Passive resistance of soft clay in deep excavations
T. Tamano, H.Q. Nguyen & M. Kanaoka
Osaka Sangyo University, Osaka, Japan
H. Matsuzawa
OYO Corporation, Nagoya, Japan
S. Mizutani
Pacific Consultants Co. Ltd., Osaka, Japan
ABSTRACT: This paper presents investigations on passive resistance of soft clays in vertical stress-relief
condition of deep excavations using an intensive numerical experiment in association with a physical experiment.
Passive pressure behavior of soil is examined under effects of multi processes that are progressing simultaneously
during the excavation process. Reliability and applicability of Rankine’s theory of passive pressure are discussed.
INTRODUCTION
Oil pressure jacks
P3
P’2
P2
Load cells
Steel frames
Loading plate
69cm
P’3
Water level
3cm
Upper sand drainage layer
Moveable wall
Watertight wall
Backfill of soft clay
Lower
sand drainage layer
Watertight wall
Drainage pipe Concrete block
50cm
25cm 16cm
During the excavation process of deep excavations,
passive behavior of soils, especially clays, is complicated as the soils shall experience multi processes that
are progressing simultaneously. It is difficult to elucidate the passive behavior of clays from field measurements (Tamano et al. 1996, Hashash & Whittle 2002),
and is inappropriate to evaluate the soil resistance by
classical passive pressure theories, like Rankine’s or
Coulomb’s, since these theories give solutions only in
steady condition. Attempts using physical experiments
(Ichihara et al. 1977, Sugimoto 1985) contributed
information about passive behavior of overconsolidated soft clay in different modes of wall-displacing,
but due to limitations of the utilized experimental procedure these studies failed to reproduce reasonably the
real passive condition and behavior of soft clays in
deep excavations.
This paper presents enhancements made by a
numerical experiment carried out in association with
an available physical experiment (Ichihare et al. 1977).
Finite element analyses were performed with different modeling procedures aimed at better simulating
the real condition and soil behavior in deep excavations. Dependency of soil resistance on the excavation
progressing rate is concerned.
Horizontal
pipe
P1
Load cell
75cm
1
15cm
200cm
Figure 1. Schematic diagram of the apparatus (Ichihara
et al. 1977).
dimensions of 2000 × 2000 × 750 mm. The moveable wall was 2000 mm-wide and consisted of two
1000 × 750 mm wall sections, namely L-wall and
R-wall.
During the wall-displacing process the wall was
rotated around a fixed horizontal axis at its top. Load
cells were used to measure the consolidation loads and
components of the forces acting on the wall sections.
Six earth pressure cells and twenty manometer-type
pore water pressure chips were embedded in the backfill to measure total horizontal earth pressures and pore
water pressures.
2 THE PHYSICAL EXPERIMENT
2.1 Experimental apparatus
2.2
Figure 1 shows the experimental apparatus. The soil
bin was fabricated of steel members with inside
The organic soft clay used in the experiment was gathered from a construction site in Nagoya port area
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Copyright © 2006 Taylor & Francis Group plc, London, UK
Backfill characteristics
(Gs = 2.63, LL = 81.0%, PL = 40%, w = 71∼85%).
The soft clay was added with water and kneaded well
before being filled in the soil bin. After prepared, the
clay backfill had a thickness D0 of 550 mm, water content w of 91%, void ratio e0 of 2.40, and unit weight
γw of 14.5 kN/m3 .The upper and lower drainage layers were of fine river sand with thicknesses of 300 mm
and 150 mm, respectively, and were separated from the
clay by filter paper sheets. Water table was kept at a
level of 730 mm from the bin bottom.
0
(cm)
3 THE NUMERICAL EXPERIMENT
3.1
Soil parameters
Table 1 gives majors input parameters of the soft clay.
ref
ref
ref
The stiffness modulus (E50 , Eoed , and Eur ) were evaluated from oedometer test results (alternative input
values: CC = 0.57, CS = 0.06, and e0 = 2.40). Value of
the power factor m was obtained by best-fitting numerical predictions to the measured settlement curve during consolidation and swelling stages. Friction angle
φ was approximated by the empirical correlation:
sinφ = 0.81 − 0.233 × log(IP), where IP = 41. Cohesion c = 0 kPa was adopted for the remolded soft clay
while cohesion of the over-consolidated clay (after
swelled) was evaluated by analyses that simulated
80
<Roller, closed flow & closed
consolidation boundary>
Upper sand layer (to be removed)
40
20
0
(cm)
Pre-described displacements
Rigid wall
Backfill of soft clay
(Hardening Soil model)
Soil-wall interface (Rint=0.54)
Internal interface (Rint=1.0)
Lower sand layer
(Mohr-Coulomb Soil model)
<Fixed, closed flow & closed consolidation boundary>
Figure 2. Finite element plane-strain model.
Table 1.
model).
Input parameters of the soft clay (Hardening Soil
E50
(kPa)
Eoed
(kPa)
Eur
(kPa)
m
c
(kPa)
φ
(deg)
kx = ky
(m/sec)
1732
1340
11300
0.9
0.1
26
5.0E-09
ref
4
ref
ref
SIMULATION RESULTS
A primary analysis was aimed at closely simulating
the physical experiment. Figure 3 compares predicted
passive resistance PPFEM with the measured normal
forces acting on the two wall sections PnL and PnR .
Value of Rankine’s solution PPRankine = 7.60 kN/m
was calculated using the Rankine’s formula in
terms of effective stresses: pP = sZ × tan2 (π/4 +
φ /2) + 2c × tan(π /4 + φ /2). It is interesting that a
calculation using the formula in terms of total stresses:
pP = σZ + 2su (Tanaka 1994, Hashash & Whittle 2002)
gives almost the same value PPRankine = 7.55 kN/m
(in these calculations, hydrostatic water pressure
pw was added to obtain the total passive pressure
pP = pP + pw ).
The analysis well predicted the magnitude of soil
resistance and reasonably reproduced its development.
Both the measured and predicted resistances are about
20% larger than the Rankine’s solution. Figure 4 shows
that the analysis predicted a decrease of the resistance
during standing period, apparently due to consolidation effects. The steady resistance at the end of the
period is almost identical to the Rankine’s solution.
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Copyright © 2006 Taylor & Francis Group plc, London, UK
60
the unconfined compression tests, which resulted in
best-fitted value c = 5 kPa.
Finite element modeling
Soil-water coupled analyses were performed in plane
strain mode. Figure 2 shows geometry and boundary
conditions of the analysis model. The sand layers were
modeled by the linear elasto-plastic Mohr-Coulomb
Soil model, and the soft clay was modeled by the
Hardening Soil model (Schanz et al. 1999). Interface
elements (Rint = 0.54) were used to model the soil-wall
interface, and internal interface elements (Rint = 1.0)
were implemented along the movement path of the
wall toe to account for large deformations of soil.
3.2
40
Vertical uniform load
60
2.3 Experimental process
The backfill was consolidated in two stages with vertical loads q1 = 12.5 kPa (476 hrs) and q2 = 28.3 kPa
(598 hrs); then unloaded and swelled in 337 hrs. Prior
to the wall-displacing test, the backfill had a thickness H = 341 mm, water content w = 69%, unit weight
γw = 15.6 kN/m3 , and degree of saturation Sr = 100%.
During the wall-displacing test, the wall was rotated
at a rotation speed of 0.370 /min in 26 minutes to a maximum angle of 10◦ (dMAX = 117 mm). The monitoring
was continued in 70 hrs after the wall had stopped.
Shear strength of the backfill at depths z = 100 mm and
z = 300 mm (from the backfill surface) was evaluated
by in-situ vane tests and unconfined compression tests.
20
Passive resistance (kN/m)
10
8
PPRankine
PnR
6
PnL
(7.60kN/m)
PPFEM
Measured
Predicted
4
L
R
(Pn , Pn : normal resistance forces acting
2
on the left and right wall sections)
0
0
20
40
60
80
100
Average wall displacement d (mm)
120
Figure 5. Predicted distribution of excess PWP at d = dMAX .
Figure 3. Measured and predicted passive resistances.
instant unloading
Passive resistance (kN/m)
10
PPFEM
8
t
Group A
Td / d=44mm
PPRankine
complete consolidation complete swelling w.displacing
Ts
standing
instant unloading
6
Wall displacing
PnR
PnL
P'wFEM
Wall standing
4
t
Group B
complete consolidation
Td /d =44mm
Ts
swelling + wall displacing
standing
Tu / d=44mm or d=4.4mm
Ts
P'PFEM
2
Group C
Res. of hydrostatic pressure
0
0.01
t
complete consolidation unloading +swelling +w.displacing
0.1
1
10
Elapsed time (hour)
standing
100
Figure 6. Modeling procedures implemented in analysis
groups.
Figure 4. Variations of soil resistance in time domain.
Severe decreases of the measured resistances are supposed an experimental problem induced by spilling of
soils through an opening at the wall toe.
In the physical experiment, pore water pressure
chips embedded at distances of 400 mm and 800 mm
away from the wall recorded no significant changes of
pore water pressure during the wall-displacing period.
It was clarified by the analysis that excess pore water
pressure intensively develops within a limited region
close to the wall (Fig. 5). However, at ultimate soil
resistance, the pore water pressure contributes more
than 40% to the total resistance and has magnitude
about four times as large as the hydrostatic water
pressure.
5
5.1
EFFECTS OF SIMULTANEOUSLY
PROGRESSING PROCESSES
Modeling procedures of three
analysis groups
A parametric study was conducted to investigate
effects of multi processes: “unloading”, “swelling” and
“wall displacing” that would be progressing simultaneously during the excavation process. Figure 6 describes
modeling procedures implemented in three analysis
groups. The modeling procedure used in Group A is
similar to the described experimental procedure. Analyses in Group B are supposed to simulate the condition
of real excavations where excavation works (“unloading”) progress speedily and are followed by a delay
period for “swelling” and “wall-displacing”, before the
wall is stiffly strutted. Analyses in Group C are aimed
at modeling excavations that progress moderately with
all wall displacements occur within the progressing of
the excavation works.
In analyses of Groups A and B, a maximum wall
displacement dMAX = 44 mm was imposed in varied
displacing time intervals Td . In analyses of Group C,
the vertical load was gradually removed in varied
unloading time intervals Tu during which a wall displacement dMAX of either 44 mm or 4.4 mm was being
imposed. It was interpreted from the primary analysis results that the large displacement dMAX = 44 mm
(d/H ∼13%) shall fully mobilize the soil resistance
while the small displacement dMAX = 4.4 mm shall
partially mobilize the soil resistance. A standing time
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Copyright © 2006 Taylor & Francis Group plc, London, UK
wall displacing period: PPMAX = PPdmax (see Fig. 7a).
Regardless the displacing rate (dMAX /Td ), 95%
magnitude of PPMAX is mobilized at displacement of
20 mm (d/H ∼6%), where pore water pressure PW
also reaches its maximum value. The PW then stays
constant or even starts decreasing. The effective
pressure PP increases continually along with the
wall displacement (see Fig. 7b).
– Value of the PPMAX increases with the increase of
displacing time interval Td , i.e. decrease of wall
displacing rate. At slow displacing rates, in despite
of a decrease of PW due to consolidation, there is
substantially more room for the mobilizing of the
effective pressure PP ; thus, it results in a net increase
of the total resistance.
– During standing period, further decrease of the PW
due to consolidation causes a decrease of the total
resistance from the maximum value PPMAX to a
smaller steady value PPS (see Fig. 8a). The decrease
is seen prominent at fast displacing rate where the
contribution of the pore water pressure PW to the
total resistance is more substantial.
– In Figure 8b, values of PPMAX and PPS are normalized
by P0 , which is the resultant of at-rest horizontal
interval Ts was given to finally attain the steady passive resistances. Table 2 summarizes variables adopted
in this parametric study.
5.2 Analysis results
5.2.1 Analyses of Group A
Figures 7–8 present predictions of the analyses in
Group A. The results are interpreted as follows:
– Similar to observations in the physical experiment,
maximum resistances are attained at the end of the
Table 2. Variables adopted in the parametric study.
Variables
Group A
Group B
dMAX , mm
Td , hour
Tu , hour
44
44
0.05/0.5/5/10/25/50
–
Group C
44/4.4
–
0.05/0.5/5/10/25/50
10
6
8
4
Td = 50hr
Td = 25hr
Td = 10hr
2
0
Td = 5hr
Td = 0.5hr
Td = 0.05hr
10
20
30
40
Wall displacement, d (mm)
(a) Development of total passive resistance PP.
0
Td = 50hr
Td = 25hr
Td = 10hr
10
Resistance components (kN/m)
PP, Pw (kN/m)
8
8
PW
0
10
20
30
40
50
Wall displacement, d (mm)
(b) Development of resistance components P’P and PW.
10-4
10-3
102
6
5
4
MAX
PP
3
, Maximum passive resistance
PPS, Steady passive resistance
PPRankine,Rankine's solution
2
1
10
Displacing time interval, Td (hour)
(b) Passive resistances as function of wall-displacing rate.
Figure 7. Responses of soil during wall-displacing
(Group A).
0.1
Figure 8. Maximum and steady resistances (Group A).
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Copyright © 2006 Taylor & Francis Group plc, London, UK
PPS
10-2
10-1
100
101
Elapsed time (hour)
(a) Variation of PP and PW in time domain.
4
0
Td = 0.05hr Td = 0.5hr Td = 5hr Td = 50hr
4
0
P'P
2
6
PPMAX
2
Td = 5hr
Td = 0.5hr
Td = 0.05hr
6
PP
Pw
50
Normalized passive resistance PP /P0
Passive resistance, PP (kN/m)
10
earth pressure. Slow displacing rates are seen to
increase the magnitude of both PPMAX and PPS . It is
also indicated that only at very slow displacing rates
the steady soil resistance will be attained within the
displacing process.
5.2.2 Analyses of Group B
Figure 9a shows the developments of the total resistances PP that appear quite similar to predictions of
Group A. However, Figure 9b notes that the resistance
components develop differently. As for the effective pressure PP , because of the elimination between
increases due to wall displacing and decreases due to
soil swelling, there is no more a positive increasing
trend of PP along with the increase of Td . In case of the
pore water pressure PW , the effect of wall displacing
outbids the effect of soil swelling: net increase of PW
at fast displacing rates is larger than at slow displacing
rates. In Figure 10b, the dependency of PPMAX on the
displacing rate is shown contrary to that predicted in
Group A.
5.2.3 Analyses of Group C
Results of analyses in Group C are presented in
Figures 11–14. Load-displacement curves of this
analysis group are distinguished from the curves
of Group A and B. Figure 11a shows that soil
resistance reaches an extreme large maximum resistance PPMAX (PPMAX /P0 ∼9.2) at small displacement
9
12
6
3
Td = 50hr
Td = 25hr
Td = 10hr
0
-3
Td = 5hr
Td = 0.5hr
Td = 0.05hr
Td = 0.05hr Td = 0.5hr Td = 5hr Td = 50hr
4
10
20
30
40
Wall displacement, d (mm)
(a) Development of total passive resistance PP.
0
50
-8 -4
10
10-2 10-1
100
101
102
Elapsed time (hour)
(a)Variation of PP and PW in time domain.
P'P
Normalized passive resistance PP /P0
Resistance components (kN/m)
9
6
Pw
0
Td = 50hr
Td = 25hr
Td = 10hr
-3
-6
Td = 5hr
Td = 0.5hr
Td = 0.05hr
0
10
20
30
40
50
Wall displacement, d (mm)
.
(b) Development of resistance components PP and PW
Figure 9. Responses of soil during wall-displacing
(Group B).
6
10-3
PPMAX (Group A)
5
4
PPS (Group A)
3
PMAX
p ,Maximum passive resistance
PPS, Steady passive resistance
2
PPRankine, Rankine's solution
0.1
1
10
Displacing time interval, Td (hour)
(b) Passive resistances as function of wall-displacing rate.
Figure 10. Maximum and steady resistances (Group B).
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PPS
-4
0
3
PPMAX
PP
Pw
8
PP, Pw (kN/m)
Passive resistance, PP (kN/m)
12
The steady resistances PPS are slightly larger than
predictions of Group A, but exhibit a similar trend
to increase along with the displacing time interval
(Fig. 10b). It is because the variation of steady resistance is mostly governed by the development of the
effective pressure rather than that of the pore water
pressure.
Because the soil swelling keeps progressing after
the wall has stopped displacing, it induces intensive
decreases of both PW and PP , especially in case of
fast displacing rates where the ratio PPMAX /PPS is as
large as 1.36 (Fig. 10a). At very slow displacing rates,
PPS is almost attained at the end of the wall displacing
process, thus PPMAX and PPS become nearly identical. In
this condition, the predicted PPMAX and PPS of analyses
in Group A and B are close to each other.
20
Tu= 50hr
Tu= 25hr
Tu= 10hr
5
0
0
20
30
40
Wall displacement, d (mm)
(a) Development of total passive resistance PP.
Tu= 50hr
Tu= 25hr
Tu= 10hr
PP, PW (kN/m)
50
Tu= 5hr
Tu= 0.5hr
Tu= 0.05hr
P'P
PPdmax
PPS
10-3
10
8
6
4
PPMAX
PPdmax
2
PPS
PPRankine
1
10
Unloading time interval, Tu (hour)
(b) Passive resistances as function of wall-displacing rate.
Pw
0
8
10-2 10-1
100
101 102
Elapsed time (hour)
(a) Variation of PP and PW in time domain.
5
0
Tu = 0.05hr Tu = 0.05hr Tu = 5hr Tu = 50hr
0
10-4
15
10
PPMAX
4
Tu= 5hr
Tu= 0.5hr
Tu= 0.05hr
10
20
Resistance components (kN/m)
12
PPdmax
Passive resistance at
the end of wall displacing
10
PP
Pw
16
PPMAX
Maximum passive resistance
15
Normalized passive resistance PP/P0
Passive resistance, PP(kN/m)
20
20
30
40
50
Wall displacement, d (mm)
(b) Development of resistance components PP and PW.
0.1
10
Figure 12. Maximum & steady resistances (Group C,
dMAX = 44 mm).
Figure 11. Responses of soil during wall-displacing
(Group C, dMAX = 44 mm).
d = 10 mm then reduces to a considerably smaller
resistance PPdmax (PPdmax /P0 ∼5.9) at the end of the
displacing process. In all analysis cases,values of
these resistances, including the steady resistance, are
almost equal. Developments of the resistance components during the wall displacing period and standing period reveal that the simultaneously progressing
of the three processes of “unloading”, “swelling”
and “wall displacing” somehow produces a particular condition where the consequential total resistance
becomes independent of the progressing rate of the
excavation process.
It is remarked that Group C has maximum resistances PPMAX extremely larger than those of either
Group A or B, but steady resistances PPS quite
similar to those of Group B. Thus, the decrease from
PPMAX to PPS is much emphatic: PPMAX /PPS ∼2.0. Ratios
of PPMAX and PPdmax to PPRankine are around 2.4 and 1.5,
respectively.
Analyses with the small wall displacement
dMAX = 4.4 mm predicted a similar developing trend
of soil resistance (see Fig. 13a). Soil resistances
attain maximum value at very small wall displacements of 2∼2.5 mm; thereafter, they slightly reduce
to PPdmax . During standing period, further decreases
of the resistances occur and the final steady resistance PPS almost equal to the initial earth pressure
(see Fig. 14a).
Figure 14b shows that both the maximum and steady
passive resistances increase along with the increase
of the unloading interval Tu . The ratio PPMAX /PPS
is about 1.30∼1.40, not as excessive as in case
of large displacement (dMAX = 44 mm), but the two
resistances do not likely converge to each other neither when the progressing rate is instantaneous nor
extremely slow.
6
1. Physical experiment and numerical analysis performed following a simple experimental procedure
can hardly simulate the complicated condition and
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Copyright © 2006 Taylor & Francis Group plc, London, UK
CONCLUSIONS
Passive resistance, PP(kN/m)
12
12
8
PPMAX
6
Maximum passive resistance
4
PPdmax
Passive resistance at
the end of wall displacing
Tu= 50hr
Tu= 25hr
Tu= 10hr
2
0
Tu= 5hr
Tu= 0.5hr
Tu= 0.05hr
2
3
4
5
Wall displacement, d (mm)
(a) Development of total passive resistance PP.
P'P
Tu= 50hr
Tu= 25hr
Tu= 10hr
4
Tu= 5hr
Tu= 0.5hr
Tu= 0.05hr
2
0
-2
Pw
0
6
Tu= 0.05hr Tu= 0.5hr Tu= 5hr Tu= 50hr
4
PPdmax PPS
2
10-3
10-2
10-1
100
Elapsed time (hour)
101
102
(a) Variation of PP and PW in time domain.
10
6
8
-2
10-4
1
8
PPMAX
0
Normalized passive resistance PP /P0
Resistance components (kN/m)
PP,PW (kN/m)
10
0
PP
Pw
10
1
2
3
4
5
Wall displacement, d (mm)
(b) Development of resistance components PP and PW.
6
5
4
3
2
PPMAX
PPS
PPdmax
PPRankine
1
10
Unloading time interval, Tu (hour)
(b) Passive resistances as function of wall-displacing rate.
Figure 13. Responses of soil during wall-displacing (Group
C, dMAX = 4.4 mm).
0.1
Figure 14. Maximum & steady resistances (Group C,
dMAX = 4.4 mm).
REFERENCES
behavior of soft clay in deep excavations. Using
appropriate modeling procedures was illustrated to
enhance the modeling capacity of numerical analyses that gave better understanding of features in
passive behavior of soft clay in conditions of deep
excavations.
2. The Rankine’s formula was elucidated as a reasonable lower-bound solution for the steady passive resistance of soil. The solution considerably
underestimates the actual passive resistance of clay
that is being mobilized during the progressing of
excavation process.
3. Decrease of soft clay resistance during the standing
period was clarified substantial. This reality should
be properly concerned in engineering practice of
deep excavations in clays because the decrease of
passive resistance of soils will induce redistribution of forces in the supporting structures as well as
additional movements of the wall.
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Copyright © 2006 Taylor & Francis Group plc, London, UK