Field Monitoring and Numerical Analysis of the Effect of Air Temperature and Water Load on the Static Behavior of a Tied-Arch Aqueduct

Abstract

This study presents part of a pilot work for the structural health monitoring of a large tied-arch reinforced concrete aqueduct in eastern China. Based on field-monitored data for over a year, it mainly focuses on the effect of air temperature and water load variations on the static behavior of a typical span of the aqueduct through field monitoring and 3D FE model analysis. It is found that the longitudinal deformation of the composite tied-arch shows a good linear relationship with the air temperature during the non-operation period and also has a good bilinear correlation with the air temperature and water level during operation. However, isolation of the air temperature effect from the second bilinear correlation using the first linear relationship results in a poor correlation between the longitudinal deformation and water level due to the dominance of the temperature effect. Therefore, it is recommended to use the bilinear regression to predict the longitudinal deformation of the tied-arch during operation. The vertical deformation of the tied-arch is insignificantly affected by air temperature, whereas it shows a fair bilinear correlation with the air temperature and water level during operation, which can be used to provide a reasonable estimation of the vertical deformation of the tied-arch. The strain measurements of the tied-arch using vibrating-string gauges are more complicated due to the notable influence of the ambient temperature and solar radiation, but the relatively consistent bilinear regression of the strains versus the air temperature and water level can still give fair predictions for the strains of the bottom tension rods during operation. The 3D FE model can provide a fair estimation for the vertical deformation of the tied-arch under water load, but its predictions for longitudinal deformation and strains are less satisfactory when compared to monitored data excluding temperature effects.

1. Research Background

Built in 2006, the Jiehe River aqueduct is a key component of a domestic water supply project in Shandong Province, China. The aqueduct features a tied-arch structural type with 21 spans, each measuring an equal length of 51.6 m. The reinforced concrete composite tied-arch of each span is comprised of two parallel identical pieces, each consisting of an arch ring and a bottom tension rod. The aqueduct is essentially a bridge transporting water instead of traffic. To implement health monitoring, the temperature effect on its structural responses needs to be investigated.

Compared with bridges, studies on the temperature reactions of aqueducts have been conducted much less, so this literature review mainly focuses on relevant research on bridges. The temperature effect has a significant influence on the static and dynamic behavior of all types of bridges, including beam, arch, cable-stayed, and cable-suspension bridges [1]. For the dynamic monitoring of arch bridges, it has been found that temperature variation can affect their dynamic properties, especially modal frequencies [1,2,3,4,5]. In regard to static structural responses, the temperature distribution in an arch bridge is a complex non-linear issue due to some uncertain factors, including the thermal conductivity of concrete, surface convection, and solar radiation, which is normally examined by FE model simulations and in situ monitoring. Zhou et al. proposed a comprehensive approach for long-term deformation monitoring of long-span bridges, which integrated Persistent Scatterer Interferometry (PSI) with the bridge’s temperature field obtained from a transient heat transfer analysis of the FE model [6]. Borlenghi et al. examined the relationship between the observed rotations of a masonry arch bridge and environmental factors, including air temperature, employing a linear regression model to mitigate the impacts attributed to temperature variations [7]. Zhu et al. tried to establish a correlation between the thermal responses of a long-span steel truss arch bridge and its spatial temperature change by employing the elastic beam theory, which was then confirmed by in situ monitoring data [8]. Ietka et al. observed different temperature distributions and variation patterns in the arch and at the deck of a reinforced concrete arch bridge and found that the displacements of the expansion joints could be reasonably estimated from the monitored temperature data [9]. Xia et al. developed a unified 3D FE model to incorporate thermal and structural analyses for an arch bridge, and the analytical results were essentially consistent with the monitored data [10]. By integrating the FE model simulation with field monitoring, Fu et al. found the deformation anomaly of a beam-arch bridge during construction was induced by the temperature field disparity in the structure [11]. Using long-term monitoring data of a long-span arch bridge, Zhou et al. found that seasonal temperature change had a significant impact on the longitudinal and vertical deformations, and the vertical displacement exhibited a nonlinear relationship with the temperature [12,13]. Zhao et al. studied the temperature effects on the deck deflection of an arch bridge to find that the girder deformation caused by temperature change was much less than that induced by the train and applied the wavelet transform to separate the deflection caused by temperature and train [14]. Wang et al. conducted a 3D beam FE model analysis on the temperature-induced stresses and displacements of the concrete box-girder arch bridge using the temperature gradients of the web obtained from a 2D plane FE model [15]. Yarnold et al. evaluated the long-term monitoring data from a long-span steel tied-arch bridge using benchmark studies and indicated a nonlinear relationship between temperature, strains, and displacements [16]. Wang et al. found a linear relationship between the static strains of the steel truss arch girder of a long-span bridge and its temperature field [17]. As for aqueduct monitoring, Jiang et al. introduced an extreme learning machine (ELM) algorithm based on particle swarm optimization (PSO) using air temperature, water level, and aging as influence factors to estimate the vertical deformation and crack openings of an aqueduct [18].

For most of the aforementioned studies involving in situ temperature monitoring to obtain the interior temperature gradients, thermometers are usually either embedded in the structural members through drilled holes or installed during fabrication. However, in this study, which is a pilot work for an SHM (structural health monitoring) system for the entire aqueduct, the owner does not allow hole-drilling in the composite tied-arch due to concerns about potential structural damage. Therefore, the investigation into the impact of temperature on the static behavior of the aqueduct necessitates reliance on the field measurements of air temperature.

2. Research Methodology

Based on field monitoring data and 3D FE model analysis, the research methodology of this study can be illustrated in the following flowchart (Figure 1).

3. Installation of the Structural Monitoring System

The span #8 of the aqueduct is located right in the middle of the riverbed and has the highest moment frame supports among all spans at the upstream and downstream ends. It is selected as the target span for this study.

Part of the monitoring system is shown in Figure 2. The static level gauge detects the vertical displacement at its location by measuring the liquid level variation inside its chamber. Due to its work mechanism, all gauges in the same assembly set should be installed at about the same elevation. For the sake of field installation and future maintenance, two sets of static level gauges are mounted on the top of the left and right sidewalls of the trough above the composite tied-arch, and each set has one gauge at the upstream end, mid-span, and downstream end of the trough, respectively, which are designated as (1) in Figure 2. An ultrasonic water level gauge is fixed onto the side surface of the first upstream transverse link beam at the top of the trough, which is designated as (2) in Figure 2.

Four joint meters (LVDTs), two on each side of the composite tied-arch, are installed across the expansion joints at the upstream and downstream abutments, which are designated as (3) in Figure 2. Vibrating-string strain gauges are installed at the upstream end, mid-span, and downstream end of the arch ring and bottom tension rod on each side of the composite tied-arch, which are designated as (4) in Figure 2. To avoid the complex stress condition at the joints between the arch ring and tension rod, the gauges at both ends of those two members are set at least one cross-dimensional size away from the joints. A detailed layout of monitoring devices at the upstream abutment of the composite tied-arch is shown in Figure 3.

The structural monitoring system was installed in November 2023 and started data collection on 1 December of the same year. The sampling interval for all monitoring devices is set to be about 1 min (60 s), and the monitoring data are transmitted to the control center via a 4G wireless network. This research covers the analysis of the monitored data for over a year from 1 December 2023 to 31 December 2024, during which the aqueduct underwent operation (water conveyance) from 9 March 2024 to 2 May 2024.

4. Longitudinal Deformation of the Composite Tied-Arch

4.1. Evaluation of the Effects of Air Temperature and Water Load

The typical variation in the LVDT readings of the expansion joints at abutments on both sides of the composite tie arch with the air temperature (hereinafter referred to as T) during a 15-day non-operation (trough empty) period from 15 November 2024 to 30 November 2024 is shown in Figure 4. It can be seen that the LVDT readings at the downstream abutment expansion joints on both sides essentially exhibit the same magnitude and variation pattern, while those at the two upstream abutments basically maintain around a near zero status due to the fixed basin-type rubber bearings at those locations. It can also be seen that the LVDT readings at the downstream abutment expansion joints are very sensitive to the air temperature, with daily maximum and minimum readings appearing almost concurrently with the daily highest and lowest air temperatures, respectively.

For each side of the composite tied-arch, the longitudinal deformation (designated as ΔL) is the sum of the readings of the LVDTs at upstream and downstream abutment joints, and the ΔL of the whole composite tied-arch is taken as the average of both sides.

The LVDTs are initialized to 0 right after installation at a temperature of −3 °C; so, the daily extreme air temperature change (hereinafter referred to as ΔT_dex) is taken as the daily highest or lowest (if lower than −3 °C) temperature minus −3 °C, and the daily extreme ΔL (hereinafter referred as ΔL_dex) is calculated using the daily maximum or minimum readings of LVDTs with respect to daily highest or lowest temperatures. The relationship between ΔL_dex and corresponding ΔT_dex during the non-operation period from 1 December 2023 to 31 December 2024 is plotted in Figure 5, which exhibits a good correlation with a R² of 0.9738 and a RMSE of 1.33 mm. The regression also shows a ±1 °C air temperature change tends to cause a longitudinal deformation of ±0.51 mm for the composite tied-arch.

During the aqueduct operation from 9 March 2024 to 2 May 2024, the variation in ΔL_dex with ΔT_dex and the water level occurring at the same time as ΔL_dex (hereinafter referred to as W_dex) is shown in Figure 6. It can be seen that even under water conveyance, the longitudinal deformation of the composite tied-arch still closely follows the air temperature changes.

To perform a multiple linear regression, taking ΔT_dex (°C) and W_dex (m) as two independent variables and ΔL_dex (mm) as the dependent variable, the optimal fitting function can be expressed as follows:

ΔL_dex = −2.063 + 0.5669 × ΔT_dex + 2.874 × W_dex

(1)

The relationship between the monitored and regression values of ΔL_dex during the aqueduct operation from 9 March 2024 to 2 May 2024 is shown in Figure 7, which has a good correlation with an R-square of 0.9434 and a RMSE of 0.81 mm. It is also found that the t-statistic for ΔT_dex (25.11) is higher than that for W_dex (6.36), indicating that ΔT_dex is statistically significant.

4.2. Isolation of Air Temperature Effect from the Monitored ΔL

During aqueduct operation, the temperature-dependent portion of the monitored ΔL of the composite tied-arch specified by the regression equation in Figure 5 is excluded from ΔL_dex, which includes both the effects of temperature and water level, and then the supposed water-dependent remainder is plotted against W_dex in Figure 8. The correlation only has an R² of 0.4362 and an RMSE of 0.87 mm, and the reason for this seemingly poor relationship may be attributed to the fact that the correlation between ΔL_dex and ΔT_dex shown in Figure 5 already has a relatively larger RMSE of 1.33 mm.

By comparing Figure 5 with Figure 8, it can be noted that the air temperature change has a more significant contribution to the longitudinal deformation of the composite tied-arch than the water level in the trough.

5. Vertical Deformation of the Composite Tied-Arch

The variation in the static level gauge readings of the right assembly set with the air temperature during a 15-day non-operation period from 10 October 2024 to 25 October 2024 is shown in Figure 9. It can be seen that the reading (i.e., liquid level) of the mid-span gauge rises with the increase in the air temperature, while those of the gauges at both the upstream and downstream ends drop.

For each side of the composite tied-arch, the vertical deformation is the measurement of the static level gauge at the mid-span minus the average of the measurements of the gauges at both ends of the span, and the vertical deformation of the whole composite tied-arch (designated as ΔV) is taken as the average of such calculated values of both sides. Due to the viscosity of the liquid in the long connecting tube between two adjacent static level gauges, the liquid level fluctuation in the gauge chamber may not be able to capture the instant deformation of the composite tied-arch. Therefore, in the monitored data analysis, the daily average measurement of each static level gauge is used, and then the daily average vertical deformation of the composite tied-arch (hereinafter referred to as ΔV_dav) can be calculated. The daily average air temperature can also be achieved from thermometer readings, and, by subtracting the temperature at the static level gauge initialization (readings reset to 0), the daily average air temperature change (hereinafter referred to as ΔT_dav) is obtained. Thus, the relationship between ΔV_dav and ΔT_dav during the non-operation period from 1 December 2023 to 31 December 2024 is illustrated in Figure 10.

It can be seen from Figure 10 that, under the non-operation status, the correlation between ΔV_dav and ΔT_dav is very poor, which indicates that no definitive statistical relationship can be established between the two parameters. However, there is a general trend that the monitored ΔV_dav data points are, to some extent, evenly distributed about the ΔT_dav axis, and the magnitudes essentially fall into a narrow range of −1 mm~1 mm.

During the aqueduct operation from 9 March 2024 to 2 May 2024, the variation in the gauge readings of the right assembly set with the water level inside the trough is shown in Figure 11. It can be found that, under the water conveyance status, besides the regular fluctuation in temperature, as seen in Figure 9, the readings of the mid-span gauge deviate from the general trend under empty trough conditions and notably rise above those of the gauges at the upstream and downstream ends.

To perform a multiple linear regression, taking ΔT_dav (°C) and the daily average water level (hereinafter referred to as W_dav, m) as two independent variables and ΔV_dav (mm) as the dependent variable, the optimal fitting function can be expressed as follows:

ΔV_dav = −0.7955 + 0.0504 × ΔT_dav + 1.916 × W_dav

(2)

The correlation between the monitored and regression values of ΔV_dav during aqueduct operation from 9 March 2024 to 2 May 2024 is illustrated in Figure 12, which has an R-square of 0.8166 and an RMSE of 0.28 mm, indicating that the regression function (2) can provide rational predictions for the vertical deformation of the composite tied-arch during operation. It is also found that the t-statistic for ΔT_dav (5.34) is lower than that for W_dav (11.68), indicating that W_dav is statistically significant.

6. Strains of the Composite Tied-Arch

6.1. Evaluation of the Effects of Air Temperature and Water Load

The monitored strain is calculated using the following equation:

ε = k₁ × (f_i² − f₀²) + (Y₁ − Y₂) × (T₁ − T₀)

(3)

where ε is the strain of the test location (με); k₁ is the modification factor provided by the manufacturer (με/Hz²); f₀ is the frequency of the gauge at initialization (Hz); f_i is the tested frequency of the gauge (Hz); Y₁ is the thermal expansion coefficient of the gauge string provided by the manufacturer (12.2 με/°C); Y₂ is the thermal expansion coefficient of concrete (10 με/°C); T₁ is the temperature at test (°C); T₀ is the temperature at gauge initialization (°C).

The typical variation in the strains measured at the upstream end of the left tension rod with the air temperature during a 15-day non-operation (empty trough) period from 1 October 2024 to 15 October 2024 is shown in Figure 13, and the other gauges essentially follow the same trend. The daily fluctuation of the monitored strains lags notably behind the air temperature, with the maximum measurement occurring normally at late night or even early morning of the next day.

Since the temperature change has already been considered in Equation (3) for strain measurement, the daily average strain (hereinafter referred to as ε_dav) of each gauge is used to establish a relationship with the daily average temperature (hereinafter referred to as T_dav). The correlations of two typical gauges during the non-operation period from 1 December 2023 to 31 December 2024 are shown in Figure 14 and Figure 15, and those of the others are listed in

Table 1. Correlations between ε_dav and T_dav of all gauges during the non-operation period from 1 December 2023 to 31 December 2024.

Side	Location	Regression/με	R2	RMSE/με
Left	Upstream end of tension rod	εdav = 2.0439 × Tdav + 42.045	0.6758	17.4
Left	Mid-span of tension rod	εdav = 2.9485 × Tdav + 37.304	0.6913	24.0
Left	Downstream end of tension rod	εdav = 3.4175 × Tdav − 8.3034	0.7872	21.7
Right	Mid-span of tension rod	εdav = 6.3813 × Tdav − 15.411	0.8125	29.4
Right	Downstream end of tension rod	εdav = 1.7471 × Tdav − 46.815	0.6269	16.4
Left	Upstream end of arch ring	εdav = 2.2227 × Tdav − 3.7161	0.7424	15.4
Left	Top of arch ring	εdav = 5.2157 × Tdav − 9.8842	0.8724	24.8
Left	Downstream end of arch ring	εdav = 0.5835 × Tdav − 20.202	0.2531	12.3
Right	Upstream end of arch ring	εdav = −4.0363 × Tdav + 72.835	0.6414	36.5
Right	Top of arch ring	εdav = 1.1526 × Tdav − 23.496	0.2786	21.4
Right	Downstream end of arch ring	εdav = 2.3488 × Tdav − 19.446	0.7525	15.5

.

It can be seen from Figure 14 and Figure 15 and Table 1 that the correlations between ε_dav and T_dav of all strain gauges on both arch rings and tension rods are relatively poor compared with that observed from joint meters, as shown in Figure 5, especially for those on arch rings with very low R² values. In general, gauges on tension rods exhibit better correlations than those on arch rings.

During aqueduct operation from 9 March 2024 to 2 May 2024, taking T_dav (°C) and W_dav (m) as independent variables and ε_dav (με) as the dependent one, the optimal fitting functions for all strain gauges on both arch rings and tension rods are listed in

Table 2. Correlations between ε_dav, T_dav, and W_dav of all gauges during operation from 9 March 2024 to 2 May 2024.

Side	Location	Regression */με	R2	RMSE/με
Left	Upstream end of tension rod	ε = 2.367 × T + 59.33 × W + 40.058	0.8824	7.9
Left	Mid-span of tension rod	ε = 1.61 × T + 29.19 × W + 63.92	0.6879	8.3
Left	Downstream end of tension rod	ε = 4.201 × T + 54.18 × W − 44.216	0.7872	14.3
Right	Mid-span of tension rod	ε = 4.936 × T + 45.86 × W − 22.576	0.7149	18.1
Right	Downstream end of tension rod	ε = 1.842 × T + 79.7 × W − 62.442	0.7643	14.4
Left	Upstream end of arch ring	ε = 1.598 × T − 5.784 × W − 26.538	0.3821	8.6
Left	Top of arch ring	ε = 4.161 × T + 11.75 × W − 40.416	0.6127	15.9
Left	Downstream end of arch ring	ε = −0.0528 × T − 9.119 × W − 16.771	0.0819	8.6
Right	Upstream end of arch ring	ε = −2.599 × T + 20.15 × W + 77.724	0.3337	15.2
Right	Top of arch ring	ε = 0.0773 × T + 2.858 × W − 60.761	0.0746	11.3
Right	Downstream end of arch ring	ε = 2.071 × T − 6.924 × W − 31.296	0.4202	10.2

* To simplify the expression, ε_dav, T_dav, and W_dav are replaced with ε, T, and W, respectively.

, which indicates that gauges on tension rods still maintain consistent correlations compared with those in Table 1, whereas gauges on arch rings become even worse. The regression results of all gauges on tension rods are shown in Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20.

6.2. Isolation of Air Temperature Effect from Monitored ε

It can be seen from Table 1 and Table 2 that the correlations between ε_dav, T_dav, and W_dav for the gauges on arch rings during both the non-operation and operation periods of a year are generally poor and inconsistent. Therefore, when performing the isolation of the temperature effect from the monitored strains during operation, only the gauges on tension rods are selected. For each gauge, the temperature effect approximated by the regression equations in Table 1 is excluded from ε_dav, and then an average is taken for all gauges on the tension rods on each side, which is plotted against the daily average water level W_dav as shown in Figure 21 and Figure 22. The two figures show that the correlation of the left rod is much better than that of the right, with a higher R² and a lower RMSE, and this may be attributed to the direct exposure of the right (south) rod to sunlight which can cause more negative temperature impact on gauge readings. The correlations also show a general trend that 1 m deep water in the trough tends to generate a tensile strain of 43.1 με and 43.6 με for the left and right tension rods, respectively.

7. 3D Model Analysis for Structural Monitoring of the Aqueduct

An appropriate 3D FE model that can be highly representative of the static and dynamic responses of the aqueduct is very important to its long-term structural monitoring. The model can give reasonable predictions for the deformation and stress states of the structure under different load conditions, some of which may not be frequently encountered during operation, thus supplementing the structural monitoring database. Through the comparative study of the field-monitored data and model analysis results, it is possible to identify potential hazards and provide a rational evaluation for the structural safety of the aqueduct.

A 3D structural model of the entire aqueduct was created by SAP2000 V23.3.0. The middle part of the model is shown in Figure 23, which includes the target monitoring span—span #8. From top to bottom, the model comprises the reinforced concrete U-shaped trough segments (including 3 cm-wide contraction joints), the composite tied-arch (including post-tensioned tendons inside tension rods), transverse bent frames erected from the tied-arch, moment frame supports holding up the composite tied-arch, and pile foundations. The rubber bearings of the composite tied-arch, fixed basin-type at upstream ends, and sliding basin-type at downstream ends are incorporated in the model using link elements with shear and rotational stiffness properly defined. The non-conventional bearings made of two layers of thin asphaltic felt for prefabricated U-shaped concrete trough segments are also simulated. The structural model was verified by a comparative analysis of in situ dynamic tests and modal analysis prior to this study [19], which also provided an approximation of elastic moduli for the concrete of main load-bearing members, including the composite tie arch, transverse bent frames, and moment frame supports.

This 3D FE model is used to obtain and compare the analytical data with their monitored counterparts from the real structure under different load conditions. The vertical and longitudinal deformations of the composite tie arch are calculated using displacements along vertical and horizontal directions at specified nodes, and the strains of the main arch ring and tension rod are evaluated by the compressive or tensile stresses of corresponding frame elements in the model as shown in Figure 24.

7.1. Analytical Longitudinal Deformation of the Composite Tied-Arch

The longitudinal deformation of the composite tied-arch (ΔL) in the 3D FE model is computed using the longitudinal displacements at nodes 5 and 6 specified in Figure 24, of which the positions are in line with those of the LVDTs on the aqueduct as shown in Figure 2.

The model analysis indicates that a ±1 °C uniform temperature change in all truss members can induce a ΔL of ±0.46 mm (+ stands for expansion), and, although the air temperature change ΔT may be somewhat different from the real temperature variation inside the truss members due to some uncertain factors, such as the thermal conductivity of concrete, surface convection, and solar radiation, it can still be noted that this ±0.46 mm in ±1 °C deformation pattern is in general agreement with the regression equation specified in Figure 5, which predicts that a ±1 °C air temperature change tends to produce a ΔL of ±0.51 mm.

The model analysis also shows that 1 m deep water in the trough will create a ΔL of 1.86 mm. If the temperature-effect-excluded ΔL_dex specified in Figure 8 is considered as the “monitored” ΔL of the composite tied-arch under only water load during operation, it is then plotted with analytical ΔL obtained from the 3D model under the same water levels, and the result is shown in Figure 25. The correlation between this monitored and the analytical ΔL under only water load bears a strong resemblance to that between the temperature-effect-excluded ΔL_dex and W_dex illustrated in Figure 8, and, as mentioned earlier in Section 4.2 of this paper, the poor relationship is mainly due to the fact that this monitored ΔL assumed under only water load is still greatly affected by air temperature, which makes it impractical for the 3D model to provide an accurate prediction on the longitudinal deformation of the tied-arch during operation.

7.2. Analytical Vertical Deformation of the Composite Tied-Arch

The vertical deformation of the composite tied-arch (ΔV) in the 3D FE model is computed using the vertical displacements at nodes 7, 8, and 9 specified in Figure 24, of which the positions are in line with those of the static level gauges on the aqueduct as shown in Figure 2. A schematic diagram of the composite tied-arch’s deformation induced by water inside the aqueduct trough is shown in Figure 26.

The model analysis shows that 1 m deep water in the trough will induce a downward ΔV of 2.17 mm, while, by contrast, a ±1 °C uniform temperature change in all structural members can only cause a minor ΔV of ±0.022 mm (+ stands for upward), indicating an insignificant effect of the temperature change on ΔV, which is in conformance with the non-definitive correlation between ΔV_dav and ΔT_dav during the non-operation period as shown in Figure 10. Therefore, the monitored ΔV_dav is assumed to be primarily dependent on water load by neglecting the temperature influence during operation and plotted with the analytical ΔV obtained from the model under the same water level W_dav, which is shown in Figure 27. The correlation has an R² coefficient of 0.7052 and an RMSE of 0.35 mm. Although the correlation may not seem high, the 3D model can still give reasonable estimations of monitored ΔV due to the relatively low RMSE.

7.3. Analytical Strains of Tension Rods

In the 3D structural model, the bottom tension rods of the composite tied-arch are simulated with divided frame elements. The strains of the frame elements at the upstream end, mid-span, and downstream end of each rod under water load are first obtained from the model analysis, and then an average is taken to represent the average strain of the rod. It is found that, under a 1 m deep water load, both the left and right rods will undergo an average tensile strain of 44.2 με, which is essentially in line with the correlations shown in Figure 21 and Figure 22.

Taking the temperature-effect-excluded ε_dav specified in Figure 21 and Figure 22 as the “monitored” ε under only water load for each rod and the strains obtained from the 3D model under daily average water levels during operation as the corresponding analytical ε, the relationships between those two parameters for both rods are shown in Figure 28 and Figure 29. The variation trend of the monitored ε of the left rod (not exposed to direct sunlight) under water load is generally consistent with the analytical ε, and the correlation has an R² of 0.6640 and a relatively low RMSE of 8.6 με, whereas, for the right rod under direct sunlight exposure, there is a higher degree of dispersion between the monitoring results and model predictions.

8. Discussion and Conclusions

Using field monitoring data collected for over a year, this research investigates the static behavior of a typical span of a large tied-arch aqueduct under variations of air temperature and water load in an effort to predict the deformations and strains of the aqueduct during operation in order to set up a baseline for the structural safety evaluation. It serves as a feasibility study for the implementation of an SHM system for the entire aqueduct and can also provide a valuable reference for the structural monitoring of other large-scale aqueducts under similar operating conditions.

Through the evaluation of the structural monitoring data over a year and the 3D model analysis for the aqueduct, the following conclusions can be drawn:

(1)

The variation in the longitudinal deformation of the composite tied-arch closely follows the trend of the air temperature fluctuation during both the non-operation and operation periods of the aqueduct, with its daily maximum and minimum values occurring almost simultaneous with the daily highest and lowest air temperatures, respectively.

(2)

The daily extreme longitudinal deformation of the composite tied-arch ΔL_dex not only has a good linear relationship with the daily extreme air temperature change ΔT_dex during the non-operation period but also a good multiple linear correlation with ΔT_dex and the ΔL_dex-related water level W_dex during operation. However, it is impractical to isolate the temperature effect from the multiple linear regression due to the resulting poor correlation between ΔL_dex and W_dex. The multiple linear regression can provide good estimations for the longitudinal deformation of the composite tied-arch under different combinations of temperature and water level.

(3)

During the non-operation period, the air temperature has an insignificant effect on the vertical deformation of the composite tied-arch, and the two sets of monitored data also show a very poor relationship. The multiple linear regression of the daily average vertical deformation ΔV_dav versus the daily average temperature change ΔT_dav and daily average water level W_dav exhibits a fairly good correlation during operation, which can give reasonable predictions for the vertical deformation of the composite tied-arch.

(4)

The measurement of vibrating-string strain gauges is greatly influenced by the air temperature, particularly for those installed on the right side of the composite tied-arch exposed to solar radiation. During the non-operation period, the correlations between the daily average strain ε_dav and daily average air temperature T_dav of all gauges are generally weak, especially for those on arch rings. During operation, the multiple linear regressions of ε_dav versus ΔT_dav and W_dav for gauges on tension rods, in particular, those on the left side not exposed to solar radiation, present more consistent correlations than those on arch rings, which can be used to provide fair approximations for the strains of the tension rod.

(5)

It is found that the 3D FE model can make fair predictions on the vertical deformation of the composite tied-arch under water load, whereas the consistencies between the temperature-excluded monitored data and model analysis results for the longitudinal deformation and strains of the composite tied-arch seem not quite as promising.

(6)

Evaluation of field monitoring data shows that temperature has a greater influence on the longitudinal deformation and strains of the tied-arch of the aqueduct than water loads, which aligns with the findings of previous studies on arch bridges that temperature actions are normally more significant to even prevail over other load effects. However, it is practically difficult to conduct an accurate thermal analysis for the aqueduct due to the lack of monitored data on temperature distribution in structural members and the complex thermal boundary conditions, and the frame elements used in the FE model to simulate the main load-bearing members of the tied-arch are also not suitable for thermal analysis. Therefore, when the SHM for the entire aqueduct is to be installed in the future, an optimized implementation scheme of temperature gauges needs to be investigated to better understand the thermal behavior of the aqueduct under only minimal damage to its structural integrity. Meanwhile, the 3D FE model should be improved to be able to incorporate both structural and thermal analyses efficiently.