CN111914458B - Method for controlling line shape of arch ring of reinforced concrete arch bridge - Google Patents

Method for controlling line shape of arch ring of reinforced concrete arch bridge Download PDF

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CN111914458B
CN111914458B CN202010832268.7A CN202010832268A CN111914458B CN 111914458 B CN111914458 B CN 111914458B CN 202010832268 A CN202010832268 A CN 202010832268A CN 111914458 B CN111914458 B CN 111914458B
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cantilever
segment
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arch ring
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CN111914458A (en
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周建庭
吴月星
张洪
张劲泉
辛景舟
杨俊�
刘增武
张兰
王宗山
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Chongqing Jiaotong University
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Abstract

The invention discloses a reinforced concrete arch bridge arch ring linear control method, which comprises the following steps: s1, obtaining reinforced concrete arch bridge arch design parameters; s2, completing construction of the No. 1 cantilever casting segment based on the design parameters of the reinforced concrete arch bridge arch, and setting i to 2; s3, calculating the vertical formwork elevation of the i-th cantilever casting segment, and finishing the casting of the i-th cantilever casting segment based on the vertical formwork elevation of the i-th cantilever casting segment; s4, if i is equal to N, step S5 is executed by adding 1 to the value of i, and if i is less than N, step S3 is returned to by adding 1 to the value of i; s5, calculating the installation elevation of the ith stiff skeleton segment, and finishing the construction of the ith stiff skeleton segment based on the installation elevation of the ith stiff skeleton segment; s6, if i is equal to M, the process ends, and if i < M, the value of i is incremented by 1, and the process returns to step S5. The invention can accurately control the arch ring segment line shape of the reinforced concrete arch bridge constructed by combining the inclined pull buckle hanging cantilever pouring with the stiff framework.

Description

Method for controlling line shape of arch ring of reinforced concrete arch bridge
Technical Field
The invention relates to the field of arch bridge construction, in particular to a reinforced concrete arch bridge arch ring linear control method.
Background
The inclined pull buckle hanging cantilever pouring reinforced concrete box type arch bridge is used as a new process for arch bridge construction, has the advantages of good structural integrity, low manufacturing cost, less post maintenance, high construction stability, strong spanning capability and the like, is suitable for construction of suspended casting arches in multi-mountain canyon terrains in western regions of China, and therefore has great competitiveness in western regions of China.
The construction of the reinforced concrete arch bridge by combining the inclined pull buckle hanging cantilever casting with the stiff framework has large construction difficulty due to the longer suspension casting section. Along with the increase of the cast-in-place length and the weight of the cantilever, conditions such as large stress of a rod piece and excessive downward deflection of a cantilever end easily occur to construction temporary structures such as a hanging basket and the like, the cast-in-place requirement of the cantilever is difficult to meet, and the linear control difficulty of the arch ring segment is correspondingly increased. As a new arch bridge construction process, in the prior art, a method which can accurately control the arch ring segment line shape of the reinforced concrete arch bridge constructed by combining inclined pull buckle hanging cantilever casting with a stiff framework does not exist.
Therefore, how to accurately control the arch ring segment line of the reinforced concrete arch bridge constructed by combining the inclined pull buckle hanging cantilever casting with the stiff framework is a problem which needs to be solved urgently by the technical personnel in the field.
Disclosure of Invention
Aiming at the defects of the prior art, the technical problems actually solved by the invention are as follows: and accurately controlling the shape of the arch ring segment of the reinforced concrete arch bridge constructed by combining the inclined pull buckle hanging cantilever pouring with the stiff framework.
A linear control method for an arch ring of a reinforced concrete arch bridge is suitable for the reinforced concrete arch bridge constructed by combining inclined pull buckle hanging cantilever casting with a stiff framework, the middle part of the arch ring of the reinforced concrete arch bridge is a stiff framework section wrapped with concrete, two sides of the arch ring are cantilever casting sections, the number of the cantilever casting sections from an arch foot to the middle direction is sequentially 1 to N, and the number of the stiff framework sections from the arch foot to the middle direction is sequentially N +1 to M; the method for controlling the arch ring line shape of the reinforced concrete arch bridge comprises the following steps:
s1, acquiring design parameters of the reinforced concrete arch bridge arch;
s2, completing construction of the No. 1 cantilever casting segment based on the design parameters of the reinforced concrete arch bridge arch, and setting i to 2;
s3, calculating the vertical formwork elevation of the i-th cantilever casting segment, and finishing the casting of the i-th cantilever casting segment based on the vertical formwork elevation of the i-th cantilever casting segment;
s4, if i is equal to N, step S5 is executed by adding 1 to the value of i, and if i is less than N, step S3 is returned to by adding 1 to the value of i;
s5, calculating the installation elevation of the ith stiff skeleton segment, and finishing the construction of the ith stiff skeleton segment based on the installation elevation of the ith stiff skeleton segment;
s6, if i is equal to M, the process ends, and if i < M, the value of i is incremented by 1, and the process returns to step S5.
Preferably, in step S3, the vertical mold level of the i-th cast-as-cantilever segment
Figure BDA00026384177500000218
Calculated as follows:
Figure BDA0002638417750000021
in the formula (I), the compound is shown in the specification,
Figure BDA0002638417750000022
showing the designed elevation of the center of the arch ring section of the cantilever end of the No. i cantilever casting section,
Figure BDA0002638417750000023
the design pre-camber value of the cantilever end arch ring section of the No. i cantilever casting section is shown,
Figure BDA0002638417750000024
the main arch ring deformation correction value when the No. i cantilever casting segment is cast is shown,
Figure BDA0002638417750000025
the deformation value of the cradle when the No. i cantilever casting segment is cast is shown, h is the height of the main arch ring,
Figure BDA0002638417750000026
and the horizontal inclination angle of the arch axis of the cantilever-end arch ring of the No. i cast-in-place cantilever section is shown.
Preferably, the method for obtaining the design pre-camber value of the reinforced concrete arch bridge comprises the following steps:
and establishing a Midas/civil model, solving a design pre-camber value of the arch ring span center, wherein the design pre-camber values of the rest positions of the arch ring are distributed in proportion according to the influence line of the horizontal thrust of the arch springing.
Preferably, the first and second electrodes are formed of a metal,
Figure BDA0002638417750000027
including the correction value of the time-varying effect of the main arch ring deformed concrete when the No. i cantilever casting segment is cast
Figure BDA0002638417750000028
And the corrected value of the on-site actual measurement temperature when the No. i cantilever casting segment is cast
Figure BDA0002638417750000029
Preferably, the first and second electrodes are formed of a metal,
Figure BDA00026384177500000210
showing the predicted hanging basket deformation value of the i-th cantilever casting segment obtained based on the hanging basket pre-pressing load test result,
Figure BDA00026384177500000211
showing the hanging basket finite element simulation result value under the working condition of casting the No. i cantilever casting section of the arch ring,
Figure BDA00026384177500000212
the measured deformation value of the hanging basket of the i-1 th cantilever casting section is represented;
based on the cradle pre-pressing load test result, recording the cradle actual measurement deformation value under each graded load, obtaining the graded load and cradle deformation mapping relation, and obtaining the cradle deformation prediction value of the No. i cantilever casting segment by adopting linear fitting
Figure BDA00026384177500000213
Figure BDA00026384177500000214
Wherein a and b are both constant terms, G2Denotes the weight of the No. 2 arch ring cast-in-place segment, GiThe weight of the i-th cast-in-cantilever segment arch ring is represented;
establishing a cradle finite element simulation model under the working condition of casting the i-th cantilever casting section, simulating the concrete wet load of the arch ring of the i-th cantilever casting section by adopting a linear load, and simulating the diaphragm plate of the arch ring by adopting a concentrated force to obtain the concrete suspension bracket finite element simulation model
Figure BDA00026384177500000215
Actually measured deformation value of hanging basket adopting No. i-1 cantilever casting segment
Figure BDA00026384177500000216
As
Figure BDA00026384177500000217
Preferably, in step S5, the i-th stiff skeleton segment is installed at an elevation
Figure BDA0002638417750000031
Calculated as follows:
Figure BDA0002638417750000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002638417750000033
showing the designed elevation of the center of the section of the arch ring at the cantilever end of the No. i stiff skeleton section,
Figure BDA0002638417750000034
the design pre-camber value of the cantilever end arch ring section of the No. i stiff skeleton section is shown,
Figure BDA0002638417750000035
the temperature correction value measured on site when the No. i stiff skeleton section is installed is shown, h' represents the truss height of the section steel stiff skeleton section,
Figure BDA0002638417750000036
representing horizontal inclination angle delta of cantilever end arch ring arch axis of No. i stiff skeleton segment'Actual total displacement of stage/stepAnd the actual total displacement value of the stage/step of installing the cantilever end control point of the stiff skeleton section in the i-th stiff skeleton section construction stage in the finite element simulation model for the staged construction of the main arch ring is represented.
In conclusion, the invention discloses a linear control method for an arch ring of a reinforced concrete arch bridge, which is suitable for the reinforced concrete arch bridge constructed by combining inclined pull buckle hanging cantilever casting with a stiff framework, wherein the middle part of the arch ring of the reinforced concrete arch bridge is a stiff framework section wrapped with concrete, the two sides of the arch ring are cantilever casting sections, the numbers of the cantilever casting sections from an arch foot to the middle direction are sequentially from 1 to N, and the numbers of the stiff framework sections from the arch foot to the middle direction are sequentially from N +1 to M; the method for controlling the arch ring line shape of the reinforced concrete arch bridge comprises the following steps: s1, acquiring design parameters of the reinforced concrete arch bridge arch; s2, completing construction of the No. 1 cantilever casting segment based on the design parameters of the reinforced concrete arch bridge arch, and setting i to 2; s3, calculating the vertical formwork elevation of the i-th cantilever casting segment, and finishing the casting of the i-th cantilever casting segment based on the vertical formwork elevation of the i-th cantilever casting segment; s4, if i is equal to N, adding 1 to the value of i, then executing step S5, if i < N, adding 1 to the value of i, then returning to step S3; s5, calculating the installation elevation of the ith stiff skeleton segment, and finishing the construction of the ith stiff skeleton segment based on the installation elevation of the ith stiff skeleton segment; s6, if i is equal to M, the process ends, and if i < M, the value of i is incremented by 1, and the process returns to step S5. The invention can accurately control the arch ring segment line shape of the reinforced concrete arch bridge constructed by combining the inclined pull buckle hanging cantilever pouring with the stiff framework.
Drawings
For purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made in detail to the present invention as illustrated in the accompanying drawings, in which:
FIG. 1 is a flow chart of a method for controlling the arch ring linearity of a reinforced concrete arch bridge disclosed by the invention;
FIG. 2 is a schematic structural diagram of an arch bridge according to an embodiment of the present invention;
FIG. 3 is a cross-sectional view of the corresponding arch springing of the arch bridge of FIG. 2;
FIG. 4 is a corresponding standard cross-sectional view of the arch bridge of FIG. 2;
FIG. 5 is a longitudinal pouring sequence diagram of an arch ring of an closure section corresponding to the arch bridge in FIG. 2;
fig. 6 and 7 are horizontal pouring sequence diagrams of closure segment arch rings corresponding to the arch bridge in fig. 2;
FIG. 8 is a front view of the novel triangular truss hanging basket;
FIG. 9 is a side view of the novel triangular truss cradle;
FIG. 10 is a schematic view of an arch ring coordinate calculation coordinate system according to the present invention;
FIG. 11 is a schematic diagram of the reaction-displacement theorem of equivalence;
FIG. 12 is a layout view of the anchoring end of the hanging basket load test;
FIG. 13 is a schematic diagram of a hanging basket finite element simulation model under the working condition of casting the i-th cantilever casting section;
FIG. 14 is a graph comparing the theoretical value and the measured value of the main arch ring line shape after the rope is loosened and arched by using the method of the present invention to linearly control the arch bridge of FIG. 2;
FIG. 15 is a schematic diagram of a local coordinate system of the main arch ring and various parameters.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the invention discloses a linear control method for an arch ring of a reinforced concrete arch bridge, which is suitable for the reinforced concrete arch bridge constructed by combining inclined pull buckle hanging cantilever casting with a stiff framework, wherein the middle part of the arch ring of the reinforced concrete arch bridge is a stiff framework segment externally coated with concrete, the two sides of the arch ring are cantilever casting segments, the number of the cantilever casting segments from an arch foot to the middle direction is 1 to N in sequence, and the number of the stiff framework segment from the arch foot to the middle direction is N +1 to M in sequence; the method for controlling the arch ring line shape of the reinforced concrete arch bridge comprises the following steps:
s1, acquiring design parameters of the reinforced concrete arch bridge arch;
s2, completing construction of the No. 1 cantilever casting segment based on the design parameters of the reinforced concrete arch bridge arch, and setting i to 2;
s3, calculating the vertical formwork elevation of the i-th cantilever casting segment, and finishing the casting of the i-th cantilever casting segment based on the vertical formwork elevation of the i-th cantilever casting segment;
s4, if i is equal to N, step S5 is executed by adding 1 to the value of i, and if i is less than N, step S3 is returned to by adding 1 to the value of i;
s5, calculating the installation elevation of the ith stiff skeleton segment, and finishing the construction of the ith stiff skeleton segment based on the installation elevation of the ith stiff skeleton segment;
s6, if i is equal to M, the process ends, and if i < M, the value of i is incremented by 1, and the process returns to step S5.
Taking the arch bridge shown in fig. 2 as an example, the bridge span is arranged to be 2 × 30+17 × 13.2 (main span 210m) +3 × 30m, and the total length of the bridge is 391.4 m. The main bridge is a deck type reinforced concrete box arch bridge with the net span of 210m, the net rise is 42m, the net rise-span ratio is 1/5, the arch axis adopts a catenary, and the arch axis coefficient m is 1.67. The approach bridge on one side is a continuous T-beam with 2 x 30m prestressed concrete simply supported first and then structure, and the approach bridge on the other side is a continuous T-beam with 3 x 30 prestressed concrete simply supported first and then structure. The main bridge plane is located on a straight line, and the main bridge longitudinal plane is located on a convex curve with i being +/-0.5% and R being 25445.380 m.
The transverse partition plate corresponding to the arch ring box girder at the upper arch row frame adopts a thickness of double 25cm except for the positions of No. 1 and No. 14 upright columns, and the rest positions adopt 35 cm; transverse partition plates between the bent upright posts are 25cm in length, water is maintained for drainage construction, the interior of the box is kept dry, and phi 5cm drain holes are formed in the arch feet of the box, the chamfer positions of the transverse partition plates and the bottom plate and the bottom of the transverse partition plates; and a phi 5cm vent hole is formed in the top plate of the web plate.
The arch ring construction buckle cable is arranged at the position of the transverse partition plate at the end part of each segment, and the anchorage device adopts a fixed end round P anchor. And cutting the buckling cable after the construction of the main arch ring is finished, and grouting and filling the cable hole.
As shown in FIGS. 3 and 4, the arch ring has a single-box single-chamber cross section, a width of 7.0m and a height of 3.5 m. The thickness of the top plate and the bottom plate of the cast-in-place section of the arch support is gradually changed from 80cm to 40cm, and the thickness of the web plate is gradually changed from 80cm to 50 cm. The thickness of the web plate is 50cm, and the top and bottom plates of other segments of the arch ring are 40 cm.
The main arch ring is constructed by adopting a cantilever pouring and stiff framework combination method. No. 1 segment of the arch ring is cast in place by a full-hall support, No. 2 to 14 segments of the arch ring are cast by hanging cantilevers by inclined pull buckles, a stiff framework arch and a suspension casting reinforced concrete arch are combined in construction of a mid-span HZ closure segment, the 14 segments are cast by hanging the cantilevers by inclined pull buckles, the steel truss arch is formed by the remaining 24.65m closure segment by adopting a steel structure, no additional buckle anchor cable is arranged, and finally the closure of the main arch ring of the bridge is completed by wrapping concrete outside the steel truss arch. The composite steel reinforced skeleton is divided into 3 sections, the 1 st section is embedded into 14 # arch ring concrete, and the 2 nd and 3 rd sections are integrally hoisted and spliced. The construction process of 2-14 sections is as follows:
after the nth section of concrete reaches the design strength, tensioning the nth group of buckles and anchor cables;
moving the hanging basket to the n +1 th section pouring position;
and thirdly, casting the (n + 1) th segment.
In consideration of the existing construction capacity and construction convenience, the pouring of the outer concrete adopts the following scheme: and (3) casting the arch ring closure section in a low-temperature ring-dividing manner, synchronously and symmetrically casting the concrete of the arch box bottom plate and the 1/2 web plate by two working surfaces, and after the concrete reaches the strength, symmetrically casting the concrete of the arch box top plate and the 1/2 web plate by two working surfaces. The longitudinal and transverse pouring sequence of the closure segment arch ring concrete is shown in fig. 5, 6 and 7.
For the section length that faces in being suitable for this engineering work progress, big scheduling problem, specially provide a novel triangle truss-like basket of hanging (as shown in fig. 8, fig. 9), mainly include main girder bearing system, main girder bearing system middle part each side is provided with 1 vice C type couple, C type couple top is connected with running gear, the running gear bottom is located the walking track at the arch box top of watering the section, be provided with the connecting plate on the C type couple, the connecting plate left and right sides respectively is connected with the arm-tie that is located main girder bearing system preceding basket and back basket side through many brace-stayed suspender, be provided with anti-roller device on the back basket, be provided with promotion bearing anchor jib on main girder bearing system. The upper chord member and the lower chord member of the hanging basket are composed of trusses formed by section steel, the trusses are connected with a hanging hook pin shaft through steel hanging belts, the hanging hook is formed by welding box-shaped sections through steel plates, the hanging hook is stressed only when the hanging basket travels, and the self weight of the hanging basket and the wet weight of concrete are borne by an anchor hanging rod when the arch box concrete is poured.
Compared with the traditional hanging basket for the suspended casting reinforced concrete arch bridge, the novel triangular hanging basket can expand the suspended casting length to unprecedented 8m, realizes the maximum inclination angle of 39.6 degrees, bears the suspended casting weight of 188t, and has the advantages of high strength, high rigidity, simple device, clear stress, high structure efficiency and the like. In addition, current cradle anchor jib anchor is usually anchored at arch ring cantilever end bottom plate, and for improving arch ring section cantilever department atress performance, novel triangular truss cradle moves anchor jib anchor position to the arch ring roof from the arch ring bottom plate. Various loads such as concrete wet weight are also transmitted to the arch ring top plate through the cradle anchor suspension rod, so that the conversion from tension at the arch ring section web plate to compression at the arch ring top plate is realized, the local stress of the arch ring section is obviously improved, and the main tensile stress of the arch ring is obviously reduced. The novel triangular truss hanging basket is used for a new arch ring section suspension casting construction technology, ensures the linear smooth roundness in arch ring cantilever construction, and ensures the construction safety and construction quality of an arch bridge.
For the box-shaped arch bridge with the same height, the elevation of any section of the main arch ring can be calculated according to an arch axis equation, the height of the section and the inclination angle of the section of the arch ring.
Establishing an xoy coordinate system as shown in fig. 10, and setting an arch axis equation of the arch ring as follows:
Figure BDA0002638417750000061
in the formula: m represents an arch axis coefficient; k is a coefficient for calculation of the number of the pixels,
Figure BDA0002638417750000062
f represents the calculated rise; xi is a coefficient of the calculation,
Figure BDA0002638417750000063
l represents the computational span.
The horizontal tilt angle at x position from the dome is calculated as:
Figure BDA0002638417750000064
setting the height of the main arch ring as h, and when the cross section of the arch ring is equal in height, the height y of the arch back isOn the upper partComprises the following steps:
Figure BDA0002638417750000065
the corresponding x-coordinate is:
Figure BDA0002638417750000066
however, during the design of construction drawings and the construction of bridges, the origin of the coordinate system is often established at the center of the arch springing section, as shown in the XOY coordinate system in fig. 10, where the arch axis coordinate from the X position is:
Figure BDA0002638417750000067
Figure BDA0002638417750000068
in specific implementation, for the arch ring established in the XOY coordinate system, the elevation of the vertical mold of the center of the cantilever end section of the arch ring of the i-th cast-in-place section is as follows:
Figure BDA0002638417750000069
however, in the actual suspension casting construction process, when the concrete formwork erection of the arch ring segment is positioned, the elevation of the bottom edge of the section of the box girder at the cantilever end of the arch ring is often controlled, so that the step S3 is performedFor the XOY coordinate system, the vertical mold elevation of the No. i cast-in-place cantilever segment
Figure BDA0002638417750000071
Calculated as follows:
Figure BDA0002638417750000072
in the formula,
Figure BDA0002638417750000073
showing the designed elevation of the center of the arch ring section at the cantilever end of the No. i cantilever casting section,
Figure BDA0002638417750000074
the design pre-camber value of the cantilever end arch ring section of the No. i cantilever casting section is shown,
Figure BDA0002638417750000075
the deformation correction value of the main arch ring when the No. i cantilever casting segment is cast is shown,
Figure BDA0002638417750000076
the deformation value of the cradle when the No. i cantilever casting segment is cast is shown, h is the height of the main arch ring,
Figure BDA0002638417750000077
and the horizontal inclination angle of the arch axis of the cantilever-end arch ring of the No. i cast-in-place cantilever section is shown.
The distance from the bottom edge of the arch ring to the center of the arch springing section is as follows:
Figure BDA0002638417750000078
the specific process of calculating the elevation of the vertical mold is as follows:
(1) obtaining the net span L of the main arch ring according to the design construction drawingoNet rise f0Arch axis coefficient m, arch ring height H, section truss height H' of steel section stiff skeleton and arch raising lineElevation h0；
(2) According to the formula
Figure BDA0002638417750000079
Acquiring a calculation coefficient k;
(3) horizontal inclination angle of arch axis of cantilever end arch ring of No. i cantilever casting section
Figure BDA00026384177500000710
Main arch ring calculating span
Figure BDA00026384177500000711
Main arch ring calculating rise
Figure BDA00026384177500000712
Horizontal inclination angle of arch springing section of main arch ring
Figure BDA00026384177500000713
If it is not
Figure BDA00026384177500000714
Then order
Figure BDA00026384177500000715
Recalculated until
Figure BDA00026384177500000716
Exiting the loop;
(4) main arch ring calculation span
Figure BDA00026384177500000717
Main arch ring calculation rise
Figure BDA00026384177500000718
(5) As shown in fig. 15, a local coordinate system is established with the arch springing arch line position as an origin, the great mileage direction as the X-axis forward direction, and the vertical direction as the Y-axis forward direction. Inputting X coordinate value X0Ceni at the position of the cantilever end arch axis of the segment of the arch ring i, and then
Figure BDA00026384177500000719
Figure BDA00026384177500000720
Figure BDA0002638417750000081
(6) The elevation of the vertical mold of the arch ring suspension casting segment is
Figure BDA0002638417750000082
In the specific implementation process, the first-stage reactor,
Figure BDA0002638417750000083
the construction monitoring unit needs to check and confirm the construction. Typically arch bridge design pre-camber values consist of 3 parts: the deformation of the arch ring under constant load, such as the dead weight of the arch ring, the arch building and the bridge deck slab, the second-stage pavement and the like, the deformation of the arch ring after 10-year contraction and creep action and the maximum downwarp value of the arch ring under one-half static live load. Through establishing a Midas/civil model, the design pre-camber value of the arch ring span is obtained, and the design pre-camber values of the rest positions of the arch ring are distributed in proportion according to the influence line of the horizontal thrust of the arch springing.
The arch foot horizontal thrust influence line has 2 acquisition modes in general:
1) by using a unit force P ═ 1, which passes through each point on the deck (if finite element method is used, it acts on each node on the deck one by one), the required elements (internal force, displacement, counterforce, etc.) are calculated in turn, and the line of influence is obtained. Assuming that the bridge deck has n nodes, it is necessary to perform n loads and calculate n times. This method is inefficient.
2) And calculating a reaction influence line of the support by using a reaction-displacement mutual equality theorem. As shown in fig. 11, the bridge deck has n nodes, and m (m ═ 1,2,3, …, n) is any one of the nodes. According to the reaction force-displacement theorem, the reaction force Rkm of the support k caused by the unit force P of 1 acting on the m point is equal to the displacement of the support k in the direction of Rkm (positive in the direction of Rkm) caused by the unit displacement Δ k of 1 in the direction of pkm.
According to the definition of the influence line, the reaction force Rkm of the support k caused by the unit force P of 1 acting at the m point is the value of the influence line of the support reaction force Rk at the m point. Since m is any node on the bridge surface, the value of the influence line of the reaction force Rk at each point is the deflection delta mk of each point of the bridge surface caused by the fact that delta k is 1, namely
Rkm(m＝1,2,3,…,n)＝δmk(m＝1,2,3,…,n)
Then, by utilizing the theorem of mutual equivalence of reaction force and displacement, the problem of solving the influence line of the reaction force becomes the problem of solving the deflection caused by the unit displacement of the support.
And establishing a bare arch finite element model, enabling the arch springing to generate forced displacement in the longitudinal bridge direction unit, and acquiring the vertical deflection value of each node of the arch ring in the model at the moment, namely the numerical value of the horizontal thrust influence line of the arch springing.
In the specific implementation process, the first-stage reactor,
Figure BDA0002638417750000084
correction value of time-varying effect of main arch ring deformed concrete during casting of No. i cantilever casting section
Figure BDA0002638417750000085
And the corrected value of the on-site actual measurement temperature when the No. i cantilever casting segment is cast
Figure BDA0002638417750000086
Figure BDA0002638417750000087
And (3) removing the difference value between the accumulated displacement value (considering the concrete time-varying effect) of each control point (the cantilever end of each segment of the arch ring) under the working condition of all buckles and anchor cables for constructing the arch ring segment finite element simulation model in stages and the displacement value (not considering the concrete time-varying effect) of each control point when the arch ring is arched at one time. The inclined pull buckle hanging cantilever pouring combined with the stiff framework construction reinforced concrete arch bridge has obvious concrete time-varying effect due to longer construction duration, and in the staged construction process of the main arch ring, under the condition of adopting stress and linear double control, the loose cable cannot be ensured to form an arch linear shape and a one-piece arch linear shapeThe secondary arch line forming is inosculated, so that the concrete time-varying effect correction needs to be carried out on the construction elevation of the main arch ring section.
Obtaining
Figure BDA0002638417750000091
The method comprises the following steps: based on the established staged construction arch ring section finite element simulation model, selecting the construction stage of the No. i suspension casting section of the casting arch ring, saving the finite element simulation model in the current construction stage as an independent static model, carrying out heating/cooling treatment on the main arch ring (the temperature change amount is any unit change amount), and obtaining the mapping relation between the temperature change and the displacement change of the No. i suspension casting section control point (section cantilever end) of the arch ring. Before pouring concrete of the No. i suspension casting section of the arch ring, carrying out on-site temperature measurement of the position of the No. i suspension casting section of the arch ring, and acquiring a deformation temperature correction value of the main arch ring based on a unit temperature change and displacement change mapping relation of the No. i suspension casting section of the arch ring (the position of a cantilever).
In the specific implementation process, the first-stage reactor,
Figure BDA0002638417750000092
showing the predicted hanging basket deformation value of the i-th cantilever casting segment obtained based on the hanging basket pre-pressing load test result,
Figure BDA0002638417750000093
showing the hanging basket finite element simulation result value under the working condition of casting the No. i cantilever casting section of the arch ring,
Figure BDA0002638417750000094
the measured deformation value of the hanging basket of the i-1 th cantilever casting section is represented;
based on the cradle pre-pressing load test result, recording the cradle actual measurement deformation value under each graded load, obtaining the graded load and cradle deformation mapping relation, and obtaining the cradle deformation prediction value of the No. i cantilever casting segment by adopting linear fitting
Figure BDA0002638417750000095
Figure BDA0002638417750000096
Wherein a and b are both constant terms, G2Denotes the weight of the No. 2 arch ring cast-in-place segment, GiRepresenting the weight of the i-th cast-in-place cantilever segment arch ring;
after the cradle is assembled on the arch ring 1# segment, for ensuring construction quality and safety, a loading pre-pressing test must be carried out on the cradle before the next process construction so as to test whether the carrying capacity of the cradle meets the design requirements, verify the rationality of the design of the cradle, and simultaneously the pre-pressing test can eliminate the inelastic deformation of the cradle and obtain the elastic deformation value of grading loading. Taking the arch bridge shown in fig. 2 as an example, the load test specifically comprises the following operation steps:
(1) the test is carried out by arranging a vertical anchor cable on the original ground and reversely pulling the hanging basket by the steel strand, and the hanging basket is assembled and then tested by 2# segment load.
(2) After the casting of the segment No. 1 is completed, as shown in fig. 12, 4 vertical anchor cables (a single anchor cable is a 6 phi j15.24mm steel strand) are respectively constructed at two ends of the bottom cross beam, the length of each anchor cable is 17m and 19m, the length of each anchor cable anchored into a rock is not less than 10m, when the anchor cables are tensioned, a concrete base of 50 x 30cm is cast on the original site, a 2I40b I-shaped steel box is installed on the top surface of the base, the anchor cables are tensioned on the I-shaped steel boxes, and grouting is performed on anchor cable holes.
(3) And (3) after tensioning the 1# section buckle cable, dismantling the 1# cast-in-place section support, assembling a hanging basket (the bottom die is not installed), installing 2I-shaped steel boxes of 2I40b on the top surface of the cantilever end of the hanging basket to serve as a counter-pulling longitudinal beam, welding leveling steel boxes at corresponding positions of the top surface of the longitudinal beam, and arranging 4 leveling steel boxes.
(4) And (3) installing a load test vertical steel bundle, wherein a single vertical steel bundle is made of a 4 phi j15.24mm steel stranded wire, the lower end of the vertical steel bundle is a fixed end and is anchored on a steel box on the top surface of the base, and the upper end of the vertical steel bundle is a tensioning end and is anchored on a leveling steel box on a longitudinal beam on the top surface of the hanging basket.
(5) The 2# segment is 1886KN in weight, each vertical steel bundle is carried out according to a loading sequence (141.5kN → 330.1kN → 471.5kN → 585.8kN) of 30% → 70% → 100% → 110% → 120%, when the loading sequence is added to a graded load position, a front end settlement value of the cradle is observed, whether abnormality exists at the connection position between the structures of the cradle is detected, after the abnormality does not exist, the suspension is stopped for 10 minutes after the detection, data is recorded, the suspension is stopped for 25 minutes again, the next-stage tensioning is carried out after the data is recorded, after the final tensioning is carried out to 120%, the abnormality exists in the cradle is detected again, the front end settlement of the cradle is observed, the suspension is stopped for 60 minutes, and unloading is started after the abnormality does not exist.
As shown in fig. 13, a finite element simulation model of the cradle under the working condition of casting the i-th cantilever casting section is established, the wet load of the concrete of the arch ring of the i-th cantilever casting section is simulated by adopting a linear load, and the diaphragm of the arch ring is simulated by adopting a concentrated force, so that the method can be obtained
Figure BDA0002638417750000101
Actually measured deformation value of hanging basket adopting No. i-1 cantilever casting segment
Figure BDA0002638417750000102
As
Figure BDA0002638417750000103
The actual deformation of the hanging basket is calculated according to the difference of the elevation of the measuring point before and after the section concrete is poured, namely
Figure BDA0002638417750000104
In the formula, HBefore pouring、HAfter pouringAnd respectively the elevations of the same measuring point position before and after the concrete of the arch ring section is poured.
And in the formula, a deformation calculation method of subtracting the deformation after pouring before pouring is adopted, so that the actual deformation of the obtained hanging basket is a positive value.
The following points need to be noticed in the measurement of the elevation before and after the concrete pouring of the arch ring section:
1) in order to obtain the actual deformation value of the cradle, elevation measurement must be carried out before and after the concrete of the arch ring segment is poured. The measurement should be carried out in a period of relatively stable air temperature and relatively stable temperature field of the arch ring section, namely before the sunrise in the morning. When the weather is cloudy, the measurement can be carried out in flexibly selected time intervals because the temperature difference change is relatively small.
2) Because the cantilever pouring concrete arch bridge adopts a construction method of arch foot fixed connection and the rigidity of the section of the arch ring is high, the deformation value of the hanging basket is relatively small when the construction is carried out on the first sections. In order to reduce errors caused by measuring instruments, a precise level gauge is preferably adopted for measurement.
3) Along with the increase of section concrete placement, the arch ring deflection increases correspondingly, and at this moment, still with the spirit level measurement priority, when measuring the difficulty, can consider to adopt the total powerstation to measure.
In specific implementation, the reinforced concrete arch bridge span is provided with the steel reinforced framework within a certain length range in the construction process of combining inclined pull buckles with cantilever pouring and the reinforced framework, and the steel reinforced concrete arch bridge span is made of steel without concrete time-varying effect, so that the reinforced concrete arch bridge span is provided with the steel reinforced framework
Figure BDA0002638417750000111
In the actual construction process of the stiff skeleton, the stiff skeleton is spliced and welded in a tangent line, and hanging basket construction does not exist, so that the stiff skeleton is not constructed
Figure BDA0002638417750000112
Therefore, in step S5, the installation elevation of the i-th stiff skeleton segment
Figure BDA0002638417750000113
Calculated as follows:
Figure BDA0002638417750000114
in the formula (I), the compound is shown in the specification,
Figure BDA0002638417750000115
showing the designed elevation of the center of the arch ring section of the cantilever end of the No. i stiff skeleton section,
Figure BDA0002638417750000116
representing the cross section of cantilever end arch ring of No. i stiff skeleton segmentThe pre-camber value of the design of (1),
Figure BDA0002638417750000117
the temperature correction value measured on site when the No. i stiff skeleton section is installed is shown, h' represents the truss height of the section steel stiff skeleton section,
Figure BDA0002638417750000118
representing a horizontal inclination angle delta 'of a cantilever end arch ring arch axis of No. i stiff skeleton segment'Actual total displacement of stage/stepAnd the actual total displacement value of the stage/step of installing the cantilever end control point of the stiff skeleton section in the i-th stiff skeleton section construction stage in the finite element simulation model for the staged construction of the main arch ring is represented.
According to (1) to (5) in the specific calculation process of the elevation of the vertical mold, the installation elevation of the control point (top edge of the cantilever end of the segment) of the stiffened framework segment in the span of the arch ring can be expressed as follows:
Figure BDA0002638417750000119
taking the arch bridge shown in fig. 2 as an example, by adopting the method disclosed by the invention, in the aspect of arch ring line shape, the main arch ring is closed, the fastening anchor cable is removed, the full bridge is subjected to through measurement, and the measurement points are arranged at the outer side, the middle and the inner side of the top plate of each segment. The maximum difference between the measured value and the theoretical value is only 2.5cm, the standard requirement is met, and the main arch ring is proved to have good linear control and no saddle shape. The main arch wire shape after the rope is arched is shown in figure 14.
In addition, in the invention, after each cast section of the cantilever is cast, the cast section can be inspected according to the elevation of the cast section and the elevation of the tensioned buckles and anchor cables.
After the concrete of the arch ring is poured, the hanging basket is subjected to the wet weight action of the concrete of the segment, the hanging basket is subjected to downwarping deformation, and the actual deformation of the hanging basket after the concrete of the No. i cantilever pouring segment is set as
Figure BDA00026384177500001110
Then hang No. iThe top edge elevation of the arch ring after the concrete pouring of the arm pouring section is as follows:
Figure BDA00026384177500001111
from the formula, it can be seen that:
when in use
Figure BDA00026384177500001112
When the method is used, the theoretical deformation of the cradle is consistent with the actual measurement deformation of the cradle, and at the moment, the height of a measuring point at the top edge of the arch ring can be simplified into
Figure BDA0002638417750000121
Under general conditions, the theoretical deformation of the cradle is not equal to the actual measurement deformation of the cradle, namely
Figure BDA0002638417750000122
Let the difference between the two be
Figure BDA0002638417750000123
When in use
Figure BDA0002638417750000124
When, Δ fDeformation of hanging basketIf the deformation value is more than 0, the theoretical deformation value of the hanging basket is larger;
when in use
Figure BDA0002638417750000125
When, Δ fDeformation of hanging basketAnd < 0, the theoretical deformation value of the hanging basket is smaller.
However, both of the above two cases can be expressed by the formula, that is, the elevation of the measuring point at the top edge of the arch ring of the i-th cast-in-place cantilever segment is:
Figure BDA0002638417750000126
the deformation value of the hanging basket is measured at each time, the inclination of the segments is gradually reduced along with the increase of the number of the segments, and the wet weight of the previous segment decomposed by the inclination of the segments is correspondingly reduced and is applied to the hanging basket in the vertical (gravity) direction.
After the arch ring concrete reaches the design strength, symmetrical, graded and synchronous tensioning can be carried out according to the cable buckling force and the cable anchoring force which are calculated through monitoring. Due to the effect of the guy wire, the arch ring segment will flex upwards. According to the deformation relation, the calculation formula of the height of the top edge of the section i after tensioning is as follows:
Figure BDA0002638417750000127
in the formula:
Δfdeformation by tensionThe deformation difference (displacement) between the buckled cable after tensioning and the buckled cable before tensioning is obtained.
During the simulation calculation of the finite element software model, the 'accumulated displacement' of the segment is extracted from the arch ring constructed by the cast-in-place method, and the value is deltaAccumulated displacementThe elevation calculation formula of the segment after the buckle cable is tensioned can be expressed as follows:
Figure BDA0002638417750000128
under the combined action of system errors, accidental errors, environmental errors and measurement errors, the actual measured elevation is often different from the theoretical calculated elevation.
In order to solve the measurement error caused by the difference of the front measurement point and the rear measurement point, fixed measurement points are arranged on the arch ring, and obvious marks are made. When measuring each time, the measuring points are always fixed on the measuring points, so that the problem of different measuring points is solved.
Because the height measuring points are placed on the bottom die of the bottom plate of the arch ring when the suspended casting segments are used for erecting the die, once casting is completed, the height measuring points need to be transferred to the top edge of the arch back, and fixed measuring points also need to be arranged on the arch ring.
Finally, it is noted that the above-mentioned embodiments illustrate rather than limit the invention, and that, while the invention has been described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (2)

1. The linear control method is characterized in that the method is suitable for a reinforced concrete arch bridge constructed by combining inclined pull buckle hanging cantilever casting with a stiff framework, the middle part of an arch ring of the reinforced concrete arch bridge is a stiff framework section wrapped with concrete, two sides of the arch ring are cantilever casting sections, the number of the cantilever casting sections from arch feet to the middle direction is sequentially 1 to N, and the number of the stiff framework section from the arch feet to the middle direction is sequentially N +1 to M; the method for controlling the arch ring line shape of the reinforced concrete arch bridge comprises the following steps:
s1, acquiring design parameters of the reinforced concrete arch bridge arch;
s2, completing construction of the No. 1 cantilever casting segment based on the design parameters of the reinforced concrete arch bridge arch, and setting i to 2;
s3, calculating the vertical formwork elevation of the ith cantilever casting section, and completing the casting of the ith cantilever casting section based on the vertical formwork elevation of the ith cantilever casting section; in step S3, the vertical formwork level of the i-th cast-in-place cantilever segment
Figure FDA0003634246880000011
Calculated as follows:
Figure FDA0003634246880000012
in the formula (I), the compound is shown in the specification,
Figure FDA0003634246880000013
showing the designed elevation of the center of the arch ring section of the cantilever end of the No. i cantilever casting section,
Figure FDA0003634246880000014
the design pre-camber value of the cantilever end arch ring section of the No. i cantilever casting section is shown,
Figure FDA0003634246880000015
the main arch ring deformation correction value when the No. i cantilever casting segment is cast is shown,
Figure FDA0003634246880000016
the deformation value of the cradle when the No. i cantilever casting segment is cast is shown, h is the height of the main arch ring,
Figure FDA0003634246880000017
representing the horizontal inclination angle of the arch axis of the arch ring at the cantilever end of the No. i cantilever casting section;
wherein the content of the first and second substances,
Figure FDA0003634246880000018
correction value of time-varying effect of main arch ring deformed concrete during casting of No. i cantilever casting section
Figure FDA0003634246880000019
And the corrected value of the on-site measured temperature when the No. i cantilever casting segment is cast
Figure FDA00036342468800000110
Figure FDA00036342468800000111
Showing the predicted hanging basket deformation value of the i-th cantilever casting segment obtained based on the hanging basket pre-pressing load test result,
Figure FDA00036342468800000112
showing the hanging basket finite element simulation result value under the working condition of casting the No. i cantilever casting section of the arch ring,
Figure FDA00036342468800000113
the measured deformation value of the hanging basket of the i-1 th cantilever casting section is represented;
based on the cradle pre-pressing load test result, recording the cradle actual measurement deformation value under each graded load, obtaining the graded load and cradle deformation mapping relation, and obtaining the cradle deformation prediction value of the No. i cantilever casting segment by adopting linear fitting
Figure FDA00036342468800000114
Figure FDA00036342468800000115
Wherein a and b are both constant terms, G2Denotes the weight of the No. 2 arch ring cast-in-place segment, GiRepresenting the weight of the i-th cast-in-place cantilever segment arch ring;
establishing a cradle finite element simulation model under the working condition of casting the i-th cantilever casting section, simulating the concrete wet load of the arch ring of the i-th cantilever casting section by adopting a linear load, and simulating the diaphragm plate of the arch ring by adopting a concentrated force to obtain the concrete suspension bracket finite element simulation model
Figure FDA00036342468800000116
Actually measured deformation value of hanging basket adopting No. i-1 cantilever casting segment
Figure FDA0003634246880000021
As
Figure FDA0003634246880000022
S4, if i is equal to N, step S5 is executed by adding 1 to the value of i, and if i is less than N, step S3 is returned to by adding 1 to the value of i;
s5, calculating the installation elevation of the ith stiff skeleton segment, and finishing the construction of the ith stiff skeleton segment based on the installation elevation of the ith stiff skeleton segment; in step S5, the installation elevation of the i-th stiff skeleton segment
Figure FDA0003634246880000023
Calculated as follows:
Figure FDA0003634246880000024
in the formula (I), the compound is shown in the specification,
Figure FDA0003634246880000025
showing the designed elevation of the center of the arch ring section of the cantilever end of the No. i stiff skeleton section,
Figure FDA0003634246880000026
the design pre-camber value of the cantilever end arch ring section of the No. i stiff skeleton section is shown,
Figure FDA0003634246880000027
the temperature correction value measured on site when the No. i stiff skeleton section is installed is shown, h' represents the truss height of the section steel stiff skeleton section,
Figure FDA0003634246880000028
representing horizontal inclination angle delta of cantilever end arch ring arch axis of No. i stiff skeleton segment'Actual total displacement of stage/stepRepresenting the actual total displacement value of the stage/step of installing the cantilever end control point of the stiff framework segment in the construction stage of the ith stiff framework segment in the finite element simulation model for the staged construction of the main arch ring
S6 is terminated if i is equal to M, and if i < M, the value of i is added by 1, and the process returns to step S5.
2. The reinforced concrete arch bridge arch ring line shape control method of claim 1, wherein the method for obtaining the design pre-arch degree value of the reinforced concrete arch bridge comprises:
and establishing a Midas/civil model, solving a design pre-camber value in the arch ring span, wherein the design pre-camber values at the other positions of the arch ring are distributed in proportion to the arch springing horizontal thrust influence line.
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