Monitoring of Tidal Variation and Temperature Change-Induced Movements of an Immersed Tunnel Using Distributed Optical Fiber Sensors (DOFSs)

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Introduction
Immersed tunnels have been widely used as fxed links under rivers and waterways. Tere are currently over 150 immersed tunnels in service worldwide, and about one-third of these have been in service for over 50 years [1]. With more and more immersed tunnels exceeding half of their designed lifespan, assessing the structural condition of existing immersed tunnels is increasingly becoming an important task for infrastructure managers in order to reliably plan the necessary maintenance.
Many immersed tunnels have shown signs of structural deterioration, leading to issues such as excessive diferential settlements, large joint deformations, joint leakages, or local concrete cracking [2][3][4]. At present, deformation monitoring of immersed tunnels is mostly limited to vertical settlements, measured by manual levelling at yearly or sometimes multiyear intervals. For example, settlements of most immersed tunnels in the Netherlands are monitored at yearly or even longer intervals with an accuracy of one millimeter (or worse) [5,6]. Tese monitoring campaigns only capture the tunnel deformation behavior over a relatively long time span, which can be adequate to evaluate long-term tunnel safety [7]. However, such yearly (or in rare cases half-yearly) monitoring fails to capture the short-term deformation behavior of immersed tunnels.
With increasing attention for tunnel structural safety, the short-term (daily or monthly) deformation behavior of immersed tunnels has become an important aspect of structural health monitoring. For example, seasonal thermal expansion of segments has been observed, which may lead to seasonal variation in joint openings and can negatively impact the structural safety of the rubber seals used in immersion joints [8,9], but how this impacts the overall tunnel structure has not been monitored. Also, for some immersed tunnels, it was hypothesized that the daily tidal fuctuation in the waterway above would induce a cyclic vertical response of the tunnel [10], but such tidal efects on immersed tunnels are rarely studied as the too-low frequency of the present monitoring techniques does not provide precise data to verify these claims. To address these knowledge gaps, this study investigates the short-term (daily or monthly) deformation behavior of immersed tunnels through on-site higher frequency structure monitoring at subhourly intervals, based on an innovative distributed optical fber sensing system.
A distributed optical fber sensor (DOFS) is a type of sensing technique which is capable of distributed and longdistance sensing. By attaching a long optical fber cable (up to 100 kilometers) to the host structure, the spatial-resolved strain or temperature along the fber axis can be measured with a signal interrogator [11,12]. DOFS has been applied in civil engineering monitoring, including in buildings and bridge structures [13] and tunnels [14][15][16], among others [13]. Terefore, DOFS has a high potential to set up a remotecontrolled deformation monitoring system for an existing immersed tunnel, which can provide higher frequency measurements than the current manual levelling practice.
In this study, a distributed optical fber sensor (DOFS) system is used in the First Heinenoordtunnel in the Netherlands, an immersed tunnel opened in 1969, and this system proves to be capable of measuring immersion and dilation joint deformations (joint opening and uneven settlement) at half-hour intervals. Te short-term (daily) deformation behavior of the Heinenoordtunnel under tidal loads is subsequently modeled using a coupled fow simulation in a transverse cross-section model in PLAXIS, and the calculated vertical movements of the tunnel are compared to monitoring results. Te simulation confrms that tidal fuctuation in the river generates signifcant variations in excess pore water pressures and deformations within the soil layers underlying the tunnel, and this mechanism is the main cause of the cyclic vertical response of the tunnel observed in the DOFS measurements. In the rest of this paper, frst, some background on the immersed tunnel structure and Heinenoordtunnel is introduced. Second, the design of a DOFS-based monitoring system is demonstrated, followed by detailing of feld sensor instrumentation and data acquisition. Tird, the monitoring results are presented, and the short-term (daily) joint deformation behavior is discussed. Lastly, the efects of river tidal variation on the tunnel are investigated based on monitoring results and numerical modeling.

Joint Deformation in Immersed Tunnels
Structurally, a segmented immersed tunnel consists of a chain of tunnel elements joined underwater. Te construction of an immersed tunnel generally starts from the prefabrication of elements. For ease of concreting, a long element (usually around 100 meters) is subdivided into multiple shorter segments, as depicted in Figure 1.

Joint Deformation Modes.
Two types of joints exist within a segmented immersed tunnel, namely, immersion joints and dilation joints (as indicated in Figure 1). Immersion joints are formed when elements are immersed and connected under the water, while dilation joints are formed when the elements are manufactured segment by segment in a dry dock [1]. Te joints within an immersed tunnel make it more adaptive to the efects of longitudinal uneven settlements and thermal expansion, as compared to a continuous nonjointed tunnel structure. Structural deformations along the tunnel tend to show as relative deformation at the joints.
Te temperature variation causes thermal expansion and contraction of tunnel segment bodies, which triggers opening and closure at tunnel joints in the longitudinal direction, as shown in Figure 2(a). Tese resultant joint openings or closures infuence the gasket sealing performance and are associated with some observed safety issues, such as joint leakage [6], local concrete cracking [2], and damage of gasket seals [3,17].
In addition, tidal fuctuations in the river above the tunnel are observed to trigger a cyclic vertical response on the immersed tunnel [10]. It is assumed that this vertical response tends to be more pronounced at the discontinuous joint location, which potentially causes a relative uneven settlement at two sides of a joint, as illustrated in Figure 2(b). Tese patterns of cyclic joint deformation may compromise structural integrity. However, there is hardly any feld monitoring available to confrm this assumed behavior.

Te First Heinenoordtunnel.
In this study, the First Heinenoordtunnel (hereafter Heinenoordtunnel for short) in the Netherlands is selected for feld monitoring, in order to investigate the structural behavior of an immersed tunnel under daily temperature variations and tidal impacts. Te Heinenoordtunnel is a typical Dutch immersed tunnel constructed under the Oude Maas River, as shown in Figure 3. Tis tunnel has a rectangular cross section (30.7 m wide and 8.6 m high) and was opened to service in 1969. It consists of 5 concrete elements longitudinally, each about 115 m long, and a single element is further divided into 6 segments of about 19 m in length individually. Te total length of the immersed tunnel section is 574 m, with 31 joints in total, including 25 dilation joints, 5 immersion joints, and a closure joint, as shown in Figure 4.
After over 50 years of the service period, the structural integrity of the Heinenoordtunnel has become an issue, and at two locations, coinciding with dilation joints, signifcant leakages have been observed, which implies excess joint opening may have occurred. Observations from similar immersed tunnels and indoor experiments show that seasonal temperature loading may negatively impact structural safety, but no defnitive measurements confrming or denying this behavior are available for the Heinenoordtunnel, and a yearly or multiyear monitoring interval will not show such seasonal infuences [8].
In addition, excessive joint opening may lower the structural integrity, and tidal fuctuations in the Oude Maas River (with a maximum tide amplitude of about 1.4 m and a half-day period) may also trigger a structural response on the tunnel, including joint opening and relative vertical deformation. Monitoring the joint deformations under tidal impacts better enables the tunnel manager to assess the structure's safety status.
In this study, the DOFS is designed to a build remotecontrolled monitoring system which instruments all the joints of Heinenoordtunnel (see Figure 4), to measure the daily (short-term) joint deformations in two directions, namely, the horizontal joint opening and the vertical uneven settlement (between the two sides of the joint), as demonstrated in Figure 2

Distributed Optical Fiber Sensor (DOFS).
Within DOFS, several diferent solutions exist, based on diferent light scattering phenomena that occur when light travels within optical fbers, including Raman, Rayleigh, and Brillouin scattering [19]. In this study, DOFS based on Brillouin scattering is used. In brief, Brillouin scattering occurs when light propagates within an optical fber core, and it creates a frequency shift between the Brillouin backscattered light and the original propagating light [11]. Tis Brillouin frequency shift (BFS) ∆] shows linear dependency on the fber strain (ε) and temperature variation (∆T), as shown in (1): where C ε and C t are strain and temperature sensitivity coefcients. By independently measuring the local temperature, preferably using an unstrained parallel section of fber, the temperature component C t ∆T, can be corrected for, and the strain distribution along the fber can be obtained. A complete DOFS system consists of a long optical fber (referred as sensing fber) plus a signal interrogator (including data-taking software). For structural deformation monitoring,   the optical fber should be attached to the host structure properly while one or both of the fber ends are connected to the interrogator for signal processing and data-taking. Commercially available (Brillouin scattering) interrogators can be distinguished as Brillouin optic time-domain refectometry or analyzer (BOTDR/A) and Brillouin optic frequency-domain refectometry or analyzer (BOFDR/A) and other types [11,19]. Tese systems difer in the precise method used to measure BFS, resulting in diferences in spatial accuracy and attainable measurement frequency. Te BOTDA and BOFDA require a full optical fber loop attached by both ends to the analyzer but typically have a much higher spatial resolution and accuracy than a BOTDR or BOFDR. Tese, on the other hand, can work with a single-ended fber instead of requiring a complete fber loop, which allows for more fexible and extended fber layouts. For this study, a BOFDA analyzer is used, as the higher spatial resolution is benefcial for the fber layout in this project, and a full optical fber loop can be installed in the tunnel with relative ease. In addition, the BOFDA interrogator is more afordable than other qualifed (BOTDA) interrogators, which reinforced the decision in favor of BOFDA.

DOFS-Based Monitoring System
Design. For immersed tunnel monitoring in this study, the DOFS is designed to precisely monitor the localized deformations at specifc joint locations (joint opening and uneven settlement) along the tunnel, rather than the (directly measured) distributed strain along tunnel segment bodies. Moreover, the monitoring system, once installed, shall not impose any interference with regular road trafc in the tunnel. Given this, a preferred feld monitoring confguration should be designed as a long optical fber cable that extends along the tunnel axis longitudinally and specifcally ftted to serve as a sensor block at individual joints for deformation sensing (joint opening and uneven settlement), while the fber ends extend to outside the tunnel to the interrogator located within the nearby service building, as shown in Figure 4.
At individual joints, two short sections of the fber are fxed at 3 points, labeled as fxation points P1-P3 in Figure 5. Te two strained fber lines (FL1 and FL2) plus 3 fxation points form a sensor block which detects two-directional joint deformations (joint opening along the y-axis and uneven settlement along the z-axis). When a certain displacement along the y-and z-axes has occurred over the joint, FL1 will detect only the horizontal component, which simplifcation is valid as the impact of any vertical deformation on the strain in FL1 is negligible. Te mathematical relation for transferring the measured fber strain to joint deformations is illustrated as follows.
At the time interval i, the relation between fber strain and deformation for FL1 can be established as For FL2, it follows that and the height diference between P1 and P3 is given by where l 1 /l 2 are the gauge lengths of FL1/FL2, l 1,i /l 2,i are the lengths of FL1/FL2 at the interval i, ∆f 1,i /∆f 2,i are the measured Brillouin frequency shifts of FL1/FL2 at the interval i (with temperature efects deducted), ε 1.i /ε 2.i are the measured strains of FL1/FL2 at the interval i, ∆y i is the extension of FL1 at the interval i, h i is the height diference between P1 and P3, and c ε indicates the strain sensitivity. For a measurement at the same location at a subsequent time interval j, the displacement-strain relations will be equal to equations 2-7, and the joint deformation relative to the interval i can be derived from an observed change in Brillouin frequency shifts as In order to verify the applicability and potential error sources of the designed sensor block (as illustrated in Figure 5) for joint deformation measuring, an experimental validation study has been conducted by Zhang and Broere [20]. According to the laboratory experiment results, the designed sensor block can efectively detect two-directional joint deformations and capture these with submillimeter  accuracy; a maximum relative error of only 6% for joint opening and less than 10% for joint uneven settlement were observed. In summary, the designed sensor layout proves to have a more than acceptable accuracy and an excellent performance for feld monitoring.

Field Sensor Installation and Data Acquisition.
For feld sensor instrumentation in the Heinenoordtunnel, the sidewall in the west tube is selected (see Figure 6). Here, the adopted sensing fber is a polyurethane sheath fber typed NZS-DSS-C07 with a diameter of 2 mm. Tis type of fber, manufactured by Nanzee Sensing Company, has a strain sensitivity of 48.55 MHz/0.1% and a maximum working strain of above 1.2% [21]. In feld installation, the optical fber is frst bonded to small fxing pads at designated points (see Figure 6(a)), and in a subsequent feld work, the three pads are fxed on the wall at precise distances. Hence, a sensor block at the joint can be set up with reduced difculty. Special cover boards made of thin steel plates are also prepared to protect the bare sensing fber from potential external impacts (see Figure 6). Note that fber line 3 (FL3) in Figure 6(a) is unstrained and aligned parallel to FL2 for the sake of easy protection. Te feld sensor parameters (gauge length and dimensions) are determined with reference to the dimensions of the joint gap and shown in Figure 5 and detailed in Table 1. Te installed DOFS sensor inside the tunnel is schematically shown in Figure 6.
Te frst 13 joints (including 3 immersion joints and 10 dilation joints between) from the north side of the tunnel were successfully instrumented in frst-stage feldwork, and data-taking with hourly periods started from December 16, 2020. Te other 17 joints were instrumented in second-stage feldwork, and monitoring began on June 11, 2021; since then, a complete optical fber sensing loop covering the whole 30 tunnel joints was available. It should be noted that the second dilation joint (counting from the north) of the 5 th element was not instrumented due to working space limitations. BOFDA interrogator type fTB2505 manufactured by fbrisTerre Systems GmbH is used to measure the Brillouin frequency shift. Tis device has a stated spatial resolution of 0.2 m (up to 2 km), a spatial accuracy of 0.05 m, and fber strain accuracy of 2 microstrain, according to fbrisTerre [22].

Monitoring Result Analysis
Te measured BFS of an unstrained fber length is theoretically only related to temperature variations. Terefore, at each joint, the BFS of a short unstrained fber section (about 40 cm long) directly adjoining the strained fber lines (in a sensor block) is measured for temperature sensing as well as temperature-efect compensation. Te ambient temperature measured at each joint in the Heinenoordtunnel can be derived from the following equation: where C t is the temperature sensitivity coefcient of the optical fber (1.89 MHz/°C), f t.0 indicates the BFS at reference temperature T 0 (here, a room temperature of 22.8°C), and f t.i is the measured BFS at the time interval i. As an initial accuracy check of the measurement by using the DOFS system, the temperature results were validated to closely follow the observed meteorological temperatures in the Heinenoord area (see Zhang and Broere [23]), which indicates that the monitoring accuracy of the DOFS system is acceptable. In the following sections, monitoring results of two periods of three successive days each are analyzed. Te frst period runs from December 17 to December 19, 2020, which represents the frst three days since monitoring of the northernmost 13 joints started; the second period runs from June 12 to June 14, 2021, which was the frst three days since monitoring of all 30 joints started. Tese two selected periods cover both a winter and summer season, which will help indicate diferences in daily tunnel behavior between diferent seasons. In the monitoring result analysis below, the joints are numbered as in Figure 7 to easily distinguish between immersion and dilation joints: Ij indicates the jth immersion joint from north to south end, while Dik represents the kth dilation joint (from north end) within the ith element. For example, I1 refers to the frst immersion joint, while D12 indicates the second dilation joint (from north) within the frst element.

Temperature Result in the Winter Period.
Te observed temperatures at 13 joints from December 17 to December 19, 2020, are available in the attached supplementary fles in this paper. Te monitoring results clearly show the daily temperature fuctuation, and there are diferences in the observed temperatures between joints, but these diferences lie within a range of 2°C. In addition, results also show diferences between the temperature fuctuations within a daily period at diferent joints. For example, for the three immersion joints, the temperature fuctuation on December 18 is the most signifcant at I1 (the north portal), with a variation of approximately 5.8°C during the entire day, while that of I2 ranks second for a total of change of 5.2°C, and the temperature at I3 shows the smallest fuctuation of 4.1°C. As could be expected, the temperature further inside the tunnel tends to fuctuate less than that at the portal. Another signifcant aspect observed in the daily behavior at joints I1, I3 and D11, as shown in Figures 8 and 9, is the two regular opening and closing cycles during a 24-hour period, which are attributed to the tunnel responding to tidal efects in the river. Tis aspect is discussed in more detail in Section 4.3.

Joint Uneven Settlements in the Winter Period.
For joint uneven settlements, if the north side (of the joint) is assumed static, a positive settlement value indicates the south side moves upwards, while a negative value indicates a downward settlement (Figure 11). Uneven settlement results of three immersion joints (I1-I3) are displayed in Figure 12, and those of the dilation joints are shown in Figures 13 and  14. Te monitoring shows that, except for joints D11 and D25, eight of the dilation joints show a negative uneven settlement (within a range of 0 to −0.12 mm) compared to the baseline  Comparing the behavior of the three immersion joints, I1 exhibits quite distinct behavior as the settlement curve within a daily period shows two recurring peaks and troughs, with an amplitude of about 0.25 mm. Note that I1 forms the transition between the northern tunnel service building and the immersed section. As the northern tunnel entrance ramp and service building are found on piles and have shown insignifcant settlements over time [24], the measured troughs in Figure 12 indicate that the immersed tunnel moves up and down periodically. Tis daily cyclic behavior is explained as the tunnel response to tidal efects and discussed in detail below. In addition, when comparing the magnitude of the uneven settlements with the joint opening, it can be concluded that the magnitude of joint opening is generally larger than that of uneven settlements.    Te temperature results show that there is a high consistency in the temperature fuctuation occurring at all joints, while a more detailed look into the data will reveal that further inside the tunnel the temperature is slightly lower than the two ends during this summer period. Te joint openings, during this period, lie within a range of −0.20-0.22 mm. It can be seen that the joint opening generally is negatively correlated with a temperature change and that a decrease in temperature generally corresponds to an increase of joint opening.
From the uneven settlement results in Figure 17, the most distinctive behavior is the two troughs observed for joints I1 and I6, which match quite well and repeat with a period of about 12.5 hours, while the settlement results of the other 28 joints do not signifcantly show such a cyclic behavior (the measured uneven settlement at I6 is positive, but for a more straightforward comparison with the other joints, its values are inverted in Figure 17). Note that I1 and I6 are the immersion joints at the north and south ends of the immersed section and form the transitions to the piled tunnel abutments. Considering the specifc sensor installation at these two immersion joints, the regular troughs indicate the entire immersed tunnel section moves up and down cyclically, almost as a rigid body, with reference to the service buildings. Tis phenomenon is attributed to tidal efects in the river and is discussed in Section 4.3.

Correlation of Joint Deformation with Temperature.
Te Pearson correlation coefcients between joint uneven settlements and joint openings on one hand and temperature on the other hand have been calculated, and as shown in Tables 2 and 3, the opening of all joints shows a negative correlation with temperature. At several joints, the correlation is distinctively signifcant, such as joints I1, D12, D21, D25, and D32. Tis indicates that the joint gap has a tendency to open at a low temperature (like in a winter period), while it closes at a high temperature (like in a summer period). Te expectation that seasonal joint opening and closure occurs, driven by temperature change, is validated by the observations in the Heinenoordtunnel.
Te correlation of joint uneven settlements with temperature is listed in Tables 4 and 5. It is clear that the correlation coefcients determined for each joint vary signifcantly. Of all 30 joints, 19 joints (for example D11, D14, and D21) show a negative correlation during the entire representative periods, whereas for 2 joints (I3 and I5), the correlation remains positive, and for the other 9 joints, it varies (and can be both negative and positive). Looking at each individual joint, it can be seen that the correlation varies quite signifcantly with time, which means that the impact of the temperature on uneven settlements at the joints is not that signifcant and clearly less signifcant than for the joint opening behavior. It should also be noted that the uneven settlement of most joints (except I1, I6, and D11) in the studied periods is quite small, within a range of −0.1 mm-0.1 mm, and the accuracy of the correlation with temperature at several joints may be infuenced by correction errors for temperature efects on the fber strain.

Impact of Tidal Efects.
Te daily cyclic behavior of the measured deformation at several joints, characterized by two regular peaks and troughs in the observed opening (see Figures 8 and 9) and uneven settlement (see Figures 12-17), has a roughly 12-hour period which is consistent with the tidal fuctuations observed in the Oude Maas River at the location of Heinenoord.
Te Heinenoordtunnel lies inland within the estuary of the Maas River where the river is still infuenced by the tidal fuctuation from the North Sea. Te tide above the Heinenoordtunnel is obtained from the nearby Goidschalxoord tidal station, and it shows a tidal variation between 1.1 and 1.4 m (relative to the mean sea level) with the expected period of 12 hours and 25 minutes (for reference to [25]), as shown in Figure 18.
According to the measurement results, both the joint opening and uneven settlements of some joints (mainly the immersion joints and D11) show a consistent twicedaily cyclic behavior which is closely linked to the tidal cycle. Figures 12 and 17 reveal the signifcance of the tidal efects on the whole immersed section in a vertical direction, while cyclic joint opening at D11 and I1 (in Figures 8 and 9) indicates that the tidal impact also leads to tilting of some segments and hence a resultant joint opening variation (such as the frst segment bounded by I1 and D11).
However, the measurements also show the tidal impact on the segment behavior difers between the diferent seasons. Figure 18 shows the joint opening behavior of D11 in summer and winter seasons compared to tidal levels (tidal data for December 17-18, 2020, and June 12-13, 2021 are highly similar, and only the tidal data for December 2020 have been plotted). It can be seen that, during the winter season (both in December 2020 and December 2021), the cyclic behavior of the joint opening is much more pronounced than during the summer season in June 2020. As the measured joint opening indicates, joint D11 closes in summer and opens again in winter. Tis implies that the seasonal joint deformation afects the robustness of the tunnel to tidal impacts, or in other words, the tidal impact on the tunnel joint deformation varies between seasons (for more information, see [26]).
Correlating the observed tunnel deformations to the tidal variations poses some additional issues. Te joint uneven settlement results (of I1 and I6, from June 12 to June 14) and the corresponding tidal curve are plotted in Figure 19. It is interesting to note that the immersed tunnel behaves more like a rigid body, settles downwards with an increasing tidal level, and returns upwards with decreasing tide, as shown in Figure 20. Te amplitudes of the daily cyclic deformation (the maximum diference of uneven settlement within a daily period) of I1 and I6 are Structural Control and Health Monitoring 9 slightly diferent. Tis cyclic vertical behavior of the tunnel under tide impact is further investigated via a numerical simulation.

Numerical Simulation
In order to simulate the observed vertical response of the tunnel due to tidal variations, a 2D fnite element simulation is conducted in PLAXIS 2D, commercial fnite element modeling software for geotechnical engineering. In the simulation, fve 2D models are built and simulated individually, which correspond to fve representative transverse cross sections coinciding with the middle of each tunnel element as shown in Figure 4. By comparing the vertical deformation results in each 2D model, the relative uneven settlement at immersion joints is calculated and further compared to the monitoring results.    Te soil parameters for each soil stratum are obtained from a site investigation report of the Second Heinenoordtunnel [28,29]. Tis bored tunnel was constructed in 1996 directly parallel to the immersed First Heinenoordtunnel, at a distance of about 80 m, and far more detailed site investigation data are available from this project compared to the original immersed tunnel design reports from 1964 [24]. From this site investigation, the approximate soil profle from the top down for the frst immersed tunnel element (E1) is listed in Table 6. Te soil strata beneath the other elements are generally quite similar to those in Table 6, although slight variations occur longitudinally along the tunnel.
Te bottom of the soil domain is set as an impermeable boundary (as the geological investigation reveals an overconsolidated clay layer below); the top boundary (riverbed) is set as permeable with a head equal to the designated tidal level; at the two side boundaries, both dynamic head (equal to the dynamic hydrostatic water pressure, for the upper sand layers, between −0.25 and −21 m) and seepage boundary conditions (for the lower clayey layers, between −21m and −38 m) are specifed. Te tidal variation is simulated by setting a user-defned time-history series of tidal levels as the piezometric head of the free water table at the top of the model. For this case study, the measured tidal levels of June 14, 2021, are used (see Figure 22). Te concrete tunnel structure is modeled as a nonporous medium, with a unit weight of 25 kN/m 3 , a void ratio of 0.03, Poison's ratio of 0.2, and an elastic modulus of 30 GPa.
In the initial construction stage, dredging the trench removed the upper 9-10 m thick soil layers, which caused a signifcant unloading of the underlying soil layer. In the subsequent construction stages, the soil was reloaded but to a lower stress level than initial. Here, the hardening soil (HS) model [30] is used, as it captures the unloading-reloading behavior of the soil from the initial construction to the longterm operational period. In the tidal-efect simulation, a preloading and subsequent unloading loop of 10 kN is      imposed at the top of the soil domain, and thereafter, the coupled fow consolidation process is simulated. Figure 23 shows the deformation of the tunnel-soil domain at low tide (with a tide height of −0.595 m below the mean water level), and the settlement at the tunnel bottom is about +0.24 mm. Figure 24 shows the deformation of the tunnel-soil domain at the frst tide peak (with a tide height of +0.585 m above the mean water level), and the settlement at the tunnel bottom is about −0.11 mm. Due to boundary efects of the prescribed variable head at the sides, the soil shows a slightly larger deformation than in the center close to the tunnel, which is the area of interest for this study. Close to the tunnel (about 90 m left and right of the tunnel walls), the settlement results are stable. Te simulation results are compared to the measured uneven settlement of I1 in Figure 22. For comparison, the measured and simulated settlement results are presented relative to the frst measurement point (on June 14). It can be seen that the phenomenon of the cyclic vertical movement of the tunnel under tidal impacts is captured well in the numerical simulation, and the two curves show a highly consistent behavior, although the calculated vertical response of the tunnel (with an amplitude of about 0.41 mm) is larger than the measured result from the DOFS sensor (with an amplitude of about 0.33 mm), which may be attributed to the uncertainties in soil parameter determination.

Simulation Results and Discussion.
Te variation of excess pore water pressure within the soil domain helps reveal the seepage within each layer. Figure 25 displays the vertical distribution of soil compression and the excess pore water pressure within the soil profle at high tide. It can be seen that, in the upper soil layers (−2.25 m to −24 m, mainly sand layers), excess pore water pressures generated by tidal fuctuation are insignifcant. However, within the thick clay layer (−24 to −29 m) and the bottom sand layer (−29 to −38 m), the resultant excess pore water pressure is signifcant. Te excess pore water pressure results within the clay (the layer middle point, below the tunnel at −26.49 m NAP) and sand layer (the layer middle point, below the tunnel at −32.27 m NAP) are also plotted in Figure 26, and it can be seen that the excess pore water pressure shows a cyclic variation with tidal fuctuation. At low tide, the lower soil layers (clay and bottom sand) bounce back, and water fows into these layers, which results in a positive excessive pore water pressure, while at high tide, the soil layers are compressed and water is squeezed out, which leads to a negative excessive pore water pressure.
In addition, the simulation results demonstrate that the majority of soil deformation under tidal loads occurs in the thick clay layer (−24 to −29 m) and the bottom sand layer (−29 to −38 m), as indicated in Figure 25. Te most signifcant compression occurs in the bottom sand layer and the thick clay layer, while for the upper sand layers, both deformation and excess pore water pressure development are insignifcant. Figure 27displays the compression deformation curve of these two layers under tidal fuctuation, and it can be concluded that these two layers are more tidesensitive than shallow sand layers, and they contribute dominantly to the cyclic response of soil domains under tidal fuctuation.
Similar simulations have been made for the transverse cross sections of all fve tunnel elements (E1-E5) taking into account the local variation in soil layers and the depth of the tunnel, and the results are shown in Figure 28. It can be seen that the periodical vertical movements of all fve elements under tidal impacts are quite consistent, with only minor diferences (the uneven settlement) between two adjoining elements compared to their individual absolute settlement. Furthermore, the uneven settlements at the joints (between two adjoining elements) are calculated and depicted in Figure 29, and it shows that the frst and last immersion joints (I1 and I6) exhibit the most signifcant deformation under tidal impacts, while the rest of joints present less signifcant deformation, compared to I1 and I6. Although the simulated joint uneven settlements are slightly larger than the monitored results, this diference is reasonable, considering the uncertainties in the soil parameters used and the simplifcations made in the 2D model setup. In summary, the simulation results are consistent with the   Structural Control and Health Monitoring monitored tunnel response in Figure 19, which indicates that the uneven settlements at joints other than I1 and I6 are small (as not to be detected with any signifcance by the DOFS), and hence, the whole immersed tube section behaves more like a rigid body and moves upwards and downwards periodically with tidal fuctuations.

Conclusions
Short-term (daily or monthly) deformation behavior under temperature variations and tidal impacts is an interesting but mostly overlooked aspect, in structural health monitoring of existing immersed tunnels. In this study, a distributed optical fber sensor (DOFS) is used to monitor relative joint movements in the Heinenoordtunnel, and short-term (daily) deformation behavior based on feld monitoring is investigated in detail. Te main conclusions in this study are as follows. First, the distributed optical fber sensor (DOFS) is an efective instrument to construct a monitoring system for immersed tunnel joint deformations that is robust enough for feld conditions and is proven to be capable of conducting high frequency monitoring (where high frequency means half-hour intervals compared to year or multiyear intervals for traditional techniques), which highlights its applicability in immersed tunnel monitoring.
Second, the hypothesis that cyclic joint opening and closure driven by temperature variations occurs in the immersed tunnel is validated. Specifcally, the joint opening is negatively correlated with temperature variations, which indicates that the joint gap has a tendency to open at a low average temperature and to close at high temperatures.
Tird, tidal variations in the river above the tunnel generate a vertical response of the immersed tunnel. Monitoring results show that the whole immersed section behaves more or less like a rigid body and moves upwards and downwards periodically with tidal variations, with a submillimeter movement amplitude. Te cyclic movement can be explained by a coupled fow and consolidation model of underlying soil layers under tidal variations. Te numerical simulation also shows that, at the Heinenoordtunnel, the tidal fuctuation generates an insignifcant response in the upper sandy soil layers but triggers a signifcant variation on the excess pore water pressure and deformation within the thick clay layer and the bottom sand layer, which contributes the most to the cyclic vertical response of the tunnel monitored by using the DOFS.
Finally, monitoring results also indicate that the tidal variations give rise to tilting of some segments in the tunnel, but the extent of this tilting behavior varies between winter and summer seasons. Te reduced tilt response in summer, when the tunnel structure is expanded and the joint openings are reduced (i.e., the rubber GINA gaskets are compressed more), implies that the seasonal joint deformation afects the response of the tunnel to tidal and other load variations.

Data Availability
Te data used to support the fndings of this study are provided in the supplementary materials.

Conflicts of Interest
Te authors declare that they have no conficts of interest.