CN115859418A - Offshore wind power large-diameter single-pile horizontal dynamic response analysis method - Google Patents
Offshore wind power large-diameter single-pile horizontal dynamic response analysis method Download PDFInfo
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Abstract
The invention provides a method for analyzing horizontal dynamic response of a large-diameter offshore wind power single pile, belongs to the technical field of civil engineering, simplifies the single pile into a Timoshenko beam model, simulates a soil body into an improved Pastnak foundation model, provides a physical mechanical model considering shear deformation of a pile body and simultaneously considering a soil body shear effect and a plastic yield characteristic, and overcomes the defect that the conventional theoretical technology is insufficient for simulating the interaction of a large-diameter offshore wind power single pile and soil power. In addition, the actual stress condition of the pile top is comprehensively considered, a pile foundation dynamic response model under the combined action of horizontal dynamic load, dynamic bending moment and vertical load is established, the layering characteristic of a soil body is processed by adopting a transfer matrix method, and the problem of horizontal dynamic response analysis of the offshore wind power large-diameter single pile in the layered foundation under the action of complex multidirectional load is solved. The analysis method provided by the invention can better provide theoretical value for the pile body deformation and internal force development rule of the offshore wind power large-diameter single pile under the action of complex load.
Description
Technical Field
The invention relates to the technical field of civil engineering, in particular to an offshore wind power large-diameter single-pile horizontal dynamic response analysis method.
Background
With the rapid development of offshore wind power engineering in China, pile foundations are widely applied as one of the important forms of offshore wind power foundations, and the stress analysis of large-diameter single piles in an offshore complex multidirectional load environment is concerned day by day. On the one hand, when the horizontal vibration response problem of a large-diameter single pile is researched at present, for calculation convenience, a Bernoulli-Euler theory is adopted mostly, a pile foundation is simulated into a slender rod piece model, the bending deformation of a pile body is only considered in the theoretical model, the influence of the shearing deformation of the large-diameter pile on the horizontal dynamic response of the pile foundation under the action of multidirectional dynamic load is also very obvious, and at the moment, a more appropriate Timoshenko model is adopted for the pile body. On the other hand, although some pile foundation horizontal load analysis methods also begin to adopt a more reasonable pasermak foundation model to replace the traditional Winkler foundation model, the method is mostly limited to the viscoelastic behavior of the soil body, the plastic yield characteristic of the soil body around the pile is not considered, which is also dangerous in practical engineering, and an improved pasermak foundation model is urgently needed to be provided so as to perfectly consider the stress characteristic of the plastic yield of the soil body.
Disclosure of Invention
The invention aims to provide an offshore wind power large-diameter single pile horizontal dynamic response analysis method, and solves the technical problem that influence of neglected pile body shear deformation on pile foundation horizontal dynamic response when a large-diameter single pile adopts a Bernoulli-Euler model in the existing analysis method.
The method is more reasonable by considering the horizontal dynamic response analysis of the offshore wind power large-diameter single pile under the vertical load effect, based on a Timoshenko beam model and an improved Pasternak foundation model, and simultaneously combining the offshore wind power large-diameter single pile horizontal dynamic response analysis method considering the plastic yield characteristic of the soil body.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a horizontal dynamic response analysis method for a large-diameter single offshore wind power pile comprises the following steps:
step1: establishing an offshore wind power large-diameter Timoshenko single-pile horizontal dynamic response analysis model under the combined action of horizontal translational load, dynamic bending moment and vertical load in a Paternak layered foundation;
step2: establishing a horizontal power control differential equation of a pile body unit in the layered foundation based on the Timoshenko Liang Lilun and the Passternak foundation theory;
and 3, step 3: and (3) solving the horizontal dynamic control differential equation in the step (S2) to obtain single-pile horizontal vibration analysis parameters of the elastic deformation section and the plastic deformation section of the soil body around the pile in the layered foundation, wherein the parameters at least comprise horizontal displacement, section corners, bending moment and shearing force of the pile body.
Further, in the step1, the assumed conditions include that offshore wind power large-diameter single piles are equivalent to circular uniform-section and homogeneous elastomers, the piles are simulated to be Timoshenko beam models, the plastic yield characteristics of soil bodies are considered, the foundation soil is assumed to be a viscoelastic-plastic foundation, the soil bodies around the piles are simulated to be improved Pastnak foundation models, the piles are divided into i layers according to the soil layers, each layer is divided into j sections, and the pile-soil interfaces are not separated and do not slide relatively.
Further, the expression form of the horizontal dynamics control differential equation in step2 is:
in the formula:
denotes the partial derivative symbol u (i,j) (z,t)、θ (i,j) (z, t) and V (i,j) Representing the horizontal displacement, the rotation angle and the vertical load of the top end of the pile body unit of the jth section of the ith layer, z and t represent the depth position and time, A p 、G p 、E p 、I p 、ρ p And D p Respectively representing the cross-sectional area, the shear modulus, the elastic modulus, the section moment of inertia, the density and the calculated diameter of the pile body, wherein kappa is the shear coefficient of the cross-sectional shape of the pile body, and k is si 、c si And G si Respectively representing the rigidity coefficient, the damping coefficient and the shear coefficient of the i-th layer soil body, wherein the calculation formula is as follows:
in the formula: e si 、ρ si 、β si And V si Respectively the elastic modulus, density, hysteretic damping ratio and shear wave velocity of the i-th layer of soil, d is the diameter of the pile body, a 0 Is a dimensionless frequency, omega is a horizontal dynamic excitation circular frequency, wherein, a 0 ＝ωd/V si ，
ν si The poisson ratio of the ith layer soil is taken as the ratio;
when the pile top of the large-diameter single offshore wind power pile bears steady-state simple harmonic excitation, the horizontal displacement and the corner of the pile body are converted into:
in the formula: u. of (i,j) (z)、θ (i,j) (z)、M (i,j) (z) and Q (i,j) (z) the ith layer and the jth section of pile body waterThe method comprises the following steps of horizontal displacement amplitude, pile body section corner amplitude, bending moment amplitude and shearing force amplitude.
Further, in step 3, in order to obtain the horizontal vibration analysis parameters of the large-diameter marine wind power single pile in the layered foundation, the horizontal dynamic control differential equation in step S2 needs to be solved, but considering the complexity of directly solving the equation, the analysis parameters in step S3 are obtained by combining a stress analysis transfer matrix method.
Further, the solving process of the horizontal power control differential equation comprises the following steps:
step 3.1: according to a stress analysis transfer matrix method, establishing a pile body transfer matrix of an elastic deformation section of a soil body around a pile:
in the formula: the superscript e represents the elastic deformation state of the soil body around the pile, and omega represents the frequency of the horizontal dynamic excitation circle; vertical force
Wherein: gamma ray P Indicates the concrete weight of the pile body is U p Indicates the perimeter of the pile body, L k Indicates the length of the pile body, tau, corresponding to the k-th layer soil i The pile side frictional resistance corresponding to the i-th layer soil;
rewriting the expressions (4) to (7) into a matrix form:
in the formula:
wherein:
laplace transformation is performed on the formula (8) to obtain:
in the formula: f e (s e )＝L[S e (z e )]Subscript j 0 The top of each small section of pile body unit is shown; l represents Laplace transform, s e The argument after Laplace transformation is used;
equation (9) can be converted to:
inverse Laplace transform is performed on equation (10), and the following results are obtained:
in the formula:
L -1 representing inverse Laplace transform;
will j = j 1 By substituting formula (11), one can obtain:
in the formula:
L -1 represents the Laplace inverseChange, subscript j 1 The end of each small section of pile body unit is shown;
in the elastic deformation stage of the soil body, the transmission coefficient matrix of the pile body unit
In the formula:
a 2,4 ＝-H e R e (α 1 -α 2 )/β 1
a 3,4 ＝-H e (β 2 α 3 -β 3 α 4 )/β 1
wherein: alpha is alpha 1 ＝cosh(β 2 z)α 2 ＝cosh(β 3 z)，α 3 ＝sinh(β 2 z)，α 4 ＝sinh(β 3 z)，
Step 3.2: according to a stress analysis transfer matrix method, establishing a pile body transfer matrix of a plastic deformation section of a soil body around a pile:
the equations (14) to (17) are rewritten into a matrix form:
in the formula: the superscript p represents the plastic deformation state of the soil body around the pile,
wherein:
Laplace transformation is performed on equation (18) to obtain:
in the formula: f p (s p )＝L[S p (z p )]，P p (s p )＝L[f p (z p )]Subscript j 0 The top of each small section of pile body unit is shown; l represents Laplace transform, s p The argument after Laplace transformation is used;
equation (19) can be converted to:
inverse Laplace transformation is performed on equation (20), and the following results are obtained:
in the formula:
L- 1 denotes inverse Laplace transform, let j = j 1 By substituting formula (21), it is possible to obtain:
in the formula:
subscript j 1 The end of each small section of pile body unit is shown;
suppose that:
then: />
Combined type (23) - (24), in the plastic yield stage of the soil body, the transmission coefficient matrix T of the pile body unit (i p ,j1) ：
Step 3.3: combining the formula (13) and the formula (25) to obtain a matrix transfer equation of any point xi of the pile body:
in the formula: when the point eta is located at the elastic deformation of the soil body, namely eta =1,2 … xi, T η Get the
And (3) calculating: when the soil body is plastically yielding, T η Taking or combining>
Calculating, namely responding to the whole pile body structure when eta = n;
step 3.4: determining boundary conditions of the pile top and the pile bottom:
the boundary conditions of the pile top and the pile bottom are as follows:
and then combining the formula (26) to obtain the horizontal displacement, section corner, bending moment and shearing force of the pile body unit corresponding to any xi point of the pile body.
Further, the process of solving the horizontal power control differential equation further comprises the following step 3.5: because the plastic yield region of the soil body is unknown before solving, repeated generation-reaching calculation is required until the plastic region is not developed any more, and the specific calculation process is as follows:
step 3.5.1: when k =1, assuming that the soil body on the pile side does not reach the yield displacement, all pile body units are solved according to elasticity to obtain the horizontal displacement u of each point ξ,step1 ；
Step 3.5.2: u of each segment ξ In sequence u u Comparison, i.e., ξ =1,2 … n, if u ξ ≥u u If k =2, adopting plastic solution to pile body unit during iterative calculation
Otherwise still solves according to elasticity>
And then combining a matrix transfer equation to calculate the horizontal displacement u of each point when k =2 ξ,step2 ；
Step 3.5.3: and repeating the steps until the plastic region depth in the k +1 iteration step is not developed compared with the plastic region depth in the k iteration step, and stopping iteration.
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
the invention establishes a more reasonable pile foundation physical mechanical model based on a Timoshenko beam model and an improved Passternak foundation model, and the model can consider the bending and shearing deformation of the pile body of a large-diameter single pile and simultaneously consider the shearing effect of the soil body around the pile and the plastic yield characteristic when the soil body achieves plastic deformation. In addition, when the offshore wind power large-diameter single pile bears horizontal dynamic load and dynamic bending moment, the influence of an upper fan structure on the vertical load generated by the large-diameter single pile is considered, the effect of three types of loads is comprehensively considered, the horizontal vibration problem of the large-diameter wind power single pile under the complex multidirectional loading action on the sea can be solved, and the pile-soil coupling interaction of the large-diameter single pile under the complex loading action in the actual offshore wind power engineering can be better simulated. The analysis method provided by the invention can better provide theoretical value for the pile body deformation and the internal force change rule of the offshore wind power large-diameter single pile under the action of complex multidirectional dynamic load.
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FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a schematic diagram of a pile foundation model of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings by way of examples of preferred embodiments. However, it should be noted that the numerous details set forth in the description are merely intended to provide a thorough understanding of one or more aspects of the present invention, even though such aspects of the invention may be practiced without these specific details.
As shown in fig. 1-2, a method for analyzing horizontal dynamic response of large-diameter single offshore wind power pile comprises the following steps:
s1: the method comprises the following steps of introducing the following assumed conditions, and establishing an offshore wind power large-diameter Timoshenko single-pile horizontal dynamic response analysis model under the combined action of horizontal translational load, dynamic bending moment and vertical load in the Paternak layered foundation: the assumed conditions include: the offshore wind power large-diameter single pile is equivalent to a round uniform-section homogeneous elastomer, and the pile is simulated to be a Timoshenko beam model; considering the plastic yield characteristic of the soil body, assuming that the foundation soil is a viscoelastic-plastic foundation, and simulating the soil body around the pile into an improved Passternak foundation model; dividing the soil layer into i (i = N) layers, and dividing each layer into j (j = N) sections; it is assumed that the pile-soil interfaces do not separate and relative slippage does not occur.
S2: based on Timoshenko Liang Lilun and Paternak foundation theory, establishing a horizontal power control differential equation of a pile body unit in a layered foundation, wherein the expression form of the horizontal power control differential equation is as follows:
compared with the existing traditional Bernoulli-Euler model and Winkler model, the equation of the formula (1) gives the physical quantity G considering the shear deformation of the pile body p Partial and consideration of physical quantity G of shear deformation of soil body around pile si Partial expression forms.
In the formula:
denotes the partial derivative symbol u (i,j) (z,t)、θ (i,j) (z, t) and V (i,j) Representing the horizontal displacement and the corner of the jth section of the ith layer of pile body unit and the vertical load of the top end of the pile body unit; z and t represent depth position and time; a. The p 、G p 、E p 、I p 、ρ p And D p Respectively representing the area of the section of the pile body, the shear modulus, the elastic modulus, the section moment of inertia, the density and the calculated diameter; kappa is the shear coefficient of the section shape of the pile body; k is a radical of si 、c si And G si Respectively representing the rigidity coefficient, the damping coefficient and the shear coefficient of the i-th layer soil body, wherein the calculation formula is as follows:
in the formula: e si 、ρ si 、β si And V si Respectively the elastic modulus, density, hysteresis damping ratio and shear wave velocity of the ith layer of soil; d is the diameter of the pile body; a is a 0 Is a dimensionless frequency, omega is a horizontal dynamic excitation circular frequency, whichIn (a) 0 ＝ωd/V si ，
ν si Is the poisson's ratio of the i-th layer of soil.
When the large-diameter single pile top of the offshore wind power is subjected to horizontal steady-state simple harmonic excitation, the horizontal displacement and the corner of the pile body are converted into:
in the formula: u. of (i,j) (z)、θ (i,j) (z)、M (i,j) (z) and Q (i,j) And (z) respectively representing the horizontal displacement amplitude, the section corner amplitude, the bending moment amplitude and the shearing force amplitude of the jth section of the pile body on the ith layer.
In the above formula (3), for the convenience of expression of the following formula, e in the following formula will be expressed iωt Reduction is performed.
S3: and (3) solving the horizontal dynamic control differential equation in the step (S2) to obtain single-pile horizontal vibration analysis parameters of the elastic deformation section and the plastic deformation section of the soil body around the pile in the layered foundation, wherein the parameters at least comprise the horizontal displacement, the section corner, the bending moment and the shearing force of the pile body.
In the step S3, in order to obtain the horizontal vibration analysis parameters of the large-diameter marine wind power single pile in the layered foundation, the horizontal dynamic control differential equation in the step S2 needs to be solved, but considering the complexity of directly solving the equation, the analysis parameters can be obtained by combining a stress analysis transfer matrix method, and the method includes the following steps:
step S31: according to a stress analysis transfer matrix method, establishing a pile body transfer matrix of an elastic deformation section of a soil body around a pile:
in the formula: vertical force
Wherein: gamma ray P Indicates the concrete weight of the pile body, U p Indicating the perimeter of the pile body, L k Indicates the length of the pile body corresponding to the soil of the kth layer, tau i The pile side frictional resistance corresponding to the i-th layer soil.
For convenience of representation, equations (4) to (7) are rewritten in a matrix form:
in the formula:
wherein:
laplace transformation is performed on the formula (8) to obtain:
in the formula: f e (s e )＝L[S e (z e )]Subscript j 0 The top of each small section of pile body unit is shown; l denotes the Laplace transform, s e Is the independent variable after Laplace transformation.
Equation (9) can be converted to:
inverse Laplace transform is performed on equation (10), and the following results are obtained:
in the formula:
L -1 representing the inverse Laplace transform.
Will j = j 1 By substituting formula (11), it is possible to obtain:
in the formula:
L -1 denotes the inverse Laplace transform, subscript j 1 The end of each small section of shaft unit is shown.
In the elastic deformation stage of the soil body, the transmission coefficient matrix of the pile body unit
In the formula:
a 2,4 ＝-H e R e (α 1 -α 2 )/β 1
a 3,4 ＝-H e (β 2 α 3 -β 3 α 4 )/β 1
wherein: alpha is alpha 1 ＝cosh(β 2 z)α 2 ＝cosh(β 3 z)，α 3 ＝sinh(β 2 z)，α 4 ＝sinh(β 3 z)，
C e 、R e 、K e 、B e And H e Both of the formulae (8) and (iv) are shown;
step S32: according to a stress analysis transfer matrix method, establishing a pile body transfer matrix of a plastic deformation section of a soil body around a pile:
for convenience of illustration, equations (14) to (17) are rewritten in a matrix form:
in the formula:
wherein:
laplace transformation is performed on equation (18) to obtain:
in the formula: f p (s p )＝L[S p (z p )]，P p (s p )＝L[f p (z p )]Subscript j 0 The top of each segment is represented; l denotes the Laplace transform, s p And the argument is the argument after Laplace transformation.
Equation (19) can be converted to:
inverse Laplace transformation is performed on equation (20), and the following results are obtained:
in the formula:
L -1 the inverse Laplace transform is shown,
will j = j 1 Substituted for formula (21) to give
In the formula:
subscript j 1 The end of each small section of shaft unit is shown.
Suppose that:
then:
combined type (23) - (24), in the plastic yield stage of the soil body, the transmission coefficient matrix of the pile body unit
Step S33: combining the formula (13) and the formula (25) to obtain a matrix transfer equation of any point xi of the pile body:
S ξ ＝T ξ ·T ξ-1 …T η …T 2 ·T 1 ·S 0 (26)
in the formula: when point η (η =1,2 … ξ) is in the elastic phase, T η Get
And (3) calculating: plastic region time, T η Fetch and hold>
Calculating; when eta = n, the response is the whole pile body structure.
Step S34: determining boundary conditions of the pile top and the pile bottom:
the boundary conditions of the pile top and the pile bottom are as follows:
and then combining the formula (26) to obtain the horizontal displacement, section corner, bending moment and shearing force of the pile body unit corresponding to any point xi of the pile body.
After the step S34, the following is also included:
because the plastic region is unknown before solving, repeated generation-reaching calculation is needed until the plastic region does not develop any more. The specific calculation process is as follows:
(1) First step (step 1: k = 1): assuming that all the soil bodies on the pile side do not reach the yield displacement, all the pile body units are solved according to elasticity to obtain the horizontal displacement u of each point ξ,step1 ；
(2) U of each segment ξ (xi =1,2 … n) in order of u u Comparison, if u ξ ≥u u Then, in the second step (step 2: k = 2), a plastic solution is applied to the pile body unit during the iterative calculation
Otherwise still answer the answer in accordance with the elasticity>
And then combining a matrix transfer equation to calculate the horizontal displacement u of each point when step2 is obtained ξ,step2 ；
(3) And repeating the steps until the plastic region depth in the k +1 iteration step is not developed compared with the plastic region depth in the k iteration step, and stopping iteration.
The method simplifies the single pile into a Timoshenko beam model, simulates the soil body into an improved Pasternak foundation model, provides a physical mechanical model considering the shear deformation of the pile body and the shear effect and the plastic yield characteristic of the soil body, and overcomes the defect that the conventional theoretical technology is insufficient in simulating the interaction of the offshore wind power large-diameter single pile and the soil power. In addition, the actual stress condition of the pile top is comprehensively considered, a pile foundation dynamic response model under the combined action of horizontal dynamic load, dynamic bending moment and vertical load is established, the layering characteristic of a soil body is processed by adopting a transfer matrix method, and the problem of horizontal dynamic response analysis of the offshore wind power large-diameter single pile in the layered foundation under the action of complex multidirectional load is solved. The analysis method provided by the invention can better provide theoretical value for the pile body deformation and internal force development rule of the offshore wind power large-diameter single pile under the action of complex load.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be construed as the protection scope of the present invention.
Claims (6)
1. A horizontal dynamic response analysis method for a large-diameter single offshore wind power pile is characterized by comprising the following steps: the method comprises the following steps:
step1: establishing an offshore wind power large-diameter Timoshenko single-pile horizontal dynamic response analysis model under the combined action of horizontal translational load, dynamic bending moment and vertical load in a Paternak layered foundation;
step2: establishing a horizontal power control differential equation of a pile body unit in the layered foundation based on the Timoshenko Liang Lilun and the Passternak foundation theory;
and step 3: and (3) solving the horizontal dynamic control differential equation in the step (S2) to obtain single-pile horizontal vibration analysis parameters of the elastic deformation section and the plastic deformation section of the soil body around the pile in the layered foundation, wherein the parameters at least comprise horizontal displacement, section corners, bending moment and shearing force of the pile body.
2. The offshore wind power large-diameter single-pile horizontal dynamic response analysis method according to claim 1, characterized in that: in the step1, the assumed conditions comprise that offshore wind power large-diameter single piles are equivalent to circular uniform-section and homogeneous elastomers, the piles are simulated to be Timoshenko beam models, the plastic yield characteristics of soil bodies are considered, the foundation soil is assumed to be a viscoelastic-plastic foundation, the soil bodies around the piles are simulated to be improved Passternak foundation models, the piles are divided into i layers according to the soil layers, each layer is divided into j sections, and the pile-soil interfaces are not separated and do not slide relatively.
3. The offshore wind power large-diameter single-pile horizontal dynamic response analysis method according to claim 1, characterized in that: the expression form of the horizontal power control differential equation in the step2 is as follows:
in the formula:
denotes the partial derivative symbol u (i,j) (z,t)、θ (i,j) (z, t) and V (i,j) Representing the horizontal displacement, the rotation angle and the vertical load of the top end of the pile body unit of the jth section of the ith layer, z and t represent the depth position and time, A p 、G p 、E p 、I p 、ρ p And D p Respectively representing the cross-sectional area, the shear modulus, the elastic modulus, the section moment of inertia, the density and the calculated diameter of the pile body, wherein kappa is the shear coefficient of the cross-sectional shape of the pile body, and k is si 、c si And G si Respectively representing the rigidity coefficient, the damping coefficient and the shear coefficient of the i-th layer soil body, wherein the calculation formula is as follows:
in the formula: e si 、ρ si 、β si And V si Respectively the elastic modulus, density, hysteretic damping ratio and shear wave velocity of the i-th layer of soil, d is the diameter of the pile body, a 0 Is a dimensionless frequency, omega is a horizontal dynamic excitation circular frequency, wherein, a 0 ＝ωd/V si ，
ν si Is the Poisson's ratio of the i-th layer soil;
when the pile top of the large-diameter offshore wind power single pile bears steady-state simple harmonic excitation, the horizontal displacement and the corner of the pile body are converted into:
in the formula: u. of (i,j) (z)、θ (i,j) (z)、M (i,j) (z) and Q (i,j) And (z) respectively representing the horizontal displacement amplitude, the section corner amplitude, the bending moment amplitude and the shearing force amplitude of the jth section of the pile body on the ith layer.
4. The offshore wind power large-diameter single-pile horizontal dynamic response analysis method according to claim 1, characterized in that: in step 3, in order to obtain the horizontal vibration analysis parameters of the large-diameter offshore wind power single pile in the layered foundation, the horizontal dynamic control differential equation in the step S2 needs to be solved, but considering the complexity of directly solving the equation, the analysis parameters in the step S3 are obtained by combining a stress analysis transfer matrix method.
5. The offshore wind power large-diameter single-pile horizontal dynamic response analysis method according to claim 4, characterized in that: the solving process of the horizontal power control differential equation comprises the following steps:
step 3.1: according to a stress analysis transfer matrix method, establishing a pile body transfer matrix of an elastic deformation section of a soil body around a pile:
in the formula: vertical force
Wherein: gamma ray P Indicates the concrete weight of the pile body, U p Indicating the perimeter of the pile body, L k Indicates the length of the pile body corresponding to the soil of the kth layer, tau i The pile side frictional resistance corresponding to the i-th layer soil;
rewriting the expressions (4) to (7) into a matrix form:
in the formula:
wherein:
Laplace transformation is performed on the formula (8) to obtain:
in the formula: f e (s e )＝L[S e (z e )]Subscript j 0 The top of each small section of pile body unit is shown; l denotes the Laplace transform, s e The argument after Laplace transformation is used;
equation (9) can be converted to:
inverse Laplace transform is performed on equation (10), and the following results are obtained:
in the formula:
L -1 representing inverse Laplace transform;
will j = j 1 By substituting formula (11), one can obtain:
in the formula:
L -1 denotes the inverse Laplace transform, subscript j 1 The end of each small section of pile body unit is shown;
in the elastic deformation stage of the soil body, the transmission coefficient matrix of the pile body unit
In the formula:
a 2,4 ＝-H e R e (α 1 -α 2 )/β 1
a 3,4 ＝-H e (β 2 α 3 -β 3 α 4 )/β 1
wherein: alpha is alpha 1 ＝cosh(β 2 z) α 2 ＝cosh(β 3 z)，α 3 ＝sinh(β 2 z)，α 4 ＝sinh(β 3 z)，
Step 3.2: according to a stress analysis transfer matrix method, establishing a pile body transfer matrix of a plastic deformation section of a soil body around a pile:
the equations (14) to (17) are rewritten in a matrix form:
in the formula:
wherein:
laplace transformation is performed on equation (18) to obtain:
in the formula: f p (s p )＝L[S p (z p )]，P p (s p )＝L[f p (z p )]Subscript j 0 The top of each small section of pile body unit is shown; l denotes the Laplace transform, s p The independent variable after Laplace transformation is used as the independent variable;
equation (19) can be converted to:
inverse Laplace transform is performed on equation (20) to obtain:
in the formula:
L -1 the inverse Laplace transform is shown,
substituting j = j1 into equation (21) can obtain:
in the formula:
subscript j 1 The end part of each small section of pile body unit is shown; />
Suppose that:
then:
combined type (23) - (24), in the plastic yield stage of the soil body, the transmission coefficient matrix of the pile body unit
Step 3.3: combining the formula (13) and the formula (25) to obtain a matrix transfer equation of any point xi of the pile body:
S ξ ＝T ξ ·T ξ-1 …T η …T 2 ·T 1 ·S 0 (26)
in the formula: when the point eta is located at the elastic deformation of the soil body, namely eta =1,2 … xi, T η Get the
And (3) calculating: when the soil body is plastically yielded, T η Get
Calculating, namely responding to the whole pile body structure when eta = n;
step 3.4: determining boundary conditions of the pile top and the pile bottom:
the boundary conditions of the pile top and the pile bottom are as follows:
and then combining the formula (26) to obtain the horizontal displacement, section corner, bending moment and shearing force of the pile body unit corresponding to any xi point of the pile body.
6. The offshore wind power large-diameter single-pile horizontal dynamic response analysis method according to claim 5, characterized in that: the process of solving the horizontal power control differential equation further comprises the following step 3.5: because the plastic yield region of the soil body is unknown before solving, repeated generation-reaching calculation is required until the plastic region is not developed any more, and the specific calculation process is as follows:
step 3.5.1: when k =1, assuming that the soil body on the pile side does not reach the yield displacement, all pile body units are solved according to elasticity to obtain the horizontal displacement u of each point ξ,step1 ；
Step 3.5.2: u of each segment ξ In sequence u u Comparison, i.e., ξ =1,2 … n, if u ξ ≥u u If k =2, adopting plastic solution to pile body unit during iterative calculation
Otherwise still answer the answer in accordance with the elasticity>
And then combining a matrix transfer equation to calculate the horizontal displacement u of each point when k =2 ξ,step2 ；
Step 3.5.3: and repeating the steps until the plastic region depth in the k +1 iteration step is not developed compared with the plastic region depth in the k iteration step, and stopping iteration.
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