The Ground Reaction Curve due to Tunnell ing under Draina ge Condition Young-jin Shin 1 , Byoung-min Kim 2 , Shin-in Han 3 , In-mo Lee 4 , and Daehyeon Kim 5 1 School of Civil Engineering, Purdue University, West Lafayette: [email protected]2 Underground Space Construction Technology Centre, Seoul, Korea 3 Department of Civil Engineering, Korea University, Seoul, Korea 4 Department of Civil Engineering, Korea University, Seoul, Korea: [email protected]5 Indiana Department of Transportation, West Lafayette ABSTRACT: When a tunnel is exca vated below the grou ndwate r table , water flows into the excavated wall of tunnel and seepage forces are acting on the tunnel wall. Such seepage forces significantly affect the ground behavior. The ground response to tunnelling is understood theoretically by the convergence-confinement method, which consists of three elements: longitudinal deformation profile, ground reaction curve, and sup por t cha rac ter isti c curve. The see page for ce s are likely to have a str ong influence on the ground reaction curve which is defined as the relationship between internal pressure and radial displacement of the tunnel wall. In this paper, seepage forces arising from the ground water flow into a tunnel were estimated quantitatively. Magnitude of seepage forces was determined based on hydraulic gradient distribution around tunnel. To estimate seepage forces, different cover depths and groundwater table levels were considered. Using these results, the theoretical solutions for the ground reaction curve (GRC) with consideration of seepage forces under steady-state flow were derived. INTRODUCTION When a tunnel is excavated below the groundwater table, groundwater may flow into the tunnel and, consequently, seepage forces may develop in the ground seriously affecting the behavior of the tunnel. Ground response to tunnelling can be understood theoretically by the convergence-confinement method. This method is based on the pr inc iple for whic h a tunne l is sta bil ized by contr oll ing its dis pla ce me nts af te r installation of a support near the tunnel face. The convergence-confinement method is based on three elements: the longitudinal deformation profile, the ground reaction curve, and the suppor t cha rac ter isti c curve. The long itud ina l def ormatio n pro file assuming no support shows the radial displacement of the tunnel cross-section in the longitudinal direction from the tunnel face. The support characteristic curve describes . o r g b y K a i s t K o r e a A d v a n c e d I n s t . O f o n 1 0 / 0 8 / 1 2 . F o r p e r s o n a l u s e o n l y . N o o t h e r u s e s w i t h o u t p e r m i s s i o n . C o p y r i g h t ( c ) 2 0 1 2 . A m e r i c a n S o c i e t y o f C i v i l E n g i n e e r s . A l l
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7/27/2019 The Ground Reaction Curve due to Tunnelling under Drainage Condition
The Ground Reaction Curve due to Tunnelling under Drainage Condition
Young-jin Shin1, Byoung-min Kim
2, Shin-in Han
3, In-mo Lee
4, and Daehyeon Kim
5
1School of Civil Engineering, Purdue University, West Lafayette: [email protected]
2Underground Space Construction Technology Centre, Seoul, Korea
3Department of Civil Engineering, Korea University, Seoul, Korea
4Department of Civil Engineering, Korea University, Seoul, Korea: [email protected]
5Indiana Department of Transportation, West Lafayette
ABSTRACT: When a tunnel is excavated below the groundwater table, water flows
into the excavated wall of tunnel and seepage forces are acting on the tunnel wall.
Such seepage forces significantly affect the ground behavior. The ground response totunnelling is understood theoretically by the convergence-confinement method, which
consists of three elements: longitudinal deformation profile, ground reaction curve,
and support characteristic curve. The seepage forces are likely to have a strong
influence on the ground reaction curve which is defined as the relationship between
internal pressure and radial displacement of the tunnel wall. In this paper, seepage
forces arising from the ground water flow into a tunnel were estimated quantitatively.
Magnitude of seepage forces was determined based on hydraulic gradient distribution
around tunnel. To estimate seepage forces, different cover depths and groundwater
table levels were considered. Using these results, the theoretical solutions for theground reaction curve (GRC) with consideration of seepage forces under steady-state
flow were derived.
INTRODUCTION
When a tunnel is excavated below the groundwater table, groundwater may flow
into the tunnel and, consequently, seepage forces may develop in the ground seriously
affecting the behavior of the tunnel. Ground response to tunnelling can be understood
theoretically by the convergence-confinement method. This method is based on the
principle for which a tunnel is stabilized by controlling its displacements afterinstallation of a support near the tunnel face. The convergence-confinement method is
based on three elements: the longitudinal deformation profile, the ground reaction
curve, and the support characteristic curve. The longitudinal deformation profile
assuming no support shows the radial displacement of the tunnel cross-section in the
longitudinal direction from the tunnel face. The support characteristic curve describes
394
Copyright ASCE 2008 GeoCongress 2008GeoCongress 2008 o
m a
s c e l i b r a r y . o r g b y K a i s t K o r e a A d
v a n c e d I n s t . O f o n 1 0 / 0 8 / 1 2 . F o r p e r s o n a l u s e o n l y .
N o o t h e
r u s e s w i t h o u t p e r m i s s i o n .
C o p y r i g h t ( c ) 2 0 1 2 .
A m e r i c a n S o
c i e t y o f C i v i l E n g i n e e r s .
A l l
7/27/2019 The Ground Reaction Curve due to Tunnelling under Drainage Condition
the increasing pressure that acts on the supports as the radial displacement of the
tunnel increases. Lastly, the ground reaction curve shows the increasing trends of
radial displacement as the internal pressure of the tunnel decreases. Tunnelling belowthe ground water table induces additional seepage stresses (Shin et al., 2007), and the
seepage forces are likely to have a strong influence on the ground reaction curve.
Previous studies on the ground reaction curve by Stille (1989), Wang (1994),
Carranza-Torres( 2002), Sharan (2003), and Oreste (2003) did not consider seepage
forces. The effects of seepage forces on the tunnel face or the support system were
The radial displacement for a circular tunnel can be worked out based on the elasto-plastic theory. The strains in the plastic region are composed of elastic and plastic
strains, and are expressed as Eqn. (18) and (19), respectively. The superscripts e and
p represent the elastic and plastic parts, respectively. By considering compressive
strains and radially inward displacements to be positive, the relationship between
strain and displacement at any point in a soil-mass can be written as follows:e p
r r r = +(18)
e p
= +(19)
r r
du
dr
=
(20)
r u
r
=
(21)
The plastic strain can be represented by using the plastic flow rule. When the
volume expansion effect is important in plastic strain, generally the non-associated
flow rule is valid; otherwise, the associated flow rule is valid. The plastic potential
function, Q , when using non-associated flow rule, is as follows:
( , ) 2 0r r Q f k c k
# # = = =
(22)
where 1 sin1 sin
k # # #
+=
, the parameter # is the dilation angle.
The plastic parts of radial and circumferential strains can be related as follows:
r
p pk
# = (23)
Eqn. (20) ~ (23) lead to the following differential equation.
( )r r du uk f r
dr r # + =
(24)
where ( )e
r k f r # + =e (25)
Eqn. (24) can be solved by using the following boundary condition for the radial
displacement, ( )er r r u=
, at the elasto-plastic interface (Brady and Brown, 1993).
( ) ( )( )2e er r r vo r r r
bu
G
= =
=
(26)
where G is the shear modulus of the soil-mass.
Eqn. (24) - (26) lead to the following expressions for the radial displacement:
( )( )e
e
k r k k e
r r r r r
r u r r f r dr u
r
#
# #
=
= +
(27)
In order to evaluate the integral in the above equation, expressions for er and e
can be obtained by the following equation (Brady and Brown, 1993):
2
1[(1 2 ) ]
2
e
r
DC
G r % = +
(28)
GEOCONGRESS 2008: GEOSUSTAINABILITY AND GEOHAZARD MITIGATION 399
Copyright ASCE 2008 GeoCongress 2008GeoCongress 2008 o
m a
s c e l i b r a r y . o r g b y K a i s t K o r e a A d
v a n c e d I n s t . O f o n 1 0 / 0 8 / 1 2 . F o r p e r s o n a l u s e o n l y .
N o o t h e
r u s e s w i t h o u t p e r m i s s i o n .
C o p y r i g h t ( c ) 2 0 1 2 .
A m e r i c a n S o
c i e t y o f C i v i l E n g i n e e r s .
A l l
7/27/2019 The Ground Reaction Curve due to Tunnelling under Drainage Condition
Eqn. (26) can be solved by using Eqn. (28) and (29). The expression for the radial
displacement in the plastic region at the opening surface 0r r = is given by Eqn. (30).
0
1 1 1 1
( ) 0 0 0 ( )
0
1[ (1 2 )( ) ( )] ( )
2 e
k k k k k k er r r e e r r r
r u r C r r D r r u
G r
# # # # # # % + +
= == +
(30)
The ground reaction curve is estimated by using the theoretical solutions for the
cases in which the cover depth of the tunnel, C , and water height, H , are 10 timesthe diameter of tunnel, D . As shown in Figure 5, the ground reaction curve with
consideration of seepage force shows larger radial displacement than the ground
reaction curve for the dry condition; this result means that there is no ground water
when the cover depth of the tunnel, C , is 10 times the diameter of the tunnel, D .
This is due to the fact that even if the effective overburden pressure can be decreased
by the arching effect during tunnel excavation, seepage forces still remain.
FIG. 5. The ground reaction curve ( / 10C D = , / 10 H D = )
CONCLUSIONS
The flow of groundwater has a significant effect on the radial displacement of a tunnel
wall. While the effective overburden pressure is reduced slightly by the arching effect
during tunnel excavation, seepage forces still remain. Therefore, the presence of
groundwater induces larger radial displacements of the tunnel wall than those in the
case of dry condition.
GEOCONGRESS 2008: GEOSUSTAINABILITY AND GEOHAZARD MITIGATION400
Copyright ASCE 2008 GeoCongress 2008GeoCongress 2008 o
m a
s c e l i b r a r y . o r g b y K a i s t K o r e a A d
v a n c e d I n s t . O f o n 1 0 / 0 8 / 1 2 . F o r p e r s o n a l u s e o n l y .
N o o t h e
r u s e s w i t h o u t p e r m i s s i o n .
C o p y r i g h t ( c ) 2 0 1 2 .
A m e r i c a n S o
c i e t y o f C i v i l E n g i n e e r s .
A l l
7/27/2019 The Ground Reaction Curve due to Tunnelling under Drainage Condition
This paper was supported by the Underground Space Construction Technology Center
under the Ministry of Construction and Transportation in Korea (Grant C04-01).
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