CN112883605B - Method for determining initial yield bending moment of bridge pile foundation section - Google Patents
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Abstract
The invention relates to the technical field of bridge construction engineering, in particular to a method for determining an initial yield bending moment of a bridge pile foundation section. The method comprises the following steps: selecting a plurality of pile foundations with different pile diameters and different section reinforcement rates, calculating section initial yield bending moment of each pile foundation under the action of different axial forces, and taking the pile diameter, the section reinforcement rates, all axial forces and the section initial yield bending moment corresponding to the pile diameter, the section reinforcement rates and all axial forces of one pile foundation as a set of sampling data to obtain a plurality of sets of sampling data; dividing each group of sampling data into a small eccentric section and a large eccentric section; and fitting the calculated data of all the small eccentric sections and the large eccentric sections respectively to determine a small eccentric section fitting equation and a large eccentric section fitting equation. The method can solve the problems that in the prior art, the calculation workload of an analysis method adopting bending moment-curvature is large, the analysis is long in time consumption, and the method is not suitable for the bridge engineering feasibility research stage.
Description
Technical Field
The invention relates to the technical field of bridge construction engineering, in particular to a method for determining an initial yield bending moment of a bridge pile foundation section.
Background
The bridge substructure pile foundation is a deep foundation type with long history and wide application, can better adapt to complex geological conditions and has the advantages of large bearing capacity, good stability, small differential settlement and the like compared with other types of foundations. However, since the pile foundation is buried underground, earthquake damage is not easy to find, and the post-earthquake excavation inspection data is less disclosed, the knowledge of the earthquake damage of the pile foundation is not enough, so the pile foundation is always a difficult point of bridge earthquake-resistant design. The design theory of capacity protection is introduced for the first time in the rule of highway bridge anti-seismic design, the pile foundation is definitely regulated for the first time that the pile foundation cannot be designed according to ductile members under the action of E2 earthquake, and the pile foundation is generally difficult to design into a inclined pile form due to construction reasons, so that the earthquake action often controls structural design, and the problem of pile foundation anti-seismic safety is always concerned by engineering industry.
At present, the checking standard of bridge anti-seismic design standard on pile foundations under two-stage leveling action (E1 earthquake action and E2 earthquake action) is as follows: (1) when E1 earthquake acts, the response bending moment of the section earthquake is less than or equal to the initial yield bending moment of the section; (2) when E2 earthquake acts, the section earthquake response bending moment is less than or equal to the section equivalent yield bending moment. It can be seen that the checking calculation of the earthquake-proof design involves the value of 2 yield bending moments, namely the initial yield bending moment of the section and the equivalent yield bending moment of the section. The initial yield bending moment of the cross section is defined as the bending moment corresponding to the first yield (considering the corresponding axial force) of the steel bars at the outermost layer of the cross section, and when the earthquake response is smaller than the initial yield bending moment, the whole cross section is kept in an elastic working range.
The equivalent yield bending moment of the section is the bending moment obtained by adopting a bilinear broken line principle according to the curve of the relation between the bending moment and the curvature of the section, at the moment, the section is damaged in repairability, part of the steel bars enter yield, the width of cracks can exceed the allowable value, but the concrete protection layer is intact, and the whole structure is kept in the elastic range. The section equivalent yield bending moment can be obtained according to the relevant calculation formula of the section ultimate bearing capacity by adopting the principle of a section equivalent rectangular method according to the relevant regulations of bridge static force design specifications (highway reinforced concrete and prestressed concrete bridge and culvert design specifications). However, the static design specification does not give a related calculation formula for the initial yield bending moment of the section, because the initial yield bending moment of the section is mainly obtained by introducing a nonlinear constitutive relation of the material, and the value must be calculated by adopting a bending moment-curvature analysis method. The bending moment-curvature analysis method has large calculation workload and long analysis time consumption, is mainly suitable for the preliminary design and construction diagram design stage of the bridge needing to be subjected to detailed anti-seismic analysis, and is not suitable for the feasibility research stage of bridge engineering.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method for determining the initial yield bending moment of the section of the bridge pile foundation, which can solve the problems that the calculation workload is large and the analysis is long in time consumption due to the adoption of a bending moment-curvature analysis method in the prior art, and is not suitable for the feasibility research stage of bridge engineering.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention provides a method for determining an initial yield bending moment of a bridge pile foundation section, which comprises the following steps:
selecting a plurality of pile foundations with different pile diameters and different section reinforcement rates, calculating section initial yield bending moment of each pile foundation under the action of different axial forces, and taking the pile diameter, the section reinforcement rates, all axial forces and the section initial yield bending moment corresponding to the pile diameter, the section reinforcement rates and all axial forces of one pile foundation as a set of sampling data to obtain a plurality of sets of sampling data;
dividing each group of sampling data into a small eccentric section and a large eccentric section;
and fitting the calculated data of all the small eccentric sections and the large eccentric sections respectively to determine a small eccentric section fitting equation and a large eccentric section fitting equation.
Based on the technical scheme, the finite element analysis calculation data of each group are divided into a small eccentric section and a large eccentric section according to the maximum section initial yield bending moment value and the corresponding axial force in each group of calculation data.
On the basis of the technical scheme, the finite element analysis and calculation data of all the small eccentric sections and the large eccentric sections are respectively fitted, and a first polynomial fitting or a second polynomial fitting is adopted.
Based on the technical proposal, when adopting the one-time polynomial fitting,
the small eccentric section fitting equation is: m is M 1 ＝w 1 D+x 1 ρ-y 1 N-z 1 ；
The large eccentric section fitting equation is: m is M 2 ＝w 2 D+x 2 ρ+y 2 N-z 2 ；
Wherein: w (w) 1 、x 1 、y 1 、z 1 、w 2 、x 2 、y 2 And z 2 The coefficient is D, the diameter of pile foundation, ρ, the section reinforcement ratio and N, the axial force.
On the basis of the technical proposal, w 1 The value is 88026.14 and x 1 The value is 1485610, y 1 Take on a value of 0.72 and z 1 The curved value is 132741.
On the basis of the technical proposal, w 2 The value is 19565.73 and x 2 The value is 1112850, y 2 Take a value of 0.55 and z 2 The value is 46909.2.
Based on the technical proposal, when adopting the quadratic polynomial fitting,
the small eccentric section fitting equation is:
M 1 ＝a 1 D 2 -b 1 N 2 -c 1 D-d 1 N+e 1 ρ+f 1 D×ρ+g 1 D×N-h 1 ρ×N+i 1 D×ρ×N+j 1
the large eccentric section fitting equation is:
M 2 ＝a 2 D 2 -b 2 N 2 -c 2 D-d 2 N+e 2 ρ+f 2 D×ρ+g 2 D×N+h 2 ρ×N-i 2 D×ρ×N+j 2
wherein: a, a 1 、b 1 、c 1 、d 1 、e 1 、f 1 、g 1 、h 1 、i 1 、j 1 、a 2 、b 2 、c 2 、d 2 、e 2 、f 2 、g 2 、h 2 、i 2 And j 2 The coefficient is D, the diameter of pile foundation, ρ, the section reinforcement ratio and N, the axial force.
Based on the technical proposal, a 1 The value is 14549.23, b 1 The value is 3.72 multiplied by 10 -6 、c 1 The value is 37691.9, d 1 The value is 0.67244, e 1 Take the value of 0, f 1 The value is 4223097 g 1 The value is 0.325113, h 1 The value is 19.2113, i 1 Take on a value of 8.578193 and j 1 Is 38330.85.
Based on the technical proposal, a 2 The value is 6516.15, b 2 The value is 2.08X10 -6 、c 2 The value is 30095.4, d 2 The value is 2002551, e 2 The value is 0.21, f 2 The value is 1293179 g 2 The value is 0.33, h 2 The value is 2.25, i 2 Take on a value of 2.53303 and j 2 The value is 34340.26.
Based on the technical scheme, the value range of the diameter D of the pile foundation is 1.5-3.2m, and the value range of the section reinforcement ratio is 0.5-2%.
Compared with the prior art, the invention has the advantages that: the method comprises the steps of calculating the section initial yield bending moment of each pile foundation under the action of different axial forces through pile foundations with different pile diameters and different section reinforcement rates, dividing each group of sampling data into a small eccentric section and a large eccentric section, fitting the calculated data of all the small eccentric section and the large eccentric section respectively, and determining a small eccentric section fitting equation and a large eccentric section fitting equation. A more accurate set of fitting equations can be obtained. The set of equations can quantitatively determine the initial yield bending moment of pile foundations with different pile diameters and different section reinforcement rates under the action of different axial forces, and has the advantages of simple calculation, less time consumption and high efficiency. The practical application of a plurality of large-span bridges shows that the method has strong practicability and effectiveness. Meanwhile, the problems that the calculation workload of an analysis method adopting bending moment-curvature is large, the analysis is long in time consumption and is not suitable for the bridge engineering feasibility research stage are avoided.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method of determining an initial yield bending moment of a section of a bridge pile foundation in an embodiment of the invention;
FIG. 2 is a graph showing three curves with a cross-sectional reinforcement ratio of 0.5% in the embodiment of the present invention;
FIG. 3 is a graph showing three curves with a cross-sectional reinforcement ratio of 0.75% in the embodiment of the present invention;
FIG. 4 is a graph showing the comparison of three curves with a section reinforcement ratio of 1% in the embodiment of the present invention;
FIG. 5 is a graph showing the comparison of three curves with a cross-sectional reinforcement ratio of 1.25% in the embodiment of the present invention;
FIG. 6 is a graph showing three curves with a cross-sectional reinforcement ratio of 1.5% in the embodiment of the present invention;
fig. 7 is a graph showing the comparison of three curves with a cross-sectional reinforcement ratio of 1.75% in the embodiment of the present invention.
Fig. 8 is a graph showing the comparison of three curves with a cross-sectional reinforcement ratio of 1.75% in the embodiment of the present invention.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present application based on the embodiments herein.
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the invention provides a method for determining an initial yield bending moment of a bridge pile foundation section, which comprises the following steps:
s1: and selecting a plurality of pile foundations with different pile diameters and different section reinforcement rates, calculating section initial yield bending moment of each pile foundation under the action of different axial forces, and taking the pile diameter, the section reinforcement rates, all axial forces and the section initial yield bending moment corresponding to the pile diameter, the section reinforcement rates and all axial forces of one pile foundation as one set of sampling data to obtain a plurality of sets of sampling data.
In this embodiment, the different pile diameters D include: 1.5m, 1.8m, 2.0m, 2.2m, 2.5m, 2.8m, 3.0m and 3.2m, different section bar arrangement rate ρ includes: 0.50%, 0.75%, 1.00%, 1.25%, 1.50%, 1.75% and 2.00%.
S2: each set of sampled data is divided into a small eccentric section and a large eccentric section.
Preferably, the finite element analysis calculation data of each group are divided into a small eccentric section and a large eccentric section according to the maximum section initial yield bending moment value and the corresponding axial force in the calculation data of each group.
The axial force corresponding to the maximum section initial yield moment value, namely the limit breaking axial force value of the pile foundation, is shown in table 1.
TABLE 1 boundary failure axis force values of pile foundations at different pile diameters and section reinforcement rates
S3: and fitting the calculated data of all the small eccentric sections and the large eccentric sections respectively to determine a small eccentric section fitting equation and a large eccentric section fitting equation.
Preferably, the finite element analysis calculation data of all the small eccentric segments and the large eccentric segments are respectively fitted, and a first-order polynomial fitting or a second-order polynomial fitting is adopted.
Preferably, when fitting with a one-time polynomial,
the small eccentric section fitting equation is: m is M 1 ＝w 1 D+x 1 ρ-y 1 N-z 1 ；
The large eccentric section fitting equation is: m is M 2 ＝w 2 D+x 2 ρ+y 2 N-z 2 ；
Wherein: w (w) 1 、x 1 、y 1 、z 1 、w 2 、x 2 、y 2 And z 2 The coefficient is D, the diameter of pile foundation, ρ, the section reinforcement ratio and N, the axial force.
Preferably, w 1 The value is 88026.14 and x 1 The value is 1485610, y 1 Take on a value of 0.72 and z 1 The curved value is 132741.
Preferably, w 2 The value is 19565.73 and x 2 The value is 1112850, y 2 Take a value of 0.55 and z 2 The value is 46909.2.
Preferably, when fitting with a quadratic polynomial,
the small eccentric section fitting equation is:
M 1 ＝a 1 D 2 -b 1 N 2 -c 1 D-d 1 N+e 1 ρ+f 1 D×ρ+g 1 D×N-h 1 ρ×N+i 1 D×ρ×N+j 1
the large eccentric section fitting equation is:
M 2 ＝a 2 D 2 -b 2 N 2 -c 2 D-d 2 N+e 2 ρ+f 2 D×ρ+g 2 D×N+h 2 ρ×N-i 2 D×ρ×N+j 2
wherein: a, a 1 、b 1 、c 1 、d 1 、e 1 、f 1 、g 1 、h 1 、i 1 、j 1 、a 2 、b 2 、c 2 、d 2 、e 2 、f 2 、g 2 、h 2 、i 2 And j 2 The coefficient is D, the diameter of pile foundation, ρ, the section reinforcement ratio and N, the axial force.
Preferably, a 1 The value is 14549.23, b 1 The value is 3.72 multiplied by 10 -6 、c 1 The value is 37691.9, d 1 The value is 0.67244, e 1 Take the value of 0, f 1 The value is 4223097 g 1 The value is 0.325113, h 1 The value is 19.2113, i 1 Take on a value of 8.578193 and j 1 Is 38330.85.
Preferably, a 2 The value is 6516.15, b 2 The value is 2.08X10 -6 、c 2 The value is 30095.4, d 2 The value is 2002551, e 2 The value is 0.21, f 2 The value is 1293179 g 2 The value is 0.33, h 2 The value is 2.25, i 2 Take on a value of 2.53303 and j 2 The value is 34340.26.
In the above embodiment, M 1 And M 2 The initial yield bending moment of the section of the small eccentric section and the large eccentric section are respectively.
Preferably, the value range of the diameter D of the pile foundation is 1.5-3.2m, and the value range of the section reinforcement ratio is 0.5-2%.
The fitting effect adopts a statistical decision coefficient r 2 And a significance P value.
Determining coefficient r 2 The important statistic is the ratio of regression square sum to total square sum, the value is between 0 and 1, and the value can reflect the relative degree of regression contribution, namely the percentage which can be explained by the regression relation in the total variation of the dependent variable Y. r is (r) 2 Is the index most commonly used for evaluating the quality degree of regression models, r 2 The larger (close to 1), the regression of the fitCheng Yue.
The significance P value is the probability that the test statistic calculated from the sample observation falls into the reject domain when the original assumption is true. The smaller the P value, the more adequate the reason for rejecting the original hypothesis. In general, P <0.01 indicates a strong determination result.
When a first term fitting is used, the fitting equation M 1 Wherein r is 2 0.896 and a P value of 0. Fitting equation M 2 Wherein r is 2 0.9094 and p value of 0.
When quadratic fitting is used, the fitting equation M 1 Wherein r is 2 0.9956 and p value 0. Fitting equation M 2 Wherein r is 2 0.9726 and a p value of 0.
Therefore, the fitting equation of the quadratic term is better than the fitting equation of the first term, and the quadratic term is generally selected as the fitting equation.
Taking a large-diameter pile (pile diameter of 3.5 m) and a small-diameter pile (pile diameter of 1.5 m) as examples, the reinforcement ratio of the section cross section is from 0.5% to 2%, and comparing 3 calculated curves (3 curves such as a linear polynomial fitting curve, a quadratic polynomial fitting curve and a theoretical curve) of the section bending moment-curvature, and judging the actual effect by observation, as shown in fig. 2-8.
As can be seen from fig. 2 to 8:
(1) for a large-diameter pile (pile diameter is 3.5 m), as the section reinforcement ratio increases, the deviation between the fitting effect of the linear polynomial and the theoretical value tends to increase, and particularly when the structure is in a large eccentric compression state, the deviation result is more obvious; the fitting effect of the quadratic polynomial is in a large eccentric compression state and a small eccentric compression state of the structure, and the deviation is small.
(2) For a small-diameter pile (pile diameter is 1.5 m), when the pile is in different section reinforcement ratios, the fitting effect of the linear polynomial is inferior to that of the quadratic polynomial (when the pile is in a small eccentric compression section, the fitting determination coefficient r of the linear polynomial and the quadratic polynomial) 2 0.896 and 0.9956, respectively; when the large eccentric compression and the eccentric tension are carried out, the fitting of the linear polynomial and the quadratic polynomial determines the coefficient r 2 0.9094 and 0.9726 respectively). Thus, use is made ofThe fitting effect of the quadratic polynomial is generally better than that of the linear polynomial.
In summary, through pile foundations with different pile diameters and different section reinforcement rates, the section initial yield bending moment of each pile foundation under the action of different axial forces is calculated, each group of sampling data is divided into a small eccentric section and a large eccentric section, the calculation data of all the small eccentric section and the large eccentric section are respectively fitted, and a small eccentric section fitting equation and a large eccentric section fitting equation are determined. A more accurate set of fitting equations can be obtained. The set of equations can quantitatively determine the initial yield bending moment of pile foundations with different pile diameters and different section reinforcement rates under the action of different axial forces, and has the advantages of simple calculation, less time consumption and high efficiency. The practical application of a plurality of large-span bridges shows that the method has strong practicability and effectiveness. Meanwhile, the problems that the calculation workload of an analysis method adopting bending moment-curvature is large, the analysis is long in time consumption and is not suitable for the bridge engineering feasibility research stage are avoided.
It should be noted that in this application, relational terms such as "first" and "second" and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The foregoing is merely a specific embodiment of the application to enable one skilled in the art to understand or practice the application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (9)
1. A method for determining an initial yield bending moment of a section of a bridge pile foundation, comprising the steps of:
selecting a plurality of pile foundations with different pile diameters and different section reinforcement rates, calculating section initial yield bending moment of each pile foundation under the action of different axial forces, and taking the pile diameter, the section reinforcement rates, all axial forces and the section initial yield bending moment corresponding to the pile diameter, the section reinforcement rates and all axial forces of one pile foundation as a set of sampling data to obtain a plurality of sets of sampling data;
dividing each group of sampling data into a small eccentric section and a large eccentric section, and dividing each group of finite element analysis calculation data into the small eccentric section and the large eccentric section according to the maximum section initial yield bending moment value and the corresponding axial force in each group of calculation data;
and fitting the calculated data of all the small eccentric sections and the large eccentric sections respectively to determine a small eccentric section fitting equation and a large eccentric section fitting equation.
2. The method for determining the initial yield bending moment of the section of the bridge pile foundation according to claim 1, wherein the finite element analysis and calculation data of all the small eccentric sections and the large eccentric sections are respectively fitted by adopting a first polynomial fitting or a second polynomial fitting.
3. A method of determining an initial yield moment of a cross-section of a bridge pile foundation according to claim 2, wherein, when fitting using a first order polynomial,
the small eccentric section fitting equation is: m is M 1 ＝w 1 D+x 1 ρ-y 1 N-z 1 ；
The large eccentric section fitting equation is: m is M 2 ＝w 2 D+x 2 ρ+y 2 N-z 2 ；
Wherein: w (w) 1 、x 1 、y 1 、z 1 、w 2 、x 2 、y 2 And z 2 The coefficient is D, the diameter of pile foundation, ρ, the section reinforcement ratio and N, the axial force.
4. A method of determining the initial yield bending moment of a section of a bridge pile according to claim 3, wherein w 1 The value is 88026.14 and x 1 The value is 1485610, y 1 Take on a value of 0.72 and z 1 The curved value is 132741.
5. A method of determining the initial yield bending moment of a section of a bridge pile according to claim 3, wherein w 2 The value is 19565.73 and x 2 The value is 1112850, y 2 Take a value of 0.55 and z 2 The value is 46909.2.
6. A method of determining an initial yield moment of a cross section of a bridge pile foundation according to claim 2, wherein, when fitting using a quadratic polynomial,
the small eccentric section fitting equation is:
M 1 ＝a 1 D 2 -b 1 N 2 -c 1 D-d 1 N+e 1 ρ+f 1 D×ρ+g 1 D×N-h 1 ρ×N+i 1 D×ρ×N+j 1
the large eccentric section fitting equation is:
M 2 ＝a 2 D 2 -b 2 N 2 -c 2 D-d 2 N+e 2 ρ+f 2 D×ρ+g 2 D×N+h 2 ρ×N-i 2 D×ρ×N+j 2
wherein: a, a 1 、b 1 、c 1 、d 1 、e 1 、f 1 、g 1 、h 1 、i 1 、j 1 、a 2 、b 2 、c 2 、d 2 、e 2 、f 2 、g 2 、h 2 、i 2 And j 2 Is the coefficient, DThe pile foundation diameter is represented by ρ, the section reinforcement ratio is represented by N, and the axial force is represented by N.
7. The method of determining the initial yield bending moment of a cross section of a bridge pile foundation of claim 6, wherein a 1 The value is 14549.23, b 1 The value is 3.72 multiplied by 10 -6 、c 1 The value is 37691.9, d 1 The value is 0.67244, e 1 Take the value of 0, f 1 The value is 4223097 g 1 The value is 0.325113, h 1 The value is 19.2113, i 1 Take on a value of 8.578193 and j 1 Is 38330.85.
8. The method of determining the initial yield bending moment of a cross section of a bridge pile foundation of claim 6, wherein a 2 The value is 6516.15, b 2 The value is 2.08X10 -6 、c 2 The value is 30095.4, d 2 The value is 2002551, e 2 The value is 0.21, f 2 The value is 1293179 g 2 The value is 0.33, h 2 The value is 2.25, i 2 Take on a value of 2.53303 and j 2 The value is 34340.26.
9. A method of determining the initial yield bending moment of a section of a bridge pile according to claim 3 or 6, wherein the diameter D of the pile is in the range 1.5-3.2m and the reinforcement ratio of the section is in the range 0.5% -2%.
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