Journal of JSCE, Vol. 2, 7-24, 2014

THREE-DIMENSIONAL ANALYSIS OF NEGATIVEWATER PRESSURE PROPAGATIONFOR PUMPING WELL WITH EFFECTS
ON GROUNDWATER FLOW
Atsushi TSUTSUMI1, Kenji JINNO2, Tetsuji OZAKI3, Hisao NAKAYAMA4
and Ronny BERNDTSSON5
1Member of JSCE, SG Technical Consultant Corporation (Aoba 1-19-22, Higashi-ku, Fukuoka 813-0025, Japan)

E-mail: a_tutumi@hiz.bbiq.jp
2Member of JSCE, Professor Emeritus, Kyushu University(Izumigaoka 1-4-5, Munakata City, Fukuoka 811-4142, Japan)
E-mail: kj55jp@ybb.ne.jp
3Member of JSCE, Asahi-Techno Corporation (Hirai 5-11-8, Edogawa-ku, Tokyo 132-0035, Japan)
E-mail: ozakit02@gmail.com
4Member of JSCE, Siesta Club Corporation (Shin-tateiwa 9-8, Iizuka City, Fukuoka 820-0004, Japan)
E-mail: hisat.nakayama@gmail.com
5Professor, Lund University, Sweden (Box 118, 221 00 Lund, Sweden)
E-mail: Ronny.Berndtsson@tvrl.lth.se

The application of negative water pressure by vacuum in pumping wells results in a drawdown ofgroundwater table at excavation sites. Due to the vacuum, negative water pressure will propagate aroundthe pumping well. As a result, a large potential gradient is induced and groundwater drawdown is enhanced. In the present paper, a numerical model for three-dimensional unconfined groundwater flow towards a pumping well (Deep Well, hereafter DW) is developed and evaluated. First, the accuracy of themodel is confirmed by comparing the pumping rates at steady state given by the DW formula. Second, thenumerical model for negative water pressure (hereafter, NWP) is described. The model can be used inpractical applications together with the water balance equation to describe groundwater inflow andpumping rate in a pumping well so that time-dependent boundary conditions are considered with thethree-dimensional groundwater flow equation. How the saturated-negative pressure zone develops aroundthe pumping well is shown. Detailed relationships between water level, pumping rate, and propagation of
the negative pressure zone are described and analyzed. The analyses show that the model results can beused to operate air and water pumps more efficiently for water balance and groundwater drawdown.
Key Words : groundwater drawdown, vacuum pump, 3-dimensional groundwater numerical simulation,
propagation of negative water pressure

well. As a result, groundwater drawdown is efficiently achieved by vacuum in the well. Hereafter,
we refer to this method as NWP (Negative Water
Pressure method). There are several interesting
characteristics of NWP. An air vacuum and a water
pump operate simultaneously in the well to create
large negative water pressure. Accordingly, the piezometric head, which is the summation of waterpressure head, air pressure, and elevation, becomes
negative in and around the pumping well. Due to theextremely low piezometric head, the NWP water

1. INTRODUCTION
Prior to excavation at building sites, it is necessary
to draw down the groundwater table to the target
level of the construction. The well point method(WP), deep well method (DW), and shallow sumpmethod (SS) are commonly used techniques for this,considering site-specific conditions. Recently, a new
method using both air vacuum pump and water pumphas been developed. The method creates a large
gradient of piezometric head around the pumping

7

Drain ofgroundwater

Drain ofgroundwater
Drain of air

Negative airpressure

Well pipe
strainer
Atmosphericpressure

Pa

Well
P0

Filter gravel(diameter : 5~10 mm)○
P

Well pipeP○

P : Water pump○

NWP

Wire screen(~6 m)
Water intake
aperture

DW

Fig. 1 Comparison of NWP and DW structures.

NWP, the upper part is sealed by a cap and negative
air pressure in the well is maintained by vacuum.
Furthermore, the water pressure in the well is lowered even more by a groundwater drainage pump. As
a result, the groundwater pressure in the vicinity of
NWP becomes negative and a large piezometric
gradient in the surrounding soil is developed. In thissituation, a negative piezometric domain is formed
around the well.
The principle of NWP differs from that of thevacuum deep well (VDW) method in that the NWP
water intake aperture is located at the bottom part of
the well. In the case of VDW, vacuum is appliedalong the entire well screen. The disadvantage of this,however, is that the vacuum pump may easily suckair in the unsaturated zone and thus the vacuum
power may be significantly reduced.
As illustrated for the NWP, the 6 m long wire
screen is usually set at the lower part of the well. The
apparent permeability of the wire screen should behigh compared to the original aquifer. The open
space between the wire screen and well wall is 2~3
cm. Groundwater enters through this open space andthen flows into the well through the water intake
aperture. Filter gravel ranging from 5 to 10 mm indiameter is used to fill the outside of the wire screen
similarly as for the DW. Since the permeability of thefilter gravel and the open space is large, negative
water pressure in the well can easily propagate to thesurrounding aquifer area. As a result, a large potential
gradient is created.
It should be noted, however, that the unsaturated
air above the groundwater table may be sucked into
the negative water pressure zone when the unsaturated region approaches the high- permeability domain. If air in the unsaturated region enters the NWP
well, negative air pressure may weaken and decrease
the piezometric head in the well. Thus, it is important

intake aperture can be placed close to the excavationlevel. Further, the time required to lower groundwater to the target level is shorter, compared to othermethods. The number of NWP applications is rapidly
increasing due to the efficiency of this method. For
example, NWP was employed at the foundation
construction of a water gate for tsunami protection
near an estuary1) and at the excavation work of a
subway connection to the airport at Sendai, Japan2).
Besides, NWP is often used to vacuum groundwaterpollutants such as volatile organic carbons and oil toremediate polluted soil and groundwater3), 4). The
studies by Nakagawa et al.5) for a cross section and
Hosokawa et al.6) for a cylindrical domain demonstrated that negative water pressure zones around
NWP wells develop in a clear way. However, to better
understand the characteristics of three-dimensional
groundwater flow around the NWP zone, more detailed analyses are necessary. Thus, the paper develops a water balance equation for a NWP well to
calculate water inflow rate and variations of waterlevel in the well. Then, the change in piezometrichead in the well is used as boundary condition in the
groundwater flow equation. It is shown that couplingwater balance and groundwater equations is important to better understand the effects of the NWP
method. The paper is concluded by discussing thepractical applications of the modeling results.

2. PRINCIPLES OF THE NEGATIVE WATER PRESSURE METHOD (NWP)
Figure 1 shows a comparison between the layouts
of DW and NWP. In general, the upper part of DW is
open to the atmosphere and groundwater flows into
the well by gravitation through the well screen. For

8

3. THREE-DIMENSIONAL SATURATED-UNSATURATED FLOW EQUATION
AND NWP PRINCIPLES(1) Fundamental groundwater flow equation
For three-dimensional groundwater analyses, thefollowing equations are applied:

Relative perm eability k r (-)

Relative permeability
kr=k/ks

Water pressure head h(m )to control air pressure around the well. This can beachieved by continuously managing the water balance, change in water level, and piezometric head in
the NWP well by model simulations.

Pressure head hVolumetric water content θ

Fig. 2 Water retention curve used in the present simulation.

Cw    S s  h   u  v  wthu   k  
x

x

y

z
h
, v   k  
yTable 1 Parameters used in the simulation8), 9).

(1) h 
w   k    1
 z 
where the first is the continuity equation and thesecond is Darcy’s equation extended to unsaturated
flow. The relationship between the water pressure
head h and volumetric water content  needs to begiven to solve Eqn. (1). For this, the Van-Genuchten7)
model is applied:Se   rs  r 1

1     h  n  m   s   r   S e

1/ m

Cw 

1/ 2
k  k s  Se 

1  

Ss (m )ks (m s )Parameters for unsaturated soil
α
m
n
θs
θr
(m-1)

1.0×10-3

5.0×10-5

4.91

-1

1 m

1/ m
1  Se 1  S e1 m



m

(2)

7.14

0.34

0.075

(2) Relationship between air pressure Pa and water pressure head h at the water intake aperture
Figure 3 shows the relationship between the waterlevel hw(t), air pressure Pa(t), and water pressure headhs(t) at the aperture elevation after time t. Let Zs denote the elevation of aperture from the NWP wellbottom. Then, the water pressure head hs(t) at theaperture becomes:


m

0.86

the present analyses. It is also assumed that thepermeability is homogeneous and isotropic. The
parameters α and m (or n) are referred from soil
properties shown in the soil catalogue No.4118 by
Mualem8). Figure 2 illustrates the water retention
curve and relationship between the volumetric watercontent and relative permeability kr (=k/ks) when theparameters in Table 1 are applied9). Since we intend
to visualize the propagation of negative water pressure in the saturated region around the pumping wellfor typical soil conditions, representative soil parameters are used.

, m  11 n

m

-1

2

where Cw is specific moisture capacity (m-1);  isparameter, which takes 1 in saturated region and 0 in
unsaturated region; Ss is specific storage coefficient(m-1); Se is effective saturation ratio; θs is saturated
volumetric water content; θr is residual volumetricwater content; ks is saturated permeability (original
permeability of soil in saturation); h is water pressure
head (m); t is time (s); (u, v, w) is Darcy velocity
components in x, y, and z directions (m s-1);  isvolumetric water content; k(θ) is permeability dependent on volumetric water content (m s-1); and (x,y, z) is Cartesian coordinates (m).
Note that the non-Darcy flow is not considered inhs (t )  hw (t )  Z s 

Pa (t )
w  g(3)

The piezometric head Hs(t) under air vacuum pressure Pa(t) is:

9Air vacuum pump

Groundwater pumping
rate : qout (0 ~ Qmax)

Air pressure：Pa(t)

ha 

Pa(t)

Water level in thewell: hw(t)Paw  g0

Wire screen
W : space width
Groundwatertable: Pa=0

vzd

Water pressure head at intake
aperture：hs(t)Ls(K): Mesh interval tocalculate qin by Eqn.(8)

vr(K)
P

Lm : Length of wire screen

Level of water intake
aperture：Zs
vzu

Length of water
intake aperture：Lsa

Fig. 3 Water level, air pressure, water pump, and water pressure head in NWP well.

than in the original soil permeability. In general, thisnarrow zone around the pumping well supports theoriginal soil from collapsing. The material in thiszone is usually gravel or coarse sand larger than theoriginal particle diameter. Also, the wire screen for
the aperture taking groundwater has less resistance tothe fluid flow. The purpose of the present study is todemonstrate that negative water pressure develops
around this high-permeability zone under the effectof enhanced pressure by air vacuum pump. In thepresent simulation, the apparent permeability is set
approximately two orders of magnitude larger thanthe permeability of the original soil. It is obvious thatthe extension of the negative pressure around the welldepends on the air vacuum pressure and the apparent
permeability.
Assuming that the groundwater inflow rate qin canbe approximated by a cylindrical mesh:

H s (t )  hs (t )  Z sP (t )  hw (t )  Z s  a   Z s
w  g P (t )
 hw (t )  a
w  g(4)where w is the density of water and g is the gravity
acceleration. It is obvious that Hs(t) becomes smaller
than hw(t) when Pa(t) is negative.
(3) Water balance equation, control of pumping
rate, and vacuum pressure in the NWP well
Equation (5) represents the water continuity in the
well:

Aw

dhw
q in qout
dt(5)

where Aw is cross-sectional area of the well, qin isgroundwater inflow rate into the well through theintake aperture, and qout is pumping rate.
Assuming that Darcy’s law is applicable, thegroundwater velocity components entering throughthe wire screen can be written as:
vr   k a  H ( x, y , z , t )r(6)vz  ka 

 H ( x, y , z , t )
z

(7)

q

in

  [ 2   rw  W   Ls ( K )  v r ( K ) ]K   v zu  v zd    rw  W   rw
2

2



(8)

where vr(K) is the radial velocity at vertical grid
number K of the well, rw is the well radius, W is thespace width between wire screens and the exteriorwall of well, Ls(K) is the K-th mesh interval to calculate qin by Eqn.(8), and vzu and vzd represent the vertical velocity components in the upward and downward directions along the well, respectively. Thechange in water depth hw(t) in Eqn. (5) can be calculated if qin in Eqn. (8) and qout are given at every
time step. It is obvious from Eqn. (4) that the piezometric head Hs(t) changes corresponding to thechanges in hw(t) and Pa(t). Note that Pa(t) is an operating variable to control the drawdown of

where vr is the velocity component in the radial direction, vz represents the vertical component, andH(x,y,z,t) is the piezometric head. The apparent
permeability ka around the wire screen is set larger

10

Pumping rate
qout=Qmax

Pumping rate:
qout=qin

Vacuumpump
Air pressure headat t=0 in the well:
ha =Pa/(w g)=0 m

Initial waterlevel in thewell: hw(0)Vacuum pump
Air pressure head:-hmax  ha  0,
hmax : maximum vacuum
pressure head

Wire screen
Water levelhw(t)Water pump
P

P

Water intake
aperture
Start

qin

Target water levelin the wellqin

The water level is almost
reaching the target level

Fig. 4 Control of pumping rate qout and air pressure Pa(t).

groundwater level. If Pa(t) is set close to atmosphericpressure Pa(t)≈0, Hs(t) will be equal to hw(t). Hs(t)will decrease when Pa(t) is set at the maximum
vacuum capacity. It should be noted that Hs(t) in thehigh- permeability zone will be approximated equal
to the potential head in the well, if the potential loss
due to the water flow through the well aperture andgravel zone is negligible. In the numerical simulation
for the groundwater flow, the potential Hs(t) orpressure head hs(t) shown in Eqn. (4) can be given as
the boundary condition at the well screen. It should
be noted that continuity equation Eqn. (5) is simultaneously integrated with Eqn. (1). The change inhw(t) is given to Eqn. (3) to update hs(t) and then hs(t)is used as the boundary condition for Eqn. (1). Eqns.
(1) and (5) are coupled through qin using Eqns. (6),(7), and (8). Water depth in the well hw(t) describedby Eqn. (5) changes with qin and qout. When hs(t) as
boundary condition for the groundwater flowchanges, qin is affected. Remember that the groundwater discharge from the NWP well qout is controllable up to its maximum pump capacity Qmax.
Therefore, there are two control variables for the
NWP well: Pa(t) and qout. It is necessary to take account of the groundwater table around the well. If thegroundwater table decreases too much, soil air above
the groundwater table may be sucked into thepumping well. If this situation occurs, Pa(t) will also
weaken, resulting in a low pumping power. In conclusion, drawdown of groundwater by the NWP iscontrolled by the water balance in the well and thethree-dimensional groundwater flow.
The left-hand side of Figure 4 illustrates the situation when the pump is ready to start. The pumping
rate in the well, qout(t), will reach its maximum ca-

pacity Qmax, while Pa(t) gradually decreases withtime. The right-hand side of Fig. 4 illustrates thesituation when water level in the well almost reaches
the target elevation. At this stage, qout needs to bebalanced by qin. Process control is used to optimize
the water level. This is exemplified as follows:
1) The water pumping rate qout is set equal to Qmax,
as soon as the switch is on.
2) Since qin for the initial stage is less than Qmax,
drawdown of water level in the well will start tooccur.
3) Monitor the water level in the well, and set thepumping rate qout equal to qin so that the waterlevel in the well is maintained at steady state.
The air pressure Pa(t) decreases from atmosphericpressure to the minimum negative pressure (-7 m inthe present simulation) after a few minutes and Pa(t)is maintained at this level. The water level in the wellgradually decreases. An instantaneous drawdown of
water level in the well could cause instability in the
numerical simulation. However, since the pump capacity is limited, a quick drawdown is not likely.
(4) Apparent permeability and boundary condition at the wire screen
The aquifer permeability was set at 5.0×10-5 m s-1.
An apparent permeability for the wire screen region(thin space between the wire screen and exterior of
the well wall of NWP) was set equal to 2.010-2 m s-1.
This is 400 times larger permeability compared to theaquifer soil. Note that for actual sites it is necessary
to use the permeability based on field tests.
Figure 5 illustrates the calculation grid around thewater intake aperture. The thick line is the well wall.

11

aperture of water intake where soil is saturated. This
assumes that the groundwater table remains at a highlevel. Therefore, the permeability near the NWP wellis equal to the saturated permeability ks even though
the water pressure head is negative. Needless tomention, the other parameters,  takes 1 and Cw takes
0 in Eqn. (1), respectively. In the vadose zone above
the groundwater table, the water pressure head h isnegative. On the other hand, the water pressure head
below the groundwater table is positive. As mentioned earlier, the water pressure head near the NWP
well becomes negative when vacuum is applied. Thismeans that there should be another interface where
the water pressure head will be zero. Typically, sucha location is found between the saturated domain
with h>0 and h<0 around the well. During simulation, a curved interface with h=0 develops.
In summary, there are two regions with negative
water pressure head: The first is in the unsaturated
zone. In this region, the permeability changes withvolumetric water content. The second is the region
where negative water pressure propagates. Here, thepermeability is equal to ks because soil is saturated.
The detailed calculation algorithm to identify theunsaturated region with negative pressure head ispresented in Figure 6. The groundwater table elevation is found from the numerical solution as the location with the zero pressure head changes frompositive to negative values. Similarly, there are grid
points with negative pressure head in the saturated
region around the well screen. The location of thegroundwater table and the curved interface, which isformed around the well screen, is easily plotted using
commercial software for contour mapping. It should
be noted, however, that judgment is necessary for thepermeability coefficient when water is saturated, but
the calculated pressure head is negative. Such condition can be found as condition (II) in Fig. 6. In thepresent study, the water level hw(t) in the NWP well
was controlled so that the groundwater level wasmaintained higher than the curved interface thatformed around the NWP well. It is important to notethat the soil at any grid points can remain below thegroundwater table when such a control is done.
The formation of the NWP region around thepumping well is confirmed by several reports fromaxisymmetrical laboratory experiments and numerical simulations4), 5). However, the behavior of thethree-dimensional NWP flow for various conditions
has not yet been sufficiently investigated for practicalapplications at construction sites. In the present
study, the finite difference method with successive
over-relaxation (SOR) was adopted. Needless tomention, the finite element method is also applicable.In the present section, the two cases are simulated.

Well wall

Water levelin the well

Section of wire screen Lm

K*+6
K*+5
K*+4
Length of water
intake aperture Lsa

Ls(K)
K*+3
K*+2
K*+1

K*
Well bottom

I

I+1

I+2

I+3

Space between wire screen andwell wall (high permeability zone)◎ : Grid point where the time dependent boundary
condition hs(t) is assigned: Grid point at the high permeability zone
: Grid point in the aquifer soil
K*: Grid number in the vertical direction at the well bottom

inflow, and air pressure in the well.Fig. 5 Grid meshes
near the water intake aperture.

Impervious boundary condition is given at these grid
points. The water intake aperture is represented bydouble circles and grid points by K=K*+1 and K*+2
in the vertical direction, in which K* denotes the grid
number of the well bottom in the vertical direction.
Also, K=K*+3,· · ·, and K*+6 denote the grid number of the section of wire screen in the present simulation. The colored region represents thehigh-permeability zone at the space between theexterior well wall and wire screen. For permeability
in the numerical simulation, the harmonic average ofthe adjacent grids is used.

4. NUMERICAL METHOD
In the following example, the groundwater inflow
through the aperture, qin, is obtained by summationaccording to Eqn. (8). The water pressure head hs(t)shown in Eqn. (3) or the piezometric head Hs(t) in
Eqn. (4) is given at grid points for intake aperture at
every time step. The permeability of the original
aquifer soil is equal to the saturated permeability as
long as the negative pressure region is maintained
outside the well. Whether the soil near the well issaturated or unsaturated by the groundwater can beevaluated by checking the curved interface with zerowater pressure head h(x,y,z,t) during simulation. In
practice, the location of zero pressure is the point
where h(x,y,z,t) changes from positive to negativevalues. In the NWP method, a negative water pressure head hs(t) is given as boundary condition at the12

Initial condition : Unsaturated region  h(x,y,z,t)<0 and <s
Saturated region  h(x,y,z,t)0 and =s
Calculate Se, Cw, k by Eqn.(2) and set  = 0 or 1
Start : Time=0
Condition (I): Saturated
and pressure head >0

Output resultst  t+Δt

Condition(II): Saturated
but pressure head<0

For grid point(I,J,K):

=s, Se(s)=1.0, Cw(s)=0.0,k(s)=ks,  =1.0

No
h(I,J,K,t)<0 ?

Solve Eqn.(1) by SOR method

Yes

Condition(III): Unsaturated
and pressure head<0

Are there any grid
points around (I,J,K)
with <s ?

No
Time<Max Time?

Yes

No

Yes
Apply Eqn.(2):<s, Se= Se(), Cw=Cw(), k=k()Stop/End

Fig. 6 Calculation flowchart to define the saturated region with negative pressure head.

setup, respectively. The ground elevation is EL. +2.0
m. The aquifer is homogeneous and isotropic. Twoaquifer conditions were studied: Fig. 7(b) shows animpervious hydraulic base located at depth EL.-15 m(Case 1 and Case 2). The other one in Fig. 7(b) assumes that the impervious hydraulic base is located at
EL.-25 m (Case 3). Rainwater infiltration is notconsidered. The boundary condition is set on thesquare 100 m apart from the center of the calculation
domain. The groundwater level is set at EL.+1.0 m asa constant boundary condition. Note that the squaredomain is approximated by a cylinder with equivalent areal size when the well formula is applied. In thepresent case, a radius of 112.8 m gives the equivalent
areal size. Similarly, the equivalent well radius with
0.258 m is used to represent the 0.5 m×0.5 m square
mesh. The bottom of the well is set at the impervious
hydraulic base (EL. -15 m). The water level in thewell is maintained at 4 m above the hydraulic base,corresponding to EL.-11 m. The bottom of the well is
the same in Case 1 and Case 2, but the water level ismaintained at EL.-4 m. For Case 3, the bottom of thewell is set at a depth of the hydraulic base (EL.-25m), and the water level in the well is set at EL.-20 m.
Fig. 7(c) illustrates the NWP well. As shown, thebottom of the well is set at EL.-14 m and the hydraulicbase at EL.-15 m. The water intake aperture is set at
EL.-14 m. The length of the intake aperture is 0.5 m.

The first case analyzes DW for unconfined groundwater with infinite radius of influence and uniform
permeability. The groundwater enters from the wellscreen by gravity. Capillary water flow takes place
along the groundwater table toward the well. Seepage
boundary condition is adopted above the water levelin the DW well. The elevation of the groundwatertable in the unconfined aquifer is obtained by thenumerical solution as mentioned previously.
At the vertical strainer above the seepage point in
the DW well, the velocity component perpendicular
to the well screen is set equal to zero as a boundary
condition. The simulation is continued until thegroundwater flow asymptotically reaches a steadystate. The groundwater pumping discharge at steadystate is compared with the well discharge formula.
The second case is the numerical simulation ofdrawdown by the NWP method. The resulting
groundwater drawdown, development of negative
pressure zone, and change in pumping rate arecompared with DW.
(1) Calculation conditionsa) Geological and boundary conditions
Figure 7 shows the boundary and hydro-geologicalconditions. Fig. 7(a) represents the plane view of thesimulation domain. Fig. 7(b) is the calculation condition for the DW setup, and Fig. 7(c) for the NWP

13

100m
100m

Constant waterlevel (EL.+1.0m)

100m

100m

(a) Plane view of the calculation region
Impervious boundary(ground surface：EL.+2.0m)
DW
Initial water level(EL.+1.0m)
Seepage boundary(well screen)

for Case 2

Constant water levelboundary (EL.+1.0m)

4m

Water levelin the well

Hydraulic base(EL.-15m)

Impervious hydraulic base: for Cases 1 and 2; EL.-15.0m,
for Case 3; EL.-25.0m(b) Calculation condition for DW
Impervious boundary(ground surface：EL.+2.0m)
NWP wellfor Case 2

1m 1m

Water level

Screen length

Initial water level(EL.+1.0m)

Impervious
well wall

Constant water levelboundary (EL.+1.0m)
Assigned waterlevel in the well

Length of aperture 0.5m

Impervious hydraulic base (EL.-15.0m)(c) Calculation condition for NWP
Fig. 7 Boundary and hydro-geological conditions.

The wire screen is 6 m long from the well bottom.
The target water level in the NWP well is set 1 m
above the bottom. Table 2 summarizes the simulation condition.
b) Grid size and time increment
Figure 8 shows a plane view of the finite difference grid used for the discretization of Eqn. (1). A
fine grid in x and y directions is used around the wellin the horizontal plane. The minimum grid size at thewell is 0.25 m, while a 26.2 m grid is used near theconstant water level boundary. In the vertical direction, 0.2 m uniform grids are used for the case withthe hydraulic base EL.-15.0 m. The total number ofgrids in this case was 409,446. In the case where thehydraulic base is set at EL.-25.0 m, a 0.25 m uniform

grid size is used from the ground surface down to thelevel in the well (-20m), and then the grid size isgradually increased toward the hydraulic base. The
number of grids in this case became 433,251.
The initial groundwater elevation is set at EL.+1.0
m. A static pressure distribution is initially assumed.
In the NWP simulation, there is a possibility that alarge gradient of the piezometric head may occur
around the pumping well with time due to the effectof air pressure Pa(t). To avoid unstable fluctuations in
the numerical simulation for the initial period, thetime increment t was set to 0.01 seconds and thengradually increased at the rate of 1.01 every time step
until t reached 6.0 seconds. The convergence criteria

14

Table 2 Calculation condition for DW and NWP.
Unit (m)Elevation of groundsurface (EL)Elevation of hydraulic base (EL)Elevation of wellbottom (EL)
Target water level(EL)
Groundwater levelat the calculation
boundary (EL)Strainer length (EL)DW(case1)

DW(case2)

DW(case3)

NWP

+2.0

+2.0

+2.0

+2.0

-15.0

-15.0

-25.0

-15.0

-15.0

-15.0

-25.0

-14.0

-4.0

-11.0

-20.0

-13.0

+1.0

+1.0

+1.0

+1.0

-15.0~+1.0-15.0~+1.0-15.0~+1.0-14.0~-8.0

Elevation of water
intake aperture-13.5~-14.0

Air pressurehead(m)

0.0

0.0

0.0

-7.0

Calculation size ofsquare(m)

200

200

200

200

(m)

10

5

0

(m)

5

10m

(m)

Fig. 8 Plane view of the finite difference mesh.

two-step confirmation made sure that the numericalprogram for groundwater drawdown by DW wasapplicable for the NWP simulation by changing theboundary conditions.
Figure 9 illustrates the groundwater level obtainedby the Dupuit’s assumption10)~15) for the unconfined
flow neglecting unsaturated flow. It is assumed thatthe vertical velocity component far from the pumping
well is negligible. It should be noted, however, thatthe formula for pumping rate is valid even when thevertical component is neglected. The formula forpumping rate Qwell and the shape of groundwater level
H(r) are expressed by Eqns.(9a) and (9b):in the SOR for the finite difference method was set tosatisfy 5.010-4 m at every grid point. This convergence criterion is considered to be sufficiently
small.
(2) Numerical simulation for DW and comparison
with the well formula
The accuracy of the numerical model was checkedby numerical simulation for DW. After the accuracyof the numerical solution for DW was confirmed, thecalculation conditions of NWP were given to thesame program. Once the accuracy of the DW was
confirmed, the NWP solution would be reliable. The

15

Qwell  k H R2  H w2



Water level (EL. m)

(9a)

2

ln( R / rw )数値解
Numerical solution
井戸公式
Well formula10

HR  Hw ln R / r 
ln R / rw 2

H (r )  H R 
2

2

‐1

(9b)

‐2

1.5HR‐3‐4

where HR is the groundwater level at the radius of
influence R, Hw is the water level in the well, and rw is
the well radius. There are many literatures discussing
the accuracy of numerical codes. In general, the solutions are accurate if careful attention is paid to thediscretization of the fundamental equations10)-15).
Because the present paper examines the effect ofapplying vacuum in a pumping well on the groundwater flow, simple boundary conditions are considered. The results for the three cases are presented inFig. 9. In each case, the hydraulic base of the aquifer
and the water level in the well are different in the
numerical simulation. The full line for each caseshows the groundwater level by the numerical solution and the broken line is obtained by the wellformula in Eqn. (9b). D. Chenaf and R. Chapuis15)
performed a detailed analysis of groundwater level
for an unconfined aquifer and seepage face at a wellstrainer. They remarked that the groundwater level inthe Dupuit’s formula (9b) coincides with the observed groundwater level in the distant region beyond 1.5HR. However, the deviation between thewell formula and the numerical solution of thegroundwater level becomes large in the region within
1.5HR. This fact is also seen in Fig. 9 and Fig. 10. In
Fig.10, the three lines represent the piezometric headat EL.-12, EL.-16, and EL.-21.7 m. The groundwaterlevel is also plotted in the same diagram. The present
numerical solution confirms that the Dupuit’s assumption for the groundwater level is not valid forthe region within 1.5HR.
Strictly speaking, the groundwater discharge to thewell is different from the well formula. The reason
for this is the disregard for the unsaturated water flow
above the groundwater table. This was also noted by
D. Chenaf and R. Chapuis15). They concluded that the
groundwater discharge by the numerical simulation
is at most 5% larger than that of the well formula.
Since the numerical simulation in the present study is
carried out for the saturated-unsaturated flow, thisdifference is reasonable. The steady state pumping
rate by the present numerical simulation is listed inTable 3. The difference coincides with their remarks.
It is clear that the Dupuit’s formula for the pumping
rate is analytically derived based on the continuity ofwater during steady state. Although neglecting thevertical velocity component is not valid near the

‐5
0.1
1
10
Radius (m) 100(a) Case1 (Hydraulic base at EL.-15 m, water level in the well EL.-4 m)

Water level (EL. m)
2

井戸公式
Numerical solution
数値解Well formula

0
‐2
‐4
‐6

1.5HR

‐8
‐10
‐12
‐14
0.1

1

10

100

Radius (m)(b) Case 2 (Hydraulic base at EL.-15m, water level in the well EL.-11 m)
Water level (EL. m)
5

Numerical solution
井戸公式
Well formula
数値解

0
‐5
‐10

1.5HR (m)

‐15
‐20
‐25
0.1

1

10

100

Radius (m)(c) Case 3 (Hydraulic base at EL.-25 m, water level in the well EL.-20 m)

Fig. 9Groundwater table by numerical simulation
and well formula in steady state.

Piezometric head (m)51.5HR
0
‐5
‐10
‐15
‐20
‐25
0.1

1

10

100

Radius (m)Groundwater level (h=0 by
the numerical simulation)
数値解による地下水面
井戸公式による地下水面
Groundwater level by Well formula (Eqn. (9b))
EL‐16mPiezometric head along EL.-12 m
Piezometric head along EL.-16 m
Piezometric head along EL.-21.7 m

EL‐12mEL‐21.7m

Fig. 10 Distribution of groundwater level and piezometrichead by the numerical simulation and well formula(Case 3).

16

Table 3 Comparison of groundwater discharge for Dupuit’s
formula Eqn.(9a) and numerical simulation for DW.
(unit: m3 min-1)(D) Dupuit’s(N) Numerical
Deviation
Cases
formulasolution for DW(D)-(N)-3.7 (%)
0.224
0.215
Case 1-3.1 (%)
0.389
0.378
Case 2-3.1 (%)
1.057
1.024
Case 3

Elevation (EL. m)
0Capillary zone:
unsaturated and h<0

Groundwater table

Contour linesof piezometrichead H-5

pumping well, the continuity of water is kept at any
horizontal coordinate when the groundwater flow
along the capillary fringe is neglected.
It should also be noted that the numerical results
for steady state pumping rate by Chenaf and Chapuis15) with FEM and by the authors with FDM arevery close. The height of the groundwater table andthe pumping rate at steady state are indispensible
factors to be checked with numerical solutions. Since
the NWP program gives the reliable result for thesefactors at steady state after the transient period, it isexpected that the present program also shows reasonable behaviors during the transient period.

-10
Reference Vectors

1.2(m
hr-1)
1.2
(m/hr)

-10

-5

0

5

10
Radius (m)(a) Groundwater table and piezometric headaround the well by DW after 4 days.
Elevation (EL. m)
0(3) Characteristics of groundwater table near the
NWP wellFigure 11 shows the elevation of the groundwatertable, piezometric head distribution, and the negative
pressure-saturated region inside a radius of 10 m after
4 days, obtained by the numerical simulation for DW
and NWP. Fig. 11(a) represents the groundwatertable of DW for Case 2 in Fig. 7(b), while Fig. 11(b)is a result of NWP. In the case of DW, the gradient ofgroundwater table is steeper than that of the NWP
near the well strainer. The reason for NWP having amore flat gradient of the groundwater table near thewell screen can be explained as follows: In the caseof NWP, the water intake aperture is suited at thelowest part of the well and impermeable boundary
condition is set at the rest of the well wall. Thiscondition for the NWP results in a groundwater tablethat becomes flat near the well wall.
On the other hand, the well strainer is set along theentire depth in the case of DW. This structure allows
the groundwater to flow into the well through thestrainer at any depth. The difference in the groundwater table near the DW and NWP wells is a result by
the given different boundary conditions.

Capillary zone:
unsaturated and h<0

Groundwater table-5

Contour linesof piezometrichead H-10
Reference Vectors

1.3(m
hr-1)
1.3 (m/hr)

-10
-5
0
saturated and h<0 zone
inside the curved surface

5

10
Radius (m)(b) Groundwater table and piezometric headaround the well by NWP after 4 days.

Fig.
Groundwatertable
tableandandpiezometricpiezometricheadhead
distribuFig.11
11 Groundwater
distribution
by DW
aroundthe well
after after
4 daystion aroundthe well4 daysby andDWNWP.
and NWP.

water flow and drawdown of the piezometric head by
NWP are presented.
(1) Calculation condition
Let us examine the case where the well bottom islower than the sheet wall. Figure 12 shows a planeview of the hypothetical calculation domain having
200 m sides in x and y directions. Groundwater is
supplied from these sides. The square zone is the
excavation site with 14.8 m length at each side. The
excavation depth is enclosed by the sheet wall withdepth reaching EL. -21.7 m, which is 3.3 m above thehydraulic base (EL. -25 m). Here, the permeability ofthe sheet wall is set equal to 1×10-7 m s-1. The excavation depth is set at EL. -10 m, which is 12 m below
the ground surface. Table 4 lists the well structure

5. NUMERICAL ANALYSIS FOR A HYPOTHETICAL EXCAVATIONAs mentioned previously, the NWP simulation canbe done by changing the boundary conditions of any
software developed for DW. The water balance
equation for the well is recommended to control airpressure. In this section, the characteristics of ground17

Midpoint
200 m

Well
A’

14.8 mA
Well wall
Sheet wallinterior side

Sheet wall

14.8 m200 m(a)Plane view of the calculation region

Pump

P

EL.-25
Hydraulic base(EL.-25 m)

Ground surface EL.+2 m
Groundwater table atinitial stage EL.+1 m

Excavation
elevation(EL.-10 m)

Strainer

Water levelin the well

Water depth 2 m

DW

Hydraulic base
EL.-25 m(b) Calculation condition for DW

Wire screen 6m

NWP

1m 1m

Water levelin the wellDepth of sheet wall
EL.-21.7 m

Ground surface EL.+2 m
Groundwater table atinitial stage EL.+1 m

Excavation
elevation(EL.-10 m)

Depth of sheet wall
EL.-21.7 m

Intake aperture
Hydraulic base(EL.-25 m)

Hydraulic base EL.-25 m(c)Calculation condition for NWP

Fig. 12Calculation
domainandandsetup
setup ofof DW,
andandsheet
wall.wall.
Fig. 12Calculation
domain
DW,NWP,
NWP,
sheet

Table 4 Well and sheet wall characteristics of the excavation.
DW

NWP

500 mm

500 mmPumping capacity

2.4 m3 min-1

2.1 m3 min-1

Elevation of well bottom

EL.-25 m

EL.-24 m

Strainer setting EL.+1.0 m

EL.-23.5~-24 m (Lsa=0.5 m)

Target water elevation for excavation

EL.-23 m

EL.-23 m

Position of wire screen-

EL.-18~-24 m (Lm=6.0 m)

Bottom of sheet wall

EL.-21.7 m

EL.-21.7 m

Minimum vacuum head-min(Pa /wg)=-7 m

Well diameter18

Air pressure head (m)0Inflow rate qin , pumping rate qout (m3 min-1)

3.0

5

Air pressure head

‐1
‐2
‐3

Water level(EL.m)
Water inflow rate qin, Pumping rate qout (m3 min-1)

2.5

0

Pumping rate qout

2.0

‐10

1.5

‐7
‐8

1.0

Pumping rate qout

‐20

2.0
1.5
1.0

Inflow rate qin

300 s

‐30
‐35

0.0
0

60

120

180

240

300

360

420

480

540

Target water levelin the well;EL.-23 m

Water level

‐25
0.5

‐9
‐10

‐15

-7m; Minimum airpressure head

‐6

2.5

‐5

‐4
‐5

3.0

0.5

440 s

Water inflow rate qin

0.0

600

0

60

120

180

240

300

360

420

480

540

600

Time (s)Time (s)Fig. 14 Variations of pumping rate, water inflow rate,
and water level in the well.

Fig. 13 Variations of pumping rate, groundwaterand pump capacity. The water intake aperture for
NWP is set at EL. -23.5~-24.0 m with Lsa=0.5 m. The
wire screen length is set between EL. -18 and -24 m
with Lm=6.0 m.

Flow rate below the sheet wall
(m3 min-1)
Water inflow rate qin, pumping rate (m3 min-1)(2) Resultsa) Variations in groundwater inflow, pumping
discharge, and air pressure in the NWP wellIn the present example, the maximum water pumpcapacity was set to 2.1 m3 min-1 and the negative
maximum capacity of vacuum pressure head in thewell was -7 m. Figure 13 shows the variations ingroundwater inflow rate into the well, pumping rate,
and air pressure head immediately after the water andair pumps are switched on. The air pump is operated
so that the air pressure decreases linearly down to -7
m taking 300 seconds, and then maintained at -7 m as
air pressure head. In the figure, the water inflow rate
slightly changes after 300 seconds when the airpressure head is fixed at -7 m.
Figure 14 shows the variations in pumping rate
and water level in the well. With a constant pumping
rate at 2.1 m3 min-1, the water level in the well decreases as calculated by the water balance in Eqn. (5).
After 440 seconds, the water level reaches the target
water level EL. -23 m. The groundwater inflow rateincreases up to 1.7 m3 min-1 after 440 seconds. It
should be noted that the water level in and around thewell further decreases and it may reach the water
intake aperture. Thus, there is a possibility that air inthe unsaturated zone above the groundwater table
may be sucked into the well. Once air enters the well,
the vacuum effect will decrease. Therefore, waterlevel, water pumping rate, and air pressure need to becontrolled to avoid such a situation. In the present
example, the following hypothetical operation wastested. Figure 15 shows the changes in water inflow
rate qin through the aperture, water pumping rate

0.15

0.25

3.0

0.20

2.5

Pumping
rate qout

Flow rate below
the sheet wall (m3 min-1)

2.0
1.5

0.10

Water
inflowrate qin

1.0

0.05

0.5

0.00

0.0

440 s
0

5

10

Flow rate is almost
zero for 0~3 min

15

20

25

30

Time (min)Fig. 15 Variations of pumping rate, water inflow rate,
and flow rate below the sheet wall.

qout, and flow rate under the sheet wall. In the hypothetical operation, qout is adjusted equal to qin so thatthe water level in the well can be maintained at EL.
-23 m after 440 seconds.
b) Characteristics of groundwater drawdown
time series
The three thick lines in Figure 16 represent thevariations in the groundwater drawdown at threelocations immediately after start of pumping by
NWP. The thickest line represents the variation at theexterior wall of NWP followed by the variation at the
midpoint and the interior points of the sheet wall in
Fig. 12. The broken lines show those of DW obtainedat the same points. The variations at the three points
by NWP are seen to be almost identical until 16hours. Distinct delays are observed after 23 hours.
First, the drawdown at the interior point of the sheet
wall is delayed. The drawdown at the midpoint follows.As time passes, the deviation becomes large. In
the case of DW, more distinct changes can be observed. The largest drawdown occurs at the well wall.

19

Inflow rate qin (m3 min-1)

Elevation (EL. m)

2.5

2
0

2

‐2

1.5

‐4
‐6

NWP
1

‐8

Target of excavation elevation

‐10

DW

DW

‐12
‐14

NWP

0

‐16
0

24

48

0.5

72

96

120

144

0

168

10

20

30

40

50

Time (hr)Time (hr)Inflow rate qin (m3 min-1)

Elevation (EL. m)

2.5

Maintain the water level by pump in20

well afterofaround
5 minutes;
out=qFigure 17 theComparisons
groundwater
inflowqrate
tointhe well

2

DW

‐2
‐4

1.5

NWP
Maintain the water level by water pump in
the well after around 7.3 minutes; qout=qin
Stop of vacuum of
air pressure after 5 minutes

‐6

1

‐8
‐10

DW

Target of excavation elevation

‐12

0.5

NWP

‐14

0

‐16
0

12

24

36

0

48

10

20

30

40

50

60

Time (min)Time (hr)
井戸壁部（負圧井戸）
Well wall (NWP)

中間点（負圧井戸）
Midpoint (NWP)

矢板内側（負圧井戸）
Sheet wall (NWP)

井戸壁部（DW）
Well wall (DW)

中間点（DW）
Midpoint (DW)

矢板内側（DW）
Sheet wall (DW)

Fig. 17 Comparisons of groundwater inflow rate
to the well.

Fig. 16 Comparison of groundwater drawdown between
NWP and DW.

groundwater pumping rate qout and the groundwaterflow below the sheet wall become 1.060 and 0.185
m3 min-1, respectively, after 24 hours, and 0.990 and
0.195 m3 min-1, respectively, after 48 hours. It is
confirmed that qout asymptotically approached thegroundwater flow below the sheet wall. Figure 17
shows the change in the groundwater inflow rate for
the NWP and DW. The inflow rate to DW well increases sharply during the first minute and thengradually increases up to 5 minutes.
The water level in the well approaches the target
level after 5 minutes. Therefore, the pumping rate qout
is set equal to qin to maintain the same level. It should
be noted in such operation that the water level in DW
can be further lowered if the pumping rate qout is stilllarger than qin.
However, in this case, unnecessary groundwater
may be pumped up. In the case of NWP, the inflow
rate in the well slowly increases up to 7.3 minutes
and then decreases. This period, when the rising
speed is changed, corresponds to the pump operation.
After 5 minutes, the air vacuum pump is stopped.

The drawdown at the midpoint and interior points
follow. The deviations gradually increase but they
approach a steady state. Only 17 hours after the start,
the drawdown of the groundwater level at the threepoints by DW is larger than that by NWP. This can be
explained by the fact that the water inflow rate depends on the product of velocity and inflow area. The
DW has a longer strainer than NWP as long as thegroundwater level remains high. This means that
more groundwater can enter the DW well than that of
the NWP. On the other hand in NWP, the inflow
takes place through the aperture with a screen length
Lm = 6.0 m, which is shorter than that for the DW.
Besides, as shown in Table 3, the maximum capacityof DW is set to 2.4 m3 min-1 and this is larger than 2.1
m3 min-1 for the NWP. This implies that the inflow
rate by DW for the initial period is large and waterlevel therefore decreases quickly. The groundwaterflow rate toward the excavation site below the sheet
wall is almost 0 until 2~3 minutes after pumping.
After that, the groundwater flow rate under the sheet
wall gradually increases during approximately 1
hour. After 1 hour, it reaches a constant rate. The

20

Ground elevation (EL. m)

Ground elevation (EL. m)
Well pipe00Groundwater table
after 6 hours
12 hours-5

Sheet wall-5

12 hours
24 hours

24 hours
36 hours
48hours-10

144 hours
168 hours

52.8hours

-15

-15

Negative pressure-saturated zone

-20

Wire screen
05Water level inthe well

DW

Water intake-5

Sheet wall

-20

NWP
-10

36hours
96 hours
Target elevation of
excavation (EL.-10 m)

48hours

Target elevation of
excavation (EL.-10 m)

-10

-15

Well pipe

Groundwater table
after 6 hours

10

-25

15

-15

-10

-5

0

5

10

15

Distance from well (m)Distance from well(a) Formation of negative water pressure around the wellwith time and drawdown of the water level inside the
excavation site(b) Drawdown of the water level inside the excavation site

Fig. 18 Drawdown of groundwater table by NWP and DW.

Unsaturated capillary region
above the groundwater table

Elevation (EL. m)
5
地下水面

Lowest point飽和負圧領域上端
ofgroundwater table

0

Groundwater
table

‐5
‐10

Negative pressure-saturated zone

‐15

Curved surfaceof zero pressure
head

Highest point of negative
pressure-saturated zone

‐20
‐25
0

12

24

36

48

60

Time (hr)Water intake
aperture

Fig. 19 Changes in groundwater elevation (●) and highest point along the NWP well (○) with time.

The drawdown of groundwater table by NWP at the
excavation site takes place uniformly during 12~24
hours. A negative pressure-saturated zone is formed
around the well wall. This zone expands upwards
along the wire screen. On the other hand for DW, thedrawdown of the groundwater table during the first 6
hours is rapid but gradually decreases similar to thatfor the NWP. Specifically, the groundwater tableseems to reach a steady state after 24 hours. The
groundwater table shape by NWP at 24 hours is morehorizontal, compared to the DW. It is also observedthat the NWP drawdown of the groundwater tabletakes about 25 hours, while for DW it takes 96 hours
until the groundwater table reaches the target level of
excavation. To evaluate the groundwater table andthe expansion of the negative pressure-saturated zone
with time by NWP, schematic illustrations are shownin Figure 19.

On the other hand, at 7.3 minutes, the groundwater
pumping rate is set equal to the inflow rate so that thewater level in the well can be kept at the target level
after 7.3 minutes. It should be noted that NWP has
two control variables: the water pump discharge andthe control of air pressure in the well. This advantage
can be implemented by the water balance equation inwhich the air vacuum pressure in the well can beeasily controlled.
c) Characteristics of water level drawdown in the
excavation site
Figure 18 shows the groundwater table and thenegative pressure-saturated zone along the A-A’cross section in Fig. 12(a). Fig. 18(a) represents thechanges in the groundwater table and the negative
pressure-saturated zone around the wire screen
formed by NWP. Fig. 18(b) shows the change ingroundwater table by DW.

21

Groundwater table: h=0m

Ground elevation (m)Groundwater table: h=0m

Ground elevation (m)

0

0

-5

-5

-10

-10

h=0m
-15

-15

-20

-20

-25

-25

m
-15
-10
-5
0
5
10
15
m
(b)
Groundwater
drawdown
andpiezometric
head(a) Groundwater drawdown and piezometric head
distribution by DW with same screen length
distribution by NWP with same strainer length(after 6 days)(after 2 days)
Fig. 20 Comparisons of groundwater table drawdown using NWP and DW, respectively.
-15

-10

-5

0

5

10

15

The elevation of the groundwater table along thewell wall and the line of zero water pressure head arepresented. The symbol ‘○’ represents the highest
point of the line of zero water pressure head, while‘●’ represents the lowest elevation of the groundwater table around the well wall at the left part of Fig.
19. It is observed that the groundwater table goes
down and the negative pressure-saturated zone
gradually expands with time. The two lines approacheach other more closely after 48 hours. As explained
previously, the groundwater table along the wire
screen and the curved surface of zero water pressure
head will meet unless either the water pumping rate is
reduced or air vacuum pressure is weakened. Soil air
in the unsaturated zone overlying the groundwatertable will be quickly sucked into the well. As a result,the air vacuum in the NWP will be weakened. Then,the efficiency of the NWP decreases. To avoid suchsituations, the operator of NWP usually opens thevalve to let air into the well.

Groundwater table: h=0m

Ground elevation (m)
0

-5

-10

-15

-20

-25
-15

-10

-5

0

5

10

15

m

Fig. 21 Drawdown of groundwater table by DW when thescreen is set along the well depth (after 6 days).

aperture in Fig. 20(a). This line indicates the boundary between the negative pressure-saturated zone as
Condition (II) and positive pressure-saturated zone as
Condition (I) in Fig. 6. The groundwater table inside
the excavation site reaches the target depth EL. -10 m
after 2 days. On the other hand, the groundwater tablefor case (b) is still above EL. -7 m even after 6 days.
This difference is caused by the larger gradient of thepiezometric head toward the well for case (a) than the
one for case (b). To analyze the effects of the strainer
length for DW, a longer strainer is set over the entire
depth as shown in Figure 21. It is seen that the
groundwater table is lowered to EL. -9 m after 6 days
and the level is lower than in Fig. 20(b). However,
the groundwater level is still higher than in Fig.
20(a). It is obvious in the present simulation thateither the longer strainer or lower well elevation
depth is necessary for DW if the groundwater needs
to be lowered similar to that for NWP.

(3) Effect of well depth, length of strainer of DW,
and wire screen of NWP
It is important to analyze whether there are significant differences when the well depths, lengths ofstrainer of DW or wire screen of NWP are changed.
The sheet wall is set deeper than that of the welldepth. As shown in Figure 20, the target excavation
depth is set at EL. -10 m for (a) NWP and (b) DW. In
case (a), the water intake aperture is set at EL. -20 m
and the wire screen of length 4 m for the NWP. On
the other hand, the strainer of 4 m is set for DW incase (b). The red thick lines with the notation ‘h=0’ inFig. 20(a) after 2 days and Fig. 20(b) after 6 days
represent the lines of zero water pressure head.
As explained previously, a curved interface with
the notation ‘h=0’ is formed around the water intake

225. The three virtual observation points were locatedat the well wall, midpoint, and interior of the sheet
wall to compare the drawdown of the groundwatertable. In the case of DW, the shape of drawdown
was not the same. The drawdown speed of thegroundwater table became slower with time. Thisimplied that the groundwater table by DW wasreaching a steady state. On the other hand, thedrawdown rate of groundwater table was almost
constant by the NWP. This is an advantage for excavation works.
6. The time necessary for drawdown by NWP was 2days until the groundwater table was lowered to thetarget excavation elevation, while it took 6 days by
DW when the same well strainer was used. Even
with a 20 m strainer for DW, it took 6 days to lower
the groundwater table below the target excavation
elevation.
In the future, optimal control for groundwater
drawdown can be automated if signals from pumping
rate, air and water pressure gauges, and groundwaterlevel near the NWP well are transmitted continuously.
The NWP has also been applied to remediation ofsoil and groundwater pollution by applying its strong
vacuum power. Furthermore, it should be noted that
air vacuum power can enhance water drainage, which
results in compaction of the soil. Also, deformationof soil surface may take place if too much air vacuum
power is applied. For these purposes, it is importantto establish two-phase analyses for both water andgaseous phase transportation under the effect of the
NWP.

6. CONCLUSION
The characteristics of the NWP method were analyzed and discussed. This method was used to enhance the drawdown of the groundwater table bysimultaneous air vacuum and water pumping. The
accuracy of the numerical model for the DW method
was checked in advance of the NWP simulations. By
comparing model results with research findings fromliterature and Dupuit’s well formula, the numericalsolution of DW for the groundwater table and thepumping rates at the steady state were shown to be ingood agreement. Then, the NWP was applied to ahypothetical excavation site surrounded by a sheet
wall. The following results were obtained:
1. The water balance equation for water in thepumping well was coupled with the groundwaterflow simulation. The water balance, change in waterlevel, effect of vacuum, water inflow and outflow inthe well were considered. By this coupling, thetime-dependent water pressure head in the well was
set as the boundary condition for the groundwaterflow simulation. It indicates that coupling of thewater balance equation in the well with the numerical simulation for NWP is significant to control
well operation.
2. The numerical simulation of DW was carried out
to confirm the accuracy of the steady state pumping
rate and the groundwater table. The numerical solution was compared with Dupuit’s formula. The
pumping rate by the numerical simulation of DW
agreed reasonably well with Dupuit’s formula. The
elevation of the groundwater table was also in good
agreement beyond the radius of 1.5HR. The
groundwater elevation inside the radius of 1.5HRdeviated gradually toward the pumping well. These
results are all similar as remarked by Chenaf andChapuis15).
3. In their paper, the groundwater pumping rate by
the saturated-unsaturated numerical simulation for
DW usually gave at most 5% larger value than thatof Dupuit’s formula. In the present simulation for
DW, the deviation was 3~4% larger. This fact isalso demonstrated by the present simulation.
4. In the numerical simulation for DW and NWP, theshape of groundwater table near the pumping well
was steep for DW and flat for NWP. This difference
was a result of the difference in the boundary condition assumed at the well wall. The drawdown
speed of the groundwater table for the initial period
by DW was faster than for NWP. However, its
speed became slow and asymptotically reached asteady state. On the other hand, NWP could lower
the groundwater table at an almost constant ratefrom the beginning.

ACKNOWLEDGMENT: The authors express theirsincere appreciation to Mr. Sigekichi Takahashi,
Asahi Co. Ltd., for his support and comments, which
helped in completing the present research.
REFERENCES
1)

2)

3)

4)

23

Komura, T., Goda, K., Takahashi, S. and Ozaki, T.:
Groundwater drawdown at the tidal gate foundation construction site, Proceedings of VI section of 65th Annual
Meeting of the Japanese Society of Civil Engineers, pp.
543-544, 2010 (in Japanese).
Ohta, K., Kohno, E. and Takahashi, S.: Groundwater workfor the construction of the underground access railway to
Sendai Air Port-Super well point method and vacuum press
type recharge well, The Foundation Engineering &Equipment, Vol. 34, No. 3, pp. 55-59, 2006 (in Japanese).
Ozaki, T., Yamauchi, D., Shirakawa, T., Chiba, M. andTakahashi, S.: Remediation for the polluted soil by VOCs
using strong vacuum, Technical News of the Center of Soil
Environment, Geo-Environmental Protection Center, No.
10, pp. 1-6, 2005 (in Japanese).
Ozaki, T. and Takahashi, H.: Remediation for soil andgroundwater by super well point principle and remediation
example, Journal of Civil Engineering, Vol. 53, No. 8, 2012
(in Japanese).

5)

6)

7)

8)

9)

Nakagawa, K., Momii, K., Jinno, K., Wada, S., Park, K. H.,
Nakayama, H. and Takahashi, S.: Numerical study ofgroundwater drawdown by super well point method, Proceedings of Spring Conference, Japanese Association of
Groundwater Hydrology, pp. 94-97, 2006 (in Japanese).
Hosokawa, T., Takahashi, S., Jinno, K., Nakayama, H. andPark, K. H.: Analysis of saturated-unsaturated groundwater
seepage flow for the new version of vacuum deep well,
Proceedings of Autumn Conference, Japanese Associationof Groundwater Hydrology, pp. 84-87, 2006 (in Japanese).
Van-Genuchten, M. T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil
Science Society of America Journal, Vol. 44, No. 5, pp.
892-898, 1980.
Mualem, Y.: A catalogue of the hydraulic properties of
unsaturated soils, Hydrodynamics and Hydraulic Laboratory, Israel, 1976.
Jinno, K., Momii, K., Fujino, K., Nakagawa, K., Hosokawa, T., Egusa, N. and Hiroshiro, Y.: Numerical Analysis ofMass Transport in Groundwater, pp. 83-85, Kyushu University Press, 2001 (in Japanese).
10) Matsuo, S. and Kono, I.: Groundwater Lowering Technology, Kajima Publishing, pp. 69-71, 1970 (in Japanese).
11) Kinzelbach, W.: Groundwater Modeling, Elsevier Publishers, Chapter 3, 1986.
12) Bear, J. and Verruijt, A.: Modeling Groundwater Flow and
Pollution, D. Reidel Publishing, pp. 225-284, 1987.
13) Fetter, C. W.: Applied Hydrogeology (4th edition), pp.
150-165, 2001.
14) Sato, K. and Iwasa, Y.: Groundwater Hydraulics, Springer,
pp. 33-41, 2003.
15) Chenaf, D. and Chapuis, R.: Seepage face height, watertable position, and well efficiency at steady state, Ground
Water, Vol. 45, No. 2 (March-April), pp. 168-177, 2007.
(Received October 24, 2012)24