0073] In equation (4), It is the total effective vibration mass. It is the vertical viscous damping coefficient of the soil. It is the vertical frictional resistance between the pile and the soil, which can be obtained from formulas (2) and (3).

[0074] (5)

[0075] , , , , , , , It is the natural frequency of the soil at the bottom of the pile. It is the damping ratio;

[0076] Substituting the introduced variables and formula (5) into formula (4), we get:

[0077] (6)

[0078] Dimensionless processing of the above equation yields the following result. , , , ;

[0079] Substituting equation (5) into equation (6), we obtain the dimensionless dynamic equation of the cubic power nonlinear hyperbolic hysteresis model of the dynamic foundation system:

[0080] (7)

[0081] in, ;

[0082] (8)

[0083] This represents the vertical relative displacement of the pile. For dimensionless restoring force, this formula is the dimensionless restoring force hyperbolic constitutive relation of the dynamic equation of the vertical vibration of the pile; the relationship between soil restoring force and displacement is modeled as a cubic power nonlinear hyperbolic hysteresis model of soil, and R-K45 is introduced to solve the nonlinear equation (7).

[0084] Due to the increased torsional vibration, there is a circumferential relative motion at the pile-soil contact surface. Based on the soil properties, there is an interaction between the soil and the vibratory hammer-pile system, resulting in circumferential frictional resistance in the pile, the magnitude of which is determined by the soil properties and depth. The equations of motion for both the vibratory hammer and the pile are established based on their respective forces and boundary conditions. Assuming the vibratory hammer is a rigid body, the circumferential differential equation for the force analysis of the vibratory hammer is as follows:

[0085] (9)

[0086] The vibratory hammer body has a solution of the following form:

[0087] (10)

[0088] It is the moment of inertia of the vibratory hammer body. From the initial state The constant that determines Depend on The constant that determines It is the undamped natural frequency. , is the natural frequency of damped vibration. It is the torsional damping coefficient between the pile and the soil. It is the torsional spring coefficient between the pile and the soil. It is the amplitude of forced vibration. , Represents phase difference;

[0089] Assuming the pile is an elastic rod, establish the torsional vibration wave equation for the pile:

[0090] (11)

[0091] The boundary conditions for the piles are:

[0092] (12)

[0093] The frictional resistance torque is generated during the interaction between the pile's exterior and interior and the soil. It is the length parameter of the pile;

[0094] The torsional vibration solution of the pile was obtained using the method of separation of variables;

[0095] (13)

[0096] in, It is the density of the pile. It is the torsional wave velocity of the pile. It is the shear modulus of the pile. It is the polar moment of inertia of the pile; by solving equation (11) using the method of separation of variables, the coefficients are obtained by solving equations (11), (12) and (13) simultaneously. Sum of coefficients ;

[0097] Formulas for the torsional moment of the pile at different locations during vibratory hammer-pile torsional vibration. as follows:

[0098] (14)

[0099] in, , It is the torsional vibration period; the shear stress at different locations of the pile is solved by calculating the torsional vibration of the pile. ;

[0100] (15)

[0101] It is the torsional section modulus of the pile;

[0102] Step 4: Establish the soil dynamics equations;

[0103] During the pile driving process, frictional resistance torque is generated by the interaction between the pile's exterior and interior and the soil. The annular section at the bottom of the pile generates a vertical harmonic excitation force on the soil. The stress wave generated by the linear vibration excitation force and the torsional moment causes the soil to move vertically and circumferentially. By performing an integral transformation on the vertical and torsional excitations using the Fourier-Bessel function, and after introducing the soil wave equation, the Green function is used to solve the soil wave equation, and the vertical, torsional and radial responses of the soil under the two excitations are obtained.

[0104] The wave equation for soil in cylindrical coordinates is established as follows:

[0105] (16)

[0106] It is the soil excitation vector. , , Representing the soil in The soil is stimulated in the direction of the excitation. The direction of the excitation, the soil in The motivation that drives the direction;

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] It is the Lamé constant of soil. It is the shear modulus of soil;

[0113] A positive Fourier-Bessel transform is applied to the excitation source and the soil response;

[0114] (17) (18)

[0115] The corresponding inverse Fourier-Bessel transform is as follows;

[0116] (19)

[0117] (20)

[0118] , , , Representing the soil in Displacement response in the direction, soil in Displacement response in the direction, soil in Displacement response in the direction; It is an integral factor. It is a cylindrical coordinate axis direction, It is about The matrix, It is a Bessel function of the first kind with order n. Wavenumber It is an azimuth matrix;

[0119] In formulas (17), (18), (19) and (20),

[0120]

[0121]

[0122]

[0123] It is an indicator used to determine , , The value of needs to be determined when the load is a vertical excitation. The first row of matrix elements and n =0, when the load is a torsional load about the vertical axis, then it is necessary to use The second row of matrix elements n =0; Is the order of n Bessel functions of the first kind yes First derivative;

[0124] It is a diagonal matrix; when the vertical load is about When axially symmetric, When the load is a torsional load about a vertical axis, In cylindrical coordinates, the wave equation of soil is as follows:

[0125] (twenty one)

[0126] It is the response matrix of soil;

[0127] The wave equation of soil in the frequency-wavenumber domain is shown below:

[0128] (twenty two)

[0129] , , These are the soil masses in the frequency-wavenumber domain. Response of soil in the direction, soil in the frequency-wavenumber domain Response of soil in the direction, soil in the frequency-wavenumber domain Response in direction, , , These are the soil masses in the frequency-wavenumber domain. Excitation under direction, soil in frequency-wavenumber domain Excitation under direction, soil in frequency-wavenumber domain Incentives under a specific direction;

[0130] Formula (22) is separated into two uncoupled equations, where the P-wave is a pair of coupled two-degree-of-freedom equations and the S-wave is a single-degree-of-freedom equation. The specific forms of the two equations are as follows:

[0131] (twenty three)

[0132] (twenty four)

[0133] Consider a total thickness of A homogeneous medium, with its upper surface free and its lower surface fixed, exists at a depth of... And the radius is The torsional excitation frequency at the point is The harmonic torsional load and vertical excitation frequency are The harmonic vertical load; taking the upper surface as the origin of the coordinate system, the circumferential load and vertical load are expressed as follows:

[0134] (25)

[0135] When harmonic torsional loads and harmonic vertical loads are applied to the soil, a torsional drag torque is generated. The torsional resistance torque and Irrelevant, and about The axis is antisymmetric; the Fourier-Bessel transforms of the harmonic torsional load and the harmonic vertical load are as follows:

[0136] (26)

[0137] Equations (23) and (24) with respect to degrees of freedom , and It is decoupled; in the frequency-wavenumber domain, the wave equation of the soil is reformulated as follows:

[0138] (27)

[0139] (28)

[0140] Horizontal wavenumber is denoted as To solve equations (27) and (28), we consider the boundary conditions and the homogeneity problem, and divide them by the shear modulus. To distinguish specific cases, the solution for the soil response is expressed as: The wave equation and boundary conditions for the soil are shown below:

[0141] (29)

[0142] , representing the P-wave velocity; Represents S-wave velocity; Represents the characteristic value of the P wave. Represents the characteristic value of the S-wave; based on the boundary conditions For soil and wave number The corresponding normal diffusion mode, Satisfying the eigenvalue equation and Based on modal superposition, the wave diffusion problem is solved and the displacement is expressed as a superposition of normal modes; the solution for the ring load is obtained according to the Hankel transform;

[0143] (30)

[0144] (31)

[0145] It refers to the depth to which the soil is stimulated. It is soil j-th order mode in the direction, It is the radius of action of the torsional excitation. It is the j-th mode of soil in the z-direction. The square of the j-th order eigenvalue of soil;

[0146] Step 5: Redistribution of frictional force at the pile-soil contact surface;

[0147] Due to the increased torsional moment, the pile generates torsional vibration. When the pile vibrates to the torsional direction, the direction of the frictional force between the pile and the soil changes. The direction of the frictional force is no longer along the axial direction of the pile, but opposite to the direction of the velocity at the micro-element on the pile surface. When the velocity and frictional force are vector-decomposed into the axial and circumferential directions of the pile, the frictional force along the axial direction of the pile is less than the total frictional force at the pile-soil contact surface, thereby reducing the axial frictional force at the pile-soil contact surface. Under the same excitation force or impact load, the penetration speed and penetration depth of the pile are increased.

[0148] The pile-soil interaction is influenced by the friction interface description, cumulative friction cycles, and elastoplastic soil response model; according to the Mohr-Coulomb criterion, the frictional resistance... It's about depth. The function is shown in the following formula:

[0149] (32)

[0150] It is the friction between the inner wall of the pile and the soil. It is the friction between the outer wall of the pile and the soil. It is the contact area between the inner wall of the pile and the soil. It is the contact area between the outer wall of the pile and the soil. It is the pile-soil interaction friction angle, It's the viscosity of the soil; It is the earth pressure coefficient. It is the effective self-weight of soil per unit;

[0151] The circumferential frictional resistance moment along the pile-soil interface is derived from the following formula:

[0152] (33)

[0153] and These are the contact area between the inner wall of the pile and the soil, and the contact area between the outer wall of the pile and the soil, respectively. It is the internal friction angle of the soil. and These are the frictional torque at the inner wall of the pile and the frictional torque at the outer wall, respectively.

[0154] The absolute velocity of the pile-soil interaction determines the distribution of frictional force between them; the pile displacement is known. Displacement of soil The speed of obtaining the pile The speed of the soil ;

[0155] The relative velocity difference between the pile and the soil is shown in the following formula:

[0156] (34)

[0157] (35)

[0158] It is the total relative velocity between the pile and the soil. Between pile and soil Relative velocity in direction, Between pile and soil Relative velocity in direction;

[0159] According to the principle of velocity vector decomposition (35), the friction force distribution law at the pile-soil friction interface is as follows:

[0160] (36)

[0161] Among them, circumferential frictional resistance axial frictional resistance ;

[0162] According to formula (36), the velocity vector determines the distribution of frictional force, and the velocity vector is determined by the ratio of the torsional vibration excitation frequency to the vertical excitation frequency. Considering the limit of shear stress that the pile can withstand, the vibration frequency ratio is selected to maximize the effect of two-dimensional dynamic driven vibratory pile driving.

[0163] Example: Numerical analysis of pile-soil coupling dynamics during two-dimensional dynamically driven vibratory pile driving and pulling process;

[0164] During the simulation, the frequency corresponding to the maximum amplitude was selected as the torsional frequency based on the amplitude-frequency characteristic curve for analytical and numerical comparison; the vertical vibration frequency was selected as 24Hz; and the excitation frequency range of the soil amplitude-frequency characteristic curve was selected as 0-150Hz.

[0165] (1) Comparison of TSM (theoretical solution method) and FEM (numerical solution method) for the response of vibratory hammer-pile system;

[0166] exist Figure 8 The curves showing the vertical relative displacement and velocity of the pile, derived from RK-45, reveal that during pile penetration, the penetration rate gradually decreases as the penetration depth increases. When the penetration depth reaches a certain level, the pile stops sinking and instead vibrates in place. Figure 9The curves in the figure show the rotation angle and angular velocity of the vibratory hammer during torsional vibration, with an angular vibration amplitude of 0.00664 rad ( Figure 9 (a)), the angular velocity vibration amplitude is 2 rad / s ( Figure 9 (b)).

[0167] exist Figure 10 The curve in the figure represents the pile's response to torsional moment, with the blue and red curves representing the rotation angles at the pile top and bottom, respectively. Figure 10 It is clear from the diagram that the rotation angles of the two piles are not the same. This is because the frictional resistance torque of the soil creates a difference in rotation angle between the pile bottom and the pile top. The magenta dotted line represents the angle difference between the pile top and the pile bottom (also called torsional deformation). Figure 11 The analytical and numerical results of pile shear stress were compared. Figure 11 In (a), (z=0m), (z=2m), (z=4m), and (z=7m) represent the shear stress at different locations on the pile. The results show that the shear stress at the pile top is equal to... The shear stress at the bottom of the pile is equal to Furthermore, the shear stress gradually decreases from the pile top to the pile bottom. During the simulation, when... At that time, due to the sudden change in the pile bottom torque, stress fluctuations will occur, and these stress waves will propagate along the pile body, causing fluctuations in the simulation results. Figure 11 (b)).

[0168] (2) Comparison of TSM and FEM of soil response

[0169] The amplitude-frequency characteristics of the soil were analyzed when studying the torsional vibration frequency. Figure 12 The results are compared between the theoretical solution and the numerical simulation. The torsional vibration frequency gradually increases from 0Hz to 150Hz, and the maximum amplitude can be seen from the curve to be around 48Hz.

[0170] Calculate the effects of torsional and vertical vibrations on the soil. The frequencies of torsional and vertical vibrations are selected as follows: =48Hz and =24Hz. Figure 13 and Figure 14 These respectively demonstrate the propagation trend of the soil's vibration response along the radial coordinate under torsional and vertical vibrations. Figure 13 As can be seen, the soil response is greatest at the radius of torsional excitation. With increasing radial wavenumber, when the radial wavenumber ( When ) equals 1, the torsional response of the soil has decayed to zero. Figure 14The vertical displacement response curve of the soil under vertical excitation can be seen, and the soil response is maximum at the excitation radius. As the radial wavenumber increases, the vertical response of the soil oscillates and decays with increasing radial wavenumber. When the radial wavenumber ( When the value is 8, the torsional response can be ignored.

[0171] exist Figure 15 Tables 16 and 17 show the soil response at different depths under torsional and vertical vibrations. Figure 15-17 In the middle, when the load is applied at a depth m and radius At position m, the soil response at the applied load is the largest, and the soil response decays rapidly with increasing distance from the vibration source on the vertical coordinate. Figure 17 In the middle, since the ground surface (z=0m) is in a free state, the soil will be affected by stress waves in this state and the displacement will be non-zero. At a depth of z=4m (fixed constraint), the soil response will gradually decay to zero.

[0172] (3) Vibration frequency ratio The impact;

[0173] This study investigates the influence of torsional vibration frequency and vertical vibration frequency on the distribution of frictional force. Based on... Figure 18 As shown, when (torsional vibration frequency) =0Hz, vertical frequency At Hz = 24Hz, the vertical frictional force between the pile and the soil is equal to the total frictional force of 11676N (red dashed line); when (torsion frequency is) =24Hz, vertical frequency At 24Hz, the vertical friction force is 8256N (blue dashed line), and the circumferential friction force is 8256N (blue solid line); when (torsion frequency is) =48Hz, vertical frequency At 24Hz, the vertical friction force is 5222N (magenta dashed line), and the circumferential friction force is 104400N (magenta solid line). During pile driving, vertical friction force (pile driving resistance) is the cause of impediment to pile driving, while circumferential friction resistance has no impeding effect on pile driving. Figure 18 The calculation results show that as the frequency ratio increases, the vertical friction decreases while the circumferential friction increases.

[0174] Based on the frictional redistribution mechanism, comparisons were made. , and The ratio of the three vibration frequencies The calculation results under the given circumstances. From Figure 19As can be seen from this, when the penetration depth At that time, there were three points. (62.95s, 2m) (49.73s, 2m) and (42.98s, 2m), the pile driving time decreases with increasing vibration frequency ratio. When the pile driving time t=150s, corresponding to three points... (150s, 2.643m) (150s, 3.469m) and (150s, 4.616m) The pile penetration depth increases with the increase of the vibration frequency ratio. The comparison of the calculation results verifies that the friction redistribution mechanism is effective, and increasing torsional vibration can improve the pile penetration speed and depth.

Claims

1. A vibratory pile hammer driven collaboratively by multiple two-dimensional power units, characterized in that, It includes multiple two-dimensional power drive units; when the number of two-dimensional power drive units is odd, they are evenly distributed around each other in a circle, with the center line of the vibrating hammer (1) and the pile (2) as the center, and the plane of the circle is perpendicular to the direction of the center line of the vibrating hammer (1) and the pile (2); when the number of two-dimensional power drive units is even, they are arranged in pairs in a centrally symmetrical manner. Multiple two-dimensional power drive units work together to provide linked linear vibration excitation force and linked torsional vibration excitation force, which are decoupled from each other. Each two-dimensional power drive unit includes a linear vibration exciter group and a torsional vibration exciter group. The linear vibration exciter group and the torsional vibration exciter group are decoupled. The linear vibration exciter group of each two-dimensional power drive unit provides linear vibration excitation force. All linear vibration excitation forces are arranged on a circumference centered on the axis of the vibrating hammer (1) and the pile (2). The plane of the circumference is perpendicular to the axis of the vibrating hammer (1) and the pile (2). All linear vibration excitation forces are evenly or symmetrically distributed on the circumference. Each linear vibration exciter group operates synchronously with the same amplitude, frequency, and phase. The torsional vibration exciter groups of each two-dimensional power drive unit operate synchronously and provide local torsional vibration excitation force respectively. When the number of two-dimensional power drive units is odd, the direction of the local torsional vibration excitation force is arranged clockwise or counterclockwise, and the amplitude, frequency and phase are the same; when the number of two-dimensional power drive units is even, the local torsional vibration excitation force is arranged in pairs with the axis of symmetry of the vibrating hammer (1) and the pile (2) as the axis of symmetry, and the amplitude, frequency and phase are the same. All local torsional vibration excitation forces work synchronously and collaboratively to form a periodic torsional couple, which serves as the periodic torsional couple of the entire vibratory hammer (1) and pile (2) around their axis of rotation. Each of the two-dimensional power drive units is equipped with a torsional vibration exciter group, which includes multiple rotating shafts with eccentric rotors. The multiple rotating shafts are arranged vertically or horizontally in sequence, and the rotating shafts are coupled by a strong coupling mechanism to achieve synchronous operation. When the rotating shafts are arranged vertically, the axis of rotation of all rotating shafts and the axis of symmetry of all rotating shafts are aligned. Parallel to the radial plane of the pile body; when the eccentric rotors on all the shafts run to the axis of the vibrating hammer (1), the phase difference between two adjacent eccentric rotors is 180 degrees; when the number of shafts is even, the eccentric rotors on adjacent shafts have the same mass moment, the phase is symmetrical about the radial direction of the vibrating hammer (1), and they rotate in the opposite direction; when the number of shafts is odd, the phase between the eccentric rotors on each adjacent shaft is symmetrical about the radial direction of the vibrating hammer (1), and they rotate in the opposite direction. The sum of the mass moments of the eccentric rotors in the clockwise rotation direction is equal to the sum of the mass moments of the eccentric rotors in the counterclockwise rotation direction. When the shafts are arranged laterally, the center lines of all shafts and the overall axis of symmetry of all shafts are perpendicular to the radial plane of the pile body; when the resultant force of the excitation force generated by the eccentric rotors on all shafts is perpendicular to the line connecting the center of mass of the torsional vibration exciter group to the axis of the vibrating hammer (1), the phase difference between two adjacent eccentric rotors is 180 degrees; when the number of shafts is even, the mass moments of the eccentric rotors on adjacent shafts are the same, the phases are symmetrical about the axial direction of the vibrating hammer (1), and they rotate in the opposite direction; when the number of shafts is odd, the phases of the eccentric rotors on each adjacent shaft are symmetrical about the axial direction of the vibrating hammer (1), and they rotate in the opposite direction, and the sum of the mass moments of the eccentric rotors in the clockwise rotation direction is equal to the sum of the mass moments of the eccentric rotors in the counterclockwise rotation direction.

2. The vibratory pile hammer driven by multiple two-dimensional power units according to claim 1, characterized in that, Each of the two-dimensional power drive units is provided with a linear vibration exciter group, which includes at least two strongly coupled vibration exciters; each vibration exciter is provided with an eccentric rotor; the vibration exciters in the linear vibration exciter groups of all two-dimensional power drive units are symmetrical about the axis of the vibrating hammer (1) in the axial direction, or are evenly distributed on the circumference of a circle with the axis as the center and perpendicular to the plane where the axis is located; the eccentric rotor of the linear vibration exciter group of each two-dimensional power drive unit is arranged symmetrically about the axial direction of the vibrating hammer (1); when the eccentric rotor of all vibration exciters rotates... When the rotor runs to the direction perpendicular to the axis of the vibrating hammer (1), the phase difference between two adjacent eccentric rotors is 180 degrees. When the number of vibrating exciters in the linear vibration exciter group is even, the mass moment of each eccentric rotor is the same, and the phase between each adjacent eccentric rotor is symmetrical about the axial direction of the vibrating hammer (1) and rotates in the opposite direction. When the number of vibrating exciters in the linear vibration exciter group is odd, the phase between each adjacent eccentric rotor is symmetrical about the axial direction of the vibrating hammer (1), rotates in the opposite direction, and the sum of the mass moments of the eccentric rotors in the clockwise rotation direction is equal to the sum of the mass moments of the eccentric rotors in the counterclockwise rotation direction.

3. The vibratory pile hammer driven by multiple two-dimensional power units according to claim 1, characterized in that, Each two-dimensional power drive unit's linear vibration exciter group is a single piston exciter or includes multiple piston exciters; for a linear vibration exciter group composed of multiple piston exciters, multiple piston exciters are driven to perform reciprocating motion with the same amplitude, frequency and phase through synchronous control; the piston exciters of multiple two-dimensional power drive units are arranged symmetrically about the axis of the vibrating hammer (1) or are evenly distributed on the circumference of the plane perpendicular to the axis with the axis as the center.

4. The vibratory pile hammer driven by multiple two-dimensional power units according to claim 1, characterized in that, Each two-dimensional power drive unit's torsional vibration exciter group is a single piston exciter or includes multiple piston exciters; for a torsional vibration exciter group composed of multiple piston exciters, multiple piston exciters are driven to perform reciprocating motion with the same amplitude, frequency and phase through synchronous control; the piston exciters of multiple two-dimensional power drive units are arranged symmetrically about the radial direction of the vibrating hammer (1), or are evenly distributed on the circumference of the plane perpendicular to the axis line with the axis line as the center.

5. The vibratory pile hammer driven by multiple two-dimensional power units according to claim 1, characterized in that, The linear vibration exciter groups of adjacent two-dimensional power drive units achieve synchronous operation through a strong coupling mechanism and a coupling; the two ends of the coupling are respectively connected to the strong coupling mechanism connected to the linear vibration exciter groups of adjacent two-dimensional power drive units.

6. The vibratory pile hammer driven by multiple two-dimensional power units according to claim 1, characterized in that, The torsional vibration exciter groups of adjacent two-dimensional power drive units achieve synchronous operation through a strong coupling mechanism and a coupling; the two ends of the coupling are respectively connected to the strong coupling mechanism connected to the torsional vibration exciter groups of adjacent two-dimensional power drive units.

7. The vibratory pile hammer driven by multiple two-dimensional power units according to claim 1, characterized in that, The excitation force for linear vibration is either low-frequency large amplitude or high-frequency small amplitude, and the excitation force for torsional vibration is either low-frequency large amplitude or high-frequency small amplitude.

8. The vibratory pile hammer driven by multiple two-dimensional power units according to claim 1, characterized in that, When the vibration exciter of the linear vibration exciter group is an eccentric rotor, and the torsional vibration exciter group is a rotating shaft with an eccentric rotor, the angle between the rotation plane of the eccentric rotor of the linear vibration exciter group and the rotation plane of the eccentric rotor of the torsional vibration exciter group in each two-dimensional power drive unit is 0-90 degrees.

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