CN116842762A - Method for calculating internal force deformation of pile body of passive pile of layered foundation - Google Patents
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Abstract
The invention discloses a method for calculating internal force deformation of a pile body of a passive pile of a layered foundation, which comprises the following steps: parameters such as foundation soil layer pile side friction resistance, pile end resistance, soil layer horizontal foundation coefficients, total layer number of soil layers, soil body weight, cohesive force, internal friction angle strength indexes and the like in the pile length range of the passive pile are determined; calculating the horizontal additional stress depth direction distribution of the passive pile position caused by roadbed load, and calculating the lateral distribution load of the pile body by using a horizontal soil arch theory; determining the pile body axial force distribution form and fitting the pile body axial force distribution form into a secondary parabolic equation; establishing a lamellar foundation passive pile internal force deformation analysis model considering the influence of pile body axial force, forming a linear equation set based on differential format and related to pile body lateral displacement, and obtaining passive pile body lateral deformation distribution; and calculating the turning angle, bending moment and shearing force of the passive pile, and determining the distribution of the internal force and lateral deformation of the passive pile in the depth direction. The method improves the calculation efficiency and the precision of the whole solving process.
Description
Technical Field
The invention relates to the field of passive pile structure engineering design of roadbed engineering, in particular to a method for calculating internal force deformation of a pile body of a passive pile of a layered foundation.
Background
Engineering piles can be divided into active piles and passive piles according to the interaction between pile bodies and soil around the piles. The pile foundation directly bears external load and actively transmits stress to soil around the pile, and the pile foundation is an active pile; the pile is not loaded, but is influenced by the horizontal movement of soil body around the pile under the action of dead weight and external load. The isolation pile essentially belongs to a passive pile, and the influence range of additional sedimentation and horizontal displacement caused by the load of a newly constructed roadbed is effectively limited through deformation coordination and interaction force transmission of the pile body and soil mass around the pile. The passive isolation pile is widely applied to the existing high-speed railway additional settlement control, and the additional stress in the foundation soil body caused by the newly built roadbed is effectively isolated through the isolation and blocking effect of the passive isolation pile on the horizontal additional stress, so that the existing roadbed is effectively protected, the excessive settlement deformation of the existing roadbed is prevented, and the normal operation of a high-speed railway train is threatened. In addition, the side piles close to the toe area in the pile-supported roadbed bear the pile top load and the horizontal additional stress load caused by embankment filling, and the side piles are characterized by passive pile bearing deformation. Although the passive isolation pile is widely applied to the existing high-speed railway engineering, researches on the action mechanism, the pile soil action mechanism, the load transmission mechanism, key design parameters and the like of the passive isolation pile are not deep, and the influence of the layered distribution of the foundation and the nonlinear distribution of the axial force of the pile body on the bearing of the passive pile cannot be effectively reflected. Therefore, research of a passive pile body internal force analysis and calculation method universally applicable under the condition of the layered foundation is necessary to be carried out, and a foundation is laid for passive pile structure selection, design parameter optimization and the like.
At present, the method for analyzing the internal force deformation of the passive pile is generally divided into two major types, namely a test method and a theoretical method, and the method for carrying out the deformation and the internal force solving of the passive pile by adopting a two-stage method is also a mainstream method at present aiming at the stress deformation characteristics of the passive pile. The passive pile field test results are fewer, the geotechnical centrifugal model test is more effective for the passive pile, the centrifugal model test can intuitively simulate the deformation and stress change process of the prototype geotechnical structure, and the geotechnical pile field test method has the advantage that other test means cannot compare. However, the model test has obvious scale effect and can not truly reflect the stress state of the passive pile. The theoretical research method adopts a two-stage method to be most visual and limited, the horizontal displacement of the soil body caused by foundation pit excavation is a fixed value in the first stage, the displacement is free horizontal displacement of the soil body under the condition of no pile, the free soil body displacement is used as a known condition in the second stage, the free soil body displacement is applied to a passive pile and the reaction of the passive pile is calculated, and the free soil body displacement can be obtained by adopting actual measurement or through finite element calculation. However, the two-stage theoretical analysis method can not effectively reflect pile shaft axial force distribution and lamellar foundation influence, and the design of a passive pile engineering in actual engineering still has great blindness.
Disclosure of Invention
The invention aims to provide a pile body internal force calculation method for a layered foundation passive pile with nonlinear distribution of horizontal load and pile body axial force of the layered foundation.
For this purpose, the invention adopts the following technical scheme:
a method for calculating the internal force deformation of a pile body of a passive pile of a layered foundation comprises the following steps:
s1, determining pile length of passive pileLFormation parameters within the range:
the stratum parameters comprise pile side friction depth direction distribution parametersf s (z) And pile end resistanceq b ，zCalculating a point depth for the additional stress;
s2, determining lateral distribution load of pile body of passive pile caused by roadbed loadq(z)：
Taking the left slope foot of the roadbed filled soil body as a section coordinate zero point to obtain the roadbed load divisionA cloth range; determining the section position coordinates of the passive side pile according to the relative distance between the passive side pile and the left end point of the roadbed; thereby obtaining the horizontal additional stress in the depth direction of the passive pileσ(z) Distribution; determining different levels of additional stressσ(z) The pile body and the soil body between the piles under the action share the load, and then the pile body load in the depth direction of the driven pile body is obtainedq(z) A distribution curve;
s3, calculating a pile shaft axial force fitting equation of the passive pile:
according to the roadbed load distribution range and the relative position of the passive pile, determining pile top load in the equivalent area range of the single pile of the passive pileN 0 The method comprises the steps of carrying out a first treatment on the surface of the Pile side friction obtained according to S1f s (z) And pile end blockq b Calculating the axial force of the pile bodyN(z) Distribution;
，
in the method, in the process of the invention,Dthe pile diameter is the pile diameter of the passive pile;zcalculating the depth of the point for the additional stress, wherein the pile top is taken as a coordinate zero point and is downwards positive;
determining the axial force of the driven pile body at least five positions on the pile body according to the above method, and obtaining a quadratic parabolic fitting equation of the axial force of the driven pile body by applying a multipoint quadratic parabolic fitting method:
，
in the method, in the process of the invention,a 0 、a 1 anda 2 fitting equation coefficients for the pile shaft axial force of the passive pile respectively;
s4, establishing a pile body internal force deformation analysis model of the layered foundation passive pile body considering the influence of the pile body axial force:
adopting elastic foundation beam theory, according to equation obtained in S3 and pile body load obtained in S2q(z) The following formula is established:
，
in the method, in the process of the invention,EIthe section rigidity of the passive pile is;bthe equivalent width of the passive pile is;ylateral displacement of the passive pile;k s is a horizontal foundation coefficient;
s5, constructing a differential solution equation of the internal force deformation of the pile body of the passive pile:
the passive pile is equally spaced and dispersed into pile body micro-segments, the formula in S4 is differentiated and dispersed into a linear equation set, and then the solution is carried out, so that the lateral deformation of the pile body of the passive pile is obtainedy(z) Distribution in the depth direction;
s6, determining the internal force and deformation of the pile body of the passive pile:
the lateral deformation of the pile body obtained according to the step S5y(z) Obtaining the distribution of the internal force and lateral deformation of the passive pile body in the depth direction, wherein the internal force of the passive pile body comprises a bending momentM(z) And shear forceQ(z) The lateral deformation comprises horizontal displacement and rotation angleθ(z)。
In the step S1, the step of determining the formation parameter is as follows:
s11, determining the number I of soil layers in the pile length range of the passive pile, and determining the pile side friction resistance in each soil layer rangef si And pile end resistanceq bi （1≤i≤I）；
S12, obtaining horizontal foundation coefficients of the corresponding soil layers according to the foundation soil layer land survey reportk si Soil body weightγ i Cohesive forcec i And internal friction angleφ i ；
S13, further obtaining pile side friction depth direction distribution parameters according to the foundation soil layer rangef s (z) And pile end resistanceq b 。
In step S2, for the natural foundation or the foundation equivalent to the uniform composite foundation pile group foundation, a Boussinesq theoretical formula under the action of point load is adopted to obtain the horizontal additional stress in the depth direction of the passive pileσ(z) Distribution:
，
in the method, in the process of the invention,P i1 the load is dispersed into a series of loads for equivalent points of the ground surface position by the roadbednContinuously distributing point loads;xcalculating the horizontal distance between the point and the point load acting position for the additional stress;zcalculating a point depth for the additional stress;Rcalculating the distance between the point and the point load acting position for the additional stress;vis the poisson ratio of soil body.
In step S2, when the foundation is a pile foundation, a Mindlin theoretical formula is adopted to obtain horizontal additional stress in the depth direction of the passive pileσ(z) Distribution:
，
in the method, in the process of the invention,R 1 =[r 2 +(z-c) 2 ] 1/2 ，R 2 =[r 2 +(z+c) 2 ] 1/2 ，r 2 =x 2 +y 2 ，vpoisson ratio of soil body;P i2 pile body equivalent point loads of all supporting pile bodies;nthe number of equivalent point loads of the pile body is set;rcalculating the distance between the points for the load action point and the additional stress;cis the depth coordinate of the load acting point.
Preferably, in step S2, the horizontal earth arch theory is adopted, the reasonable arch axis with the earth arch axis in a quadratic parabolic form is considered, and the additional stress of different levels is determined according to the limit stress state at the arch crown and arch foot positionsσ(z) The pile body and the soil body between the piles under the action share the load, and then the pile body load in the depth direction of the driven pile body is obtainedq(z) A distribution curve.
In step S3, the pile side friction is determinedf s (z) By further considering triangular linear distribution or piecewise rectangular distributionf s (z) And (5) carrying out equivalent adjustment on the parameters.
In S3, when a quadratic parabolic fitting method is applied to determine an axial force distribution equation, pile tops and 0.25 are respectively takenL、0.5L、0.75LAnd the axial force of the pile body of the pile end 5 points is driven, and a parabolic fitting coefficient is determined by adopting a least square method.
In step S5, according to the expression of the one-fourth order differential format:
，
and carrying out differential dispersion on the differential control equation of the internal force deformation of the passive pile body to obtain a pile body deformation differential equation in a standard format:
，
according to the passive foundation pile body nodes, bringing the lateral displacement of each node into the pile body deformation differential equation to obtainn+1 linear system of equations.
Preferably, the discrete pile body micro-segment length in S5 is less than or equal to 0.5 and m, the micro-segment number is more than or equal to 20, and after the differential equation corresponding to the boundary constraint conditions of the pile top and the pile end is supplemented to form a complete linear equation set, the passive pile body deformation is directly carried outy(z) And (5) solving.
In S6, the following method is used for lateral deformation through the pile bodyy(z) And obtaining the pile body corner, bending moment and shearing force of the passive pile:
，
in the method, in the process of the invention,θ(z) The corner of the pile body is a passive pile body;M(z) Is the pile body bending moment of the passive pile;Q(z) Is the shearing force of the pile body of the passive pile.
Compared with the prior art, the method has the following beneficial effects:
1. the passive pile body internal force deformation analysis model is solved by adopting a differential method, the differential format engineering applicability of the component is stronger, the common influence of nonlinear distribution of foundation soil layers and nonlinear distribution of pile body axial force can be fully reflected, and the method is suitable for the passive pile body internal force analysis and solving under the horizontal load nonlinear distribution and various boundary conditions.
2. The whole solving process is more scientific, direct, effective and accurate.
3. The method can realize the calculation solution of the whole solving process directly through programming, has higher calculation efficiency and calculation precision, and can be applied to passive pile type selection and pile distribution scheme design in roadbed engineering.
Drawings
FIG. 1 is a flow chart of a method for calculating internal force deformation of a pile body of a passive pile of a layered foundation;
FIG. 2 is a schematic diagram of typical layered foundation distribution for pile-supported foundations and passive pile loading for side piles;
FIG. 3 is a schematic view of a passive pile horizontal soil arch load bearing;
FIG. 4 is a schematic diagram of the stress state of the pile body micro-segment of the passive pile;
FIG. 5 is a schematic diagram of the discrete and finite difference computation of the pile body micro-segment of the passive pile;
FIG. 6a is a passive pile body horizontal load in an example analysisq(z) A distribution curve;
FIG. 6b is a passive pile shaft axial force in an example analysisN(z) A distribution curve;
FIG. 7a is a passive pile body lateral displacement in an example analysisy(z) A distribution curve;
FIG. 7b is a passive pile shaft bending moment in an example analysisM(z) A distribution curve;
FIG. 7c is a passive pile body shear in an example analysisQ(z) A distribution curve.
Wherein:
1. 2 parts of foundation surface, 3 parts of soil layer interface, 4 parts of roadbed filled soil body, 5 parts of side pile passive piles and zero part of section coordinate
6. Section position coordinates 7 pile body distribution load
Detailed Description
The method for calculating the internal force deformation of the pile body of the layered foundation passive pile is described in detail below with reference to the accompanying drawings.
Referring to fig. 1, the method of the present invention comprises the steps of:
s1, determining stratum parameters in a pile length range of a passive pile:
determining the number of soil layers within the length range of the passive pile according to the actual distribution range of the soil layers of each foundation of the road base in FIG. 2I。
1) When pile side friction and pile end friction indexes are obtained through an in-situ test method, starting from the foundation surface 1, taking a soil layer interface 2 as a boundary, and determining pile side friction in each soil layer range by adopting a soil layer thickness weighted average methodf si And pile end resistanceq bi （1≤i≤I). Wherein:
when the double-bridge static cone penetration data is adopted, the side friction resistance of each soil layer pile can be directly carried out by using the side resistance and end resistance indexes of the double-bridge static cone penetration test indexesf si And pile end resistanceq bi （1≤i≤I) Assigning a value;
when single-bridge static cone penetration data are adopted, the ratio penetration ratio obtained by single-bridge static cone penetration is firstly required to be determinedP s The index is weighted and averaged according to the soil layer range, and the penetration ratio is controlled by different soil layer ratiosP s Conversion relation between pile side friction parameters and pile end friction parameters of the same pile is carried out on pile side friction of each soil layerf si And pile end resistanceq bi （1≤i≤I) And (5) assigning values.
2) When pile side friction and pile end friction indexes are obtained through experience or standard table look-up method, according to foundation soil layer type and passive pile type parameters, based on foundation experience or standard table look-up method, directly determining pile side friction of corresponding soil layerf si And pile end resistanceq bi （1≤i≤I）。
3) Further obtaining the horizontal foundation coefficient of the corresponding soil layer according to the foundation soil layer foundation survey reportk si Soil body weightγ i Cohesive forcec i And internal friction angleφ i 。
4) According to foundation soil layer range, further obtaining pile side friction depth direction distributionParameters (parameters)f s (z) Pile tip resistance depth direction distribution parameterq b (z) And foundation coefficient distribution parametersk s (z)。
S2, determining horizontal additional stress of passive pile position caused by roadbed loadq(z)：
According to the shape and the actual size of the roadbed filling soil body 3 in fig. 2, the additional load external load on the surface of the roadbed is further considered, and the left slope foot of the roadbed filling soil body 3 is taken as a section coordinate zero point 5, so that the roadbed load distribution range can be obtained; considering that the side piles of the roadbed are passive piles, and according to the relative distance between the side pile passive piles 4 and the left end point of the roadbedx B Determining the section position coordinates 6 of the side pile passive pile, and obtaining horizontal additional stress in the depth direction of the passive pile by using Boussinesq theoretical formula under the action of point load of formula (1) when the natural foundation or equivalent to the homogeneous composite foundation pile group foundation according to the bearing foundation type of the roadbedσ(z) Distribution:
（1）
in the method, in the process of the invention,P i1 the load is dispersed into a series of loads for equivalent points of the ground surface position by the roadbednContinuously distributing point loads;xcalculating the horizontal distance between the point and the point load acting position for the additional stress;zcalculating a point depth for the additional stress;Rcalculating the distance between the point and the point load acting position for the additional stress;vis the poisson ratio of soil body.
When the foundation is a sparse pile foundation, the horizontal additional stress in the depth direction of the passive pile is obtained by adopting a Mindlin theoretical formulaσ(z) Distribution:
（2）
in the method, in the process of the invention,；/>；/> ；vpoisson ratio of soil body;P i2 pile body equivalent point loads of all supporting pile bodies;nthe number of equivalent point loads of the pile body is set;rcalculating the distance between the points for the load action point and the additional stress;cis the depth coordinate of the load acting point.
Horizontal additional stress at the location of the passive pile 4σ(z) After distribution is determined, according to the effective dead weight stress of the foundation at different depths, the pile diameter, the pile spacing and the foundation soil body strength parameters of the passive piles are further considered, with reference to a horizontal soil arch bearing schematic diagram of fig. 3, the reasonable arch axis with the soil arch axis in a quadratic parabolic form is considered, and according to the limit stress states at the arch crown and arch foot positions, different levels of additional stress can be determinedσ(z) The pile body and the soil body between the piles under the action share the load, and then the pile body load in the depth direction of the driven pile body is obtainedq(z) Distribution curve 7.
S3, calculating a pile shaft axial force fitting equation of the passive pile:
determining pile top load in equivalent area range of single pile of passive pile according to relative position of road foundation load distribution range and passive pile in figure 2N 0 Wherein, pile top loadN 0 In the determining process, the effect of the raft and the reinforcement cushion layer on the pile top sharing load improvement can be further considered. After pile top load calculation is completed, pile side friction resistance within the range of the pile body of the passive pile obtained in step 1 is obtainedf s (z) And pile end blockq b Calculating the axial force of the pile body by using the method (3)N(z) Distribution:
（3）
in the method, in the process of the invention,Dthe pile diameter is the pile diameter of the passive pile;zthe depth coordinate is that the pile top is the coordinate zero point and the downward direction is positive.
In addition, pile side frictionf s (z) The distribution form of the friction resistance is directly determined according to stratum parameters, and can be further considered as triangular linear distribution or segmented rectangular distribution, and friction resistance is applied to the pile sidef s (z) And carrying out equivalent adjustment on the distribution parameters.
The axial force distribution of the driven pile body is generally nonlinear distribution, and in order to facilitate the establishment and the solution of a driven pile body internal force deformation analysis model considering the influence of the axial force of the pile body, the driven pile body internal force deformation analysis model is considered to be fitted into a quadratic parabolic equation. In the conventional treatment, pile tops and 0.25 percent of pile weight are respectively takenL、0.5L、0.75LAnd the passive pile body axial force at 5 points or more of the pile end is obtained by applying a multipoint quadratic parabolic fitting method and calculating through least square fitting, so as to obtain a passive pile body axial force quadratic parabolic fitting equation:
（4）
in the method, in the process of the invention,a 0 、a 1 anda 2 and fitting equation coefficients for the pile shaft axial force of the passive pile respectively. S4, establishing a pile body internal force analysis model of the layered foundation passive pile body considering the influence of the pile body axial force:
s4, establishing a pile body internal force analysis model of the layered foundation passive pile body considering the influence of the pile body axial force:
according to pile body distribution load 7 of a pile bearing roadbed side pile passive pile 4 in fig. 2, considering a pile body lateral deformation second order effect caused by non-linear distribution of pile body axial force, according to a pile body micro-segment stress state of the passive pile in fig. 4, considering that a post-pile soil body generates elastic support counter force linearly related to lateral displacement, applying an elastic foundation beam theory, and according to a load-bearing balance state of the passive pile micro-segment, establishing a pile body stress strain differential equation of the passive pile:
（5）
in the method, in the process of the invention,EIthe section rigidity of the passive pile is;bthe equivalent width of the passive pile is;yis the lateral displacement of the passive pile.
The (5) is a fourth-order partial derivativeEquation, second order term, first order term and constant term are foundation depth coordinateszHorizontal foundation coefficient when considering the effect of layered foundationk s And the method is also continuously changed along with stratum, so that the analysis and solution of the stress-strain differential equation of the pile body of the passive pile are difficult to directly obtain. In practical application, the solution of the partial differential equation of the stress strain in the formula (5) is generally solved by adopting a differential method.
S5, constructing a differential solution equation of internal force deformation of the pile body of the passive pile, and establishing a relation of lateral deformationy(z) Is a linear system of equations:
fig. 5 is a diagram of pile body micro-segment discrete and finite difference calculation of a passive pile, wherein the passive pile 6 is uniformly spaced and discrete into pile body micro-segments, and in order to ensure the accuracy of the calculation of the internal force and deformation of the passive pile after the discrete, the length of the pile body micro-segments after the discrete is generally not more than 0.5 m and the number of the micro-segments is not less than 20. According to the expression form of one-fourth order difference format in the formula (6): :
（6）
differential discrete is carried out on the differential control equation (5) of the internal force deformation of the passive pile body, and a pile body deformation differential equation expression (7) in a standard format is obtained:
（7）
from the passive foundation pile shaft node in fig. 5, the lateral displacement of each boundary point is carried into (7), and the total determination can be determinedn+1 linear system of equations;
but co-include in the equation setn+5 passive pile body lateral displacement position variables need to be respectively supplemented with four linear equation sets according to boundary conditions. According to the boundary constraint conditions of the pile top, the pile end free, the hinging, the fixing and the sliding of the passive foundation pile, four boundary constraint equation sets can be supplemented, so that the number of the linear equation sets is equal to the number of the unknown quantity, and the whole equation can be solved. Obtain the lateral deformation of the pile body of the passive piley(z) Distribution in the depth direction.
S6, determining the internal force and deformation of the pile body of the passive pile:
after the side displacement of the pile body of the passive pile is obtained according to the steps, according to the first-order, second-order and third-order partial differential formats of the side deformation of the pile body with respect to the depth, the turning angle, bending moment and shearing force of the passive pile in the deep direction are calculated according to the formula (8), and the distribution of the internal force (bending moment and shearing force) and the side deformation (horizontal displacement and turning angle) of the pile body of the passive pile in the depth direction is obtained:
（8）
in the method, in the process of the invention,θ(z) The corner of the pile body is a passive pile body;M(z) Is the pile body bending moment of the passive pile;Q(z) Is the shearing force of the pile body of the passive pile.
Example 1
In order to facilitate understanding and application of technical staff in the industry, the following example calculation is carried out by combining stratum parameter determination within the pile length range of the passive pile, passive pile position horizontal additional stress calculation caused by roadbed load, pile body lateral distribution load analysis, pile body axial force secondary parabolic fit equation solving, passive pile body internal force deformation analysis model building and differential solving process of pile body internal force deformation, and finally, pile body internal force and lateral deformation distribution of the layered foundation is obtained.
The method is characterized in that the determination of the stratum parameters of the layered foundation mainly depends on the land survey report of the target site, the pile side friction and pile end resistance of the foundation layer can be based on double-bridge static initial detection and single-bridge static initial detection data in-situ test, so that the operation process flow is simplified, and the parameters can also be directly determined according to a standard table lookup method.
The following calculation methods refer to each process parameter or measurement unit of the calculation parameter, and standard unit systems are adopted unless otherwise specified.
1. Formation parameters:
the total number of foundation strata in the long range of the roadbed piles is 3, the foundation strata is a typical layered foundation with a weak interlayer, and basic parameters of the foundation strata are as follows:
number of soil layersI：ILayer 3;
layer thickness of soil layer: 10 m,10 m;
soil layer friction resistancef si Parameters: 30 kPa,15 kPa,30 kPa;
soil layer end resistanceq bi Parameters: 1500 kPa,750 kPa,1500 kPa;
soil layer horizontal foundation coefficientk si Parameters: 8000 kN/m 3 ，4000 kN/m 3 ，8000 kN/m 3 ；
Soil layer weightγ i Parameters: 20 kN/m 3 ，20 kN/m 3 ，20 kN/m 3 ；
Soil layer cohesive forcec i Parameters: 20 kPa,10 kPa,20 kPa;
inner friction angle of soil layerφ i Parameters: 30 °,15 °,30 °;
2. roadbed parameters:
the roadbed is a standard double-line roadbed with the height of 4.5 and m, the slope gradient of a side slope is 1:1.5, the top width of the roadbed is 13.6 m, the reinforced foundation is a precast pile composite foundation, and the pile top and the pile end are free boundaries; the side piles are positioned at the right slope toe position and are spaced from the left slope toex B =25.55 m. Pile distribution parameters of the reinforced foundation are as follows:
prefabricating pile length:L=30 m；
pile diameter D of precast pile: 0.5 m;
perimeter of precast pile:U=1.57 m；
cross section of precast pile:A p =0.1963 m 2 ；
precast pile spacing: 3.0 m×3.0 m.
And calculating the horizontal additional stress distribution of the passive pile position by using a Busssinesq method, and calculating the pile body load of the side pile passive pile by using a horizontal soil arch theory, so as to obtain a distribution curve in the depth direction of the pile body load as shown in figure 6 a.
3. Pile shaft axial force parameter:
the vertical load of the pile top sharing roadbed filling body is 140 kN, and the pile side friction is considered to be deep in the passive pile body according to the pile side frictionThe approximate linear distribution in the degree direction obtains the passive pile turning shaft force distribution, and the passive pile turning shaft force distribution is fitted into a quadratic parabolic distribution equation by a least square method, and the corresponding parabolic distribution coefficients are respectivelya 0 =139.31，a 1 =4.9044，a 2 = -0.2410, the corresponding axial force profile is fig. 6b.
Pile body micro-segment length in solving process of passive pile body internal force deformation modelh=0.5 m, the pile body is discretized into 60 micro-segments, and the complete lateral displacement of the micro-segment node position is constructed by supplementing four boundary condition linear equation setsyAnd (3) directly obtaining the lateral displacement of the pile body micro-segment node position through a linear equation set unknown quantity iteration solving method. Further obtaining the distribution of pile body bending moment, shearing force and rotation angle in the depth direction on the basis, and finally obtaining the lateral displacement of the pile body of the passive pile taking the situation of foundation layered distribution and nonlinear pile body axial force distribution into consideration, as shown in fig. 7 a; pile body bending moment, as shown in fig. 7 b; pile body shear force as shown in fig. 7 c.
Claims (10)
1. The method for calculating the internal force deformation of the pile body of the passive pile of the layered foundation is characterized by comprising the following steps of:
s1, determining pile length of passive pileLFormation parameters within the range:
the stratum parameters comprise pile side friction depth direction distribution parametersf s (z) And pile end resistanceq b ，zCalculating a point depth for the additional stress;
s2, determining lateral distribution load of pile body of passive pile caused by roadbed loadq(z)：
Taking the left slope foot of the roadbed filled soil body as a section coordinate zero point to obtain a roadbed load distribution range; determining the section position coordinates of the passive side pile according to the relative distance between the passive side pile and the left end point of the roadbed; thereby obtaining the horizontal additional stress in the depth direction of the passive pileσ(z) Distribution; determining different levels of additional stressσ(z) The pile body and the soil body between the piles share the load under the action, and the depth of the pile body of the passive pile is obtainedUpward pile body loadq(z) A distribution curve;
s3, calculating a pile shaft axial force fitting equation of the passive pile:
according to the roadbed load distribution range and the relative position of the passive pile, determining pile top load in the equivalent area range of the single pile of the passive pileN 0 The method comprises the steps of carrying out a first treatment on the surface of the Pile side friction obtained according to S1f s (z) And pile end blockq b Calculating the axial force of the pile bodyN(z) Distribution;
，
in the method, in the process of the invention,Dthe pile diameter is the pile diameter of the passive pile;zcalculating the depth of the point for the additional stress, wherein the pile top is taken as a coordinate zero point and is downwards positive;
determining the axial force of the driven pile body at least five positions on the pile body according to the above method, and obtaining a quadratic parabolic fitting equation of the axial force of the driven pile body by applying a multipoint quadratic parabolic fitting method:
，
in the method, in the process of the invention,a 0 、a 1 anda 2 fitting equation coefficients for the pile shaft axial force of the passive pile respectively;
s4, establishing a pile body internal force deformation analysis model of the layered foundation passive pile body considering the influence of the pile body axial force:
adopting elastic foundation beam theory, according to equation obtained in S3 and pile body load obtained in S2q(z) The following formula is established:
，
in the method, in the process of the invention,EIthe section rigidity of the passive pile is;bthe equivalent width of the passive pile is;ylateral displacement of the passive pile;k s is a horizontal foundation coefficient;
s5, constructing a differential solution equation of the internal force deformation of the pile body of the passive pile:
the passive pile is equally spaced and dispersed into pile body micro-segments, the formula in S4 is differentiated and dispersed into a linear equation set, and then the solution is carried out, so that the lateral deformation of the pile body of the passive pile is obtainedy(z) Distribution in the depth direction;
s6, determining the internal force and deformation of the pile body of the passive pile:
the lateral deformation of the pile body obtained according to the step S5y(z) Obtaining the distribution of the internal force and lateral deformation of the passive pile body in the depth direction, wherein the internal force of the passive pile body comprises a bending momentM(z) And shear forceQ(z) The lateral deformation comprises horizontal displacement and rotation angleθ(z)。
2. The method for calculating the internal force deformation of the pile body of the layered foundation passive pile according to claim 1, which is characterized in that: the step of determining the formation parameters in S1 is as follows:
s11, determining the number I of soil layers in the pile length range of the passive pile, and determining the pile side friction resistance in each soil layer rangef si And pile end resistanceq bi （1≤i≤I）；
S12, obtaining horizontal foundation coefficients of the corresponding soil layers according to the foundation soil layer land survey reportk si Soil body weightγ i Cohesive forcec i And internal friction angleφ i ；
S13, further obtaining pile side friction depth direction distribution parameters according to the foundation soil layer rangef s (z) And pile end resistanceq b 。
3. The method for calculating the internal force deformation of the pile body of the layered foundation passive pile according to claim 1, which is characterized in that: s2, for a natural foundation or an equivalent homogeneous composite foundation pile group foundation, a Boussinesq theoretical formula under the action of point load is adopted to obtain horizontal additional stress in the depth direction of the passive pileσ(z) Distribution:
，
in the method, in the process of the invention,P i1 the load is dispersed into a series of loads for equivalent points of the ground surface position by the roadbednContinuously distributing point loads;xcalculating the horizontal distance between the point and the point load acting position for the additional stress;zcalculating a point depth for the additional stress;Rcalculating the distance between the point and the point load acting position for the additional stress;vis the poisson ratio of soil body.
4. The method for calculating the internal force deformation of the pile body of the layered foundation passive pile according to claim 1, which is characterized in that: s2, when the foundation is a pile foundation, obtaining horizontal additional stress in the depth direction of the passive pile by adopting a Mindlin theoretical formulaσ(z) Distribution:
，
in the method, in the process of the invention,R 1 =[r 2 +(z-c) 2 ] 1/2 ，R 2 =[r 2 +(z+c) 2 ] 1/2 ，r 2 =x 2 +y 2 ，vpoisson ratio of soil body;P i2 pile body equivalent point loads of all supporting pile bodies;nthe number of equivalent point loads of the pile body is set;rcalculating the distance between the points for the load action point and the additional stress;cis the depth coordinate of the load acting point.
5. The computing method according to claim 1, wherein: in S2, adopting a horizontal soil arch theory, considering a reasonable arch axis with a soil arch axis in a quadratic parabola form, and determining different levels of additional stress according to the limit stress states of the arch crown and arch foot positionsσ(z) The pile body and the soil body between the piles under the action share the load, and then the pile body load in the depth direction of the driven pile body is obtainedq(z) A distribution curve.
6. The computing method according to claim 1, wherein: in step S3, the pile side friction is determinedf s (z) By further considering triangular linear distribution or piecewise rectangular distributionf s (z) And (5) carrying out equivalent adjustment on the parameters.
7. The computing method according to claim 1, wherein: in S3, when a quadratic parabolic fitting method is applied to determine an axial force distribution equation, pile tops and 0.25 are respectively takenL、0.5L、0.75LAnd the axial force of the pile body of the pile end 5 points is driven, and a parabolic fitting coefficient is determined by adopting a least square method.
8. The method for calculating the internal force deformation of the pile body of the layered foundation passive pile according to claim 1, which is characterized in that: s5, according to the expression of the one-fourth order differential format:
，
and carrying out differential dispersion on the differential control equation of the internal force deformation of the passive pile body to obtain a pile body deformation differential equation in a standard format:
，
according to the passive foundation pile body nodes, bringing the lateral displacement of each node into the pile body deformation differential equation to obtainn+1 linear system of equations.
9. The method for calculating the internal force deformation of the pile body of the layered foundation passive pile according to claim 8, which is characterized in that: s5, after the discrete pile body micro-segment length is less than or equal to 0.5 and m and the micro-segment number is more than or equal to 20, supplementing a differential equation corresponding to pile top and pile end boundary constraint conditions to form a complete linear equation set, and directly performing quiltDeformation of movable pile bodyy(z) And (5) solving.
10. The method for calculating the internal force deformation of the pile body of the layered foundation passive pile according to claim 1, which is characterized in that: in S6, the following method is used for lateral deformation through the pile bodyy(z) And obtaining the pile body corner, bending moment and shearing force of the passive pile:
，
in the method, in the process of the invention,θ(z) The corner of the pile body is a passive pile body;M(z) Is the pile body bending moment of the passive pile;Q(z) Is the shearing force of the pile body of the passive pile.
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