Introduction

The Daqiao station is part of the Xinzhuang line of the Taipei Mass Rapid Transit (MRT) system (Fig. 1). As the down-track and up-track tunnels pass one above the other beneath the Tanshui River, the excavation extended to 41 m below the ground surface. A 1.8 m thick, 58 m deep diaphragm wall and steel struts were used to retain the substantial lateral pressures.

Fig. 1
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Geological profiles of Sungshan formation in the Taipei basin and the location of the construction site (after Hwang and Moh 2007)

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Jet grouting within the diaphragm wall was used to reduce both the ingress of water and the heave pressures which would occur with such a deep excavation. Based on past experience, 22 wells were designed and constructed, of which two were used to conduct single-well and double-well pumping tests to obtain appropriate hydraulic parameters for the gravel formation. Pumping tests in12 wells were then carried out to understand the characteristics of drawdown and to verify the parameters obtained from single-well and double-well pumping tests.

The full depth of the gravel formation is not known hence the wells were considered partial penetration wells. In this case, many other factors were involved in the derivation of hydraulic parameters, e.g., the influence of the piezometric level of the gravel formation due to the presence of the Tanshui River, leakage problems, large-diameter well effect and the multi-aquifer system. As geological formations and well situations are idealized in well formulae, field situations such as occur in Taiwan cannot be easily accommodated in theoretical formulae. For this reason, a simple method was developed to evaluate the hydraulic parameters from the results of the partial penetration wells with the above-mentioned complications taken into consideration. The results from the single-well and double-well pumping tests were used to derive the drawdown induced by the group well using the linear superposition method. In addition, drawdowns at remote sites were measured to investigate the characteristics of drawdown during such massive pumping tests.

Geology and hydrogeology

Figure 1 shows the location of the study site and wells and two geological cross-sections derived from the site investigation for the Taipei MRT (Hwang and Moh 2007). Generally, the Taipei basin consists of a thick alluvium formation (the Sungshan Formation) which overlies the Chingmei gravel formation. The Sungshan Formation consists of alternating soft clay and sand layers, of which six have been distinguished (Fig. 1). Generally, the Formation is some 40–55 m in thickness in the centre of the basin (Huang et al. 1987), increasing to >100 m in the north.

Figure 2 shows the layout of the site works at Daqiao, while Fig. 3 shows the depth at which the six individual Sungshan horizons occur. The underlying Chingmei gravel formation comprises predominantly gravel, with some sand and occasional interbedded clay seams. Teng et al. (1999) record that the thickness of the Chingmei gravel formation is about 50 m thick in the center of the basin while at the Daqiao construction site it is likely to be 32–33 m thick. Figure 4 shows the grain size distribution for the Chingmei gravel formation, obtained from samples carefully collected from the central part of each grab during the construction of the diaphragm wall. It can be seen that the material comprised 60–80% gravel, 15–33% sand and less than 7% fine soil.

Fig. 2
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Plan view of the construction site and layout of pumping wells and observation wells

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Fig. 3
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Profiles of pumping wells and geological formation a m–m and b n–n

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Fig. 4
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Grain size distribution of the soil in the Chingmei formation at the site

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Below the Chingmei gravel formation is the Xinzhuang formation, which has similar hydrogeological conditions although it includes more interbedded clay seams. As little boring data are available, the bottom of the Xinzhuang gravel formation is not known.

As the silty clay soil in Sungshan II (Fig. 1) acts as an aquiclude, Sungshan I (silty sand) and the two underlying gravel formations can be considered as a confined aquifer, with the groundwater level some 7 m below the ground surface. The groundwater levels in Sungshan III and V, all silty sand, are at 5.5 and 3.2 m, respectively. The reason why the groundwater at the construction site is not in a truly hydrostatic condition is due to over-pumping for more than 20 years. Because pumping was prohibited some 30 years ago, the groundwater levels are gradually recovering. In addition, the groundwater level in the gravel formation near the Tanshui River fluctuates periodically as a result of tidal effects (Liu 1996), which also had to be taken into account when deriving the hydraulic parameters for the analysis of construction dewatering.

Design of pumping wells and pumping tests

Twenty-two pumping wells were installed to lower the groundwater level in the gravel formation during excavation (Fig. 2). Due to the limited space outside the excavation zone, the pumping wells were embedded in the diaphragm wall. Figure 5 shows the construction details of a typical pumping well used in this project and Table 1 lists the diameter and depth of the wells and the lengths/depth of the screens. As suggested by Driscoll (1986) and Huisman (1972), the wells were filled with 3–6 mm diameter gravel which was densified using hydraulic vibration. Electronic piezometers were also installed. Figure 3 shows the depth of the pumping wells, together with the geological profile. Observation wells S1017, S1021 and S1023 were installed at a depth of 68 m in the gravel formation outside the excavation zone.

Fig. 5
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Construction details of the pumping wells

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Table 1 Depth, diameter and screen length of the pumping wells
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Initially, step drawdown tests were undertaken in pumping wells PW-18 and PW-20 to determine their pumping capacity, which was established as approximately 6 m3/min. A constant rate pumping test was then carried out in PW-20 over three consecutive days. For some reason, the pumping was paused for 3 min at 1,065 min. After completion of the PW-20 pumping and full recovery of the groundwater level, a constant rate pumping was undertaken in PW-18 over a 24-h period.

After completion of the single-well pumping tests, PW-18 and PW-20 were simultaneously pumped at a constant rate of 6 m3/min, followed by a similar test involved 12 wells. Figure 6 shows the scheduling of the operation of group-well pumping. The objective of the double-well and group-well pumping tests was to investigate the characteristics of drawdown across the Taipei basin and to verify the parameters obtained from the single-well pumping tests. Figure 7 shows the operation of the pumping tests.

Fig. 6
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Scheduling of the operation of group-well pumping

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Fig. 7
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Photos of the PW-18 single-well pumping test (left) and group-well pumping test (right)

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Analysis of hydraulic properties

Periodic fluctuation

As shown in Fig. 8 (PW-20) and 9 (PW-18), the drawdown in the single-well pumping tests was affected by the tidal regime. It was found that the groundwater level in the gravel formation varies over a 2-week period with sinusoidal fluctuation (Fig. 10). In addition, there were two intermediate cycles and two small cycles each day. Shih et al. (1999) found that the groundwater level near the Tanshui River fluctuates with the same frequency as the astronomical tides, K 1, M 2 and M 4. The periods of the astronomical tides K 1 and M 2 are equal to 23.9345 and 12.4206 h, respectively, which correspond to the periodic fluctuation shown in Fig. 10.

Fig. 8
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Relationship of drawdown and elapsed time in semi-log scale (PW-20)

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Fig. 9
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Relationship of drawdown and elapsed time in semi-log scale (PW-18)

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Fig. 10
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Typical periodic fluctuation of the groundwater level in the Chingmei gravel formation before the pumping tests

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Several methods to obtain the hydraulic parameters of the groundwater of aquifers directly connected to the sea are reported in the literature (e.g., Ferris 1951; Carr and Van Der Kamp 1969; Erskine 1991; Trefry and Johnston 1998; Chapuis et al. 2006). However, the methods are difficult to apply to this case as the fluctuation of the groundwater level is due to dynamic loading of the river water induced by the tidal effect (Liu 1996) and information on the water level in the tidal Tanshui River was not obtained during the period of the pumping tests.

The testing indicated that the daily peak amplitude occurred at 21 min after the onset of the pumping test for PW-20 and after 31 min for PW-18. From the drawdown curves shown in Figs. 8 and 9, the straight-line section in the drawdown-time semi-logarithm relationship was achieved 2 min after the commencement of the pumping test. The groundwater level rises to a maximum of 20 mm in PW-20 and 40 mm in PW-18 after 19 and 29 min, respectively. As seen in Figs. 8 and 9, moving forward an additional 19 and 29 min from the daily peak in time axis (i.e., 40 and 60 min from the onset of pumping), the groundwater will be on the same level or amplitude during the fluctuation. Assuming leakage is not a serious problem, the drawdowns at 2 and 40 min for PW-20 and 2 and 60 min for PW-18 (the two points on the Cooper-Jacob straight line section) can be adopted for the derivation of hydraulic parameters.

Partial penetration well effect

As shown in Fig. 3, the length of well screens in this project was actually less than the aquifer thickness, hence the partial penetration effect should be considered in the derivation of the S value. Kruseman and de Ridder (1990) and Karen and Jonathan (1991) proposed a typical shape of drawdown curve where there is a partial penetration effect. It can be seen from Fig. 11 that line B, representing the drawdown curve from the partial penetration well, has a similar slope to line A, induced by the full penetration well. This implies that the coefficient of transmissivity, T, derived from the drawdown curve resulting from the partial penetration well (using Cooper and Jacob’s 1946 method) should be close to the real value.

Fig. 11
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Schematic representation of partial penetration well effect and large-diameter well effect

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On the other hand, the horizontal intercepts of extension of straight segments of the two drawdown curves differ from each other by several orders of magnitude. The value of coefficient of storage, S, deduced from line B would therefore result in a large error. The vertical distance, Δs 1, between the two lines is related to the partial penetration well effect. The more observation wells close to pumping wells, the larger the vertical distance between two lines and the larger the error of coefficient of storage deduced from line B. As shown in Fig. 11, line C, starting from the point a where the maximum curvature of line B occurs, is displaced but parallel to the lower section of line B. The vertical shifted distance, Δs 3, is less than Δs 1, hence the use of line C will significantly reduce the error in the calculated S value.

The error of coefficient of storage, S, evaluated from the pumping test results can be significantly reduced if the above-mentioned method (parallel shifting of the drawdown curve) is adopted. Point b in Fig. 11 represents a state where the partial penetration well effect is stable while point c, the onset of the straight line, denotes the steady state of drawdown affected by the partial penetration well effect. In the pumping tests of PW18 and PW20, the points b and c occurred at 0.4 and 2 min, respectively, after initiation of the pumping test. Therefore, 2 min after the initiation of the pumping tests can be adopted as one of the two points in the straight line method by Cooper and Jacob (1946).

Large-diameter well effect

Pumping of the large-diameter well will initially take out the water stored in the well, after which drawdown of the groundwater can commence. This is discussed by Chapuis and Chenaf (2003) and Kruseman and de Ridder (1990), who report that the S value calculated from drawdown curves can be influenced by water storage in monitoring and pumping wells, even for normal diameter pipes, especially for early time data.

The typical shape of the time-drawdown curve for the large-diameter well pumping in the initial stages is similar to that of the partial penetration effect, as shown by line D in Fig. 11. When the large-diameter well effect diminishes or approaches zero, the data will move to the straight section of Theis’s curve (1935) , as indicated by point d in Fig. 11, which was defined as a critical time (t c) by Papadopulos and Cooper (1967) and Schafer (1978). If the time at point d is earlier than that at point c, it implies that the large-diameter well effect disappears while the partial penetration well still has some effect on the drawdown curve and vice versa. In general, the storage effect will last longer for wells with large diameters and low specific capacities (Driscoll 1986).

The well diameters for PW-20 and PW-18 were 500 and 400 mm, respectively (Table 1). Assuming groundwater did not flow into the well during pumping, with a pumping rate of 6 m3/min, the drawdowns in PW-20 and PW-18, the calculated (dashed line) and actual drawdowns are shown in Fig. 12. The deviation between the dashed lines and the actual drawdowns is at 0.1 and 0.15 min, respectively. This implies that the large-diameter well effect begins to decrease; the critical time for PW-20 and PW-18 was calculated as 1.32 and 1.18 min respectively, using the Schafer (1978) equation. Thus, after 2 min of pumping, the large-diameter well and/or water storage effect should have disappeared. Drawdown data should be on the straight section of the Theis (1935). The S value calculated based on the drawdown at 2 min as one of the two data points in the Cooper-Jacob straight line method can therefore be regarded as reasonable.

Fig. 12
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Comparison of the actual drawdown and assuming groundwater did not flow into the wells

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Leakage effect

As reported by Huang et al. (1987) and Ou (2006), the coefficient of permeability of the Sungshan II silty clay is around 10−9 m/s. Compared with some urban soils such as the San Francisco bay mud, Boston blue clay or Mexico City clay, the Taipei silty clay is of low plasticity and has a relatively larger permeability. Nevertheless, Sungshan II is still treated as an impermeable soil. With the 12 m thickness of Sungshan II (Fig. 3), it is likely that the water in the permeable Sungshan III silty sand may percolate through the Sungshan II into the Sungshan I due to the extensive and long-term pumping in the gravel formation. In addition, Sungshan II is not present throughout the whole of the Taipei basin, such that Sungshan I and Sungshan III can be in hydraulic continuity. Such complications may result in misleading inferences regarding the hydraulic parameters.

Figure 13 displays the variation of groundwater level in Sungshan III during the single- and double-well pumping test of PW-18 and indicates the groundwater level in Sungshan III was little affected by these tests. Figure 14 shows the piezometric pressure within the soil at the elevations of −19.3, −35.0, −40.9 and −68 m, i.e., in the Sungshan III (silty sand), Sungshan II-upper part (silty clay), Sungshan II-boundary to Sungshan I (silty clay) and gravel formation. As shown in the Fig. 14, when the groundwater level in the gravel formation drops significantly due to the group-well pumping test, the porewater pressure in Sungshan II, near the boundary of Sungshan I, changed little initially and then fell to some 9.96 m elevation. The groundwater level then recovered with time after the group-wells pumping test stopped. Consolidation or porewater pressure dissipation in Sungshan II may play an important role in this phenomenon.

Fig. 13
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Variation of groundwater level in Sungshan III measured by S1019 during the pumping tests

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Fig. 14
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Variation of groundwater level measured in different depths of piezometers during the group-well pumping test

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In Sungshan II, away from the boundary with Sungshan I, the influence of porewater pressure induced by the group-wells pumping test reduced, while in Sungshan III (silty sand) the porewater pressure showed little change. From this it is considered that the leakage of the groundwater from Sungshan III (silty sand) through the Sungshan II (silty clay) into Sungshan I (silty sand) or the gravel formation, could be excluded and the effect of the long-term pumping would be minimal despite the postulated hydraulic continuity between Sungshan III and I at some distance from the pumping site. Furthermore, the relative lower coefficient of permeability of Sungshan I and III may result in a delayed response in the gravel formation where the coefficient of permeability K is as high as 10−3 m/s.

Estimation of the hydraulic properties

Table 2 lists the hydraulic properties derived from the pumping tests in PW-20 and PW-18, taking into account the effects of periodic fluctuation, partial penetration, large diameter and leakage. The table indicates considerable errors for S (about one order) if the drawdown curve is not shifted from line B to line C in a parallel manner. The average of T and S, evaluated from the adjusted curves induced by two pumping wells, is 5.58 m2/min and 0.000873, respectively.

Table 2 Hydraulic parameters derived from single-well pumping tests by Cooper and Jacob (1946) method
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As shown in Fig. 11, the vertical distance between the original drawdown curve and adjusted curve, Δs 2, represents the drawdown affected by the partial penetration well effect. The relationship between Δs 2 and distance of observation wells to the pumping wells is shown in Fig. 15. The minimum distance where the partial penetration well has no effect on drawdown curve was evaluated as 97.0 m when Δs 2 = 0. Therefore, according to Hantush (1961), the thickness of the aquifer at the construction site is estimated as 97.0 m/1.5 or 65 m.

Fig. 15
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Relationship of modified additional drawdown Δs 2 and distance r in semi-log scale

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As mentioned above, the thickness of the Chingmei gravel formation at the Daqiao construction site is inferred to be about 32 m. During the site investigation and process of well installation, it was found that the well depths were all located below the second interbedded clay seam (Fig. 3). The underlying clay seam is still gravel—the Xinzhuang formation—but as there are no borehole data below the second clay seam, the actual depth of the gravel at the construction site is unknown. However, in a borehole some 650 m from the construction site, a 2–4 m thick clay seam was found at a depth of 105–109 m below the ground surface. Assuming the Sungshan I (silty sand) and gravel extend to a depth of 105–109 m, the aquifer would be 63–67 m in thickness, which is consistent with that inferred from the pumping test results.

Assuming the average of 65 m as the aquifer thickness, the coefficient of permeability for the gravel formation can therefore be estimated by T/D, which is equal to 5.58 m2/min/65 m or 1.4 × 10−3 m/s.

Drawdown prediction

Double-well pumping test

As mentioned above, the double-well pumping tests in PW-20 and PW-18 followed the single-well pumping tests. Figure 16 shows the drawdown curve for three observation wells. Theis’ non-equilibrium formula with the hydraulic parameters, T = 5.58 m2/min and S = 0.000873 (obtained from the single-well test results) and the superposition method were used to predict the drawdown Δs T. Additional drawdown due to the partial penetration well effect is evaluated through Fig. 15 or regression equation Δs 2 = −0.398ln r + 1.8225. The actual drawdown induced by a single-well pumping at a specific distance is then the sum of Δs T and Δs 2. The drawdown induced by simultaneous two-well pumping can then be obtained by superimposing the drawdown evaluated from each single-well pumping, as indicated by a solid line and two dash lines in Fig. 16. This reflects the fact that the drawdowns from the single-well pumping test results are affected by a number of factors, e.g., spatial variation of geological formations, multi-aquifer systems, etc.

Fig. 16
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Comparison of drawdowns measured by the PW-18 and PW-20 double-well pumping test and those predicted using the Cooper and Jacob’s equation and measured single-well pumping test results

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Group-wells pumping test

As shown in Fig. 6, 12 wells with a pumping rate of 6 m3/min were employed for the group-well pumping test. The test began with four wells for 4 h and one well was added every hour until all 12 wells were open for a period of 776.1 min. To understand the recovery of drawdown during a power cut, the pumping was paused for 11.5 min and then continued with 12 wells again.

Figure 17 shows a comparison of the drawdowns in the observation wells and those predicted using the method in the preceding section. As shown in the figure, the predicted drawdowns generally agree with the measured values.

Fig. 17
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Comparison of the drawdowns measured from the group-well pumping test and those predicted using Cooper and Jacob’s equation

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Drawdown at the remote site

As the gravel formation is of high permeability and spreads over the whole Taipei basin, observation wells were also installed at sites ZH, GL, WL and DA at distances of 1,027, 1,925, 3,285 and 5,197 m, respectively, from the pumping wells, to investigate the effect of pumping at the Daqiao construction site on the Taipei basin.

As shown in Fig. 18, the drawdown basically decreased with increasing distance from the construction site. At site ZH, 1,027 m away from the pumping well, the maximum drawdown was 2.0 m for the 12 wells with a pumping duration of 776.1 min and pumping rate of 6 m3/min, whereas the drawdown at site DA was very small—even a slight increase. It is considered that either the gravel formation at site DA is not connected with that at the Daqiao construction site or that the groundwater recharge outweighs the drawdown as site DA is located at the margin of the basin.

Fig. 18
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Comparison of the drawdowns at the remote sites measured from the group-well pumping test at the construction site and those predicted using Cooper and Jacob’s equation

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Figure 18 compares the drawdowns observed from the remote observation wells with the hydraulic parameters evaluated at the Daqiao construction site. The predicted drawdowns at GL are close to those obtained from field measurements, but the predicted drawdowns at ZH and WL are quite different from the field measurements. This could be due to the spatial variation of geological formations and/or some leakage.

Discussion and conclusions

In order to avoid uplift of the excavation floor due to water pressure in the gravel formation some 50.8 m below the ground surface, 22 wells were constructed at the construction site. Single-well pumping tests were undertaken to derive the hydraulic parameters of the gravel formation, but as its depth was not known, the wells were assumed to be partial penetration wells. The geological and hydrogeologic conditions at the construction site were not as simple as the assumptions made in well formulae and many other factors, such as the tidal fluctuations, the large diameter of the wells and the possibility of leakage, had to be considered.

Field observations indicated the groundwater level in the gravel formation fluctuates over a 2-week period. The drawdowns at two points, with the same amplitude during the periodic fluctuation and on the Cooper-Jacob straight line section, were adopted to eliminate the tidal influence.

Use of the drawdown curve where there is a partial penetration well effect may result in errors of up to one order in the coefficient of storage, although the coefficient of transmissivity may still be realistic. The parallel shifting of the drawdown curve suggested in this paper resulted in consistent hydraulic parameters for two single-well pumping tests.

The large-diameter well effect deforms the drawdown curve in the early stage—in this case much earlier than the partial penetration well effect.

The piezometers installed in the overlying layers indicated that there was minimal leakage even though the aquiclude may not be present in some areas.

From the testing and calculations discussed, the coefficients of storage, transmissivity and permeability for the gravel formation were found to be 0.000873, 5.58 m2/min and 1.4 × 10−3 m/s, respectively. The drawdowns predicted using the above parameters are generally close to those obtained from field measurements of the two-wells and group-well pumping test results.

To investigate the influence of the dewatering on the Taipei basin, the groundwater levels at locations in the Taipei basin remote from the construction site were studied during the pumping tests. It was found that pumping water in the gravel formation will cause a significant drawdown at most of the remote sites. The parameters evaluated at the construction site differ considerably from the field measurements at these sites because of the spatial variation of geological formations and/or leakage.