Keywords

1 Introduction

Concrete-filled steel tubular arch bridges, known for their large spans and excellent structural performance, are widely used in mountainous road bridges. Cable hoisting technology plays a pivotal role in addressing the construction challenges of these bridges, characterized by high technological requirements, strong specialization, and elevated construction difficulty. Taking the Xianfeng Chaoyang Bridge as a case study, this paper utilizes Visual Basic (VB) visual programming for the force analysis of the main cable under different working conditions. Finite element simulations are employed for validation. The design schemes for the main cable, main tower, and main anchor of the cable hoisting system are optimized, using the Xianfeng Chaoyang Bridge as a case study, with valuable insights for reference in similar projects.

2 Bridge Overview

The Xianfeng Chaoyang Bridge has a width of 12 m, with a bridge span arrangement of 30 m (prestressed box girder) +195 m (superstructure steel pipe concrete arch) +25 m (prestressed box girder). The total length of the bridge is 271 m, and the width is 12 m. It is a second-level highway with two lanes in each direction. The main bridge adopts a net span of 195 m steel pipe concrete truss superstructure arch bridge, with a net span-to-rise ratio of 1/5. The arch axis is aligned with the catenary line, and the arch axis coefficient is m = 2.2. The arch ribs are of equal-section steel pipe concrete truss structure. The construction of the main bridge adopts the cable hoisting construction process. The entire bridge consists of two truss arch ribs, and each main arch rib is hoisted in 13 segments on each side, with a total of 26 arch rib hoisting segments for the entire bridge. The arch foot section has the heaviest arch ribs, with a single segment weight of 75.032 tons. The columns on the arch are made of steel pipe concrete, with a lighter weight and not used as hoisting control. Each cap beam weighs 65.52 tons. The 16-m small box beam on the arch edge is relatively heavy, with a maximum weight of 42.38 tons. The approach bridge 30-m box beam has a maximum weight of 104.52 tons, and the 25-m box beam has a maximum weight of 79.56 tons. The overall layout is shown in Fig. 1.

Fig. 1.
figure 1

Cable Hoisting System Overall Layout Diagram.

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3 Optimization Research on Cable Hoisting Technology

In traditional cable hoisting systems, the calculation of the load-bearing cable is challenging, and obtaining accurate values through tension equations is difficult. The calculation workload is also significant, especially when considering various conditions and temperature changes, making the calculation process complex. Load-bearing cables often span large distances and bear significant weights, falling into the category of long-span cables. With numerous cable lines in each group, the installation of cables in an unloaded state results in inconsistent forces and shapes due to various factors. Additionally, under heavy-load conditions during the operation of the trolley, forces continuously change, leading to uneven tension in each load-bearing cable and a potential inclination of the trolley, making adjustments difficult [1, 2].

Due to limitations in conventional universal joint materials, the traditional assembled main tower cannot meet the load requirements of large-span, heavy arch rib main coupling systems, resulting in poor structural safety. Conventional main anchors using gravity-type anchors have large construction volumes, long construction cycles, and do not fully exploit the mechanical properties of the rock and soil, resulting in poor economic efficiency.

Given the shortcomings in traditional cable hoisting system design outlined above, optimization and technological innovations are proposed.

  1. (1)

    Optimization of Load-Bearing Cable Calculation. In traditional calculations, the process is cumbersome and lacks precision. Applying the principles of static equilibrium, a software programming calculation was employed to optimize the calculation of the load-bearing cable length. Two approaches were taken: first, assuming the sag of the load-bearing cable and calculating the length S based on geometric relationships; second, assuming the sag of the load-bearing cable and obtaining the elastic elongation ΔS by calculating the tension within the main cable, resulting in the adjusted length S\(^\prime\) = S0 + ΔS. When S≈S\(^\prime\) (within the required precision), the assumed sag of the load-bearing cable is considered solved. Iterative calculations were performed after software programming, ensuring high speed and precision, meeting practical requirements, and significantly improving work efficiency.

  2. (2)

    Optimization of Load-Bearing Cable Tension Balance. In conventional cable hoisting systems without a balancing pulley, the trolley often tilts during operation, posing safety risks. To ensure even force distribution in the suspension cables, a series of large-tonnage pulleys totalling 150 tons were connected in tandem to automatically adjust the tension uniformly. The arrangement of the balancing pulleys is shown in Fig. 2.

Fig. 2.
figure 2

Balancing Pulley Tandem Arrangement Diagram.

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  1. (3)

    Optimization of Main Tower Structure. The traditional universal joint tower frame fails to meet the requirements of large-span, heavy cable hoisting due to issues with tower deformation and material strength. To address this, the tower frame was modified based on the assembly materials of the universal joint tower frame. The columns were constructed using φ630 × 14 steel pipes, connected longitudinally through flanges, with four on each side, totalling eight steel pipe columns for the entire tower. The remaining components were assembled using universal joint materials, significantly improving both safety and cost-effectiveness.

  2. (4)

    Optimization of Main Anchor Structure. The traditional gravity-type anchor has a large construction volume. To address this, a combination anchor consisting of “pile + baffle” was introduced, fully exploiting the mechanical properties of the rock and soil. This greatly enhanced the anchor's resistance to pulling and tilting. The main anchor structure is depicted in Fig. 3.

Fig. 3.
figure 3

Main Anchor Structure Diagram.

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4 Overall Design Scheme

The overall arrangement of the load-bearing cables for the cable hoisting machine spans (100 + 341 + 86) m, with one set of load-bearing cables installed on the upstream and downstream sides, respectively. When considering the in-place positioning of the arch ribs, a single set of main cables supports the load. The 16-m small box beam is hoisted by a single set of main cables, while the 25-m and 30-m box beams are lifted and installed by two sets of main cables. Therefore, the entire bridge is designed with two sets of transport cables, each with a rated load capacity of 76 tons. Two sets of lifting pulley assemblies, each with a rated net lifting weight of 38 tons, are installed on each transport cable. When both sets of main cables evenly bear the load, the maximum lifting weight can reach 152 tons. The cable hoisting system consists of main cables, lifting cables, traction cables, front and rear wind ropes, trolleys, lifting pulley assemblies, cable saddles, towers, anchors, and winches.

  1. (1)

    Two sets of 7φ56 mm (6 × 37S + FC) synthetic fiber core steel cables are arranged at the top of the tower as main cables, aligned with the installed rib axis. Both sets of main cables can be laterally moved in an unloaded state. Considering the requirements for hoisting attachment cables, equipment maintenance, transporting small machinery, and construction assistance, one set of 1φ56 mm (6 × 37S + FC) synthetic fiber core steel cables is arranged on the inner side of each set of main cables at the top of the tower (1.2 m from the center of the main cables) as working cables.

  2. (2)

    The structures of the tower frames on both sides are essentially the same, with a total height of 47.255 m, and the tower tops on both sides are at the same elevation. The tower frame columns are constructed using φ630 × 14 steel pipes, connected longitudinally through flanges, with four on each side, totalling eight steel pipe columns for the entire tower. Horizontal and diagonal belly rods within the column frame use universal joint components 2N4 and 2N5, respectively. The horizontal diagonal belly rods use 2N5 components. The 2N4 and 2N5 belly rods are connected to the column steel pipes by bolts and welded splice plates. The tower frame is 2.4 m wide longitudinally (center-to-center distance between front and rear columns), with a width of 2.4 m on each side of the column horizontally, an 8.4 m width at the central bracket, a full width of 17.6 m at the top of the tower, and a full width of 13.2 m at the tower base. Universal joint components are used for the lateral connection systems between upper and lower river columns at the tower top and central portions. For the central lateral connection systems, 2N4 and 2N5 components are used. For the upper connection system, 4N3(2N3) components are used for lateral diagonal belly rods based on the force requirements, 4N4 components are used for upper and lower lateral horizontal rods, and 4N1(2N1) components are used for vertical rods, with the remaining using 2N4 and 2N5 components.

  3. (3)

    For each installation segment of the steel pipe arch rib upstream and downstream, one set of fastening cables is installed, totaling six sets on each side of the rib. Cables 1 to 4 in each set use 2φ40 mm steel cables (6 × 37S + FC 1670 Mpa), and cables 5 and 6 use 2φ48 mm steel cables (6 × 37S + FC 1670 Mpa). Each set consists of one cable on each side of the rib. Fastening cables for Sects. 1 and 2 on both sides are guided over the bearing pulley at the top of the abutment and anchored on the pre-embedded tension plates inside the bridge tower. Fastening cables for Sects. 3 to 6 are guided over the seat pulley at the top of the tower and anchored on the front anchor beam in front of the main anchor after passing through the pulley [3].

  4. (4)

    Each shore is equipped with a structurally identical main anchor, used for anchoring the main cable, working cable, fastening cable, tower rear wind cable, etc., during the installation of the arch rib on that shore. The main anchor is symmetrically arranged relative to the axis of the cable hoisting machine. The main anchor is designed as a pile foundation support structure. The design includes six reinforced concrete piles for each anchor, with a pile diameter of 2.5 m and a pile anchoring depth of 8.5 m. The support platform has a plan dimension of 13.5 m × 9.5 m, a height of 2.5 m, and the front and rear rows of piles protrude from the support platform. Horizontal horizontal anchor beams are set for anchoring steel cables, and the anchor beam has a diameter of 2.2 m. On both the left and right sides, the rear anchor beams anchor a set of main cables and corresponding lifting traction connection cables. The front anchor beams on the left and right sides anchor the working cables, fastening cables, and tower rear wind cables on their respective sides. The anchor is constructed with C40 reinforced concrete, with the requirement that the pile foundation and support platform are embedded in the rock layer, and the foundation bearing capacity is not less than 0.5 Mpa.

  5. (5)

    The wind cable ropes for the arch ribs use 2φ20 mm (6 × 37 + FC) synthetic fiber core steel cables. The angle between the wind cable and the ground should not exceed 30°, and the horizontal projection angle of the wind cable with the bridge axis should not be less than 50°. The actual placement is adjusted based on on-site topography measurements, aiming to meet the aforementioned requirements for the wind cable angles. The initial tension of the wind cable should be adjusted according to the actual wind cable angles. To reduce the non-elastic impact of the wind cable sag, the initial tension on one side of the wind cable is controlled at 60 KN, and the tension on the other side is calculated based on the principle of equal lateral horizontal force. Since the lateral stability during the installation of the double ribs is relatively good, wind cables are only installed on the 1st, 3rd, and 5th segments of the arch ribs. For both ribs, a total of 4 × 6 = 24 wind cable ropes are required. In addition to maintaining lateral stability during the arch rib installation process, the arch rib wind cables are mainly used to control and adjust the transverse axis of the arch rib during the installation process.

5 Installation of Steel Pipe Arch Ribs

Each arch rib is divided into 13 hoisting segments, with a total of 16 hoisting segments for the entire arch rib. There are 12 K-braces between ribs, and a horizontal brace in the shape of the letter “M” is installed at the top of the arch. The steel pipe arch ribs are installed symmetrically from the arch foot to the arch top, meeting the symmetry requirements on both sides and upstream and downstream. Each arch rib segment should be installed after the installation of the horizontal brace to ensure the lateral stability of the arch rib. The specific sequence is shown in Fig. 4, and the installation is carried out in numerical order from small to large according to the numbering.

Fig. 4.
figure 4

Arch Rib Installation Sequence Diagram.

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Installation of the Arch Foot Hoisting Segment: For each shore's arch foot hoisting segment, the arch rib is divided into left and right sides, creating two hoisting segments. Initially, the downstream side of the arch rib truss piece from the Chaoyang Temple shore is hoisted to the side of the arch seat using cable hoisting. Gradually, the arch rib segment's foot end is placed above the arch seat. With the help of pre-embedded components on the arch seat and the use of chain pulleys and lifting pulley assemblies, the foot end of the arch rib segment is gradually adjusted to the position along the arch rib axis. The temporary hinge seats on both sides slowly insert into the embedded seat plates on the arch seat. Adjust one side's hinge seat hole alignment, fix it with M150 hinge seat bolts, then adjust the alignment of the other side's hinge seat hole, and fix it with M150 hinge seat bolts. At this point, the foot end of the first segment is in place. Adjust the arch rib axis using lateral cable wind at one end of the span, simultaneously install the fastening cables, adjust the installation elevation according to the design benchmark height, and gradually loosen the front hoisting cables. When all the force is transferred to the fastening cables and the arch rib elevation and axis meet the design and code requirements, release the hoisting hooks. Then, using the same method, install the downstream side of the arch rib truss piece for the Chaoyang Temple shore's arch foot segment. Once the arch foot segments on both upstream and downstream sides of the Chaoyang Temple shore are installed, begin installing the wind braces for the arch foot segment. Lift the entire assembly using two sets of main cables. After the wind braces are in place, temporarily secure them with planks and bolts, and then proceed with welding the joints. Use the same method to install the arch foot segment for the Jimingba shore [4].

Installation of General Hoisting Segments (Segments 2 to 6): The construction of general hoisting segments follows the hoisting procedure and construction method of the arch foot hoisting segment. Starting from the first segment of the arch seat, the construction proceeds symmetrically from both shores towards the mid-span, assembling up to the sixth segment. After the installation of symmetrical segments upstream and downstream is complete, the corresponding wind braces should be installed before proceeding to install the subsequent segments.

Transport the arch ribs using the four hoisting points of the two sets of main cables. Adjust the spatial orientation of the arch ribs by slightly lifting or lowering each hoisting point. After adjusting the arch rib truss pieces in place, temporarily connect the lower end joint with the adjacent upper end joint using flanges and bolts. Initially, connect 1 to 2 bolts for each joint, leaving the bolts slightly loose. Once all the bolts for the lower end four-legged steel pipe joints are fastened, tighten each joint bolt in a loop. Then release the lower end hoisting hook, hang the fastening cables, and adjust the lateral adjusting wind cables. Finally, tension the fastening cables. After adjusting the elevation and the axis of the arch rib to meet the design requirements, release the upper end hoisting hook and weld the circumferential weld seams between segments. The elevation of the arch rib is adjusted using the fastening cable pulley assembly, and the lateral axis is adjusted using the arch rib wind cables.

Following the hoisting procedure, after each set of fastening cables is in place, a thorough inspection of the previously fastened cables is required to determine if any cable adjustment operation is needed. The cable adjustment operation, based on the adjustment forces and arch rib elevations jointly issued by the design and monitoring parties on-site, involves using corresponding fastening cables, pulley assemblies, and hoists for each fastening cable. The operation is synchronized, carried out in symmetrical stages, and uses spectrum analyzers to test the cable forces to ensure a smooth cable adjustment process. This ensures the safety of the weld seams between sections, the weld seams of the lateral and transverse connections, and the safety of the bolted connections of the structural components. For each fastening segment, the arch rib axis and elevation must be checked to avoid cumulative errors in the arch rib's alignment and elevation, which may lead to difficulties in adjustment. This ensures effective control of the installation accuracy.

Stability measures during the arch rib hoisting process: For every other section of the arch rib hoisted in place (set at 1st, 3rd, and 5th sections), a pair of 2φ20 mm wind cables is set up upstream and downstream. There are a total of 24 arch rib wind cables throughout the bridge. This is done to adjust the arch axis and ensure its safe stability during the cantilever construction phase. The wind cable forces are calculated to ensure a safety factor of no less than 3, ensuring a certain margin in case the actual cable forces during construction differ from the calculated values.

Installation of the Closure Section: After the installation of the arch ribs and transverse braces is completed, preparations for the closure section are initiated. Before the closure of the arch ribs, the structure is observed in its maximum cantilever state for at least 24 h. Temperature impact observations are carried out within the design temperature range, and precise measurements of the closure length are taken. Based on the measurement results, precise cutting is carried out. The closure section is assembled according to the design requirements, with adjustments and positioning structures set as per the design specifications. Joint plates are installed at the closure, and the closure section is positioned accordingly. Following the closure requirements provided by the monitoring unit, the closure section is welded in place within the specified temperature range [5].

The closure section hoisting is typically scheduled during lower temperatures. As the temperature rises, in accordance with the principle of thermal expansion of steel structures, the spacing between the closure section and the two sides of the arch ribs gradually decreases. When it reaches the design dimensions, positioning horseboards are installed, welded, and locked, completing the closure construction.

6 Analysis of Cable Hoisting Calculation

Utilizing SAP2000 for the calculation of a spatial truss structure, the connections between the chord and the web members within each segment are considered as fully restrained. During the installation process of the steel tube arch ribs, the arch foot is treated as a hinged structure, taking into account the hinged support points. The calculation of the tie rods is incorporated using two-end hinged bar elements, and the connections between the tie rods and the anchoring towers or anchorages are considered as fixed hinges. The tie rods and wind cables are simulated using only tension-only truss elements [6]. The finite element simulation model is illustrated in Fig. 5.

Fig. 5.
figure 5

Finite Element Simulation Model.

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First, calculate the tension forces of each cable using the ‘zero bending moment method’ (considering the hinge joints between the arch feet and each section). Then, use the calculated tension forces along with the self-weight of the arch to perform calculations for the pre-closure state (at this stage, the arch feet are hinged, and sections are considered fixed between them). Adjust the tension forces slightly to ensure that the vertical displacements of the arch nodes meet the specifications (height difference within L/3000 and ±50 mm). At the same time, check that the bending moments in the arch sections are small, and the stresses are within the allowable range according to the specifications. The determined tension forces at this point are considered the tension forces for each cable in the pre-closure state. Next, use the ‘inversion method’ to calculate the tension forces, arch stresses, and node displacements for each stage. This is done to control the tension forces and deformations of the arch during the dismantling process. If significant deformation occurs during the dismantling process, make slight adjustments to the tension forces. Ensure that the stresses in the arch sections are within the allowable range for each stage, and design the tension forces with a safety factor not less than 3.0 [7]. The calculated maximum tension forces for a single cable are shown in Table 1.

Table 1. Table of Results for Maximum Cable Tension due to Self-Weight of Arch Rib (KN)
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In the actual process of arch rib installation, the construction control principle of ‘mainly focusing on shape control, with cable tension as a supplement’ is followed. As the arch rib segments are installed, the cable tension shows a uniformly increasing trend, and the uniformity is good both upstream and downstream. The measured tension is controlled within 10% of the theoretical value, indicating high accuracy in cable tension calculation. The shape of the arch rib after cable loosening approaches the theoretical control target, with a shape deviation controlled within 20 mm, meeting the requirements for standard errors and demonstrating good shape control [8, 9]. The stress analysis results of the arch rib are shown in Fig. 6.

Fig. 6.
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Arch Rib Stress Analysis Results Chart.

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7 Conclusion

Through the study of the key construction technology of cable hoisting for the large-span steel-concrete arch bridge of Xianfeng Chaoyang Bridge, it has been successfully applied in engineering practice, achieving excellent results.

  1. (1)

    The optimization and innovation of the cable hoisting system have achieved remarkable results in the installation and construction control of the arch ribs, especially the development of software for the calculation of the suspension cables, greatly improving the design efficiency.

  2. (2)

    For the tension self-balancing of the supporting cables and the optimization of the main tower and main anchor structure, it not only ensures the safety of the cable system but also achieves significant economic value, saving 35% compared to traditional structural construction measures.