1. Introduction
Arch bridges demonstrate high structural rigidity, cost-effectiveness, and adaptability to complex terrain [[
1], [
2], [
3], [
4], [
5], [
6], [
7], [
8], [
9]]. The arch bridge cost can be reduced by 1/3 compared to other bridge types [
2]. Long-span arch bridges fall under three categories: concrete–filled steel tubular (CFST) arch bridges, skeleton-reinforced concrete (SRC) arch bridges, and steel arch bridges, with the corresponding maximum spans reaching 575 [
3,
6,
10,
11], 600 [
12], and 580 m (under construction), respectively. The Third Pingnan Bridge (CFST arch bridge, 575 m, completed in 2020) saved 90 million and 30 million CNY compared to suspension and cable-stayed bridges, respectively [
13,
14]. The Tian’e Longtan Grand Bridge (SRC arch bridge, 600 m, completed in 2024) [
12] saved 110 million CNY compared to a cable-stayed bridge. An arch bridge spanning 600 or 700 m is a more cost-effective solution than a suspension bridge spanning 1000 m for valleys [
4]. However, the development of conventional arch bridges has been hindered due to their substantial self-weight, high construction expenses, and complex erection processes [
4,
5,
15]. These constraints have slowed development of the spanning capacity (from 518 to 600 m), with the 600 m mark remaining an unresolved engineering frontier. Consequently, all long-span bridges exceeding 600 m are cable-stayed or suspension systems, incurring substantially high expenditures and carbon footprints [
15].
Ultra-high-performance concrete (UHPC) is a cement-based composite with ultra-high compressive strength [[
16], [
17], [
18], [
19], [
20], [
21]]. The material is superior to steel and normal concrete in cost, carbon emissions, and axial loading [
14]. Shao et al. [
15] and Shao [
16] introduced a steel–UHPC composite truss (SUCT) arch bridge that could increase the span to 600–1000 m. Moreover, compared with traditional arch bridges and other bridge types, SUCT arch bridges are light, cost-efficient, environmentally friendly, and practically feasible [
14,
15]. For a mountainous area, the cost and carbon emissions of the SUCT arch bridge were 65% and 62% of those of the suspension bridge, respectively [
15].
Constructing long-span arch bridges is more challenging than cable-stayed and suspended bridges. Several large-scale temporary facilities (cables, buckle towers, ground anchors, etc.) are required to erect arch rings. Moreover, the non-bracket construction of the arch ring is usually carried out using the cantilever segment assembly method combined with a cable-stayed buckle system [[
22], [
23], [
24]]. The cost of large-scale temporary facilities accounts for approximately 20%. Reducing this cost is a promising approach for improving the cost competitiveness of arch bridges. Reducing the self-weight of the arch ring in the cantilever state is therefore of paramount importance.
For a steel arch, the construction of the entire section is carried out simultaneously [
22] (
Fig. 1(a)), with welding resulting in a heavy arch ring in the cantilever state. For the CFST and SRC arches, the steel-tube truss arch is first closed, followed by the pouring of concrete [
3,
6,
12] (
Figs. 1(b) and (c)). The self-weight of the arch ring in the cantilever state is approximately 50% of that of the steel arch bridge. However, when concrete is poured, a complex process is required to adjust the loads using cables. Meanwhile, the pre-closed steel tube truss arch experiences serious stress superposition because it must bear the weight of the concrete poured during the subsequent phase. The concrete shrinkage and creep in the later stages also result in additional loads on the steel tube truss arch. Therefore, a stronger steel-tube truss arch is required, further increasing steel consumption and cost. To reduce the expenses associated with temporary facilities, a two-stage arch formation technique was proposed in Ref. [
25] to construct a UHPC box arch bridge with a span of 1000 m. However, the pre-closed arch ring experienced a 35% increase in the maximum compressive stress, and its self-weight in the cantilever state was still too large, resulting in the loss of construction feasibility.
Existing construction methods for other arch bridge types are unsuitable for SUCT arch bridges. Therefore, a more intelligent cyclic construction method is proposed. To solve the problem of stress superposition, an automated sliding connector was proposed to connect different arches [
15,
26]. According to a previous study [
14], when the span is 375 m, the construction cost of an SUCT arch bridge using two closure processes for cyclic construction is equivalent to that of a CFST arch bridge. The proposed method can provide technical support for constructing SUCT arch bridges to improve quality further, reduce cost, and increase span. However, in this method, the load distribution relationship between different arches during cyclic construction remains unknown, and the relative advantages mentioned above have not been validated. To bridge this knowledge gap, the load distribution relationship between different arches of SUCT arch bridges was experimentally investigated in this study.
First, the cyclic construction method is briefly introduced and compared with the existing construction methods. A static test was also performed on an SUCT arch-ring specimen using the cyclic construction method. The mechanical behavior and load distribution relationship of the arch ring during the cyclic construction were studied when sliding connectors were in the slidable and locked states, respectively. Furthermore, a comparative analysis was conducted. Finally, an optimized design for the sliding connectors was developed based on the experimental results.
2. Brief introduction to the cyclic construction method
The cyclic construction method can be divided into six stages, as shown in
Fig. 2.
Stage 1: The inner arch was divided into several segments for prefabrication, which were then assembled in the cantilever state using temporary cables (
Fig. 2(a)).
Stage 2: The cables were loosened stepwise once the inner arch was closed. After the deformation was complete, the inner arch could bear the loads alone, and the cables were removed (
Fig. 2(b)).
Stage 3: The cables removed from the inner arch were moved to the outer arch, which was constructed using the same method. The sliding connectors were divided into two parts to connect to the UHPC chords of different arches (
Fig. 2(c)). While installing an outer arch, it is essential to ensure that the two parts are in contact to provide lateral support for the outer arch.
Stage 4: The two parts of the sliding connector can slide relative to the contact surface to release the displacement of the outer arch and ensure that no apparent stress superposition occurs in the inner arch (
Fig. 2(d)). Once the outer arch is closed, the cables are loosened stepwise, and the outer arch slides down along the contact plane. In this case, the inner arch exhibited minimal deformation.
Stage 5: The sliding connectors are fixed after the sliding is completed. All arches function as a unified structure supporting the loads, and the cables are removed (
Fig. 2(e)).
Stage 6: The above processes are repeated until the entire arch ring is completed, and the structures above the arch are constructed (
Fig. 2(f)). Compared with full-section construction, the temporary facilities only need to bear smaller loads when the cyclic construction method is adopted. The cables are reused, significantly reducing the construction cost and carbon emissions, thus ensuring the construction feasibility of SUCT arch bridges.
Compared with the construction of CFST and SRC arch rings, the construction of SUCT arch rings has the following characteristics: ① It is a prefabricated assembly construction that does not require on-site large-volume UHPC pouring. Therefore, the complex process of adjusting the loads using cables is not required, and the quality of the UHPC is easily guaranteed. ② The pre-closed arch rings did not exhibit significant stress superposition. ③ The weight of the truss arch with a single closure is approximately 1/n of the total weight of the arch ring (n is the number of cycles), equivalent to the weight of a steel tube truss arch. ④ The construction costs were essentially the same.
Compared with the construction of steel arch rings, the construction of SUCT arch rings has the following characteristics: ① There is no need to weld between segments, which can reduce the cost. ② The weight of the truss arch with single closure is approximately 50% of that of the steel truss arch and approximately 40% of the steel box arch, significantly reducing the construction cost and installation risk.
Overall, the cyclic construction method has certain advantages over the existing construction methods, making it possible to achieve the technical scheme of SUCT arch bridges using conventional construction techniques and equipment.
3. Experimental program
As SUCT arch bridges have not yet been practically used, this study refers to the trial-designed 1000 m level SUCT arch bridge documented in Ref. [
15] as the research benchmark. Due to experimental constraints, strict scaling down would result in an excessively small-scale ratio, making the specimen fabrication extremely difficult. Moreover, such an undersized scaling ratio can compromise the authenticity of the experimental results. Therefore, this specimen did not constitute a standard scaled-down model. Authenticity was ensured by maintaining consistency in the key parameters between the specimen and reference prototype, manifested explicitly in two aspects. At the design level, our research team’s recent study has shown that the main factors affecting the arch ring’s mechanical response and load distribution relationship during cyclic construction are the inclination angles of both the truss arch and sliding surface, as well as the friction coefficient of the sliding system. Therefore, these three parameters and the rise–span ratio were guaranteed the same as those of the reference prototype. At the loading level, the loading method conformed to the construction process of an actual bridge.
3.1. Details of the specimen
The specimen was a SUCT arch ring of equal height and variable width. The calculated span was 16 m, and the rise–span ratio was 1/6. The arch axis follows a quadratic parabolic curve. With reference to several existing CFST truss arch bridges, the section height was taken as 480 mm with a height–span ratio of 1/33.33. The section width gradually increased from 1286 mm at the crown to 2225 mm during spring. To effectively limit the concrete slabs and thrust forces during loading within a suitable range, and considering the convenience of pouring, a reinforced UHPC square solid section with a side length of 75 mm was adopted for both the upper and lower chords, connected by N-shaped truss steel web members to form a single truss arch. The steel bars in the UHPC chords had diameters of 6 mm. Four truss arches were provided in the lateral direction, each inclined inward at 10.3°. The inner pair of truss arches was interconnected with lateral braces, forming a structural unit called the inner arch. This inner arch was then connected to two outer truss arches (collectively termed the outer arch) via 60 sliding connectors, completing the assembly of the entire arch ring. To minimize the welding volume and mitigate deformation, lateral braces and web members were fabricated from C-channel steel with a height of 50 mm, flange width of 37 mm, and web thickness of 4.5 mm or flange thickness of 7 mm (designated as C50 mm × 37 mm × 4.5/7 mm). Steel columns were arranged at the K-joints formed by the connection between the upper chords and web members to place the spreading beams for loading. The details and dimensions of the specimens are shown in
Fig. 3.
For the K-joints, three or four steel plates were placed around the chords and welded together. The studs with a diameter φ of 13 mm and a height of 35 mm (φ13 mm × 35 mm) were set on the steel plates to connect to the UHPC, and the steel plates were directly welded to the web members. The truss arch is severed at the crown and divided into two segments for fabrication. Four steel joints were arranged at the crown and connected to UHPC using studs. These steel joints were welded directly during closure operations. Enlarged UHPC pedestals were placed in a spring and poured with the UHPC arch ribs to ensure their integrity. The steel bars in the UHPC arch ribs were extended to a certain length into the pedestals to ensure sufficient anchoring strength. The bottom of the pedestals was arranged with steel plates and studs, which were directly welded to the abutment when the truss arches were installed. The abutments were anchored using bolts, and two-tie beams were set up for the connection.
The designed sliding connector consisted of five parts (
Fig. 4): Brace #1, sliding plate, chute, Brace #2, and Brace #3. The contact surfaces between the sliding plate and chute were left untreated to preserve their original coefficient of friction. Brace #1 was welded to the inner arch after welding with a sliding plate, and Brace #3 was welded to the outer arch. Brace #2 was welded to the chute and placed inside Brace #3 for assembly into a sleeve, an optimized scheme based on the sliding connector proposed in Ref. [
15]. When the outer arch is installed, under the influence of factors such as fabrication errors and deformation of the truss arches, the chute and sliding plate cannot be in perfect contact but rather are in a state with gaps or positional conflicts, which prevents the sliding connector from working properly. In this case, each sliding connector can be in contact before sliding using the sleeve structure for transverse adjustment. Subsequently, the sleeve structure is locked to support the outer arch permanently. The angle of the sliding system was set to 10.3° to ensure that the outer arch slid almost in its plane. To ensure that the outer arch could slide freely, longitudinal gaps of 15 mm were reserved at both ends, a transverse gap of 10 mm was allocated, and sufficient sliding allowance was maintained in the primary sliding direction.
3.2. Test setup, loading, and measurements
The dead load (self-weight) plays a leading role in a super-long-span arch bridge. Applying multiple uniformly distributed vertical concentrated loads is a common method for simulating dead loads [
12]. In this experiment, nineteen loading points with intervals of 800 mm were arranged to simulate the dead load of the 1000 m level arch ring. Moreover, two sets of independent lever systems were used to apply loads to the arch ring to simulate the cyclic construction, as shown in
Fig. 5. According to the principle of stress equivalence, an amplification factor of 10 was adopted for the lever systems to achieve the level of high compressive stress in the 1000 m level arch ring (i.e., the maximum compressive stress in the UHPC chords is approximately 40 MPa [
15]) and to control the number of concrete slabs within a reasonable range. The levers were anchored to the tie and spread beams above the steel columns using four screws. At the loading end, concrete slabs with a single mass of 30 kg were placed block-by-block symmetrically from the crown to the spring to simulate gradually loosening the cables. Six reaction beams anchored in the trench were installed to prevent excessive deformation of the tie beams under multiple concentrated loads.
When the inner arch was loaded (
Fig. 5(a)), as shown in
Fig. 2(b), the lateral braces did not produce a transverse displacement. Therefore, spreading beams and columns were welded to prevent slippage. The inner arch was loaded with nine concrete slabs, and the target compressive stress level was achieved by considering the loading devices and self-weight. When the outer arch after closure was loaded (
Fig. 5(b)), corresponding to
Fig. 2(d), two hinge supports were added between the columns and spreading beams to avoid limiting the transverse displacement of the outer arch. The outer arch was loaded with up to 11 concrete slabs to increase the sliding distance, and then two concrete slabs were unloaded to be consistent with the inner arch. Finally, to compare the mechanical response of the arch ring during sliding, all sliding connectors were welded and locked, and two concrete slabs were loaded on the outer arch.
Under load
F of the concrete slabs, the response quantities to be monitored include the horizontal displacement at the spring, vertical displacement of the arch ring, strain of the web members, and UHPC chords on the transverse right side, as shown in
Fig. 6. These measurements were obtained using a dial and strain gauges that were symmetrically set in the longitudinal direction. The dial gauges were set at the spring,
L/4, crown, and 3
L/4, where
L is the span. The strain gauges for UHPC were arranged on the upper edge of the upper chords (S-1), lower edge of the upper chords (S-2), upper edge of the lower chords (S-3), and lower edge of the lower chords (S-4) of the left-side sections S1–S12 and right-side sections S1’–S12’. Strain gauges were arranged on the web members (from W-1 to W-3) with relatively large internal forces near the spring. It is noted that the symbols S and W denote the section and web member, respectively, and the numerical indices 1–12 and 1’–12’ indicate numbering assigned to distinct spatial positions. The variables
x,
hi, and
ho denote longitudinal coordinates and vertical displacements of the inner and outer arches.
3.3. Material properties
Two types of steel fibers, hooked and straight, were used in the UHPC. As eccentric compression members, chords are primarily subjected to high compressive stresses, and the tensile-strength requirement of UHPC is low. Therefore, the total volume content of the steel fibers was 2%. The UHPC in the arch ring was poured and steam cured in two batches [
27]. The steel members of the arch ring were Q235 and Q345. Both UHPC and steel were in the elastic stage during the loading process, and UHPC was always under compression. Therefore, the compressive properties of UHPC and the elastic properties of steel were the focus of the material tests.
The compressive strength (cubes and prisms) and elastic modulus of the UHPC were tested according to the corresponding standards [[
27], [
28], [
29]]. The corresponding average values of UHPC in the inner arch (outer arch) are 145.8 MPa (147.9 MPa), 138.1 MPa (138.4 MPa), and 41.5 GPa (43.4 GPa), respectively. According to the corresponding standard [
30], the elastic modulus of the steel is 206 GPa.
4. Results and discussions
This section evaluates the mechanical response and load distribution relationship of the arch ring during cyclic construction in terms of displacements, internal forces, and stresses at two distinct states: slidable (State 1) and locked (State 2). A comparative analysis is also provided.
4.1. Loading on the outer arch (slidable)
State 1: The sliding connectors are in the slidable state, as shown in
Fig. 7.
4.1.1. Displacement response
After loading 11 concrete slabs on the outer arch, the two abutments demonstrated a horizontal relative displacement of 0.29 mm, resulting in a negligible impact on the arch ring. The load–vertical displacement response is shown in
Fig. 8(a). The vertical displacements of the arch ring vary approximately linearly with the load. Moreover, the vertical displacements of the inner arch were significantly smaller than those of the outer arch. None of the sliding connectors experienced jamming problems. Moreover, a comparison of the vertical displacements at the 1/4 and 3/4 spans indicated that the loads exhibited a certain asymmetry in the longitudinal direction. Furthermore, the loads near the 3/4 span of the inner arch significantly exceeded those near the 1/4 span, whereas the outer arch exhibited the reverse pattern.
As the elastic moduli of UHPC in the inner and outer arches are comparable (41.5 and 43.4 GPa, respectively), the ratio of their vertical displacements can be approximated (
Fig. 8(b)). The ratios of the vertical displacements at the 1/4 span, crown, and 3/4 span of the inner arch were 13.59%, 12.37%, and 27.4%, respectively, with an average value of 17.79%. These results indicated that most of the load on the outer arch was borne by it. If the crown displacements are taken as reference, approximately 12% of the load is transferred to the inner arch.
4.1.2. Internal force response
According to the UHPC strains at the upper and lower edges of the chords and the plane section assumption, the strains of the steel bars in the sections can be obtained. The internal forces (axial forces and bending moments) in the chords and total internal forces can be calculated (
Fig. 9(a)). The variables
Nu and
Mu represent the axial forces and bending moments in the upper chord, respectively.
Nl and
Ml denote those in the lower chord, while
Na and
Ma correspond to the total axial forces and bending moments in the chord, respectively. Variable
h denotes the distance between the centerlines of the chords.
Figs. 9(b)–(n) show the distribution and ratio relation of the internal forces along the longitudinal direction. The bending moments that induce tensile stresses at the top fiber of the section are designated as negative. Due to asymmetric loading, the internal forces in the outer arch failed to transition smoothly along the longitudinal direction, particularly in the left half-span.
According to
Figs. 9(b)–(g), the ratios of the axial forces in the chords of the inner arch remained below 20%. Moreover, the ratios of the total axial forces were generally below 10%, with a more uniform distribution. This indicates that the inner arch shared approximately 10% of the load on the outer arch. The greater loads near the 3/4 span caused the axial force ratio in the upper chord to be the largest (19.61%), whereas the corresponding value in the lower chord was the smallest (1.25%). The average axial forces in the upper and lower chords and the average total axial force of the inner arch are −8.1, −13.0, and −21.1 kN, respectively. The corresponding ratios were 7.13%, 10.74%, and 8.99%, respectively, close to the crown deflection ratio (12.37%). The ratio of the lower chord (10.74%) was larger than that of the upper chord (7.13%), indicating that the lower chord bore more load. However, the average axial forces in the upper and lower chords of the outer arch are −105.7 and −108.2 kN, respectively, which are relatively uniform.
According to
Figs. 9(h)–(m), the bending moments in the chords of the outer arch and the corresponding ratios fluctuate significantly along the longitudinal direction. The spring section is often the one with the largest tensile and compressive stresses in the UHPC, namely, the control section. The negative bending moments can further increase the tensile and compressive stresses, leading to more unfavorable effects. Therefore, the ratios of the bending moments in the sections (S1, S2, S1’, and S2’) near the spring are presented and discussed. For the upper chord of the inner arch, the ratios of bending moments are 55.04% (S1), 32.54% (S2), 126.43% (S1’), and 40.95% (S2’), respectively. For the lower chord of the inner arch, the corresponding ratios were 52.96% (S1), 603.8% (S2), 23.16% (S1’) and 54.62% (S2’). For the total bending moments of the inner arch, the corresponding ratios are 22.18% (S1), 28.19% (S2), 31.11% (S1’), and 30.57% (S2’). The inner arch near the spring shared approximately 25.5% of the bending moments, significantly larger than the ratios of the axial forces, as shown in
Fig. 9(n). This is unfavorable for the mechanical performance of the inner arch, which indicates that it is the weakest link in the arch ring.
4.1.3. Stress response
Figs. 10(a)–(h) illustrate the distribution and ratio relation of the stresses in the UHPC chords at various positions (S-1–S-4). Similarly, the UHPC stresses in the outer arch exhibited large fluctuations, particularly in the left half-span at S-2 to S-4. The ratios of the stresses at S-1–S-4 of the inner arch were generally within 20%, and the fluctuations were relatively small. The greater loads near the 3/4 span increase the compressive stresses (−4.3 and −3.5 MPa) and corresponding ratios (22.63% and 16.72%) at S-1 and S-2 significantly. However, S-3 and S-4 demonstrate lower values (−0.6 and 0.2 MPa, 4.06% and −1.65%). For the control sections (S1 and S1’) at the spring, due to the relatively large negative bending moments shared by the upper and lower chords of the inner arch, the compressive stresses (−2.1 and −8.1 MPa) and corresponding ratios (17.25% and 20.88%) at S-2 and S-4 increase significantly. However, S-1 and S-3 demonstrate lower values (3.0 and −1.7 MPa, −109.47% and 6.46%). For the spring sections, the tensile stress increments at S-1 and compressive stress increments at S-4 were relatively small, with no cracks or crushing. However, this phenomenon increases the risk of cracking and crushing the arch ring during long-term service, compromising both the crack resistance and bearing capacity.
The average stresses at S-1–S-4 of the inner arch are −1.1, −1.6, −2.0, and −2.3 MPa, respectively. The corresponding ratios were 5.68%, 8.47%, 9.68%, and 11.79%, indicating a progressive increase. This trend further indicates that the lower chord bore more load and that the compressive stress ratio at S-4 was the largest. However, the average stresses at S-1–S-4 of the outer arch are −17.5, −17.5, −18.7, and −17.1 MPa, respectively, which are relatively uniform.
Figs. 10(i) and
(j) show the distribution (envelope diagram) and ratio relation of the maximum compressive stresses
Smax at S-1–S-4 for all the sections along the longitudinal direction. The inner arch’s maximum compressive stress and corresponding ratio are −8.1 MPa (S-4) and 20.88% at the spring. The compressive stress (−4.3 MPa) and corresponding ratio (19.95%) near the 3/4 span also increase significantly. The compressive stresses and their corresponding ratios at the left half-span of the outer arch were greater with more intense fluctuations. The maximum compressive stress is −35.9 MPa (S3-3, the upper edge of the lower chord of the S3 section).
The average stresses of the inner and outer arches were −3.3 and −24.8 MPa, respectively. The corresponding ratios are 11.90% and 88.10%, respectively. According to
Fig. 10(k), in the inner arch, both the ratios of average stress at S-1–S-4 and the ratios of average stress at maximum compressive stress
Smax are less than 12% (5.7%–11.9%), which are very close to the ratios of the crown deflection (12.37%) and axial forces (7.13%–10.74%), indicating that the loads allocated to the inner arch are relatively small.
Fig. 11 shows the load–stress response and ratio relationship of the steel web members. The variation in the stresses in the web members was approximately linear with the load. When
N = 11, the stresses at W-1–W-3 of the outer arch are −31.6, 25.1, and −30.9 MPa, respectively. Stress levels were relatively low. The stresses at W-1–W-3 of the inner arch are −7.0, 3.0, and −5.9 MPa, respectively. The corresponding ratios were 18.13%, 10.68%, and 16.03%, with an average of 14.95%; these values were also close to the ratios of the stresses at S-1–S-4 and
Smax.
4.2. Loading on the outer arch (locked)—Comparative analysis
State 2: The upper and lower ends of the sliding connectors were welded and locked, as shown in
Fig. 12.
4.2.1. Comparison of displacement
Fig. 13 shows a comparison of the ratios of the crown deflections between States 1 and 2. As shown in
Fig. 13, under State 1, the crown deflections (ratios) of the inner and outer arches are 0.26 mm (11.71%) and 1.96 mm (88.29%), respectively. Under State 2, the corresponding values are 0.72 mm (48.32%) and 0.77 mm (51.68%).
4.2.2. Comparison of internal force
Fig. 14 shows the internal force responses of the inner and outer arches in different states. According to
Figs. 14(a)–(g), under State 1, the average axial forces in the upper and lower chords and the average total axial force of the inner arch are −0.9, −2.0, and −3.0 kN, respectively. The corresponding ratios are 4.64%, 9.13%, and 6.98%, respectively. Under State 2, the corresponding average values are −7, −8, and −15 kN. Moreover, the ratios are 45.38%, 45.05%, and 45.20%, respectively.
Because the truss arches at the left and right half-spans of the bridge have the same formwork, the loads (self-weights) on both sides are symmetrical. Therefore, the average bending moments in the spring sections (S1 and S1’) on both sides are taken for comparison and explanation. According to
Figs. 14(h)–(k), under State 1, the bending moments in the upper and lower chords and the total bending moment of the inner arch are −32.7 N·m, −40 N·m, and −1.27 kN·m, respectively. The corresponding ratios are 63%, 34%, and 25%, respectively. Under State 2, the corresponding values are −40 N·m, −44.1 N·m, and −1.99 kN·m, and the corresponding ratios are 40%, 37%, and 48%.
4.2.3. Comparison of stress
Figs. 15(a)–(k) compare the stresses in UHPC under different states and their corresponding stress ratios. Under State 1, the average stresses at S-1–S-4 and
Smax of the inner arch are −0.1, −0.2, −0.3, −0.4, and −0.5 MPa, respectively. The corresponding ratios are 2.83%, 6.34%, 7.81%, 10.36%, and 10.66%. Under State 2, the corresponding average values are −1.1, −1.2, −1.4, −1.3, and −1.8 MPa, and the ratios are 46.43%, 44.31%, 46.51%, 43.39%, and 45.58%.
Fig. 15(l) compares the stresses in the web members under different states. Under State 1, the stresses at W-1–W-3 of the inner arch are −1.3, 0.7, and −0.8 MPa, respectively. The corresponding ratios were 18.31%, 13.73%, and 12.9%, respectively. Under State 2, the corresponding values are −3.1, 2.1, and −2.2 MPa, and the corresponding ratios were 47.69%, 48.84%, and 38.6%, respectively.
4.2.4. Discussion
In State 2, the responses of the displacements, internal forces (axial forces and bending moments), and stresses in the inner and outer arches are very similar, indicating that the 60 locked sliding connectors can effectively transmit the loads to the inner arch. Because the outer arch directly bears loads, its crown deflection, internal forces, and stresses are slightly greater than those of the inner arch, accounting for approximately 55%. However, the ratios of the crown deflection, axial forces, and stresses in the inner arch were approximately 10% in State 1. The ratios of the negative bending moments in the spring were relatively large (approximately 25.5%).
Fig. 16 shows a response comparison of the total internal forces and stresses in the arch ring (inner arch + outer arch) under different states. Among them, the total stress was the sum of the UHPC stresses in the inner and outer arches of the envelope diagram (
Fig. 15(i)). In States 1 and 2, the responses of the total internal forces and stresses followed the same variation trends and characteristics. Under State 2, the average total bending moment at the spring on both sides is −4.17 kN·m, 83.07% of that under State 1 (−5.02 kN·m). The average total axial force and total stress are −33.2 kN and −3.9 MPa, respectively, 78.12% and 75% of those under State 1 (−42.5 kN and −5.2 MPa). Moreover, the total crown deflection of the arch ring was 1.49 mm, which was 67.12% of that in State 1 (2.22 mm). These results indicate that the external loads applied to the arch ring in State 2 were approximately 75% of those in State 1. Specifically, the applied external loads in States 1 and 2 exhibit certain fluctuations.
The inner arch exhibits a certain superposition effect, acting as a weak link in the entire arch ring, and is one of the key factors influencing structural mechanical performance.
Figs. 17(a)–(c) show the ratios of the total internal forces and compressive stresses of UHPC
Smax in the inner arch in State 1 to the corresponding values in State 2.
Fig. 17(d) shows the contribution ratios of the axial forces and bending moments to the compressive stresses of UHPC
Smax under States 1 and 2. For sections S1 and S2, the total axial forces in State 1 were only 15.05% and 10.29% of those in State 2, respectively. However, the compressive stresses in State 1 were 68.39% and 53.11% of those in State 2, and the ratios were relatively large. This is mainly because the negative bending moments in State 1 are 100% and 139.67% of those in State 2, respectively, with very large ratios that are completely different from those in Sections S1’ and S2’. According to
Fig. 17(d), the relatively large negative bending moments in State 1 further increase the compressive stresses, and the contribution ratios reach 46.93% and 28.31%, respectively. However, the corresponding values in State 2 were only 0.48% and 1.26%, respectively. For sections S1’ and S2’, the contribution ratios of the negative bending moments to the compressive stresses under States 1 and 2 were similar.
As shown in
Fig. 17(e), under the premise that the loads in State 2 were approximately 75% of those in State 1, the average values of the total axial forces and
Smax in the inner arch in State 1 were only 20% and 31%, respectively, of those in State 2. The stresses at W-1–W-3 in State 1 were 42%, 35%, and 38%, respectively, of those in State 2. Moreover, the crown deflection (0.26 mm) of the inner arch in State 1 was 36% of that in State 2 (0.72 mm). Using sliding connectors (slidable) can significantly reduce the superposition of displacements, internal forces, and stresses caused by the truss arches in the subsequent construction stage compared with those completed in the previous stage.
When only one inner arch was present, two concrete slabs were placed. In this case, the average value of the maximum compressive stresses at the spring on both sides is −6.4 MPa. Under State 1, the compressive stress increases by only 20.06% (−1.3 MPa). However, under State 2, the compressive stress increases by 43.08% (−2.8 MPa). In a practical arch ring, if the different arches are rigidly connected (State 2), the inner arch must be made very strong, which is not a cost-effective solution. In particular, the cost of temporary facilities increases significantly, thereby reducing the feasibility of construction. The use of sliding connectors can solve this problem.
5. Optimized design
According to the above analysis, in State 2, approximately 45% of the load was transferred to the inner arch. However, in State 1, only approximately 10% of the loads were transferred, accounting for only approximately 20% of those in State 2. However, approximately 25.5% of the negative bending moments in the spring are transferred to the inner arch, and this ratio is slightly higher. The outer arch transferred relatively large transverse loads and small vertical loads to the inner arch via sliding connectors, thereby fully verifying the feasibility of the cyclic construction method.
However, a certain vertical load was transferred to the inner arch. Under State 1 (
N = 11), the maximum tensile and compressive stresses (3.0 and −8.1 MPa) are generated at the left spring. The relatively large negative bending moments obviously influenced the maximum tensile and compressive stresses, and the contribution ratios reached 84.26% and 39.36%, respectively, thus increasing the risk of cracking and crushing during the spring. Therefore, during the later asymmetric loading process of the arch ring, the left spring of the inner arch cracked and crushed before that of the outer arch, as shown in
Fig. 18. Moreover, because the contact force transfer states of each sliding connector are not entirely identical, the loads transferred to the inner arch may exhibit an asymmetry that is difficult to control and quantify. All these issues must be considered in the subsequent optimization of the sliding connectors.
In State 1, the inner and outer sliding connectors can slide relatively easily. The loads transferred to the inner arch are normal force
Fn and friction
Ff. The resultant forces are
Fx in the transverse direction and
Fz in the vertical direction, respectively, as shown in
Fig. 19(a).
Fz causes stress superposition in the inner arch. Compared with State 2, the relative sliding of the sliding connector can release most of the vertical shear force
Fz and bending moment
My generated by
Fz. To further reduce the vertical component
Fz, lubricating the sliding plate and chute to reduce the friction coefficient is recommended, thereby reducing the stress superposition caused by the friction
Ff. However, regardless of the inclined angle of the truss arches, it is recommended to set the sliding surface to a vertical state (0°), as shown in
Fig. 19(b), further reducing the stress superposition caused by the normal force
Fn.
For the optimized scheme, it can be realized that the outer arch does not transfer the vertical load to the inner arch, but only transfers the transverse load, as shown in
Fig. 20(a). In this case, almost no stress superposition and no relatively large adverse negative bending moment are generated in the spring, which can further improve the crack resistance and bearing capacity of the arch ring. Moreover, the stresses in the different arches are almost the same, and the problem of load asymmetry transferred to the inner arch can be solved entirely. This is the direction for further evolution of sliding connectors in the next phase.
When a vertical sliding surface is adopted for the sliding connectors, the outer arch does not produce a transverse displacement during the sliding process. This differs from the case in which an inclined sliding surface is adopted. When connected by lateral braces, the inner arch hardly produces a transverse displacement during the deformation process. Therefore, the outer arch after the deformation was almost parallel to the inner arch, and both were approximately at the same height, as shown in
Fig. 20(b). It should be noted that, like the inner arch, the outer arch also undergoes a slight out-of-plane deformation due to the absence of lateral displacement. Specifically, the outer arch will rotate by a small angle (
θ) about the spring, and this deformation will be slightly larger compared to the case with the inclined sliding surface. This resulted in additional bending moments in the spring. However, the additional bending moments induced by the slight out-of-plane deformation were very small, and the compressive stress reserves at the spring were sufficiently large, thereby eliminating the risk of cracking. Moreover, no cracks were observed in the spring of the inner arch during the experiment, thereby confirming the feasibility of the optimized scheme.
When the arch ring has 8 truss arches in the transverse direction, such as the 1000 m level SUCT arch bridge [
15],
Fig. 21 compares the load distribution relationship of each truss arch under the three schemes (no sliding connectors, current design, and optimized design). When the sliding connector was not employed, the load borne by the innermost arch increased by 108%, with a highly uneven load distribution among the truss arch rows. When the current design was adopted, the load borne by the innermost arch increased by only 18%, and the loads borne by each row of the truss arches tended to be uniform. When using the optimized design, the loads borne by each row of truss arches were almost equal, which is the ideal state. Generally, a sliding connector is an indispensable device for cyclic construction and must be continuously optimized.
In summary, the experimental results demonstrated good applicability to practical engineering. However, the complex mechanical behavior and uncertainties of practical bridges in real-world environments cannot be fully replicated in laboratory tests, which is one of the limitations of this study. Therefore, when conditions permit, mutual verification between research findings and practical applications is highly recommended. In the future, the working mechanism of the sliding connectors will be further studied to propose a design method. The load transfer mechanism of the sliding connectors and the stress superposition law of the inner arch during the sliding process will be studied further. The proposed optimized scheme is examined in detail in combination with numerical analysis, and parameter analysis is performed on multiple schemes with different sliding surface inclination angles to capture their influence law. Another research topic is the mechanical performance of the arch ring after completing cyclic construction. Moreover, for super-long-span practical bridges, the displacement of the arch ring increases significantly. The configuration of the sliding connectors must be further optimized to lay a foundation for promoting the construction of SUCT arch bridges.
6. Conclusions
This paper briefly introduces and compares a cyclic construction method with existing construction methods. Through an experimental investigation, the mechanical response and load distribution relationship of the arch ring during cyclic construction were discussed. An optimized design for sliding connectors was also developed. The main conclusions are as follows:
(1) Using the cyclic construction method, the weight of the truss arch with a single closure was approximately 1/n of the total weight of the arch ring, which can provide technical support for the construction of SUCT arch bridges to improve quality further, reduce cost, and increase span.
(2) In State 1, when the sliding connector was in the slidable state, the ratios of the crown deflections, axial forces, and stresses in the inner arch were all approximately 10%. Only the ratios of the negative bending moments in the spring were relatively large, approximately 25.5%. In State 2, when the sliding connector is in the locked state, the responses of the displacements, internal forces, and stresses in the different arches exhibit a close alignment, indicating that the 60 locked sliding connectors can effectively transfer loads to the inner arch.
(3) In State 1, the sliding connectors released most vertical shear forces, and the corresponding bending moments were transferred to the inner arch. Consequently, only approximately 10% of the loads were transferred to the inner arch, representing approximately 20% of those in State 2.
(4) Under State 1 (N = 11), the maximum tensile and compressive stresses in the inner arch are 3.0 and −8.1 MPa (20.88% of the ratio) at the spring, and the contribution ratios of the relatively large negative bending moments at the spring to them are 84.26% and 39.36%, respectively. Therefore, during the later asymmetric loading process of the arch ring, the left spring of the inner arch cracked first and was crushed before the outer arch.
(5) By optimizing the sliding surface to a vertical state (0°) and lubricating the sliding plate and chute, the negative bending moments at the spring and vertical loads were not transferred to the inner arch, and no stress superposition was expected, which further improved the crack resistance and bearing capacity of the arch ring.
(6) When employing the optimized design, the load borne by the innermost arch was reduced to 48% and 85% of those under the non-sliding connector scheme and current design, respectively. Furthermore, the load distribution across all truss arch rows tended to be uniform.
CRediT authorship contribution statement
Guang He: Writing – review & editing, Writing – original draft, Validation, Methodology, Investigation, Conceptualization. Xudong Shao: Methodology, Investigation, Conceptualization. Suiwen Wu: Visualization, Investigation. Junhui Cao: Resources, Investigation. Xudong Zhao: Methodology, Investigation, Conceptualization. Wenyong Cai: Writing – review & editing, Investigation.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors gratefully acknowledge the support of the National Natural Science Foundation of China (52250004) and the Postgraduate Scientific Research Innovation Project of Hunan Province (CX20220379).
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