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Tunnelling under
compressed air - Practical experiences, experimental investigations and finite
element modelling
R. F. Stark1,*, G. Oettl1, G. Hofstetter1,
G. Kammerer2, S. Semprich2
1Institute for Strength of Materials,
University of Innsbruck
2Institute for Soil Mechanics and
Foundation Engineering, Technical University Graz
*Institute for Strength of Materials,
University of Innsbruck
Technikerstr. 13, A-6020 Innsbruck, Austria
Tel.: ++43(0)512 507 6722, Fax: ++43(0)512 507 2908
E-mail: Rudolf.Stark@uibk.ac.at
Abstract
In this paper practical experiences with tunnelling under compressed air
as well as related field and laboratory tests are presented and a mathematical
model capable to simulate the dewatering process of soil subjected to
compressed air is described. Ongoing experimental and theoretical
investigations described here are part of an Austrian joint research initiative
on "Numerical Simulation in Tunnelling" supported by the Austrian
Science Fund.
For the construction of section 30 of the subway in Essen, Germany, the
New Austrian Tunnelling Method (NATM) in combination with compressed air was
applied. On site measurements revealed the air loss through the shotcrete
lining to be an important design parameter. Additionally, measured surface
settlements turned out to be smaller compared with driving under atmospheric
conditions. At a full-scale field test the dependence of the air permeability
on the degree of water saturation and the influence of the flow of air on the
soil deformations were studied by pumping compressed air into a bore hole.
Currently laboratory tests are conducted in order to investigate the influence
of the air permeability of cracks in the shotcrete lining on the development of
the flow field of compressed air in the surrounding soil. In particular, the
volume of air loss through a crack in a shotcrete lining element and the
adjacent ground, the pressure distribution in the ground and the intensities of
the flow forces are measured.
Theoretical investigations currently focus on the development of a
numerical model which allows to predict deformations in the soil and ground
settlements due to both soil dewatering and tunnel excavation. The model can be
described as an extension of Biot's consolidation theory by modelling the soil
skeleton as a deformable elasto-plastic medium and taking into account both the
seepage of water and the flow of air through the soil skeleton. The
mathematical description of the soil as a three-phase medium relies on averaged
values for the density of the three-phase mixture, for the stresses, acting on
the surfaces of a differential volume element of the mixture, and for the
velocities of the fluid phases relative to the soil skeleton. In addition the dependence
of water permeability and air permeability of the soil on the degree of water
saturation of the soil is taken into account.
Keywords: compressed air; three-phase model; New Austrian Tunnelling
Method; NATM; air loss; dewatering; tunnelling under compressed air; pneumatic
tunnelling; finite element modelling
Indrotuction
In many
metropolises new high-capacity traffic ways often have to be constructed
underground. This poses great demands on analysis, design and construction of
such tunnels since in urban areas in many instances the effects of ground
settlements on existing buildings may be crucial. The importance of the problem
is reflected by the fact that a joint research initiative on "Numerical
Simulation in Tunnelling", funded by the Austrian Science Fund, has been
established. Eight research groups from the Technical University Graz, the
University of Innsbruck and the Technical University of Vienna are working to
set up a sound theoretical framework which allows better understanding and
interpretation of both empirical approaches and field measurements related to
the New Austrian Tunnelling Method (NATM). Two groups are concerned with
groundwater and its implications with respect to the analysis and design of
tunnels. The research program, conducted at the Institute for Soil Mechanics and
Foundation Engineering at the Technical University Graz, in the first phase
deals with experimental and theoretical investigations on the loss of
compressed air through the shotcrete lining of the tunnel and the soil and on
the ground displacements caused by the application of compressed air. The aim
of the research project, conducted at the Institute for Strength of Materials
at the University of Innsbruck, is to develop and to apply three-dimensional
numerical models for tunnelling below the groundwater table using compressed
air as a means for dewatering the soil in the vicinity of the tunnel face.
The paper
is organized as follows: In section 2 members of the group from Graz present
practical experiences with tunnelling under compressed air and currently conducted
experimental work. Section 3 focuses on the mathematical model for tunnelling
under compressed air, which is currently developed by the group from Innsbruck.
2 Practical and experimental considerations on tunnelling under compressed air
2.1 Subway Construction in Essen using NATM
and Compressed Air
One part of the research program covers data aquisition of tunnels
constructed with the NATM in combination with compressed air with respect to
the assessment of the numerical models to be developed. One of these tunnels is
the contract section 30 of the subway in Essen, Germany.[1]. The section was
located in soft cohesive soils, mainly consisting of silt. Fig. 1 (a) shows the
soil profile and the groundwater level. Both the two single track tubes and the
two station tubes were constructed parallel and nearly simultaneously applying
the full-face driving method. The area of the cross section of the single track
tubes was 36 m² and in the station it varied from 61 m² to 180 m². The
thickness of the shotcrete lining varied between 18 and 30 cm. The head of the
excess air pressure in the tunnel and the air loss during regular excavation
are shown in Fig. 1 (b). Due to the quite uniform soil profile in section 30,
the air loss at the tunnel face remained constant during the excavation and
roughly amounted to 30 m³/min for both tubes together. The air loss through the
shotcrete lining increased from 20 m³/min to 220 m³/min for both tubes together
due to the increasing surface of tunnel lining under air pressure with the
advancing tunnel face. Hence, a considerable amount of compressed air escaped
through imperfections and cracks in the shotcrete lining.
During excavation ground deformations at different cross sections of the
tunnel were measured. It turned out that the measured surface settlements were
smaller compared with driving under atmospheric conditions. This was due to the
air pressure in the tunnel and in the adjacent soil and due to the upwards
directed flow forces resulting from air flow in the ground [2].
Figure 1: Soil profile and air loss at contract section
30 of the subway in Essen
2.2 IN-SITU Air Permeability Test in Essen
In connection with the application of compressed air at the subway
construction site in Essen, the German contractor Bilfinger+Berger carried out
a full-scale field test. To investigate the air permeability of the Essen soil
and to study the influence of the flow of air on the soil deformations,
compressed air was pumped into a bore hole [3]. The air displaced the water in
the pores of the initially saturated soil. This process continued until
steady-state conditions of the air flow in the soil were attained. The
following parameters were measured: the volume of air pumped into the bore
hole, the excess air pressure in the bore hole, the pressure distribution in
the ground and the displacements of the ground surface [4]. In total, three
sets of tests were carried out. Excess air pressure was applied at depths
between 11 m and 21 m below ground surface with pressure levels up to 2.35 bar.
In test 1B the air was pumped into the ground at a depth ranging from 18 to 21m
below surface. The soil conditions described from top to bottom were as
follows: A layer of 2.5 m of fill was followed by silt down to a depth of 11.5
m and marl underneath.
Figure 2 shows the head of excess air pressure applied in the bore hole
and the air loss measured during test 1B. The final excess air pressure of 2.35
bar was applied in three steps. At each step the air pressure was kept constant
for about one day. The air flowing through the ground displaced the groundwater
resulting in an increase of soil permeability with time. Therefore the air loss
increased even at constant pressure levels.
Figure 2: In-situ air permeability test in Essen (test
1B)
2.3 Laboratory Test
Within the joint research initiative a laboratory test has been carried
out in order to investigate the influence of the air permeability of the cracks
in the shotcrete lining on the development of the flow field of compressed air
in the surrounding soil. In particular, the volume of air loss through the
tunnel lining, the intensities of the flow forces and the resulting
displacements in the ground have been measured.
For this test (Fig. 3) a shotcrete slab with dimensions of 100 ´ 100 ´ 16 cm with a crack of prescribed width,
varying from 0.1mm to 0.8mm, was manufactured. A box filled with different
soils (sand/silt) was then placed on top of the slab. In order to simulate
in-situ stress conditions the soil was loaded in vertical direction. This combined
shotcrete-soil element was subjected to an excess air pressure varying up to 2
bar. During the test the pressure and the temperature of the air before
entering the shotcrete crack, the air pressure at 17 points in the soil, the
volume of the air flow, the crack width at four points of the shotcrete
element, the total load on the soil surface and the total flow forces in the
soil were monitored.
The results of the laboratory tests and of the field tests as well as
the measurements at the construction site, will provide valuable data for the
verification of numerical models for tunnelling under compressed air, which are
described briefly in the following section.
Figure 3: Setup of the laboratory test
3.1 Introductory remarks
The objective of this research project is to develop a numerical model
which allows to predict deformations in the soil and ground settlements due to
both soil dewatering and tunnel excavation. In addition, it allows the
assessment of the loading of the tunnel lining. The starting point is a
generalized Biot consolidation theory [5], treating the soil as a three-phase
medium, consisting of the soil skeleton, water and compressed air. Within the
current project the extension of Biot's consolidation theory is characterized
by modelling the soil skeleton as a deformable elasto-plastic medium and taking
into account both the seepage of water and the flow of air through the soil
skeleton. Since compressed air is to be applied for dewatering the soil,
transient conditions and complex interrelations will exist between pore water
pressure, air pressure, seepage and deformations of the soil skeleton. In the
adopted approach a finite element mesh is used, including both water saturated
and unsaturated regions of the soil. The change of the location of the phreatic
surface within this mesh is computed by an iterative strategy, taking into
account the dependence of water permeability and air permeability of the soil on
the degree of water saturation of the soil.
3.2
THREE-PHASE FORMULATION
Fig. 4 (a) shows an element of "real" soil which is made up of
its constituents, soil grains, water and air. Fig. 4 (b) depicts a conceptual
model of the same soil element after employing an averaging process, i.e., the
three constituents no longer occupy discrete parts of the element, but rather
fill continuously the entire volume, according to their percentile share.
Hence, the mathematical description of a three-phase medium relies on averaged
values for the density of the three-phase mixture, for the stresses, acting on
the surfaces of a differential volume element of the mixture, and for the
velocities of the fluid phases relative to the soil skeleton [5].
a) b)
Figure 4: Three phase medium: (a) actual distribution
of the three phases, (b) conceptual model, assuming each phase to fill the
entire domain
Assuming that each phase of the medium fills the entire domain of the medium (Fig. 4 (b)), the averaged density of the three-phase material is obtained by
(1)
and the averaged total stress of a three-phase medium is given as
(2)
In (1) and (2) 
and 
denote the density
and the stress, respectively, ~ denotes an averaged value, the superscripts 
and 
refer to the solid phase and to the fluid phases water and
air, respectively, 
is the effective stress, carried by the soil skeleton and
referred to the unit area of the three-phase mixture. 
is the porosity, 
denotes the degree of
saturation of the respective fluid phase 
and 
is the hydrostatic
stress in a fluid phase (tension is defined to be positive). With these
definitions the governing equations of the multi-phase mixture are obtained as
follows: The equations of motion for a fluid phase yield Darcy's law for the
respective fluid phase
(3)
where 
denotes the
permeability of the porous medium with respect to the fluid phase 
, 
is the unit weight of
the fluid and 
the respective
component of the gravitational acceleration. Neglecting terms related to
acceleration for quasi-static problems, the equations of motion for the
three-phase medium degenerate to the equilibrium equations
(4)
Assuming the grains of the deformable soil
skeleton to be incompressible, the mass balance equation for the soil skeleton
yields
(5)
where 
. The sum of the mass balance equations for the soil skeleton
and for a fluid phase 
can be derived as
(6)
with 
as the averaged
velocity of the fluid phase 
, relative to the velocity of the soil skeleton. The
constitutive rate equations for nonlinear behaviour of the soil skeleton are
given as
, (7)
where 
and 
are the tangent
material matrix and the strain rate of the soil skeleton, respectively. 
is determined on the
basis of an elastic-plastic material model for the soil skeleton, such as the
Drucker-Prager model or the cap model. A cap model [6] generally will be
preferred to the simple Drucker-Prager model because of its capability to
account for plastic deformations even under predominantly hydrostatic stress
states. The constitutive equation for a compressible barotropic fluid phase 
reads as
(8)
with 
or 
and 
denoting the bulk
modulus of the respective fluid phase. The constitutive equation for 
is defined in terms
of the capillary stress 
by
(9)
the relationship between 
and 
to be determined from
experiments.
For the numerical solution of problems, involving a three-phase medium,
the weak formulations of the equilibrium equations for the three-phase mixture
and of the mass balance equations for the fluid phases are required. In the
framework of the FEM, spatial discretization of the weak formulations of the
set of three equations obtained requires subdivision of the domain under
consideration into finite elements. Within a single element the displacements
of the soil-skeleton and the hydrostatic stresses in the water phase and the
air phase are interpolated in terms of the respective vectors of nodal values
and of suitable shape functions. This procedure results in a coupled system of
three nonlinear equations, containing the vector of nodal displacements and the
vectors of nodal hydrostatic stresses in the fluid phases as unknowns. Finally
the coupled system of equations has to be integrated numerically in the time
domain.
4. Conclusion
The aim of this research work within the framework of the Austrian joint
research initiative Numerical Simulation in Tunnelling is a synthesis of
practical experiences and experimental investigations on the one hand with mathematical
modelling on the basis of the finite element method on the other hand. Experimental
and theoretical investigations related to tunnelling under compressed air have
been presented. Experiences at a construction site in Essen using the NATM in
combination with compressed air and investigations on a full-scale field test
have been discussed and laboratory tests on a shotcrete-soil element have been
presented. A three-phase formulation for water saturated soil, subjected to
compressed air has been described briefly and the governing equations have been
presented. A key feature of the solution strategy is to account for the
intrinsic coupling of dewatering and the deformations in the soil skeleton in a
physically consistent manner.
Acknowledgement
The projects presented in this contribution have been funded by the
Austrian Science Fund under project numbers S08005-TEC and S08006-TEC. This
support is gratefully acknowledged.
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