Advancements and innovations of the construction of 600-m scale concrete arch bridges

Abstract

In recent years, the successive completions of the Pingnan Third Bridge with an effective span of 560 m and the Tian’e Longtan Bridge with an effective span of 600 m in the Guangxi Zhuang Autonomous Region, China, signify that the spanning capacity of concrete arch bridges has entered the 600-m class. This also demonstrates that concrete-filled steel tubular (CFST) arch bridges and steel-reinforced concrete (SRC) arch bridges are the two most competitive bridge-type solutions for constructing super-long arch bridges. To further summarize the construction and innovation experience of the 600-m scale concrete arch bridges, this study focuses on key computational and field-measured data from the design and construction processes of the Pingnan Third Bridge and the Tian’e Longtan Bridge. Accordingly, a detailed analysis of the similarities and differences between the two subtypes of concrete arch bridges (CFST arch bridge and SRC arch bridge) were provided, and their respective applicable conditions, span growth potential, and further optimization directions were identified. The research findings can provide valuable references for scheme selection as well as detailed design and construction of future super-long arch bridges.

Graphical abstract

Keywords

600-m scale concrete arch bridges / CFST arch bridges / SRC arch bridges / computational and field-measured data / applicable conditions / span growth potential

1 Introduction

Between the year 2017 and 2024, the author led the design and construction of two landmark large-span arch bridges, namely, the Pingnan Third Bridge, a 560 m-span concrete-filled steel tubular (CFST) arch bridge, and the Tian’e Longtan Bridge, a 600-m-span steel-reinforced concrete (SRC) arch bridge. These two bridges boast spans surpassing all steel arch bridges, ranking second and first in the world for arch bridge span length, respectively. Prior to this, it was widely believed that steel arch bridges could span up to 1000 m, yet the longest span of all steel arch bridges was only 552 m. Concrete arch bridges were thought to be capable of spanning up to 400 m, but the longest span of existing concrete arch bridges built out of China was only 390 m. CFST arch bridges, which fall between steel arch bridges and concrete arch bridges in terms of construction materials, were considered to have a span capacity of 500 m, but the longest span of the constructed CFST arch bridges out of China was only 240 m. However, the Pingnan Third Bridge and the Tian’e Longtan Bridge have successfully broken through the span limitations of both CFST arch bridges and concrete arch bridges. Moreover, their construction costs were lower than those of comparable cable-stayed bridges, attracting widespread attention from both the engineering and academic communities.

The history of arch bridge construction has proven that the increase in span length and the resulting economic competitiveness primarily relies on advancements in construction technologies [1]. Two papers have been published by the author in 2018 and 2024 to highlight China’s significant progress over the past three decades in the design and construction of CFST arch bridges and SRC arch bridges, using the Pingnan Third Bridge and the Tian’e Longtan Bridge as case studies [2,3]. In the papers, the key innovations made by Chinese engineers in overcoming the challenges of arch bridge construction, including arch rib erection, risk mitigation, quality control, cost reduction for large temporary facilities, and the economic competitiveness enhancement, were highlighted. This paper serves as a supplement to the above two published papers. Through a comprehensive analysis of the critical computational data and the field-measured data from the Pingnan Third Bridge and the Tian’e Longtan Bridge, this paper aims to identify the similarities and differences between CFST arch bridges and SRC arch bridges, their respective applicable conditions, and potential pathways for further optimization. The feasibility of achieving longer spans for both types of arch bridges was also evaluated.

2 Overview of the Pingnan Third Bridge and the Tian’e Longtan Bridge

The Pingnan Third Bridge is a super-long CFST arch bridge spanning the Xunjiang River on the Lipu–Yulin Expressway in Guangxi Zhuang Autonomous Region, China, with a total length of 1035 m and a clear width of 25.9 m. The bridge has an effective span of 560 m, ranking second among all arch bridges built worldwide (ranking first at the time of completion). The bridge started construction on August 7, 2018, and was completed on December 28, 2020. The total construction cost of the bridge was 595.57 million yuan, which is 30 million yuan less than that of a comparable cable-stayed bridge. Moreover, it is expected to save 170 million yuan in maintenance costs over the next 100 years compared to a cable-stayed bridge with an equivalent span. A photo of the completed bridge is shown in Fig. 1.

The Tian’e Longtan Bridge is a super-long SRC arch bridge spanning the Longtan Reservoir on the Nandan-Xialao Expressway in Guangxi Zhuang Autonomous Region, China, with a total length of 2488.55 m and a clear width of 23.5 m. The bridge has an effective span of 600 m, ranking first among all arch bridges in the world. The bridge began construction in June 2020 and was opened to traffic on February 1, 2024. While the initial construction budget was 1.2784 billion yuan, the actual construction cost was only 1.2324 billion yuan. Compared to a cable-stayed bridge with the same span, the construction cost was reduced by 125 million yuan and the maintenance cost was expected to be 480 million yuan less over the next 100 years. A photo of the completed bridge is shown in Fig. 2.

2.1 Main section of the Pingnan Third Bridge

The main section of the Pingnan Third Bridge is a half-through CFST trussed arch with an effective span of 560 m. The arch ring consists of two parallel, equal-width arch trusses, featuring a rise-span ratio of 1/4 and an arch axis coefficient of 1.5, as illustrated in Fig. 3(a). Each truss adopts a four-chord cross-section, with heights of 8.5 m at the arch crown and 17.0 m at the arch springing. The width of each truss is 4.2 m and each chord has a diameter of 1.4 m. The chords are CFST components that consists of Q420 steel tube and C70 concrete specified by the Chinese code. To ensure lateral stability of the 560 m CFST arch, the dual arch trusses are interconnected by composite lateral bracings, i.e., K-shaped upper bracings and I-shaped lower bracings, which forms a 34.3 m-wide arch ring, as shown in Fig. 3(b). The bridge deck employs a steel-concrete composite system, comprising steel grid beams overlaid with a 15 cm-thick steel fiber-reinforced concrete slab (including a bottom steel plate 8 mm in thickness). The hangers are prefabricated, full-bundle extruded steel strand cables.

The connection between the hangers and the arch trusses, as well as between the hangers and the deck beams, is achieved using integral swaging anchorage, as illustrated in Figs. 4 and 5, respectively. The abutments on both the northern and southern banks are gravity-type thrust-resistant structures. The southern abutment was built on a spread foundation upon bedrock, while the northern abutment utilizes a composite foundation of a diaphragm wall encapsulating a grouting-reinforced pebble layer.

The steel consumption of the bridge totals 14558 t, including 8440 t for the steel tubular arch truss of the arch ring and 6118 t for the steel grid beams of the deck system. The steel tubular arch truss is divided into 44 segments, with the largest segment weighing 214 t, measuring 37.1 m in length, 4.2 m in width, and 13.0 m in height. The adjacent arch truss segments are interconnected by means of conventional inner flange joints, as depicted in Fig. 6. The steel grid beams consist of 37 segments, each weighing 165 t. Both the steel tubular arch truss and steel grid beams underwent a process of shop fabrication, waterway transportation, on-site cable crane lifting, and, for the arch truss, cable-stayed fastening-hanging cantilevered assembly. The shop prefabrication rate for the superstructure components reached 85%. The entire bridge site construction was formwork-free and involved only precast segment installation and in-tube concrete pouring. Approximately 1000 m³ of concrete was pumped into each chord tube. The in-tube concrete in each chord tube was continuously poured in about 12 h using a four-level quasi-vacuum-assisted pressure pumping technique. The total superstructure construction period was only 402 d, significantly shorter than that of a cable-stayed or suspension bridge with equivalent spans.

2.2 Main section of the Tian’e Longtan Bridge

The main section of the Tian’e Longtan Bridge is an SRC deck-type twin-ribbed arch bridge. The main arch consists of two parallel arch ribs, each forming a catenary curve. The effective span of the arch is 600 m, with a rise of 125 m, a rise-span ratio of 1/4.8, and an arch axis coefficient of 1.9, as shown in Fig. 7(a). The twin arch ribs are spaced 16.5 m apart transversely. Each rib adopts a uniform-width, variable-height concrete box section, with heights of 12 m at the springing and 8 m at the crown, and a consistent width of 6.5 m (Fig. 7(b)). Thirty transverse concrete-box connections, spaced 40 m apart longitudinally, are placed between the twin arch ribs corresponding to each spandrel column position. Both the arch ribs and transverse connections utilize C60 concrete specified by the Chinese code. The construction of the arch ribs was carried out using the stiff skeleton method. The steel tubular arch truss of each CFST stiff skeleton is fabricated into 24 segments, with adjacent segments connected by a novel external bolt-welding composite joint, as illustrated in Fig. 8.

During the preliminary design stage of the Tian’e Longtan Bridge, three alternative bridge schemes, i.e., CFST arch bridge, SRC arch bridge, cable-stayed bridge, were evaluated. The results showed that construction costs of the SRC arch bridge scheme were comparable to the CFST arch bridge scheme, but with lower maintenance costs. Compared to the cable-stayed bridge scheme, the SRC arch bridge scheme could save 125 million yuan in construction costs and 480 million yuan in maintenance costs over a 100-year period. As a result, the SRC arch bridge scheme was selected as the preferred option.

The Tian’e Longtan Bridge set a world record for the span length of arch bridges, and surpasses the previous record of a concrete arch bridge by 155 m. At the invitation of the project owner, the first author led the design and construction of the bridge. To achieve bracket-free construction of the 600 m-span SRC arch bridge, there were only two available construction methods: the stiff skeleton method and the hanging basket-assisted cantilevered casting method [4]. Before the construction of the Tian’e Longtan Bridge, a total of 12 concrete arch bridges worldwide with spans exceeding 300 m had been built by the stiff skeleton method and all of them are located in China. Among them, four bridges have spans greater than 400 m, with the largest being the 445 m-span Beipan River Bridge on the Shanghai–Kunming High Speed Railway, completed in 2016. The longest-span concrete arch bridge built outside of China with the stiff skeleton method is the Esla Bridge in Spain, a double-track railway bridge with a span of 210 m.

Outside of China, most large-span concrete arch bridges have employed the hanging basket-assisted cantilevered casting method. Among the 67 concrete arch bridges worldwide with spans exceeding 200 m, 20 have adopted this method, with the longest span being the 384-m Almonet Bridge in Spain, completed in 2016. In China, 9 concrete arch bridges have utilized this method for the construction of arch rings, with the longest span being the 335-m Shuoluo River Bridge on the Luzhou-Gulin Highway in Sichuan Province. Two well-known studies, including one on the design of a 600 m-span concrete arch bridge conducted by Japanese scholars in 2003 [5] and the other on the design of a 1000 m-span concrete arch bridge by Croatian scholars in 2004 [6], both also adopted the hanging basket-assisted cantilevered casting method.

However, in leading the design and construction of a super-long arch bridge like the Tian’e Longtan Bridge, the first author found that the stiff skeleton method had obvious advantages over the hanging basket-assisted cantilevered casting method. First, the construction risk for the former is generally lower since it involves a much shorter period of temporary cable suspension. For instance, the arch ring of the 335 m-span Shuoluo River Bridge was cantilever-cast on temporary cable-suspended basket for as long as 600 d, whereas the arch ring of the 416 m-span Nanpan River Bridge on the Nanning–Kunming High Speed Railway in China was completed within just 450 d using the stiff skeleton method. The 450-d timeline included 120 d for the erection of the steel tubular stiff skeleton under temporary cable suspension, only one-fifth of the time required for the Shuiluo River Bridge. Second, the construction of the 600-m-span CFST stiff skeleton of the Tian’e Longtan Bridge can draw on the experience of building the Pingnan Third Bridge, which is a 560-m-span CFST arch bridge. Third, it had been proved that the costs of the two construction methods were essentially the same. Therefore, the stiff skeleton method was finally selected for the construction of the Tian’e Longtan Bridge. Using this method, the arch ring was completed in 427 d, with only 100 d spent on the cantilevered assembly of the steel tubular stiff skeleton under temporary cable suspension.

The stiff skeleton method was invented in 1898 by an Austrian engineer, Josef Melan. The stiff skeleton acts as a support structure of bracket during arch construction, playing a critical role in the construction safety, alignment, and stress distribution of the arch [7]. However, because the material for the stiff skeleton in the early days was profile steel, it resulted in excessive steel consumption and so limited its adoption worldwide. Chinese engineers revolutionized this method in two aspects. First, they replaced the traditional profile steel with concrete-filled steel tubes for the stiff skeleton, reducing steel consumption by half [4]. Second, they introduced a new technique to control the time-dependent transient stresses of the CFST stiff skeleton during the pouring of encasing concrete [8]. These innovations significantly enhanced the economic viability and construction safety of concrete arch bridges using the stiff skeleton method.

3 Key innovations of the two bridges

During the construction of the Pingnan Third Bridge and the Tian’e Longtan Bridge, systematic innovations were introduced to reduce construction risks, enhance arch ring quality, and minimize the costs of large temporary facilities. These innovations not only ensured the successful completion of both bridges, but also substantially advanced the construction techniques for CFST arch bridges and SRC arch bridges, two highly promising modern arch bridge types.

3.1 Innovations in the Pingnan Third Bridge

First, a comprehensive design method for large-span thrust arch bridges on non-rock foundations was proposed [9,10]. The geological surveys had showed that the southern bank of the Pingnan Third Bridge consists of mostly exposed rocks, while the northern bank is composed of a clay layer over a pebble layer, each approximately 15 m thick. Based on the conventional design principles, such ground conditions are considered unsuitable for constructing a large-span thrust arch bridge. To address this challenge, superstructure optimization and foundation innovation were conducted to reduce load effects and enhance foundation resistance, respectively. These innovations led to the successful construction of the large-span thrust arch bridge on pebble foundation in plain areas, thereby significantly expanding the applicability of thrust arch bridges.

Second, one-time tensioning and dismantling of buckle cables were introduced for all arch segments during the assembly and closure of the 560 m steel tubular arch truss using the cable-stayed fastening-hanging cantilevered assembly method [11–13]. To control buckle tower deviation during the hoisting of arch segments, an active force control approach was developed to replace the conventional passive stiffness control approach. Specifically, real-time monitoring of tower-top displacements was conducted using the Beidou Navigation Satellite System and a smart jack was used to automatically adjust the cable forces acting on the tower when deviation occurred. As a result, the tower-top displacements were controlled within 2 cm, far lower than those achieved using the conventional passive stiffness control approach. Moreover, this innovative approach enabled the recycling of 5000 t of the steel tower components, accounting for 42% of the large temporary facility costs of the bridge [14].

Third, to ensure dense and shrinkage-free pouring of the C70 in-tube concrete of the arch chord, a four-level quasi-vacuum-assisted pressure pumping method was adopted [15]. Simultaneously, the temporal-spatial distribution of volumetric deformation of the in-tube concrete under the confinement effects from the steel tube were revealed. Accordingly, a precise shrinkage compensation technology for the in-tube concrete throughout the entire service period were proposed. Combining the shrinkage compensation technology with raw material homogenization and pouring process optimization, the achievement of zero shrinkage in the in-tube concrete throughout its entire service life was realized [16]. The measured ultrasonic wave velocities of the CFST chord at 7, 14, 28, 715, and 1826 d ranged between 4600 and 5100 m/s in both vertical and horizontal directions, indicating the absence of de-bonding and voids.

Benefited from the above innovations, the measured structural responses of the bridge closely matched the design values. For instance, upon the completion of deck paving, the differences between the measured and predicted steel tube stresses at the springing, L/8, L/4, and crown of the arch were merely 4.4%, 11.0%, 3.9%, and 3.8%, respectively, as detailed in Table 1. In addition, the difference between the measured and predicted arch crown deflection is only 3.9%, as presented in Table 2. The predicted structural responses were obtained from a refined finite element (FE) model. In this model, all materials were modeled using linear elastic constitutive relationships. Cables and hangers were simulated using link elements, while all other structural components were represented by beam elements. The CFST chord was modeled employing the “dual element” method. The construction process was simulated using the “birth and death element” technique.

The design principles and effects of the above innovations are detailed in Refs. [2,3].

3.2 Innovations in the Tian’e Longtan Bridge

The Tian’e Longtan Bridge is a 600-m-span SRC arch bridge with a trussed CFST stiff skeleton. Thanks to the design and construction experience gained from the Pingnan Third Bridge, the fabrication and installation of the CFST arch truss—serving as the stiff skeleton, were accomplished with relative ease, despite its substantial weight of 8150 t and the 2960 m³ of C80 concrete pumped into the steel tubes. In contrast, the main challenge lay in pouring the 28000 m³ of C60 encasing concrete, weighing approximately 70000 t, onto the CFST stiff skeleton. To tackle the challenge, the author and his team had conducted extensive research and introduced a series of innovations, including selection of proper stiff skeleton stiffness, development of a new encasing concrete material, improvement in the concrete pouring technique, reduction of arch rib stress, and optimization of longitudinal reinforcement, with the detailed innovations illustrated in Ref. [3].

Supported by the above innovations, the 28000 m³ of encasing concrete on the arch rib of the Tian’e Longtan Bridge was successfully poured in three layers on eight working platforms over a total of 36 cycles within 6 months. Throughout the construction period, the stresses and deflections in the arch ribs remained within the theoretical values. More remarkably, the bridge withstood a magnitude 4.4 earthquake, which occurred 15 d after the bridge was opened to traffic, without any damage, despite the epicenter being only 15 km away from the bridge site.

4 Comparison between the two bridges

4.1 Characteristics of the steel-reinforced concrete arch bridge

Both the SRC arch bridge and the CFST arch bridge fall under the broader category of concrete arch bridges with a stiff skeleton. The stiff skeleton of the former is a CFST arch truss, while that of the latter is a hollow steel tubular arch truss. The arch ring (or rib) of the SRC arch bridge is constructed through a self-erecting process involving the following steps. First, a steel tubular arch truss is assembled via a cantilever method to form a hinge-less steel arch. Next, concrete is poured into the chord tubes of the steel tubular arch truss to form a CFST arch truss. Finally, formwork is installed on the CFST arch truss and then the encasing concrete is poured onto the arch ribs in multiple layers. Since the arch axis keeps changing during the continuous pouring of the encasing concrete, there cannot be a so-called specific arch axis which consistently aligns with the compression line. Consequently, the bending moment within the arch is not negligible, resulting in relatively high compressive stress in the bottom plate layer and low compressive stress in the top plate layer.

The CFST arch truss, i.e., the stiff skeleton, of the SRC arch bridge primarily serves as a temporary bracket-support structure during the pouring of encasing concrete, playing a critical role in the quality and safety of the arch ring (or rib) formation. Once the integral SRC arch is formed, the load is mainly sustained by the concrete of the arch rib, while the CFST arch truss only functions to enhance the ductility of the concrete. Therefore, whether the CFST arch truss enters into the plastic state or not has minimal impact on the load-bearing capacity of the arch ribs. The encasing concrete generally has a large cross section as it must fully enclose the stiff skeleton and utilizes high-strength concrete, resulting in a strong load-bearing capacity the arch rib. Additionally, the large cross-sectional size of the arch rib makes the SRC arch bridge more suitable for a deck-type design. However, the large volume of high-strength encasing concrete makes crack prevention a challenging task [17]. Controlling the transient tensile stress in the CFST stiff skeleton is also quite difficult [8]. The extended concrete pouring duration increases the probability of exposing the arch structure to strong winds and drastic temperature fluctuations, resulting in relatively high construction risk.

The encasing concrete on the Tian’e Longtan Bridge totals 28000 m³ and weighs 70000 t. It accounts for 77% of the total weigh of the arch ribs (91000 t) and 56% of the total superstructure weight (125000 t). The encasing concrete was divided to three layers for pouring, including the bottom plate layer, web layer, and top plate layer. Each layer was poured on eight working platforms with 8 pumps simultaneously pouring on 4 platforms at each pouring cycle. Finally, it took a total of 36 cycles and 184 d to pouring all the encasing concrete of the bridge. During the pouring process, the transient tensile and compressive stresses in the arch ribs were controlled within 1 and 15 MPa, respectively (Fig. 9). The arch crown deflection was measured at 478 mm, representing 37% of the total dead load deflection (1281 mm). Upon completion of the arch construction, the cumulative arch crown deflection reached 1156 mm, accounting for 90% of the total dead load deflection, as shown in Table 3, which signified the end of the high-risk construction phase of the SRC arch bridge. The predicted values presented in Table 3 were derived from a refined elastic FE model of the Tian’e Longtan Bridge, which accurately simulates the entire construction process. In this model, the encasing concrete was modeled using shell elements, while all other structural components were represented by beam elements. Additionally, the approach bridges were incorporated into the FE model to accurately account for their influence on the structural behavior of the main bridge.

Upon completion of the pouring of the encasing concrete, the concrete stress at the top plate layer of the arch ribs is nearly zero. To prevent additional loads in this region—aside from the self-weight of the arch ribs, continuous rigid frames for the spandrel structures are placed within 72 m from the arch springing. This design helps minimize the negative moments at the arch springing section. In the central 480 m region, heavier prestressed T-shaped continuous concrete beams are installed, contributing to generate positive moments at both the arch crown and arch springing sections and to increases the compressive stress at the top plate layer of the arch springing section where it has the least compressive stress reserve. According to the measured data, the compressive stress at the top plate layer of arch springing section increased to 3.5 MPa under dead load alone, and it is 0.7 MPa under the combined effect of dead and live loads. Meanwhile, the increased positive moment at the arch crown reduces the compressive stress at the bottom plate layer of the crown section where it initially has a relatively high compressive stress. Overall, such arrangement of the spandrel structure is not only cost-effective but also significantly improves the stress distribution in the arch ribs.

4.2 Characteristics of the concrete-filled steel tubular arch bridge

CFST arch bridges can be constructed in deck-type, half-through, or through configurations. The arch ring is self-erected in two stages. First, the steel tubular arch truss is installed using cable-stayed fastening-hanging cantilevered assembly method to form a hinge-less steel arch. Then concrete is poured into the chord tubes of the arch truss to create a hinge-less CFST arch. Throughout the whole construction process, the axis of the arch remains unchanged, allowing it to be aligned with the compression stress line. The chord tubes of the CFST arch bridge have significantly larger diameters than those of SRC arch bridges with an equivalent span, resulting in a much greater volume of in-tube concrete. To prevent blockage during in-tube concrete pouring, multi-level continuous pumping is typically employed, with the number of levels determined by the workable duration of the concrete. Additionally, the steel tubular arch truss of the CFST arch bridge is considerably heavier than that of an SRC arch bridge, which makes both arch truss installation and in-tube concrete pouring the primary risk factors during CFST arch bridge construction.

For the Pingnan Third Bridge, the 8440-t steel tubular arch truss was installed in 44 segments utilizing a cable-stayed cantilevered assembly method. Each chord was filled with 958 m³ of concrete over a 12-h period via a four-level pumping process. Upon completion of the in-tube concrete pouring, the arch crown deflection reached 601 mm, accounting for 71% of the total deflection under dead load (844 mm), as detailed in Table 2. The compressive stress in the upper chord steel tube at the arch crown was measured at 89.8 MPa, representing 67% of the total stress under dead load (135 MPa), as listed in Table 1. These results indicate that the critical construction risks for the CFST arch bridge were mitigated once the in-tube concrete pouring was completed. During the in-tube concrete pouring process, the steel tubular arch truss acts as both bracket-support structure and bracket. Once completed, the steel tubular truss became a key load-bearing component, working in conjunction with the in-tube concrete to sustain all service loads.

4.3 Similarities and differences between the two types of arch bridges

A direct comparison between the 600-m-span Tian’e Longtan Bridge and the 560-m-span Pingnan Third Bridge indicates that the former has twice the stiffness, three times the arch ring weight, 1.4 times the arch ring construction cost, double the construction duration, and requires 70000 more labor-d for arch ring construction compared to the latter. These differences also reflect the general characteristics of SRC arch bridges and CFST arch bridges. As illustrated, CFST arch bridges typically offer advantages such as high rate of shop prefabrication, bracket-free superstructure construction, and minimal on-site work, making it easier and more efficient to build. Additionally, CFST arch bridges are known for their low maintenance requirements, excellent durability, and high stiffness. Therefore, CFST arch bridges are the preferred choice when large-scale arch truss fabrication and waterway transportation to the bridge site are feasible. However, in mountainous areas where shop prefabrication and the transportation of large components are limited, and where operational and maintenance conditions are challenging, SRC arch bridges are generally favored.

It is noteworthy that both the Tian’e Longtan Bridge and the Pingnan Third Bridge utilize CFST as the primary load-bearing component. Generally, the local stability of the steel tube in CFST component is enhanced by the support of the in-tube concrete, while the ductility and strength of the in-tube concrete are improved by the confinement effect provided by the steel tube. This composite action results in a compressive capacity significantly greater than the sum of the individual capacities of the steel tube and concrete. However, achieving this synergistic enhancement effect requires effective interaction between the steel tube and the in-tube concrete. Previous research has indicated that the shear bond strength at the steel-concrete interface comprise three components: chemical adhesion, mechanical interlock, and frictional resistance [18]. In the past, ordinary in-tube concrete with shrinkage or minimal expansion was commonly used in CFST arch bridges. In these bridges, there are no confinement effect from steel tube to in-tube concrete in CFST arch under service loads since the steel tube’s Poisson’s ratio is greater than that of the concrete in the elastic stage, resulting in no interface friction resistance. This challenge was successfully addressed during the construction of the Pingnan Third Bridge through the use of high-performance concrete admixtures containing magnesium oxide calcinated at different temperatures [16]. These admixtures can induce continuous expansion in the in-tube concrete, counteracting shrinkage during the hydration process. This not only prevents interfacial delamination but also generates pressure against the tube wall, thereby creating interfacial friction resistance even under the elastic conditions. As a result of the developed shear bond strength at the steel-concrete interface, no shear connectors are required between the steel tube and the in-tube concrete, enabling effective composite action between the two materials.

5 Discussion

5.1 Advantages, status, and development potential of the two arch bridge types

The primary load-bearing component of arch bridges is the arch rib (or arch ring), which mainly resists axial compressive forces under dead load. When the spandrel structures are properly arranged and the arch axis is properly designed, the arch experiences nearly pure axial compression under dead load, and only slight eccentric compression under combined dead and live loads. This minimizes the risk of fatigue failure and enhances the durability of the arch bridge. Among all types of arch bridges, concrete arch bridge is particularly competitive for spans ranging from 200 to 600 m. Their arch ring requires minimal maintenance and can be constructed relatively easily using either the stiff skeleton method or the hanging basket-assisted cantilevered casting method. CFST arch bridges, on the other hand, feature an efficient steel-concrete composite arch structure. This structural system offers strong competitiveness for spans between 100 and 600 m, combining the benefits of high strength, durability, and construction efficiency.

Both SRC and CFST arch bridges offer favorable constructability and economic viability, driving their widespread application and span length increase in China over the past three decades. Traditionally, it was widely accepted that steel arch bridges could achieve spans up to 1000 m, concrete arch bridges up to 400 m, and CFST arch bridges up to 500 m. However, the Pingnan Third Bridge surpassed all existing steel arch bridges in span length, ranked as the second longest arch bridge in the world. It broke through the previously-assumed span limit of CFST arch bridges and far surpassed the longest CFST arch bridge built out of China (240 m). The Tian’e Longtan Bridge is holding the world record for the span of arch bridges, exceeding the previous record of concrete arch bridges by 155 m and surpassing the famous KRK Bridge in Croatia by 210 m.

As listed in Table 1, the measured maximum compressive stress in the steel tubes of the arch truss of the Pingnan Third Bridge was 135 MPa under dead load whereas the designed maximum compressive stress under the standard load combination was 238 MPa. This indicates that the actual stress levels were well below the material strength limits. The diameter of the chord steel tube of the bridge is 1400 mm, with wall thicknesses of 34, 30, and 26 mm. According to the design code, the minimum allowable ratio of diameter to wall thickness is 25, which implies that the wall thickness of the chord tubes of the Pingnan Third Bridge could be increased up to 56 mm if necessary. The above analysis shows the considerable potential for further increasing the span length of CFST arch bridges. The feasibility of constructing a 700-m-span CFST arch bridge has been explored by the author in Ref. [19]. Similarly, for the Tian’e Longtan Bridge, the actual maximum compressive stress in the concrete under standard load combination was only 20.7 MPa—comparable to that of a 400 m-span concrete arch bridge. These findings support the conclusion that building a 700-m-span SRC arch bridge is feasible, provided that the skeleton stiffness and the encasing concrete strength are appropriately designed.

Both CFST and SRC arch bridge construction involves the erection of a steel tubular arch truss—essentially a steel arch structure. And as noted above, steel arch bridges can achieve spans up to 1000 m. The subsequent construction steps primarily involve pouring in-tube concrete and, in the case of SRC bridges, pouring the encasing concrete. From a construction standpoint, this suggests that the span length of both CFST and SRC arch bridges could potentially exceed 700 m. However, it is noteworthy that, as of 2022, only 116 bridges worldwide have spans larger than 700 m, and all of them are either suspension or cable-stayed bridges. These two types of bridges are generally more suitable for super-long spans than arch bridges. Therefore, while it may be technically feasible, constructing a 700-m-span arch bridge may no longer hold practical significance.

5.2 Discussions on the moment amplification factor of arch ribs

Under the combined effects of material and geometric nonlinearities, the axial force in the cross-section of slender, eccentrically compressed arch ribs of large-span arch bridges remains relatively close to that predicted by linear elastic analysis. However, the bending moment in the arch rib cross-section undergoes noticeable changes, which must be carefully considered at the design stage. It is widely accepted that the refined FE analysis can accurately capture these dual nonlinear effects and provide a reliable estimate of the structure’s load-carrying capacity. However, such analyses typically require extensive computation time and significant processing resources, limiting their practicality in comparing bridge schemes or optimizing parameters for large bridges. To address the challenge, a simplified alternative approach has been developed. This method utilizes sectional moment magnification factors to approximate the effects of material and geometric nonlinearities. It has been widely adopted and has been incorporated into nearly all mainstream bridge design codes worldwide.

During the design of the Tian’e Longtan Bridge, the author and his team compared the moment magnification factors for the critical arch rib sections using the formulas recommended by five domestic and international codes. The calculation results reveal significant variations in the moment magnification factors across different codes, with the maximum difference reaching several times [3]. Moreover, even if the minimum moment magnification factor among these results (i.e., 3.7) was used for the reinforcement design, the required longitudinal reinforcement area for the arch ribs of the Tian’e Longtan Bridge would be nearly 20 times that of the arch ribs in two famous SRC arch bridges—the Yongning Bridge in Guangxi Zhuang Autonomous Region and the Yangtze River Bridge in Wanzhou District, Chongqing Municipality. Notably, these two bridges have been in service for nearly 30 years without any transverse cracking in their arch rings. Such strikingly different calculation results indicate that the current method for determining the moment magnification factor in SRC arch bridges may be flawed, and likely to lead to an overestimation of their second-order effects.

The above conjectures are also supported by evidence from many prior research studies and engineering practices. For instance, as early as the 1980s and 1990s, several scholars in China, including Lou Zhuanghong from the Highway Research Institute of the Ministry of Communications of China [20] and Professor Xie Youfan from Southwest Jiaotong University [21], highlighted that the moment magnification factor prescribed by the Chinese codes for reinforced concrete arch bridges was significantly overestimated. Instead, they suggested a much smaller moment magnification factor, around 1 or 1.05. Additionally, Li [22] from Southwest Jiaotong University conducted an experiment on a 4.5-m-span reinforced concrete arch bridge, where the measured moment magnification factor at failure was found to be only 1.039.

The practice outcome of the Tian’e Longtan Bridge also provides a sound evidence for our conjecture on the sectional moment amplification factor of concrete arch ribs. To be specific, after thorough research and analysis as well as approval by expert arguments, the formulas suggested by Li [23] were finally adopted for the bridge, as illustrated in Eqs. (1)–(3). The calculated maximum moment amplification factor was 1.51, far lower than the value of 3.7 derived from the current design code for highway concrete bridges in China. Accordingly, the amount of longitudinal reinforcement for the top and bottom plate layers of the arch ribs was significantly reduced to two layers of 16 mm-diameter reinforcement, spaced 15 cm apart. This accounts for only 1/16 of the amount specified by the current design code for highway concrete bridges in China.

(1){\psi }_{\text{springing}}=\frac{1-0.382N_{L/4}/N_{\text{cr}}}{1-N_{L/4}/N_{\text{cr}}},

(2){\psi }_{L/4}=\frac{1-0.014N_{L/4}/N_{\text{cr}}}{1-N_{L/4}/N_{\text{cr}}},

(3){\psi }_{3L/16}=\frac{1+0.121N_{L/4}/N_{\text{cr}}}{1-N_{L/4}/N_{\text{cr}}},

where {\psi }_{\text{springing}}, {\psi }_{L4}, and {\psi }_{3L/16} denotes the moment amplification factors of the arch springing, L/4, and 3L/16 sections, respectively; N_{L/4} represents the elastic axial force in L/4 section; N_{\text{cr}} is the critical axial force for elastic instability calculated using the Euler formula.

However, the measured arch displacements (Table 3) and chord tube stresses (Table 4) of the bridge, which are influenced by geometric nonlinear effects, show excellent agreement with those calculated by the linear elastic FE model. Also, the measured values generally slight lower than calculated ones. Moreover, as mentioned, the bridge has successfully withstood a 4.4-magnitude earthquake, with the epicenter located near the bridge site, as shown in Fig. 10 and Table 5. These field-measured results strongly confirm that even for the world’s longest arch bridge, the Tian’e Longtan Bridge, the second-order effects are minimal. Next, the author and his team plan to conduct a full arch model test to further validate this conclusion. Based on these findings, a more rational method for calculating the moment magnification factor is expected. This method will not only provide a more accurate assessment of the load-carrying capacity of SRC and CFST arch bridges at the design stage, but it will also be crucial for correctly evaluating the load-carrying capacity of existing arch bridges.

5.3 Recommendations for future improvements and researches

1) The construction of the Pingnan Third Bridge incorporated the achievements made by Chinese engineers in the research and practice of CFST arch bridges over the past 30 years. Although it achieved a series of technological breakthroughs, it also has shortcomings. The first shortcoming is the use of conventional internal flange joints to connect the chord tubes of adjacent arch truss segments. If external bolt-welding composite joints had been used, the high-altitude welding workload could be reduced by two-thirds. This innovative joint was developed by the author and his team and has been successfully implemented in the CFST skeleton of the Tian’e Longtan Bridge, as shown in Fig. 8 [24]. Second, the bridge arch followed a traditional design with a variable height, where the height of the arch truss at the arch springing was twice that at the arch crown. However, during the design of another super-large-span CFST arch bridge by the first author and his team recently, it was found that reducing the height ratio between the arch springing and the arch crown could still meet all load-bearing requirements while reducing material consumption and easing the work involved in arch segment transportation and installation. Third, by controlling the shrinkage of in-tube concrete using composite expansive materials, the debonding problem in the CFST arch can be effectively mitigated [16]. However, further research is required to determine the optimal pressure that the in-tube concrete exerts on the steel tube wall.

2) The encasing concrete for the arch ribs of the Tian’e Longtan Bridge was poured in three layers: the bottom plate layer (8822 m³), the web plate layer (10918 m³), and the top plate layer (8251 m³), with each layer accounting for approximately one-third of the total volume. The advantage of this division is that the volume for each pouring cycle is similar. However, the bottom plate layer was poured solely under the support of the CFST truss arch, while the other two layers were poured under the support of a steel-concrete composite structure, consisting of the CFST truss arch and the bottom plate layer, or the bottom plate layer and the web plate layer. Consequently, the increases of arch deflection and steel tube stress during the pouring of the bottom plate layer are much larger than those of the other two layers. Specifically, the increase of arch crown deflection during the pouring of the bottom plate layer was 12 times greater than that during the pouring of the web or top plate layers. Likewise, the increase of steel tube stress in the upper chord at the arch crown during the pouring of the bottom plate layer was 6 times higher than that during the pouring of the web or top plate layers. Therefore, provided that the concrete can cover the lower chord steel tubes, minimizing the volume of the bottom plate layer encasing concrete is the most effective method to reduce the arch deflection and steel tube stresses. In addition, the pouring of the encasing concrete for the Tian’e Longtan Bridge consumed 80000 labor-d, 2538 t of temporary steel, 1424 m³ of timber, and 185 d of work, highlighting an urgent need to enhance the mechanization and automation of this construction process.

3) The web plate layer of encasing concrete for the arch ribs of the Tian’e Longtan Bridge, totaling 10918 m³, was poured after the bottom plate layer of encasing concrete. By the time the web plate layer of concrete was poured, the bottom plate layer of concrete had already undergone shrinkage, which constrained the shrinkage of the newly-poured web plate layer of concrete. Similarly, the web plate layer of concrete constrained the shrinkage of the newly-poured top plate layer of concrete. As a result, tensile cracking is likely to occur at the interface between these layers of concrete in the arch ribs. In addition, as shown in Table 6, the pouring of the web plate layer of concrete consumed 30000 labor-d, 418 t of temporary steel, 633 m³ of timber, and 85 d of work. Therefore, if the top and bottom plate layer thicknesses were increased and the web plate layer eliminated, it would not only reduce the stress in the arch rib concrete but also save on construction costs for SRC arch bridges. Furthermore, replacing the conventional steel web members with concrete-filled weathering steel tubes would ensure a maintenance-free operation throughout the service life of the bridge. These optimizations could further enhance the competitiveness of SRC arch bridges.

4) The load-bearing advantages of arch bridges have long been confirmed through theoretical analysis and practical validation. The Anji Bridge in China, with a history of 1400 years, remains standing to this day, while the 800-year-old Lugou Bridge in China, successfully withstood the passage of a 400-t flatbed truck, further demonstrating the superior durability and load-bearing capacity of arch bridges. According to the surveys conducted by the EU Sustainable Bridges Project from 2004 to 2007, arch bridges account for over 50% of the railway bridges in Europe, with almost all bridges over 100 years old being arch bridges. Moreover, their construction costs are often relatively lower [25]. The Ministry of Transport of China has made enhancing the resilience of transportation infrastructures as a key objective of the 15th Five-Year Plan. Arch bridges, which are rarely subject to collapse in service due to their inherent robustness, align perfectly with this goal. Consequently, increasing the proportion of arch bridges in newly-built projects is essential.

However, as listed in Table 7, the proportion of arch bridges built in China has been steadily declining over the past decade. The underlying reasons for this decline are twofold. First, historically, arch bridge had the highest accident rate during construction among the four major bridge types. Second, both the design and construction of arch bridges are highly complex, yet their construction costs are relatively low, which leads to lower design fees that are generally determined by multiplying the construction cost by a standard coefficient. Consequently, designers have shown little interest in arch bridges. Fortunately, solutions to these challenges are emerging. First, thanks to the continuous efforts of Chinese engineers over the past several decades, especially the experience gained from constructing super-large arch bridges represented by the Tian’e Longtan Bridge and the Pingnan Third Bridge, the accident rate during arch bridge construction has significantly decreased in recent years. Second, the unreasonable standard for arch bridge design fees can be adjusted, and standard drawings can be developed to improve design quality while reducing workload. Coupled with further government incentives, these measures are expected to accelerate the resurgence of arch bridge construction.

6 Conclusions

1) Among the two primary methods for constructing large-span concrete arch bridges at the current stage, the stiff skeleton method entails substantially lower construction risk than the hanging basket-assisted cantilevered casting method, as the main arch remains temporarily stayed by cables for a significantly shorter duration.

2) Both the SRC arch bridges and CFST arch bridges belong to the broader category of concrete arch bridges with a stiff skeleton, while the roles of the steel components within their stiff skeletons differ.

3) Pouring the encasing concrete constitutes the primary risk during construction of SRC arch bridges, while erecting the steel arch truss and infilling concrete into the steel tubes constitute the primary risks during construction of CFST arch bridges.

4) When conducting the comparative selection of bridge types, if large-scale steel components can be shop-fabricated and waterborne transportation to the bridge site is feasible, CFST arch bridges should be the preferred choice. For bridge sites in mountainous regions with challenging heavy-haul transportation conditions, a lack of fabrication sites for large components, and difficult operation and maintenance, SRC arch bridges may be prioritized.

5) The construction of SRC arch bridges and CFST arch bridges with spans exceeding 700 m is technically feasible; however, their economic viability and market demand require further investigation.

6) The current calculation methods for the sectional moment magnification factor of reinforced concrete arches may possess inherent flaws, and likely severely overestimates their second-order effects.

7) In the next stage, adopting the novel external flange bolt-welding composite joints, optimizing the arch-truss height, and determining the optimal expansion rate of in-tube concrete constitute key optimization and research priorities for CFST arch bridges. Reducing the pouring volume of bottom plate layer of arch rib, enhancing construction mechanization and automation, and replacing concrete web plates with steel web members represent primary technical pathways to improve structural performance and boost competitiveness for SRC arch bridges.

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