CN115329449B - Method for calculating optimal reserved interval of upper and lower sections of piles by reverse self-balancing pile testing method - Google Patents

Method for calculating optimal reserved interval of upper and lower sections of piles by reverse self-balancing pile testing method Download PDF

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CN115329449B
CN115329449B CN202211257326.3A CN202211257326A CN115329449B CN 115329449 B CN115329449 B CN 115329449B CN 202211257326 A CN202211257326 A CN 202211257326A CN 115329449 B CN115329449 B CN 115329449B
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冯东伟
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Hubei University of Technology
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Abstract

The invention discloses a method for calculating the optimal reserved space of upper and lower sections of piles by a reverse self-balancing pile testing method, wherein a general calculation analysis model is established, the basic factors such as bearing characteristics, stress modes and the like of the upper and lower sections of piles can be fully considered aiming at the soil around the piles, the soil at the pile ends, the pile body and bedrock, a complex three-dimensional calculation model is converted into a plane strain problem, a pile-soil foundation simplified analysis model is established, and a calculation formula of pile top deformation and pile body internal force is deduced. In the practice of the reverse self-balancing pile testing method, the design precision can be improved, and the ultimate bearing capacity of the foundation pile can be tested accurately.

Description

Method for calculating optimal reserved interval of upper and lower sections of piles by reverse self-balancing pile testing method
Technical Field
The invention belongs to the field of civil engineering, relates to a bearing capacity testing technology of foundation piles, and particularly relates to a method for calculating an optimal reserved interval of upper and lower piles by a reverse self-balancing pile testing method.
Background
Since the 21 st century, with the further development of economy, high-tech technologies have been applied to various fields. The foundation construction projects of widely applied pile foundations such as expressways, railways, high-rise buildings, offshore buildings and the like are developed rapidly, the pile foundations are usually underground or underwater, the foundation construction projects belong to concealed projects, the construction procedures are more, the technical requirements are high, the construction difficulty is high, quality problems are easy to occur, the bearing capacity of the foundation pile is a comprehensive index reflecting the properties of pile body materials, pile side soil and pile end soil and the construction method, and therefore, the research on the bearing capacity of the foundation pile is very important for practical projects. The pile foundation self-balancing detection method has the advantages that the loading device is simple, the bearing capacity of the pile foundation can be effectively detected, the problem of static load tests in special environments such as underwater, side slopes and underground can be effectively solved, large-tonnage static load tests can be effectively carried out according to the characteristics of specific strata, and the pile foundation self-balancing detection method gains reliability due to the characteristics such as unique method and simplicity and convenience in operation. However, the self-balancing test method is different from the traditional static load test pile in stress state, so that the conversion coefficient from the negative friction resistance to the positive friction resistance of the self-balancing test pile cannot be determined. Patent CN 111894051 discloses a reverse self-balancing model test device for pile foundation bearing capacity and a test method thereof, wherein loads of back-to-back movement and opposite movement of an upper-section pile and a lower-section pile are sequentially applied through two jacks at the top of a lower-section pile and the top of an upper-section pile. Compared with a pile foundation self-balancing detection method, the method has the advantages that the problem of determining the negative friction conversion coefficient can be effectively solved, and the uplift bearing capacity of the foundation pile can be measured. The opposite movement of the pile bodies is mainly to obtain the side friction of the upper pile section, but if the side friction of the upper pile section does not reach the limit state before the pile bodies are contacted, the limit bearing capacity of the foundation pile is lower than the actual value. In order to accurately measure the ultimate bearing capacity of the foundation pile, a certain distance is reserved between the bottom of the load box and the bottom of the upper section of pile, but if the pile distance is too small, the upper section of pile and the lower section of pile are contacted without exerting ultimate resistance to generate mutual extrusion, so that the ultimate bearing capacity is difficult to obtain; if the reserved distance between the upper segment pile and the lower segment pile is too large, although the side frictional resistance of the pile can be fully exerted, the ultimate bearing capacity of the pile is obtained, the specification requirement of a test pile method on a load box is improved, the test cost is increased, the work load of pouring concrete of a pile body at the position of the load box after the test pile is finished is increased, the later-stage pouring section is longer, the integrity of the foundation pile is influenced, and the strength of the foundation pile is further influenced. Therefore, it is necessary to design a set of algorithm to calculate the optimal reserved space between the upper and lower piles by the reverse self-balancing pile test method.
Disclosure of Invention
The invention aims to provide a method for calculating the optimal reserved space of upper and lower sections of piles by a reverse self-balancing pile testing method, which is used for calculating the optimal reserved space of the upper and lower sections of piles, preventing the upper and lower sections of piles from being mutually extruded when the lateral resistance of the piles is not fully exerted, and simultaneously avoiding the waste of manpower, material resources and financial resources caused by overlarge optimal reserved space.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for calculating the optimal reserved space of an upper section pile and a lower section pile by a reverse self-balancing pile testing method is characterized by comprising the following steps:
step 1, determining the upper-section pile bottom ultimate displacement according to the pile-soil size∂ 1 The calculation formula is as follows:
Figure 223123DEST_PATH_IMAGE001
formula (7)
In the above formula, the first and second carbon atoms are,S 1 the pile soil at the top of the upper pile section is relatively displaced,A p is the cross-sectional area of the pile body,E p in order to obtain the modulus of elasticity of the pile,Z 1 the total length of the upper section of the pile is,c a is the cohesive force between the pile side surface and the soil,Kthe lateral pressure coefficient of the soil on the pile side,
Figure 858766DEST_PATH_IMAGE002
is the vertical effective stress of the soil on the side of the pile,
Figure 705499DEST_PATH_IMAGE003
is the friction angle between the pile side surface and the soil,
Figure 899720DEST_PATH_IMAGE004
representThe distance between any point and the top of the upper pile section,G z indicates the distance from the top of the upper section of the pile to bezUpper weight of time;
step 2, according to the body stress characteristics, applying the cohesive force of the pile end on the pile bottom of the lower section of the pileF f Will beF f Determining the limit displacement of the pile top of the lower section pile as a boundary condition∂ 2 The calculation formula is as follows:
Figure 97483DEST_PATH_IMAGE005
formula (8)
The boundary conditions of equation (8) are: when in usez=Z 2 When the temperature of the water is higher than the set temperature,axial force
Figure 910718DEST_PATH_IMAGE006
In the above-mentioned formula, the compound has the following structure,S 2 the pile soil at the bottom of the lower pile is relatively displaced,Z 2 the total length of the lower section of the pile,zthe distance between any point and the pile top of the lower section of the pile,G z the distance from the pile bottom of the lower section of the pile is shown aszUpper part weight of (a);
step 3, respectively obtaining the upper-section pile top ultimate displacement through calculation or simulation analysis according to the pile-soil interaction mechanismS 1 And lower section pile bottom ultimate displacementS 2 Respectively substituting into the formula (7) and the formula (8) to obtain the upper-section pile bottom ultimate displacement ∂ 1 And lower section pile top ultimate displacement ∂ 2 ；
Step 4, calculating the combined displacement of the upper section of pile and the lower section of pile to be ∂ max =∂ 1 +∂ 2 (ii) a Resultant displacement ∂ max Plus height of the load boxS i The optimal reserved space between the upper and lower piles is obtainedS。
Further, in the step 1, the pile bottom limit displacement ∂ of the pile-soil size upper section pile is realized 1 The calculation formula is determined as follows:
step 1.1, determining the size of pile soil, and calculating the upper-section pile bottom ultimate displacement ∂ according to the formula (1) 1
Figure 890919DEST_PATH_IMAGE007
Formula (1)
In the above formulaN Z The axial force of the pile body is used;
step 1.2, calculating the stress relation of the upper-section pile according to the formula (2)
Figure 131408DEST_PATH_IMAGE008
Formula (2)
In the above-mentioned formula, the compound has the following structure,τ z is far from the pile top of the upper section of the pilezThe friction resistance value of the side of the position,U p the length of the circumference of the pile body is,
Figure 82046DEST_PATH_IMAGE009
the pile shaft force can be obtained by integrating the formula (2)N Z The calculation formula of (2);
step 1.3, calculating the extreme value of side friction resistance according to the formula (3)τ s The side frictional resistance extreme value is expressed by coulomb's formula similar to the shear strength of soil as follows:
Figure 698972DEST_PATH_IMAGE010
formula (3)
σ z Normal pressure acting on the pile-side surface at depth z, vertical effective stress with the pile-side soil
Figure 910511DEST_PATH_IMAGE011
Proportional mixing;
step 1.4, calculating the normal pressure acting on the pile side surface at the depth z according to the formula (4)σ z The calculation formula is as follows:
Figure 321900DEST_PATH_IMAGE012
formula (4)
In the above formulaK S Extruding the pile to obtain the lateral pressure coefficient of the side soil of the pileK a <K S <K p (ii) a For non-extruded piles, the soil in the pile hole is removedK a <K S <K 0 (ii) a WhereinK a 、K 0 、K p Active, static and passive earth pressure coefficients, respectively;
step 1.4, two soil particles in a saturated soil body bear an object with G gravity, the soil particles are in point contact, and the real load of the action of the two soil particlesP si 1=G-F，FIs topsoilThe buoyancy to which the particles are subjected;
contact area between two soil particlesA ci Not zero, the actual load of the interaction between the soil particles is caused by the action of the pore water pressure uP si Increase, i.e.
P si 2=G-F+A ci u formula (5)
P si 2 is the real load when the contact area of two soil particles is not zero;
step 1.5 vertical effective stress of pile side soil
Figure 494256DEST_PATH_IMAGE013
The calculation formula is as follows:
Figure 914873DEST_PATH_IMAGE014
formula (6)
A m The area of the soil in the radius is effectively influenced by the pile;
step 1.6, combining and arranging the formulas (1) to (6) to obtain the upper-section pile bottom ultimate displacement ∂ of the upper-section pile 1 Equation (7).
Further, in the step 3, the upper-section pile top limit displacementS 1 And lower section pile bottom ultimate displacementS 2 The calculation method is as follows:
the displacement of the soil around the pile is assumed according to a shear displacement method and a pile-soil interaction mechanism as follows:
Figure 980918DEST_PATH_IMAGE015
formula (9)
In the formulaS（z) Representing the displacement of the pile body relative to the soil around the pile;τ（z) For distance of pile topzPile side frictional resistance at the location;r 0 is the pile radius;r m in order to influence the radius of the pile body, namely the negligible range of pile side shear deformation,r m =2.5L(1-v s )，Lthe pile length;G s the shear modulus of the soil on the pile side is,G s =E s /2(1+v s )，E s and v s respectively representing the elastic modulus and Poisson's ratio of each layer of soil;
static analysis of differential unit
Figure 94367DEST_PATH_IMAGE016
Formula (10)
The elastic compression of the differential unit is:
Figure 754019DEST_PATH_IMAGE017
formula (11)
Substituting the formula (11) into the formula (10) to obtain
Figure 40644DEST_PATH_IMAGE018
Formula (12)
Substituting equation (9) into equation (12) to make
Figure 836561DEST_PATH_IMAGE019
Wherein:kis the shear stiffness coefficient of the pile soil,
Figure 215852DEST_PATH_IMAGE020
to obtain
Figure 97221DEST_PATH_IMAGE021
Formula (13)
For upper pile
Figure 781012DEST_PATH_IMAGE022
Formula (14)
In the formulaγIs heavy, representing the weight per unit volume,S 1 (z) represents the displacement of the upper pile body from the pile top at the position of z
Is obtained by the formula (14)
Figure 431436DEST_PATH_IMAGE023
Formula (15)
In the formulaC 1 、C 2 Is constant and is determined by the boundary condition of the pile body,K（z) Representing the axial force at a distance z from the pile top;
dividing the test pile into units according to the soil layer of the foundationiUnit soil thickness ofh i ，z b Is shown asiThe distance between the bottom of the soil layer and the pile top,z t is shown asiThe distance between the top of the soil layer bottom and the pile top,z t =z b +h i (ii) a Then it is firstiInternal force at bottom of soil layer test pile unitK（z b ) And displacement ofS 1 （z b ) Is composed of
Figure 214584DEST_PATH_IMAGE024
Formula (16)
In the formula:
Figure 583249DEST_PATH_IMAGE025
first, theiInternal force at top of soil layer test pile unitK（z t ) And displacement ofS 1 （z t ) Comprises the following steps:
Figure 518668DEST_PATH_IMAGE026
formula (17)
In the formula:
Figure 289178DEST_PATH_IMAGE027
wherein:z t =z b +h i the relation between the internal force and the displacement of the top and the bottom of the test pile unit is obtained by the following formula:
Figure 649752DEST_PATH_IMAGE028
formula (18)
In the formula
Figure 505712DEST_PATH_IMAGE029
Considering continuity of internal force and displacement of each unit of the pile body, the relation between the displacement of the pile top and the pile bottom and load is as follows:
Figure 734568DEST_PATH_IMAGE030
formula (19)
In the formula:
Figure 625164DEST_PATH_IMAGE031
，nthe number of layers;
the jack is taken to load the upper section of pile
Figure 156639DEST_PATH_IMAGE032
The upper section pile bottom loading force is expressed as
Figure 765475DEST_PATH_IMAGE033
WhereinK 1 For upper pile stiffness, so for a given jack loading valueQNamely thatK（z= 0) upper pile top limit displacement
Figure 407809DEST_PATH_IMAGE034
Is shown as
Figure 277545DEST_PATH_IMAGE035
Formula (20)
The ultimate displacement of the pile bottom of the lower section pile is calculated in the same wayS 2 。
The invention has the beneficial effects that:
the invention provides a reliable and simple method for calculating the optimal reserved interval of the upper and lower sections of the reverse self-balancing test pile, which not only can accurately test the bearing capacity of the foundation pile, but also can save the workload and the cost of the test pile, reduce the influence of a post-pouring section on the overall strength of the pile after the test pile is finished, and has great engineering value.
The invention establishes a universal calculation analysis model, can fully consider the factors such as the basic bearing characteristics, the stress mode and the like of the soil around the pile, the soil at the end of the pile, the pile body and the bedrock, converts a complex three-dimensional calculation model into a plane strain problem, establishes a pile-soil foundation simplified analysis model, deduces the calculation formulas of the deformation of the pile top and the internal force of the pile body, and provides theoretical support for the design of the optimal reserved space of the upper and lower piles at the position of the load box in the practice of a reverse self-balancing pile test method.
Based on an elastic theory method, the invention establishes a reverse self-balancing test pile method pile-soil foundation calculation analysis model, and further deduces the ultimate displacement of the reverse self-balancing test pile when the upper section pile is pressed. In the practice of a reverse self-balancing pile test method, the design precision can be improved, and the ultimate bearing capacity of the foundation pile can be accurately tested.
Drawings
Fig. 1 shows a pile top loading model in an embodiment of the invention, wherein a in fig. 1 is an initial state of the pile top being unloaded,Sin order to reserve the space between the upper pile and the lower pile,S i the height of the pile body load box is shown, b in fig. 1 is a schematic diagram in the pile top loading process, S' is the distance between an upper pile and a lower pile after loading, and c in fig. 1 is a schematic diagram of complete loading of the pile top.
FIG. 2 is a plot of pile side friction as a function of pile cross-section versus relative displacement.
FIG. 3 is a diagram of a contact model between soil particles in a saturated soil body.
Fig. 4 is a schematic diagram of a finite element model with a reverse self-balancing test pile model, wherein a in fig. 4 is a finite element geometric model diagram, and b in fig. 4 is a mesh division diagram of the finite element model.
Fig. 5 is a load-displacement curve diagram of the engineering pile static load foundation pile in the embodiment of the invention.
Fig. 6 is a load-displacement curve of the pile jack.
Fig. 7 is a load-displacement curve for a pile jack.
Reference numerals: 1-upper pile section, 2-pressure sensor, 3-pile body jack, 4-lower pile section and 5-soil around the pile.
10-foundation piles; 11-pile-surrounding soil mass; 12-partial enlargement of the finite element model; 100-fine silt and silt; 200-fine silt and 300-stroke argillite.
Detailed Description
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used only for convenience in describing the present invention and for simplicity in description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention. Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified. In the description of the present invention, it is to be noted that, unless otherwise explicitly specified and limited, the specific meanings of the above terms in the present invention can be specifically understood by those skilled in the art.
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit of the invention defined and defined in the claims and all inventive concepts conceived to be protected thereby.
As shown in fig. 1, the invention provides a method for calculating an optimal reserved interval of upper and lower section piles by a reverse self-balancing pile test method, which comprises the following steps:
step 1, determining upper section pile bottom ultimate displacement ∂ according to pile-soil size 1 Formula for calculation
Step 1.1, determining the size of pile soil, and calculating the upper-section pile bottom ultimate displacement ∂ according to the formula (1) 1
Figure 979922DEST_PATH_IMAGE036
Formula (1)
In the above formulaN Z The axial force of the pile body is taken as the axial force;
step 1.2, calculating the stress relation of the upper-section pile according to the formula (2)
Figure 810475DEST_PATH_IMAGE037
Formula (2)
τ z The distance from the pile top of the upper section pile is the Z-position side friction resistance value,U p the circumference of the pile body is long;
step 1.3, pile side friction resistanceτIs a function of the cross-section of the stake to relative displacement ∂, as shown in FIG. 2, curve OCD, but can be generally simplified to OAB. Limit value ofτ s The side frictional resistance extreme value is expressed as follows using the coulomb formula analogous to the shear strength of soil:
Figure 256500DEST_PATH_IMAGE038
formula (3)
σ z Normal pressure acting on the pile-side surface at depth z, vertical effective stress with the pile-side soil
Figure 246321DEST_PATH_IMAGE039
In proportion;
step 1.4, calculating the normal pressure acting on the pile side surface at the depth z according to the formula (4)σ z The calculation formula is as follows:
Figure 119599DEST_PATH_IMAGE012
formula (4)
In the above formulaK S Extruding the pile to obtain the lateral pressure coefficient of the side soil of the pileK a <K S <K p (ii) a For non-squeezed soil piles, soil in pile holes is removedK a <K S <K 0 (ii) a WhereinK a 、K 0 、K p Active, static and passive earth pressure coefficients, respectively;
step 1.4, two soil particles in the saturated soil body bear an object with G gravity, and the left graph in FIG. 3 shows that the soil particles are in point contact and the real load of the two soil particles isP si 1=G-F，FIs the buoyancy force borne by the upper soil particles;
contact area between two soil particlesA ci Is not zero, and the real load of the interaction between the soil particles is caused by the action of the pore water pressure uP si Increase, i.e.
P si 2=G-F+A ci u formula (5)
P si 2 is the real load when the contact area of two soil particles is not zero;
step 1.5 vertical effective stress of pile side soil
Figure 171869DEST_PATH_IMAGE040
The calculation formula is as follows:
Figure 687164DEST_PATH_IMAGE041
formula (6)
A m The area of the soil in the radius is effectively influenced by the pile;
step 1.6, combining and arranging the formulas (1) to (6) to obtain the upper-section pile bottom ultimate displacement ∂ 1 The calculation formula is as follows:
Figure 406858DEST_PATH_IMAGE042
formula (7)
In the above formula, the first and second carbon atoms are,S 1 the pile soil at the top of the upper pile section is relatively displaced,A p is the cross-sectional area of the pile body,E p in order to obtain the modulus of elasticity of the pile,Z 1 the total length of the upper section of the pile is the total length,c a is the cohesive force between the pile side surface and the soil,Kthe lateral pressure coefficient of the soil on the pile side,
Figure 77136DEST_PATH_IMAGE043
is the vertical effective stress of the soil on the side of the pile,
Figure 616702DEST_PATH_IMAGE044
is the friction angle between the pile side surface and the soil,
Figure 404529DEST_PATH_IMAGE004
to representThe distance between any point and the top of the upper pile section,G z indicates the distance from the top of the upper section of the pile to bezUpper weight of time;
step 2, according to the stress characteristics of the pile body, applying the stress on the pile bottom of the lower section of the pileF f Will beF f Combining the formulas (1) to (6) as boundary conditions, and determining the limit displacement of the pile top of the lower section pile∂ 2 The calculation formula is as follows:
Figure 978730DEST_PATH_IMAGE045
formula (8)
The boundary conditions of equation (8) are: when in usez=Z 2 Axial force of time
Figure 318445DEST_PATH_IMAGE046
In the above formula, the first and second carbon atoms are,S 2 the pile soil at the bottom of the lower pile is relatively displaced,Z 2 the total length of the lower section of the pile,zis the distance from the pile top of the lower pile,G z the distance from the pile bottom of the lower section of the pile is shown aszUpper part weight of (a);
step 3, respectively obtaining the upper-section pile top ultimate displacement through calculation or simulation analysis according to the pile-soil interaction mechanismS 1 And lower section pile bottom ultimate displacementS 2 Respectively substituting into the formula (7) and the formula (8) to obtain the upper-section pile bottom ultimate displacement ∂ 1 And lower section pile top ultimate displacement ∂ 2 ；
The invention provides a limit displacement of the top of an upper pileS 1 And lower section pile bottom ultimate displacementS 2 The calculation method is as follows:
according to the pile-soil interaction mechanism proposed by a shear displacement method, RANDOLPH and the like, the displacement of soil around the pile can be assumed as follows:
Figure 610886DEST_PATH_IMAGE047
formula (9)
In the formulaS（z) Representing the displacement of the pile body relative to the soil around the pile;τ（z) For distance of pile topzPile side frictional resistance at the location;r 0 is the pile radius;r m in order to influence the radius of the pile body, namely the negligible range of pile side shear deformation,r m =2.5L(1-v s ) L is the pile length;G s the shear modulus of the soil on the pile side is,G s =E s /2(1+v s )，E s and v s respectively representing the elastic modulus and Poisson's ratio of each layer of soil;
static analysis of differential cells
Figure 671246DEST_PATH_IMAGE048
Formula (10)
The elastic compression of the differential unit is:
Figure 224587DEST_PATH_IMAGE049
formula (11)
Substituting the formula (11) into the formula (10) can obtain
Figure 344989DEST_PATH_IMAGE050
Formula (12)
Substituting the equation (9) into the equation (12) to make
Figure 544633DEST_PATH_IMAGE051
Wherein:kis the shear stiffness coefficient of the pile soil,
Figure 674263DEST_PATH_IMAGE052
can obtain the product
Figure 19794DEST_PATH_IMAGE053
Formula (13)
For upper pile
Figure 170153DEST_PATH_IMAGE054
Formula (14)
In the formulaγIn order to indicate the weight per unit volume for the weight,S 1 (z) displacement at z position of upper pile shaft
From the formula (14), it can be obtained
Figure 30661DEST_PATH_IMAGE055
Formula (15)
In the formulaC 1 、C 2 Is constant and is determined by the boundary condition of the pile body,K（z) Representing the axial force at a distance z from the pile top;
dividing the test pile into units according to the soil layer of the foundationiUnit soil thickness ofh i ，z b Is shown asiThe distance between the bottom of the soil layer and the pile top,z t is shown asiThe distance between the top of the soil layer bottom and the pile top,z t =z b +h i (ii) a Then it is firstiInternal force at bottom of soil layer test pile unitK（z b ) And displacement ofS 1 （z b ) Is composed of
Figure 963982DEST_PATH_IMAGE056
Formula (16)
In the formula:
Figure 367282DEST_PATH_IMAGE057
first, theiInternal force at top of soil layer test pile unitK（z t ) And displacement ofS 1 （z t ) Comprises the following steps:
Figure 95066DEST_PATH_IMAGE058
formula (17)
In the formula:
Figure 209915DEST_PATH_IMAGE059
wherein:z t =z b +h i the relation between the internal force and the displacement of the top and the bottom of the pile testing unit obtained by the above formula is as follows:
Figure 946927DEST_PATH_IMAGE060
formula (18)
In the formula
Figure 204733DEST_PATH_IMAGE061
Considering the continuity of the internal force and displacement of each unit of the pile body, the relation between the pile top and the displacement and the load of the pile bottom can be obtained as follows:
Figure 368998DEST_PATH_IMAGE062
formula (19)
In the formula:
Figure 345044DEST_PATH_IMAGE063
n is the number of layers;L 1 is the length of the upper section of the pile
Loading the upper pile by jack
Figure 744802DEST_PATH_IMAGE064
Then the upper section pile bottom loading force is expressed as
Figure 591535DEST_PATH_IMAGE065
WhereinK 1 For upper pile stiffness, so for a given jack loading valueQNamely, it isK（z= 0) upper pile top limit displacement
Figure 785756DEST_PATH_IMAGE066
Is shown as
Figure 452360DEST_PATH_IMAGE067
Formula (20)
The ultimate displacement of the pile bottom of the lower pile can be solved in the same wayS 2 。
Step 4, calculating the combined displacement of the upper section of pile and the lower section of pile to be ∂ max =∂ 1 +∂ 2 (ii) a Using displacement ∂ max And adding the height of the load box to obtain the optimal reserved interval of the upper and lower piles.
Engineering example: the west side of a certain engineering project is a perpetual street, the east side of the project is a perpetual flying street, the north side of the project is a multi-layer house with a brick-concrete structure, the south side of the project is a planned road, a shallow foundation slab house is arranged in the middle of the road, and peripheral traffic is convenient. The survey hole arrangement area field is level, mostly is the greenbelt, belongs to the Changjiang river and piles up the plain area one-level terrace, and the place is undulant less. The field soil is divided into three layers, wherein the first layer is formed by fine silt and silt, the average layer thickness is 15m, the fine silt is in a slightly-medium dense state, and the fine silt mainly comprises quartz, feldspar micanite sheets and a thin-layer silt; the second layer is fine silt, the average layer thickness is 20m, the second layer is in a medium-dense to compact state, the main components are quartz and feldspar-sandwiched mica sheets, the lower part of the second layer is 1-2m clamped with a small amount of pebbles, the content is about 5% -10%, and the particle size is 1.5-3.0 cm; the third layer is the stroke argillite, most of rock cores are short columns, a small number of rock cores are broken blocks, the coring rate is about 70-75%, and the basic quality grade of the rock mass belonging to the extremely soft rock is V grade. The stroke argillite is a uniform low-compressibility soil layer which is distributed in the whole field and can be used as a foundation bearing layer for building main buildings and skirt buildings. The characteristic value of the vertical bearing capacity of the single pile is 6653KN, and the pile soil parameters are shown in table 1.
TABLE 1 pile soil parameter table
Figure 390229DEST_PATH_IMAGE068
The assumed conditions are as follows: to simplify the calculation, the following assumptions are made when establishing finite elements:
(1) The soil body is considered to be homogeneous elastic-plastic material, the pile body is homogeneous ideal elastic body, the bending deformation of the pile body is not considered, and the shearing expansion of the soil is not considered.
(2) And considering the contact interface between the pile body of the pile and the soil body, and keeping the friction coefficient between the pile and the rock soil unchanged in the analysis process.
(3) The soil body is analyzed by adopting total stress, the influence of pore water pressure is not considered, and the inclination of a rock stratum is not considered.
(4) The two sides of the finite element model are assumed to have no displacement in the horizontal direction, and the bottom is completely fixed.
Specifically calculating: the total length of the pile is 50m, the diameter of the pile is 0.8m, 20 times of the diameter of the pile is horizontally taken in a soil layer, and 2 times of the length of the pile is vertically taken.
For the upper section of pile, determining the parameters of the pile body as follows:A p =2.001m 2 ，K 1 =1.2，
Figure 357048DEST_PATH_IMAGE069
=32°，
Figure 423968DEST_PATH_IMAGE070
=294.52kpa；
for the lower section of the pile,A p =2.001m 2 ，K 2 =0.7，
Figure 702503DEST_PATH_IMAGE071
=34°，
Figure 178483DEST_PATH_IMAGE072
=294.52kpa；
the total ultimate bearing capacity of the upper and lower sections of the reverse self-balancing pile is 14712kN and the downward ultimate displacement of the pile top of the upper section of the pile is calculated through simulation analysisS 1 =20.72mm, and cohesive force c between pile side surface of upper pile and soil a1 =5437kN, limit displacement of lower pile bottom upwardsS 2 =16.73mm, cohesive force c between pile side surface of lower section pile and soil a2 =3473kN。
From the equations (7) and (8)
Figure 999809DEST_PATH_IMAGE073
=20.72-7.95=12.77mm
Figure 676778DEST_PATH_IMAGE074
=16.73-4.78=11.95mm
∂ max =12.77+11.95=24.72mm；
The above-described embodiments of the invention are verified using finite element models as follows:
1. geometric model
As shown in FIG. 4, finite element software was usedAbaqusThe pile-soil model is built, and according to the characteristics of the pile-soil model, the pile-soil model can be made into two-dimensional shapeEquation is equivalent, so two-dimensional modeling is used herein. The total length of the foundation pile 10 is 50m, the pile diameter is 0.8m, the soil layer is horizontally 20 times of the pile diameter, the pile length is 2 times of the pile length in the vertical direction, namely the model calculation width is 16m, the calculation depth is 100m, the soil around the pile is 15m fine silt with silt 100, 20m thick fine silt 200 and 65m thick stroke argillite 300 in sequence from top to bottom. The pile body adopts a linear elastic model, the soil body adopts an elastic-plastic model, and specific calculation is carried out according to the Mokolun yield criterion. The top of the soil mass model is free edge unconstrained, the bottom of the soil mass model adopts fixed constraint, and the outer side of the soil mass model is radial displacement constraint; the pile top is free and unconstrained.
In the division of the unit grid, the part close to the pile body is densely divided, and the part far away from the pile body is sparse. The pile and the soil body adopt C3D8R, namely a node quadrilateral linear plane strain reduction integral unit, and the type of the unit is more accurate in the solution result of the displacement. The finite element geometric model is shown in fig. 4.
2. Interaction of
The pile and the rock soil adopt a surface-surface contact pair type, and because the rigidity of the pile relative to the rock soil is high, the pile is a main control surface, the rock soil is a subordinate surface, and the contact tracking method of the pile and the soil body adopts limited slippage. The contact property between the pile and the rock-soil contact surface comprises two aspects, namely that a 'hard contact' is adopted in the normal direction and separation is allowed, and that a coulomb penalty rigidity algorithm is adopted in the tangential direction to determine the friction coefficient. The part of the bottom of the lower section pile, which is contacted with the soil body, is provided with bonding strength, so that the lower section pile is not easy to pull up.
3. Load calculation step
The calculation step is to simulate the process of the stress of the pile foundation.
(1) And (5) analyzing the ground stress of the soil body. Simulating the original state of soil body, removing pile in model, only analyzing ground stress of soil body, applying displacement constraint to side surface and bottom surface of pile and soil, applying dead load to soil body, and adoptingGeostaticThe analysis step carries out soil stress self-balancing calculation, and the self-balancing convergence condition is that the soil displacement is less than 10 -5 m。
(2) And (5) pile-soil contact calculation. The method is used for simulating the load action of the soil body after pile forming on the pile, the pile is added into the model, the displacement constraint between the pile and the soil is cancelled, so that the pile and the soil are in contact, and meanwhile, the influence of the self weight of the pile is taken into account.
(3) And (4) loading the pile body. And (3) applying upward uniformly distributed load to the bottom of the upper section pile, applying downward uniformly distributed load to the top of the lower section pile, and adopting a graded loading mode.
(4) And (4) unloading the pile body and applying uniform load (simulating the unloading stress state of the foundation pile).
(5) And (4) loading the pile top. And applying downward uniformly distributed load to the pile top of the upper section of the pile, applying upward uniformly distributed load to the pile top of the lower section of the pile, and adopting a graded loading mode.
FIG. 5 is a load-displacement curve of a static load numerical simulation, the load of the pile top is gradually increased along with the slow change of the settlement of the pile top, the whole displacement curve does not have a load abrupt change point, the curve is a typical slow-change curve, and the load corresponding to the displacement of 40mm is preferably selected, namelyQ=12844kN, the actual engineering single pile vertical bearing capacity characteristic value isRa =6653KN, the ultimate bearing capacity is 13306KN, the difference between the two is 462KN. Therefore, the parameter setting, the grid division, the interaction and the like of the model are consistent with the engineering design, and the actual conditions of the engineering pile can be reflected.
In a simulation working condition, the optimal reserved space ∂ in the most appropriate pile is determined, a balance point L is selected to be 35m in the simulation process, a loading mode that a pile body is loaded first and then a pile top is loaded is adopted, and S =30mm is calculated.
Fig. 6 and 7 are load-displacement curves of the reverse self-balancing test with a space of 30mm, fig. 6 is a load-displacement curve of the pile and the body jack under the loading of the reverse self-balancing test, and it can be seen from fig. 6 that after the displacement of the pile bottom of the upper section pile is increased to 12.17mm, the load of the pile bottom is hardly changed along with the increase of the vertical displacement of the pile bottom, which indicates that the bearing capacity of the upper pile reaches the limit value when the displacement is equal to 12.17mm, namely Q is the limit value uu - =3521kN; the load of the lower pile top is increased along with the gradual increase of the displacement of the lower pile top, the load displacement curve is a typical gradual change curve, and the ultimate bearing capacity of the load displacement curve is taken asQ ud + =7720kN. The residual deformation amount of the pile bottom of the unloaded upper section pile is small, the resilience amount of the pile bottom is 8mm, and the resilience amount of the pile top of the lower section pile is almost 0mm. Drawing (A)7 is a load-displacement curve under the loading of the pile jack of the reverse self-balancing test, and for the loading of the upper section pile jack, the ultimate bearing capacity displacement curve of the upper section pile has an obvious inflection point, and the ultimate bearing capacity of the upper section pile is the load corresponding to the displacement equal to 13.87mm, namely the upper section pile is the load corresponding to the displacement equal to 13.87mmQ uu + =3981kN, the displacement curve of fig. 7 has obvious inflection points, and it is easy to judge that the ultimate bearing capacity of the lower pile is the load corresponding to the displacement equal to 9.74mmQ ud - =4120kN。
Reverse self-balancing ultimate loadQ Press and press =Q uu + +Q ud + K1 of 0.8, and self-balancing ultimate bearing capacity of 11701KNQ u = (3521-422)/0.8 +7716=11589KN, the reverse self-balancing and static load limit bearing forces are 1147KN, and the self-balancing and static load limit bearing forces are 1255KN. The pile body is unloaded and rebounded after being loaded, 8mm of space is reserved between the piles, when the pile top is loaded, the upper section of the pile moves downwards by 13.87m, at the moment, the lower section of the pile moves by 9.74m, and the upper section of the pile and the lower section of the pile move by 23.61mm together under the action of the pile top, which is consistent with the calculation of ∂ max And if the error is not less than 24.72mm, comparing the calculation result of the finite element model with the derivation result of the formula of the invention to obtain an error rate of 4 percent, and proving that the formula is feasible to a certain extent.
The above embodiments are merely illustrative of the present invention and are not to be construed as limiting the invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that various combinations, modifications or equivalents may be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention, and the technical solution of the present invention is covered by the claims of the present invention.

Claims (3)

1. A method for calculating the optimal reserved space of upper and lower sections of piles by a reverse self-balancing pile testing method is characterized by comprising the following steps:
step 1, determining the upper-section pile bottom ultimate displacement according to the pile-soil size∂ 1 The calculation formula is as follows:
Figure 460240DEST_PATH_IMAGE001
formula (7)
In the above formula, the first and second carbon atoms are,S 1 for the ultimate displacement of the pile top of the upper section of the pile,A p is the cross-sectional area of the pile body,E p in order to obtain the modulus of elasticity of the pile,Z 1 the total length of the upper section of the pile is the total length,c a is the cohesive force between the pile side surface and the soil,Kthe lateral pressure coefficient of the soil on the pile side,
Figure 69076DEST_PATH_IMAGE002
is the vertical effective stress of the soil on the side of the pile,
Figure 976989DEST_PATH_IMAGE003
is the friction angle between the pile side surface and the soil,zthe distance between any point of the pile body and the top of the upper pile section,G z indicates the distance from the top of the upper section of the pile to bezUpper weight of time;
step 2, according to the stress characteristics of the pile body, applying the stress on the pile bottom of the lower section of the pileF f Will beF f Determining the limit displacement of the pile top of the lower section pile as a boundary condition∂ 2 The calculation formula is as follows:
Figure 345260DEST_PATH_IMAGE004
formula (8)
The boundary conditions of equation (8) are: when in usez=Z 2 Axial force of time
Figure 47637DEST_PATH_IMAGE005
In the above formula, the first and second carbon atoms are,S 2 the ultimate displacement of the pile bottom of the lower pile,Z 2 the total length of the lower section of the pile,zis the distance from the pile top of the lower pile,G z the distance from the pile bottom of the lower section of the pile is shown aszUpper part weight of (a);
step 3, calculating according to the pile-soil interaction mechanism orRespectively obtaining the ultimate displacement of the pile top of the upper section of the pile through simulation analysisS 1 And lower section pile bottom ultimate displacementS 2 Respectively substituting into the formula (7) and the formula (8) to obtain the upper-section pile bottom ultimate displacement ∂ 1 And lower section pile top ultimate displacement ∂ 2 ；
Step 4, calculating the combined displacement of the upper pile and the lower pile to be ∂ max =∂ 1 +∂ 2 (ii) a Resultant displacement ∂ max Plus height of the load boxS i The optimal reserved space between the upper and lower piles is obtainedS。
2. The method for calculating the optimal reserved space between the upper pile and the lower pile by the reverse self-balancing pile test method according to claim 1, which is characterized by comprising the following steps of: in step 1, the pile bottom limit displacement of the upper-section pile is ∂ 1 The calculation formula is determined as follows:
step 1.1, calculating the upper-section pile bottom ultimate displacement ∂ according to the formula (1) 1
Figure 878189DEST_PATH_IMAGE006
Formula (1)
In the above formulaN Z The axial force of the pile body is taken as the axial force;
step 1.2, calculating the stress relation of the upper-section pile according to the formula (2)
Figure 58635DEST_PATH_IMAGE007
Formula (2)
τ z The distance from the pile top of the upper section pile is the Z-position side friction resistance value,U p the circumference of the pile body is long;
step 1.3, calculating the extreme value of side friction resistance according to the formula (3)τ s The extreme value of the side friction resistance is represented by the Coulomb formula similar to the shear strength of soil
Figure 48457DEST_PATH_IMAGE008
Formula (3)
σ z Is depth ofzNormal pressure acting on the pile side surface and vertical effective stress of the pile side soil
Figure 921735DEST_PATH_IMAGE009
In proportion;
step 1.4, calculating the normal pressure acting on the pile side surface at the depth z according to the formula (4)σ z
Figure 505163DEST_PATH_IMAGE010
Formula (4)
In the above formulaK S Extruding the pile to obtain the lateral pressure coefficient of the side soil of the pileK a <K S <K p (ii) a For non-extruded piles, the soil in the pile hole is removedK a <K S <K 0 (ii) a WhereinK a 、K 0 、K p Active, static and passive earth pressure coefficients, respectively;
step 1.4, two soil particles in the saturated soil body bear one gravity ofGThe soil particles are point contact, and the real load acted by the two soil particlesP si 1=G-F，FIs the buoyancy force borne by the upper soil particles;
contact area between two soil particlesA ci Non-zero pore water pressureuThe effect of (2) is to make the real load of the interaction between the soil particlesP si Increase, i.e.
P si 2=G-F+A ci u formula (5)
P si 2 is the real load when the contact area of two soil particles is not zero;
step 1.5 vertical effective stress of pile side soil
Figure 489299DEST_PATH_IMAGE011
The calculation formula is as follows:
Figure 208994DEST_PATH_IMAGE012
formula (6)
A m The area of the soil in the radius is effectively influenced by the pile;
step 1.6, combining and arranging the formulas (1) to (6) to obtain the upper-section pile bottom ultimate displacement ∂ of the upper-section pile 1 Equation (7).
3. The method for calculating the optimal reserved interval between the upper section pile and the lower section pile by the reverse self-balancing pile test method according to claim 2, wherein in the step 3, the ultimate displacement of the pile top of the upper section pile isS 1 And lower section pile bottom ultimate displacementS 2 The calculation method is as follows:
the displacement of the soil around the pile is assumed according to a shear displacement method and a pile-soil interaction mechanism as follows:
Figure 377807DEST_PATH_IMAGE013
formula (9)
In the formulaS（z) Representing the displacement of the pile body relative to the soil around the pile;τ（z) For distance of pile topzPile side frictional resistance at the location;r 0 is the pile radius;r m in order to influence the radius of the pile body, namely the negligible range of pile side shear deformation,r m =2.5L(1-v s ) L is the pile length;G s the shear modulus of the soil on the pile side is,G s =E s /2(1+v s )，E s andv s respectively representing the elastic modulus and Poisson's ratio of each layer of soil;
static analysis of differential cells
Figure 182952DEST_PATH_IMAGE014
Formula (10)
The elastic compression of the differential unit is:
Figure 970779DEST_PATH_IMAGE015
formula (11)
Substituting the formula (11) into the formula (10) to obtain
Figure 810559DEST_PATH_IMAGE016
Formula (12)
Substituting equation (9) into equation (12) to make
Figure 884694DEST_PATH_IMAGE017
Wherein:kthe shear stiffness coefficient of the pile soil is obtained
Figure 911556DEST_PATH_IMAGE018
Figure 503075DEST_PATH_IMAGE019
Formula (13)
For upper pile
Figure 197361DEST_PATH_IMAGE020
Formula (14)
In the formulaγIs heavy, representing the weight per unit volume,S 1 (z) represents the displacement of the upper pile body from the pile top at the position of z
Is obtained by the formula (14)
Figure 583343DEST_PATH_IMAGE021
Formula (15)
In the formulaC 1 、C 2 Is a constantThe number is determined by the boundary condition of the pile body,K（z) Representing the axial force at a distance z from the pile top;
dividing the test pile into units according to the soil layer of the foundationiThe unit soil layer thickness ish i ，z b Is shown asiThe distance between the bottom of the soil layer and the pile top,z t is shown asiThe distance between the top of the soil layer bottom and the pile top,z t =z b +h i (ii) a Then it is firstiInternal force at bottom of soil layer test pile unitK（z b ) And displacement ofS 1 （z b ) Is composed of
Figure 989179DEST_PATH_IMAGE022
Formula (16)
In the formula:
Figure 118809DEST_PATH_IMAGE023
first, theiInternal force at top of soil layer test pile unitK（z t ) And displacement ofS 1 （z t ) Comprises the following steps:
Figure 402023DEST_PATH_IMAGE024
formula (17)
In the formula:
Figure 224485DEST_PATH_IMAGE025
wherein:z t =z b +h i the relation between the internal force and the displacement of the top and the bottom of the test pile unit is obtained by the following formula:
Figure 350573DEST_PATH_IMAGE026
formula (18)
In the formula
Figure 283894DEST_PATH_IMAGE027
Considering the continuity of the internal force and displacement of each unit of the pile body, the relation between the pile top and the displacement and the load of the pile bottom is as follows:
Figure 687194DEST_PATH_IMAGE028
formula (19)
In the formula:
Figure 680557DEST_PATH_IMAGE029
n is the number of layers;
loading the upper pile by jack
Figure 903728DEST_PATH_IMAGE030
The upper section pile bottom loading force is expressed as
Figure 765374DEST_PATH_IMAGE031
WhereinK 1 For upper pile stiffness, so for a given jack loading valueQNamely K (z = 0) upper-section pile top ultimate displacement
Figure 23180DEST_PATH_IMAGE032
Is shown as
Figure 921866DEST_PATH_IMAGE033
Formula (20)
The ultimate displacement of the pile bottom of the lower section pile is calculated in the same wayS 2 。
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