CN109680730B - Pile top vertical force calculation method considering foundation pile compression and pulling resistance rigidity difference - Google Patents
Pile top vertical force calculation method considering foundation pile compression and pulling resistance rigidity difference Download PDFInfo
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Abstract
The invention discloses a pile top vertical force calculation method considering the difference of compression and pulling rigidity of a foundation pile, aiming at the problem of pile top vertical force calculation when the compression rigidity and the pulling rigidity of the foundation pile are different under a rigid foundation, firstly establishing a deformation coordination equation, a constitutive equation and a balance equation of the foundation pile, and obtaining a general formula for calculating the pile top vertical force of the foundation pile through simultaneous solution; then introducing a proportional coefficient of the pulling-resistant rigidity and the compressive rigidity of the foundation pile, and obtaining a pile top vertical force calculation formula when the compressive rigidity and the pulling-resistant rigidity of the foundation pile are different by using a general formula; finally, according to the rule that a linear relation exists between the pile top vertical force and the coordinate value of the pile center, a pile body numbering rule that the pile body number is sequentially increased along with the increase of the pile top vertical force is given, and a pile top vertical force solving method taking the uplift-resistant pile quantity as a parameter is established on the basis of the numbering rule.
Description
Technical Field
The invention relates to the technical field of civil engineering, in particular to a pile top vertical force calculation method considering the difference of compression and pulling rigidity of foundation piles.
Background art:
the calculation formula of the pile top vertical force of the foundation pile under the rigid foundation is given in code specifications such as building pile foundation technical specification JGJ 94-2008 and design regulations (trial) for foundation of wind turbine generator system FD 003-; these equations are only applicable to all foundation piles with the same constant in compressive stiffness and pullout stiffness. In actual engineering, the pulling rigidity of the same foundation pile is generally lower than the compression rigidity; when the compressive stiffness and the uplift stiffness of the foundation pile are different, how to calculate the vertical force at the top of the foundation pile, what influence can be brought to the vertical force at the top of the pile by the stiffness change, and what influence can be brought to the design scheme of the pile foundation, are problems which need further research.
Disclosure of Invention
The invention aims to provide a pile top vertical force calculation method considering the difference of compression and pulling rigidity of a foundation pile so as to solve the defects caused in the prior art.
A pile top vertical force calculation method considering foundation pile compression and pull-out rigidity difference comprises the following steps:
the method comprises the following steps: aiming at a rigid foundation, connecting n piles below the foundation; establishing a basic plane coordinate system by taking any point o (generally, the geometric centroid of the basic bottom surface) in the basic bottom surface as an origin; equivalently loading each load above the bottom surface of the foundation to a point o, and enabling the equivalent resultant force of the vertical load to be N, the equivalent resultant force of the horizontal load to be H and the equivalent bending moment vector sum in the horizontal plane to be M; the x axis in the horizontal plane is vertical to the vector direction of M, the right direction is a positive direction, and the direction of anticlockwise rotation by 90 degrees is a y axis direction; let the distance from the center of the ith pile to the y-axis be xi(the piles on the right side of the y-axis are positive and the piles on the left side are negative);
step two: for any foundation pile under the rigid foundation, the vertical rigidity of the foundation pile is Ki(ii) a When pile top is pressed Ki＝KNConstant, when pile top is pulled out Ki＝KT(is another constant); to facilitate dimensionless analysis, let KT＝αKNThen α ═ KT/KN；
Step three: under the action of H, N and M, the vertical force of the pile top of the ith pile is Ni(ii) a M of the n piles are uplifted piles numbered 1, 2,…, m; the rest n-m piles are pressed piles which are numbered as m +1, m +2, … and n; the uplift force N of each uplift pile topT,iAnd pile top pressure N of each pressed pileN,iComprises the following steps:
in formula (1): 1, 2, …, m; in formula (2): i ═ m +1, m +2, …, n, in particular when m ═ 0 (both pressed piles) or m ═ n (both uplifted piles), there are:
step four: numbering the piles according to the sequence of the x coordinate values of the centers of the piles from small to large and the sequence of the y coordinate values of the centers of the piles from small to large when x is the same, wherein the pile numbers are sequentially increased from 1 to n; then, N is calculated by the formula (3)i；
Step five: for N obtained in the fourth stepiE.g. N1～NnAre all equal to or greater than 0, or N1～NnAre all less than or equal to 0, then NiThe final result is obtained, and the calculation is terminated;
step six: for N obtained in the fourth stepiE.g. only N1～NmIf less than 0, then calculate N using equation (1)1～NmCalculating N by using the formula (2)m+1～Nn(ii) a If N is present at this time1～NmAre all less than or equal to 0 and Nm+1～NnAre all greater than or equal to 0, then each NiThe final result is obtained, and the calculation is terminated; otherwise, the value of m is continuously changed (e.g. N)mIf the value is more than 0, subtracting 1 from the value of m; such as Nm+1If less than 0, adding 1 to m value), and calculating corresponding N by using formula (1)1～NmCalculating the corresponding N by using the formula (2)m+1～NnUp to N1～NmAre all less than or equal to 0 and Nm+1～NnAll are equal to or greater than 0, at this time, each NiThe final result is obtained, and the calculation is terminated;
step seven: for N obtained in the fourth stepiE.g. only Nn-m+1～NnIf the number is less than 0, the pile body number is adjusted according to the following principle: numbering the piles according to the sequence of the x coordinate values of the centers of the piles from large to small and the sequence of the y coordinate values of the centers of the piles from small to large when x is the same, wherein the pile numbers are sequentially increased from 1 to n; then in the adjusted numbering, only N is present1～NmLess than 0; then, the adjusted serial numbers are used for calculating N by using the formula (1)1～NmCalculating N by using the formula (2)m+1～Nn(ii) a If N is present1～NmAre all less than or equal to 0 and Nm+1～NnAre all greater than or equal to 0, then each NiThe final result is obtained, and the calculation is terminated; otherwise, the value of m is continuously changed (e.g. N)mIf the value is more than 0, subtracting 1 from the value of m; such as Nm+1If less than 0, adding 1 to m value), and calculating corresponding N by using formula (1)1～NmCalculating the corresponding N by using the formula (2)m+1～NnUp to N1～NmAre all less than or equal to 0 and Nm+1～NnAll are equal to or greater than 0, at this time, each NiI.e. the final result, the calculation is terminated.
Preferably, the third step includes the following steps:
step 301: under the action of N (positive when the downward pressure is positive and negative when the upward pull is negative) and M (positive when the vector direction and the y axis are in the same direction and negative when the vector direction is reverse), the vertical displacement of the o point on the bottom surface of the base is set as s (positive when the downward direction is positive and negative when the upward direction is negative), and the rotation angle of the bottom surface is set as theta (positive when the clockwise direction is positive); the distance from the center of the ith pile to the y axis is xi(the pile on the right side of the y axis is positive and the pile on the left side is negative), and the vertical displacement of the pile top is si(positive downward and negative upward), and the vertical deformation rigidity (the comprehensive rigidity of the pile and the foundation) of the foundation pile is Ki(si) The corresponding vertical force of pile top is Ni；
Step 302: the bending rigidity of the horizontal section of the pile body is far smaller than that of the rigid foundation, the connection between the pile top and the foundation is simplified into hinging, and the influence of H on the vertical force of the foundation pile is ignored; the vertical stress distribution on the horizontal section of any pile is approximately uniform;
step 303: according to the coordination principle of vertical deformation (conforming to the assumption of a flat section) of the bottom surface of the rigid foundation, the constitutive relation of the vertical force of the pile top and the static balance principle, the method can be obtained as follows:
si＝s+xi·tgθ，Ni＝Ki(si)·si，
step 304: the transformation coordination equation, the constitutive equation, and the equilibrium equation in the simultaneous solution step 303 can be given by the following formula (j is a summation index, j is 1, 2, …, n):
step 305: when the foundation pile is pressed or pulled up, on the premise that the vertical force does not exceed the bearing capacity characteristic value of the foundation pile, the linear constitutive relation is assumed to be satisfied between the vertical force of the pile top and the vertical displacement of the pile top, and on the premise that the vertical rigidity of any one foundation pile is constant K when the foundation pile is pressedNThe vertical rigidity in the upward pulling process is constant KT(ii) a Let KT＝αKNAccordingly, α ═ KT/KN(ii) a Then, in the formula shown in step 304, K is taken for any foundation pile when it is a pressed pilei(si)＝KNWhen it is an upper pile, take Ki(si)＝KT＝αKN；
Step 306: supposing that M piles in the N piles are uplift piles under the action of N and M, and the numbers of the M piles are 1, 2, … and M; the rest n-m piles are pressed piles numbered m +1, m +2, … and n, and K of the pressed pilesi(si)＝KNAnd K of the upper pulling pilei(si)＝αKNSubstituting into the formula shown in step 304 to obtain formula (1) and formula (2) in step three;
step 307: when m is 0 (i.e. all piles are pressed piles), K of all foundation pilesi(si)＝KN(ii) a Will Ki(si)＝KNSubstituting into the formula shown in step 304 to obtain formula (3) in step three; when m is n (i.e. all piles are uplift piles), K of all foundation pilesi(si)＝αKN(ii) a Will Ki(si)＝αKNSubstituting into the formula shown in step 304, the formula (3) in step three can be obtained as well.
Preferably, the principle of solving the vertical force of each pile top in the fourth step to the seventh step is as follows:
step 401: as can be seen from formulas (1) to (3): the pile top vertical force of the foundation pile and the x coordinate value of the pile center have a linear relation, and the pile top vertical force is increased or decreased monotonously along with the increase of the x value; under special conditions (when M is 0, alpha is 1, and point o is the centroid of the pile group), the vertical force of the pile tops of all the piles is the same;
step 402: when α ≠ 1, in order to find NT,iAnd NN,iIf the pile is pulled up, the coordinate value of x at the center of the pile is increased or increased from the minimum x in all piles according to the change rule of the vertical force of the pile top in step 401, and accordingly, N is increased graduallyT,iGradually increasing from a minimum value (a value of ≦ 0); when N is presentiWhen the pressure is more than or equal to 0, the pressure is transited to a pressed area of the foundation pile, and N is increased along with the increase of xN,iGradually increasing or gradually decreasing the x coordinate value of the center of the upper pile pulling from the maximum x in all the piles, and correspondingly, NT,i(a value of 0 or less) is still gradually increased from the minimum value; when N is presentiWhen the pressure is more than or equal to 0, the pressure is transited to a pressed area of the foundation pile, and N is reduced along with the reduction of xN,iGradually increasing;
step 403: according to the characteristics of the vertical force distribution of the pile top, if the pile at the position of the minimum x is an uplift pile, the pile number of the pile is numbered as No. 1 (if the x of a plurality of piles is the same, the pile with the minimum y is taken as No. 1); then numbering the piles according to the sequence of the x coordinate values of the centers of the piles from small to large, and when x is the same, numbering the piles according to the sequence of the y coordinate values of the centers of the piles from small to large, and sequentially increasing the numbers to n; if the pile at the position of the maximum x is the uplifted pile, the pile number of the pile is numbered as No. 1 (if x of a plurality of piles is the same, the pile with the minimum y is taken as No. 1); numbering the piles according to the sequence of the x coordinate values of the centers of the piles from large to small, and when the x is the same, numbering the piles according to the sequence of the y coordinate values of the centers of the piles from small to large, and sequentially increasing the numbers to n;
step 404: under the pile number compiling rule specified in step 403, if uplift piles exist and the number of the uplift piles is m, the numbers of the uplift piles are determined to be 1, 2, … and m, and the uplift force N on the pile top is obtainedT,iThe result is obtained by formula (1); correspondingly, the pressed piles are numbered m +1, m +2, … and N, and the pile top pressure N isN,iThe result is obtained by the formula (2); and N ism＝NT,m≤0、Nm+1＝NN,m+1≥0；
Step 405: under the pile number compiling rule specified in step 403, if uplift piles exist, when the number m of uplift piles is solved by adopting a trial algorithm, for the assumed m, if N is satisfied at the same timeT,m≤0、NN,m+1If the value is more than or equal to 0, the value m is the evaluated value; correspondingly, the vertical force of each pile top is the actual vertical force of the pile top.
Preferably, the shape of the foundation plane in the step one can be circular, polygonal and any other shape in practical application, and the foundation piles can be randomly arranged below the foundation on the premise that the pile spacing and the pile-to-foundation edge distance meet the construction requirements in the specification.
Preferably, in the step 305, when the actual engineering foundation is designed, the cross section, the pile length, the pile body material, the pile circumference, the pile foundation layer, and the like of each pile under the rigid foundation are all made to be correspondingly the same.
Preferably, a boundary exists between the pile pulling area and the pressed pile area in the step 402, and the pile top vertical force values of the foundation piles close to the boundary must have different signs (or only one value is 0, and the other value is either positive or negative).
The invention has the advantages that: in actual engineering, the pulling rigidity of the same foundation pile under a rigid foundation is generally lower than the compressive rigidity; the calculation method provided by the invention shows through detailed analysis that: when the uplift rigidity of the foundation pile is gradually reduced, the pile top uplift force of the uplift effect control pile is gradually reduced, and the pile top pressure of the compression effect control pile is gradually increased. When the arrangement scheme of the pile foundation under the rigid foundation is controlled by the uplift of the foundation pile, if the uplift rigidity of the foundation pile is lower than the compressive rigidity, the control value of the uplift force can be reduced by utilizing the calculation method provided by the invention; for the circular fan foundation, each pile on the outer ring of the circular fan foundation can be a control pile, so that the pile foundation engineering quantity can be reduced to a certain extent. On the contrary, when the arrangement scheme of the pile foundation under the rigid foundation is controlled by the compression resistance of the foundation pile, if the uplift rigidity of the foundation pile is lower than the compression rigidity, the factor is not considered, the control value of the pile top pressure is smaller, and the design result is probably unsafe; when the calculation method provided by the invention is adopted, the vertical pressure of the pile top can be correctly calculated, and the reliability of a design result is better ensured.
Drawings
FIG. 1 is a schematic view of the calculation of vertical force of a rigid foundation pile according to the present invention;
FIG. 2 is a layout diagram of the pile positions of a foundation of a certain engineering wind turbine in the invention;
FIG. 3 is a graph showing the trend of the vertical force variation of the pile top of the foundation pile of the foundation part of the engineering wind turbine.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
As shown in fig. 1 to 3, a pile top vertical force calculation method considering a difference in compression and pullout stiffness of a foundation pile includes the steps of:
the method comprises the following steps: aiming at a rigid foundation, connecting n piles below the foundation; establishing a basic plane coordinate system by taking any point o (generally, the geometric centroid of the basic bottom surface) in the basic bottom surface as an origin; equivalently loading each load above the bottom surface of the foundation to a point o, and enabling the equivalent resultant force of the vertical load to be N, the equivalent resultant force of the horizontal load to be H and the equivalent bending moment vector sum in the horizontal plane to be M; the x axis in the horizontal plane is vertical to the vector direction of M, the right direction is a positive direction, and the direction of anticlockwise rotation by 90 degrees is a y axis direction; pile of the ithHas a distance x from the center to the y-axisi(the piles on the right side of the y-axis are positive and the piles on the left side are negative);
step two: for any foundation pile under the rigid foundation, the vertical rigidity of the foundation pile is Ki(ii) a When pile top is pressed Ki＝KNConstant, when pile top is pulled out Ki＝KT(is another constant); to facilitate dimensionless analysis, let KT＝αKNThen α ═ KT/KN；
Step three: under the action of H, N and M, the vertical force of the pile top of the ith pile is Ni(ii) a M piles in the n piles are uplift piles, and the numbers of the uplift piles are 1, 2, … and m; the rest n-m piles are pressed piles which are numbered as m +1, m +2, … and n; the uplift force N of each uplift pile topT,iAnd pile top pressure N of each pressed pileN,iComprises the following steps:
in formula (1): 1, 2, …, m; in formula (2): i ═ m +1, m +2, …, n, in particular when m ═ 0 (both pressed piles) or m ═ n (both uplifted piles), there are:
step four: numbering the piles according to the sequence of the x coordinate values of the centers of the piles from small to large and the sequence of the y coordinate values of the centers of the piles from small to large when x is the same, wherein the pile numbers are sequentially increased from 1 to n; then, N is calculated by the formula (3)i；
Step five: for N obtained in the fourth stepiE.g. N1～NnAre all equal to or greater than 0, or N1～NnAre all less than or equal to 0, then NiI.e. the final result, the calculation is terminated；
Step six: for N obtained in the fourth stepiE.g. only N1～NmIf less than 0, then calculate N using equation (1)1～NmCalculating N by using the formula (2)m+1～Nn(ii) a If N is present at this time1～NmAre all less than or equal to 0 and Nm+1～NnAre all greater than or equal to 0, then each NiThe final result is obtained, and the calculation is terminated; otherwise, the value of m is continuously changed (e.g. N)mIf the value is more than 0, subtracting 1 from the value of m; such as Nm+1If less than 0, adding 1 to m value), and calculating corresponding N by using formula (1)1～NmCalculating the corresponding N by using the formula (2)m+1～NnUp to N1～NmAre all less than or equal to 0 and Nm+1～NnAll are equal to or greater than 0, at this time, each NiThe final result is obtained, and the calculation is terminated;
step seven: for N obtained in the fourth stepiE.g. only Nn-m+1～NnIf the number is less than 0, the pile body number is adjusted according to the following principle: numbering the piles according to the sequence of the x coordinate values of the centers of the piles from large to small and the sequence of the y coordinate values of the centers of the piles from small to large when x is the same, wherein the pile numbers are sequentially increased from 1 to n; then in the adjusted numbering, only N is present1～NmLess than 0; then, the adjusted serial numbers are used for calculating N by using the formula (1)1～NmCalculating N by using the formula (2)m+1～Nn(ii) a If N is present1～NmAre all less than or equal to 0 and Nm+1～NnAre all greater than or equal to 0, then each NiThe final result is obtained, and the calculation is terminated; otherwise, the value of m is continuously changed (e.g. N)mIf the value is more than 0, subtracting 1 from the value of m; such as Nm+1If less than 0, adding 1 to m value), and calculating corresponding N by using formula (1)1～NmCalculating the corresponding N by using the formula (2)m+1～NnUp to N1～NmAre all less than or equal to 0 and Nm+1～NnAll are equal to or greater than 0, at this time, each NiI.e. the final result, the calculation is terminated.
Notably, the third step includes the following steps:
step 301: the foundation is N (the lower pressure is positive and the upper drawing is negative)) And M (the vector direction and the y axis are in the same direction and in the reverse direction, the vector direction and the y axis are in the negative direction), the vertical displacement of the o point of the bottom surface is set as s (the downward direction is positive and the upward direction is negative), and the rotation angle of the bottom surface is set as theta (the clockwise direction is positive); the distance from the center of the ith pile to the y axis is xi(the pile on the right side of the y axis is positive and the pile on the left side is negative), and the vertical displacement of the pile top is si(positive downward and negative upward), and the vertical deformation rigidity (the comprehensive rigidity of the pile and the foundation) of the foundation pile is Ki(si) The corresponding vertical force of pile top is Ni；
Step 302: the bending rigidity of the horizontal section of the pile body is far smaller than that of the rigid foundation, the connection between the pile top and the foundation is simplified into hinging, and the influence of H on the vertical force of the foundation pile is ignored; the vertical stress distribution on the horizontal section of any pile is approximately uniform;
step 303: according to the coordination principle of vertical deformation (conforming to the assumption of a flat section) of the bottom surface of the rigid foundation, the constitutive relation of the vertical force of the pile top and the static balance principle, the method can be obtained as follows:
si＝s+xi·tgθ，Ni＝Ki(si)·si，
step 304: the transformation coordination equation, the constitutive equation, and the equilibrium equation in the simultaneous solution step 303 can be given by the following formula (j is a summation index, j is 1, 2, …, n):
step 305: when the foundation pile is pressed or pulled up, on the premise that the vertical force does not exceed the bearing capacity characteristic value of the foundation pile, the linear constitutive relation is assumed to be satisfied between the vertical force of the pile top and the vertical displacement of the pile top, and on the premise that the vertical rigidity of any one foundation pile is constant K when the foundation pile is pressedNThe vertical rigidity in the upward pulling process is constant KT(ii) a Let KT＝αKNAccordingly, α ═ KT/KN(ii) a Then the disclosure shown in step 304In the formula, for any one foundation pile, when it is a pressed pile, K is takeni(si)＝KNWhen it is an upper pile, take Ki(si)＝KT＝αKN；
Step 306: supposing that M piles in the N piles are uplift piles under the action of N and M, and the numbers of the M piles are 1, 2, … and M; the rest n-m piles are pressed piles numbered m +1, m +2, … and n, and K of the pressed pilesi(si)＝KNAnd K of the upper pulling pilei(si)＝αKNSubstituting into the formula shown in step 304 to obtain formula (1) and formula (2) in step three;
step 307: when m is 0 (i.e. all piles are pressed piles), K of all foundation pilesi(si)＝KN(ii) a Will Ki(si)＝KNSubstituting into the formula shown in step 304 to obtain formula (3) in step three; when m is n (i.e. all piles are uplift piles), K of all foundation pilesi(si)＝αKN(ii) a Will Ki(si)＝αKNSubstituting into the formula shown in step 304, the formula (3) in step three can be obtained as well.
In this embodiment, the principle of solving the vertical force of each pile top in the fourth step to the seventh step is as follows:
step 401: as can be seen from formulas (1) to (3): the pile top vertical force of the foundation pile and the x coordinate value of the pile center have a linear relation, and the pile top vertical force is increased or decreased monotonously along with the increase of the x value; under special conditions (when M is 0, alpha is 1, and point o is the centroid of the pile group), the vertical force of the pile tops of all the piles is the same;
step 402: when α ≠ 1, in order to find NT,iAnd NN,iIf the pile is pulled up, the coordinate value of x at the center of the pile is increased or increased from the minimum x in all piles according to the change rule of the vertical force of the pile top in step 401, and accordingly, N is increased graduallyT,iGradually increasing from a minimum value (a value of ≦ 0); when N is presentiWhen the pressure is more than or equal to 0, the pressure is transited to a foundation pile compression area along with xIncrease of NN,iGradually increasing or gradually decreasing the x coordinate value of the center of the upper pile pulling from the maximum x in all the piles, and correspondingly, NT,i(a value of 0 or less) is still gradually increased from the minimum value; when N is presentiWhen the pressure is more than or equal to 0, the pressure is transited to a pressed area of the foundation pile, and N is reduced along with the reduction of xN,iGradually increasing;
step 403: according to the characteristics of the vertical force distribution of the pile top, if the pile at the position of the minimum x is an uplift pile, the pile number of the pile is numbered as No. 1 (if the x of a plurality of piles is the same, the pile with the minimum y is taken as No. 1); then numbering the piles according to the sequence of the x coordinate values of the centers of the piles from small to large, and when x is the same, numbering the piles according to the sequence of the y coordinate values of the centers of the piles from small to large, and sequentially increasing the numbers to n; if the pile at the position of the maximum x is the uplifted pile, the pile number of the pile is numbered as No. 1 (if x of a plurality of piles is the same, the pile with the minimum y is taken as No. 1); numbering the piles according to the sequence of the x coordinate values of the centers of the piles from large to small, and when the x is the same, numbering the piles according to the sequence of the y coordinate values of the centers of the piles from small to large, and sequentially increasing the numbers to n;
step 404: under the pile number compiling rule specified in step 403, if uplift piles exist and the number of the uplift piles is m, the numbers of the uplift piles are determined to be 1, 2, … and m, and the uplift force N on the pile top is obtainedT,iThe result is obtained by formula (1); correspondingly, the pressed piles are numbered m +1, m +2, … and N, and the pile top pressure N isN,iThe result is obtained by the formula (2); and N ism＝NT,m≤0、Nm+1＝NN,m+1≥0；
Step 405: under the pile number compiling rule specified in step 403, if uplift piles exist, when the number m of uplift piles is solved by adopting a trial algorithm, for the assumed m, if N is satisfied at the same timeT,m≤0、NN,m+1If the value is more than or equal to 0, the value m is the evaluated value; correspondingly, the vertical force of each pile top is the actual vertical force of the pile top.
In this embodiment, the shape of the foundation plane in the first step may be circular, polygonal or any other shape in practical application, and the foundation piles may be arbitrarily arranged below the foundation on the premise that the pile spacing and the pile-to-foundation edge distance meet the construction requirements in the specification.
In this embodiment, in the step 305, when the actual engineering foundation is designed, the cross section, the pile length, the pile body material, the pile circumference, the pile bottom soil layer, and the like of each pile under the rigid foundation are all made to be the same.
In this embodiment, there is a boundary between the pile pulling area and the pressed pile area in step 402, and the pile top vertical force values of the foundation piles immediately adjacent to the boundary must have different signs (or only one value is 0, and the other value is either positive or negative).
The following examples illustrate the application of the invention in engineering and its economic benefits:
taking a certain onshore wind power engineering fan foundation as an example, the pile top vertical force of each pile under different alpha values is calculated by using the formulas (1) to (2) and corresponding calculation programs, and the influence of alpha on the pile top vertical force is analyzed. The engineering fan foundation is a rigid foundation, and pile positions below the foundation are arranged as shown in figure 2; adopting a tubular pile, wherein the outer diameter of the section of the pile is 0.6m, the inner diameter of the section of the pile is 0.34m, and the length of the pile is 34 m; 26 outer ring piles are distributed uniformly along the ring direction of 8.8m, and 8 inner ring piles are distributed uniformly along the ring direction of 6.4 m; establishing a coordinate system by taking the annular basic central point o as a coordinate origin; correspondingly, N20800 kN, M130000 kn.m; the pile body is numbered as shown in figure 2. Through calculation, the pile top vertical force of each pile under different alpha values is shown in table 1, and the change condition of the pile top vertical force of a representative pile is shown in fig. 3.
Table 1 summary of vertical forces of pile tops of piles under different alpha values
As can be seen from table 1 and fig. 3: along with the increase of alpha (namely, the increase of the pulling-resistant rigidity), the number of the upper pulling piles is gradually reduced and tends to a certain value, the pile jacking force of the same upper pulling pile in the edge area (the area far away from the y axis and the lower same area) is gradually increased, and the pile jacking force of the same upper pulling pile in the middle area (the area near to the y axis and the lower same area) is slightly fluctuated; the number of the pressed piles is gradually increased and tends to a certain value, the pile top pressure of the same pressed pile in the edge area is gradually reduced, and the pile top pressure of the same pressed pile in the middle area is gradually increased. For the same alpha value, in all the piles, the pile top pulling force of the upper pulling pile (the outermost edge upper pulling pile, namely the pile number 1) farthest from the y axis is always the maximum pulling force, and the pile top pressure of the pressed pile (the outermost edge pressed pile, namely the pile number 34) farthest from the y axis is always the maximum pressure.
And further analyzing the vertical force change conditions of the uplift effect control pile (pile No. 1) and the compression effect control pile (pile No. 34). For the pile control of the uplift effect, the influence of the change of alpha on the uplift force of the pile top is large; when alpha is increased from 0 to 1.0, the pile top uplift force is increased from 0 to 403 kN. For the pile controlled by the compression effect, when the alpha is increased from 0 to 1.0, the pile top pressure is reduced from 2002kN to 1627kN, and is reduced by about 19 percent; when alpha is more than or equal to 0.3, the pressure of the pile top is slowly reduced.
Two groups of values of alpha-0.7 and alpha-1.0 are selected for comparison. When alpha is reduced from 1.0 to 0.7, the uplift effect controls the uplift force of the pile top of the pile to be reduced from 403kN to 333kN, and the uplift force is reduced by about 18%; the pile top pressure of the pile is controlled by the compression effect to be increased from 1627kN to 1651kN, which is about 1 percent. In actual engineering, when a tubular pile scheme is adopted, in order to ensure the uplift safety of a foundation pile, the uplift resistance of the uppermost section of tubular pile is often taken as the uplift bearing capacity, and pile foundation arrangement is possibly controlled by the uplift of the foundation pile; at the moment, if the pulling-resistant rigidity of the foundation pile is lower than the compressive rigidity, the pile foundation engineering quantity can be reduced to a certain extent compared with the conventional design method (the pulling-resistant rigidity and the compressive rigidity of the foundation pile are the same.
Two groups of values of alpha-0.3 and alpha-1.0 are selected for comparison. When alpha is reduced from 1.0 to 0.3, the uplift effect controls the uplift force of the pile top of the pile to be reduced from 403kN to 208kN, and the uplift force is reduced by about 48%; the pile top pressure of the pile is controlled by the compression effect to be increased from 1627kN to 1718kN, which is increased by about 5%. For an end bearing pile (such as a short pile with a pile bottom in a rock stratum) with a shallow buried depth of a pile bottom bearing layer, the uplift rigidity of the foundation pile is generally far lower than the compressive rigidity, and the uplift bearing capacity is generally far lower than the compressive bearing capacity. At this time, if pile foundation arrangement is controlled by pile resistance, the pile foundation engineering amount can be reduced by considering the difference between the two rigidities.
Still taking the project shown in fig. 2 as an example, it is assumed that the project pile foundation arrangement is controlled by pile uplift. In each pile foundation design scheme, foundation piles are uniformly distributed on the inner ring and the outer ring shown in figure 2 along the annular direction, and the N, M value is kept unchanged. Through calculation, the maximum pulling force and the maximum pressure of the pile top of the foundation pile in each scheme are shown in table 2.
TABLE 2 List of maximum uplift force of pile top of foundation pile in each pile foundation design scheme of a certain project
As can be seen from table 2, if α is 0.8, the pile uplift bearing capacity is 360kN, and the pile foundation arrangement scheme is controlled by the uplift of the pile foundation, the number of piles can be reduced from 37 (scheme 4) to 34 and the pile foundation engineering amount can be reduced by 8% when the design is performed by using the method in comparison with the conventional design method (α is 1.0).
From the above, in practical engineering, for the pile foundation under the rigid foundation, the difference between the compressive stiffness and the uplift stiffness of the foundation pile has a great influence on the pile jacking force of the uplift effect control pile and a certain influence on the pile jacking pressure of the stressed effect control pile. When the pile foundation arrangement scheme is controlled by the uplift of the foundation pile, if the uplift rigidity of the foundation pile is lower than the compressive rigidity, the uplift force control value can be reduced compared with the conventional design method, and the uplift rigidity is smaller and the amplitude reduction is more obvious; for the circular fan foundation, each pile on the outer ring of the circular fan foundation can be a control pile, so that the pile foundation engineering quantity can be reduced to a certain extent. On the contrary, when the arrangement scheme of the pile foundation under the rigid foundation is controlled by the compression resistance of the foundation pile, if the uplift rigidity of the foundation pile is lower than the compression rigidity, the factor is not considered, the control value of the pile top pressure is smaller, and the design result is probably unsafe; when the calculation method provided by the invention is adopted, the vertical pressure of the pile top can be correctly calculated, and the reliability of a design result is better ensured.
It will be appreciated by those skilled in the art that the invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The embodiments disclosed above are therefore to be considered in all respects as illustrative and not restrictive. All changes which come within the scope of or equivalence to the invention are intended to be embraced therein.
Claims (6)
1. A pile top vertical force calculation method considering foundation pile compression and pull-out rigidity difference is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: aiming at a rigid foundation, connecting n piles below the foundation; taking any point o in the base bottom surface, and taking the geometric centroid of the base bottom surface as an origin to establish a base plane coordinate system; equivalently loading each load above the bottom surface of the foundation to a point o, and enabling the equivalent resultant force of the vertical load to be N, the equivalent resultant force of the horizontal load to be H and the equivalent bending moment vector sum in the horizontal plane to be M; the x axis in the horizontal plane is vertical to the vector direction of M, the right direction is a positive direction, and the direction of anticlockwise rotation by 90 degrees is a y axis direction; let the distance from the center of the ith pile to the y-axis be xiThe pile on the right side of the y axis is positive, and the pile on the left side is negative;
step two: for any foundation pile under the rigid foundation, the vertical rigidity of the foundation pile is Ki(ii) a When pile top is pressed Ki＝KNIs constant, when the pile top is pulled out, Ki＝KTIs another constant; to facilitate dimensionless analysis, let KT＝αKNThen α ═ KT/KN；
Step three: under the action of H, N and M, the vertical force of the pile top of the ith pile is Ni(ii) a M piles in the n piles are uplift piles, and the numbers of the uplift piles are 1, 2, … and m; the rest n-m piles are pressed piles which are numbered as m +1, m +2, … and n; the uplift force N of each uplift pile topT,iAnd pile top pressure N of each pressed pileN,iComprises the following steps:
in formula (1): 1, 2, …, m; in formula (2): i ═ m +1, m +2, …, n, in particular when m ═ 0, all pressed piles, or m ═ n, all uplifted piles, there are:
step four: numbering the piles according to the sequence of the x coordinate values of the centers of the piles from small to large and the sequence of the y coordinate values of the centers of the piles from small to large when x is the same, wherein the pile numbers are sequentially increased from 1 to n; then, N is calculated by the formula (3)i；
Step five: for N obtained in the fourth stepiE.g. N1～NnAre all equal to or greater than 0, or N1～NnAre all less than or equal to 0, then NiThe final result is obtained, and the calculation is terminated;
step six: for N obtained in the fourth stepiE.g. only N1～NmIf less than 0, then calculate N using equation (1)1～NmCalculating N by using the formula (2)m+1～Nn(ii) a If N is present at this time1～NmAre all less than or equal to 0 and Nm+1～NnAre all greater than or equal to 0, then each NiThe final result is obtained, and the calculation is terminated; otherwise, the value of m is continuously changed, e.g. NmIf the value is more than 0, subtracting 1 from the value of m; such as Nm+1If the value is less than 0, adding 1 to the value m, and calculating the corresponding N by using the formula (1)1～NmCalculating the corresponding N by using the formula (2)m+1～NnUp to N1～NmAre all less than or equal to 0 and Nm+1～NnAll are equal to or greater than 0, at this time, each NiThe final result is obtained, and the calculation is terminated;
step seven: for N obtained in the fourth stepiE.g. only Nn-m+1～NnIf the number is less than 0, the pile body number is adjusted according to the following principle: preferably according to the sequence of x coordinate value of the pile center from large to small, and according to the y coordinate value of the pile center from small when x is the sameNumbering the piles in the sequence from the large number to the n number, wherein the pile number is sequentially increased from the number 1; then in the adjusted numbering, only N is present1～NmLess than 0; then, the adjusted serial numbers are used for calculating N by using the formula (1)1～NmCalculating N by using the formula (2)m+1～Nn(ii) a If N is present1～NmAre all less than or equal to 0 and Nm+1～NnAre all greater than or equal to 0, then each NiThe final result is obtained, and the calculation is terminated; otherwise, the value of m is continuously changed, e.g. NmIf the value is more than 0, subtracting 1 from the value of m; such as Nm+1If the value is less than 0, adding 1 to the value m, and calculating the corresponding N by using the formula (1)1～NmCalculating the corresponding N by using the formula (2)m+1～NnUp to N1～NmAre all less than or equal to 0 and Nm+1～NnAll are equal to or greater than 0, at this time, each NiI.e. the final result, the calculation is terminated.
2. The pile top vertical force calculation method considering the difference in compression and pullout stiffness of a foundation pile according to claim 1, wherein: the third step comprises the following steps:
step 301: the foundation is under the action of N and M, wherein N is positive in downward pressure and negative in upward drawing; the direction of the M vector is positive and negative along the same direction with the y axis, the vertical displacement of the o point of the bottom surface is s, the downward direction is positive and the upward direction is negative, and the corner theta of the bottom surface is positive clockwise; the distance from the center of the ith pile to the y axis is xiThe pile on the right side of the y axis is positive, the pile on the left side is negative, and the vertical displacement of the pile top is siPositive downward and negative upward, and the vertical deformation rigidity of the foundation pile is the comprehensive rigidity of the pile and the foundation, and is Ki(si) The corresponding vertical force of pile top is Ni；
Step 302: the bending rigidity of the horizontal section of the pile body is far smaller than that of the rigid foundation, the connection between the pile top and the foundation is simplified into hinging, and the influence of H on the vertical force of the foundation pile is ignored; the vertical stress distribution on the horizontal section of any pile is approximately uniform;
step 303: according to the coordination principle of vertical deformation of the bottom surface of the rigid foundation, the constitutive relation of vertical force of the pile top and the static balance principle, the method can be obtained as follows:
si＝s+xi·tgθ，Ni＝Ki(si)·si，
step 304: the deformation coordination equation, the constitutive equation, and the balance equation in step 303 are simultaneously solved, so as to obtain the following formula, where j is a summation index, and j is 1, 2, …, n:
step 305: when the foundation pile is pressed or pulled up, on the premise that the vertical force does not exceed the bearing capacity characteristic value of the foundation pile, the linear constitutive relation is assumed to be satisfied between the vertical force of the pile top and the vertical displacement of the pile top, and on the premise that the vertical rigidity of any one foundation pile is constant K when the foundation pile is pressedNThe vertical rigidity in the upward pulling process is constant KT(ii) a Let KT＝αKNAccordingly, α ═ KT/KN(ii) a Then, in the formula shown in step 304, K is taken for any foundation pile when it is a pressed pilei(si)＝KNWhen it is an upper pile, take Ki(si)＝KT＝αKN；
Step 306: supposing that M piles in the N piles are uplift piles under the action of N and M, and the numbers of the M piles are 1, 2, … and M; the rest n-m piles are pressed piles numbered m +1, m +2, … and n, and K of the pressed pilesi(si)＝KNAnd K of the upper pulling pilei(si)＝αKNSubstituting into the formula shown in step 304 to obtain formula (1) and formula (2) in step three;
step 307: when m is 0, namely all the piles are pressed piles, K of all the foundation pilesi(si)＝KN(ii) a Will Ki(si)＝KNSubstituting into the formula shown in step 304 to obtain formula (3) in step three; when m is n, i.e.When all piles are uplifted piles, K of all foundation pilesi(si)＝αKN(ii) a Will Ki(si)＝αKNSubstituting into the formula shown in step 304, the formula (3) in step three can be obtained as well.
3. The pile top vertical force calculation method considering the difference in compression and pullout stiffness of a foundation pile according to claim 1, wherein: the principle of solving the vertical force of the pile top of each pile in the fourth step to the seventh step is as follows:
step 401: as can be seen from formulas (1) to (3): the pile top vertical force of the foundation pile and the x coordinate value of the pile center have a linear relation, and the pile top vertical force is increased or decreased monotonously along with the increase of the x value; under special conditions, namely when M is equal to 0, alpha is equal to 1 and point o is the centroid of the pile group, the vertical force of the pile tops of all the piles is the same;
step 402: when α ≠ 1, in order to find NT,iAnd NN,iIf the pile is pulled up, the coordinate value of x at the center of the pile is increased or increased from the minimum x in all piles according to the change rule of the vertical force of the pile top in step 401, and accordingly, N is increased graduallyT,iGradually increasing from a minimum value less than or equal to 0; when N is presentiWhen the pressure is more than or equal to 0, the pressure is transited to a pressed area of the foundation pile, and N is increased along with the increase of xN,iGradually increasing or gradually decreasing the x coordinate value of the center of the upper pile pulling from the maximum x in all the piles, and correspondingly, NT,iStill increasing stepwise from a minimum value equal to or less than 0; when N is presentiWhen the pressure is more than or equal to 0, the pressure is transited to a pressed area of the foundation pile, and N is reduced along with the reduction of xN,iGradually increasing;
step 403: according to the characteristics of the vertical force distribution of the pile top, if the pile at the position of the minimum x is an uplift pile, the pile number of the pile is numbered as No. 1, and if the x of a plurality of piles is the same, the pile with the minimum y is taken as No. 1; then numbering the piles according to the sequence of the x coordinate values of the centers of the piles from small to large, and when x is the same, numbering the piles according to the sequence of the y coordinate values of the centers of the piles from small to large, and sequentially increasing the numbers to n; if the pile at the position of the maximum x is an uplifted pile, the pile number of the pile is numbered as No. 1, and if the x of a plurality of piles is the same, the pile with the minimum y is taken as No. 1; numbering the piles according to the sequence of the x coordinate values of the centers of the piles from large to small, and when the x is the same, numbering the piles according to the sequence of the y coordinate values of the centers of the piles from small to large, and sequentially increasing the numbers to n;
step 404: under the pile number compiling rule specified in step 403, if uplift piles exist and the number of the uplift piles is m, the numbers of the uplift piles are determined to be 1, 2, … and m, and the uplift force N on the pile top is obtainedT,iThe result is obtained by formula (1); correspondingly, the pressed piles are numbered m +1, m +2, … and N, and the pile top pressure N isN,iThe result is obtained by the formula (2); and N ism＝NT,m≤0、Nm+1＝NN,m+1≥0；
Step 405: under the pile number compiling rule specified in step 403, if uplift piles exist, when the number m of uplift piles is solved by adopting a trial algorithm, for the assumed m, if N is satisfied at the same timeT,m≤0、NN,m+1If the value is more than or equal to 0, the value m is the evaluated value; correspondingly, the vertical force of each pile top is the actual vertical force of the pile top.
4. The pile top vertical force calculation method considering the difference in compression and pullout stiffness of a foundation pile according to claim 1, wherein: the shape of the base plane in the step one can be circular or polygonal in practical application, and the foundation piles can be randomly arranged below the base on the premise that the pile spacing and the distance from the pile to the edge of the base meet the construction requirements in the specification.
5. The pile top vertical force calculation method considering the difference in compression and pullout stiffness of a foundation pile according to claim 2, wherein: in the step 305, when the actual engineering foundation is designed, the cross section, the pile length, the pile body material, the pile circumference and the pile bottom soil layer of each pile under the rigid foundation are all made to be correspondingly the same.
6. The pile top vertical force calculation method considering the difference in compression and pullout stiffness of a foundation pile according to claim 3, wherein: a boundary exists between the area of the uplifted pile and the area of the pressed pile in the step 402, and the pile top vertical force values of the foundation piles close to the two boundaries are different in sign; or only one value is 0 and the other value is either positive or negative.
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