ICSE6 Paris - August 27-31, 2012
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
ICSE6-144
Seepage Failure of Sand in Three Dimensions –Experiments and
Numerical Analyses–
Tsutomu TANAKA1, Shuang SONG1, Yuki SHIBA1, Shinya KUSUMI1, and Kazuya INOUE1
1
Department of Agricultural and Environmental Engineering, Kobe University
Nada Kobe 657-8501, Japan: ttanaka@kobe-u.ac.jp :
Abstract: In the deep and large excavations of soil with a high ground water level, sheet piles or diaphragm
walls are often used to retain soil and water. Under such conditions, three dimensional seepage flow occurs
through soil, and seepage failure is often a problem. The three-dimensionally concentrated flow lowers the
safety factor for seepage failure more than the two-dimensional condition. To clarify the seepage failure
mechanism, seepage failure experiments are conducted under three-dimensional flow conditions for various
cases. Secondly, Prismatic failure concept 3D is presented and analyses of FEM seepage flow and stability
against the seepage failure of soil are carried out. The characteristics of seepage failure of soil in three
dimensions are then discussed from the viewpoint of experiments and numerical analyses. Finally whether or
not the axisymmetric approximation is appropriate to model three dimensional seepage failure phenomena is
discussed.
Key words
Seepage failure, Experiment, Three dimensional flow, Hydraulic head difference, Prismatic failure concept
3D, Axisymmetric modeling.
I
INTRODUCTION
In excavations of soil with a high ground water level, sheet piles or diaphragm walls are often used to
retain soil and water. Under such conditions, seepage flow occurs through soil, and seepage failure is often a
problem. For excavation involving a large area, seepage failure is a problem in two dimensions. In contrast,
the more the region of a cofferdam is restricted, the greater the seepage flow concentrates threedimensionally within the cofferdam [Miura et al. 2000, Hirose and Tanaka 2007]. The three-dimensionally
concentrated flow lowers the safety factor for seepage failure more than the two-dimensional condition.
In this paper, seepage failure experiments are conducted under three-dimensional flow conditions for
various cases, and analyses of FEM seepage flow and
stability against seepage failure of soil are carried out.
From experiments, the hydraulic head differences at an
water tank
abrupt change of discharge Hd, at the onset of soil
sheet pile wall
200
deformation Hy, and at failure Hf are next considered,
400
1000
and theoretical critical hydraulic head differences based
on the Prismatic failure concept HPF are then discussed.
1000
II
THREE DIMENSIONAL EXPERIMENTS
drainage
II.1
Test apparatus
A test apparatus was designed for studying 3D
seepage failure of soil within a cofferdam as shown in
Figure 1. The test apparatus consists of three parts: (1)
seepage and water tanks, (2) constant-head device and
(3) open piezometers.
1535
supply of water
hole
(Unit mm)
Figure 1: Schematic sketch showing test apparatus
ICSE6 Paris - August 27-31, 2012
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
(1) Seepage and water tanks: The main apparatus consists of a seepage tank on the center/right side and
water tank on the left/rear side as shown in Figure 1. The seepage tank is made of stainless steel, 1,000mm
wide, 1,300mm high and 1,000mm deep. The front of the tank is made of transparent glass for observation of
the behavior of soil particles inside and the right side of the tank is equipped with 283 piezometer holes for
the measurement of pore water pressures. Twenty-nine piezometer holes are also installed at the bottom of
the seepage tank. The left and rear sides of the tank are fitted with partitions 700mm high. A cofferdam is
mounted on the right/front side with surface size 200mm400mm. The outside of the cofferdam is referred to
as upstream, and the inside as downstream. There are inlet ports, through which persons can enter and work,
on the left and rear sides of the water tank.
(2) Constant-head device: The upstream water head is given to a sand model stepwise by raising a
constant-head device. Seepage water flows through a sand model under the difference in water head H
between the downstream water level at the top of the right-hand-side drainage hole and the upstream water
level kept constant by the constant-head device.
(3) Open piezometers: The 16 plates with 20 pipes 1,500mm long and 8mm in inside diameter are used for
open piezometers. Pore water pressures can be read from 320 open piezometers connected to measuring
points (i.e. piezometer holes) in the right wall and bottom of the seepage tank.
II.2
Test materials
Table 1: Physical properties of soil
Physical properties*
Lake Biwa sand 3
Lake Biwa Sand 3 is used for tests. The physical
properties and grain size distribution are illustrated in
Table 1 and Figure 2. From Table 1 and Figure 2, the
test material is classified as uniform and fine sand.
II.3
Gs
Uc
D50
emax
emin
k15
Procedure for making sand models and
setting up the test equipment
(mm)
(104 m/s)
2.668
1.404
0.283
1.115
0.761
7.263
* Gs : specific gravity, Uc : coefficient of uniformity, D50:
Percent finer by weight (%)
The test procedure for making sand models and
50% size of sand particles, emax, emin : the maximum and
setting up the test equipment is as follows:
minimum void ratio, k15: coefficient of permeability at
15C for sand of Dr=50%
(1) Test sand is put into several containers and the
mass of the sand is weighed.
(2) The test sand is soaked with water for about
100
one week until it is fully saturated with water due to
80
deaeration through being stirred several times.
60
(3) The seepage tank is filled with water.
40
(4) The sand saturated with water is poured by
hand, little by little, upstream from the water tank,
20
and downstream from the outside of the seepage
0
tank. The sand is placed in 10 to 20 layers and
0.01
0.1
1
10
compacted with an aluminum rod 7mm in diameter,
Grain size (mm)
1,000mm in length and 100g in weight for upstream
soil and 5mm in diameter, 1,000mm in length and
Figure 2: Grain size distribution of soil
55g in weight for downstream soil. For each layer,
the compacting rod is dropped from about 100mm height; 50 times for upstream and 8 times for downstream
soil.
(5) For waterproofing, plates are mounted on the inlet ports on the left and rear sides of the water tank.
(6) Drainage apparatus on the right side of the seepage tank and thermometers in water of the seepage tank
on up- and downstream sides are set up.
(7) The datum (i.e. the reference level) is set up using first-rate level PL1.
(8) The 16 plates for piezometers are adjusted to the exact height from the Datum using PL1.
(9) The sand model is placed in this state for one night so that it can be in a stable condition.
(10) The seepage failure test is started the next day.
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ICSE6 Paris - August 27-31, 2012
II.4
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
Procedure for seepage failure test
An upstream water head is raised stepwise until the sand
model deforms and collapses. The increase in hydraulic head
difference H is 20% of the critical hydraulic head difference
of the sand model Hc at early steps (H<0.8 Hc). H is then
gradually reduced by half, by half and so on, and finally 2% of
Measurement line
Hc in the vicinity of H= Hc. At each step of H, the following
items are measured, after verifying that the seepage flow is in a
steady state:
(1) Quantity of water flowing through soil is measured a few
times and averaged.
(2) Temperatures of water on up- and downstream sides of
the seepage tank are measured and averaged.
(3) The quantity of discharge is translated to the value at 15
degrees Centigrade, Q15.
(4) Pore water pressures are measured at all points of Figure 3: Measurement line of the height
piezometer holes in sand and water to give “Standard of soil surface
measurements” and at certain selected points for “Simplified measurements”. Using the measured pore water
pressures, the difference between hydraulic heads on the up- and downstream sides H is calculated, an H-Q15
curve is plotted, and equi-potentials by experiment are drawn on the right-hand-side wall from standard
measurements.
(5) The heights of the soil surface are measured at several chosen points along the measurement line shown
in Figure 3. The measurement line is a bisector of the right angle of
Down
the inside corner of the rectangular diaphragm wall.
Upstream
stream
The series of tests for sand models is numbered from E0301 to
d
E0317 as shown in Table 2. Notation is as follows referring to Figure
D
D
4: T1 and D1 are the total depth of soil and penetration depth of sheet
T
piles on the upstream side, T and D are those on the downstream
T
side, d (=D1D) is the excavation depth for the excavation model,
and Dr is the relative density of soil.
1
1
Figure 4: Notation
Table 2: A series of test-sand models
Exp.No. (Mnemonic name)
e
Dr (%)
' (gf/cm3)
d (ｍ)
T (m)
D (m)
D/T
Excavation
E0301
（30, 30)
0.945
48.1
0.858
0.000
0.299
0.102
0.342
No
E0302
（35, 35)
0.932
51.7
0.863
0.000
0.348
0.151
0.435
No
E0303
（35, 35)
0.941
49.1
0.859
0.000
0.350
0.152
0.435
No
E0304
（35, 30)
0.930
52.2
0.864
0.051
0.296
0.100
0.337
Yes
E0305
（30, 30)
0.943
48.7
0.859
0.000
0.298
0.101
0.340
No
E0306
（40, 40)
0.933
51.4
0.863
0.000
0.399
0.202
0.507
No
E0307
（40, 35)
0.939
49.7
0.860
0.050
0.349
0.152
0.436
Yes
E0308
（35, 27.5)
0.935
50.9
0.832
0.073
0.275
0.078
0.285
Yes
E0309
（27.5, 27.5)
0.942
48.7
0.859
0.000
0.274
0.078
0.284
No
E0310
（40, 30)
0.941
49.1
0.859
0.101
0.299
0.102
0.342
Yes
E0311
（45, 45)
0.936
50.6
0.862
0.000
0.449
0.252
0.562
No
E0312
（35, 27.5)
0.936
50.6
0.862
0.075
0.274
0.077
0.282
Yes
E0313
（35, 30)
0.943
48.6
0.859
0.053
0.297
0.100
0.338
Yes
E0314
（35, 30)
0.938
50.1
0.861
0.050
0.299
0.102
0.342
Yes
E0315
（40, 40)
0.932
51.6
0.863
0.000
0.399
0.202
0.507
No
E0316
（50, 50)
0.934
51.1
0.862
0.000
0.498
0.302
0.606
No
E0317
（40, 40)
0.938
49.9
0.861
0.000
0.398
0.201
0.506
No
1537
ICSE6 Paris - August 27-31, 2012
III
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
PRISMATIC FAILURE CONCEPT 3D
The Prismatic failure concept 3D presented by Tanaka et al. (2012) is used for estimating the stability
against seepage failure of soil. In the Prismatic failure concept 3D, we assume that the body of soil lifted by
seepage water has the shape of a prism with a certain height and width adjoining the sheet pile wall. The rise
of the prism is resisted by the submerged weight, W’, and frictions FRL and FRCR on the left and right sides
and FRF and FRCB, on the front and back sides. The safety factor Fs with respect to the rise of the prism, which
is subjected to the excess pore water pressure on its base, Ue, is given as:
W ' FRL  FRCR  FRF  FRCB
,
(1)
Fs 
Ue
For the hydraulic head difference H between up- and downstream sides, safety factors, Fs, are calculated
for all of the prisms within a cofferdam. The safety factor Fs takes the minimum Fs min for a certain prism
among all of the prisms. The calculation is iterated for another hydraulic head difference, H, until the
condition whereby Fs min becomes nearly equal to 1.0 is found. H=Hc at which the condition Fs min=1.0 is
applied is defined as the critical hydraulic head difference. The prism with a value of Fs min=1.0 among all of
the prisms for H=Hc is defined as the critical prism. We could say that the critical prism is separated from the
underlying soil at its base when H exceeds Hc. Safety factors using the Prismatic failure concept when
considering frictions are discussed below.
IV
IV.1
EXPERIMENTAL RESULTS
H-Q15 curve and reproducibility of experiments
Q 15 (×10-6 m3 /s)
Figure 5 shows the H-Q15 curve for test
Hf =18.4cm
E0301. It is observed from Figure 5 that Q15
Hd =15.3cm
45.0
E0301
increases linearly with increasing H until a
40.0
Linear approx. (E0301)
certain value Hd. Hd value is referred to as
35.0
E0305
the hydraulic head difference at which the
Hf =18.5cm
30.0
H-Q15 curve diverts from linearity. The
25.0
linear relationship does not hold and a
Hd =15.5cm
20.0
discharge by experiment increases abruptly
15.0
when H goes beyond Hd.
10.0
As stated below, at almost the same point
5.0
as Hd , the soil surface begins to settle on
0.0
the upstream side and rise on the
0.0
5.0
10.0
15.0
20.0
downstream side. This is because, just at
H(×10-2 m)
this point, the soil loosens on the
downstream side, the void space enlarges,
Figure 5: H-Q15 curves for test E0301 and E0305
permeability of the soil grows larger, and
discharge increases non-linearly with H. As
H increases beyond Hd , Q15 becomes larger with increasing H more steeply than before, and the ground
finally collapses at the hydraulic head difference at failure Hf.
To confirm the reproducibility of experiments, experimental data of test E0305 (2009.05.09) having the
same conditions as E0301 (2008.10.11) are plotted as circles in Figure 5. It is found, from Figure 5, that both
test results are best-fitting. For tests E0301 and E0305, the characteristic head differences Hy=15.3, 15.5cm
at the onset of deformation and Hf=18.4, 18.5cm at failure are given, respectively. The reproducibility of
experiments is verified for characteristics in seepage flow and seepage failure phenomena.
IV.2
Change in shapes of soil surface
Let us consider test E0311 (Hd = 33.35cm, Hf = 49.17cm). Figures 6 (a)-(d) show the changes in shape of
the surface of the sand model along the surface height measurement line with increase in H, from H=5.92cm
at the first step to H=48.73cm at one step before failure.
The model sand is in a stable state at early steps of H (Figure 6 (a)). When H increases beyond a certain
value Hy, the model sand changes in shape near the sheet pile wall. The surface of the soil in the vicinity of
1538
ICSE6 Paris - August 27-31, 2012
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.0
(a) At the early step of H (H=5.92cm)
0.2
0.4
0.6
0.8
1.0
(b) At the H value just beyond Hy (H=33.67cm)
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
(c) At the H value beyond Hy (H=43.30cm)
(d) At the one step before failure (H=48.73cm)
Figure 6: Changes in shape of surface of sand model along the surface height measurement line with increase
in H (E0311: Hy=33.35cm and Hf =49.17cm)
1539
Figure 7: A close-up photo of the upstream inverse
conical shape at H=38.05 cm (E0311)
60
Hyd =32.8cm
Upstream
Downstream
50
40
Y(cm)
the sheet pile wall subsides on the upstream side and
rises on the downstream side (Figure 6 (b)). The value
of Hy is referred to as the hydraulic head difference at
onset of deformation. Some soil particles are observed
to move from the upstream to downstream sides near
the bottom tip of the sheet pile wall. Subsidence of the
upstream soil surface and rising of the downstream soil
surface proceed with steps of increasing H (Figure 6
(c)). The upstream soil surface is an inverse conical
shape centered at the outer corner of the rectangular
diaphragm wall. A close-up photo of the upstream
inverse conical shape is shown in Figure 7 at H=38.05
cm (E0311). The rise in the downstream soil surface
occurs uniformly within a certain width from the sheet
pile wall in the case where the penetration depth of
sheet piles on the downstream side D is small, but
occurs uniformly as a whole within a cofferdam in the
case where D is large. As H increases and approaches
Hf, the upstream subsidence shows a clear inverse
conical shape, and sand particles are observed to roll
down on the slope of the upstream soil surface (Figure
6 (d)).
Fine grains of soil boil at the downstream soil surface
and the water becomes dirty. Immediately after H
reaches Hf, a bulk of soil moves slowly from up- to
downstream, and after few seconds the downstream
soil is spouted out in the water. As if it were
transmitted, the upstream sand moves from up- to
downstream around the bottom tip of the sheet pile and
the sand model collapses with a loud noise. After the
sand model collapses, up- and downstream soils come
to settle with certain stable angles. The angle on the
Hyu =33.0cm
30
20
10
0.0
10.0
20.0
30.0
40.0
H(cm)
Figure 8: H-Y curve (E0311)
50.0
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
upstream side is thought to be an angle of repose in water.
For Lake Biwa sand 3 of Dr=50%, the angle of repose in
water is between 29.3 and 39.0 (average 34.8 degrees).
Figure 8 shows the hydraulic head difference H and the
height of the soil on the surface height measurement line
Y. It is found from H-Y curve that the height of the soil
surface is constant with increasing H until a certain value
Hy. When H increases beyond Hy, the soil surface begins
to settle on the upstream side and rise on the downstream
side. Hy values are obtained on up- and downstream sides;
Hyu and Hyd, respectively. The larger value of these two is
taken as Hy, which is referred to as the hydraulic head
difference at onset of deformation. Figure 9 shows the
relationship between Hd and Hy obtained by a series of
experiments. From Figure 9, it is obvious that the
experimental results lead to the interesting conclusion Hy=
Hd.
40.0
35.0
30.0
25.0
20.0
15.0
10.0
10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
Hd (cm)
Figure 9: Relationship between Hd and Hy
Relationship between hydraulic head differences Hc (by theory) and Hy (by experiment)
1.6
Hy
Hf
Theory by PFC
1.4
1.2
Hcw/T'
From the precise discussion on seepage
failure of soil in front of sheet piles in two
dimensions [Tanaka et al. 2005], it is
concluded that the deformation of soil is
unrecoverable and should be avoided in
practice. The hydraulic head difference at
the onset of deformation Hy is so important
for designing excavation of soil with high
ground water level that we discuss the
value of Hy (=Hd). For Lake Biwa sand 3
of Dr=50%, the theoretical hydraulic head
difference by Prismatic failure concept 3D,
HPF [Tanaka et al. 2012] is analyzed taking
the anisotropy of the test sand to be
kxx/kzz=1.20 [Tanaka et al. 2011].
Analyses were conducted using a Fortran
program FEMSEE6E for FEM seepage
flow
analyses
with iso-parametric
elements composed of 27 nodes, and a
Fortran program SEEPFL66 for the
stability analyses based on the pfc 3D.
These two programs, not coupled, were
coded in the authors' Laboratory.
Figure 10 (a) shows the relationship
between D/T and Hcw/T’ for a noexcavation model and (b) the relationship
between d/(D+d) and Hcw/(T+d)’ for an
excavation model (D1=35cm constant),
respectively. The experimental results are
also plotted in Figures 10 (a) and (b). It is
observed from Figures 10 (a) and (b) that
the calculated critical hydraulic head
differences HPF are very close to the
measured Hy (=Hd). The Prismatic failure
concept 3D is proved to be a useful
method for calculating critical hydraulic
1.0
0.8
0.6
0.4
0.2
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
D/T
(a) Relationship between D/T and Hcw/T’ for no excavation
model
1.0
0.9
Hcw/(T+d) '
IV.3
45.0
Hy (cm)
ICSE6 Paris - August 27-31, 2012
0.8
0.7
0.6
0.5
0.4
0.3
Theory by PFC
Hy
Hf
0.2
0.1
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
d/(D+d)
(b) Relationship between d/(D+d) and Hcw/(T+d)’ for excavation
model (D1=35cm)
Figure 10: Critical hydraulic head differences
1540
ICSE6 Paris - August 27-31, 2012
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
head difference at the onset of deformation of soil within a cofferdam. The difference between Hf and Hy
increases with increase in D/T for the no-excavation model, whereas it is constant with increase in d/(D+d)
for the excavation model. As presented by Tanaka and Sakane (2003), the Hf –Hy value depends on the soil
depth on the upstream side, and the phenomenon of soil from deformation to failure is referred to as selfstabilizing. In two dimensions, the equation Hf = 1.106Hy is applied irrespective of D/T values, which means
that soil has a self-stabilizing effect of approximately 11%. In contrast, in an axisymmetric condition, the
self-stabilizing effect depends on D/T: 29% for D/T = 0.34, 32% for D/T = 0.43 and 75% for D/T = 0.51. In
three dimensions, the self-stabilizing effects are from 19% to 53% with increasing D/T. Therefore, in
axisymmetric and three-dimensional conditions, the self-stabilizing effect is larger than in two dimensions,
and becomes large with increases in D/T.
V
AXISYMMETRIC MODELING OF THREE-DIMENTIONAL SEEPAGE FLOW
H c w/T'
In the experiment, one quarters of three dimensional region is
examined as shown in Figure 11. The surface shape of the cofferdam is
rectangular with the shorter length at 1 and longer length at 2.
Sheet pile
Considering an inscribed circle in the shorter side of the rectangle as
shown in Figure 11, an axisymmetric seepage flow through the soil
1
within a cylindrical wall is used to model such a three-dimensional flow.
Let us consider the three dimensional and approximate axisymmetric
conditions: T=40cm, D=20cm and R=20cm for the non-excavation sand
2
models, where R is the radius of the circular wall in the axisymmetric
condition. Figure 12 shows the relationship between the penetration
ratio of sheet piles D/T and the non-dimensional value of Hc, Hcw/T’. It
is found from Figure 12 that the three dimensional seepage failure Figure 11: Axisymmetric modeling
phenomena are well approximated using the axisymmetric seepage of 3D flow (in plane figure)
failure. For further details, the following points may be made:
(1) D/T  0.40 Hc values are larger in the
1.2
axisymmetric case than in the three-dimensional case;
Calculated for 3Dflow
in particular the approximate accuracy with respect to
1.0
Calculated for AXSflow
Hc, (Hc AXS  Hc 3D)/Hc 3D, is about +10% for D/T 
0.31. This means that assuming that the 3D flow is the
0.8
same as AXS flow leads to an overestimation of Hc,
and generates unreasonable results with respect to
0.6
seepage failure.
(2) D/T > 0.40 Hc values are smaller in the
0.4
axisymmetric case than in the three-dimensional case;
the approximate accuracy, (Hc axi  Hc 3D)/Hc 3D, is less
0.2
than 10%. This means that assuming that the 3D flow
0.0
is the same as AXS flow leads to an underestimation of
0.2
0.3
0.4
0.5
0.6
0.7
Hc, and generates uneconomical designs with respect to
D/T
seepage failure.
For the excavation sand models, the three
Figure 12: Relationship between D/T and Hcw/T’
dimensional and approximate axisymmetric conditions
(Axisymmetric modeling of 3D flow)
also gave almost the same Hc values.
VI
CONCLUSIONS
In excavations of soil with a high ground water level, sheet piles or diaphragm walls are often used to
retain soil and water. Under such conditions, seepage flow occurs through soil, and seepage failure is often a
problem. For excavation involving a large area, seepage failure is a problem in two dimensions. In contrast,
the more the region of a cofferdam is restricted, the greater the seepage flow is concentrated threedimensionally within the cofferdam. The three-dimensionally concentrated flow lowers the safety factor for
seepage failure more than the two-dimensional condition.
1541
ICSE6 Paris - August 27-31, 2012
- Tanaka et al.: Seepage Failure of Sand in Three Dimensions.
In this paper, seepage failure experiments were conducted under three-dimensional flow conditions for
various cases of total depths of soil, T, and penetration depths of sheet piles, D, and analyses of FEM seepage
flow and stability against the seepage failure of soil were carried out. The following results were obtained:
(1) With an increase in the hydraulic head difference between up- and downstream sides, H, the discharge
at 15 degrees Centigrade, Q15, increases linearly for a smaller value of H, but changes abruptly beyond the
point H=Hd. Hd is referred to as the hydraulic head difference at an abrupt change of the H-Q15 curve. As H
increases beyond Hd, Q15 becomes larger with increasing H more steeply than before, and the ground finally
collapses at the hydraulic head difference at failure Hf.
(2) In correlation with the above phenomenon regarding the H and Q15 relationship, the height of the soil
surface changes at the front (downstream) and rear (upstream) of the sheet piles. When H increases beyond
Hy, a downstream rise and upstream drop of the soil surface occur. Sand particles move from up- to
downstream sides under the bottoms of the sheet piles. The upstream soil surface is an inverse conical shape
centered at the outer corner of the rectangular diaphragm wall. Hy is referred to as the hydraulic head
difference at the onset of soil deformation. As H increases above Hy, the deformation of soil proceeds
gradually and the ground finally collapses, as described above.
(3) The ground is subjected to irreversible damage and cannot be restored when H increases beyond Hy.
(4) The experimental results led to the interesting conclusion Hy= Hd.
(5) The hydraulic head differences at deformation in the experiment, Hy (=Hd), are nearly equal to the
theoretical critical hydraulic head differences based on the Prismatic failure concept, Hc, for the same cases.
(6) With respect to seepage failure problem, an axisymmetric seepage flow through soil within a
cylindrical wall can be used to model such a three-dimensional flow.
VII REFERENCES
Miura, K., Supachawarote, C., and Ikeda, K. (2000). – Estimation of three dimensional seepage force
inside cofferdam regarding boiling type of failure. Proceedings of the Geotech –Year 2000, Developments in
Geotechnical Engineering: 371-380.
Hirose T. and Tanaka T. (2007). – A case study on seepage failure of excavated bottom soil in a steelsheet-pile-wall cofferdam. Transactions of the Japanese Society of Irrigation, Drainage and Reclamation
Engineering (in Japanese), 75 (2): 145-156.
Tanaka T., Hirose, D. and Kusumi, S. (2012). – Seepage failure of sand within a cofferdam in three
dimensions –Prismatic failure concept 3D and analytical consideration–. Report of Research Center for
Urban Safety and Security, Kobe University (in Japanese), (16): in printing.
Tanaka T., Hirose T., Inoue K. and Nagai, S. (2005). – Performance-based design concept of soil for
seepage failure within cofferdam. Transactions of the Japanese Society of Irrigation, Drainage and
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Tanaka, T. and Sakane, K. (2003). – Self-stabilizing effect in seepage failure of soil in an axisymmetric
condition. Proceedings of the 12th Asian Regional Conference on Soil Mechanics and Geotechnical
Engineering: 833-836.
Tanaka, T., Naganuma, H., Shinha, M., Kusumi, S. and Inoue, K. (2011). – Anisotropic permeability of
soil on 3D seepage failure experiments. Proceedings of the 68th annual meeting of the Kyoto Branch of
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