CN112948939A - Single-pile dynamic stability analysis method and system under ship impact load action - Google Patents

Single-pile dynamic stability analysis method and system under ship impact load action Download PDF

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CN112948939A
CN112948939A CN202110273235.8A CN202110273235A CN112948939A CN 112948939 A CN112948939 A CN 112948939A CN 202110273235 A CN202110273235 A CN 202110273235A CN 112948939 A CN112948939 A CN 112948939A
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姚文娟
张志宏
程泽坤
李武
房霆宸
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University of Shanghai for Science and Technology
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Abstract

The invention discloses a method and a system for analyzing the dynamic stability of a single pile under the action of ship impact load, which are used for analyzing the nonlinear dynamic stability problem of a pile foundation under the action of ship impact and wave instantaneous impact load, a double-parameter foundation model is adopted to establish a nonlinear dynamic basic equation of a partially embedded pile under the action of ship impact and wave instantaneous impact load, a Galerkin integration method is used to obtain a dynamic differential control equation only with time variability, and a fourth-order Runge-Kutta method is adopted to solve the equation for displacement so as to obtain a displacement type function of a pile body. And after the displacement function is calculated, a displacement-time course curve of the pile body is obtained, and the unstable load of the pile body is obtained according to judgment of a B-R criterion. The invention considers the action of the soil body on the pile side to effectively improve the destabilizing load, and the restraining action of the soil body can lead the pile body to experience a section of stable vibration before the destabilizing; compared with the traditional Winkler model, the instability load and pile body displacement time-course curve calculated by adopting the two-parameter model are more in accordance with the engineering practice.

Description

Single-pile dynamic stability analysis method and system under ship impact load action
Technical Field
The invention belongs to the technical field of geotechnical engineering, and particularly relates to a nonlinear dynamics calculation method for a pile foundation under the action of ship impact and wave instantaneous impact load.
Background
Offshore structures are not only subjected to waves, currents, earthquakes, etc., but may also be impacted by ships at certain times, and although such events occur with a low probability, they pose a significant safety risk to the offshore structures once they occur. The effect of the general meeting of wave load and boats and ships impact the effect separately to study in the present study, and the circumstances that can take place two kinds of loads and strike the pile body simultaneously under some special circumstances, will have very big safety risk to the pile foundation this moment, and it is extremely likely to be under two kinds of load effects direct destruction, brings huge harm for upper portion building.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to overcome the defects in the prior art and provide a method and a system for analyzing the dynamic stability of a single pile under the action of ship impact load, which are used for calculating the nonlinear dynamics theory of a pile foundation under the action of ship impact and wave instantaneous impact load. The method reasonably sets the displacement function of the pile body, and then obtains a dynamic differential control equation only with time variability by using a Galerkin integration method. The method comprises the steps of obtaining a pile body displacement function by solving an equation, obtaining a displacement time-course curve of the pile body after the displacement function is calculated, judging and obtaining the instability load of the pile body according to a B-R criterion, and finally analyzing and researching a series of influence factors so as to solve the problems in the background art.
In order to achieve the purpose of the invention, the invention adopts the following technical scheme:
a single pile dynamic stability analysis method under the action of ship impact load adopts a double-parameter foundation model, establishes a nonlinear dynamic basic equation of a partially embedded pile under the action of ship impact and wave instantaneous impact load, obtains a dynamic differential control equation only with time variability by using a Galerkin integration method, and obtains a displacement type function of a pile body by performing displacement solution on the equation by using a fourth-order Runge-Kutta method; and (4) calculating by using a displacement function to obtain a displacement-time course curve of the pile body, and judging according to a B-R criterion to obtain the unstable load of the pile body.
Preferably, the method for analyzing the dynamic stability of the single pile under the action of the ship impact load, which is disclosed by the invention, is used for calculating and analyzing nonlinear dynamic data of the pile foundation under the action of ship impact and wave instantaneous impact load, and comprises the following steps of:
(1) displacement expression in the model was performed:
the pile foundation model is shown in figure 1, the vertical load of the pile top is set as P,
Figure BDA0002975512710000011
for a simplified mass of the superstructure, fzIs the wave load, (s-h) is the height range of the wave load effect, q1Is the impact load of the ship, (h)0S) is the range of action of the impact load of the ship, where q is1Is regarded as a rectangular load; the counter force of the foundation in the soil layer is calculated by adopting a two-parameter foundation model, and the counter force of the soil body is added with parameters of shearing action on the basis of the simplified Winkler foundation model, namely the two-parameter foundation; s is the thickness of the soil layer; w (z, t) is transverse to the pile bodyDisplacement, wherein u (z, t) is the vertical displacement of the pile body;
Figure BDA0002975512710000021
wherein:
Figure BDA0002975512710000022
l is the wavelength;
Figure BDA0002975512710000023
t is the wave period, rho is the density of the sea water and is 1030kg/m3；
g is gravity acceleration, and is 9.8m/s2(ii) a H is the wave height; alpha is a phase angle; z is a radical of1Depth of water, dLThe depth of the pile body into water is not included;
Figure BDA0002975512710000024
J1' is a first order Bessel function of the first kind, Y1' is first order;
u(x,z,t)＝u0(z,t)-zw,x(z,t)
w(x,z,t)＝w0(z,t)
wherein u is0(t)，w0(t) vertical displacement and horizontal displacement of the middle surface of the pile foundation respectively;
the nonlinear strain component of the considered geometry is expressed as:
Figure BDA0002975512710000025
the strain in other directions is 0, alpha is a parameter factor, and when alpha is 0, the geometric nonlinearity is not considered; when α ≠ 0, it means that geometric nonlinearity is considered; the stress-strain relationship of the material adopts the linear relationship shown in FIG. 2;
the stress-strain relation of the material adopts a linear relation, and sigma is equal to Eeε，
Here, only the elastic constitutive is considered, i.e. σ < σsIn the case of (1), thisWhen E ise≡E；
The relationship between the stress and the internal force and the constitutive equation can be known as follows:
Figure BDA0002975512710000026
M＝EIw，zz
m is bending moment in the pile body, N is axial force of the pile body, E is elastic modulus of the pile body, A is sectional area of the pile body, and I is sectional inertia moment of the pile body;
(2) establishing a kinetic equation:
taking part of the pile body structure for internal force analysis, as shown in fig. 3:
assuming that the top end of the pile foundation is hinged and the bottom is consolidated, the support reaction force of the pile top is obtained by a method of solving a simple hyperstatic beam according to the structure diagram of the part of the pile body in fig. 3, and the calculation is as follows:
Figure BDA0002975512710000031
then, taking the upper part of any z section of the pile body at any time for analysis, as shown in fig. 3, considering the stress balance of the pile body in the z direction and the moment balance around the o' point, obtaining the following balance equation:
Figure BDA0002975512710000032
Figure BDA0002975512710000033
obtaining the following formula according to the displacement boundary condition of the pile body:
z＝0,w(0,t)＝0,w,z(0,t)＝0,u(0,t)＝0
z＝l,w(l,t)＝0,w,zz(l,t)＝0,
Figure BDA0002975512710000034
assuming that the shaft is stationary before it is hit by the vessel and waves, the initial conditions of the equation are:
Figure BDA0002975512710000035
solving u and w according to the initial condition and the displacement boundary condition by combining a nonlinear dynamic differential equation; the method is characterized in that u and w are solved according to the initial condition and the displacement boundary condition by combining the nonlinear dynamic differential equation, but due to the complexity of the equation, the precise solution cannot be directly obtained through the differential equation, so that the numerical solution is obtained by adopting a numerical calculation method;
solving a nonlinear dynamic differential equation by adopting a numerical calculation method and a mode of combining a Galerkin method and a Longge-Kutta method; first assume that the equation has a functional solution of the form:
Figure BDA0002975512710000036
Figure BDA0002975512710000037
the solutions of these two assumed shape functions satisfy the above-mentioned displacement boundary conditions, and then the two function solutions are substituted into the above equation to obtain:
Figure BDA0002975512710000038
Figure BDA0002975512710000041
and processing the two equations by adopting a Galerkin method to obtain the following nonlinear dynamic differential control equation only containing time variables:
Figure BDA0002975512710000042
Figure BDA0002975512710000043
wherein λ1～λ7The coefficient of the differential equation obtained by the Galerkin method is calculated mainly by the following equation, and the specific calculation formula is as follows:
Figure BDA0002975512710000044
Figure BDA0002975512710000045
Figure BDA0002975512710000046
Figure BDA0002975512710000047
Figure BDA0002975512710000048
Figure BDA0002975512710000051
Figure BDA0002975512710000052
obtaining a numerical solution of U and W by carrying out numerical calculation on the formula, and then replacing the numerical solution into an assumed function solution to obtain displacement response functions U (z, t) and W (z, t) of the pile body;
and the numerical value calculation part adopts a fourth-order Runge-Kutta method to calculate, after the displacement response function of the pile body is obtained, the buckling instability damage of the structure is considered to occur according to the B-R criterion, namely the severe response increment caused by the structure under the micro impact increment, by drawing the displacement time-course curve of the pile body, so as to judge and obtain the instability load of the pile body.
A single-pile dynamic stability analysis system under the action of ship impact load comprises:
a storage subsystem for storing a computer program;
the information processing subsystem: the method is used for realizing the steps of the single-pile dynamic stability analysis method under the action of the ship impact load when a computer program is executed.
Compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable advantages:
1. the invention considers the action of the soil body on the pile side to effectively improve the destabilizing load, and the restraining action of the soil body can lead the pile body to experience a section of stable vibration before the destabilizing; compared with the traditional Winkler model, the instability load and pile body displacement time-course curve calculated by adopting the two-parameter model are more in accordance with the engineering practice;
2. the invention adopts a Longge-Kutta method to carry out numerical solution; the displacement function of the pile body can be obtained by solving the equation, the displacement time-course curve of the pile body can be obtained after the displacement function is calculated, and then the unstable load of the pile body is obtained by judging according to the B-R criterion; the method can reduce the cost, accurately meet the engineering practice and is suitable for popularization and use.
Drawings
FIG. 1 is a diagram of a pile-soil model according to the present invention.
Fig. 2 is a stress-strain plot of a material as described in the present invention.
Fig. 3 is a calculation model diagram of the pile body part structure in the invention.
Fig. 4 is a diagram showing the setting of the boundary conditions of the model and the application of the load in the present invention.
FIG. 5 is a graph of a model mesh partition as described in the present invention.
FIG. 6 is a graph comparing a theoretical solution to a finite element solution as described in the present invention.
Fig. 7 is a graph of displacement versus time course of the pile body under different impact loads according to the present invention.
FIG. 8 is a graph of the relative displacement versus time course of two foundation models as described in the present invention.
FIG. 9 is a comparison graph of the influence of the soil body parameter k on the destabilizing load in the invention.
Fig. 10 is a graph comparing the effect of pile top mass on destabilizing loads in the present invention (λ ═ 110).
Fig. 11 is a graph showing the effect of the mass M0 on the destabilizing load (λ ═ 70) in the present invention.
Detailed Description
The above-described scheme is further illustrated below with reference to specific embodiments, which are detailed below:
the first embodiment is as follows:
in this embodiment, referring to fig. 1-2, a method for analyzing dynamic stability of a single pile under the action of ship impact load, which adopts a two-parameter foundation model, establishes a basic nonlinear dynamical equation of a partially embedded pile under the action of ship impact and wave instantaneous impact load, obtains a dynamical differential control equation only with time variability by using a galaogin integration method, and obtains a displacement type function of a pile body by performing displacement solution on the equation by using a fourth-order longge-kuta method; and (4) calculating by using a displacement function to obtain a displacement-time course curve of the pile body, and judging according to a B-R criterion to obtain the unstable load of the pile body.
In the embodiment, a Longge-Kutta method is adopted to carry out numerical solution; the displacement function of the pile body can be obtained by solving the equation, the displacement time-course curve of the pile body can be obtained after the displacement function is calculated, and then the unstable load of the pile body is obtained by judging according to the B-R criterion; the method can reduce cost, can accurately meet engineering practice, and is suitable for popularization and use.
Example two:
this embodiment is substantially the same as the first embodiment, and is characterized in that:
in this embodiment, a method for analyzing the dynamic stability of a single pile under the action of a ship impact load is used for calculating and analyzing nonlinear dynamic data of a pile foundation under the action of ship impact and wave instantaneous impact load, and includes the following steps:
(1) displacement expression in the model was performed:
setting P as the vertical load of the pile top,
Figure BDA0002975512710000061
for a simplified mass of the superstructure, fzIs the wave load, (s-h) is the height range of the wave load effect, q1Is the impact load of the ship, (h)0S) is the range of action of the impact load of the ship, where q is1Is regarded as a rectangular load; the counter force of the foundation in the soil layer is calculated by adopting a two-parameter foundation model, and the counter force of the soil body is added with parameters of shearing action on the basis of the simplified Winkler foundation model, namely the two-parameter foundation; s is the thickness of the soil layer; w (z, t) is the horizontal displacement of the pile body, and u (z, t) is the vertical displacement of the pile body;
Figure BDA0002975512710000062
wherein:
Figure BDA0002975512710000063
l is the wavelength;
Figure BDA0002975512710000064
t is the wave period, rho is the density of the sea water and is 1030kg/m3；
g is gravity acceleration, and is 9.8m/s2(ii) a H is the wave height; alpha is a phase angle; z is a radical of1Depth of water, dLThe depth of the pile body into water is not included;
Figure BDA0002975512710000071
J1is a first order Bessel of the first kindFunction, Y1' is first order;
u(x,z,t)＝u0(z,t)-zw,x(z,t)
w(x,z,t)＝w0(z,t)
wherein u is0(t)，w0(t) vertical displacement and horizontal displacement of the middle surface of the pile foundation respectively;
the nonlinear strain component of the considered geometry is expressed as:
Figure BDA0002975512710000072
the strain in other directions is 0, alpha is a parameter factor, and when alpha is 0, the geometric nonlinearity is not considered; when α ≠ 0, it means that geometric nonlinearity is considered;
the stress-strain relation of the material adopts a linear relation, and sigma is equal to Eeε，
Here, only the elastic constitutive is considered, i.e. σ < σsIn this case, Ee≡E；
The relationship between the stress and the internal force and the constitutive equation can be known as follows:
Figure BDA0002975512710000073
M＝EIw，zz
m is bending moment in the pile body, N is axial force of the pile body, E is elastic modulus of the pile body, A is sectional area of the pile body, and I is sectional inertia moment of the pile body;
(2) establishing a kinetic equation:
taking the part of the pile body structure for internal force analysis:
assuming that the top end of the pile foundation is hinged and the bottom is consolidated, the method for solving the simple hyperstatic beam is utilized to obtain the support counterforce of the pile top according to the partial structure diagram of the pile body, and the calculation is as follows:
Figure BDA0002975512710000074
then, the upper part of an arbitrary z section of the pile body at an arbitrary moment is taken for analysis, the stress balance of the pile body in the z direction and the moment balance around the o' point are considered, and the following balance equation is obtained:
Figure BDA0002975512710000075
Figure BDA0002975512710000081
obtaining the following formula according to the displacement boundary condition of the pile body:
z＝0,w(0,t)＝0,w,z(0,t)＝0,u(0,t)＝0
z＝l,w(l,t)＝0,w,zz(l,t)＝0,
Figure BDA0002975512710000082
assuming that the shaft is stationary before it is hit by the vessel and waves, the initial conditions of the equation are:
Figure BDA0002975512710000083
solving u and w according to the initial condition and the displacement boundary condition by combining a nonlinear dynamic differential equation;
solving a nonlinear dynamic differential equation by adopting a numerical calculation method and a mode of combining a Galerkin method and a Longge-Kutta method; first assume that the equation has a functional solution of the form:
Figure BDA0002975512710000084
Figure BDA0002975512710000085
the solutions of these two assumed shape functions satisfy the above-mentioned displacement boundary conditions, and then the two function solutions are substituted into the above equation to obtain:
Figure BDA0002975512710000086
Figure BDA0002975512710000087
and processing the two equations by adopting a Galerkin method to obtain the following nonlinear dynamic differential control equation only containing time variables:
Figure BDA0002975512710000091
Figure BDA0002975512710000092
wherein λ1～λ7The coefficient of the differential equation obtained by the Galerkin method is calculated mainly by the following equation, and the specific calculation formula is as follows:
Figure BDA0002975512710000093
Figure BDA0002975512710000094
Figure BDA0002975512710000095
Figure BDA0002975512710000096
Figure BDA0002975512710000097
obtaining a numerical solution of U and W by carrying out numerical calculation on the formula, and then replacing the numerical solution into an assumed function solution to obtain displacement response functions U (z, t) and W (z, t) of the pile body;
and the numerical value calculation part adopts a fourth-order Runge-Kutta method to calculate, after the displacement response function of the pile body is obtained, the buckling instability damage of the structure is considered to occur according to the B-R criterion, namely the severe response increment caused by the structure under the micro impact increment, by drawing the displacement time-course curve of the pile body, so as to judge and obtain the instability load of the pile body.
The method analyzes the nonlinear dynamics stability problem of the pile foundation under the action of ship impact and wave instantaneous impact load, adopts a two-parameter foundation model to establish a nonlinear dynamics basic equation of a partially embedded pile under the action of ship impact and wave instantaneous impact load, obtains a dynamics differential control equation only with time variability by using a Galerkin integration method, and obtains a displacement type function of the pile body by performing displacement solution on the equation by using a fourth-order Runge-Kutta method. After the displacement function is calculated, a displacement-time course curve of the pile body can be obtained, and the unstable load of the pile body is obtained according to judgment of a B-R criterion. According to the invention, through example calculation, the unstable load can be effectively improved by considering the action of the soil body on the pile side, and the pile body can undergo a section of stable vibration before the instability due to the constraint action of the soil body; compared with the traditional Winkler model, the instability load and pile body displacement time-course curve calculated by adopting the two-parameter model are more in accordance with the engineering practice.
Example three:
this embodiment is substantially the same as the first embodiment, and is characterized in that:
in the embodiment, modeling analysis is performed by using ABAQUS finite element software, and the correctness of a theoretical solution is verified. The model unit adopts a three-dimensional entity unit with the unit type of C3D8R, and the reduction productThe hourglass control is carried out, and the total unit number is 100458; the model size is that pile length l equals 55m, pile diameter d equals 2m, and the soil body model is a cube of 40x50x40 m. The parameters are selected as follows: the elastic modulus E of the pile body is 30Gpa, the Poisson ratio is 0.2, the depth of the pile body embedded into the soil body is 30m, and rho is 2.6 multiplied by 103kg/m3(ii) a The boundary condition of the model is set as that the bottom end is fixed, the displacement in the x direction is limited in the x direction, and the displacement in the y direction is limited in the y direction; the wave load and the impact load of the ship are directly applied to the corresponding positions of the pile body after calculation, and contact is arranged at the pile-soil interface. The load application and meshing of the finite element model is shown in detail in fig. 4. The calculation method comprises the following steps:
the embodiment adopts a nonlinear dynamical fundamental equation for the pile foundation under the action of ship impact and wave instantaneous impact load. Fig. 4 is a diagram of a model with boundary condition setting and load application of the model, and it is seen from the diagram that the model mainly bears vertical static load and horizontal impact load, and the horizontal impact load is composed of two parts, one part is impact load of a ship and the other part is attack load of waves; the soil body is divided into a plurality of geometric examples, and the grids are encrypted at the part close to the pile foundation, as shown in figure 5, and the encrypted parts of the grids are clearly seen in the figure.
Through finite element simulation, a displacement time-course curve of the pile body is obtained, so that the following results are obtained:
as can be seen from fig. 6, the theoretical solution is relatively well matched with the results of finite element simulation, which indicates the correctness of theoretical derivation, so the results of theoretical derivation will be used below for specific unstable load calculation and parameter analysis.
Selecting a round section pile with the pile length l equal to 55m and the pile diameter d equal to 1.8m for analysis, E equal to 30Gpa and I equal to pi d4/64，υ＝0.2，ρ＝2.6×103kg/m3And the pile body flexibility lambda is 85.6. The displacement time course curve of the pile body obtained by the function equation is shown in figure 7, wherein q is shown in the figurecThe sum of the loads distributed for the vessel and the waves, wherein the wave load is calculated according to the wave parameters, the wave load remains unchanged during the analysis, qcThe increase of (b) mainly refers to the increase of the impact load of the ship.
From fig. 7 it can be seen that when the vessel and the wave jointly hit the load qcWhen the displacement is less than 2345kN, the displacement of the pile body is in a stable vibration state; along with the increase of load, the displacement of pile body increases gradually, and when the load of impact increases to a certain extent, the pile body is no longer in stable vibration state, and the displacement lasts the increase, shows at this moment that the pile body has unstability under the impact load effect. In addition, we can find an interesting phenomenon from the graph, as the load increases, when q iscWhen the time t is about 0.8 second, the displacement of the pile body changes suddenly and does not vibrate stably any more, the displacement begins to develop towards infinity, the instability of the pile body occurs for the first time, and the load at the moment is the minimum load of the instability of the pile body; and then as the load continues to increase, when q is takencAt 3245kN we find that the time of pile instability is advanced, and when q is reachedc3545kN, the displacement of the pile body is towards infinity from the beginning, the pile body directly begins to be unstable, previous researches regard the load at the moment as unstable load, and as seen from the figure, the pile body is already unstable under the action of the previous load, different from the unstable at the moment, the unstable pile body firstly vibrates in a stable state for a period of time, then the displacement tends to infinity, and when q is equal to q, the unstable pile body firstly vibrates in a stable state for a period of time, and then the displacement tends to infinity is achievedcAt 3545kN, shaft displacement tends directly to infinity. This also indicates that the shaft will be destabilized faster and faster after the load exceeds the minimum destabilizing load.
Fig. 7 is a comparison of pile body displacement responses calculated by two foundation models, and it can be seen from the figure that, by using the two-parameter foundation model, after considering the shear stiffness of the soil body, the displacement of the pile body is significantly reduced, and the instability load of the corresponding pile body is also significantly improved compared with that calculated by the Winkler model, which also shows that, when the pile body under the impact load calculation is stable, the result calculated by using the two-parameter foundation model is more practical, while the Winkler model is a traditional foundation model, which brings great convenience to our research.
When the wave load is used as the stability of the pile body under the action of simple harmonic load, it is found that a soil resistance parameter k on the pile side has a relatively large influence on the stability, and whether a soil resistance coefficient k has the same influence on the stability of the pile foundation under the action of impact load, next, specific research is carried out, and the influence of k on the stability of the pile body under the action of impact load is analyzed, as shown in fig. 9.
Three different foundation parameter values k are taken, and as seen from the figure, when k is smaller, the instability load is smaller relatively, the instability occurrence time of the pile body is earlier, and the steady-state vibration time is shorter; as the value of k is increased, the time of steady-state vibration is also increased, the time of instability is delayed, the corresponding minimum instability load is also rapidly increased, and when the value of k is increased to three times of the original value, the value of the instability load is increased to 2.84 times of the original value and is close to three times; in addition, as can be seen from the figure, when k is 3 × 106Taking the impact load qcWhen the load reaches the unstable load, although the pile body can first experience a section of stable vibration, the vibration amplitude at the moment is larger than that under the normal condition, and therefore instability is predicted to occur later. Through the analysis of the upper graph, the resistance coefficient k of the soil body on the pile side still plays an important role in the stability of the pile body under the action of the impact load.
Finally, the pile top mass block is analyzed
Figure BDA0002975512710000121
The influence on the destabilizing load is shown in fig. 10 and 11:
as can be seen from FIG. 10, the accompanying mass
Figure BDA0002975512710000122
The unstable load is increased along with the increase of the load,and the time for instability to occur also increases slightly with the mass; as can be seen from fig. 11, when λ is 70, that is, after the compliance of the pile body is reduced, as the mass of the pile body is increased, the destabilizing load is reduced, and the time for the pile body to destabilize is also advanced. After analysis, it is found that when the flexibility of the pile body is larger, the increase of the mass of the pile top is beneficial to the stability of the pile body, and when the flexibility of the pile body is smaller, the unstable load is reduced along with the increase of the mass, so that the stability of the pile body is adversely affected, and particularly when the flexibility is equal to a small value, the influence of the increase of the mass on the unstable load reaches a balance point, so that the influence needs to be determined according to different engineering practice.
The simulation result graphs are shown in FIGS. 7-11, and the calculation results show that: after the action of a pile side soil body is considered, when an impact load reaches an instability load, a pile body undergoes a section of steady-state vibration firstly and then displacement changes suddenly, the displacement is increased rapidly, and the pile body is unstable; when the impact load exceeds the instability load and continues to increase, the steady-state vibration section can be gradually reduced to disappear, namely, the displacement of the pile body is quickly increased once the load is applied, and the pile body is directly unstable. Compared with the traditional Winkler foundation model, the double-parameter model is more practical, and the displacement time-course curve of the pile body obtained by calculation of the double-parameter foundation model is small in displacement amplitude compared with the Winkler model, so that the obtained instability load is large. The soil resistance coefficient k of the pile side plays an important role in stabilizing the pile body, and the instability load of the pile body is correspondingly increased along with the increase of k. Along with the increase of the pile top quality, the instability load of the pile body is increased within a certain flexibility range, and the stability is improved; and when the flexibility of the pile body exceeds a certain range, the instability load is gradually reduced along with the increase of the mass, and the stability of the pile body is not favorable.
Example four:
this embodiment is substantially the same as the above embodiment, and is characterized in that:
in this embodiment, a single pile dynamic stability analysis system under boats and ships striking load effect includes:
a storage subsystem for storing a computer program;
the information processing subsystem: the steps for implementing the method for analyzing the dynamic stability of a monopile under the action of a ship impact load according to claim 1 or 2 when executing a computer program.
In the embodiment, the action of the soil body on the pile side is considered in calculation and analysis, so that the unstable load can be effectively improved, the pile body can undergo a section of stable vibration before the instability due to the constraint action of the soil body, the calculation overhead is obviously reduced, the cost is solved, and the method is suitable for popularization and application in engineering practice.
The embodiments of the present invention have been described with reference to the accompanying drawings, but the present invention is not limited to the embodiments, and various changes and modifications can be made according to the purpose of the invention, and any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention shall be equivalent substitutions, as long as the purpose of the present invention is met, and the present invention shall fall within the protection scope of the present invention without departing from the technical principle and inventive concept of the present invention.

Claims (3)

1. A single-pile dynamic stability analysis method under the action of ship impact load is characterized by comprising the following steps: the method comprises the steps of establishing a nonlinear dynamic basic equation of a partially embedded pile under the action of ship impact and wave instantaneous impact load by adopting a two-parameter foundation model, obtaining a dynamic differential control equation only with time variability by utilizing a Galerkin integration method, and performing displacement solution on the equation by adopting a fourth-order Runge-Kutta method to obtain a displacement type function of a pile body; and (4) calculating by using a displacement function to obtain a displacement-time course curve of the pile body, and judging according to a B-R criterion to obtain the unstable load of the pile body.
2. The method for analyzing the dynamic stability of the single pile under the action of the ship impact load according to claim 1, wherein the method comprises the following steps: the method for calculating and analyzing the nonlinear dynamic data of the pile foundation under the action of the ship impact and the wave instantaneous impact load comprises the following steps:
(1) displacement expression in the model was performed:
setting P as the vertical load of the pile top,
Figure FDA0002975512700000011
for a simplified mass of the superstructure, fzIs the wave load, (s-h) is the height range of the wave load effect, q1Is the impact load of the ship, (h)0S) is the range of action of the impact load of the ship, where q is1Is regarded as a rectangular load; the counter force of the foundation in the soil layer is calculated by adopting a two-parameter foundation model, and the counter force of the soil body is added with parameters of shearing action on the basis of the simplified Winkler foundation model, namely the two-parameter foundation; s is the thickness of the soil layer; w (z, t) is the horizontal displacement of the pile body, and u (z, t) is the vertical displacement of the pile body;
Figure FDA0002975512700000012
wherein:
Figure FDA0002975512700000013
l is the wavelength;
Figure FDA0002975512700000014
t is the wave period, rho is the density of the sea water and is 1030kg/m3；
g is gravity acceleration, and is 9.8m/s2(ii) a H is the wave height; alpha is a phase angle; z is a radical of1Depth of water, dLThe depth of the pile body into water is not included;
Figure FDA0002975512700000015
J1' is a first order Bessel function of the first kind, Y1' is first order;
u(x,z,t)＝u0(z,t)-zw,x(z,t)
w(x,z,t)＝w0(z,t)
wherein u is0(t)，w0(t) vertical displacement and horizontal displacement of the middle surface of the pile foundation respectively;
the nonlinear strain component of the considered geometry is expressed as:
Figure FDA0002975512700000016
the strain in other directions is 0, alpha is a parameter factor, and when alpha is 0, the geometric nonlinearity is not considered; when α ≠ 0, it means that geometric nonlinearity is considered;
the stress-strain relation of the material adopts a linear relation, and sigma is equal to Eeε，
Here, only the elastic constitutive is considered, i.e. σ < σsIn this case, Ee≡E；
The relationship between the stress and the internal force and the constitutive equation can be known as follows:
Figure FDA0002975512700000021
M＝EIw，zz
m is bending moment in the pile body, N is axial force of the pile body, E is elastic modulus of the pile body, A is sectional area of the pile body, and I is sectional inertia moment of the pile body;
(2) establishing a kinetic equation:
taking the part of the pile body structure for internal force analysis:
assuming that the top end of the pile foundation is hinged and the bottom is consolidated, the method for solving the simple hyperstatic beam is utilized to obtain the support counterforce of the pile top according to the partial structure diagram of the pile body, and the calculation is as follows:
Figure FDA0002975512700000022
then, the upper part of an arbitrary z section of the pile body at an arbitrary moment is taken for analysis, the stress balance of the pile body in the z direction and the moment balance around the o' point are considered, and the following balance equation is obtained:
Figure FDA0002975512700000023
Figure FDA0002975512700000024
obtaining the following formula according to the displacement boundary condition of the pile body:
z＝0,w(0,t)＝0,w,z(0,t)＝0,u(0,t)＝0
Figure FDA0002975512700000031
assuming that the shaft is stationary before it is hit by the vessel and waves, the initial conditions of the equation are:
Figure FDA0002975512700000032
solving u and w according to the initial condition and the displacement boundary condition by combining a nonlinear dynamic differential equation;
solving a nonlinear dynamic differential equation by adopting a numerical calculation method and a mode of combining a Galerkin method and a Longge-Kutta method; first assume that the equation has a functional solution of the form:
Figure FDA0002975512700000033
Figure FDA0002975512700000034
the solutions of these two assumed shape functions satisfy the above-mentioned displacement boundary conditions, and then the two function solutions are substituted into the above equation to obtain:
Figure FDA0002975512700000035
Figure FDA0002975512700000036
and processing the two equations by adopting a Galerkin method to obtain the following nonlinear dynamic differential control equation only containing time variables:
Figure FDA0002975512700000037
Figure FDA0002975512700000038
wherein λ1～λ7The coefficient of the differential equation obtained by the Galerkin method is calculated mainly by the following equation, and the specific calculation formula is as follows:
Figure FDA0002975512700000041
Figure FDA0002975512700000042
Figure FDA0002975512700000043
Figure FDA0002975512700000044
Figure FDA0002975512700000045
Figure FDA0002975512700000046
Figure FDA0002975512700000047
obtaining a numerical solution of U and W by carrying out numerical calculation on the formula, and then replacing the numerical solution into an assumed function solution to obtain displacement response functions U (z, t) and W (z, t) of the pile body;
and the numerical value calculation part adopts a fourth-order Runge-Kutta method to calculate, after the displacement response function of the pile body is obtained, the buckling instability damage of the structure is considered to occur according to the B-R criterion, namely the severe response increment caused by the structure under the micro impact increment, by drawing the displacement time-course curve of the pile body, so as to judge and obtain the instability load of the pile body.
3. The utility model provides a single pile dynamic stability analytic system under boats and ships striking load effect which characterized in that includes:
a storage subsystem for storing a computer program;
the information processing subsystem: the steps for implementing the method for analyzing the dynamic stability of a monopile under the action of a ship impact load according to claim 1 or 2 when executing a computer program.
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