Effects of Fluid-solid Coupling on Tunnel in a Saturated Soil Layer

Physical and Numerical Simulation of Geotechnical Engineering
7th Issue, Jun. 2012
Effects of Fluid-solid Coupling on Tunnel in a
Saturated Soil Layer
ZHANG Chuancheng1, LIU Jianjun2
1. Civil Department, Wuhan Polytechnic University, Wuhan 430023, P.R.China,
2. School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu 610500, P.R.China
[email protected]
ABSTRACT: Sometimes water is very important in the tunnel stability analysis. So water factor
should be considered if analysis the tunnel stability that is hydraulic coupled analysis. The result can
be closed to the real through hydraulic coupled analysis for tunnel. As for now the three-dimensional
continua fast Lagrangian analysis software FLAC3D is employed in the analysis. Using
finite-difference method, water seepage fields before and after reservoir built were simulated and
compared with the results, the author studied the effects of water-head change on ground water
seepage in tunnel.
KEYWORDS: uid-solid coupling, Numerical analysis Finite-difference method, Pore-pressure, Fl
1 INTODUCTION
The effective stress analysis of total stress is adopted in
tunnel for normally-consolidated saturated Soil. Since total
stress analysis can not distinguish effective stress from
pore-pressure, total stress of soil element is considered as
overall. There is bigger difference between result of total
stress analysis and reality in deformation and the stability
of tunnel. Effective stress analysis is compared with total
stress analysis. It can reflect characteristic property of the
soil body and the response of the soil body to loading.
Therefore, fluid-solid coupling of in a lake tunnel is more
and more taken seriously in Geotechnical Engineering
World. At present, the method of seepage field analysis is
more, including the theoretical and analytical method,
numerical method and graph method. Numerical method is
including to finite element method and finite-difference
method. Finite-difference method have unique advantage,
is applied in the project gradually. It has been analyzed and
calculated the difference in pore-pressure of tunnel, the
three-dimensional continua fast Lagrangian analysis
software FLAC3D is employed in the analysis.
A comprehensive study on tunnel in a saturated soil layer
though FLAC3D. The excavation site has been surrounded
by vertical impervious walls 1m thick which extend 2m
upward the excavation heave. Pore-pressure contours after
undrained excavation, pore-pressure contours after rapid
drainage of the excavation and pore-pressure contours after
groundwater flow reaches steady of change condition is
reveal in a saturated soil layer. Though the contrast, change
rule of pore-pressure of tunnel in a saturated soil layer is
reveal, study is vitally necessary for improving of safety
and efficiency roadway in a saturated soil layer.
2
FOUNDATIONAL
FLUID-SOLID COUPLING
THEORIES
OF
method, using dynamic relaxation equation, and stiffness
matrix and large-scale of equations is unnecessarily, is fit to
simulate working in geotechnical engineering and analysis
of fluid-solid coupling. The fluid transport is described by
Darcy’s law and Biot. The key equation as below:
2.1 Governing differential equations
The differential equations describing the fluid
-mechanical response of a porous material, and
corresponding to FLAC3D’s numerical implementation are
the following.
2.2 Transport law
The fluid transport is described by Darcy’s law. For a
homogeneous, isotropic solid and constant fluid density,
this law is given in the form:
^
qi  k il k ( s)[ p   f x j g j ],l
Where
qi is the specific discharge vector, p is pore
pressure,
k
is the tensor of absolute mobility coefficients
^
of the medium, k ( s ) is the relative mobility coefficient

which is a function of fluid saturation s , f , is the fluid
g
density, j , j  1,3 are the three components of the
gravity vector. For saturated/unsaturated flow in FLAC3D,
the air pressure is assumed to be constant and equal to zero.
2.3 Balance laws
For small deformations, the fluid mass balance may be

expressed as:
Where
 qi ,i  qv 
t
qv is the volumetric fluid source intensity in

[1/sec], and
is the variation of fluid content or
variation of fluid volume per unit volume of porous
material due to diffusive fluid mass transport, as introduced
by Biot (1956).
2.4 Constitutive law
FLAC3D is adapted to principle of finite-difference
© ST. PLUM-BLOSSOM PRESS PTY LTD
The constitutive response for the porous solid has the
Effects of Fluid-solid Coupling on Tunnel in a Saturated Soil Layer
DOI: 10. 5503/J. PNSGE. 2012.07.008
form:
SELECTION
p
 ij    ij  H ( ij ,  ij   ijT , k )
t
^
An excavation is planned in a saturated soil layer resting
on an impervious base. The soil layer has a thickness of
12m. The excavation will have a square cross section of
dimensions 8m × 8m, and a depth of 5m. In preparation for
this work, the excavation site has been surrounded by
vertical impervious walls 1m thick which extend 2m
upward the excavation heave.
The problem is three-dimensional, but by symmetry a
half of the domain may be considered in the analysis.
The FLAC3D model has dimensions 12m×12m×12m;
the grid has a total of 12×12×12 cubic zones of dimensions
1m×1m×1m as shown in Fig.1. Mesh of numerical
calculation as shown in Fig.1. The soil is considered as an
elastic material. Fixed restrain is exerted around in the sides
and the bottom of the model. The soil and water have the
following properties as show in table 1.
^
Where
 ij
is the co-rotational stress rate, H is the
functional form of the constitutive law,
parameter,
strain rate.
 ij
k
is a history
is the Kronecker delta, and
 ij
is the
2.5 Compatibility equations
The relation between strain rate and velocity gradient is:
1
2
 ij  [vi , j  v j ,i ]
v
is the speed that some count in medium,
direction.
3
MODEL
CONDITIONS
i, j
is
GEOMETRY,
BOUNDRY
AND
PARAMETERS
Fig. 1 Mesh of numerical calculation
Table 1 Mechanical parameters of rock masses
Bulk
modulus
Shear
modulus
Soil dry
density
Water
density
Wall
density
400 MPa
290 MPa
1200 kg/m3
1000 kg/m3
1500 kg/m3
Permeability
Porosity
10−12
m2/Pa-s
Fluid bulk
modulus
0.3
2.0 GPa
4 NUMERICAL RESULTS AND DISCUSSION
Fig. 3 Pore-pressure contours after rapid
drainage of the excavation
Fig. 2 Pore-pressure contours after
undrained excavation
38
Physical and Numerical Simulation of Geotechnical Engineering
7th Issue, Jun. 2012
Fig.4 Pore-pressure contours after
groundwater flow reaches steady state
Fig.5 Steady-state fluid flow into the
excavation
As an illustration of the modeling procedure for a staged
excavation, the analysis is divided into three stages. In the
first stage, as shown in fig.2, the water pressure in the
undrained excavation. The pore pressure is fixed at the
excavation top and at the soil surface. The model is cycled
to equilibrium to simulate a rapid (undrained) excavation
process in the fluid-flow time scale.
In the second stage, as shown in fig.3, the pressures are
removed from the excavation walls, and flow of water is
again disallowed. The model is cycled to model the effect
of rapid lowering of the water table inside the excavation.
In the third stage, as shown in fig.4, the pore pressure is
fixed at the value zero at the excavation top, flow of water
is allowed and the model is cycled further. The pore
pressure is monitored at a point located 1m below the
excavation center to detect when steady-state flow
conditions are reached. No effort is made to represent the
true time scale of consolidation effects; we are simply
interested in the final steady state. Fluid flow into the
excavation in the final steady state is as shown in fig.5.
shows the pore-pressure that is vital in a lake tunnel.
2) The research is obtained from experiential creep
model of rock mass through FLAC3D, whether the
parameters selection is reasonable, it needs to be further
verified. Deformation of rock mass monitoring is further
developed to ascertain of deformation velocity.
5 CONCLUSIONS
[5].
REFERENCES
[1].
[2].
[3].
[4].
1) Through three staged excavation analysis,
pore-pressure of change progress is reveal. The result
39
LIU Jianjun. Mathematic models for thermo- hydromechanical coupled flow of coal----–bed methane
[J].Journal of Wuhan Polytechnic University, 2002, 20(2):
91-94.
LIANG Bing, SUN Keming, XUE Qiang. There search of
fluid-solid coupling in the ground engineering [J]. Journal
of Liaoning Technical University (Natural Science), 2001,
20 (2):129-135.
Oda M. An equivalent continuum model for coupled stress
andfluid flow analysis in jointed rock masses .Water Resour.,
Resear., 1986, 22 (13):1845-1856.
Biot MA Mechanics of deformation and acoustic
propagation in porous media [J]. J. Appl. Phys., 1962, 33
(12):1482-1498.
Her-Yuan Chen, et al. Coupling fluid-flow and
geomechanics in dual-porosity modeling of naturally [C].
SPE38884, 1997: 404-415.