CN108755785A - A kind of stairstepping reducing hollow pile Calculation Methods for Internal Force - Google Patents
A kind of stairstepping reducing hollow pile Calculation Methods for Internal Force Download PDFInfo
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- CN108755785A CN108755785A CN201810560926.4A CN201810560926A CN108755785A CN 108755785 A CN108755785 A CN 108755785A CN 201810560926 A CN201810560926 A CN 201810560926A CN 108755785 A CN108755785 A CN 108755785A
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- E—FIXED CONSTRUCTIONS
- E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
- E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
- E02D33/00—Testing foundations or foundation structures
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Abstract
A kind of stairstepping reducing hollow pile Calculation Methods for Internal Force, includes the following steps：If hollow pile is divided into dried layer according to strata condition and pile body variable cross-section situation, the internal force and displacement expression formula of stake are released；Random layer iteration tensor U is obtained, and obtains the expression formula of matrix M；Conventional global artificial boundary condition matrix G is obtained by the transformational relation of eight boundary conditions[0]；Obtain the local boundary conditional vector G of first layer[1], and then solve random layer local boundary condition G[i]Finally obtain the internal force and motion vector F of random layer[i], finally acquire Internal forces and displacement.Using a kind of Calculation Methods for Internal Force of stairstepping reducing hollow pile provided by the invention, existing Internal forces computational methods are generalized to stairstepping variable cross-section hollow pile from cross-section or non-uniform pile, this method can accurately calculate internal force distribution and the pile body displacement of variable cross-section hollow pile, project cost is saved, computational methods step is clear, has good application value.
Description
Technical field
The present invention relates to a kind of stairstepping reducing hollow pile Calculation Methods for Internal Force, belong to technical field of civil engineering.
Background technology
With the rapid development of highway in China Bored Pile of Bridge, also higher and higher, stake is required to the technology of related pile foundation
The problem of problem on deformation, Carrying Capacity and the project cost on basis are also paid special attention to as engineering circles.
Currently, Design of Foundation is generally adopted by cross-section, but for the larger pile foundation construction of stake diameter, due to stake
The shared ratio of dead weight is great, and one-time-concreting underwater concrete is also more and more difficult in construction, increases the duration, and causes thanks to work
The huge consumption of material, project cost increase.Many scholars have carried out continuous exploration and innovation to the research of pile foundation, occur
Many novel piles, stairstepping reducing hollow pile is exactly one such.Stairstepping reducing hollow pile is reducing sedimentation, is increasing stake
Base safety, reduction project cost etc. have significant Social benefit and economic benefit.But at present about variable cross-section sky
The theoretical research result of heart stake is relatively fewer.
Invention content
The object of the present invention is to for insufficient existing for current hollow variable cross-section Pile Foundations Design, a kind of ladder deformation is proposed
Diameter hollow pile Calculation Methods for Internal Force.
The technical solution that the present invention realizes is as follows：
A kind of stairstepping reducing hollow pile Calculation Methods for Internal Force, includes the following steps：
(1) if hollow pile is divided into dried layer, the internal force and displacement expression formula of stake are released：
Stake overall length L is equal to the summation of every section of cross-sectional length, i.e. L=∑s Li；
According to theory of beam on elastic, per i sections of transverse deflections, the governing equation of distribution is：
In formula：piThe lateral resistance of the soil body caused by be bent due to stake；IiFor i-th of second moment of circular hollow pile,Wherein ξ=di/DiIndicate the thickness ratio of section；E is elasticity modulus；CiFor ground reaction mould
Amount；DiFor the outer diameter of i-th layer of stake；
Formula (1) is reconfigured：
X in formula (2)iSolved by following formula：
In formula (3)：
In formula：Ai,Bi,Ci,DiFor four parameters；
Other parameters φi、Mi、QiFor：
In formula,
Write as matrix form：
(2) to U[n]It is iterated calculating, obtains random layer iteration tensor U, and obtain the expression formula of matrix M：
By F[i]Expression formula reconfigure for：
It will be from known global artificial boundary condition G[0]Middle four local boundary conditions for obtaining every section of stake, define matrix：
Derive iterative relation：
After derivation, above formula is expressed as again：
G[i]Total iterative relation be finally：
G[i]=[T[i]]·{G[i-1]}；
New iteration tensor is defined as：
U[i]=[T[i]]…[T[2]]·[I]；
The expression formula of matrix M：
(3) conventional global artificial boundary condition matrix G is obtained by the transformational relation of eight boundary conditions0：
To each pile cutoff, local boundary condition is：
Xi、ΦiIndicate the lateral displacement and corner of i-th layer of bottom side；
Ri、HiThe transverse bending moment and point for indicating i-th layer of top side shear；
The adjacent segment condition of continuity is：
Global artificial boundary condition：
Conventional global artificial boundary condition matrix G0：
(4) the local boundary conditional vector G of first layer is obtained[1], and then solve random layer local boundary condition G[i]Finally
Obtain the internal force and motion vector F of random layer[i]：
The local boundary conditional vector G of first layer[1]：
Random layer local boundary condition G[i]：
G[i]=[U[i]]·{G[i-1]}；
F[i]Expression formula be：
F[i]=[W[i]]·[G[0]]。
The invention has the advantages that the present invention promotes existing Internal forces computational methods from cross-section or non-uniform pile
To stairstepping variable cross-section hollow pile, the method for the present invention can accurately calculate internal force distribution and the pile body position of variable cross-section hollow pile
It moves, has saved project cost, computational methods step is clear, has good application value.
Description of the drawings
Fig. 1 is the diagrammatic cross-section of the lower variable cross-section hollow pile of lateral load effect；
Fig. 2 is stairstepping reducing hollow pile Calculation Methods for Internal Force flow chart of the present invention.
Specific implementation mode
The flow of stairstepping reducing hollow pile Calculation Methods for Internal Force specific implementation of the present invention is as shown in Figure 2.Its calculation process
Including：
(1) if soil layer and hollow pile are divided into dried layer, the internal force and displacement expression formula of stake are released；
(2) to U[n]It is iterated calculating, obtains random layer iteration tensor U, and obtain the expression formula of matrix M；
(3) conventional global artificial boundary condition matrix G is obtained0；
(4) random layer local boundary condition G is solved[i]Finally obtain the internal force and motion vector F of random layer[i]。
The present embodiment is based on theory of beam on elastic, derives in horizontal force HtWith moment of flexure RtThe lower hollow pile body of variable cross-section of effect
Internal force and displacement calculation formula.
Used in the embodiment of the present invention is that constant method calculates laterral earth resistance on piles.
Fig. 1 is the sectional view of the lower variable cross-section hollow pile of lateral load effect, and stake is embedded in multi-layered Soils.Stake is by horizontal lotus
Carry HtWith end bending square Rt, under the action of the two power, the center line of stake deflects.
Assuming that horizontal displacement XbWith end corner ΦbBoundary condition known to.
By considering stake end situation and strata condition, if stake is divided into stem portion.
Assuming that the soil body is linear elastic materials.
Global coordinate system x-z is established, origin is located at stake top center, is labeled as O.
Establish local coordinate system xi-zi, origin is located at different cross section stake top portion.
Stake overall length L is equal to the summation in every section of section, i.e. L=∑s Li。
Base area theory of beam on elastic, per i sections of transverse deflections, the governing equation of distribution is：
In formula：piThe lateral resistance of the soil body caused by be bent due to stake；E is elasticity modulus；IiFor circular hollow pile
I-th of second moment,Wherein ξ=di/DiIndicate the thickness ratio of section；CiFor subgrade reaction system
Number.
(1) formula is reconfigured：
X in formula (2)iSolved by following formula：
In formula (3)：
In formula (4), Ai,Bi,Ci,DiIt is calculative four parameters, i is imaginary number.
Other parameters φi、Mi、QiIt is expressed as follows：
In formula (5)：
Expression formula all of the above is write as matrix form：
For each pile cutoff, local boundary condition is：
In formula：Xi、ΦiIndicate the lateral displacement and corner of i-th layer of bottom side；
Ri、HiThe transverse bending moment and point for indicating i-th layer of top side shear；
The condition of continuity of adjacent segment also meets：
Whole boundary parameter is assumed the power being applied in stake top (respectively by RtAnd HtIndicate torque and shearing) and stake bottom
The deformation in portion is (by XbAnd ΦbIndicate displacement and corner), as shown in Figure 1, these global artificial boundary conditions can be expressed as：
Equation (3) and (5) are substituted into (8), obtain constant vectors：
In formula (11)：
Bring equation (11) into (7), F[i]Expression formula can reconfigure for：
In formula (13)：
It will be from known global artificial boundary condition G[0]Middle four local boundary conditions for obtaining every section of stake, for this purpose, defining square
Battle array：
In formula (14)：
Equation (13) is substituted into formula (9) and show that most latter two condition of continuity, direct derivation go out iterative relation and is：
In formula (16)：
Expression formula (13) is substituted by the first two condition of continuity in equation (9), another iterative relation by formula (16) again
It can be expressed as：
Wherein matrixUnquote value indicates the kth row of the matrix.After some derivations, equation (18) can table again
It is shown as：
In formula (19)：
Formula (16) and (19) are put together, G[i]Total iterative relation be finally：
G[i]=[T[i]]·{G[i-1]} (21)
In formula (21)：
According to formula (21), by G[i]Value and first segment section G[1]In conjunction with being using the sequence of iterative calculation：
G[i]=[U[i]]·{G[i-1]} (23)
For convenience, new iteration tensor is defined as:
U[i]=[T[i]]…[T[2]]·[I] (24)
The global artificial boundary condition and G provided in view of equation (10)[i]Definition, the equation derived above can be decomposed into
Two equation groups：
In formula (25)：
Obtain X1And Φ1Expression formula：
Therefore G[1]Expression formula can be write as matrix form：
In formula (28)：
In formula (29)：Z2And I2It is 2 × 2 rank zero-sum unit matrixs；
G[0]It is the normal global artificial boundary condition used in calculating；
Equation (23) and equation (28) are substituted into equation (13), F[i]Expression formula may finally be written as：
F[i]=[W[i]]·[G[0]] (30)
In formula (30)：
The solution of i-th section of parameter is can be obtained, that is, acquires internal force and the displacement of stake.
Claims (1)
1. a kind of stairstepping reducing hollow pile Calculation Methods for Internal Force, which is characterized in that the described method comprises the following steps：
(1) if hollow pile is divided into dried layer, the internal force and displacement expression formula of stake are released：
Stake overall length L is equal to the summation of every section of cross-sectional length, i.e. L=∑s Li；
According to theory of beam on elastic, per i sections of transverse deflections, the governing equation of distribution is：
In formula：piThe lateral resistance of the soil body caused by be bent due to stake；IiFor i-th of second moment of circular hollow pile,Wherein ξ=di/DiIndicate the thickness ratio of section；E is elasticity modulus；CiFor ground reaction mould
Amount；DiFor the outer diameter of i-th layer of stake；
Formula (1) is reconfigured：
X in formula (2)iSolved by following formula：
In formula (3)：
In formula：Ai,Bi,Ci,DiFor four parameters；
Other parameters φi、Mi、QiFor：
In formula,
Write as matrix form：
(2) to U[n]It is iterated calculating, obtains random layer iteration tensor U, and obtain the expression formula of matrix M：
By F[i]Expression formula reconfigure for：
It will be from known global artificial boundary condition G[0]Middle four local boundary conditions for obtaining every section of stake, define matrix：
Derive iterative relation：
After derivation, above formula is expressed as again：
G[i]Total iterative relation be finally：
G[i]=[T[i]]·{G[i-1]}；
New iteration tensor is defined as：
U[i]=[T[i]]...[T[2]]·[I]；
The expression formula of matrix M：
(3) conventional global artificial boundary condition matrix G is obtained by the transformational relation of eight boundary conditions0：
To each pile cutoff, local boundary condition is：
Xi、ΦiIndicate the lateral displacement and corner of i-th layer of bottom side；
Ri、HiThe transverse bending moment and point for indicating i-th layer of top side shear；
The adjacent segment condition of continuity is：
Global artificial boundary condition：
Conventional global artificial boundary condition matrix G0：
(4) the local boundary conditional vector G of first layer is obtained[1], and then solve random layer local boundary condition G[i]Finally obtain
The internal force and motion vector F of random layer[i]：
The local boundary conditional vector G of first layer[1]：
Random layer local boundary condition G[i]：
G[i]=[U[i]]·{G[i-1]}；
F[i]Expression formula be：
F[i]=[W[i]]·[G[0]]。
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| CN201810560926.4A CN108755785B (en) | 2018-06-04 | 2018-06-04 | Internal force calculation method for stepped variable-diameter hollow pile |
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| CN201810560926.4A CN108755785B (en) | 2018-06-04 | 2018-06-04 | Internal force calculation method for stepped variable-diameter hollow pile |
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101489707B1 (en) * | 2013-11-05 | 2015-02-06 | 연세대학교 산학협력단 | Method and apparatus for estimating optimal column-pile stiffness ratio of bent pile structure with varying cross-section in consideration with column-pile interaction |
| CN105045982A (en) * | 2015-07-06 | 2015-11-11 | 华东交通大学 | Simplified method for allocating foundation pile loads of grouped pile foundation with inverted stepped variable cross section |
| CN106650131A (en) * | 2016-12-28 | 2017-05-10 | 中国能源建设集团江苏省电力设计院有限公司 | Combined loaded pile bearing capacity transfer matrix general solution method |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101489707B1 (en) * | 2013-11-05 | 2015-02-06 | 연세대학교 산학협력단 | Method and apparatus for estimating optimal column-pile stiffness ratio of bent pile structure with varying cross-section in consideration with column-pile interaction |
| CN105045982A (en) * | 2015-07-06 | 2015-11-11 | 华东交通大学 | Simplified method for allocating foundation pile loads of grouped pile foundation with inverted stepped variable cross section |
| CN106650131A (en) * | 2016-12-28 | 2017-05-10 | 中国能源建设集团江苏省电力设计院有限公司 | Combined loaded pile bearing capacity transfer matrix general solution method |
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