1 Introduction

1.1 Background

Most bridges built during the post-war construction booms of the 1950s, 1960s and 1970s are considered deficient in terms of structural capacity or functionality [14, 42]. Several are in urgent need of refurbishment due to increased traffic loads, accumulated deterioration, and more stringent bridge design codes, and face challenges of limited capital investment and maintenance [40]. Another key challenge is climate change and extreme climatic events, which can affect the structural health of bridges and their performance due to developing vulnerabilities to temperature change, flooding, wind loading, and other factors [31]. If not attended, these deficiencies may lead to bridge collapses with tragic consequences like the 51-year-old Morandi Bridge in Genoa, Italy, in August 2018, which resulted in 43 casualties [28]. To optimize performance and guard against failures and collapses, bridges are inspected on a regular basis according to standard protocols and frequencies that depend on jurisdictions [19, 29, 30] to identify structural problems and material deterioration and to plan for their remediation. The inspection frequency (e.g., every 2 years between general visual inspections in Canada and the UK), however, may be insufficient to tackle some escalating problems, especially in the later stages in the life cycle of a bridge, or during unexpected loading events. The judicious use of structural health monitoring (SHM) technologies on critical bridges can contribute to addressing some of today’s challenges. For instance, a more accurate knowledge of the life cycle performance of a bridge network through SHM can provide more complete and timely information to decision makers for an improved management of highway bridges regarding their maintenance and rehabilitation. Even as in situ monitoring technologies evolve and get integrated into modern sensor-packed smart bridges, thousands of other bridges may remain insufficiently inspected and inadequately serviced. In situ sensors are appropriate for targeted monitoring of selected structures, but cannot be practically deployed on a large scale due to the already limited budgets [43].

Satellites may help bridge engineers in identifying some of the above-mentioned problems in a timely manner by augmenting existing datasets from established condition assessment methods with new data. Several hundred satellites are monitoring our planet every day, and some of these are able to measure subtle displacements on ground structures. Satellites that carry synthetic aperture radar (SAR) are capable of providing weather-independent, high-resolution imagery of the Earth’s surface [10]. The measurement of displacements on ground structures down to the millimeter level requires the processing of several radar images taken at different times using advanced techniques, such as interferometric SAR (InSAR) [15, 16]. Ground motion maps have been available over the past 20 years and the Earth Observation (EO) industry providing this service is growing [5]. Early warning systems providing advance indications of potential bridge problems are of vital importance and current satellite technology could be exploited to rapidly identify these problems both at the single-bridge level and at the network level [1, 2, 20].

SAR interferometry is an established remote-sensing technique that can measure terrain height [3]. The technique uses two coherent radar scans to measure range differences with the accuracy of a few millimeters. If topographical information is known, then it can be compensated to estimate the change in terrain height between the two radar passes. This technique is called differential SAR interferometry (dInSAR) [25]. Its main limitation is the difficulty in separating atmospheric and land cover changes from topographical changes. Persistent scatterer interferometry (PSI) extends the dInSAR principle using many SAR acquisitions [16]. With PSI, it is, therefore, possible to analyze the temporal dimension in addition to the spatial dimensions and thus to circumvent the dInSAR limitations. The main PSI output is a point cloud where the measurements describe the temporal movements of measurement points, also called persistent scatterers (PS), in form of time series. In most cases, a linear model of ground motion is assumed for the time series analysis. PS density strongly depends on the land cover, with higher densities from urban landscapes [16]. The accuracy of the temporal displacements is in the order of 1 mm/year, as reported in a review paper by Crosetto et al. [9].

During the last 2 decades, many studies made successful use of the PSI technique for the monitoring of buildings [6], ground water extraction [26], land reclamation [13], landslides [8], mining [7, 33], tunneling operations [34], and volcanoes [35]. PSI for bridges is a relatively new application and only few studies are currently available in the literature, which recognize the value of satellites for monitoring displacements on bridges [11, 39]. Specifically, some studies showcased applications to bridge collapses [28, 36], validated measurements with ground truth data [37], and derived movement predictions for validation purposes [12]. Some other studies reported the monitoring of individual bridges [20, 22, 23, 44]. The underlying mechanisms resulting in bridge displacements that have been monitored by radar satellites include welding cracks in bridge metal supports [23], long-term bridge deflections [12, 22], extensive cracking and spalling of post-tensioned concrete girders [20], bridge collapses due to scouring [36] or due to accelerated aging [28], and deterioration to bridge articulations [37]. The University of Virginia, in collaboration with the US Department of Transportation, conducted research with the goal of implementing InSAR-monitoring techniques to allow early detection of geohazards that could potentially affect transportation infrastructure assets at the network level [1, 2]. The InSAR data were analyzed using several simple tools that were specifically developed to address specific issues including: subsidence detection, bridge motion, road smoothness, and pavement motion. The above studies have outlined how InSAR can be a valuable source of data as a complement to visual inspection, however, more of these studies are required to establish this technology in the field of bridge SHM and to increase its acceptance by bridge engineers [20]. In addition, major SAR data providers have developed their own tools to allow their clients to easily visualize processed data from radar satellite imagery. Such processed datasets are often displayed within a Google Earth image of the area of interest (AOI). These visualization tools, however, are proprietary and usually not available to the general public.

1.2 Research significance

Uncontrolled thermal expansion or contraction can severely affect bridges and can lead to connection issues, girder cracking, or other problems [41]. Displacement thermal sensitivity (expressed in mm/°C) has been identified as a unique parameter that can be determined from SAR satellite measurements on bridges [12, 22, 23], which can be monitored for the early identification of potential problems. Some non-thermally induced problems (e.g., corrosion and seizing of bridge bearings) can also be detected if they affect the thermal sensitivity of bridges. Previously, its calculation has only been determined in the longitudinal direction of the bridge [12, 22, 23], which in many cases is the most significant contribution to thermal deformations. However, there are several cases where the vertical component becomes significant and needs to be accounted for. For instance, in concrete-slab-on-steel-girder composite bridges, displacement thermal sensitivity may have a substantial vertical component since temperature changes can induce significant bending in the bridge superstructure due to the different thermal expansion rates of concrete and steel. A detailed calculation approach for displacement thermal sensitivity is, therefore, presented in this paper that also takes vertical displacement into consideration. A methodology is proposed to use displacement thermal sensitivity as a means to monitor bridge structural behavior as measured by satellites and predicted by analytical calculations, which may help early identification of potential problems that may lead to failure if not attended.

The limited availability of early warning systems based on satellite measurements has also created a strong need to fill this technology gap by developing such tools to assist bridge engineers for the continuous monitoring of bridges, providing crucial data between scheduled bridge inspections. In this context, Satellite Applications Catapult in the UK and the National Research Council of Canada partnered up with the main objective to develop a decision support tool for authorities in charge of bridge inspection and maintenance. Several consultations have been conducted in both countries to understand end-user needs and requirements. Based on these, a new tool was envisioned to integrate data from different sources (e.g., satellites, in-situ sensors, numerical models and visual inspection reports) to deliver bridge performance indicators on structural stability, integrity, risks, and safety.

In this paper, actual satellite displacement measurements from two recent case studies are presented in Sect. 2, which also served as input data for the development of the decision-support tool. Novel approaches to determine the expected displacements and thresholds for early warnings and critical alerts are discussed in Sect. 3. The development of the decision-support tool—currently in its initial phase and focusing on 3D visualization of satellite data and early warning of excessive displacements—is illustrated in Sect. 4. This tool, which can be integrated into a larger bridge management system, is expected to address the above research gaps and help authorities to make better and timely decisions based on actionable data from satellites and other sensing devices to identify safety–critical structures and quantify the risk they pose to their users.

2 InSAR displacement measurements for bridge monitoring and visualization

This section presents two case studies selected for bridge monitoring, from which the processed satellite datasets are used in the development and demonstration of the proposed data visualization and early warning platform (Sect. 4).

2.1 Bridge case studies

The 90-year-old Jacques Cartier Bridge—operated by Jacques Cartier and Champlain Bridges Inc. (JCCBI)—crosses the St. Lawrence River and links the cities of Montreal and Longueuil in the province of Quebec, Canada, which also provides access to St. Helen’s Island. The bridge has 5 traffic lanes over 40 spans of a combined length of approximately 3 km. Its main section, with a length of 590 m, comprises a steel truss superstructure carrying a high-performance concrete deck on concrete piers (Fig. 1a). The deck is made up of slabs that are not connected to the steel truss (no studs) and rest on neoprene supports. Such design allows the concrete deck to behave independently from the steel truss superstructure to prevent the transfer of thermal loads to one another.

Fig. 1
figure 1

The monitored bridges in Montreal (QC), Canada

Full size image

The 160-year-old Victoria Bridge—owned by Canadian National Railway (CN)—crosses the St. Lawrence River, and links the cities of Montreal and Saint-Lambert in Quebec, Canada. The 3-km-long bridge consists of through trusses, deck trusses, girder spans and two lift spans that carry two railway tracks and four narrow roadway lanes. The railway tracks are supported by a deck, which is mostly made of timber bridge ties, while the roadway riding surface is mostly made of steel grating. The roadway is carried on cantilevered floor beam extensions on the through trusses, which is carried under the tracks on deck trusses (Fig. 1b).

2.2 Acquired radar imagery

For the InSAR analysis, scenes have been obtained from Radarsat-2 at a 24-day repeat pass period for two satellite pass directions (ascending, when the satellite navigates from south to north poles; and descending, from north to south poles). For the monitoring of the Jacques Cartier and Victoria Bridges, the SpotLight-A (SLA) beam mode was selected, which is best suited for bridge-monitoring applications since it provides the satellite’s best ground spatial resolution (1 m × 3 m). More details on available Radarsat-2 beam modes can be found in MDA [27]. Two image stacks with opposite viewing geometries were selected. The first one was the SLA26-asc stack in ascending direction; looking sideways to the East with a 48° incidence angle (Fig. 2, left). The second one was the SLA12-des stack with a descending direction; looking sideways to the West with a 39° incidence angle (Fig. 2, right). For the InSAR analysis conducted by Greene Gondi et al. [18], a total of 19 scenes were available from the SLA-26-asc stack and 28 scenes from the SLA12-des stack, covering a 2-year monitoring period from May 2016 to August 2018.

Fig. 2
figure 2

Viewing geometries selected for monitoring the Jacques Cartier and Victoria Bridges

Full size image

It should be noted that only one single stack of radar images is normally required to monitor a bridge on an operational basis; however, two independent stacks (ascending and descending) were analyzed in this study since one of the goals was to investigate the feasibility and usefulness of performing 2D decomposition on the line-of-sight (LOS) displacement data from two independent stacks of satellite imagery (however, not the focus of this paper). Viewing the data from two different LOS may give additional perspective on the interpretation of displacement detected by each image stack [21, 32].

2.3 InSAR analysis of satellite imagery

Expanding from Sect. 1, SAR is a remote-sensing technique where a radar image is formed by collecting and processing a series of transmitted coded microwave pulses that have reflected or scattered from certain elements on the Earth’s surface. InSAR is a technique where the amplitude and phase of two complex radar images acquired at two different times are combined in a so-called interferogram. Each pixel in an interferogram comprises a phase difference (from 0° to 360°) between two distinct SAR snapshots of a given resolution cell. The interferogram phase is cumulatively sensitive to all geometric and physical variables that affect the return path of the microwaves between the satellite and Earth’s surface. Hence, the phase is proportional to surface topography, surface displacement along satellite LOS, atmospheric pressure, and water vapor. Knowing the phase difference and the radar wavelength (5.66 cm for Radarsat-2), the relative displacement of a given target over time can be estimated. The PSI method allows the detection of point-like coherent targets in the radar image that preserve their structural characteristics through time called persistent scatterers. This method was selected because it preserves the full resolution of selected targets, and provides discrimination between high- and low-quality targets, e.g., separating bridge elements from water elements [18]. The analysis of radar backscatter returns from bridges can be complicated due to the combination of layover, shadow, and multi-bounce effects. Layover effects can occur when two or more spatially separated scattering elements are at the same radar range and may thus appear to overlap in the radar image. Shadow effects can occur when incident radar signals are blocked by other parts of the structure. Multi-bounce effects can occur when radar signals bounce off more than one physical object before returning to the satellite. More details are found in Curlander and McDonough [10].

A linear phase model was fit to the PS-InSAR data using regression analysis to estimate the following parameters:

  • Residual height (m)—fitted against perpendicular baseline (stereo sensitivity) data.

  • Thermal sensitivity of displacement (mm/°C)—fitted against ambient temperature data.

  • Linear time rate of displacement (mm/year)—fitted against time from the reference image acquisition.

  • Coherence (ranging 0–1)—confirming quality of fit and reliability of processed data.

Figure 3 shows the LOS residual height, linear rate (i.e., velocity), and thermal sensitivity components of the data estimated over the Jacques Cartier Bridge from the descending stack (SLA12-des). Similarly, Fig. 4 shows the residual height, linear rate and thermal sensitivity components estimated over the Victoria Bridge from the ascending stack (SLA26-asc). It can be confirmed that the height dataset corresponds well to the known elevations of the structures, the linear time rates of displacement indicate negligible subsidence movement on the bridges, and the thermal sensitivity of displacement varies according to measured variations in ambient temperature (discussed in detail in Sect. 3). Note that the color scales in Figs. 3 and 4 were optimized to better distinguish the measured patterns and do not cover the whole range of measured values which can, however, be fully appreciated in the next two figures.

Fig. 3
figure 3

a LOS residual height (top), b LOS linear time rate (middle), and c LOS thermal sensitivity (bottom) overlaid on SAR amplitude maps from SLA12-des at Jacques Cartier Bridge for May 2016–September 2018 [18]

Full size image
Fig. 4
figure 4

a LOS residual height (top), b LOS linear time rate (middle), and c LOS thermal sensitivity (bottom) overlaid on SAR amplitude maps from SLA26-asc at Victoria Bridge for May 2016–August 2018 [18]

Full size image

3 Bridge movement prediction and proposed thresholds for early warning

The total displacement pattern that can be derived with the PSI technique is modeled by the following equation [17]:

$$d\left( t \right) = v \times t + k \times T\left( t \right) + n\left( t \right),$$
(1)

where d is the measured displacement in mm, t is the acquisition time in year, v is the deformation mean velocity in mm/year, k is a thermal coefficient in mm/°C, T is the ambient temperature in °C, and n is a function representing non-linear motion in mm.

The accuracy of the measurements at PS locations has been reported by a number of studies. For instance, the total displacement measurement accuracy was found to be within a few millimeters [24] and was reported to depend on the number of acquired images, the PS signal intensity (the higher the better), the satellite acquisition revisit time period (the smaller the better), and the atmospheric compensation [4]. The thermal sensitivity of the displacement measurements has been reported with an accuracy of 0.04 mm/°C [17]. As far as geolocation of PS is concerned, the accuracy of the geolocation itself was found to be in the order of decimeters for the horizontal directions and meters for the vertical direction [4]. PS geolocation accuracy depends on several parameters and can be improved by increasing the number of images acquired for InSAR analysis, the image resolution, the PS signal intensity, and the sensor geometrical distance between the acquisitions.

3.1 Effect of satellite viewing geometry on displacement measurement

Satellites typically look at the Earth’s surface with an inclined view, resulting in observations and measurements made along the LOS direction at a given incidence angle from the vertical. When comparing satellite measurements to theoretical calculations or numerical predictions that are typically calculated along the vertical and horizontal directions, one needs to consider the following parameters:

α: incidence angle of the satellite line-of-sight (48° for SLA26-asc and 39° for SLA12-des).

β: angle between satellite track heading and bridge azimuth (113° for SLA26 and 274° for SLA12 (J. C. Bridge); 73° for SLA26 and 234° for SLA12 (Victoria Bridge)).

With the above two parameters, the following equation can be used to determine the LOS displacement from the calculated vertical and horizontal components:

$$D_{{{\text{LOS}}}} = {-}D_{{\text{V}}} \cos \alpha {-}D_{{\text{L}}} \sin \alpha \sin \beta ,$$
(2)

where DLOS is the line-of-sight displacement (or range); DV is the vertical component of displacement; DL is the longitudinal component of displacement. As far as the horizontal displacement is concerned, Eq. (2) above indicates that InSAR measurements from Radarsat-2 will be most sensitive to the longitudinal component for east–west-oriented bridges (β ~ 90° or 270°), such as the Jacques Cartier and Victoria Bridges in Montreal, and to the lateral component for North–South-oriented bridges (β ~ 0° or 180°). Previous InSAR studies have used similar approaches [12, 38].

3.2 Prediction of bridge thermal displacement sensitivity

The displacement thermal sensitivity of a bridge is defined as the elastic displacement response of a bridge in the direction considered (i.e., vertical, longitudinal, or lateral) to a unit change in temperature (i.e., ∆T = 1 °C). It is a property of a given bridge that can be monitored using satellite data and it is believed that through its change over time, an early warning system can be established. This section outlines how displacement thermal sensitivity can be calculated for different types of bridges in both the longitudinal and vertical directions.

For bridges constructed with deck and superstructure having similar expansion coefficients, the dominant thermal expansion or contraction is expected to be in the direction of the longest dimension; hence, the longitudinal direction in the case of the Jacques Cartier and the Victoria bridges (discussed in Sect. 3.2.1). However, for a composite bridge built with a concrete deck and steel girders having significantly different thermal expansion coefficients, additional vertical deck deflections may arise due to thermal effects and, therefore, should not be neglected (discussed in Sect. 3.2.2).

3.2.1 Thermal sensitivity: for bridges with deck and superstructure of similar thermal expansion coefficients

In the vertical direction, a bridge made of deck and superstructure with similar thermal expansion coefficients will exhibit negligible vertical deflection of the deck due to a temperature change (ΔT) assuming small thermal gradient across the section depth. However, the vertical elements of the bridge are assumed to expand or contract in the axial direction due to temperature variations (Eq. 3).

In the longitudinal direction of the bridge deck, the bridge will display thermal movement proportional to the length of the bridge span under consideration and the change in ambient temperature, assuming the bridge temperature is in equilibrium with the ambient temperature (Eq. 4). Based on the above assumptions, the vertical and longitudinal components of thermal displacement can be found as follows:

$$D_{{{\text{Vth}}}} = L_{{\text{V}}} \times {\text{CTE}} \times \Delta T,$$
(3)
$$D_{{{\text{Lth}}}} = L_{{\text{L}}} \times {\text{CTE}} \times \Delta T,$$
(4)

where DVth = thermal displacement in the vertical direction; DLth = thermal displacement in the longitudinal direction; LV = length of vertical element; and LL = length of longitudinal element. Previous InSAR studies have used similar approaches [12, 22, 23].

For the Jacques Cartier Bridge, InSAR measurements were filtered to select only the data points with high coherence values (from 0.8 to 1.0) located within close proximity of the bridge footprint. Finite element model (FEM) predictions of thermal displacement sensitivity were transformed using Eq. (2) for the satellite viewing geometry corresponding to each image stack. For the SLA12-des image stack, Fig. 5 illustrates the comparison between the calculated FEM displacements and the InSAR measurements from the satellite, where a relatively good match is found, with a mean absolute error (MAE) of 0.25 mm/°C when compared to the range of measured values (− 1.0 to + 1.9 mm/°C). The predominant importance of the longitudinal component of thermal sensitivity compared to the vertical component is clearly seen. A few outlier data points, however, could not be explained readily, which may be due to InSAR-processing difficulties related to 3D geolocation, layover effects, and other factors, as explained earlier, especially when it is difficult to know exactly from which bridge element a given radar signal is originating.

Fig. 5
figure 5

Comparison between InSAR and predicted thermal sensitivity data for the LOS direction obtained from the SLA12-des stack (Jacques Cartier Bridge; May 2016–September 2018)

Full size image

For the Victoria Bridge, InSAR data points with high coherence values above 0.8 were also selected. The LOS predictions of thermal displacement sensitivity were calculated with Eq. (2) for the respective satellite viewing geometry. For the SLA26-asc image stack, Fig. 6 illustrates the comparison between the theoretically calculated displacements (Eqs. 2–4) and the InSAR measurements from the satellite, where a good match is found, with a mean absolute error (MAE) of 0.15 mm/°C when compared to the range of measured values (− 0.9 to + 1.3 mm/°C). Again, the predominant importance of the longitudinal component of thermal sensitivity is clearly seen. A few outlier data points, however, could not be explained readily, for the reasons mentioned above.

Fig. 6
figure 6

Comparison between InSAR and predicted thermal sensitivity data for the LOS direction obtained from the SLA26-asc stack (Victoria Bridge; May 2016–August 2018)

Full size image

3.2.2 Thermal sensitivity: for bridges with deck and superstructure of different thermal expansion coefficients

For a composite bridge made of a concrete deck on steel girders, significant vertical deflections of the deck may be expected to arise due to thermal effects. As steel girders freely expand or contract at a higher rate than the concrete deck due to a higher coefficient of thermal expansion (CTE), internal axial forces on concrete and steel arise under restrained movement and lead to the bending of the composite bridge deck due to temperature changes. In this section, the calculation of the vertical thermal sensitivity for 1-span, 2-span, 3-span, and 4-span concrete deck on steel girder bridges is demonstrated using a numerical example, assuming a span length L = 40 m. A typical concrete deck on steel girder bridge with four girders is illustrated in Fig. 7a and the repeating section of the bridge is zoomed in Fig. 7b. Tables 1 and 2 tabulate the dimensions and material properties selected for the unit bridge section of this example.

Fig. 7
figure 7

Typical geometry of composite bridge deck with axial forces acting on deck subject to temperature increase. a Cross-section of typical concrete deck on steel girder bridge. b Repeating unit bridge section

Full size image
Table 1 Dimensions of unit bridge section
Full size table
Table 2 Material properties of unit bridge section
Full size table

As mentioned previously, for a composite section made up of two materials with different values of CTE, such as a concrete deck on steel girder bridge, axial forces arise on the components of the composite systems when subject to a uniform thermal change as shown in Fig. 7b (noting that force direction reverses when temperature decreases). The magnitude of the force P can be calculated with the following equation below:

$$P = \frac{{\Delta T \left| {{\text{CTE}}_{{\text{s}}} - {\text{CTE}}_{{\text{c}}} } \right|}}{{\frac{1}{{A_{{\text{s}}} E_{{\text{s}}} }} + \frac{1}{{A_{{\text{c}}} E_{{\text{c}}} }}}},$$
(5)

where P = axial force acting on centroid of elements of composite system, ∆T = temperature change (∆T = 1 °C for thermal sensitivity calculation), CTEs = coefficient of thermal expansion of steel, CTEc = coefficient of thermal expansion of concrete, As = area of steel, Es = modulus of elasticity of steel, Ac = area of concrete, Ec = modulus of elasticity of concrete.

Using Eq. (5) for the calculation of the moment at the bridge extremities (M = Pd; where d is the distance between the centerlines of concrete and steel) and the boundary conditions for either a 1-, 2-, 3-, or 4-span bridge, the equation for the vertical deflection due to a 1 °C temperature increase can be formulated using the Euler–Bernoulli static beam theory. It is plotted in Fig. 8 for the dimensions of the unit bridge section selected for this example (Tables 1, 2). It is noted that the information provided in Fig. 8 is not exhaustive, and only covers simple cases of composite bridges. This approach can be expanded to frames and more complex types of bridges.

Fig. 8
figure 8

Vertical and longitudinal thermal sensitivities for composite bridges with 1, 2, 3 or 4 spans

Full size image

3.3 Thresholds for bridge displacement linear rate

Line-of-sight displacement rates are illustrated earlier in Figs. 3b and 4b for the two case study bridges considered, respectively, where each measurement point corresponds to a colour-coded permanent scatterer. These data can be aggregated to calculate the average cumulative displacement over a given period of time covered by the acquired satellite imagery. The vertical and horizontal components of these measurements can also be estimated from Eq. (2) given the satellite viewing geometry. Threshold values for either the linear displacement rate or the cumulative displacement measured along the length of the bridge can be set by the bridge authority for use in an early warning system. Thresholds may be defined based on observations, past bridge inspection measurements, or expert knowledge.

For example, in a University of Virginia study conducted for the US Department of Transportation [2], two threshold levels for the vertical movement of bridge decks were established, which are: a warning threshold (yellow flag) and a critical threshold (red flag). More specifically, month-to-month displacements measured on the bridge were used to calculate velocities for each month. If any of these monthly vertical velocities were found to exceed 1.3 cm/month (0.5 inch/month), then a critical (red flag) alarm is raised. The monthly velocities were then aggregated to calculate the median velocity over a running period of 1 year (updated monthly). If any of these median vertical velocities were found to exceed 2.5 cm/year (1 inch/year), then a warning (yellow flag) alarm is raised. This procedure may be used as a guideline to assist bridge authorities in the threshold definition for the displacement linear rate of their bridges.

3.4 Identification of excessive displacement

With visual bridge inspections being conducted under pre-determined schedules (every year, 2 years, or longer depending on types of inspection and jurisdictions), problems can go undetected between two inspections and may lead to rapid bridge deterioration or even catastrophic collapse. Bridge movement detection and early warning tools based on frequent measurements are needed for monitoring critical bridges and keeping them safe and in good condition. In the previous paragraphs, relationships were given to estimate the expected displacements to allow one to compare predictions with satellite measurements to identify locations on the bridge where movement (or stability) may become a problem if not controlled in time. In the case that a bridge authority does not have access to established relationships and threshold values for the displacement thermal sensitivity or linear time rate that can occur on a given bridge, the baseline deviation method presented next may be used. By comparing updated satellite measurements with an established baseline for a given bridge, changes can be detected without prior knowledge of the bridge’s typical displacement thermal sensitivities or linear time rates. Therefore, by relying on some simple statistical parameters that could be defined by the bridge authority, the approach can be made universal.

A key assumption of this approach is that the established baseline represents the current condition of the bridge, whether it is established during: (a) the early life of the bridge (which may represent the initial condition of the bridge), from which a deviation may indicate a deterioration; or (b) later in the life of the bridge, from which a deviation may indicate additional deterioration (most likely) or an improvement. The relationships presented earlier in Sect. 3.2 may be used to determine what would or would not be considered a worsening case.

As a first step, a baseline of the thermal sensitivity of displacement along the bridge layout needs to be established for future comparisons. For this, one stack of satellite images needs to be acquired for a typical period of 1 year to cover a full cycle of seasonal temperature variations at the bridge so that the average displacement thermal sensitivity along the bridge can be accurately determined—noting that triggers may be obtained only after the baseline assessment period is over. The stack of satellite imagery may be coming from either the satellite’s ascending or descending pass. The decision to select one pass direction over the other may be related to geometric considerations such as the location of the desired bridge features of interest for the monitoring program since ascending passes are looking sideways to the East and descending passes are looking sideways to the West for RadarSat-2. The pass selection may also depend on the time of acquisition in relation to bridge traffic and/or ambient temperature since, at near 45° latitudes, images from ascending passes are taken at around 6 pm (local time), while images from descending passes are taken at around 6 am at which time the bridge temperature may well be at equilibrium with ambient temperature.

Once a baseline is established for the linear time rate or the thermal sensitivity of displacement, then the InSAR analysis of the data may be updated once every 24 days (in the case of RadarSat-2) and the updated trend may be compared to the baseline. Given that there may be some outliers in the measurement points along the bridge layout (due to variability, unknown/uncontrolled effects, etc.), it is suggested to use a best-fit polynomial to describe the overall trends of interest to allow a meaningful comparison between the updated and the baseline datasets.

Figure 9 illustrates this approach, with randomly generated data points of thermal sensitivity values for a two-span composite bridge (properties from Tables 1 and 2), using best-fit polynomials for the baseline dataset (in green) and an updated dataset (in purple). In Fig. 9, the threshold for the warning level is indicated as δ1 and the incremental threshold for the critical level as δ2, for which the values may be defined by the bridge authority from structural or statistical considerations.

Fig. 9
figure 9

Baseline deviation method with randomly generated datasets

Full size image

In this example, a downward settlement of the middle pier was simulated after the first year of monitoring, which locally pulled down the best fit of the updated dataset at the given pier and triggered a warning between the 30,000 mm and the 50,000 mm positions on the bridge layout line. Additional settlement of the middle pier in the future may lead to a critical alert if the problem was not corrected in time after the first warning.

4 New data visualization and early warning tool

4.1 User requirements

Bilateral consultations in the UK and Canada have been carried out to capture end-user challenges, needs, and requirements for the development of the tool. End users included stakeholders from the bridge and remote-sensing communities. The consultations were designed to allow the review of requirements against existing infrastructure monitoring projects, the gathering of detailed user requirements, the understanding of how satellite data might be utilized to improve planned maintenance and structural repair, the identification of other sectors exposed to similar issues, and the identification of key activities to conduct during the development phase of the new software tool. Workshop participants expressed what they expected from such a proposed product, highlighting what features and capabilities the tool might have. Stakeholders also identified several challenges typically found in monitoring bridges.

First, they recognised that each bridge is unique considering their different superstructure, substructure, foundation, climate, and loads. For this reason, the types of bridges on which satellite technology would work best should be identified through validation case studies covering most ranges of bridges and conditions. Second, some bridges, like long-span suspension bridges, may be difficult to inspect and install sensors at hard-to-reach locations. Remote monitoring might be useful and complimentary in these cases. Third, it is not clear how extensive climate change will affect the performance and longevity of bridges, thus calling for the development and validation of additional condition assessment monitoring and decision support tools to complement the information traditionally obtained from mandatory visual inspections. As bridge inspections are typically carried out at given intervals, issues developing between two inspections might not be identified in time if continuous or frequent monitoring is not used.

Considering the above-identified requirements, one pressing issue for bridge owners is the detection of slowly developing deformation problems that may lead to sudden failures if left unmonitored for some time between visual inspections. The timely detection of these problems on the monitored bridges should trigger warnings and critical alerts. Moreover, the ranking of bridge movement issues at the network level would help engineers in prioritizing bridges for inspection and maintenance for given ranges of years based on times estimated to reach certain predefined thresholds. Finally, data integration with information from other sources including in situ sensors, weather stations, and inspection reports is also an important user requirement to complement the information provided by the satellite data.

4.2 Conceptual development plan

The development plan for the tool includes three phases. In phase 1 (3D Visualization), the focus was on developing a software platform for the 3D visualization of processed satellite data as well as other types of data that can be geolocated. The work plan included end-user consultations in the UK and Canada, development and demonstration of the 3D visualization tool using processed satellite data obtained over two selected Canadian bridges (Sect. 2), and comparison of displacement measurements from different satellite platforms (RadarSat-2 vs. Sentinel-1) and different sources (e.g., GPS elevation measurements). In phase 2 (Early Warning), the plan is to develop and implement an early warning system (Sect. 3) to allow the comparison of measured displacements with predictions for given types of bridges, to identify excessive displacements and their locations (Sect. 4), and to flag warnings and critical alerts to bridge authorities. In phase 3 (risk assessment), the plan is to apply the approach at the bridge network level to assess the risks of reaching pre-determined displacement thresholds and to help establish priorities for bridge inspection and maintenance.

4.3 Illustration of tool features

Some of the main features of the tool platform, called BRIGITAL, are showcased in the following screenshots taken from the tool graphical user interface. Its design has been carried out in Unity, which is a prevalent 3D graphics engine and development environment. Following the selection of the bridge from a drop down menu, two data display modes are available: average or temporal. The average mode is meant to show the average displacement rate and average thermal sensitivity over the full satellite data acquisition period (in this case 2 years), while the temporal mode is meant to show a given displacement dataset for a selected acquisition date.

Figure 10 illustrates Radarsat-2′s measured displacements (in mm) from the ascending satellite pass over the Jacques Cartier Bridge’s digital model. The 3D visualization requires an accurate estimate of the measurement heights and, for this, the height refinement product from PSI processing was used in the visualization. A given dataset for the specific acquisition date of 2017–04–05 is selected for display.

Fig. 10
figure 10

Displacement data acquired on 2017–04–05 over the Jacques Cartier Bridge (Radarsat-2 SLA26-asc)

Full size image

Figure 10 also shows one specific measurement point being selected, with the point information box providing the 3D geolocation coordinates, the satellite measurements (i.e., linear rate and thermal sensitivity), and a coherence value indicating the quality of the measurements. A 2D graph also displays the time series of the displacement (green curve) and corresponding ambient temperature (red curve) of the selected data point. One can observe that the bridge displacement and ambient temperature at this particular location on the bridge follow very similar patterns.

Figure 11 illustrates Radarsat-2’s average displacement time rate (in mm/year) from the ascending satellite pass over the Victoria Bridge (with the digital bridge model toggled off). Note that the data presented in Figs. 10 and 11 had been previously filtered by their latitude and longitude coordinates to only present the data which are expected to be coming from the bridge structures. The dataset can be extended to study the ground movement around the bridges and on access roads.

Fig. 11
figure 11

Average displacement rate data over the Victoria Bridge (Radarsat-2 SLA26-asc)

Full size image

Figure 12 presents Radarsat-2’s average displacement thermal sensitivity (in mm/°C) from the ascending satellite pass over the Victoria Bridge; however, being shown in the early warning mode, i.e., by identifying the data points as being either within a green, yellow or red zone based on the difference between the actual measurement and its prediction for a given location on the bridge (using the prediction method from Sect. 3). These three zones are defined by setting threshold values between the green and yellow zones (e.g., 0.5 mm), and between the yellow and red zones (e.g., 1.0 mm) in this example. The information presented in Fig. 12 agrees well with the 2D data presented earlier in Fig. 6 for the Victoria Bridge.

Fig. 12
figure 12

Early warning display of average thermal sensitivity data over the Victoria Bridge (Radarsat-2 SLA26-asc)

Full size image

5 Summary and conclusion

Many bridges in the UK and Canada are in urgent need of refurbishment and face challenges of limited capital investment. Satellites may assist bridge engineers in addressing some of these issues. By taking several images of an area of interest at different times and analyzing them with advanced processing techniques such as interferometric SAR, millimeter-level movement on ground structures can be detected and measured. Ground motion maps have been validated for several scenarios over the past 20 years and the EO industry providing this service is growing.

This paper presented InSAR basics and the methodology to apply this mature EO technology to bridges in relation to the interpretation and validation of radar satellite data, and its use for 3D visualization and early warning for excessive movement. The concept of displacement thermal sensitivity and its potential use to monitor bridge behavior was introduced. Two case studies were provided to illustrate the application, which were steel bridge structures located in Montreal, Canada (i.e., the Jacques Cartier and Victoria Bridges). For data validation purposes, calculation methods were presented to determine the extent of expected displacements (linear rate and thermal sensitivity) that can be measured by radar satellites on certain types of bridges. For instance, the mean absolute error of the displacement thermal sensitivity between theoretical calculations and satellite measurements was estimated at 0.25 mm/°C for the Jacques Cartier Bridge and 0.15 mm/°C for the Victoria Bridge. An approach was developed and illustrated to monitor the behavior and to determine and assign threshold levels in an early warning system for issuing alerts when an unexpected behavior is detected on the monitored bridges. Finally, a new 3D visualization and early warning tool was developed and demonstrated using geolocated displacement measurements displayed over digital bridge models and maps. In future development phases, the tool will serve as a platform based on satellite data and other data sources to identify and flag unexpected bridge behavior, and warn for potential bridge failures.