CN112307544A - Liquefied soil pile foundation horizontal dynamic response analysis method based on Passternak foundation model - Google Patents

Liquefied soil pile foundation horizontal dynamic response analysis method based on Passternak foundation model Download PDF

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CN112307544A
CN112307544A CN202011193106.XA CN202011193106A CN112307544A CN 112307544 A CN112307544 A CN 112307544A CN 202011193106 A CN202011193106 A CN 202011193106A CN 112307544 A CN112307544 A CN 112307544A
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崔春义
辛宇
梁志孟
王本龙
孟坤
刘海龙
裴华富
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Dalian Maritime University
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Abstract

The invention provides a liquefied soil pile foundation horizontal dynamic response analysis method based on a Passternak foundation model, which comprises the following steps: dividing soil layers in the foundation into a liquefied soil layer and a non-liquefied soil layer, enabling the liquefied soil layer on the top layer of the foundation to be equivalent to fluid, and establishing a fluid motion control equation of the liquefied soil layer under a cylindrical coordinate system; determining boundary conditions met by the liquefied soil layer during movement; determining the hydrodynamic pressure acting on the pile foundation according to a liquefied soil layer fluid motion control equation and boundary conditions; determining a dynamic balance equation of the foundation pile in the liquefied soil, and solving a horizontal displacement amplitude of the pile foundation in the liquefied soil layer; determining the relationship between the corner amplitude, the bending moment amplitude, the shear amplitude and the horizontal displacement amplitude of the top end and the bottom end of the pile foundation in the liquefied soil layer; determining the horizontal displacement amplitude of a pile foundation in a non-liquefied soil layer; determining a horizontal impedance, a sway impedance, and a horizontal-sway coupling impedance of a top of the pile foundation.

Description

Liquefied soil pile foundation horizontal dynamic response analysis method based on Passternak foundation model
Technical Field
The invention relates to the field of civil engineering, in particular to a method for analyzing horizontal dynamic response of a liquefied soil pile foundation based on a Passternak foundation model.
Background
In recent years, attention is paid to the phenomenon that buildings are damaged along with liquefaction of soil bodies in the earthquake process. With the investigation and research on the damage of the pile foundation under the condition of liquefied soil, people find that the pile foundation in the liquefied soil is often damaged due to earthquake and serious life and property loss is caused. Therefore, more and more scholars have made relevant researches on the seismic performance of the pile foundation in the liquefied soil. In the past, most of the researches consider the liquefied soil as a solid foundation, and the performance of the liquefied soil is researched by adopting a strength reduction method, so that the pile foundation performance in the liquefied soil cannot be accurately analyzed.
Disclosure of Invention
The invention provides a liquefied soil pile foundation horizontal dynamic response analysis method based on a Passternak foundation model, which aims to overcome the technical problems.
The invention provides a liquefied soil pile foundation horizontal dynamic response analysis method based on a Passternak foundation model, which comprises the following steps:
s1: dividing soil layers in the foundation into a liquefied soil layer and a non-liquefied soil layer, enabling the liquefied soil layer on the top layer of the foundation to be equivalent to fluid, and establishing a fluid motion control equation of the liquefied soil layer under a cylindrical coordinate system;
s2: determining boundary conditions that the liquefied soil layer meets when in motion;
s3: determining the hydrodynamic pressure acting on the pile foundation according to the liquefied soil layer fluid motion control equation and the boundary condition;
s4: determining a dynamic balance equation of the foundation pile in the liquefied soil according to an Euler-Bernouli beam theory and the hydrodynamic pressure, and solving a horizontal displacement amplitude of the pile foundation in the liquefied soil layer; determining the relation between the corner amplitude, the bending moment amplitude, the shearing amplitude and the horizontal displacement amplitude of the top end and the bottom end of the pile foundation in the liquefied soil layer according to an Euler beam theory;
s5: determining a dynamic balance equation of the foundation pile in the non-liquefied soil, and solving a horizontal displacement amplitude of the pile foundation in the non-liquefied soil layer;
determining the relation between the corner amplitude, the bending moment amplitude, the shearing amplitude and the horizontal displacement amplitude of the top end and the bottom end of the pile foundation in the non-liquefied soil layer according to an Euler beam theory;
the foundation piles are continuous at the interface of the liquefied soil and the non-liquefied soil, and the relation between the corner amplitude, the bending moment amplitude, the shear amplitude and the horizontal displacement amplitude of the bottom end of the pile foundation in the liquefied soil layer is the relation between the corner amplitude, the bending moment amplitude, the shear amplitude and the horizontal displacement amplitude of the top end of the pile foundation in the non-liquefied soil layer; and determining a horizontal impedance, a sway impedance, and a horizontal-sway coupling impedance of a top of the pile foundation.
Further, in S1, the liquefied soil layer fluid motion control equation is as follows:
Figure BDA0002753276710000021
wherein: phi (r, theta, z, t) is a fluid velocity potential function, r represents a radial direction, theta is a rotation angle of the micro-element in horizontal projection, z is a longitudinal coordinate, a longitudinal coordinate zero point is positioned on a free surface and is positive downwards, t is a time coordinate,
Figure BDA0002753276710000022
to calculate the sign of the partial derivatives.
Further, in S2, the boundary conditions satisfied by the liquefied soil layer are as follows:
when the bottom z of the liquefied soil layer is equal to h1Its vertical speed is zero, i.e.:
Figure BDA0002753276710000023
neglecting the influence of gravity waves on the fluid, on the surface of the liquefied soil layer:
φ|z＝0＝0 (3)
fluid at radial infinity is at rest:
φ|r→∞＝0 (4)
the continuous contact condition of the fluid and the pile foundation is as follows:
Figure BDA0002753276710000024
wherein:
Figure BDA0002753276710000025
for horizontal displacement of pile sections in liquefied soil layers, r0Is the pile body radius.
Further, based on the fact that the pile foundation is finally in steady-state vibration in the liquefied soil layer, the fluid velocity potential function is expressed as:
φ(r,θ,z,t)＝φ(r,θ,z)eiωt。 (6)
further, in S3, the hydrodynamic pressure is calculated by the following formula:
Figure BDA0002753276710000026
wherein: rholIs the density of the liquefied soil.
Further, the dynamic balance equation of the foundation pile in the liquefied soil is as follows:
Figure BDA0002753276710000031
wherein: ep、Ip、mpRespectively the elastic modulus, the section inertia moment and the unit length mass of the pile body, N0Is the axial force acting on the pile top.
Further, the dynamic balance equation of the foundation pile in the non-liquefied soil is as follows:
Figure BDA0002753276710000032
wherein:
Figure BDA0002753276710000033
the horizontal displacement of a j layer pile foundation mass point is obtained;
Figure BDA0002753276710000034
the shear stiffness coefficient of the foundation around the jth layer of piles,
Figure BDA0002753276710000035
the rigidity coefficient of soil around the pile is shown,
Figure BDA0002753276710000036
distributing damping for soil around the pile; b is00.9(1.5d +0.5) is the calculated width of the stake.
According to the invention, the liquefied soil part is simplified into fluid, the non-liquefied soil layer considers the foundation shearing effect, the layered Passternak foundation is equivalent to the layered Passternak foundation, and the pile foundation is simplified into an Euler beam model.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic flow chart of an embodiment of the present invention;
FIG. 2 is a simplified computational model diagram of the horizontal simple harmonic excitation of the pile foundation in liquefied soil and non-liquefied soil according to an embodiment of the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in figure 2, horizontal simple resonance exciting force Q is applied to the top of the pile foundation0eiωt、M0eiωtWherein Q is0、M0To the amplitude of the exciting force, N0Is axial acting force, omega is excitation circle frequency,
Figure BDA0002753276710000037
t is time. In addition, the thickness of the jth layer of soil, the stiffness coefficient of soil around the pile, the damping coefficient and the shear stiffness coefficient of the foundation are respectively hj、
Figure BDA0002753276710000041
And
Figure BDA0002753276710000042
the pile length is divided into two parts, L respectively1、L2The pile diameter is d.
The basic assumptions of the present application are as follows:
1) simplifying the pile foundation into a round uniform-section homogeneous Euler beam;
2) the soil body around the pile foundation is divided into n layers along the longitudinal direction of the pile foundation, the first layer is a liquefied soil layer, the other layers are non-liquefied soil layers, and each layer of soil body is simplified into a Passternak foundation model to describe the interaction between the pile and the soil;
3) all parts of the pile and the soil body meet the small deformation condition, and the pile-soil interface is in complete contact and has no relative sliding;
4) only horizontal displacement occurs at the pile top, and the pile bottom is fixed end constraint;
under the above assumed conditions: as shown in figure 1 of the drawings, in which,
s1: the soil layers in the foundation are divided into a liquefied soil layer and a non-liquefied soil layer, the liquefied soil layer on the top layer of the foundation is equivalent to fluid, and a fluid motion control equation of the liquefied soil layer under a cylindrical coordinate system is established;
s2: determining boundary conditions that the liquefied soil layer meets when in motion;
s3: determining the hydrodynamic pressure acting on the pile foundation according to the liquefied soil layer fluid motion control equation and the boundary condition;
s4: determining a dynamic balance equation of the foundation pile in the liquefied soil according to an Euler-Bernouli beam theory and the hydrodynamic pressure, and solving a horizontal displacement amplitude of the pile foundation in the liquefied soil layer; determining the relation between the corner amplitude, the bending moment amplitude, the shearing amplitude and the horizontal displacement amplitude of the top end and the bottom end of the pile foundation in the liquefied soil layer according to an Euler beam theory;
s5: determining a dynamic balance equation of the foundation pile in the non-liquefied soil, and solving a horizontal displacement amplitude of the pile foundation in the non-liquefied soil layer;
s5: determining a dynamic balance equation of the foundation pile in the non-liquefied soil, and solving a horizontal displacement amplitude of the pile foundation in the non-liquefied soil layer;
determining the relation between the corner amplitude, the bending moment amplitude, the shearing amplitude and the horizontal displacement amplitude of the top end and the bottom end of the pile foundation in the non-liquefied soil layer according to an Euler beam theory;
the foundation piles are continuous at the interface of the liquefied soil and the non-liquefied soil, and the relation between the corner amplitude, the bending moment amplitude, the shear amplitude and the horizontal displacement amplitude of the bottom end of the pile foundation in the liquefied soil layer is the relation between the corner amplitude, the bending moment amplitude, the shear amplitude and the horizontal displacement amplitude of the top end of the pile foundation in the non-liquefied soil layer; and determining a horizontal impedance, a sway impedance, and a horizontal-sway coupling impedance of a top of the pile foundation.
Specifically, a liquefied soil layer is equivalent to a fluid to be simulated, and according to a related theory of hydraulics, a liquefied soil layer fluid motion control equation under a cylindrical coordinate system is established:
Figure BDA0002753276710000051
wherein: phi (r, theta, z, t) is a fluid velocity potential function, r represents a radial direction, theta is a rotation angle of the micro-element in horizontal projection, z is a longitudinal coordinate, a longitudinal coordinate zero point is positioned on a free surface and is positive downwards, t is a time coordinate,
Figure BDA0002753276710000056
to calculate the sign of the partial derivatives.
Based on the assumption of the mechanical model, the liquefied soil layer needs to satisfy the following boundary conditions during movement:
(1) when the bottom z of the liquefied soil layer is equal to h1Its vertical speed is zero, i.e.:
Figure BDA0002753276710000052
wherein h is1The thickness of the liquefied soil layer.
(2) Neglecting the influence of gravity waves on the fluid, on the surface of the liquefied soil layer:
φ|z＝0＝0 (3)
(3) fluid at radial infinity is at rest:
φ|r→∞＝0 (4)
(4) the continuous contact condition of the fluid and the pile body is as follows:
Figure BDA0002753276710000053
in the formula:
Figure BDA0002753276710000054
for horizontal displacement of pile foundation in liquefied soil, r0Is the pile foundation radius.
Considering that the pile foundation is finally in steady-state vibration in the liquefied soil layer, the fluid velocity potential function can be expressed as:
φ(r,θ,z,t)＝φ(r,θ,z)eiωt (6)
using the separation variables for the above equation, the fluid velocity potential function can be set as:
φ(r,θ,z)eiωt＝R(r)Θ(θ)Z(z)eiωt (7)
substituting equation (7) for equation (1) and considering the boundary conditions (2) to (5) yields a fluid velocity potential function solution:
Figure BDA0002753276710000055
in the formula: k1(iαnr) is a first order Bessel function, A is a coefficient to be determined,
Figure BDA0002753276710000061
Figure BDA0002753276710000062
according to the Bernouli equation, the hydrodynamic pressure acting on the pile foundation can be further obtained as follows:
Figure BDA0002753276710000063
in the formula: rholIs the density of the liquefied soil.
The formula (8) may be substituted for the formula (9):
Figure BDA0002753276710000064
according to the Euler-Bernouli beam theory, the dynamic balance equation of the pile foundation in the liquefied soil is obtained as follows (z is more than or equal to 0 and less than or equal to h1)：
Figure BDA0002753276710000065
In the formula: ep、Ip、mpRespectively the modulus of elasticity, the section moment of inertia and the mass per unit length of the pile foundation, N0Is the axial force acting on the pile top.
The potential function of horizontal displacement and fluid movement speed of the pile foundation can be expressed as follows:
Figure BDA0002753276710000066
in the formula (I), the compound is shown in the specification,
Figure BDA0002753276710000067
the horizontal displacement amplitude of the pile foundation in the liquefied soil layer is obtained.
Substituting equation (12) for equation (11) may further yield the following equation:
Figure BDA0002753276710000068
in the formula: mp＝EpIp，
Figure BDA0002753276710000069
Obviously, equation (13) is a fourth-order linear constant coefficient heterogeneous differential equation, the corresponding solution of which consists of a general solution and a special solution, and the equation displacement homogeneous general solution is:
Figure BDA00027532767100000610
in the formula (I), the compound is shown in the specification,
Figure BDA00027532767100000611
coefficient D1、D2、D3、D4Will be determined by the boundary conditions.
The non-homogeneous solution of equation (13) is set as:
Figure BDA0002753276710000071
by substituting formula (15) for formula (13):
Figure BDA0002753276710000072
thus, the general solution of equation (13) is:
Figure BDA0002753276710000079
considering the continuous contact condition of the fluid and the pile body, the formulas (8) and (17) are respectively substituted for the formula (4) to obtain:
Figure BDA0002753276710000073
in the formula:
Figure BDA0002753276710000074
multiplying both sides of the formula (18) by ch (. alpha.)nz) and a further interval [0, h ]1]Integrating up, one can obtain:
Figure BDA0002753276710000075
in the formula:
Figure BDA0002753276710000076
the horizontal displacement solution of the pile body in the liquefied soil is as follows:
Figure BDA0002753276710000077
in the formula: eta1＝κS1，η2＝κS2，η3＝κS3，η4＝κS4，
Figure BDA0002753276710000078
The relational expression of the corner, the bending moment, the shearing force and the pile body displacement of the pile foundation in the liquefied soil layer can be obtained according to the Euler beam theory, and the method can be further simplified as follows:
Figure BDA0002753276710000081
T1(z) can be expressed as:
T1(z)＝[t1(z) t2(z) t3(z) t4(z)] (22)
in the formula:
Figure BDA0002753276710000082
therefore, the relation between the horizontal displacement, the corner, the bending moment and the shearing force of the top and the bottom of the partial pile section of the liquefied soil layer can be pushed out as follows:
Figure BDA0002753276710000083
considering the shear deformation of the foundation aiming at the non-liquefied soil layer, and according to the Euler beam and the Pasternak foundation correlation theory, obtaining a dynamic balance equation of a pile foundation in the jth (j is the number of the soil layer, and j is 2., m., n) layer of the non-liquefied soil layer as follows:
Figure BDA0002753276710000091
in the formula:
Figure BDA0002753276710000092
is as followsHorizontal displacement of j-layer pile foundation particles;
Figure BDA0002753276710000093
the shear stiffness coefficient of the foundation around the jth layer of piles,
Figure BDA0002753276710000094
the rigidity coefficient of soil around the pile is shown,
Figure BDA0002753276710000095
distributing damping for soil around the pile; b is0The calculated width is 0.9(1.5d +0.5) and is the calculated width of the pile, which is the shear action of the soil around the pile and acts on the pile section.
For the
Figure BDA0002753276710000096
And
Figure BDA0002753276710000097
the calculation formula is as follows:
Figure BDA0002753276710000098
Figure BDA0002753276710000099
Figure BDA00027532767100000910
in the formula:
Figure BDA00027532767100000911
the shear wave velocity of the soil around the pile;
Figure BDA00027532767100000912
and
Figure BDA00027532767100000913
each being a bullet of soil around the pileThe sexual modulus, density, damping coefficient and poisson's ratio;
Figure BDA00027532767100000914
is a dimensionless frequency;
Figure BDA00027532767100000915
the shear layer thickness of the foundation soil of the jth layer is obtained by taking the value as
Figure BDA00027532767100000916
The horizontal displacement of the pile body can be expressed as
Figure BDA00027532767100000917
In the formula (I), the compound is shown in the specification,
Figure BDA00027532767100000918
and the horizontal displacement amplitude of the mass point of the j-th layer pile foundation in the non-liquefied soil is obtained.
Is provided with
Figure BDA00027532767100000919
Substituting equation (27) for equation (24) may further result in the following equation:
Figure BDA00027532767100000920
in the formula:
Figure BDA00027532767100000921
the horizontal displacement amplitude of the pile foundation in the non-liquefied soil of the formula (28) can be solved as theta
Figure BDA00027532767100000922
In the formula (I), the compound is shown in the specification,
Figure BDA00027532767100000923
coefficient of performance
Figure BDA00027532767100000924
Will be determined by the boundary conditions.
According to the Euler beam theory, a relational expression of the corner, the bending moment, the shearing force and the horizontal displacement of the pile foundation of the j layer in the non-liquefied soil can be further obtained, and the simplification is as follows:
Figure BDA0002753276710000101
Fj(z) can be expressed as:
Fj(z)＝[f1(z) f2(z) f3(z) f4(z)] (31)
in the formula:
Figure BDA0002753276710000102
the united vertical type (23) can push out the relationship among the horizontal displacement, the corner, the bending moment and the shearing force of the top and the bottom of the pile foundation in the non-liquefied soil layer as follows:
Figure BDA0002753276710000103
in the formula: [ F ]]＝[Fn(hn)][Fn-1(hn-1)]…[F3(h3)][F2(h2)][T1(h1)][T1(0)]-1
Further consider the pile bottom as the stiff end constraint condition, then:
Figure BDA0002753276710000104
the combined type (32) and the formula (33) can obtain:
Figure BDA0002753276710000105
in the formula:
Figure BDA0002753276710000106
horizontal impedance K at pile tophSwing impedance KrAnd a horizontal-swing coupling impedance KhrRespectively as follows:
Figure BDA0002753276710000107
Figure BDA0002753276710000111
Figure BDA0002753276710000112
by solving for the horizontal impedance KhSwing impedance KrAnd a horizontal-swing coupling impedance KhrThe real part is dynamic stiffness, the imaginary part is dynamic damping, the capability of resisting deformation of the structure under specific dynamic disturbance can be evaluated, the influence rule of the pile foundation under the influence of other parameters can be further parameterized and analyzed, and theoretical guidance and reference functions can be provided for actual engineering.
The method for analyzing the horizontal dynamic response of the liquefied soil pile foundation based on the Passternak foundation takes the shearing effect of the soil body around the pile into consideration by adopting the Passternak foundation model, can better simulate the constraint action of the soil body around the pile on the pile body, and can be suitable for the problem of horizontal vibration dynamic response of the pile foundation under the action of simple harmonic load; in the traditional method, a liquefied soil body is equivalent to a solid foundation, and then a strength reduction method is adopted to discuss the performance of the liquefied soil. The definition of liquefaction in civil engineering society-the process of converting soil from solid to liquid has been varied, and under this definition, liquefied soil should behave similarly to a fluid. In consideration of the liquidity of the soil body after liquefaction, the invention simplifies the liquefied soil part into fluid; the non-liquefied soil layer is equivalent to a layered Passternak foundation, and the shearing effect and continuity of the foundation are considered. Therefore, the damage of the top layer of the pile foundation can be avoided being seen when the pile foundation is damaged and investigated, and the damage form of the pile foundation of the pile body in the liquefied part and the middle-lower layer soil can be better simulated. And the stress analysis of the pile foundation under the simultaneous action of complex loads is considered, so that theoretical guidance and reference effects can be provided for the power detection of the pile foundation.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (7)

1. A liquefied soil pile foundation horizontal dynamic response analysis method based on a Passternak foundation model is characterized by comprising the following steps:
s1: dividing soil layers in the foundation into a liquefied soil layer and a non-liquefied soil layer, enabling the liquefied soil layer on the top layer of the foundation to be equivalent to fluid, and establishing a fluid motion control equation of the liquefied soil layer under a cylindrical coordinate system;
s2: determining boundary conditions that the liquefied soil layer meets when in motion;
s3: determining the hydrodynamic pressure acting on the pile foundation according to the liquefied soil layer fluid motion control equation and the boundary condition;
s4: determining a dynamic balance equation of the foundation pile in the liquefied soil according to an Euler-Bernouli beam theory and the hydrodynamic pressure, and solving a horizontal displacement amplitude of the pile foundation in the liquefied soil layer; determining the relation between the corner amplitude, the bending moment amplitude, the shearing amplitude and the horizontal displacement amplitude of the top end and the bottom end of the pile foundation in the liquefied soil layer according to an Euler beam theory;
s5: determining a dynamic balance equation of the foundation pile in the non-liquefied soil, and solving a horizontal displacement amplitude of the pile foundation in the non-liquefied soil layer;
determining the relation between the corner amplitude, the bending moment amplitude, the shearing amplitude and the horizontal displacement amplitude of the top end and the bottom end of the pile foundation in the non-liquefied soil layer according to an Euler beam theory;
the foundation piles are continuous at the interface of the liquefied soil and the non-liquefied soil, and the relation between the corner amplitude, the bending moment amplitude, the shear amplitude and the horizontal displacement amplitude of the bottom end of the pile foundation in the liquefied soil layer is the relation between the corner amplitude, the bending moment amplitude, the shear amplitude and the horizontal displacement amplitude of the top end of the pile foundation in the non-liquefied soil layer; and determining a horizontal impedance, a sway impedance, and a horizontal-sway coupling impedance of a top of the pile foundation.
2. The method of claim 1, wherein in S1, the liquefied soil layer fluid motion control equation is as follows:
Figure FDA0002753276700000011
wherein: phi (r, theta, z, t) is a fluid velocity potential function, r represents a radial direction, theta is a rotation angle of the micro-element in horizontal projection, z is a longitudinal coordinate, a longitudinal coordinate zero point is positioned on a free surface and is positive downwards, t is a time coordinate,
Figure FDA0002753276700000012
to calculate the sign of the partial derivatives.
3. The method of claim 1, wherein in S2, the boundary conditions satisfied by the liquefied soil layer are as follows:
when the bottom z of the liquefied soil layer is equal to h1Its vertical speed is zero, i.e.:
Figure FDA0002753276700000021
neglecting the influence of gravity waves on the fluid, on the surface of the liquefied soil layer:
φ|z＝0＝0 (3)
fluid at radial infinity is at rest:
φ|r→∞＝0 (4)
the continuous contact condition of the fluid and the pile foundation is as follows:
Figure FDA0002753276700000022
wherein:
Figure FDA0002753276700000023
for horizontal displacement of pile sections in liquefied soil layers, r0Is the pile body radius.
4. The method of claim 2, wherein the fluid velocity potential function is expressed as:
φ(r,θ,z,t)＝φ(r,θ,z)eiωt。 (6)
5. the method of claim 4, wherein the hydrodynamic pressure is calculated by the following formula in S3:
Figure FDA0002753276700000024
wherein: rholIs the density of the liquefied soil.
6. The method of claim 5, wherein the equation for the dynamic balance of the piles in the liquefied soil is as follows:
Figure FDA0002753276700000025
wherein: ep、Ip、mpRespectively the elastic modulus, the section inertia moment and the unit length mass of the pile body, N0Is the axial force acting on the pile top.
7. The method of claim 5, wherein the equation for the dynamic balance of the foundation pile in non-liquefied soil is as follows:
Figure FDA0002753276700000026
wherein:
Figure FDA0002753276700000027
the horizontal displacement of a j layer pile foundation mass point is obtained;
Figure FDA0002753276700000028
the shear stiffness coefficient of the foundation around the jth layer of piles,
Figure FDA0002753276700000031
the rigidity coefficient of soil around the pile is shown,
Figure FDA0002753276700000032
distributing damping for soil around the pile; b is00.9(1.5d +0.5) is the calculated width of the stake.
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