한국지반환경공학회 논문집 제 7권 제 4호 2006년 8월 pp. 15~24
Active Earth Pressure Acting on the Cylindrical Retaining Wall of a Shaft
Chun Chun,, Byun Byungs gsik ik† ․ Shin Shin,, Young oungwa wan n*
It is well well known known that earth earth pres press sure ure on the cyli cylindr ndric ical al open open caiss aisson and cylindr ylindric ical al retainin etaining g wall wall of a shaft haft is less less than than that that at-r at-rest est and and in plan planee strai train n condi onditi tion on becau ecaus se of the the hor horizon izontal tal and and ver vertic tical arc arching hing effects effects due to wall wall displac displacement ement and and stres stress s relief. relief. In orde orderr to examine examine the earth earth pres press sure ure distri distribu bution tion of of a cylindr ylindric ical al wall, wall, model model tes tests ts were were per perfor formed med in dry dry sand sand for the care are of constan onstantt wall wall displa displac cement ement with with depth. Model test apparatus apparatus which can can control control wall displacement, displacement, wall friction, friction, and wall shape ratio was develop developed. ed. The effec effects of variou various s factor factors s that that infl influen uenc ce earth earth pr press essure ure actin acting g on on the the cyli cylindr ndric ical al retai retainin ning g wall of a shaft were investigated. : Active tive earth earth pres press sure, ure, Arching hing effec effect, t, Cylind Cylinder eric ical al retainin etaining g wall, wall, Model Model test test
원형 오픈 오픈 케이슨과 이슨과 원형 원형 수직구에 직구에 설치 설치된 흙막 흙막이 벽에 벽에 작용하는 용하는 토압 토압은, 벽체 벽체의 변위와 응력해방으로 방으로 인한 수평 및 연직 아칭효과로 아칭효과로 인하여, 인하여, 평면 평면 변형조건 변형조건에서 에서의 의 옹벽에 옹벽에 작용하는 작용하는 토압보다는 토압보다는 작은 작은 토압이 토압이 발생한다. 발생한다. 원 형벽체에 형벽체에 작용하는 작용하는 토압분포 토압분포를 를 조사하 조사하기 기 위해서, 위해서, 건조한 건조한 모래지 모래지반에서 반에서 깊이에 깊이에 따른 벽체변형 벽체변형이 이 균등한 균등한 조건의 조건의 모형실험 모형실험을 을 실시하였 실시하였다. 다. 벽체 변위, 변위, 벽면 벽면 마찰, 마찰, 벽체 벽체 형상비 형상비 등을 조절할 조절할 수 있는 모형 실험 장치가 장치가 개발되 개발되었 었 고, 모형실험을 모형실험을 통하여 원통형 원통형 벽체에 작용하는 토압에 대한 다양한 다양한 인자의 인자의 영향이 분석되었다. 분석되었다. : 주동토압, 주동토압, 아칭효과, 아칭효과, 원통형 원통형 벽체, 모형실험 모형실험
Member er,, Prof Profes esso sor, r, Depart Departme ment nt of Civi Civill Engi Enginee neeri ring ng,, Hanya Hanyang ng Univ Univ., ., Kore Korea a (E-m (E-mail ail : heng hengda dang ng@u @unit nitel el.c .co. o.kr kr)) † Memb * Memb Member er,, Dire Direct cter er,, Haky Hakyon ong g Engi Engine neer erin ing g Co., Co., Ltd. Ltd.,, Seou Seoul,l, Kore Koreaa
cylindrical retaining wall is less than at-rest
1. Introduction
and active earth pressures in plane strain A shaft which is a vertical, slender and long structure
should
be
designed
by
methods
condition because of the stress relief induced by horizontal and vertical arching effects by
different from that for the horizontal long
excavation.
tunnel. In plan the shaft is to be designed
researchers have made efforts to examine the
generally with a circular shape in spite of the
earth pressure distribution and the shape of
fact
ground
that
this
offers
less
advantageous
Noticing
this
failure
surface
the
active
point,
by
many
model
utilization of space than the rectangular one.
However,
Also, when a structure is constructed in the
distributions on cylindrical wall which have
river or in the sea, the open caisson is applied
been measured in some model tests show
to
various values, and the studies on the earth
the
foundation
of
structure
and
it
is
designed with circular section. However, this is outweighed by far by the considerable
earth
tests.
pressure
press essure with ith wall disp isplac lacemen ementt are are defic deficien ient. t. Acc Accordi ordingly ngly,,
in in
this this
and
the
the the
ear earth th
advantages ages offe offerred in the the reduc educttion of ext extern ernal
pressure
pressure due to arching effects in a horizontal
fail failu ure surfac face were observed by model tests for for
plane.
the cylindrical retaining wall of a shaft in dry
Development of cut wall displacements is
distribution
study, tudy,
shape
of
cohesi cohesionles onless s soils. soils.
essential even if the rigid lateral support such as
a
slurry
Kusakabe,
wall
1984).
is
installed
Therefore,
it
(Britto has
&
2. Arching effects
been
convinced that the earth pressure on the
(a) Stress distribution in horizontal plane
Arching is classified into horizontal and
(b) Stress distribution with distance
Fig Fig. 1. Arching effect by a circular hole (Fa (Fara et al. 1963) 63) 16 한국지반환경공학회 논문집
vertical ones by the direction of gravity. Many
shaft and the forces on the shaft wall were
authors
pressure
determined at various depths by two excavated
considering the arching. These are mostly
from monitoring methods of model Ⅰ and model
studi udies on verti ertic cal arching hing.. Vert ertica ical arching ing by
Ⅱ. In model Ⅰ, the frictional forces on the shaft
ground failure surface and soil-wall friction
wall were measured, and the active pressures on
makes the stress transfer to a stationary part
the the ring ings were calcu lculate lated d ind indirec irecttly by assuming ing a
or an adjacent wall. After all, the horizontal
constant angle of wall friction. In model Ⅱ, three
pressure
sets of strain gauges, positioned at 120
have
on
studied
the
wall
on
earth
is reduced
as the
to each
down downwa warrd ver vertic tical stres tress s decreases. In circular lar
other, were bound to each steel segment and the
shaft, ft, beside ides horizo izontal tal arc arching hing,, vertic vertical al arc arching hing
wall was calib librated to monito itor the the radial pressure
aris arises es.. As shown in Fig. ig. 1, Fara and Wright(1963)
directly. In both models, several earth pressure
proved
was
cells were placed in the sand to detect the radial
excavated, the radial and tangential stress
stres tress ses outsid tsidee the the shaft befor fore, during ing, and afte fter
were equal to the initial stresses at first and
excavatio tion. The vertic tical settle ttlem ment profile files s at the the
then if the surrounding soil particles move
grou ground nd were ere als also recor ecorde ded. d.
toward
analytically
the
cut
that
wall,
if
the
a
shaft
radial
stress
The high higher er recor ecord ded press essure ure corresp espond onds to the the
decreases in elastic and plastic zones and the
model without recess. A trend toward an ulti ltimate
tangential stress increases in elastic zone but
pressure that is ind independent of depth is apparent.
decr ecreas eases in plas plasti tic c zone zone..
The
pressure
decreases
rapidly
if
small
displac lacements are allo llowed to occur and reaches a
3. Review of existing model tests
minimum at recesses of less than 1～3mm (=2～ 6% of the the opening size). With lar larger recesses, this
3.1 Berlin model tests
force
seems to increase
slightly or remains
constan tant. The meas easured pressures were obtain taineed Müller ler-Kirchenbauer et al.( l.(1980) carried out a
by averaging readings from sensors around the
series of model tests to measure earth pressures
circumference of the shaft. Assuming an initial
exerted by dry sand on a cylindrical wall. The
vertical stress equal to the the overburden pressure,
model wall for the 65cm deep shaft with a
the calculated K0- value lues range from 0.55～1.43.
diameter of 10cm was fabricated from hollow,
During stress relief due to shaft excavation, the
cylin lindrica ical stee teel secti ectio ons. The botto ttom portio tion was
radial stress decreased significantly even at a
equipped with a sharp-edged shoe. A recess of
distance of twice ice as lon long as wall radius ius. However,
severa eral milli illim mete eters was provide ided behind ind the the shoe
Müller-Kirchenbauer
to simulate various amounts of soil displacement
continuously
during excavation. The shaft was sunk into a test
discontinu ontinuous ously ly them them dis displac placem emen ents ts but meas easured ured disc
container filled with sand (grain size ranging
for some ome dis displac placemen ements ts..
the
et earth
al.
did
not
pressures
measure
with
wall
betw etween een 0.2 0.2 and and 1.0m 1.0mm m, the the maxim aximum um por porosit osity= y=44 44% %, the the minimu imum porosity= ty=32.5% .5%) compacted to a
3.2 Cambridge centrifuge model tests
desired relative density. The soil was within the 제7 권 제 4호 2006년 8 월 17
Centrifuge tests were performed by Lade et
(1981) from radial strains measured in this
al.(1981) to study the behavior of deep, vertical
wall. For the three tests, the initial horizontal
shafts in dry sand. The model test setup
earth pressure in the near of the shaft was
consisted of a 69.5cm deep ci circular drum with
slightly higher than the earth pressure at rest
a diameter of 85cm. The shaft was free
of
excavated and made of polyethylene Melinex.
exc excavati avation on proc procee eede ded, d, the flexible wall moved
The physical properties of the shaft wall are
inward and the formulation pressures on the
tensile strength of 176.5 MPa, yield strength
shaft wall increased with depth in all three
of 98.1 MPa, and Young's modulus of 4300
cases.
MPa at 1% strain. Various instruments were
flexible wall exceed the ones predicted at
installed to study the shaft behavior. For
grea greate terr dept depth h (z/R>3～5). It is evident from the
example,
measured by
measured pres press sure ure dis distrib tribut utio ion n that that yiel yieldi ding ng and and
strain gauges bonded to the surface of the
some arching developed around the shaft. The
shaft wall wall,, and pressure cells, placed in the soil,
radial stresses decreased in response to the
radial
strains were
radial,
monitored the vertical,
stresses settlement
at
seven of
the
and
locations. lining
and
tangential
by
linearly
variable
radial
As
the
simulation
of
The observed earth pressures in
movement
permitted
during
the
the
shaft
The
vertical
excavation and the tangential stresses increased
the
vertical
in the near ear of the the elas lastic tic-plas lastic inter nterfa fac ce.
movement of the bottom of the shaft were recorded
K0=1-sinφ.
displacement
trans transduc ducers ers (LVDTs). (LVDTs).
However, Lade et al. did not measure the active ear earth pressure of the minimu imum press essure with wall displac lacements nts. He also lso meas easured the
Since it was not possible to actually ex-
radial stresses in equilibrium states between
cavate soil in the centrifuge during flight, the
ground stresses and wall resistant stresses
soil in the shaft was substituted with a fluid
depending on wall stiffness when the shaft was
that could be removed in stages to model
excavated. That is the reason why earth
stress relief due to soil excavation. A ZnCl2
pressures in the bottom of the shaft are the
3
solution of density 1.55g/cm
and a parafin
3
were used to
with a density of 0.765g/cm
simulate
two
cases
with
different
maxi maximu mum m value values s.
vertical
stresses at the shaft bottom and horizontal
4. Development of model test apparatus
stresses at the the shaft wall. The tests were performed with dry, fine
A new model test apparatus was developed in
sand. Triaxial compression tests on the sand
order to make up for the
ind indica icate a hyperb erbolic lic stres tress s-stra train curve that
Berlin and Cambridge model tests as previously
depends on the confining pressure level. The
described. A centrifugal model test apparatus
earth
with
was not utilized because the model wall was
Ber Berezan ezantz tzev ev's 's for formula mula is shown own for for comp omparison ison..
made in 75cm heights and an earth pressure can
These pressures were calculated by Lade et al.
be meas measur ured. ed.
pressure
distribution
18 한국지반환경공학회 논문집
calculated
weak
points of
4.1 Test container and sand raining controller Send raining controller
The test container with dimensions of 70cm length, 100cm width, and 75cm height was fabricated as shown in Fig. 2. Glass plates were adhered to the inside of the test container for the purpose of minimizing the effect of friction on the boundary wall. A sand raining controller
Model sylindrical wall
was made of 10mm thickness of steel plates to Linear slide guide
rain fine sands using sand curtain methods. It is moved automatically back, forth, up and down by elec electr tric ic motor otors s and and sens ensors ors.
Front wall
Constant displacement controller
4.2 Cylindrical model wall of a shaft A model wall was composed of the model shaft wall of cutting scale down a real shaft and the wall wall suppor pportt indu induc cing ing the the hor horizon izonta tall dis displac placem emen entt Fig. Fig. 2. Mod Model test test appa appara rattus
as shown in Fig. 3. The shaft wall was made of 10mm thickness of acryl pipe with the wall shape
bottom of wall
support to
be
moved as
It was sawn
smooth as possible. The corner of the wall
verti ertic cally lly into into five segments to estimate the
support was milled with an angle of 60° to
earth earth pres press sure ure with with dept depth, h, and and hor horiz izon onta tall into into
transfer a horizontal
three three segm segment ents s with with an angl anglee of 60° 60° to induc inducee
axisymmetric
the the cons onstant tant radi adial disp isplac lacemen ementt of of wa wall as
angles between sand and sa sand pa paper were
shown own
measured, and sand paper with the friction
ratios of 4.286, 5.000, and 6.522.
in
Fig. Fig.
3(b 3(b).
The The
left left
and
right ght
displacement
displacement.
into
The
an
friction
segments of model wall were fixed in ro rods
angle of 0 , 28.8
guided by ball bearings so that they can slide
model odel wall wall in ord order to sim simul ulat atee wall wall fric fricti tion on..
horizontally and smoothly. Load cells to measure
and
36.5
was attached to
An active wall displacement was induced by
the earth pressures were installed in ce n tra l
a
acryl plates. The wall wa ll support was was compo ompos sed of
displacement
a front pl plate wi with lo load cells and a rear plate
pressure on the wall was measured. Load
connected with li linear move ovement guides. It It
cells ells for meas easuri uring the the ea earth pres press sure and and
was made of of ri rigid bakelite plates of 30 30mm
LVDTs
thic thickn knes ess s to preven eventt from from being eing de defor formed by
employed. A data logger was used to collect
the earth pressure(Wong et al, 1988)
data. The measured data we were saved in the
The ball bearing rollers were fixed in the
linear movement
for
guide
controller
the
wall
so
and that
a
constant the
displacement
earth
were
portab portable le compu computer ter at cons constant tant time interval. interval.
제7 권 제 4호 2006년 8 월 19
4.3 Verification of model test apparatus Deve Develo lope ped d mode modell tes test appar apparat atus us was was ver verifie ified d whether
it
co could
measure
co correctly
the
pres press sure ure on a shaf shaftt wall. wall. Hydr Hydrostat ostatic ic pres press sure ure was was meas measur ured ed for for ver verific ificat atio ion. n. Load Load cells ells wer were calibrated before the model wall was installed led in
tes testt
preventing
con conta tain iner er.. a
For For
leakage
the the
of
pur purpos pose
water,
a
of
vinyl
enve envelo lope pe was was ins install talled ed in the the tes testt con conta tain iner er,, and wa water was filled up up. A vinyl envelope was was adher hered clos losely ely to the the wal walll for for acti acting ng uniform uniform water press pressure ure on it. it. The The meas measur ured ed hyd hydrosta ostati tic c pres press sure ure wa was in
good agreement
with ith that that calc alculat ulated ed..
5. Results of model test The purpose of this study is an examination of
earth
pressure
and
the
shape
of
failure
surfa urfac ce with with var vario ious us wall wall fric fricti tion on angle ngles s and shape hape ratios tios of the the shaft haft.. The The mode modell tes tests were were perfor performed med on the the wall shape shape ratios ratios of ① Cylindrical wall
② wall surpport
③ shaft and bearing ④ load cell
4.286, 4.286, 5.000 5.000 and and 6.522 6.522 and and the the wall wall fric friction tion angles of 0 , 28.8
⑤ bearing roller
(a) A sol solid body ody diagram
and
36.5
as shown in
Table 1. Tab Table 1. Mode Modell test est cond onditi itions ons
Test No.
(b) (b) R=17.5 cm Fig. Fig. 3. Cylin ylindr dric ical al mode modell wall all
20 한국지반환경공학회 논문집
Model dimensions
Wall friction ion (°)
T-L1
H(cm) 75.0
R(cm) 17.5
H/R 4.286
0.0
T-L2
75.0
17.5
4.286
28.8
T-L3 T-M1
75.0 75.0
17.5 15.0
4.286 5.000
36.5 0.0
T-M2
75.0
15.0
5.000
28.8
T-M3 T-S1
75.0 75.0
15.0 11.5
5.000 6.522
36.5 0.0
T-S2
75.0
11.5
6.522
28.8
T-S3
75.0
11.5
6.522
36.5
Tabl Table e 2. Soil Soil prop proper erti ties es
5.1 Earth pressure on the cylindrical retaining
Properties
wall
Values
Specific gravity (Gs)
2.64
Coefficient of uniformity (Cu)
2.52
Coefficient of curvature (C c)
1.46
Maximum dry unit weight (γdmax) Minimum dry unit weight (γdmin) Experimental dry unit weight ( γd)
100
17.0 kN/m
3
14.3 kN/m
3
16.4 kN/m
3
Experimental relative density (D r)
81 %
Unified Soil Classification System
SP 41.6°
Internal friction angle( φ) Cohesion (c)
LC-1 (z=7.8cm) LC-2 (z=22.8cm)
80
LC-3 (z=37.8cm) LC-4 (z=52.8cm)
) N ( 60 e r u s s e r p 40 h t r a E
LC-5 (z=67.8cm)
20
0.0 kPa 0 0
Sand gathered in downstream of the Han River was dried out to the sun. Physical
ranged ranged from from 0.08 0.08 to to 2.0mm. 2.0mm. A perc percent pas pass sing by weig eight of fine sa sand filled in tes test co contai tainer smaller ller tha than 1.0m .0mm diameter eter was more ore than than 80%, and and the sand sand was class lassified into into SP in the Unified Unified Soil Soil Class Classificatio ification n System. System. Sand Sand was rained by sand curtain methods, and a falling height was 1.0m. Aluminium cans of two per a layer with depth were laid on five layers to examine wheth ether relative de densities wer were unif unifor orm. m. Pressure variation with wall displacements,
model
shaft
wall.
By
comparison
conditio tion, the effects of reducing earth pressure
4
5
6
7
8
wall displacement(H/R=4.286, δ=0°)
Earth pressure distr istrib ibut utio ions ns measured by loa load cells(LC) with depth are shown in Fig. 4 when active displacements of the shaft wall of shape ratio H/R=4.286, wall friction angle δ=0° were allow lowed. The maximum pressure was developed in at-rest state when no displacement was allo llowed. ed. The pressure ure decr ecreased rapidly idly if small displacements were allowed to occur and it reaches a minimum at the walld walldis ispl plac acem emen ents ts of about 1.5% of shaft radius. When further pi (kPa) 0 .0
1 .0
2 .0
3 .0
4 .0
0 (H/R=4.286, δh=0.00mm) (H/R=4.286, δh=0.03mm)
15
with
pres pressur suree calc calculated ulated by theo theorry for for plan planee strai train n
3
Fig. Fig. 4. Var Variati iation on of ear earth pres pressu sure re with ith
effects of wall friction and wall shape ratios were examined for the earth pressure distribution on
2
W all displa cement (mm) (mm)
charact acteris eristi tic cs of sa sand used in model odel tes tests are shown in Table 2. 2. A grain si size of of sa sand was
1
30 ) m c ( z 45
(H/R=4.286, δh=0.13mm) (H/R=4.286, δh=0.43mm) (H/R=4.286, δh=1.87mm) Ko-Line Ka-Line(Coulomb)
K o-Line
due to horizontal arching with shape ratios of the
shaft wall were described. The effects of shaft
60
Ka-Line
wall heights and radii were analyzed on the shape of failure surface examined through the model odel tes tests. ts.
75
Fig. 5. Variation of earth pressure distribution with with wall wall disp displa lace ceme ment nt (H/R= (H/R=4. 4.28 286, 6, δ=0˚) 제7 권 제 4호 2006년 8 월 21
dis displac placem emen ents ts wer were allo allowe wed, d, the the ear earth pres press sure ure
resisted the the dow downwa nward movem ovemen entt of sli slid ding ing
increased slightly again. This tendency was
soil oil mas mass.
prob probab ably ly ind induced by grou ground nd yield ieldiing behi ehind the the shaft
wall.
the
wall friction is, the larger the maximum pressure
displacement of about 1.5% of shaft radius
is. Maybe, the wall friction resisting downward
can be reg rega arded as an active tive ear earth pressure ure
slidi liding ng of of soi soill mas mass due due to grav gravit ity y indu induc ces
of the minimum one.
the vertic vertical al arc arching. The weight weight of slidin sliding g
Earth
Hence,
pressure
the
pressure
is
soil soil mass mass is prob probab ably ly trans transfer ferrred to the the upper
shown in Fig. 5, when wall displacements in
part of the shaft wall. Accordingly, the earth
shape ratio H/R=4.286 and wall friction angle δ
pres press sure ure inc increas eases in the upper part of the
=0°
shaft wall and decreases in the lower part of
were
distribution
at
In ad additio ition, n, it is clea lear that that the the lon longe gerr the
allowed.
When
with
the
depth
shaft
wall
displacements were not allowed, the pressure
that.
t-rest est earth was approximately the same as at-r pressure. The pressure decreased as the wall
pi (kPa) 0.0
disp isplac lacements were fur further allo llowed. The earth
0.2
0.4
0.6
0.8
0
pressure resulted in the minimum pressure at 1.87 1.87m mm dis displac placem emen ents ts.. The deep deeper er the depth is,
15
the the large largerr ear earth pres press sures ures are are in init initia iall stat state. e. hen wall all dis displac placem emen ents ts were ere allo allow wed, ed, However, when eart arth pressures at deep loca ocatio tions decreased much
rela elative tively ly
due
to
arching hing
effe effec cts. ts.
30
) m c ( z
45
Earth Measured(H/R=4.286,δ=0°)
pressure in the lower parts of the wall was
60
Measured(H/R=4.286,δ=28.8°) Measured(H/R=4.286,δ=36.5°)
dec decreas eased with with dept depth h in acti active ve state tates s. Earth Earth
pr press essure ure
dist distrribution ibutions s
Coulomb-2D Coulomb-2D ( δ=0°)
with
75
shape shape
(a) H/R= H/R=4. 4.28 286 6
ratios and wall frictions are shown in Fig. 6.
The smaller the shape ratio is, that is, the
p i (kPa) 0.0
larger the wall radius is, the more earth
0.2
0.4
0. 6
0
pressur pressures es increase, increase, because because the wall shape shape ratios of shaft wall approach to to pl plane strain
15
condition. Another reason is that effects of earth
pressure
arc arching( ing(iincr ncrease
reduction
due
to
horizontal
of tan tangen gential tial stress)
become
30
) m c ( z
45
small. ll. The maximu imum pressure developed in the
midpoint of of the shaft wall with sm smooth wall. However,
the
earth
slightly when the wall
pressure
22 한국지반환경공학회 논문집
wall fric fricti tion on
Measured(H/R=5.000,δ=28.8°) Measured(H/R=5.000,δ=36.5°) Coulomb-2D (δ=0°)
decreased
friction angle was
greater than zero because the the
Measured(H/R=5.000,δ=0°) 60
75
(b) (b) H/R= H/R=5. 5.00 000 0
0. 8
distance of failure surface from the wall is. It
pi (kPa) 0 .0
0 .2
0 .4
0. 6
0. 8
is approximately equal to the radius of shaft
0
wall. Since the shape of failure surface is a curved shape, the vol volume ume of sli slidi ding ng soi soill
15
mass mass is les less than than that that with with fai failu lurre sur surfa fac ce ) 30 m c ( z 45
slope of 45° + φ /2. 2. However, it it is clea lear that the lo lower the wa wall height is and the smaller the shape ratio of
Measured(H/R=6.522,δ=0°) 60
the shaft shaft is, is, the smaller smaller the differ differenc encee of
Measured(H/R=6.522,δ=28.8°) Measured(H/R=6.522,δ=36.5°)
volume
Coulomb-2D (δ=0°) 75
of
sliding
soil
mass due
to
the
different shapes of failure surfaces is. The
(c) H/R=6.522
reason is probably that a big sh shape ra ratio of of
Fig. Fig. 6. Meas Measur ured ed eart earth h pres pressu sure re istr istrib ibut utio ions ns with with
the the shaft haft is is clos lose to a pla plane ne stra train cond ondition tion..
wall shape rati atios and wall frictions ons
5.2 Shape of failure surface in ground behind a
6. Conclusions
shaft Shapes of failure surface in ground behind a
shaft wall examined by model tests are shown in Fig. 7. It shows the results of model tests in radii of 17.5, 15.0, and 11.5cm with a wall height of 75.0cm. The smaller the radius of shaft wall and the shape ratio of that are, the smaller the Dista Distance nce ffrom rom the th e wwall(cm) all (cm) Distance the 0
10
20
30
40
0
Model tests were performed to examine the active
earth
pressure
distribution
on
a
cylindrical shaft wall and the shape of failure surface
of
ground
behind
uniform
displacements
of
a a
shaft, shaft
when in
dry
cohes ohesio ion nles less soils were ere induced. ed. The The effe effec cts of some influence factors on earth pressure on a cylindrical retaining wall were investigated. The follo llowing conclus lusions are made on the basis of the work presente ented d herein.
15
(1) The earth pressure decreased rapidly if if small displacements were allowed to
30
) m c ( z
45 ˚+ φ /2 Line
occur, and result in a minimum at the 1.5% wall displac displacement ements s of shaft radius adius.
45
(2) (2) The The smaller ller the the shape hape ratio tio was was and 60
R=17.5cm
the larger the wall radius was, the
R=15.0cm R=11.5cm
mor more ear earth th pres press sures ures was was becau ecaus se the the
75
Fig. 7. Effect of wall radiuses on the shape of failure surfaces
shape hape ratio atios s of shaft haft wall wall wer were sm small all in approximate plane strain condition. 제7 권 제 4호 2006년 8 월 23
(3) The The maxim maximum um pres press sure ure develo developed ped in the
(4) Th The smaller the radius of sh shaft wall
midpoint of the shaft wall with smooth
was and the larger the shape ratio of
sur surface. face. However However,, that ear earth pres pressu sure re
that
decr ecreas eased sligh lightl tly y when when the the wall wall fric fricti tion on
distance distance of failure failure surfac surfacee from the wall
angle ngle was grea greate terr than han zero because the
was. It was approximately equal to the
wall
friction
resisted
the
downward
was,
the
shorter
the
more
a
radius adius of shaft shaft wall.
movement movement of slidin sliding g soil soil mass mass. (접수일 : 2005. 11. 9 심사일 : 2005. 11. 29 심사완료일 : 2006. 1. 2)
REFERENCES
1. Britto, A. M. and Kusakabe, O.(1984), On the Stability of Supported Excavations, Can. Geotechnical Journal , Vol. 2, No. 1, pp. 1～15. 2. Fara, H. D. and Wright, F. D.(1963), Plastic and Elastic Stresses Around a Circular Shaft in a Hydrostatic Stress Field, Society of Mining Engineers, pp. 319 ～320. 3. Lade, P. V., Jessberger, H. L., Makowski, E. and Jorden, P.(1981.), Modelling of Deep Shaft in Centrifuge Tests, Proceedings 10th International Conference on Soil Mechanics and Foundation Engineering , Vol. 1, pp. 683～691.
4. Müller-Kirchenbauer, H. B., Walz, U. H. and Klapperich(1980), Experimentelle und Theoretische Untersuchungen Ver zum Erddruckproblem auf Radial Symmetrische Senkkästen und Schächte, Ver ., ., öff. des Grundbauinstitutes der TU
Berlin, H.7, p.113. 5. Wong, R. C. K. and Kaiser, P. K.(1988), Behavior of Vertical Shafts : Reevaluation of Model Test Results and Evaluation of Field Measurements, Can. Geotech. J., Vol. 25, No. 2, 2, pp. 338 ～352.
24 한국지반환경공학회 논문집
