Engineering Geology 117 (2011) 17–28

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Engineering Geology

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A case history of field pumping tests in a deep gravel formation in the TaipeiBasin, Taiwan

James C. Ni a, Wen-Chieh Cheng b,⁎, Louis Ge c

a Department of Civil Engineering, National Taipei University of Technology, Taipei, 10608, Taiwan, ROCb College of Engineering, National Taipei University of Technology, Taipei 10608, Taiwan, ROCc Department of Civil, Architectural, and Environmental, Engineering, Missouri University of Science and Technology, 1401 North Pine Street, Rolla, MO 65409, USA

⁎ Corresponding author. 1, Sec. 3, Chung-hsiao E. RdTel.: +886 2 2771 2171x2627; fax: +886 2 2781 451

E-mail address: s2428030@gmail.com (W.-C. Cheng)

0013-7952/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.enggeo.2010.10.001

a b s t r a c t

a r t i c l e i n f o

Article history:Received 8 March 2010Received in revised form 25 September 2010Accepted 2 October 2010Available online 14 October 2010

Keywords:Gravel formationPumping testPeriodical fluctuationWellbore storageSkinPartial penetration well effect

33 large-diameter wells embedded in 2-m thick, 63-m deep diaphragmwalls were constructed to reduce boththe uplift pressures and the groundwater inflow during the excavations. As the actual thickness of thepumped aquifer is unknown, the installed wells are regarded as partial penetration wells. Single-well andmulti-well pumping tests were conducted in the deep gravel formation of Taipei Basin to derive the hydraulicparameters and to investigate the drawdown characteristics at both the construction and remote sites.However, the tidal effect on the drawdown of both the pumping well and nearby observation wells was foundsignificant. Additionally, wellbore storage, skin, and leakage need to be taken into account for deriving thehydraulic parameters. Hence, a method to remove these five factors influencing the drawdown curve isdeveloped, which takes advantage from the late-time characteristics of drawdown data and the early-timebehavior of drawdown. Some currently available semi-log graphic techniques are therefore proven applicablefor parameter determination. Validity of the proposed method is verified by the good agreement between thecalculated and the measured drawdown of both the pumping well and observation well.

. Taipei, 10608 Taiwan, ROC.8..

ll rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The construction site (CR) of 125 m in length and 14.9 to 25.9 m inwidth is located at the crossing of the Xinzhuang line and the Luzhouline of the Taipei Rapid Transit System (TRTS) (Fig. 1). As thenorthbound and southbound tunnels were constructed overlappingeach other underneath the Tamshui River which directly runs into theTaiwan Strait, the excavation reached 39.5 to 41.5 m below theground surface. 33 large-diameter wells embedded in 2 m thick and63 m deep diaphragm walls along with a 5 m thick jet grouting wereconstructed to reduce the uplift pressures and retain substantiallateral pressures during such a massive underground excavation.

In the current study, five factors were involved in the derivation ofhydraulic parameters, which include periodical fluctuation, partialpenetration well effect, wellbore storage, skin, and leakage problem.As such the drawdown cannot be accommodated in theoretical wellformulae, the pumping well cannot be properly and economicallydeployed at the construction site. For most of the coastal areas thegroundwater level in the confined aquifer is affected by the tidalinfluence, which induces the periodical fluctuation of drawdownduring the pumping test. Use of the drawdown data where there is apartial penetration well effect will result in a large error in the

determination of storage coefficient. Neglecting both the wellborestorage and skin will cause serious overestimate of storage coefficientand underestimate of transmissivity. Before the derivation of para-meters, it needs to know if the late-time drawdown is affected byeither leakage from the overlying/underlying formation or rechargefrom the possible hydrogeologic boundary. Therefore, the purpose ofthis study is to propose amethod to remove these five factors involvedin the derivation of hydraulic parameters, which devotes muchattention to the late-time characteristics of drawdown data and theearly-time behavior of drawdown.

2. Site characterization

2.1. Geology and hydrogeology

Fig. 1 shows the location of the construction site CR and remotesites and two geological profiles derived from the geological database(GEOLOG) (Lee, 1990) of the Taipei Basin, which comprises theloggings from 248 boreholes drilled through a thick alluvial formation(the Sungshan formation) of alternating soft clay and silty sand layers,of which six has been distinguished, into a gravel formation (theChingmei gravel formation). The thickness of the Sungshan formationvaries from 40 to 55 m in the centre of the basin, with a maximumthickness as 110 m in the northwest (Peng et al., 1999). Plan view asshown in Fig. 2 indicates the layout of wells and location of boreholes

Fig. 1. Location of construction site CR and geological profiles in the Taipei Basin.

18 J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

while Fig. 3 shows the geological profile, in which the boundary ofevery Sungshan sublayer is denoted.

The underlying Chingmei gravel formation comprises dominantlygravel, with some sand and occasional interbedded clay seams (Fig. 3),of which the thickness seems to be varied from 30 m to 80 m (Penget al., 1999)while at the construction site CR it is likely to be 53 to 58 mthick. During the site investigation the grain size distributions fromborehole BR1 (Fig. 2) at elevation ranging from 85.3 to 87.7 m belowthe ground surface show that thematerial comprises 80–85% of gravel,10–16% of sand and less than 6% of fine-grained soil.

As Sungshan I and Chingmei formation are overlain by the silty claysoil in Sungshan II, the two permeable formations are regarded asconfined aquifer, whose groundwater level is about 7 m below thesurface. The groundwater level in Sungshan III and V are 4 m and 2 m,respectively. The groundwater at the construction site CR is not in ahydrostatic condition since it had been lowered around 40 m belowthe surface for more than 15 years (1960–1975) for domestic usage.Other than this, the periodical fluctuation of groundwater level inChingmei formation resulting from tidal influence also had to be takeninto account for the derivation of hydraulic parameters.

-6.0 m

Double-wall cofferdam

2.0 m

18.1

m

14.2

m

12.4

m

11.7

m

11.4

m

Tamshuiriver

Floodplain

-5.0 m

-4.0 m

1.0 m

3.0 m2.5 m

2.0 m

LEGENDPumping wellRiverbed level

Sheet pile

32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17

33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

ABCDEF

Zone C(Land side)

Zone A(River side)

Zone B(Transition zone)

125.7 m

25.9 m 15, 16

13, 14

11, 12

9, 10

7, 8

5, 6

3, 4

1, 2

Piezometer (ELP-No.)Borehole (BR-No.)

17, 18

19, 20

21, 22

23, 24

A

AA

A

14.9 m

BR1

BR3

BR2

Residentialarea

Retaining wall

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

19J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

2.2. Design of pumping wells and pumping test program

When the excavation at the construction site CR reached to 40 m orso below the surface, the expected substantial uplift pressures beneaththe foundation soil and the large lateral pressures needed to beminimized. Therefore, 33 pumping wells in 2 m thick and 63 m deepdiaphragm walls along with 5 m thick jet grouting were installed tolower the groundwater level in Chingmei formation and retain lateralpressures during excavations. Fig. 4 shows the construction detailsof a typical pumping well used in this pumping test program, in which4–9 mmdiameter gravelwas selected tofill thesewells (Driscoll, 1986).The formation materials adjacent to the well had been disturbed dueto the use of drilling mud during the well installation. This damagedzone where the permeability was lower than that of undisturbed

Fig. 3. Profile of pumping wells and geologica

formation materials was needed to restore its natural hydrauliccharacteristics before being put into production. Hence, the welldevelopment to repair the damaged zone and densify the surroundedgravel pack was conducted using hydraulic vibrations after thecompletion of well installation.

24 electronic piezometers were installed at 12 locations depicted inFig. 2 to monitor the change of groundwater level during and after thepumping tests, of which 12 electronic piezometers marked by oddnumberwere installed at the Sungshan I silty sand layer, and the otherswere installed at Chingmei formation. As Chingmei formation is of highpermeability and distributes over the entire basin, four observationwells, OW8-1, OW8-2, OW8-3, and OW8-4, installed at distances of 50,100, 200, and 400 m, respectively, from the construction site CR wereused to understand the interrelation of groundwater level change

l formations at the construction site CR.

Gri

tch

ambe

r

200 cm

12.5 cm

30 m

Wel

l scr

een

(13%

ope

ning

rat

io)

1 m

Jet grouting

63 m

Bentonite

Gravel pack

Fine sand

64 m

65 m

Flowmeter

Diap. wall

EL 3.5 m

EL -54.5 m

60 m

1 m

5055

m

EL -59.5 m(Bottom of diap. wall)

Cement mortar

70 cm (Borehole dia.)

1 m

5 m

Carbon steel pipeof 20 cm in dia.

Steel casing of 80 cmin dia. embedded in the diap. wall

Carbon steel casingof 45 cm in dia.

Submersible pumpwith a lift of 55 m

80 cm

Fig. 4. Construction details of the pumping wells.

20 J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

21J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

between Chingmei formation, Sungshan I, Sungshan III, and SungshanVduring the pumping tests (Fig. 5).

During this program 17 wells were selected to conduct step-drawdown test respectively and establish their pumping capacity assome 6 m3/min, of which three were selected to conduct single-wellpumping test subsequently. After completion of the single-wellpumping test, a pumping test involved with 17 wells was carried outto investigate the characteristics of drawdownat both the constructionsite and remote sites and to validate the parameters derived from thesingle-well pumping test. The test began with four wells for 240 minand four wells were added every 120 min or so until all 17 wells wereopen for a period of 3960 min. For some reason, two of them wereceased at 1260 and1390 min, respectively. Fig. 6 shows the schedule ofthe multi-well pumping test.

3. Proposed method

The proposed method of removing those five influencing factorson the drawdown curve is described herein.

3.1. Periodical fluctuation

For coastal areas where tides can have influence on the river waterelevation, the groundwater level in a deep confined aquifer can beaffected through two mechanisms: 1) leakage from the overlyingaquitard or 2) dynamic loading due to the variation of river water ele-vation. The leakage toward a deep confined aquifer from the overlyingseveral aquitard layers is possibly minimal. Therefore, the dynamicloading due to the oscillation of river water elevation is the maincontributor. Although several methods were available to determinehydraulic parameters (Carr and Van der Kamp, 1969; Chapuis et al.,

Fig. 5. Layout of monit

2006; Erskine, 1991; Ferris, 1951; Trefry and Johnston, 1998), they arenot applicable to the aforementioned problem.

The typical shape of time-drawdown curve with respect to the tidalinfluence for a well fully penetrating into a confined aquifer can be seenfrom line E in Fig. 7. The constituent of groundwater near the TamshuiRiver was studied through a two-day period groundwater level datashown in Fig. 8 by adopting time-frequency domain analysis based ontheHilbert-Huang transform (HHT). TheHHT is amethod todecomposea signal into a series of intrinsic mode functions (IMFs) (Huang et al.,1998) through data sifting for which is called the empirical modedecomposition (EMD) (Huang et al., 1998). Fig. 9 shows the IMFsobtained, ofwhich two, IMF_6 and IMF_7,were selected toperform fast-fourier transform (FFT).

It can be seen from Fig. 10 that the two dominant frequencies of thegroundwater level were equal to 4.26×10−2 and 8.51×10−2 h−1,whichwere nearly identical to that of the earth tides K1 (lunar diurnalconstituent) and M2 (lunar semi-diurnal constituent). This factimplied that the groundwater near the Tamshui River fluctuatesperiodically with the same frequency as the earth tides K1 and M2,whose periods are equal to 23.9 and 12.4 h, respectively. Neglectingthe earth tide K1 was reasonable as its influence on groundwateramplitude was relatively small as about 44 mm compared to thatinduced by the earth tide M2. Fig. 11 shows the drawdown data insemi-log scale from the three observation wells for the pumping testundertaken in Well 20 at the construction site CR, in which the slopeand horizontal intercept of extension of late-time drawdownasymptote could not be determined as a result of the tide-induceddrawdown fluctuation. The first half-sinusoidal groundwater fluctua-tion was to be found at 520 min after the onset of the pumping test.Shifting forward an additional 352 min (i.e., 520+352=872 min)from 520 min in time axis, the groundwater would be on the same

oring instruments.

20 36 44 49 49 50

Well 17

Well 25

Well 16

Well 8

Well 9

Well 14

Well 18

Well 24

Well 19

Well 23

Well 10

Well 13

Well 11

Well 12

Well 20

Well 22

Well 21

Step 1

Step 2

Step 3

Step 4

240 mins 120 mins

2005/5/1613:40

140 mins 130 mins 3130 mins 700 mins

5/1617:40

5/1622:00

5/1620:00

5/1916:00

5/1709:40

5/1711:50

CMM

3960 mins

Fig. 6. Schedule for operating multi-well pumping test.

22 J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

amplitude or elevation during fluctuation. The straight section of theTheis (1935) in semi-log relation between drawdown and time startedaround 8 min. The drawdowns at 8520, and 872 min will be consisted

A

B

C

D

Δ

Δ

b

a

s (arithmetic scale)

t or t/r(logarithmic scale)

Δ t or Δ t/r

LEGENDA Full penetration wellB Partial penetration well

C Pumping with storageC Pumping with storage and skin

A

D

E

C E Pumping with storage and tide

F

Fig. 7. Schematic illustration of the five influences, 1) periodical fluctuation, 2) wellborestorage, 3) skin, 4)partial penetrationwell, and5) leakageproblem, duringapumping test.

0 10 20 30 40 50

Time [hr]

-3

-2

-1

0

1

2

3

Wat

er le

vel [

m]

0 10 20 30 40 50

-3

-2

-1

0

1

2

3River water levelGroundwater level11/5 17:36

11/7 16:16

Fig. 8. Groundwater level in Chingmei formation and river water elevation beforesingle-well pumping tests.

in the straight section of Theis's curve. This result, therefore,reasonably removes the tidal influence from drawdown curve.

3.2. Wellbore storage

When pumping is undertaken in a large-diameter well, the initialvolume of water pumped is not coming from the surrounding aquiferbut from the water originally stored in the well casing (Chapuis andChenaf, 2003; Kruseman and de Ridder, 1990). To balance pumpinginduced pressure decline in pumped aquifer, drawdown in a nearbyobservationwell commences after a finite period of time, which can beillustrated by line C in Fig. 7 where point “a” indicates the critical time(tc) (Papadopulos and Cooper, 1967; Schafer, 1978) that the wellborestorage no longer has some influence on early-time drawdown.Neglecting it will result in overestimate of storage coefficient althoughwellbore storage in the pumpingwell only has an early-time influenceon drawdown in nearby observation wells (Black and Kipp, 1977;Mucha and Paulikova, 1986; Narasimhan and Zhu, 1993). The criticaltime can be determined using Eq. (1) where dc is the inner diameter

Time[hour]

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Gro

undw

ater

leve

l [m

]

0 10 20 30 40 50

0 10 20 30 40 50

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IMF_1

IMF_2IMF_3

IMF_4

IMF_5

IMF_6

IMF_7

Fig. 9. Intrinsic mode functions of groundwater level in Chingmei formation.

0 1 2 3 4 5 6

0 1 2 3 4 5 6

0 1 2 3 4 5 6

Frequency [cph]

0

0.004

0.008

0.012

0.016

0.02

Am

plit

ude

[m]

0 1 2 3 4 5 6

0

0.004

0.008

0.012

0.016

0.02FFT0.042553 (K1)

Frequency [cph]

0

0.04

0.08

0.12

0.16

0.2

Am

plit

ude

[m]

0

0.04

0.08

0.12

0.16

0.2FFT0.085106 (M2)

Fig. 10. Dominant frequencies of groundwater near the Tamshui River determinedusing fast-fourier transform.

0

1

2

3

4

5

0.01 0.1 1 10 100 1000 10000

Dra

wdo

wn

[m]

Elapsed time [min]

Field Data (Well 19, r=6.30 m)

Field Data (Well 14, r=16.00 m)

Field Data (Well 17, r=28.05 m)

t=520 min

t=872 min

tc=8 min

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 5 10 15 20

Gro

undw

ater

flu

ctua

tion

[m

]

Time [hr]

t=520 min

t=872 min

Fig. 11. Semi-log plot of observation-well drawdown for the determination of hydraulicparameters.

23J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

in millimeter of well casing, dp is the outer diameter in millimeter ofpump rising pipe, Q/s is specific capacity of the well in m3/day/m attime tc.

tc = 0:017 d2c−d2p� �

= Q = sð Þ: ð1Þ

The dc and dp used in this pumping test program were 200 and450 mm, respectively. Then by Eq. (1), the critical time tc wasdetermined to be 8 min. This result revealed the wellbore storageeffect vanishes at 8 min after the onset of pumping and rendered thedrawdown data in the period of 0 to 8 min are unsuitable for hydraulicparameter determination.

3.3. Partial penetration well effect

As the length of well screen used in this pumping test programwasactually less than the aquifer thickness, the partial penetration welleffect should be taken into account for the storage coefficientdetermination. The typical shape of time-drawdown curve referredto partial penetrationwell effect is similar to that of the large-diameterwell. It can be seen from line B in Fig. 7 that the additional drawdownΔs2 referred to the partial penetration well effect remains constant asthe pumping is longer than point “b” where the partial penetrationwell effect has a steady influence on drawdown. The straight section ofline B almost parallels that of line A, implying that the transmissivityestimates derived from line B should be nearly identical to the realvalue. However, the horizontal intercept of extension of straightsection of line B substantially differs from that of line A. As a result, thestorage coefficient estimates derived from line B would result in asignificant error. The partial penetration well effect on the drawdownin the nearby observation wells located 1.5 to 2 times the saturateaquifer thickness from a pumping well can be neglected (Hantush,1964).

As mentioned above, Chingmei formation at the construction siteCR is inferred to be about 52.5 m to 58.4 m thick. Although two clayseams were detected during the site investigation and process of wellinstallation, the actual thickness of Chingmei formation is not knownas little borehole loggings are available below the second interbeddedclay seam. However, the deep well, Sanchun I, about 2.5 km distancefrom the construction site CR, gives that a 2–4 m thick clay seam wasfound at a depth of 105–107 mbelow the surface, the aquiferwould be67–69 m thick. The Δs2 resulting from the partial penetration welleffect can be determined through the estimated aquifer thickness by

employing Hantush (1961a,b). Shifting the late-time drawdownasymptote of the partially penetrating well downward by Δs2, thedata should be on the straight section of Theis's curve and theestimates of storage coefficient from the adjusted curve can be derivedmore accurately.

3.4. Skin effect

The use of drilling mud during boring is to protect borehole shaftfrom collapse and improves drilling efficiency. However, drilling mudmay invade surrounding formations to create a zone where thepermeability is lower than that of undisturbed formations. In practice,it is difficult to determine the actual thickness of the disturbed zone. Asa result, the disturbed zone is usually simulated as an infinitesimallythin skin that is represented by a dimensionless parameter Sk(Streltsova, 1988) derived from a graphic method using late-timedrawdown data of pumping well:

SK = 1:1513sw 1ð ÞΔsw

− log2:25TwSr2w

� �� �ð2Þ

where sw(1) is pumping-well drawdown at t=1 min, Δsw is slope ofstraight line of late-time sw(t), Tw is transmissivity determined usingsw(t), rw is well radius. For a badly skinned pumping well, the Sk valuecan be as large as 18.57 (Chen and Chang, 2002).

Skin and wellbore storage can concurrently occur in a pumpingwell andhave influence ondrawdown in nearbyobservationwells thatare subjected of its own wellbore storage (Agarwal et al., 1970; Chenand Chang, 2006; Chu et al., 1980; Park and Zhan, 2002, 2003).Neglecting such a combinedeffectwill result in serious overestimate ofstorage coefficient and underestimate of transmissivity. Typical shapeof drawdown curve from a pumping well subject to such a combinedeffect can be illustrated as the combination of line C and line D in Fig. 7,in which Δs1 represents the skin effect induced steady head decline.From Fig. 12, asΔsw=3.35, the transmissivity (Tw) can be determinedas 0.32 m2/min by Tw=0.183Q/Δsw. The Sk value can therefore bedetermined by Eq. (2) after completing the determination of hydraulicparameters.

3.5. Leakage effect

Before determining hydraulic parameters, it needs to investigate ifthe late-time drawdown is not affected by leakage from the overlying/underlying formations. The typical shape of drawdown curve referredto leakage from an observation well fully penetrating into a confinedaquifer can be illustrated by line F in Fig. 7.

0.01 0.1 1 10 100 1000 100000

10

20

30

40

Dra

wdo

wn

[m]

Elapsed time [min]

Field Data (Well 20)

Cooper-Jacob Fit

0.32

sw(1)=22.5 m

Tw= m2/min

tc=8 min

Δsw=3.35 m

Fig. 12. Semi-log plot of pumping-well drawdown for the determination of skinparameter using late-time drawdown data.

24 J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

Fig. 13 shows the change of groundwater level in Sungshan I andChingmei formation measured from electronic piezometers depictedin Fig. 2 during the multi-well pumping test for the construction site

-14

-13

-12

-11

-10

-9

-8

-7

5/16/05 5/17/05 5/18/05 5/19/05 5/20/05 5

5/16/05 5/17/05 5/18/05 5/19/05 5/20/05 5

-45

-40

-35

-30

-25

-20

-15

Gro

undw

ater

leve

l [m

]

ELP8001ELP8011

ELP8003ELP8005

ELP8007

ELP8016ELP8002

ELP8004 ELP8ELP8

ELP8

Multi-well pumping test

13:4

0

16:0

0

Date [m/d/yy]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

Fig. 13. Variation of groundwater level measured in Sungshan I (silty sand) and Chingme

CR, during which the groundwater levels in Sungshan I graduallydeclined while those in Chingmei formation declined significantly to amaximum of 43.7 m elevation. The delayed response of groundwaterlevel in Sungshan I is attributable to its relatively low permeabilitycompared to Chingmei formation where the permeability is as high as10−3 m/s. Since the pumping was stopped, the groundwater level inChingmei formation soon recovered to 14.6 m elevation. Fig. 14 showsthe groundwater levels, with variousmonitoring elevations of−2.17 m(upper part of Sungshan V), −9.87 m (Sungshan V — boundary toSungshan IV), −33.07 m (Sungshan III) and −53.67 m (Chingmeiformation), in OW8-1 which is 50 m from the pumping wells. As thegroundwater level in Chingmei formation was substantially declined to21.35 m elevation as a result of the multi-well pumping test, thegroundwater level in Sungshan III changed little initially and thendeclined from 14.5 to 18.4 m elevation wherein those in Sungshan Vwere fluctuating with the earth tides K1 and M2. This implied that thegroundwater in Sungshan III may percolate through Sungshan II intoSungshan I or Chingmei formation.

However, a numerical modeling of groundwater flow owing toleakage from the Tamshui River was performed (Liu, 1996). The fieldwas simulated as a rectangular of 700 mby 600 mwith an observationwell located 500 m from the leakage area of 100 m by 100 m forwhichtwo boundaries were utilized to simulate river elevationwith periodic

/21/05 5/22/05 5/23/05 5/24/05

/21/05 5/22/05 5/23/05 5/24/05

-14

-13

-12

-11

-10

-9

-8

-7

-45

-40

-35

-30

-25

-20

-15

ELP8001-07 (EL. -46.5 m)ELP8011 (EL. -48.6 m)In Sungshan I (silty sand)

ELP8002 (EL. -67.03 m)ELP8004 (EL. -67.2 m)ELP8006 (EL. -66.9 m)ELP8008 (EL. -66.8 m)ELP8012 (EL. -67.0 m)ELP8016 (EL. -67.0 m)In Chingmei formation (gravel)

006012

008

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

Well 8Well 9Well 10Well 11Well 12Well 13Well 14Well 16Well 17Well 18Well 19Well 20Well 21Well 22Well 23Well 24Well 25

i formation (gravel) at the construction site CR during the multi-well pumping test.

-8

-7

-6

-5

-4

-3

-2

5/16/05 5/17/05 5/18/05 5/19/05 5/20/05 5/21/05

5/16/05 5/17/05 5/18/05 5/19/05 5/20/05 5/21/05

-8

-7

-6

-5

-4

-3

-2

-20

-19

-18

-17

-16

-15

-20

-19

-18

-17

-16

-15

Date [m/d/yy]

-22

-21

-20

-19

-18

-17

-16

-15

Gro

undw

ater

leve

l [m

]

-22

-21

-20

-19

-18

-17

-16

-15

Multi-well pumping test

OW8-11 (EL. -2.17 m)OW8-12 (EL. -9.87 m)In Sungshan V (silty sand)

13:4

0

16:0

0

OW8-13 (EL. -33.07 m)In Sungshan III (silty sand)

OW8-14 (EL. -53.67 m)In Chingmei (gravel)

OW8-11OW8-12

Fig. 14. Variation of groundwater level measured in various elevations of−2.17 m,−9.87 m,−33.07 m and−53.67 m at a distance of 50 m from the construction site CR during themulti-well pumping test.

25J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

varying head of amplitude 2 m. The result from themodeling reportedthat the amplitude of groundwater level in Chingmei formation is atmost 2% in the Tamshui River, or at most 4 cm (Liu, 1996). Bycomparing such a large leakage amount as 40 cm/s induced ground-water amplitude to the effect of the massive pumping in Chingmeiformation, this effect, therefore, excludes from the hydraulic param-eter estimates.

3.6. Estimation of hydraulic parameters

Table 1 shows the hydraulic parameters derived from the pumpingtest undertaken inWell 20 at the construction site CR, inwhich theΔs2values, resulting from the partial penetration well effect, in everyobservationwell are also reported. Table 1 also shows the considerable

Table 1Hydraulic parameters determined from the single-well pumping test data, considered perio

Pumping well Parameter Well 19 (r=6.30 m)

Well 20 Tw=0.32 m2/min Sk=1.34 T (m2/min) 3.50S 1.9×10−10

S′ 2.7×10−3

Δs2 (m) 2.24

S and S′ represent the S value derived from Cooper-Jacob (1946) and Hantush (1961a,b), re

error (about two orders) in the determination of storage coefficient ifthe drawdown curve induced by the partial penetration well is notshifted to Theis's curve in a parallel manner. The average values oftransmissivity and storage coefficient determined using the proposedmethod are 3.5 m2/min and 9.5×10−4, respectively. The Sk value isdetermined to be 1.34 by Eq. (2), reflecting mild skin situation. Basedon the average of 68 m as the aquifer thickness, the permeability forChingmei formation at the construction site CR can be determinedusing T/b, which is equal to 3.5 m2/min/68 m or 8.6×10−4 m/s.

4. Method validation

For a confined, homogeneous, and isotropic aquifer, the dimen-sionless drawdown solution for a fully penetrating pumping well

dical fluctuation, wellbore storage, partial penetration well effect, and skin.

Well 14 (r=16.00 m) Well 17 (r=28.05 m) Avg.

3.60 3.40 3.502.6×10−8 9.4×10−6 3.1×10−6

1.7×10−5 1.2×10−4 9.5×10−4

0.85 0.36

spectively.

0.01 0.1 1 10 100 1000 100000

1

2

3

4

5

Dra

wdo

wn

[m]

Elapsed time [min]

Field Data (Well 19, r=6.30 m)

Cooper-Jacob Fit

1.92E-10

3.50

Moench (1997)

S =

T= m2/min

Fig. 16. Validation of this method by comparing the calculated and measureddrawdown (Well 19).

26 J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

subject to both skin and wellbore storage is (Agarwal et al., 1970;Kabala, 2001):

swD τð Þ¼ L−1⟨ K0ffiffiffip

p + Sk

ffiffiffip

pK1

ffiffiffip

p p

p2αw

K0ffiffiffip

pð Þ + Skffiffiffip

pK1

ffiffiffip

pð Þ½ � + ffiffiffip

pK1

ffiffiffip

pð Þ� �⟩ ð3Þ

where τ=Tt/(rw2 S) is dimensionless time, and p is the Laplacetransform parameter with respect to τ, andαw=S(rw/rwc)2 is wellborestorage coefficient of the pumping well. The symbol of L−1 denotes theLaplace inversion, which can be calculated numerically using theStehfest (1970) algorithm.

As the groundwater velocity in the vicinity of an observation wellis relatively small compared to that of a pumping well, the skin effectof an observation well is generally not significant. However, eachobservation well needs a finite time to reflect the aquifer piezometricpressure decline as induced by pumping, during which time there is atime lag in the observation well, referred to as wellbore storage of anobservation well. The drawdown solution for the observation wellsubject to its own storage and to both skin andwellbore storage of thepumping well is (Moench, 1997):

soD ρ; τð Þ = L−1⟨ K0 ρffiffiffip

p = 1 + WDpð Þ

pp

2αwK0

ffiffiffip

pð Þ + Skffiffiffip

pK1

ffiffiffip

pð Þ½ � + ffiffiffip

pK1

ffiffiffip

pð Þ� �⟩

ð4Þ

where ρ=r/rw is dimensionless distance, and WD=πbroc2 /(rw2 SF) is adimensionless coefficient reflecting the wellbore storage effect of theobservation well, in which F is a shape factor accounting for the effectof well geometry and hydrogeology on the flow rate across the wellscreen. Eqs. (3) and (4) will be adopted for reproducing thedrawdown curve obtained with the estimated hydraulic parameters.The determination of WD requires the knowledge of the shape factorF. According to Hvorslev (1951), for a fully penetrating well in aconfined aquifer F=2πb/ln(Re/ro) where Re is the effective wellradius on which the flow from the observation well storage vanishes(Chen and Lan, 2009). The value of Re is normally taken as 200 ro(Butler, 1998; US Dept. of Navy, 1961). Hence, WD=2.65(roc2 /rw2 S), inwhich roc is the radius of the well casing of the observation well. Asroc=rw, WD=2.65 S. The hydraulic parameters adopted are: S=αw=

0

10

20

30

40

0.01 0.1 1 10 100 1000 10000

Dra

wdo

wn

[m]

Elapsed time [min]

Field Data (Well 20)

Cooper-Jacob Fit

0.35

Agarwal et al. (1970) and Kabala (2001)

Tw= m2/min

Fig. 15. Validation of this method by comparing the calculated and measureddrawdown (Well 20).

1.9×10−10, 2.6×10−8, and 9.4×10−6 forWell 19,Well 14, andWell 17,respectively; Sk=1.34; WD=8.2×10−6; Tw=0.32 for Eq. (3) whileT=3.50 for Eq. (4).

From Figs. 15–18 the calculated and measured drawdown for boththe pumping well and observation well are in good agreement,validating the proposed method. Early-time difference between thecalculated drawdown and measured drawdown is attributable to thepoorfield operation.On the other hand, the calculateddrawdownbeginsto slightly deviate from themeasured drawdown at around 30 min afterthe commencement of the pumping test, implying that the late-timedrawdown data are initially influenced by recharge from the possiblehydrogeologic boundary.

5. Drawdown simulation

5.1. Multi-well pumping test

The actual drawdown induced by a single-well pumping at somedistance is the sumof s+Δs2where s is derivedusing Theis (1935)withthe estimated hydraulic parameters, T=3.50 m2/min and S=0.00095,and Δs2 is determined using Hantush (1961a,b). The drawdowninduced by multi-well pumping can be calculated by superimposingthe drawdown induced by each single-well pumping. It can be seenfrom Fig. 19, the comparison between the calculated drawdowns andthose measured from ELP8002, PS8004, and PS8010 whose distance

0

1

2

3

4

0.01 0.1 1 10 100 1000 10000

Dra

wdo

wn

[m]

Elapsed time [min]

Field Data (Well 17, r=28.05 m)

Cooper-Jacob Fit

9.44E-06

3.40

Moench (1997)

S =

T= m2/min

Fig. 17. Validation of this method by comparing the calculated and measureddrawdown (Well 17).

0.01 0.1 1 10 100 1000 100000

1

2

3

4

Dra

wdo

wn

[m]

Elapsed time [min]

Field Data (Well 14, r=16.00 m)

Cooper-Jacob Fit

2.57E-08

3.60

Moench (1997)

S =

T= m2/min

Fig. 18. Validation of this method by comparing the calculated and measureddrawdown (Well 14).

0 800 1600 2400 3200 4000 4800

0 800 1600 2400 3200 4000 4800

Elapsed time [min]

7

6

5

4

3

2

1

0

-1

Dra

wdo

wn

[m]

7

6

5

4

3

2

1

0

-1

LEGENDTB (Field data)TB (Simulation)TL (Field data)TL (Simulation)SC (Field data)SC (Simulation)

Fig. 20. Comparison of drawdowns at the remote sites measured from the multi-wellpumping test at the construction site CR and those simulated using Theis (1935) andHantush (1961a,b) with the estimated hydraulic parameters.

27J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

from the pumpingwells is 0, 48.1, and 239.9 m, respectively, appears tobe quite satisfactory.

5.2. Drawdown at remote sites

Fig. 20 shows the comparison between the calculated drawdownsand those measured from sites TB, TL and SC located at distances of443.8, 1494.0 and 2276.2 m, respectively, from the pumping wells. Thecalculated drawdown at sites TB and TL is in good agreement with thefield results, but that is quite different from that measured from site SC.It is likely to interpret that either the Chingmei gravel formation at siteSC not hydraulically connects with that at the construction site CR orthat recharge outweighs the influence of piezometric level declinebecause of geological heterogeneity and/or leakage problem.

6. Discussion and conclusion

As the excavation reached 40 m below the ground surface, 33pumpingwells embedded in 2 m thick and 63m deep diaphragmwallsalong with a 5 m thick jet grouting were used to reduce both the upliftpressures and groundwater inflow during excavations. As the actualthickness of the pumped aquifer is unknown, the installed wells are

0 800 1600 2400 3200 4000 4800

0 800 1600 2400 3200 4000 4800

Elapsed time [min]

40

35

30

25

20

15

10

5

0

Dra

wdo

wn

[m]

40

35

30

25

20

15

10

5

0

LEGENDPS8004 (Field data)PS8004 (Simulation)PS8010 (Field data)PS8010 (Simulation)ELP8002 (Field data)ELP8002 (Simulation)

Fig. 19. Comparison of drawdowns measured from the multi-well pumping tests andthose simulated using Theis (1935) and Hantush (1961a,b) with the estimated hydraulicparameters.

regarded as partial penetrationwells. Single-well test was conducted toderive the hydraulic parameter estimates. After the completion ofsingle-well pumping test, multi-well pumping test was conducted toinvestigate the characteristics of drawdown at both the constructionand remote sites and to validate the parameters determined from thesingle-well pumping test. However, the tide-induced drawdownfluctuation would result in the difficulty for the determination ofparameters. Additionally, wellbore storage, skin, and leakage problemwere involved in the derivation of hydraulic parameters and needed tobe taken into consideration.

The results from time-frequency analysis show that the groundwa-ter level fluctuates periodically with the same frequency as the lunardiurnal tide K1 and lunar semi-diurnal tide M2. Hence the drawdowns,8, 520, and 872 min, with the same amplitude or elevation would beconsisted in the straight section of the Theis's curve. This eliminates thetidal influence from drawdown curve.

The storage coefficient estimates can differ from the real value bytwo orders of magnitude if the partial penetration well effect isneglected in pumping test data analysis. Shifting the late-timedrawdown asymptote of the partially penetrating well downward byΔs2, the data should be on the straight section of Theis's curve and theestimates of storage coefficient from the adjusted curve can be derivedmore accurately.

The critical time thatwellbore storage disappears or approaches zerois estimated to be around 8 min after the onset of pumping,wherein thesteady head decline induced by the skin remains. Streltsova's approach,based on late-time characteristics of drawdown data, is utilized todetermine the dimensionless skin parameter for the understanding ofskin situation.

A previous work indicated that the amplitude of groundwater levelin Chingmei formation is atmost 2% of that from the Tamshui River. Thisstrongly supports that the effect of such amassive pumping in Chingmeiformation can be excluded logically from the hydraulic parameters.However, it is noted that the late-time drawdown data are initiallyinfluenced by recharge from the possible hydrogeologic boundary at30 min after the beginning of the pumping test.

From the testing and method proposed, the coefficients oftransmissivity, storage, and permeability for Chingmei formation weredetermined to be 3.5 m2/min, 9.5×10−4, and 8.6×10−4 m/s, respec-tively. The good agreement between the calculated drawdowns usingthe appropriate well hydraulic solutionswith the estimated parameters

28 J.C. Ni et al. / Engineering Geology 117 (2011) 17–28

and the measured results for both the pumping well and observationwell validates the proposed method.

Acknowledgement

The authors wish to acknowledge Mr. G. Lee, the former graduatestudent, for thefield investigation and the data collection thatmade thisresearch possible and to express sincere thanks to one anonymousreviewer for the valuable comments and corrections to improve thearticle.

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