Research on the Safety and Stability Evaluation for a New Type of Prefabricated Aqueduct in the Construction Stage

Abstract

To address the issue of regional water resource scarcity, water diversion projects have been constructed worldwide. As an essential lifeline project, the prefabricated aqueduct is prevalently utilized in cross-regional water transfer and diversion projects. This paper was based on the prefabricated aqueduct project, which adopted fabricated technologies including the connection technology among the gravity pier, the prefabricated arch ribs, and the prefabricated bent frame columns. The PHC piles, bearing platforms, bent frame columns, arch ribs, and groove bodies were all prefabricated components that were transported to the site for installation. The connections of the prefabricated aqueduct employed to link different components were of such crucial significance that their safety and stability determined whether the overall structure would be compromised. Therefore, the main objective of this paper was to examine the stress and deformation of this prefabricated aqueduct to prevent the occurrence of security risks throughout the entire construction stage. The finite element model was established in Midas Civil, and the entire construction stage was simulated and analyzed. Coupled with on-site monitoring, the stress and deformation of the prefabricated aqueduct were evaluated. The results indicated that the tensile stress, the compressive stress, the vertical displacement, and the lateral displacement of each part of the prefabricated aqueduct met the requirements of the standard, suggesting that the overall structure with the applied connection technology was in a safe and stable state throughout the entire construction stage.

1. Introduction

Chinese per capita water resources are deficient. The overall distribution of water resources in China exhibits spatial characteristics of greater abundance in the east and scarcity in the west, and more in the south and less in the north, as well as temporal characteristics of greater volume in summer and autumn and less in spring and winter [1,2]. To alleviate the shortage of water resources in certain parts of China, numerous inter-basin water transfer projects have been constructed, such as the project of diverting water from the Yellow River to Qingdao, the project of diverting water from the Luan River to Tianjin, the project of diverting water from the Yellow River to Shanxi, and the South-to-North Water Diversion Project. The construction of the aforementioned projects has been completed and successfully implemented, which has significantly alleviated the problem of regional water resource shortage, safeguarded people’s livelihoods, and promoted economic development [3,4].

Various types of water conveyance structures, such as aqueducts, inverted siphons, pumping stations, and channels, constitute a complex water conveyance system. Among them, aqueducts, as an important type of hydraulic structure capable of crossing rivers, canyons, highways, and other obstacles, have been widely employed in water conservancy projects. Furthermore, aqueducts have profound significance for water conveyance, flood discharge, and diversion. Yang [5] utilized the numerical simulation method to compare and analyze the displacement, maximum principal stress, and maximum tensile strain in each direction of the aqueduct under three distinct working conditions. Simultaneously, Yang scored various indicators of the aqueduct through the AHP-entropy weight method and fuzzy comprehensive analysis method and established the safety level of the aqueduct based on the final scores obtained by the aqueduct, and from this, conducted a reasonable evaluation of the safety of the aqueduct. Gan et al. [6,7,8] employed Abaqus CAE 2019 software to establish a three-dimensional finite element calculation model and combined it with the homogenization theory to analyze the influence of stress, displacement, settlement, and other factors on the aqueduct structure, and then they comprehensively evaluated the structural safety performance of the aqueduct. Luo et al. [9,10,11] optimized the fuzzy comprehensive evaluation method, synthesized the subjective and objective weights, and introduced the all-optimal synthesis operator to calculate the overall objective membership degree, and then they weighted and synthesized the corresponding risk level to obtain the risk degree, thereby determining the safety category of the aqueduct. Zhao [12,13,14] established a kernel extreme learning machine (KELM) safety monitoring model for aqueducts and further proposed a method for evaluating the working performance of aqueducts based on the cloud model and information fusion to achieve an objective and comprehensive assessment of the overall working condition of aqueducts in response to the problem that the single-point monitoring model can only analyze the local structure of aqueducts. Zhang et al. [15,16,17] adopted the Arbitrary Lagrangian–Eulerian (ALE) technique, considering water depth as a variable parameter, to examine the dynamic behavior of the aqueduct under the combined effects of earthquake and wind loading and revealed that an increase in water depth leads to a corresponding increase in the maximum transversal displacement. Wu et al. [18,19,20] established a refined calculation model, incorporating nonlinear factors, to analyze the dynamic behavior and collapse sequence of the aqueduct and proposed a criterion for assessing the overall instability and malfunction of the aqueduct structure based on effective energy considerations. In conclusion, some researchers have conducted extensive studies on different structural forms of aqueducts. The results indicated that the connection among the various components of the aqueduct played a crucial role in the overall safety and stability of the structure, and it was essential to ensure the reliability of the connections when designing the structure. Meanwhile, the size of the main load-bearing components should be rationally planned to meet the requirements of load-bearing capacity and stability, while taking into account the economic design and the feasibility of construction. These findings provided a valuable idea for the structural design of the prefabricated aqueduct in this article. However, previous studies mainly focused on monitoring and evaluating the working performance of the groove body during the serviceability stage to avoid safety accidents, and there is a lack of research on the deformation and stress monitoring of the bent frame column or the arch rib, which are important parts of the aqueduct during the construction stage.

Reinforced concrete was extensively employed in large-scale water transmission projects, particularly for aqueduct structures. The traditional construction procedure of aqueduct structures entails on-site mold casting, which consumes a considerable amount of labor and material resources and is constrained by the environment and climate. With the concept of sustainable development and green environmental protection being put forward, prefabricated construction technology has been widely adopted in aqueduct construction and hydraulic engineering. This paper was based on a prefabricated aqueduct project that utilized fabricated technology, meaning that PHC piles, bearing platforms, bent frame columns, arch ribs, and groove bodies were all prefabricated and assembled components. The innovation of the project was the application of fabricated technology, including the connection technology among the gravity pier, the prefabricated arch ribs, and the prefabricated bent frame columns, as well as the connection technology of two-piece prefabricated arch ribs. Especially for the connection at the vault of the prefabricated arch, it played a crucial role in the mechanical properties of the prefabricated aqueduct during the construction stage. When the two prefabricated arch ribs were hoisted and connected by embedded parts, the entire arch was three-hinged. When reactive powder concrete was poured at the connection, the entire arch became hingeless. Since we studied the safety and stability of the aqueduct in the construction stage rather than the serviceability stage, we only considered the effects of structural self-weight and temperature stress, without taking into account the effects of water load, wind load, earthquake load, and other loads. According to the Chinese code “Code for Design of Concrete Structures” [21] and other related references, the bearing capacity and deformation are significant indicators for evaluating the safety and stability of concrete structures. In the subsequent parts of the paper, numerical simulation and on-site monitoring were carried out to investigate the maximum compressive stress, the maximum tensile stress, and the deformation in each direction of the components under different construction steps to verify the safety and stability of the prefabricated aqueduct.

2. Background Information

2.1. Project Overview

The groove body adopted the combination of a straight-line simply supported reinforced concrete girder aqueduct and an arch bent aqueduct, as depicted in Figure 1 and Figure 2. The groove body encompassed a total of 28 spans, and the structure was U-shaped. The length of the groove body was categorized into three types: 15 m, 6 m, and 8 m. From upstream to downstream, the aqueduct consisted of 10 spans of 15 m simply supported, 3 spans of 38 m arch section, 1 span of 6 m simply supported, and 2 spans of 15 m simply supported. The river-crossing aqueducts were composed of three arches, with each arch being 15 m continuous beam, 8 m simply supported beam, and 15 m continuous beam, respectively. The shell thickness of the groove body was 20 cm, and the bottom thickness was 30 cm. The lower support structure adopted two equal-section quadratic parabolic three-hinged arches. The net span of the arch rib was 36.5 m, the vector height was 9 m, the width was 0.5 m, and the thickness was 0.8 m. The cross-section size of the bent frame columns was 0.5 m × 0.6 m. The groove bodies and the arch ribs were fabricated from C50 concrete, the bent frame columns and the gravity piers were made of C40 concrete, the stress rebars and distribution rebars were made of HRB400, the stirrup was made of HPB300, and the embedded parts of the support and arch rib were composed of Q235 steel.

2.2. The Connection Technology of the Assembled Aqueduct Structure

In accordance with the requirements of the project duration, geological conditions, and other factors, a novel scheme of assembly technology was applied to this project. PHC piles, bearing platforms, bent frame columns, arch ribs, and groove bodies were all prefabricated and assembled components. This scheme presented the following advantages:

1. The upper structure adopted the conventional truck crane, which could enhance the efficiency of installation. The prefabricated hoisting and assembly of the river-crossing aqueduct could reduce the erection of high formwork support and mitigate the risk of high-altitude operation.

2. In the case of a large arch rib span, the one-time prefabricated hoisting method was prone to cause the structure to fracture during the hoisting and transportation process due to insufficient structural stress. To address this issue, the safety and stability of the structure could be guaranteed by prefabricating and hoisting the two arch ribs separately. At the design stage, it was determined through accurate calculation that during the installation process, the two arch ribs did not form a whole, and the stress state was a three-hinged arch; when the two arch ribs were connected into a whole by the embedded parts, the stress state was transformed into a hingeless arch, and the stress met the engineering requirements.

3. The connection method of UHPC concrete and the U-shaped steel bar demonstrated remarkable advantages in reducing the connection length, simplifying the construction process, and enhancing the construction efficiency.

2.2.1. The Connection Technology of Two Piece Prefabricated Arch Ribs

Two prefabricated arch ribs were reserved with embedded parts, facilitating easy assembly. Throughout the entire construction process, the connection of the vault consistently remained an axial compression member. The thickness of the embedded parts and the area of the most unfavorable section were substantial, thereby ensuring the strength and stability of the connection with ease, which was of crucial significance to the safety of the prefabricated aqueduct. The connection diagram is presented in Figure 3. The positioning plate in part 7 played an excellent role in fixing and supporting the connection. When the two prefabricated arch ribs were hoisted and connected by embedded parts, the entire arch was three-hinged. When reactive powder concrete was poured at the connection, the entire arch became hingeless. Reactive powder concrete possessed good compactness, which could form a favorable gripping effect on steel bars and significantly reduce the anchorage length required for steel bars.

2.2.2. The Connection Technology Among the Gravity Pier, the Prefabricated Arch Ribs, and the Prefabricated Bent Frame Columns

The bent frame columns, arch ribs, and groove bodies were all prefabricated components and were transported to the site for installation. The arch foot and the end of the bent column were reserved with embedded parts that could be utilized to connect different components. Subsequently, UHPC concrete and U-shaped steel bars were added to enhance the stiffness and bearing capacity of the connection. The connection diagram of each component of the prefabricated aqueduct are shown in Figure 4. The connection between the gravity pier and the arch rib was a compression-bending member that might be damaged due to a large bending moment and axial force. Hence, it is necessary to ensure the section strength and overall stability of the connection to meet the design requirements. The connection between the bent frame column and arch rib and the connection between the gravity pier and bent frame column were axial compression members that only undertook the pressure transmitted by the superstructure. There were numerous such connections, and the average load borne by each connection was small. Thus, they basically would not fail during the entire construction stage. The prefabricated socket connection was adopted between the bent frame column and gravity pier, and the insertion length was generally 1.5 times the section size of the bent frame column based on the Chinese specification “Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts” [22]. The shear key was designed for the bent frame column, and the metal bellows were embedded in the hollow part of the cylindrical connection of the gravity pier, so that the gravity pier and the prefabricated bent frame column formed a favorable occlusion connection.

3. Monitoring Program for the Aqueduct

In order to monitor the safety and stability of the aqueduct during the construction process, the embedded vibrating wire sensor and the total station were employed to monitor the stress and deformation of the cross-section of the aqueduct. The embedded vibrating wire sensor boasted high sensitivity and was capable of detecting minute vibrations or deformations. Furthermore, it displayed good long-term stability and was not easily affected by the environment. Taking a span arch aqueduct structure as the research object, the displacement measuring points were mainly distributed in the arch rib, groove body, bent frame column, pier body, and other parts, encompassing elevation monitoring and lateral deviation monitoring. The strain measuring points were mainly distributed in the arch foot, L/2 arch rib, vault, and cross-section of embedded parts. The arrangement of measuring points is shown in Figure 5.

4. Numerical Simulation of the Construction Process

4.1. Construction Step Refinement

According to the actual construction plan, the construction steps were segmented to conduct the mechanical simulation analysis of the construction process. The specific construction steps were segmented as shown in Table 1. According to the installation sequence of the components, it could be divided into three stages: The first stage was the lifting and closure stage of the arch rib, including the construction steps CS1 to CS2. The second stage was the installation stage of the bent frame column, including construction steps CS3 to CS8. The third stage was the erection stage of the groove body, including the construction steps CS9 to CS11.

4.2. Finite Element Model

The basic assumptions in the finite element analysis encompassed the following aspects:

1. The material was presumed to be homogeneous and isotropic, and there was a linear relationship between stress and strain.

2. Simplified boundary conditions were adopted, with the boundary condition between the arch rib and the foundation simplified to a fixed end, and the boundary condition between the bent frame column and the groove bodies to elastic support.

3. The effects of the embedded parts of the connections were ignored to enhance computational efficiency.

A single-span aqueduct was selected for analysis and computation based on Midas Civil 2021 software. The arch rib, bent frame column, and groove body were simulated by beam elements. A total of 210 nodes and 223 elements were divided. The x-axis of the rectangular coordinate system was along the aqueduct direction, the y-axis was in the transverse aqueduct direction, and the z-axis was in the vertically upward direction. The finite element model is shown in Figure 6. The arch foot simultaneously limited the translational degree of freedom and the rotational degree of freedom to simulate the fixed support effect of the pier on the arch rib. Since the prefabricated arch rib was a three-hinge arch during hoisting and installation, and it became a two-hinge arch when cast-in-place concrete was adopted, the beam end constraint was released from the vault after the two prefabricated arch ribs were assembled and closed.

The prefabricated groove bodies and prefabricated arch ribs were fabricated from C50 concrete, the bent frame columns were made of C40 concrete, and the embedded parts were composed of Q235 steel. The material properties of steel referred to the Chinese code “Standard for Design of Steel Structures” [23], and the material properties of concrete referred to the Chinese code “Code for Design of Concrete Structures” [21]. The mechanical parameters of materials are shown in Table 2.

The calculated loads in the construction stage mainly encompassed the structural self-weight, the demolding load, and the lifting impact load. The bulk density of concrete was 26 kN/m³. The demolding load refers to the bonding force between the concrete member and the formwork during demolding. The demolding coefficient was 1.2, and the lifting impact coefficient was 1.2. Considering the internal force caused by non-uniform changes, the temperature effect was calculated in accordance with the temperature calculation mode based on the Chinese code “General Code for Design of Highway Bridges and Culverts” [24].

5. Results and Discussion

5.1. Analysis of Finite Element Calculation

5.1.1. The Hoisting and Closing Stage of the Prefabricated Arch Ribs

The construction step CS0 to CS1 pertained to the hoisting and closing stage of the prefabricated arch ribs. Taking the construction step CS1 as an example, the stress and deformation of the prefabricated arch ribs are presented in Figure 7. During the closing stage, the prefabricated arch ribs underwent a transformation from a three-hinged arch to a hingeless one. It can be observed from the figure that the maximum stress and maximum deformation occurred near the midspan, with the values being −1.2 MPa and 0.94 mm, respectively. The levels of stress and deformation exhibited a decreasing trend from the midspan of each prefabricated arch rib to the support and vault. According to the Chinese code “Code for Design of Concrete Structures” [21] and the European code “EN 1992 Eurocode 2: Design of Concrete Structures Part 1-1: General rules and rules for buildings” [25], the stress level of the prefabricated arch ribs was lower than the allowable value, fulfilling the design requirements. In accordance with the Chinese code “Code for Design of Hydraulic Concrete Structures” [26] and the European code “EN 1992 Eurocode 2: Design of Concrete Structures Part 2: Concrete bridges—Design and detailing rules” [27], the deflection limit of the prefabricated arch rib was L/500, where L was the calculated span of the component, and for the arch rib, it was 15 m. Therefore, the overall structural deflection of the arch rib met the requirements.

5.1.2. The Installation Stage of the Bent Frame Columns

The construction step CS2 to CS7 represented the installation stage of the bent frame columns. The prefabricated arch ribs were in the most disadvantageous stress state under asymmetric load, and the overall structure might be damaged due to the failure of the connection. Taking the construction steps CS4 and CS6 as examples, the stress and deformation of the prefabricated arch ribs and bent frame columns are presented in Figure 8. When the 11# bent frame column was installed, the deformation and compressive stress at the cross-section of the left prefabricated arch rib connected by the 11# bent frame column reached the maximum values of the entire span, which were 4.57 mm and −3.30 MPa, respectively, as the left prefabricated arch rib assumed a larger load. When the 12# bent frame column was installed, the deformation and compressive stress at the midspan of the left prefabricated arch rib were the maximum values of the entire span, which were 3.25 mm and −2.94 MPa, respectively. It can be observed from the figure that since the stress level at the connection of the vault and the support was low, these connections would not be damaged.

5.1.3. The Erection Stage of the Groove Bodies

The construction step CS8 to CS10 constituted the erection stage of the groove bodies. Taking the construction steps CS8 and CS10 as examples, the stress and deformation of the prefabricated arch ribs, bent frame columns, and groove bodies are presented in Figure 9. When the 1# and 2# groove bodies were erected, the left prefabricated arch rib exhibited obvious stress and deformation due to the larger vertical load, especially at the cross-section of the left prefabricated arch rib connected by the 11# bent frame column where the stress and deformation reached the maximum values of −9.0 MPa and 13.81 mm, respectively. The stress at the connection of the support was −8.2 MPa, which met the requirements of the standard. When the 3# groove body was erected, the deformation and compressive stress reached the maximum values in the cross-section of the prefabricated arch ribs connected by the 11# bent frame column and the 14# frame bent column, which were 4.54 mm and 7.20 MPa, respectively. Meanwhile, the stress at the connection of the vault was −3.9 MPa, reaching the maximum value in the entire construction stage. Therefore, the connections of the prefabricated aqueduct used to connect different components were basically in a safe and stable state, indicating that the working performance of the connections could be fully utilized, and thus the prefabricated aqueduct would not be damaged due to the failure of these connections.

5.2. Analysis of Construction Process Monitoring

5.2.1. Deformation Monitoring

It can be observed from Figure 10a–d that the trend of deformation at the symmetrical position of the full-span arch rib was essentially consistent. The finite element simulation results of the vertical displacement and lateral displacement of the arch rib were similar to the actual monitoring results, and the relative error was within 10%, indicating that the accuracy of the finite element calculation was high. The maximum lateral displacement of measuring point No. 2 was 10 mm in the stage of installing 12# and 13# bent frame columns. The measuring points monitored at No. 1 and No. 8 reached the maximum vertical displacement of 13 mm in the stage of closing the groove bodies. The monitoring results demonstrated that during the entire construction process, the deformation of the prefabricated arch rib conformed to the Chinese code “Code for Design of Hydraulic Concrete Structures” [26] and the European code “EN 1992 Euro-code 2: Design of Concrete Structures Part 2: Concrete bridges—Design and detailing rules” [27]. Finally, some suggestions for reducing the deformation of arch ribs were presented:

1. The transverse connection and integrity between arch ribs could be enhanced by adding transverse beams to enhance the lateral stiffness of arch ribs and reduce the deformation of arch ribs.

2. Measuring tools such as total station and level needed to be used to precisely control the elevation and position of arch ribs to avoid deformation caused by errors during installation.

3. The arch ribs needed to be inspected and maintained regularly, so that damage or defects could be detected and repaired in a timely manner to prevent the further development of deformation.

5.2.2. Stress Monitoring

Arch ribs were roughly similar. Taking the left-span prefabricated arch rib as an example, the stress monitoring and calculation results of the key cross-sections are presented in Table 3 and Figure 11. The finite element calculation results were similar to the monitoring results, and the error was approximately 10%. The measured results were slightly larger than the calculation results, mainly because the temperature stress, shrinkage, and creep of concrete were considered in the actual construction stage. The finite element calculation could better simulate the stress development trend of the key cross-sections of the prefabricated arch ribs. The cross-section of the support of the prefabricated arch rib reached the maximum stress of −3.54 MPa in the construction step CS9, the cross-section of the midspan of the prefabricated arch reached the maximum stress of −6.42 MPa in the construction step CS8, and the cross-section of the vault of the prefabricated arch rib reached the maximum stress of −3.90 MPa in the construction step CS10. The maximum compressive stress of the prefabricated arch rib in each part was less than the allowable stress value based on the Chinese code “Code for Design of Concrete Structures” [21] and the European code “EN 1992 Eurocode 2: Design of Concrete Structures Part 1-1: General rules and rules for buildings” [25], which met the design requirements.

5.3. Strength and Stability Checking Calculation of the Connection

5.3.1. Strength Checking Calculation of the Arch Foot

According to the finite element calculation results, the axial force N and bending moment M of the embedded parts of the arch foot are shown in Formulas (1) and (2), respectively.

(1)$N=261.4\times \sin {44.37}^{\circ }+249.3\times \cos {44.37}^{\circ }=329.6\mathrm{kN}$

(2)$M=261.4\times 0.6\times \cos {44.37}^{\circ }-249.3\times 1.2\times \sin {44.37}^{\circ }=88.6\mathrm{kN}\cdot \mathrm{m}$

According to the large sample diagram of the embedded parts of the arch foot (Figure 4), the cross-sectional area A₁, the moment of inertia I_x, the cross-sectional modulus W_x, and the radius of gyration i_x are shown in Formulas (3)–(6), respectively.

(3)$A_1=11.503\times 4=46.012{\mathrm{cm}}^2$

(4)$I_x=4\times \left(59.96+11.503\times {17.85}^2\right)=\mathrm{14,900}{\mathrm{cm}}^4$

(5)$W_x={\displaystyle \frac{I_x}{y}}={\displaystyle \frac{\mathrm{14,900}}{20}}=745{\mathrm{cm}}^3$

(6)$i_x=\sqrt{{\displaystyle \frac{I_x}{A}}}=\sqrt{{\displaystyle \frac{\mathrm{14,900}}{46.012}}}=18\mathrm{cm}$

The section strength of the embedded part of the arch foot was calculated according to Formula (7).

(7)${\displaystyle \frac{N}{A}}+{\displaystyle \frac{M}{W_x}}={\displaystyle \frac{329.6\times {10}^3}{46.012\times {10}^2}}+{\displaystyle \frac{88.6\times {10}^6}{745\times {10}^3}}=190.5{\mathrm{N}/\mathrm{mm}}^2\le 235{\mathrm{N}/\mathrm{mm}}^2$

According to Article 8.1.1 of the Chinese code “Standard for design of steel structures” [23] and the European code “EN 1993 Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings” [28], the strength of the embedded part of the arch foot met the design requirements.

5.3.2. Stability Checking Calculation of the Arch Foot

The slenderness ratio λ_x in the weak axis direction of the embedded parts of the arch foot was as shown in Formula (8).

(8)${\lambda }_x={\displaystyle \frac{l_{ox}}{i_x}}={\displaystyle \frac{60}{18}}=3.33$

According to the “basic principle of steel structure” commonly used steel section characteristic table, it was found that the radius of gyration i₁ = 2.28 cm and the moment of inertia I₁ = 59.96 cm⁴ of the single limb to the weak axis. Therefore, the slenderness ratio λ₁, the conversion slenderness ratio λ_ox, the relative slenderness ratio λ, and the stability coefficient φ of the single limb could be calculated according to Formulas (9)–(12).

(9)${\lambda }_1={\displaystyle \frac{l_1}{i_1}}={\displaystyle \frac{12.5}{2.28}}=5.48$

(10)${\lambda }_{ox}=\sqrt{{\lambda }_x^2+{\lambda }_1^2}=\sqrt{{3.33}^2+{5.48}^2}=6.41$

(11)$\overline{\lambda }={\displaystyle \frac{{\lambda }_{ox}}{\pi }}\sqrt{{\displaystyle \frac{f_y}{E}}}={\displaystyle \frac{6.41}{3.14}}\times \sqrt{{\displaystyle \frac{235}{2.06\times {10}^5}}}=0.07\le 0.215$

(12)$\phi =1-{\alpha }_1{\overline{\lambda }}^2=1-0.65\times {0.07}^2=0.997$

The Euler critical force N_Ex could be calculated by Equations (13) and (14):

(13)$N_{Ex}={\displaystyle \frac{{\pi }^{2}EA}{{\lambda }_{ox}^2}}={\displaystyle \frac{{3.14}^2\times \mathrm{206,000}\times 4601.2}{{6.41}^2}}=2.27\times {10}^8\mathrm{N}$

(14)${\displaystyle \frac{N}{\phi A}}+{\displaystyle \frac{{\beta }_{mx}{M}_x}{W_x\left(1-\frac{N}{N_{Ex}}\right)}}={\displaystyle \frac{329.62\times {10}^3}{0.997\times 4601.2}}+{\displaystyle \frac{1.0\times 88.6\times {10}^6}{745\times {10}^3\times \left(1-\frac{329.62\times {10}^3}{2.27\times {10}^8}\right)}}=191{\mathrm{N}/\mathrm{mm}}^2\le 235{\mathrm{N}/\mathrm{mm}}^2$

According to the Chinese code “Standard for design of steel structures” [23] and the European code “EN 1993 Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings” [28], the stability of the embedded parts of the arch foot met the design requirements.

5.3.3. Strength Checking Calculation of the Vault

According to the finite element calculation results, the embedded part of the vault was an axial compression member, and the axial force N = 2.49 × 10⁵ N. According to the sample drawing of the pre-embedded parts of the vault (Figure 3), the most unfavorable cross-sectional area A₂ was shown in Formula (15). The compressive stress σ of embedded parts of the vault was shown in Formula (16).

(15)$A_2=70\times 20\times 4+20\times 20=6000{\mathrm{mm}}^2$

(16)$\sigma ={\displaystyle \frac{N}{A}}={\displaystyle \frac{2.49\times {10}^5}{6000}}=41.5{\mathrm{N}/\mathrm{mm}}^2\le 235{\mathrm{N}/\mathrm{mm}}^2$

According to the Chinese code “Standard for design of steel structures” [23] and the European code “EN 1993 Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings” [28], the strength of the embedded part of the vault met the design requirements.

5.3.4. Stability Checking Calculation of Embedded Parts of the Vault

According to the large sample diagram of the embedded parts of the vault (Figure 3), the moment of inertia I_x and the radius of gyration i_x are shown in Formulas (17) and (18), respectively.

(17)${\mathrm{I}}_{\mathrm{x}}={\displaystyle \frac{1}{12}}\times 160\times {20}^3+{\displaystyle \frac{1}{12}}\times 20\times {160}^3-{\displaystyle \frac{1}{12}}\times 20\times {20}^3=6.92\times {10}^6{\mathrm{mm}}^4$

(18)$i_x=\sqrt{{\displaystyle \frac{I_x}{A}}}=\sqrt{{\displaystyle \frac{6.92\times {10}^6}{6000}}}=34\mathrm{mm}$

Therefore, the slenderness ratio λ_x, relative slenderness ratio λ, and stability coefficient φ of the vault embedded parts could be calculated according to Formulas (19)–(22).

(19)${\lambda }_x={\displaystyle \frac{l_{ox}}{i_x}}={\displaystyle \frac{500}{34}}=14.7$

(20)$\overline{\lambda }={\displaystyle \frac{{\lambda }_x}{\pi }}\sqrt{{\displaystyle \frac{f_y}{E}}}={\displaystyle \frac{14.7}{3.14}}\times \sqrt{{\displaystyle \frac{235}{2.06\times {10}^5}}}=0.16\le 0.215$

(21)$\phi =1-{\alpha }_1{\overline{\lambda }}^2=1-0.65\times {0.16}^2=0.98$

(22)${\displaystyle \frac{N}{\phi Af}}={\displaystyle \frac{2.49\times {10}^5}{0.98\times 6000\times 235}}=0.18\le 1$

According to the Chinese code “Standard for design of steel structures” [23] and the European code “EN 1993 Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings” [28], the stability of the embedded parts of the vault met the design requirements.

6. Conclusions

1. This paper not only investigated the connection technology among the gravity pier, the prefabricated arch ribs, and the prefabricated bent frame columns based on the prefabricated aqueduct, but it also presented the assembly method between different prefabricated components. The fabricated connection can guarantee the construction quality and enhance the construction efficiency, which was highly suitable for the requirements of hydraulic construction. Finite element analysis, on-site monitoring, and formula calculation were carried out to evaluate the safety and stability of this prefabricated aqueduct.

2. The finite element analysis results indicated that the stress and the deformation of the connection at the vault were low, whether in the three-hinged state or in the unhinged state, which illustrated that the connection would not be damaged throughout the entire construction stage. The maximum stress and the deformation of the prefabricated arch rib were −1.2 MPa and 0.94 mm, respectively, in the hoisting and closing stages. The maximum stress and the deformation of the prefabricated arch rib were −3.3 MPa and 4.57 mm, respectively, in the installation stage of the bent frame columns. The maximum stress and the deformation of the prefabricated arch rib were −9.0 MPa and 13.81 mm, respectively, in the erection stage of the groove bodies.

3. The finite element simulation results of the deformation and stress of the prefabricated arch rib were similar to the actual monitoring results, and the relative error was within 10%, indicating that the accuracy of the finite element calculation was high. The deformation and stress of the prefabricated arch rib were larger in the erection stage of the groove bodies, mainly because the load transmitted to the prefabricated arch rib increased significantly with the increase in the weight of the groove bodies. The monitoring results showed that the maximum vertical displacement and lateral displacement were 13 mm and 10 mm, respectively. The maximum compressive stress of the prefabricated arch rib was −6.42 MPa, which met the requirements of the standard.

4. The simulations and monitoring indicated that the deformation and the stress of the prefabricated aqueduct met the requirements of the specification. The formula calculations demonstrated that the strength and stability of the embedded parts of the arch foot and vault also met the design requirements. Therefore, the overall structure was safe during the construction stage.

5. The safety evaluation of the aqueduct is a multi-level and multi-index issue. In this paper, the performance of the aqueduct was comprehensively analyzed and assessed merely based on the stress and deformation monitoring effect of the aqueduct. In the future, we can explore the influence of different types of evaluation indexes on the safety of the aqueduct. Anyway, it is necessary to investigate the mechanical properties of the aqueduct under water load, wind load, and earthquake load in order to evaluate its safety in the serviceability stage in our future research.

Author Contributions

Conceptualization, Y.L. and L.Z.; methodology, L.Z., H.W. and J.F.; software, H.W.; validation, W.H., J.L. and M.L.; formal analysis, Y.L.; investigation, J.L.; resources, Y.L. and L.Z.; data curation, L.Z.; writing—original draft preparation, H.W.; writing—review and editing, L.Z. and H.W.; visualization, Y.L. and L.Z.; supervision, W.H.; project administration, J.L.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

All data, models, and code generated or used during this study are contained within the article.

Acknowledgments

The authors are grateful to the editors and anonymous reviewers for their professional comments and valuable suggestions in improving the quality of the paper.

Conflicts of Interest

Authors Yamin Li, Wei Huang, Jinheng Li and Manjun Liao were employed by the company Sinohydro Bureau 8 Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

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Figures and Tables

Figure 1. The schematic diagram of the prefabricated aqueduct (unit: mm). (a) The riverbank aqueducts (150 m). (b) The river-crossing aqueducts (114 m). (c) The riverbank aqueducts (36 m).

Figure 2. The section diagram of the prefabricated aqueduct (unit: mm). (a) Straight-line simply supported reinforced concrete beam aqueduct. (b) Arch bent aqueduct.

Figure 3. The connection diagram of the precast arch rib (Unit: mm). (a) Sample drawing of the pre-embedded parts of the vault. (b) Sample drawing of different parts.

Figure 3. The connection diagram of the precast arch rib (Unit: mm). (a) Sample drawing of the pre-embedded parts of the vault. (b) Sample drawing of different parts.

Figure 4. The connection diagram of each component of the aqueduct (unit: mm). (a) The connection between the gravity pier and the arch rib. (b) The connection between the bent frame column and arch rib. (c) The connection between the gravity pier and bent frame column.

Figure 4. The connection diagram of each component of the aqueduct (unit: mm). (a) The connection between the gravity pier and the arch rib. (b) The connection between the bent frame column and arch rib. (c) The connection between the gravity pier and bent frame column.

Figure 5. The arrangement of measuring points. (a) Strain measuring points. (b) Displacement measuring points. (c) Schematic diagram of on-site installation of monitoring instruments.

Figure 6. Finite element model of a single-span aqueduct.

Figure 7. The closing stage of the prefabricated arch ribs. (a) Stress. (b) Deformation.

Figure 8. The installation stage of the bent frame columns. (a) Stress (CS4). (b) Deformation (CS4). (c) Stress (CS6). (d) Deformation (CS6).

Figure 9. The erection stage of the groove bodies. (a) Stress (CS8). (b) Deformation (CS8). (c) Stress (CS10). (d) Deformation (CS10).

Figure 10. Comparison of calculated value and monitoring value of arch rib displacement. (a) The calculated value of vertical displacement of the arch rib. (b) The monitored value of vertical displacement of the arch rib. (c) The calculated value of lateral displacement of the arch rib. (d) The monitored value of lateral displacement of the arch rib.

Figure 11. Comparison between the calculated value and the monitoring value. (a) The stress of the cross-section of the support. (b) The stress of the cross-section of the midspan. (c) The stress of the cross-section of the vault.

Table 1

Division of construction steps.

Construction Step	Arch Rib	Bent Frame Column	Groove Body
CS0	Lifting	—	—
CS1	Assembling and closing	—	—
CS2	—	Installation of 10# bent frame column	—
CS3	—	Installation of 15# bent frame column	—
CS4	—	Installation of 11# bent frame column	—
CS5	—	Installation of 14# bent frame column	—
CS6	—	Installation of 12# bent frame column	—
CS7	—	Installation of 13# bent frame column	—
CS8	—	—	Erection of 1#, 2# groove body
CS9	—	—	Erection of 4#, 5# groove body
CS10	—	—	Erection of 3# groove body

Table 2

Material parameter.

Member Type	Elastic Modulus/MPa	Yield Strength/MPa	Ultimate Strength/MPa	Tensile Strength/MPa	Compressive Strength/MPa
Groove body, arch rib	3.45 × 104	—	—	1.89	23.1
bent frame column	3.25 × 104	—	—	1.71	19.1
embedded parts	2.06 × 105	235	370	—	—

Table 3

Stress of key cross-sections of the left arch rib.

Construction Step	The Cross-Section of the Support(Measuring Point No. 3~No. 4)		The Cross-Section of the Midspan(Measuring Point No. 5~No. 6)		The Cross-Section of the Vault(Measuring Point No. 7~No. 8)
	Calculating(MPa)	Measuring(MPa)	Calculating (MPa)	Measuring (MPa)	Calculating (MPa)	Measuring (MPa)
1	−1.02	−1.12	−0.91	−0.88	−0.66	−0.72
2	−1.02	−1.16	−0.91	−0.94	−0.66	−0.76
3	−1.08	−1.21	−0.91	−0.98	−0.74	−0.79
4	−1.14	−1.22	−2.82	−2.86	−1.18	−1.24
5	−3.27	−3.43	−2.30	−2.42	−1.78	−1.82
6	−2.10	−2.22	−2.37	−2.45	−1.61	−1.66
7	−2.25	−2.36	−1.81	−1.84	−1.50	−1.60
8	−1.31	−1.38	−6.36	−6.42	−2.45	−2.51
9	−3.50	−3.54	−4.96	−5.01	−3.82	−3.88
10	−3.24	−3.30	−5.15	−5.20	−3.87	−3.90

The stress monitoring values of key cross-sections of the prefabricated arch rib were taken as the average stress values of upper and lower edges.

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