CN111382517A - Pile foundation buckling critical load analytical solution analysis method based on double-parameter foundation model - Google Patents

Pile foundation buckling critical load analytical solution analysis method based on double-parameter foundation model Download PDF

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CN111382517A
CN111382517A CN202010180939.6A CN202010180939A CN111382517A CN 111382517 A CN111382517 A CN 111382517A CN 202010180939 A CN202010180939 A CN 202010180939A CN 111382517 A CN111382517 A CN 111382517A
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pile
foundation
soil
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potential energy
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姚文娟
王雪明
顾毛亮
程泽坤
顾文胤
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Beijing Transpacific Technology Development Ltd
University of Shanghai for Science and Technology
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    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
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Abstract

The invention discloses a pile foundation buckling critical load analytical solution analysis method based on a double-parameter foundation model. Aiming at the characteristics that buckling damage is easy to occur when the free section of an ultra-long pile such as a long-span bridge and a high-pile wharf is too long and the slenderness ratio is too large, a pile soil system total potential energy functional is established according to the constraint action of soil around the pile simulated by a double-parameter foundation model, a pile foundation buckling critical load analytical solution is obtained according to a potential energy stationing value principle and a variation method, and a reliable theoretical basis is provided for preventing engineering accidents caused by the buckling damage of the ultra-long pile. The invention fully considers the counter-force modulus and the shear modulus of foundation soil, considers the self weight of a pile foundation, establishes the total potential energy functional of a pile soil system, and obtains the buckling critical load analytical solution of the pile foundation according to the potential energy standing value principle and the variation method. Compared with the results of the examples, the analytical result obtained by selecting the double-parameter foundation model has high goodness of fit with the test result of the test pile, and the model can effectively reflect the actual stress characteristic and the constraint action of the soil around the pile when the pile foundation is bent.

Description

Pile foundation buckling critical load analytical solution analysis method based on double-parameter foundation model
Technical Field
The invention belongs to the field of geotechnical engineering, relates to a pile foundation engineering technology, and particularly relates to a pile foundation buckling critical load analytical solution calculation method based on a two-parameter foundation model.
Background
The ultra-long rock-socketed pile is not only widely applied to super high-rise buildings, but also a large number of highways, railway bridges, high-pile wharfs and the like adopt pile foundations as foundation forms. However, under the influence of special topography and geomorphology in mountainous areas and hydrogeological environment, many road sections have to pass through rivers and canyons in the form of viaducts, the length of the free section of the foundation pile is often too long, when the soil around the pile is weak or easy to liquefy, the foundation pile arranged on the upper part of the rock stratum is like a slender rod piece, buckling instability damage is easy to generate, and the damage is often sudden and has serious consequences. In the current research, when the buckling stability problem of a foundation pile is calculated, a soil body is mostly assumed to be a Winkler elastic foundation, that is, the pressure p of any point on the surface of the foundation is considered to be in direct proportion to the displacement omega of the point and is irrelevant to the stress states of other points, and the essence of the foundation is to simplify the foundation into a structure formed by a plurality of linear elastic springs which are not influenced with each other and are independent with each other. The method is simple in solving process and suitable for soil bodies with low shear strength or foundations with relatively large plastic zones under the foundations, but large errors can be generated when the method is used for calculating the soil bodies with large shear stiffness, and stress diffusion and deformation cannot be considered in a Winkler foundation model, so that the theory has a large defect in practical application.
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 provides an analytical solution analysis method for critical buckling load of a pile foundation based on a two-parameter foundation model.
In order to achieve the purpose of the invention, the conception of the invention is as follows:
aiming at the theoretical defects, the double-parameter foundation model reflects the characteristics of the foundation soil by adopting two independent parameters, considers the shearing action between springs and the continuity of the foundation soil, and better accords with the actual deformation characteristics of the soil body than a Winkler foundation model. The method fully considers the counter-force modulus and the shear modulus of foundation soil, simultaneously considers the self weight of a pile foundation, establishes the total potential energy functional of a pile soil system, and obtains the buckling critical load analytical solution of the pile foundation according to the potential energy standing value principle and the variation method. Compared with the results of the examples, the analytical result obtained by selecting the double-parameter foundation model has high goodness of fit with the test result of the pile, and the model can effectively reflect the actual stress characteristic and the constraint action of the soil around the pile when the pile foundation is bent, so that the problems in the background art are solved.
According to the inventive concept, the invention adopts the following technical scheme:
a pile foundation buckling critical load analytical solution analysis method based on a double-parameter foundation model comprises the following steps:
a) based on a double-parameter foundation model, a pile foundation buckling critical load analytical solution analysis method is provided:
according to the Paternak two-parameter foundation model, a pile body deflection differential equation under the condition of two-dimensional plane strain is expressed as follows:
Figure BDA0002412506740000021
EI is the bending rigidity of the section of the pile;
y is the deflection of any point of the pile body;
gp is the shear stiffness of the foundation soil;
k is foundation reaction modulus;
b is the calculated width of the pile body;
for circular cross-section piles common in engineering: when the diameter d of the pile is less than or equal to 1m, B is 0.9(0.5+1.5 d); when the pile diameter d is larger than 1m, B is 0.9(1+ d); when Gp in the above formula is zero, the model is degraded into a Winkler foundation model;
simplifying the overlong rock-socketed pile into the problem of buckling stability of an elastic foundation beam with one end embedded and the other end free and the top of the pile acted with an axial force P, so that the stress characteristic of the foundation soil can be reflected by two parameters of the counter-force modulus and the shear modulus of the soil;
the free length of the pile top is h1；
The length of the pile body covering soil is h2；
Depth of socketed rock is hr；
The foundation reaction force q of the pile body soil covering part can be expressed as follows based on a Passternak two-parameter foundation model:
Figure BDA0002412506740000022
tanahashi fitted empirical formula for shear stiffness:
Figure BDA0002412506740000023
vsis the Poisson's ratio of the foundation soil;
ESthe modulus of elasticity of the foundation soil;
t is the thickness of the shear layer of the foundation soil;
b) for the selection of the foundation reaction force modulus K, according to the existing research, the following two calculation modes are selected:
① use m method, K ═ m (h)2-x)
m is the horizontal resistance coefficient of the pile side soil and can be determined by the specification;
② use a combination method:
Figure BDA0002412506740000031
as a preferred technical scheme, the energy method is solved by a pile foundation buckling critical load analytical solution analysis method based on a double-parameter foundation model as follows:
(a) according to the buckling analysis model of the ultra-long socketed pile, establishing a total potential energy functional equation of a pile-soil system:
the total potential energy pi of the pile soil is determined by the strain energy U of the pile bodyPBased on elastic deformation energy U of soil body on lower pile side of double-parameter foundationSLoad potential energy V of side friction resistance of pilefPile body dead weight load potential energy VgAnd pile top external force load potential energy VpThe composition is as follows:
Π＝Up+Us+Vf+Vg+Vp
pile body strain energy UPComprises the following steps:
Figure BDA0002412506740000032
elastic strain energy U for obtaining pile side soil body based on double-parameter foundation modelSComprises the following steps:
Figure BDA0002412506740000033
calculating frictional resistance load potential energy V of pile side soil bodyfIn the process, because the interaction mechanism of the pile and the soil and the actual distribution of the pile side friction resistance are relatively complex, in order to simplify the problem, the pile side friction resistance is assumed to be uniformly distributed according to the empirical practice, and V is determined when the unit area pile side friction resistance is taufExpressed as:
Figure BDA0002412506740000034
the dead weight load of the pile body can be simplified into uniform line load, the size of the load is equal to the product of the volume weight gamma and the cross section area of the concrete of the pile body, and the dead weight load potential energy V of the pile body is obtainedgComprises the following steps:
Figure BDA0002412506740000035
pile top external load potential energy VpComprises the following steps:
Figure BDA0002412506740000036
namely:
Figure BDA0002412506740000041
(b) determining a pile body deflection function and solving by an energy method:
the total potential energy pi of the pile-soil system is a function of a pile body deflection line function y, namely a functional, the problem is changed into a functional extreme value problem for solving infinite freedom, the infinite freedom is approximately simplified into finite freedom by adopting a Rayleigh-Ritz method, namely the pile body deflection function is assumed to be a linear combination of a finite number of known functions, and the general form is as follows:
Figure BDA0002412506740000042
cnis the undetermined coefficient;
Figure BDA0002412506740000043
as a function of satisfying a displacement boundary condition;
n is the number of half waves;
for the overlength socketed pile with a free section in a mountain area, the pile end is basically embedded into a stable rock stratum, so that the boundary condition of pile end embedding and pile top freedom is selected for discussion, and under a coordinate system, the corresponding pile body deflection function is as follows:
Figure BDA0002412506740000044
according to the principle of constant potential energy value, the potential energy is subjected to variation, and when the structure is in balance, delta pi is equal to 0, namely
Figure BDA0002412506740000045
Due to deltac1，δc2…δcnIs arbitrary, then there must be:
Figure BDA0002412506740000046
order to
Figure BDA0002412506740000047
The above equation can be further refined as:
(kii-X)ci+kijcj＝0
in the formula:
Figure BDA0002412506740000051
Figure BDA0002412506740000052
wherein:
Figure BDA0002412506740000053
Figure BDA0002412506740000054
Figure BDA0002412506740000055
Figure BDA0002412506740000056
when the foundation reaction force modulus is calculated by adopting an m method:
Figure BDA0002412506740000057
Figure BDA0002412506740000058
when the foundation reaction force modulus is calculated by a combination method:
Figure BDA0002412506740000059
Figure BDA00024125067400000510
when η is 0, that is, the constant method soil layer calculation coefficient is not considered, the combination method model is degenerated to an m method model, and η is 0 and substituted into Di' and HijIn this connection, D is obtainedi'＝Di，Hij'＝HijThereby verifying the correctness of the derivation;
the matrix form after the expansion of the above formula is:
Figure BDA0002412506740000061
in order to have a non-zero solution for the above formula, it is required that its coefficient determinant is equal to zero, i.e. it is
Figure BDA0002412506740000062
The above formula is a characteristic equation considering buckling stability of the double-parameter foundation ultra-long pile, and is defined by a parameter kii,kij,Emn,Fmn,amnIt can be known that the matrix is a real symmetric matrix, which is solved and the minimum eigenvalue thereof is set to be XminObtaining the buckling stable critical load P of the super-long pilecrComprises the following steps:
Figure BDA0002412506740000063
corresponding calculated length l of stabilization of foundation pilepComprises the following steps:
Figure BDA0002412506740000064
compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable advantages:
1. the method is based on a double-parameter foundation model, fully considers the counter-force modulus and the shear modulus of foundation soil, simultaneously considers the self weight of a pile foundation, establishes the total potential energy functional of a pile soil system, and obtains the buckling critical load analytical solution of the pile foundation according to the potential energy standing value principle and the variation method;
2. the method aims at the characteristics of large-span bridges, high-pile wharfs, and the like that buckling damage is easy to occur when the free sections of ultra-long piles such as the large-span bridges and the high-pile wharfs are too long and the slenderness ratio is too large, the constraint action of the soil around the piles is simulated according to the two-parameter foundation model, the total potential energy functional of the pile-soil system is established, the pile foundation buckling critical load analytical solution is obtained according to the potential energy standing value principle and the variation method, and reliable theoretical basis is provided for preventing engineering accidents caused by buckling damage of the ultra-long piles. The invention has the advantages that: the method comprises the steps of fully considering the counter-force modulus and the shear modulus of foundation soil, simultaneously considering the self weight of a pile foundation, establishing a total potential energy functional of a pile soil system, and obtaining a buckling critical load analytical solution of the pile foundation according to a potential energy standing value principle and a variation method. Compared with the results of the examples, the analytical result obtained by selecting the double-parameter foundation model has high goodness of fit with the test result of the pile, and the model can effectively reflect the actual stress characteristic and the constraint action of the soil around the pile when the pile foundation is bent.
Drawings
FIG. 1 is a model diagram of a buckling analysis of an ultra-long socketed pile according to the present invention.
Fig. 2 is a graph of critical load versus m-method depth factor β for different pile body embedments as described in the present invention.
Fig. 3 is a relationship diagram of the pile foundation critical load calculation value and the half-wave number n in the 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 to fig. 3, a pile foundation buckling critical load analytical solution analysis method based on a two-parameter foundation model includes the following steps:
a) based on a double-parameter foundation model, a pile foundation buckling critical load analytical solution analysis method is provided:
according to the Paternak two-parameter foundation model, a pile body deflection differential equation under the condition of two-dimensional plane strain is expressed as follows:
Figure BDA0002412506740000071
EI is the bending rigidity of the section of the pile;
y is the deflection of any point of the pile body;
gp is the shear stiffness of the foundation soil;
k is foundation reaction modulus;
b is the calculated width of the pile body;
for circular cross-section piles common in engineering: when the diameter d of the pile is less than or equal to 1m, B is 0.9(0.5+1.5 d); when the pile diameter d is larger than 1m, B is 0.9(1+ d); when Gp in the above formula is zero, the model is degraded into a Winkler foundation model;
simplifying the overlong rock-socketed pile into the problem of buckling stability of an elastic foundation beam with one end embedded and the other end free and the top of the pile acted with an axial force P, so that the stress characteristic of the foundation soil can be reflected by two parameters of the counter-force modulus and the shear modulus of the soil;
as shown in fig. 1, the free length of the pile top is h1；
The length of the pile body covering soil is h2；
Depth of socketed rock is hr；
The foundation reaction force q of the pile body soil covering part can be expressed as follows based on a Passternak two-parameter foundation model:
Figure BDA0002412506740000081
tanahashi fitted empirical formula for shear stiffness:
Figure BDA0002412506740000082
vsis the Poisson's ratio of the foundation soil;
ESthe modulus of elasticity of the foundation soil;
t is the thickness of the shear layer of the foundation soil;
b) for the selection of the foundation reaction force modulus K, according to the existing research, the following two calculation modes are selected:
① use m method, K ═ m (h)2-x)
m is the horizontal resistance coefficient of the pile side soil and can be determined by the specification;
② use a combination method:
Figure BDA0002412506740000083
example two:
this embodiment is substantially the same as the first embodiment, and is characterized in that:
in this embodiment, the energy method solution is performed by the pile foundation buckling critical load analytical solution analysis method based on the two-parameter foundation model as follows:
(a) according to the buckling analysis model of the ultra-long socketed pile, establishing a total potential energy functional equation of a pile-soil system:
as shown in fig. 2, the total potential energy pi of the pile soil is determined by the strain energy U of the pile bodyPBased on elastic deformation energy U of soil body on lower pile side of double-parameter foundationSLoad potential energy V of side friction resistance of pilefPile body dead weight load potential energy VgAnd pile top external force load potential energy VpThe composition is as follows:
Π＝Up+Us+Vf+Vg+Vp
pile body strain energy UPComprises the following steps:
Figure BDA0002412506740000084
elastic strain energy U for obtaining pile side soil body based on double-parameter foundation modelSComprises the following steps:
Figure BDA0002412506740000091
calculating frictional resistance load potential energy V of pile side soil bodyfIn the process, because the interaction mechanism of the pile and the soil and the actual distribution of the pile side friction resistance are relatively complex, in order to simplify the problem, the pile side friction resistance is assumed to be uniformly distributed according to the empirical practice, and V is determined when the unit area pile side friction resistance is taufExpressed as:
Figure BDA0002412506740000092
the dead weight load of the pile body can be simplified into uniform line load, the size of the load is equal to the product of the volume weight gamma and the cross section area of the concrete of the pile body, and the dead weight load potential energy V of the pile body is obtainedgComprises the following steps:
Figure BDA0002412506740000093
pile top external load potential energy VpComprises the following steps:
Figure BDA0002412506740000094
namely:
Figure BDA0002412506740000095
(b) determining a pile body deflection function and solving by an energy method:
the total potential energy pi of the pile-soil system is a function of a pile body deflection line function y, namely a functional, the problem is changed into a functional extreme value problem for solving infinite freedom, the infinite freedom is approximately simplified into finite freedom by adopting a Rayleigh-Ritz method, namely the pile body deflection function is assumed to be a linear combination of a finite number of known functions, and the general form is as follows:
Figure BDA0002412506740000096
cnis the undetermined coefficient;
Figure BDA0002412506740000097
as a function of satisfying a displacement boundary condition;
n is the number of half waves;
for an ultralong rock-socketed pile with a free section in a mountain area, the pile end is basically embedded into a stable rock stratum, so that a boundary condition of pile end embedding and pile top free is selected for discussion, and under a coordinate system shown in fig. 1, a corresponding pile body deflection function is as follows:
Figure BDA0002412506740000101
according to the principle of constant potential energy value, the potential energy is subjected to variation, and when the structure is in balance, delta pi is equal to 0, namely
Figure BDA0002412506740000102
Due to deltac1，δc2…δcnIs arbitrary, then there must be:
Figure BDA0002412506740000103
order to
Figure BDA0002412506740000104
The above equation can be further refined as:
(kii-X)ci+kijcj＝0
in the formula:
Figure BDA0002412506740000105
Figure BDA0002412506740000106
wherein:
Figure BDA0002412506740000107
Figure BDA0002412506740000108
Figure BDA0002412506740000109
Figure BDA00024125067400001010
when the foundation reaction force modulus is calculated by adopting an m method:
Figure BDA0002412506740000111
Figure BDA0002412506740000112
when the foundation reaction force modulus is calculated by a combination method:
Figure BDA0002412506740000113
Figure BDA0002412506740000114
when η is 0, that is, the constant method soil layer calculation coefficient is not considered, the combination method model is degenerated to an m method model, and η is 0 and substituted into Di' and HijIn this connection, D is obtainedi'＝Di，Hij'＝HijThereby verifying the correctness of the derivation;
the matrix form after the expansion of the above formula is:
Figure BDA0002412506740000115
in order to have a non-zero solution for the above formula, it is required that its coefficient determinant is equal to zero, i.e. it is
Figure BDA0002412506740000116
The above formula is a characteristic equation considering buckling stability of the double-parameter foundation ultra-long pile, and is defined by a parameter kii,kij,Emn,Fmn,amnIt can be known that the matrix is a real symmetric matrix, which is solved and the minimum eigenvalue thereof is set to be XminObtaining the buckling stable critical load P of the super-long pilecrComprises the following steps:
Figure BDA0002412506740000117
corresponding calculated length l of stabilization of foundation pilepComprises the following steps:
Figure BDA0002412506740000121
example three:
this embodiment is substantially the same as the previous embodiment, and is characterized in that:
in this embodiment, a pile foundation buckling critical load analytical solution analysis method based on a two-parameter foundation model is provided. In order to verify the correctness of the calculation method of the two-parameter foundation model, the following model pile test results are analyzed, compared and verified, wherein the design diameter d of the model pile is 0.020m, the weighted average side frictional resistance tau of the pile side soil is 40kPa, and the boundary conditions of the model pile are as follows: the pile end is embedded and fixed, and the pile top is free. Specific parameters are shown in table 1, and the calculated buckling load theoretical result of the ultra-long pile and the test result in the literature are shown in table 2.
Table 1. the calculation parameter table of the test pile of the present embodiment
Figure BDA0002412506740000122
TABLE 2 comparison table of buckling critical load calculation results of the present example
Figure BDA0002412506740000123
From table 2, the actual stress characteristics and the constraint action of the soil around the pile can be effectively simulated by using the two-parameter foundation model, compared with the m method, the theoretical calculation result of the combination method is closer to the experimental actual measurement result, and the maximum error is within 5%, so that the constraint capacity of the foundation soil on the pile body is known to be close to the constant after reaching a certain depth instead of linearly increasing along with the depth, namely the shallow m method is selected, and the combined pile side soil resistance mode of the deep constant method can be closer to the actual pile body constraint condition. As can be seen from fig. 2, under different pile embedment rates λ (λ ═ h)2When the m method is used for calculating the critical load of the pile foundation, the calculated value of the critical load of the pile foundation is gradually increased along with the increase of the depth coefficient β calculated by the m method, because the resistance of the soil at the pile side is larger and finally gradually stabilized as the resistance of the soil around the pile is simulated by the m method is deeper, the coefficient β corresponding to the stable critical load under different embedment rates is increased along with the increase of the embedment rate, when β takes 0.3, the calculated critical load tends to be stable, when the calculated depth coefficient is smaller than 0.3, the m method can reasonably represent the reaction coefficient of the soil at the pile side, and when the calculated depth coefficient is larger than 0.3, the constant method can more reasonably represent the reaction coefficient of the foundation.
Fig. 3 respectively analyzes the relationship between the pile foundation critical load calculation value and the value of the half wave number n in the three pile test tests, wherein the half wave number n represents that the original infinite freedom structure is simplified into only n degrees of freedom. As can be seen from fig. 3, as the half wave number n increases, the calculated value of the critical load of the pile gradually tends to the test value, and when n is 20, the calculation accuracy gradually approaches to a certain constant, thereby meeting the calculation accuracy requirement of the present invention.
In conclusion, compared with the results of the examples, the resolution result obtained by the double-parameter foundation model has high goodness of fit with the test result of the test pile, and the model can effectively simulate the actual stress characteristic and the constraint action of the soil around the pile when the pile foundation is bent. Compared with an m method, a combined pile side soil resistance mode of a shallow soil body m method and a deep soil body constant method is selected to be closer to the actual pile body constraint condition, for the calculated depth of the m method, the influence of factors such as soil body types and pile body embedment rate on the buckling stability of the ultra-long rock-socketed pile is comprehensively considered, and a reasonable calculated depth coefficient is selected. The invention obtains that the calculated depth coefficient of the m method is about 0.3 generally and the calculated value of the critical load of the pile foundation tends to be stable through analysis. A pile foundation buckling critical load analytical solution calculation method based on a double-parameter foundation model. Aiming at the characteristics that buckling damage is easy to occur when the free section of an ultra-long pile such as a long-span bridge and a high-pile wharf is too long and the slenderness ratio is too large, a pile soil system total potential energy functional is established according to the constraint action of soil around the pile simulated by a double-parameter foundation model, a pile foundation buckling critical load analytical solution is obtained according to a potential energy stationing value principle and a variation method, and a reliable theoretical basis is provided for preventing engineering accidents caused by the buckling damage of the ultra-long pile. The invention has the advantages that: the method comprises the steps of fully considering the counter-force modulus and the shear modulus of foundation soil, simultaneously considering the self weight of a pile foundation, establishing a total potential energy functional of a pile soil system, and obtaining a buckling critical load analytical solution of the pile foundation according to a potential energy standing value principle and a variation method. Compared with the results of the examples, the analytical result obtained by selecting the double-parameter foundation model has high goodness of fit with the test result of the pile, and the model can effectively reflect the actual stress characteristic and the constraint action of the soil around the pile when the pile foundation is bent.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes and modifications may be made according to the purpose of the invention, and all changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention shall be equivalent replacement ways, so long as the purpose of the present invention is met, and the present invention shall fall within the protection scope of the present invention as long as the technical principle and inventive concept of the method for analyzing and analyzing buckling critical load of a pile foundation based on a two-parameter foundation model of the present invention do not depart.

Claims (2)

1. A pile foundation buckling critical load analytical solution analysis method based on a two-parameter foundation model is characterized by comprising the following steps: the analysis method comprises the following steps:
a) based on a double-parameter foundation model, a pile foundation buckling critical load analytical solution analysis method is provided:
according to the Paternak two-parameter foundation model, a pile body deflection differential equation under the condition of two-dimensional plane strain is expressed as follows:
Figure FDA0002412506730000011
EI is the bending rigidity of the section of the pile;
y is the deflection of any point of the pile body;
gp is the shear stiffness of the foundation soil;
k is foundation reaction modulus;
b is the calculated width of the pile body;
for circular cross-section piles common in engineering: when the diameter d of the pile is less than or equal to 1m, B is 0.9(0.5+1.5 d); when the pile diameter d is larger than 1m, B is 0.9(1+ d); when Gp in the above formula is zero, the model is degraded into a Winkler foundation model;
simplifying the overlong rock-socketed pile into the problem of buckling stability of an elastic foundation beam with one end embedded and the other end free and the top of the pile acted with an axial force P, so that the stress characteristic of the foundation soil can be reflected by two parameters of the counter-force modulus and the shear modulus of the soil;
the free length of the pile top is h1；
The length of the pile body covering soil is h2；
Depth of socketed rock is hr；
The foundation reaction force q of the pile body soil covering part can be expressed as follows based on a Passternak two-parameter foundation model:
Figure FDA0002412506730000012
tanahashi fitted empirical formula for shear stiffness:
Figure FDA0002412506730000013
vsis the Poisson's ratio of the foundation soil;
ESthe modulus of elasticity of the foundation soil;
t is the thickness of the shear layer of the foundation soil;
b) for the selection of the foundation reaction force modulus K, according to the existing research, the following two calculation modes are selected:
① use m method, K ═ m (h)2-x)
m is the horizontal resistance coefficient of the pile side soil and can be determined by the specification;
② use a combination method:
Figure FDA0002412506730000021
2. the analytic solution analysis method for critical load of buckling of pile foundation based on the two-parameter foundation model according to claim 1, characterized in that: the energy method solution is as follows:
(a) according to the buckling analysis model of the ultra-long socketed pile, establishing a total potential energy functional equation of a pile-soil system:
the total potential energy pi of the pile soil is determined by the strain energy U of the pile bodyPBased on elastic deformation energy U of soil body on lower pile side of double-parameter foundationSLoad potential energy V of side friction resistance of pilefPile body dead weight load potential energy VgAnd pile top external force load potential energy VpThe composition is as follows:
Π＝Up+Us+Vf+Vg+Vp
pile body strain energy UPComprises the following steps:
Figure FDA0002412506730000022
elastic strain energy U for obtaining pile side soil body based on double-parameter foundation modelSComprises the following steps:
Figure FDA0002412506730000023
calculating frictional resistance load potential energy V of pile side soil bodyfIn time, because the interaction mechanism of the pile and the soil and the actual distribution of the pile side frictional resistance are relatively complicated, in order to simplify the problem, the method is fake according to experienceThe friction resistance of the side of the pile in unit area is tau, then VfExpressed as:
Figure FDA0002412506730000024
the dead weight load of the pile body can be simplified into uniform line load, the size of the load is equal to the product of the volume weight gamma and the cross section area of the concrete of the pile body, and the dead weight load potential energy V of the pile body is obtainedgComprises the following steps:
Figure FDA0002412506730000025
pile top external load potential energy VpComprises the following steps:
Figure FDA0002412506730000031
namely:
Figure FDA0002412506730000032
(b) determining a pile body deflection function and solving by an energy method:
the total potential energy pi of the pile-soil system is a function of a pile body deflection line function y, namely a functional, the problem is changed into a functional extreme value problem for solving infinite freedom, the infinite freedom is approximately simplified into finite freedom by adopting a Rayleigh-Ritz method, namely the pile body deflection function is assumed to be a linear combination of a finite number of known functions, and the general form is as follows:
Figure FDA0002412506730000033
cnis the undetermined coefficient;
Figure FDA0002412506730000034
as a function of satisfying a displacement boundary condition;
n is the number of half waves;
for the overlength socketed pile with a free section in a mountain area, the pile end is basically embedded into a stable rock stratum, so that the boundary condition of pile end embedding and pile top freedom is selected for discussion, and under a coordinate system, the corresponding pile body deflection function is as follows:
Figure FDA0002412506730000035
according to the principle of constant potential energy value, the potential energy is subjected to variation, and when the structure is in balance, delta pi is equal to 0, namely
Figure FDA0002412506730000036
Due to deltac1，δc2…δcnIs arbitrary, then there must be:
Figure FDA0002412506730000037
order to
Figure FDA0002412506730000038
The above equation can be further refined as:
(kii-X)ci+kijcj＝0
in the formula:
Figure FDA0002412506730000041
Figure FDA0002412506730000042
wherein:
Figure FDA0002412506730000043
Figure FDA0002412506730000044
Figure FDA0002412506730000045
Figure FDA0002412506730000046
when the foundation reaction force modulus is calculated by adopting an m method:
Figure FDA0002412506730000047
Figure FDA0002412506730000048
when the foundation reaction force modulus is calculated by a combination method:
Figure FDA0002412506730000049
Figure FDA0002412506730000051
when η is 0, that is, the constant method soil layer calculation coefficient is not considered, the combination method model is degenerated to an m method model, and η is 0 and substituted into Di' and HijIn this connection, D is obtainedi'＝Di，Hij'＝HijThereby verifying the correctness of the derivation;
the matrix form after the expansion of the above formula is:
Figure FDA0002412506730000052
in order to have a non-zero solution for the above formula, it is required that its coefficient determinant is equal to zero, i.e. it is
Figure FDA0002412506730000053
The above formula is a characteristic equation considering buckling stability of the double-parameter foundation ultra-long pile, and is defined by a parameter kii,kij,Emn,Fmn,amnIt can be known that the matrix is a real symmetric matrix, which is solved and the minimum eigenvalue thereof is set to be XminObtaining the buckling stable critical load P of the super-long pilecrComprises the following steps:
Figure FDA0002412506730000054
corresponding calculated length l of stabilization of foundation pilepComprises the following steps:
Figure FDA0002412506730000055
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Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112227434A (en) * 2020-10-30 2021-01-15 大连海事大学 Method and system for analyzing horizontal dynamic interaction of adjacent pile foundations
CN112287574A (en) * 2020-09-25 2021-01-29 上海大学 Pile foundation dynamic stability analysis and calculation method under wave load action
CN112417544A (en) * 2020-09-25 2021-02-26 上海大学 Method for solving horizontal displacement of ultra-long pile in layered foundation under action of transverse load
CN112926222A (en) * 2021-03-29 2021-06-08 苏州科技大学 Method for determining critical load of n-order telescopic boom of crane
CN112948939A (en) * 2021-03-12 2021-06-11 上海大学 Single-pile dynamic stability analysis method and system under ship impact load action
CN113529825A (en) * 2021-08-04 2021-10-22 宁波工程学院 Method for evaluating instability damage of pile hole wall under vibration load
CN113779809A (en) * 2021-09-26 2021-12-10 广州大学 Method, system and medium for predicting critical axial load of fluifiable site socketed pile
CN114282362A (en) * 2021-12-17 2022-04-05 晋能控股煤业集团有限公司 Coal mine old goaf water inrush monitoring and judging method
WO2022121749A1 (en) * 2021-01-13 2022-06-16 中国长江三峡集团有限公司 Method for calculating vertical bearing time-varying effect of single pile with consideration to non-darcy consolidation of soil body
CN117592253A (en) * 2023-11-01 2024-02-23 上海交通大学 Method for judging damage of high pile wharf of steel pipe pile
CN117933039A (en) * 2024-03-25 2024-04-26 华东交通大学 Method for calculating elastic integral buckling stress of rusted cold-formed thin-walled steel column

Non-Patent Citations (9)

* Cited by examiner, † Cited by third party
Title
WEN-JUAN YAO等: "Numerical simulation and study forsuper-long pile group under axis and lateral loads", 《ADVANCES IN STRUCTURAL ENGINEERING》 *
仇元忠: "基于突变理论及能量法的超长桩屈曲分析", 《HTTPS://D.WANFANGDATA.COM.CN/THESIS/CHJUAGVZAXNOZXDTMJAYMTEYMDESCFKXNDYXNTCZGGHQBDF4BNF5OA%3D%3D》 *
刘晓钊: "基于尖点突变理论的桩基屈曲稳定分析", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑（月刊） 建筑科学与工程》 *
姚文娟 等: "超长嵌岩桩初始后屈曲性状分析", 《岩土工程学报》 *
杨松 等: "基于能量法的超长桩屈曲稳定影响因素分析", 《长江科学院院报》 *
梁发云 等: "基于Pasternak双参数地基模型水平桩简化分析方法", 《岩土工程学报》 *
邹新军 等: "复杂地基反力模式下高承台嵌岩灌注桩的屈曲稳定分析", 《岩土力学》 *
邹新军 等: "考虑复杂地基反力分布的嵌岩灌注桩屈曲稳定分析", 《建筑科学》 *
邹新军 等: "高承台嵌岩灌注桩屈曲稳定分析的能量法统一解及工程应用", 《公路工程》 *

Cited By (18)

* Cited by examiner, † Cited by third party
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CN112417544A (en) * 2020-09-25 2021-02-26 上海大学 Method for solving horizontal displacement of ultra-long pile in layered foundation under action of transverse load
CN112287574B (en) * 2020-09-25 2021-10-08 上海大学 Pile foundation dynamic stability analysis and calculation method under wave load action
CN112227434B (en) * 2020-10-30 2022-04-08 大连海事大学 Method and system for analyzing horizontal dynamic interaction of adjacent pile foundations
CN112227434A (en) * 2020-10-30 2021-01-15 大连海事大学 Method and system for analyzing horizontal dynamic interaction of adjacent pile foundations
WO2022121749A1 (en) * 2021-01-13 2022-06-16 中国长江三峡集团有限公司 Method for calculating vertical bearing time-varying effect of single pile with consideration to non-darcy consolidation of soil body
CN112948939A (en) * 2021-03-12 2021-06-11 上海大学 Single-pile dynamic stability analysis method and system under ship impact load action
CN112926222B (en) * 2021-03-29 2022-02-11 苏州科技大学 Method for determining critical load of n-order telescopic boom of crane
CN112926222A (en) * 2021-03-29 2021-06-08 苏州科技大学 Method for determining critical load of n-order telescopic boom of crane
CN113529825A (en) * 2021-08-04 2021-10-22 宁波工程学院 Method for evaluating instability damage of pile hole wall under vibration load
CN113529825B (en) * 2021-08-04 2022-06-10 宁波工程学院 Method for evaluating instability damage of pile hole wall under vibration load
CN113779809A (en) * 2021-09-26 2021-12-10 广州大学 Method, system and medium for predicting critical axial load of fluifiable site socketed pile
CN113779809B (en) * 2021-09-26 2023-12-26 广州大学 Method, system and medium for predicting critical axial load of liquefiable field rock-socketed pile
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CN117933039B (en) * 2024-03-25 2024-05-28 华东交通大学 Method for calculating elastic integral buckling stress of rusted cold-formed thin-walled steel column

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