Characterizing the deep pumping-induced subsidence against metro tunnel using vertically distributed fiber-optic sensing

Continuous pumping of groundwater will induce uneven ground settlement, which may adversely affect the nearby metro tunnels. In this paper, taking Nantong Metro Line 1 crossing Nantong Port Water Plant as an example, the surface level measurement and subsurface deformation monitoring using vertically distributed fiber-optic sensing are implemented to acquire the surface and subsurface settlement of emergency water supply conditions. The fiber-optic cable vertically buried in the constant-temperature layer is used to measure the subsurface strain field and deduce the deformation amount of each stratum. The monitoring results show that, during the pumping, the deformation of the aquifer and ground surface is linearly compressed with time; after the pumping, the ground surface continues to settle linearly at a slower rate for about 50 days, followed by a slow linear rebound, and the aquifer is logarithmically rebounded. In addition, deep pumping causes the deformation of the aquifers to be much greater than the surface settlement; the surface settlement lags behind the settlement of the aquifers by 1–2 months; the surface rebound recovery also exhibits a similar delay. Fitting models were derived to predict the maximum settlement and curvature radius of the site, which indicates that the adverse effects against the metro tunnel are not negligible once the continuous pumping exceeds 15 days. Those insights can be referred by the practitioners for the control of urban subsidence.


Introduction
Ground subsidence is a hazardous environmental geology issue which not only reduces stratum elevations, but also yields damage to buildings and infrastructure (Herrera-García et al. 2021;Pacheco-Martínez et al. 2013). Moreover, for metro tunnels, one of the most common linear underground infrastructures in cities, the longitudinal differential deformation induced by ground subsidence, can lower their safety, durability, and waterproof performances (Peng et al. 2017;Wang et al. 2016). The variation of the groundwater level induced by human activities is a major cause of differential subsidence in urban areas (Edalat et al. 2020;Xu et al. 2016b;Xue et al. 2005). Particularly, for those cities which have to withdraw underground water as the water supply, long-term pumping activities in the water source area might induce serious subsidence problems (Chai et al. 2004;Othman and Abotalib 2019).
Given the differential settlement, former studies mainly focused on its impacts on surface buildings. However, recent studies of ground subsidence against metro tunnels have revealed that, compared with the negative impacts imposed by the settlement of ground surface, those induced by the subsurface deformation are more significant for underground infrastructure (Shen et al. 2014). Zheng et al. (2014) studied the stratified settlement caused by the extraction of confined water using field tests and found that the deformation of phreatic layers is less than that of the confined aquifer layers, which was other than the acknowledged settlement law caused by dewatering of ground surface. Note a growing consensus has suggested that ground subsidence occurs lagging behind the pumping activity (Kearns et al. 2015), and the duration 1 3 762 Page 2 of 15 of land subsidence induced by deep pumping is longer than that by surface pumping (Cui and Jia 2018). However, current theoretical models of the pumping-induced settlement remain unavailable to fully characterize the above-mentioned influencing factors (Budhu and Adiyaman 2010;Wang et al. 2018;Xu et al. 2012;Zhang et al. 2017;Zhou et al. 2017). Therefore, concerning extracting deep groundwater scenarios, current models still have to be deliberately calibrated by the field measurements (Shen and Xu 2011;Xu et al. 2016a).
As is known, the ground subsidence can be monitored by a variety of measures (Poland et al. 2006), such as leveling (Abidin et al. 2001), GPS (Baldi et al. 2009;Choudhury et al. 2018;Hu et al. 2006;Mousavi et al. 2001), InSAR (Calderhead et al. 2011;Motagh et al. 2017), and their combinations (Galloway and Burbey 2011;Saleh and Becker 2018). Note all those measures cannot acquire layered subsidence measurements; even the layered marks can acquire, in that the layered settlement meters are fixed-point arranged, the discrete subsidence measurements cannot finely characterize the subsurface deformation field (Jiang et al. 2016). The distributed fiber-optic sensing (DFOS), a novel monitoring technique, can obtain the strain field along the sensing cable. Although the DFOS has been employed to monitor the subsurface deformation field of Shengze, an abnormal post-dewatering subsiding area in Suzhou of China (Gu et al. 2018;Wu et al. 2021;Zhang et al. 2018a), few works have been documented to use DFOS to monitor the variation process of the subsurface deformation field during a rapid pumping, and no mention assesses its negative impacts against metro tunnels. The application of DFOS in the metro tunnel was mainly reflected in structural health monitoring (Gómez et al. 2020;Gue et al. 2015). Due to temperature fluctuations near the surface, this technique was not used to evaluate changes in the stratigraphic environment around the tunnel.
In this paper, taking a groundwater plant near Nantong Port, Jiangsu Province of China, as an example, a test of deep multiwell dewatering was implemented to verify the applicability and feasibility of the DFOS technique to monitor the variation of the subsurface deformation field. Feature extraction on the DFOS measurements was also performed to assess the impacts of subsurface settlement against the metro tunnel. Fitting equations were deduced to shed light on the evolutionary trend of the surface and subsurface deformation field during and after the pumping, which can be used to predict its long-term impacts against the metro tunnel.

Principle of distributed fiber-optic sensing (DFOS)
A variety of DFOSs can be used for strain field monitoring . Typically, the Brillouin optical timedomain reflectometer (BOTDR) is used in this paper. The principle of the BOTDR is based on the change in the scattered light caused by nonlinear interactions between the incident light and the phonons which are thermally excited within the light propagation medium. When occurring in an optical fiber, the backscattered light experiences a frequency shift (the Brillouin frequency), which is dependent on the temperature and strain environment of the fiber (Wu et al. 2015). Compared with other scattered lights, a substantial advantage of Brillouin scattering is that its frequency shift caused by temperature is only 0.002%/°C, which is much smaller than that caused by strain. Therefore, while measuring the Brillouin frequency shift induced by strain, the influence of the temperature on the Brillouin frequency shift can be neglected if the changes of temperature are within 2 °C. The relationship between the Brillouin frequency shift and the strain of optical fiber yields: where v B (ε) is the Brillouin frequency against strain ε, v B (0) is the Brillouin frequency shift without stain, dv B (ε)/ dε is the strain coefficient, and the proportional coefficient of strain, at a wavelength of 1.55 μm, is approximately 0.5 GHz/%. Following such a term, the strain distributed along the sensing optical fiber can be measured. Given the monitoring scenario of land subsidence, the deformation field along the sensing optical cable caused by soil compression or rebound at depth h can be calculated in accordance with the measured strain, which yields: The drilling depth of optical fiber design is 230 m in this test, the metal-reinforced single-core cable (MRC) with model NZS-DSS-C02 and the fixed-point cable (FPC) with model NZS-DSS-C08 were respectively, installed in the monitoring hole to measure the stratum deformation; the structures of these two types of fiber sensors are shown in Fig. 1. MRC, which can effectively protect the optical fibers with several metal reinforcers, has good coupling and uniformity with soil by the screw structure of the sensor surface. FPC, with a fixed-point design, can be used to measure spacial inhomogeneous and discontinuous sections (Gu et al. 2018;Shi 2017).
The DFOS can effectively sense the deformation at different locations along with the fiber. When the fiber is fully coupled with the surrounding strata, the fiber at different locations can reflect the strains of strata at different depths. The strains reflected at different locations just represent the local strains of the fiber. The optic fiber signal collected by the interrogator is discrete and the amount of data is related to the fiber measurement length and resolution. To efficiently extract the morphological distributions along with the underground depth, the measurements ought to be organized in the form of a space-time matrix B (Sun et al. 2014). Given that the total number of sampling points along the optical fiber is n and the total number of sampling times is m; B is a two-dimensional matrix with n rows and m columns, which yields: where the element ε ij is the measurements of the strain field on the measuring point with different depth i at sampling time j. The matrix can visualize the deformation distribution of different depths with time.
Now that using the DFOS for subsidence monitoring, the submatrix B s of the space-time matrix B is usually extracted to characterize the local distribution of stratum deformation field, which yields: where the time interval of sampling points of the submatrix B s is [u, v], and that of the sampling depth interval is [s, t].
The submatrix B s can also be represented as a column vector group, which yields: where The column vector E j represents the strain vector acquired by the DFOS at the depth range [s, t] at sampling time j. The column vector E j at a certain time is substituted into Eq.
(2) to obtain the ground deformation Δd at a specific depth range [s, t], which yields: where h i is the length of a certain measured micro-element section of the DFOS in the formation. The strains in the local area of the stratum can be superimposed along the fiber to obtain the deformation of the stratum in a specific depth range.

Conditions of engineering geology and hydrogeology
Nantong, a coastal city in eastern China, has planned to build four metro lines. Among those, the planned section between the Jianghai Avenue Station and the Bus Station of Metro Line 1 will travel beneath the emergency water source of the Nantong Port Water Plant. The tunnel has a circular section with a burial depth of 21 m. The lining structure has an inner diameter of 5.5 m and a thickness of 0.35 m. The strata at this depth were less subject to surface temperature fluctuations, and the DFOS can effectively monitor the compressional strata deformation. In accordance with the relevant specifications (Gao et al. 2010), the cumulative settlement of the layer where the tunnel is located should not exceed 20 mm, and the curvature radius of the longitudinal deformation curve is not less than 15,000 m. Given the emergency water supply, a large amount of groundwater will be extracted from the aquifer. This may induce subsidence within the overlying strata, which might in turn pose some threats to the operational safety of the metro. This paper characterizes the adverse impacts of emergency pumping on the metro tunnel by monitoring the subsurface deformation field induced by a test of multi-well dewatering. Nantong is located in the alluvial plain of the Yangtze River Delta, widely covered by the Quaternary strata. The thickness of the strata ranges from 200 to 360 m, which is composed of a set of multiple sedimentary cycles with alternating sand and clay layers. The sand layer is thicker and contains coarse particles, which is conducive to the enrichment and transport of pore groundwater. The pumping test was performed on the south bank of the estuary of the Tonglv Canal into the Yangtze River; as shown in Fig. 2, the groundwater resources are abundant. The geographic location of the testing site is 32°00′55″-32°01′16″ N latitude and 120°49′11″-120°49′33″ E longitude, with a site altitude of about 4.0 m. Nantong has a humid subtropical monsoon climate with an annual average temperature of 16 °C, precipitation of 1036 mm, and evaporation of 1392 mm. The Tonglv Canal that crosses the test site is a hydraulic facility that has been artificially expanded in recent decades to bring water from the nearby Yangtze River, so its water flow is mainly influenced by the Yangtze River. Table 1 lists the physical and mechanical parameters of the strata of the test site according to the preliminary investigation works. As seen from the table, the aquifers are mainly composed of sandy soils, mixed with silty clay aquitards. Among those, the silt layer at a depth of 50 m attains a great amount of water content, as well as a small compression modulus, which is the aquitard between the phreatic aquifer (PA) and the first confined aquifer (CA1). The permeability varies between the silty clay and silty sand interlayers within both ranges of 120-150 m and 180-190 m. Note both interlayers might impede the transit of groundwater, which causes the inconsistency between the deformation fields of the subsurface and the ground surface.
The groundwater is mainly loose rocks porewater, mostly stored in sand layers. In accordance with the storage condition, the groundwater can be divided into five aquifer groups from top to bottom, namely, the phreatic aquifer (PA), the first confined aquifer (CA1), the second confined aquifer (CA2), the third confined aquifer (CA3) and the fourth T o n g l v C a n a l Y a n g t z e R i v e r Nantong Nantong Port

Gangzha District
Chongchuan District R e n g a n g R iv e r

Hongqiao Rd
Qingnia n Rd  confined aquifer (CA4), as shown in Fig. 3. All adjacent aquifers are hydraulically connected, with lateral recharge from the Yangtze River and infiltration recharge between aquifers dominating along the river, and artificial pumping is the main drainage route. Note that only CA4 is not included in this pumping test. The PA consists of the silty clay, silty sand, and fine sand of the Yangtze Delta phase of Holocene (Q h ), buried upon a shallow depth of 50 m. The depth of the water level, seasonally varying from 1 to 3 m, is affected by the atmospheric precipitation and surface runoff. The layer of PA is characterized by the coarse particles in the upper and lower sections and fine particles in the middle section along the vertical direction; some sections of the lower aquifer are connected to CA1. The dewatering amount of a single well is about 10-20 m 3 /day, with poor water quality and thus few exploitations.

Fig. 2 Location of the test site
The CA1 consists of alluvial and marine loose sands of the Upper Pleistocene (Q p3 ), with a burial depth ranging from 50 to 110 m. The lithology of the aquifer mainly consists of pebbles, gravel, coarse sand, medium sand, fine sand, and silty sand; those soil particles, from coarse to fine, are vertically distributed from bottom to top. The aquifer has high permeability and thus enough groundwater supply, which is closely connected to the upper aquifer PA and lower aquifer CA2. The dewatering amount of a single well is about 2000-3000 m 3 /day, also with poor water quality.
The CA2 consists of the fine sand and silty sand layers of the fluvial and estuarine sedimentary of Middle Pleistocene (Q p2 ), buried from 130 to 150 m. Note the water barrier between CA1 and CA2 is partially missing. Due to the thin layer thickness and discontinuous distribution, its water content is small and its distribution varies widely. The dewatering amount of a single well is about 300-3000 m 3 /day, still with poor water quality.
Aquifer CA3 consists of gravelly medium sand, fine sand, and locally gravelly cobble of river-lake sediment of the Lower Pleistocene (Q p1 ), whose buried depth ranges from 180 to 240 m, with an uneven thickness ranging from 20 to 100 m. The dewatering amount of a single well is generally over 2000 m 3 /day. Influenced by the distribution of thicker aquifers near CA2, its connection with the upper aquifers is relatively independent. Both the quality and quantity of the groundwater are good and rich, which makes CA3 the main exploited freshwater aquifer of Nantong City. Note that in this test, the groundwater is extracted from aquifer CA3, with a well depth of 225 m.
Due to the flat topography of the test site, the distribution of groundwater level is uniform, the hydraulic gradient is small, and groundwater runoff is slow. The filling layer at the canal is missing due to artificial expansion, and the water is more likely to infiltrate into PA. The thickness of CA2 is largest near the riverbank and decreases at the southern of the test site. The thickness distribution of CA3 is the opposite of CA2, with the maximum thickness at the southern part of the site.

Test layout and schedule
Fifteen pumping wells, labeled from W1 to W15, of the Nantong Port Water Plant near metro line 1 were selected for this test. All wells were pumped at a rate of 8 × 10 4 L/h under the emergency water supply conditions, from August 9 to 16, 2018. The layout of the pumping wells and monitoring points is shown in Fig. 4. Two well groups exist in the test site, namely, the south well group, W1-W7, located near the water plant on the southern side, and the north well group, W8-W15, at the river bank on the northern side. In addition, 23 monitoring points of ground surface settlement, labeled as S1-S23, were deployed near the metro line and both pumping well groups.
Given the subsurface deformation field might vary from that of the surface ground, two adjacent boreholes (D1), with a depth of 230 m and a diameter of 129 mm, were deliberately drilled and a metal-reinforced single-core cable (MRC) and a fixed-point cable (FPC) were, respectively, laid inside to measure the vertical subsurface deformation field. Figure 5 illustrates the measuring layout of the DFOS monitoring system. The end of the MRC and FPC were connected to a BOTDR interrogator, which can process and record the strain field data along with the optical cable. The parameters of the interrogator are listed in Table 2.
The fiber was installed with a heavy guide at the end, and a suitable housing and pulling cable was installed on the guide. When the hole was formed, the heavy guide with the  . 3 The hydrogeological profile along the metro line fiber-optic cable fixed was brought into the hole by gravity through the pulling cable. During the lowering of the fiber, the fiber was tied and fixed to the steel cable every 2-3 m and avoids stress on the optic fiber. When the cable was lowered in place, the optic fiber was pre-stretched and its top end was fixed at the hole opening to maintain a tight tension. While keeping the fiber in tension, we backfilled the borehole and checked the signal status of the fiber to ensure the verticality of the buried fiber. Backfilling the borehole requires pre-stretching the fiber to ensure its perpendicularity. Former studies have shown that a certain degree of stretching does not affect the quality of the monitoring by the fiber (Zhang et al. 2018a).
To synchronize the deformation of fiber with the subsurface strata, the optical fiber should be buried 1 year before the test. Fine sand-clay soft aggregate, similar to the site strata, was used for the backfill material in the borehole. The deformation modulus of the backfill soil was adjusted with different ratios of fine sand and clay, and the backfill soil with the same deformation modulus to the surrounding strata at different depths in the borehole (Zhang et al. 2020). The backfill gradually consolidated over time and the optic fiber could be fully coupled with the surrounding soil under the action of subsurface envelope pressure. Former studies have shown that beyond a certain envelope pressure and burial depth, the optic fiber and the soil can exhibit strong coupling (Zhang et al. 2018b). Three rounds of DFOS measurements were acquired for calibration before the pumping 261 days (Nov. 21, 2017), 227 days (Dec. 25, 2017, and 205 days (Jan. 16, 2018) respectively, and no engineering disturbance S19 S14 S18 S17 S16 S15 S1 S2 S3 S10 S8 S4 S9 S7 S13 S5 S12 S11  activities on the site during this period. The signal gradually stabilized 227 days before the pumping (Dec. 25, 2017)), which indicates that the fiber has been sufficiently coupled to the surrounding strata. Three monitoring items, including water level, surface settlement, and subsurface deformation field, were performed during the test. The monitoring of the water level of the wells was implemented until no obvious variation can be observed. Three leveling calibrations were conducted before the pumping 59 days (June 11, 2018), 42 days (June 28, 2018), and 23 days (July 17, 2018), respectively. The monitoring schedule is depicted in Table 3. Note that three rounds of DFOS measurements were collected per occurrence date.

Water level variation
From Aug. 9 to 16, 2018, the group pumping was conducted synchronously on the 15 wells in Fig. 4. After stopping pumping for 30 days, the water level tended to be stable. The measurements exhibit that before pumping, the initial water levels of the 15 wells were almost the same, approximately − 16.1 to − 17.5 m. The water level sharply dropped during the pumping; the decline rate of water level gradually slowed. The water level attained its minimum on the seventh day of pumping. Figure 6a shows the distribution of the water level. As noted from the figure, a total level drop of 11.39-16.50 m occurred on Aug. 16. Subsequently, a sharp rebound of water level occurred on Aug. 17 right after the pumping, while the round rate obviously slowed down from Aug. 22. On August 30, 2 weeks after the pumping, the water level was almost restored to its initial value, only with a level falling of 0.05-0.65 m (Fig. 6b). The distribution of the recovery values of the water level is shown in Fig. 6c. Note that the water level distribution of each well was approximately the same as the initial level, reflecting the strong groundwater recovery capability of the test site. As seen from Fig. 6, the greatest decline of the water level occurred near the center of the northern wells (W13), which is located near both the river bank and the metro line. The rise and drop of water level exhibit similar distribution patterns, suggesting the soil permeability of the west side is greater than that of the east side, and the groundwater on the east side attains a stronger rechargeability. Figure 7 shows the distribution patterns of the ground surface settlement during the pumping. As seen from Fig. 7a, at the initial stage of pumping, a large settlement occurred on the west side of the north well group; and also, a small range of settlement occurred in the south well group. The greatest settlement occurred at the measuring point S9, with a settlement value of 2.9 mm. A tiny settlement occurred on the rest part. As seen from Fig. 7b, with the continuous pumping, a small amount of settlement appears on the wide range of the site, and the settlement area of the west side of the north well group enlarged a little. The maximum settlement occurred on measuring point S22, with a settlement value of 3.1 mm. In addition, the settlement values of the east side of the embankment and the south well group are both small, suggesting a good supply of groundwater. Figure 8 shows the distribution pattern of settlement within the 5 months after the pumping. As shown from Fig. 8a, within 2 weeks after the end of pumping, the settlement range further enlarged. The maximum subsidence during this period occurred on the west side of the river bank (S23) with a value of 3.3 mm. This phenomenon indicates that the settlement behavior lagged the deep pumping activity. As seen from Fig. 8b, the settlement area gradually merged to exhibit a large range of the settlement area, which is similar to the distribution pattern of the variation of water levels in the wells. A large settlement occurred on the west side of the north well group and the distribution is continuous. The maximum settlement during this period occurred in the central area of the river bank (S14) with a value of 3.8 mm, which was also the maximum settlement value during the whole test. This phenomenon further reflects that ground settlement lags the deep pumping. As seen from Fig. 8c, the settlement area did not vary significantly 3 months after the pumping. However, a notably concentrated settlement occurred on measuring point S21, on the west side of the embankment, with a value of 3.4 mm. As seen from Fig. 8d, the settlement at the measuring point S21 gradually dissipated and its range expanded. The settlement value decreased to 1.3 mm, and the overall settlement of the  site had tended to stabilize. Note that no obvious ground settlement occurred in this test, suggesting that the existence of multiple aquitards impeded the free transfer between different aquifers. Also, the test results indicate that the permeability of the strata on the west side is greater than that of the east side.

Characterization of the subsurface deformation field
To further study the influence of the groundwater barrier on the deformation connectivity of the strata, the subsurface deformation values acquired by DFOS were substituted into the space-time matrix B. Note the buried depth of the constant-temperature layer of the test site is from 10 to 230 m for MRC and that of FPC is 20-230 m; thus, the measurements of the strain field of the non-thermostatic layer near the surface were excluded owing to the measuring uncertainty induced by the temperature variation in the variable temperature layer. Thus, the submatrices of the constanttemperature layer were extracted to plot the strain field contours during and after the pumping, as shown in Fig. 9. As can be noted from the figure, the strain concentrates within the acquired layers in Fig. 5. Specifically, restricted by the aquiclude of the clayey layer ranging from the buried depth of 150-180 m, the greater strain mainly occurs within aquifer CA3 from the buried depth of 180-230 m. As seen from Fig. 9a, during the pumping, the strain values of MRC within the buried depth of 10-180 m were tiny. Note obvious compressive strain occurred within aquifer CA3, which corresponds to average daily subsidence of approximately 1.61-2.87 mm calculated by Eq. (7). As seen from Fig. 9b, the strain value of FPC, from 20 to 140 m, was close to 0, but fluctuated obviously from 140 to 170 m, with the strain value of about − 30 με. Note the relating soils consistent with the local clay interlayer distribution near 150 m. Significant compression subsidence was also detected in the strata within the The results monitored by MRC and FPC had a similar trend during pumping. The groundwater level drops rapidly in the initial stage of pumping, and the rate of the level drop starts to slow down after 3 h. Then, the water level dropped continuously at an ever-slowing rate with pumping. The DFOS monitoring data indicates that CA3 has synchronously produced large compressional deformation, and CA2 has also produced a small amount of (a) (b) (c) (d) compressional deformation. This phenomenon reflects that the main source of groundwater is CA3 and that the groundwater is mainly recharged laterally. As seen from Fig. 9c, d, after the pumping, the strata strain field, below the buried depth of 180 m, varied slightly, while the significant variation of the strata strain field occurred within 180-230 m underground. Although the strata exhibited compressive strain at the immediate end of pumping, tensile strain started occurring in 1 week, suggesting the existence of an obvious and rapid stratum rebound and the rebound evolved from top to bottom. One month after the end of pumping, the rebound extended from the upper part to the entire aquifer CA3. Four months after the end of pumping, the rebound rate slowed down owing to the gradual recharging of the groundwater. The stratum rebound of aquifer CA3 measured by MRC ranges from 1.89 to 2.15 mm, calculated by Eq. (7), while that of FPC measurements lies within 1.24-2.39 mm. The water level rebounded rapidly within 1 day after the end of pumping, and then rebounded slowly with a gradually slowing trend, and rebounded to the initial state after 21 days. The DFOS monitoring data shows that both CA2 and CA3 stop compressive deformation trend within 1 week after the end of pumping, and CA3 shows a significant rebound deformation after 2 months during the postpumping, indicating that the rebound of the compressive water formation lags behind the return of water level.
The stratigraphic strain field is converted to the accumulated subsurface deformation in accordance with Eq. (7). Figure 10 compares variation trends of both cumulative subsurface deformation of aquifer CA3 monitored by DFOS and the corresponding surface settlement monitored by the leveling over time. As seen from the figure, the surface settlement at point D1 increased linearly during the pumping process and remained in that increasing trend for 2 days after the end of pumping. Then it entered a slow settling process and reached the maximum settling value of 3.2 mm on day 50. The other monitoring points also showed slow settlement or remained unchanged at that time. After day 50, the monitoring points started to rebound and the site entered the recovery period. Meanwhile, a sharp compressive deformation of aquifer CA3 occurred during the pumping, and the deformation varied linearly with time. The deformation value reached the maximum of 18.24 mm on the first day after the end of the pumping, and then a rebound occurred, whose rate slowed down with time. The deformation of CA3 returned to the initial state 5 months after the end of pumping. Compared with the subsurface deformation of CA3, the surface settlement is smaller and lagged about 1-2 months, suggesting the subsidence induced by the deep pumping is gradually transmitted to the surface.

Analysis of cumulative ground settlement
As seen from Fig. 10, during the pumping state, aquifer CA3 and surface settlement increased linearly over time; during the postpumping stage, the surface settlement continued to increase linearly, but the rate decreased, while aquifer CA3 exhibited a nonlinear rebound trend. Note linear functions are used to fit aquifer CA3 and surface settlement trends during the pumping. The logarithmic function is used to fit the rebound trend of CA3 during the postpumping, and a piecewise linear function is used to fit the surface subsidence and the rebound trend of the postpumping stage, respectively. Equations (8) and (9) are the fitting functions of the deformation trends of CA3 and ground surface, respectively.
where d d (t) (in mm) is the cumulative deformation of aquifer CA3, and t (in days) is the duration.
Equation (8) suggests that continuous pumping within the aquifer would induce sharp subsurface deformation. The underground rebound follows a logarithmic trend and the rebound rate slowed down with time.
where d s (t) (in mm) is the cumulative settlement of surface, and t (in days) is the duration. Equation (9) shows that the surface will undergo linear settlement over time during the pumping and remained in that increasing trend for 2 days after the end of pumping. Then it entered a slow settling process and reached the maximum settling value on day 50, which comprises the major part of the total settlement. Subsequently, the surface rebounded linearly with time, and the time recovering to the initial state was the same as that of CA3, suggesting that the surface settlement after the pumping is closely related to the subsurface deformation.
Note that the surface settlement was divided into two phases, the former was closely associated with the pumping and the latter was closely related to CA3 stratigraphic deformation. The duration of the surface settlement was nearly 50 days, which is about 1/3 of the time required for the surface rebound, and the time required for both aquifer CA3 and surface to recover to their initial state was about 150 days. When the water source pumping continuously for t p days (t p > 7), the duration of the formation to recover to its initial state is t t then according to Eq. (8) satisfies Equation (10) is derived to obtain the total recovery duration of the strata t t and the duration of ground surface settlement t s , namely, Substituting into Eq. (9), the maximum surface settlement is According to Eq. (12), the maximum surface settlement increases approximately exponentially with the duration of the pumping. Once the dewatering lasts for more than 22 days, the ground settlement will reach 20.5 mm, exceeding the safety limit of 20 mm given by the relevant specifications (Gao et al. 2010). Therefore, the limit duration of continuous dewatering should not exceed 22 days.

Analysis of the curvature radius along the metro line
Metro tunnel, as a typical linear distribution structure, is more sensitive to uneven deformation of the ground along the line. From Figs. 7 and 8, the settlement differences in the site traversed by this metro were more significant than those in other areas. The settlement data from the settlement monitoring points along the metro line were selected (10) 72.39 − 13.69 ln t t − t p +7 + 42.57 + 2.4 t p − 7 = 0 (t p > 7). to draw the trend plot of cumulative surface settlement along the metro line with time by the linear interpolation method, as shown in Fig. 11. The settlement was much less than the specification limit of 20 mm (Gao et al. 2010). Influenced by the distribution of water wells, the maximum settlement of the northern well group was larger and more concentrated than that of the southern well group. The maximum settlement point was located near K17 + 800, with a value of 3.8 mm, which occurred 1 month after the end of pumping. The southern well group was more dispersed and the settlement value was smaller, but the influence range was larger.
In the southern well group area, there were two large settlement points near K17 + 950 and K18 + 150, respectively. The minimum settlement point appeared near K18 + 050 between the two larger settlement points, and the rebound first appeared 3 months after pumping, and the amount of rebound increased with time. In 140 days after pumping, a rebound occurred in all strata along the metro line.
In addition to the effect of absolute settlement values, excessive relative settlement reduced the subsidence curvature radius. The curvature radius, at each monitoring point along the metro line, induced by the longitudinal deformation of the tunnel was calculated by the threepoint method (Cupec et al. 2009). Statistically, a relatively small curvature radius occurred on three points (S14, S3, and S4). The variation trends of the curvature at those three points were plotted in Fig. 12. As seen from the figure, the minimum curvature radius along the metro line occurred at settlement groove 2 on September 11, with a radius of 3.89 × 10 6 m. Note that it is much greater than the 1.5 × 10 4 m defined by the specification, indicating that the short-term dewatering activity has less influence on the tunnel. Also, note that the curvature radius of those key points decreases exponentially with time during the pumping. Once the pumping lasts more than 15 days, the curvature radius will be less than the standard value. Within the first week after the end of the pumping, the curvature radius rose rapidly and then fluctuated steadily, suggesting Although the groundwater recharge at the test site was adequate and the strata were well recovered; excessive pumping could have a negative impact on the strata where the tunnel is located. Based on the DFOS monitoring results, the pumping had a great impact on the strata of the pumped aquifer, so the pumping behavior should be avoided in the aquifer where the tunnel is located. From Eq. (8), the CA3 strata were linearly compressed during pumping. When the total amount of pumping is constant, decreasing the pumping rate will slow down the compression curve, while shortening the pumping time will make the compression curve shorter. As an emergency water source, the pumping time should be as short as possible in case of providing emergency water quantity. Calculated by Eq. (8), the pumping duration of all wells at the maximum pumping rate (8 × 10 4 L/h) with the corresponding formation full recovery time is shown in Table 4. From Table 4, the recovery time of the ground deformation does not increase linearly with the pumping duration; the longer the duration of pumping, the more difficult it is for the strata to recover. Therefore, the normal duration of emergency pumping should not exceed 1 day, and under extreme conditions should not exceed 2 days. There should be a 1-month interval between pumping activities to maintain a dynamic equilibrium state for the formation deformation.

Conclusions
(1) The maximum surface settlement was about 3.8 mm, and the minimum curvature radius was 3.89 × 10 6 m, which indicates that the 1-week pumping could not have a significant negative impact on the metro tunnel.
(2) A large settlement occurred on the west side of the test site, which is similar to the variation distribution of groundwater level, suggesting the settlement distribution is affected by the formation permeability and groundwater rechargeability. (3) During pumping, the deformation of the aquifer and ground surface is linearly compressed with time; the deformation of the aquifers to be much greater than the surface settlement, and the surface settlement lags behind the settlement of the aquifer by 1-2 months. (4) After pumping, the ground surface continues to settle linearly at a slower rate for about 50 days, followed by a slow linear rebound; the aquifer is logarithmically rebounded for about 5 months. (5) Continuous pumping of groundwater sources for more than 15 days can cause significant deformations in the deep strata to be transmitted to the surface; the normal duration of emergency pumping should not exceed 1 day, and under extreme conditions should not exceed 2 days.