CN108763833A - A kind of computational methods for the foundation pit supporting pile amount of deflection considering earth resistance mutation - Google Patents
A kind of computational methods for the foundation pit supporting pile amount of deflection considering earth resistance mutation Download PDFInfo
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- G06F30/20—Design optimisation, verification or simulation
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- E—FIXED CONSTRUCTIONS
- E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
- E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
- E02D17/00—Excavations; Bordering of excavations; Making embankments
- E02D17/02—Foundation pits
- E02D17/04—Bordering surfacing or stiffening the sides of foundation pits
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Abstract
The present invention relates to a kind of computational methods of the foundation pit supporting pile amount of deflection of consideration earth resistance mutation, belong to geotechnical engineering computational methods field, the technical scheme is that：The pile deflection differential equation is derived, ground compound stratum Resistance function is determined, pile body is segmented, each piecewise differential equation calculation pile body amount of deflection of simultaneous.Present invention primarily contemplates ground Resistance functions to have mutation in ground interface, in addition having also contemplated support displacement is influenced by digging process, pile body is segmented calculating etc. using segmentation independent coordinate, engineering practice can be more bonded, it reduces supporting construction stress deformation and calculates error, so that support pile amount of deflection is calculated more accurate, ensures construction safety.
Description
Technical field
The invention belongs to geotechnical engineering computational methods fields, and in particular to a kind of foundation pit supporting pile considering earth resistance mutation
The computational methods of amount of deflection.
Background technology
In the various supporting construction of deep basal pit, campshed-steel shotcrete support form is widely used.The stress of building enclosure becomes
Shape is issues that need special attention in one of emphasis of base pit stability control and design of foundation pit and work progress.
Currently, in foundation pit stake-support supporting structure system internal force and Method for Calculating Deformation, calculate for simplicity, mostly will
Ground drag modulus is seen as along the continuously distributed form of pile body depth direction.But in Practical Project, subsurface geology is distributed more
Complexity, there is also certain differences for the physico-mechanical properties between each soil layer, especially there is the geology item of rock stratum again in existing soil layer
Under part, cannot ground drag modulus be seen as continuously distributed function again, should be segmented and account for.
On the other hand, current computational methods simply regard supporting construction as member structure mostly, do not account for foundation pit
The influence of digging process, supporting construction seems just to have existed before excavation, namely does not account for foundation pit reaction of bearing and structure
Deformation with Excavation Process variation.
Above-mentioned drawback is bound to cause serious calculating error, and security risk is caused to engineering construction.
Invention content
In order to reduce above-mentioned calculating error, make result of calculation closer to actual conditions, the present invention proposes a kind of consideration soil
The computational methods of the foundation pit supporting pile amount of deflection of drag mutation, can more accurately calculate the amount of deflection of foundation pit supporting pile.
A kind of computational methods for the foundation pit supporting pile amount of deflection considering earth resistance mutation, technical solution of the present invention are as follows：
Step (1)：Derive the excavation face pile deflection differential equation below；
Step (2)：Derive the pile deflection differential equation of excavation face or more；
Step (3)：Determining has the ground compound stratum Resistance function p=p (x, y) of mutation；
Step (4)：With the segmentation independent coordinate method for considering that digging process influences, pile body is segmented；
Step (5)：The differential equation that simultaneous is respectively segmented calculates pile body amount of deflection；
Further, in step (1), the following pile deflection differential equation of excavation face is：
Wherein, q (x) is load function, related to depth x and external load；P=p (x, y) indicates Rock soil Foundation counter-force letter
Number, distribution situation and pile body depth x and stake deformation size y are closely related.
Further, in step (2), the above pile deflection differential equation of excavation face is：
Wherein, q0Indicate the trapezoidal short side load of the lateral trapezoidal load of Rock And Soil on the outside of foundation pit, n0What is indicated is triangle
The slope size that shape distributed load changes with depth x.
Further, in step (3), ground compound stratum Resistance function p=p (x, y) value is：
Wherein, x < t epoch topsoil, when x >=t, represent rock stratum；m1And m2It is proportionality coefficient related with soil property；N is to close
In the index of depth x, different n values represent different earth resistance distribution forms；b0Indicate that the deformation of pile body internal force calculates width.
Further, in step (4), consider that digging process influence is defined as follows：
Before each support is set up, certain first displacement has been produced in its corresponding position.At each support decorating position, stake
The actual elastic compressive deformation of body is the first displacement that sometime calculated pile body net slip subtracts pile body at the Support Position.
Further, in step (4), segmentation independent coordinate method is defined as follows：
It is partial node by supporting construction position, soil layer interface, rock-soil interface and excavation face positions such as supports, by stake
Body is structural segmented at several pile elements, and each pile element establishes separate cartesian coordinate system respectively, and segmentation is established pile body and scratched
The bent differential equation.
Further, in step (5), the expression formula of the above pile body amount of deflection of excavation face is：
According to the segmentation independent coordinate method, if foundation pit supporting construction has the support of the roads n, the above pile body of excavation face can be divided
For n+1 sections of pile element bodies, n+1 segmentation Deflection Differential Equation group is listed according to step (1) respectively.
Further, in step (5), the expression formula of the following pile body amount of deflection of excavation face is：
When excavation face exists below rock stratum with soil layer, pile body can be divided into 2 sections.Stake in soil can be listed according to step (1)
The deflection equation of body is：
Pile body Deflection Differential Equation is in rock stratum：
Wherein, plIt indicates to generate in excavation of foundation pit face stake side lotus below due to top soil body gravity in soil layer
It carries, pl' indicate to generate in excavation of foundation pit face stake side load below, b due to top soil body gravity in rock stratumsTo calculate
Width.
Further, in step (5), calculating pile body Deflection Method is：
The n+1 differential equation and excavation face 2 differential equations below more than excavation face, their simultaneous are had at one
The differential equation group of the n+3 differential equation, according to the deformation at stake end boundary condition, pile body segmentation is continuous and static balance condition
To solve the differential equation of each segmentation.
The advantage of the invention is that：
Under the geological conditions that existing soil layer has rock stratum again, ground drag modulus is seen as discontinuous along pile body depth direction
The ground Resistance function of the form of distribution, ground interface has mutation.Consider the influence of Excavation Process, stake-support supporting
The internal force of structure and deformation constantly change with the propulsion of operating mode.Pile body structure is segmented into several pile elements, segmentation is established
Pile body curve differential equation.The above several points improvement can reduce foundation pit supporting pile stress deformation meter closer to engineering practice
Error during calculation, provides a strong guarantee for safe construction.
Description of the drawings：
Fig. 1 is the calculation flow chart of the present invention.
Fig. 2 is the following pile body Impact direction of excavation face and cell cube stress balance schematic diagram.
Fig. 3 is the above pile body coordinate direction of excavation face and trapezoidal stress form schematic diagram.
Fig. 4 is drag modulus stepwise schematic views.
Specific implementation mode：
In the following, mode in conjunction with the accompanying drawings, illustrates specific implementation mode in more detail.It may be noted that herein
The technology and term being related to are identical as being generally understood for this patent technical field personnel.
A kind of computational methods for the foundation pit supporting pile amount of deflection considering earth resistance mutation, calculation process is as shown in Figure 1, specific
Embodiment is as follows：
One, the excavation face pile deflection differential equation below is derived.
Relationship by moment M and shearing Q is Q=dM/dx, then：
The following pile body stress diagram in excavation of foundation pit face and coordinates computed direction are as shown in Figure 2.It is scratched according in the mechanics of materials
Degree and moment of flexure relationship, the second-order differential (d of amount of deflection y2y)/(dx2) symbol with moment M is often opposite, because of the amount of deflection unit of stake
Mm differs three orders of magnitude with pile body length unit m, and obtained pile lateral displacement curve is generally flatter, therefore to amount of deflection y
First differential (dy/dx) that is squared2Value can be ignored substantially for comparing 1, then can will be bent differential side
Journey approximation is write as：
If hypothesis Analysis Block pile body structure is the straight stake of cross-section, the moment of inertia I of pile body is constant to get the curved of pilework
Stiffness EI (E indicates the elasticity modulus of pile material) is constant.Then the excavation face pile deflection differential equation below is obtained：
Wherein, q (x) is load function, related to depth x and external load；P=p (x, y) indicates Rock soil Foundation counter-force letter
Number, distribution situation and pile body depth x and stake deformation size y are closely related.
Two, the pile deflection differential equation of excavation face or more is derived.
As shown in Figure 3, it is assumed that the above pile body of excavation face is under external load and lateral rock and soil pressure by linear distribution form
Side pressure force effect is represented by with depth x variation functions：
As can be seen from the above equation, the above pile body distribution of force form of excavation face can be seen as trapezoidal load effect, i.e. load
By an evenly load q0With a Triangle Load Distribution n0It combines and obtains, wherein n0Indicate be Triangle Load Distribution with
The slope size of depth x variations, n0=(qx-q0)/x。
The pile deflection differential equation more than excavation face is as follows：
Wherein, q0Indicate the trapezoidal short side load of the lateral trapezoidal load of Rock And Soil on the outside of foundation pit, n0What is indicated is triangle
The slope size that shape distributed load changes with depth x.
Three, ground compound stratum Resistance function p=p (x, y) is determined.
Resistance function p (x, y) is that deflection deformation occurs after the following pile body stress of excavation face to make one of Rock And Soil generation
The distribution function of resistance function of negative direction.When pile body stress generates flexure, if amount of deflection size is y, by the influence factor of Resistance function
It is indicated with drag modulus K, Resistance function p (x, y) form can be expressed as at this time：
P (x, y)=Kb0y
Due to rock stratum and larger difference of the soil layer on physics and mechanical property, drag modulus K should be in rock stratum and soil layer
It is middle to account for respectively.Drag modulus K is K in soil layer1=m1xn；Drag modulus K is constant in rock stratum, that is, is had：K2=m2。
Drag modulus stepwise schematic views are as shown in figure 4, ground compound stratum Resistance function p=p (x, y) expression formula is as follows：
Wherein, x < t epoch topsoil, when x >=t, represent rock stratum；m1And m2It is proportionality coefficient related with soil property；N is to close
In the index of depth x, different n values represent different earth resistance distribution forms；b0Indicate that the deformation of pile body internal force calculates width.
Four, with the segmentation independent coordinate method for considering that digging process influences, pile body is segmented.
Before each support is set up, certain first displacement has been produced in its corresponding position.At each Support Position, the reality of pile body
Border elastic compression is deformed into the first displacement that sometime calculated pile body net slip subtracts pile body at the Support Position.Follow-up
It is continuous and when static balance condition solves pile body amount of deflection using the deformation at boundary condition, pile body segmentation in step, it needs
Consider support displacement variation in digging process.
It is partial node by supporting construction position, soil layer interface, rock-soil interface and excavation face positions such as supports, by stake
Body is structural segmented at several pile elements, and each pile element establishes separate cartesian coordinate system respectively, and segmentation is established pile body and scratched
The bent differential equation.
Five, the differential equation that simultaneous is respectively segmented calculates pile body amount of deflection.
According to the segmentation independent coordinate method, if foundation pit supporting construction has the support of the roads n, the above pile body of excavation face can be divided
For n+1 sections of pile element bodies, n+1 segmentation Deflection Differential Equation group can be listed according to step 1 respectively.
When excavation face exists below rock stratum with soil layer, pile body can be divided into 2 sections.Pile body in soil can be listed according to step 2
Deflection equation be：
Pile body Deflection Differential Equation is in rock stratum：
Wherein, plIt indicates to generate in excavation of foundation pit face stake side lotus below due to top soil body gravity in soil layer
It carries, pl' indicate to generate in excavation of foundation pit face stake side load below, b due to top soil body gravity in rock stratumsTo calculate
Width.
The n+1 differential equation and excavation face 2 differential equations below more than excavation face, their simultaneous are had at one
The differential equation group of the n+3 differential equation.
More than excavation face and excavation face pile body deflection equation below is quadravalence constant coefficient linearity homogeneous differential equation, micro-
Divide the general solution of equation that can be solved by the method differentiated step by step.Each differential equation has 4 undetermined parameters, including n+3 micro-
The differential equation group one of equation is divided to share 4 (n+3) a undetermined parameters.
It is continuous and quiet according to the deformation at stake end boundary condition (stake top is free end, and stake bottom is fixing end), pile body segmentation
Dynamic balance condition：Pile body can obtain 4 parametric equations, the support of the roads n and ground interface in the boundary condition of top and bottom end
One shared n+2 node can obtain 4 (n+2) a Parameter Relations to deform the equilibrium condition of the condition of continuity and power at node
At equation group, then 4+4 (n+2)=4 (n+3) a parametric equation can be obtained in total.
4 (n+3) a parametric equations can solve 4 (n+3) a undetermined parameters, and then the entire amount of deflection differential side of pile body can be obtained
The solution of journey.
Claims (9)
1. a kind of computational methods for the foundation pit supporting pile amount of deflection considering earth resistance mutation, which is characterized in that include the following steps：
Step (1)：Derive the excavation face pile deflection differential equation below；
Step (2)：Derive the pile deflection differential equation of excavation face or more；
Step (3)：Determining has the ground compound stratum Resistance function p=p (x, y) of mutation；
Step (4)：With the segmentation independent coordinate method for considering that digging process influences, pile body is segmented；
Step (5)：The differential equation that simultaneous is respectively segmented calculates pile body amount of deflection.
2. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (1), the following pile deflection differential equation of excavation face is：
Wherein, q (x) be by the above soil body load action of excavation face the following pile body of excavation face load function；P=p (x, y) table
Show that Rock soil Foundation a function of reaction, distribution situation and pile body depth x and stake deformation size y are closely related.
3. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (2), the above pile deflection differential equation of excavation face is：
Wherein, q0Indicate the trapezoidal short side load of the lateral trapezoidal load of Rock And Soil on the outside of foundation pit, n0What is indicated is triangle point
The slope size that cloth load changes with depth x.
4. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (3), ground compound stratum Resistance function p=p (x, y) value is：
Wherein, x < t epoch topsoil, when x >=t, represent rock stratum；m1And m2It is proportionality coefficient related with soil property；N is about depth
The index of x is spent, different n values represent different earth resistance distribution forms；b0Indicate that the deformation of pile body internal force calculates width.
5. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (4), consider that digging process influence is defined as follows：
Before each support is set up, certain first displacement has been produced in its corresponding position.At each support decorating position, pile body
Actual elastic compressive deformation is the first displacement that sometime calculated pile body net slip subtracts pile body at the Support Position.
6. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (4), segmentation independent coordinate method is defined as follows：
It is partial node by supporting construction position, soil layer interface, rock-soil interface and excavation face positions such as supports, by pile body knot
Structure is segmented into several pile elements, and each pile element establishes separate cartesian coordinate system respectively, and it is micro- that pile body flexure is established in segmentation
Divide equation.
7. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (5), the expression formula of the above pile body amount of deflection of excavation face is：
According to the segmentation independent coordinate method, if foundation pit supporting construction has the support of the roads n, the above pile body of excavation face can be divided into n+
1 section of pile element body lists n+1 segmentation Deflection Differential Equation group respectively according to the step (1).
8. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (5), the expression formula of the following pile body amount of deflection of excavation face is：
When excavation face exists below rock stratum with soil layer, pile body can be divided into 2 sections.According to the step (2), can list in soil
The deflection equation of pile body is：
Pile body Deflection Differential Equation is in rock stratum：
Wherein, plIt indicates to generate in excavation of foundation pit face stake side load below, p due to top soil body gravity in soil layerl’
It indicates to generate in excavation of foundation pit face stake side load below, b due to top soil body gravity in rock stratumsTo calculate width.
9. a kind of computational methods of foundation pit supporting pile amount of deflection considering earth resistance mutation according to claim 1, special
Sign is：In the step (5), calculating pile body Deflection Method is：
Their simultaneous are had n+3 by the n+1 differential equation and excavation face 2 differential equations below more than excavation face at one
The differential equation group of a differential equation, according to the deformation at stake end boundary condition, pile body segmentation is continuous and static balance condition come
Solve the differential equation of each segmentation.
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| CN109763484A (en) * | 2019-01-31 | 2019-05-17 | 四川省交通运输厅交通勘察设计研究院 | A kind of H type pile load calculation method |
| CN113051801A (en) * | 2021-03-30 | 2021-06-29 | 广东汇涛工程科技有限公司 | Error analysis method for measuring horizontal displacement of deep layer of foundation pit by tilt angle sensor |
| JPWO2020100237A1 (en) * | 2018-11-14 | 2021-09-24 | 日本電気株式会社 | Information processing equipment, control methods, and programs |
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