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Proceedings of Indian Geotechnical Conference
December 15-17,2011, Kochi (Paper No. Q-357)
EPB TUNNEL STRESS-STRAIN BEHAVIOUR NUMERICAL MODELLING, APPLYING
DIFFERENT MATERIALS CONSTITUTIVE MODELS - QUEJIGARES TUNNEL, SPAIN
Roberto Rodríguez Escribano. Geological and geotechnical dept manager, Prointec. AETOS. [email protected]
José Estaire Gepp. Professor, Geotechnical laboratory, CEDEX. [email protected]
Marta Estefanía López Sierra. Geological and geotechnical department project manager, Icyfsa. [email protected]
Juan Tebar Molinero. Construction manager, ADIF. [email protected]
ABSTRACT: Tunnels design requires the determination of two basic data such as stress-strain over the support-lining,
analyzed throughout the years with different calculation methodologies. The theoretical knowledge will be applied to the
collected and analyzed information for a tunnel with EPB excavators constructive process, specifically the “Quejigares
Tunnel”. To reach these goals, a 2D numerical model has been developed, applying the “contraction model” method, in
order to compare the stresses and strains results, with the measured results at work, and with the help of certain theoretical
adjustments, it has been achieved to extract a set of conclusions on the advantages and disadvantages of the different
geotechnical analysis tools employed in tunnels design, as well as the importance of a proper geological-geotechnical
model (understood as profile and characterization parameters which defines it).
INTRODUCTION AND OBJECTIVES
This research work is presented as an application to a real
case, specifically to the Quejigares tunnel (Granada, Spain),
excavated by means of an EPB tunnelling machine, Fig. 1,
with its theoretical basis in the state of the present art of
calculation methodologies for tunnels and especially
numerical methods, along with their interrelation with
constitutive models representing the behaviour of the
materials. It ends by drawing a series of conclusions on the
advantages and drawbacks of the various tools of
geotechnical analysis of tunnels that are used. (Note: in this
paper the decimal sign used is the comma “,” and the
thousands separator is the full point “.”)
Fig. 1 Panoramic photograph of the EPB tunnelling
machine.
In this way, by calibrating the methodology with a practical
case, the Quejigares tunnel, the paper aims to demonstrate
that the objectives stated in Fig. 2 are achieved.
Fig. 2 Summary of the objectives of the study.
DESCRIPTION OF THE REFERENCE WORK
The work that has been designed and executed is located on
the high speed railway line between Bobadilla and Granada,
section Arroyo de la Viñuela-Quejigares, with a length of
4,9 km, approximately 3,4 km of it (68% of the section)
being in a tunnel, 3,3 km of which are in mine. It consists
of a bi-tube tunnel, with a free cross-section of 55 m2, not
including the electrified single track and the two platforms,
with pedestrian evacuation galleries every 500 m.
For its execution a mixed EPB tunnelling machine has been
used (Herrenknecht S-516), with a length of 120 m (12 m
of shield plus head and 108 m of back-up), provided with
168 picks and 56 cutters, the diameter of the cutting wheel
with a clearance over-cut being 9,37 m, the diameter of the
shield being between an initial 9,34 m and final 9,31 m, and
the exterior diameter of the lining for the segments being
9,07 m with interior diameter of 8,43 m, and thickness 32
cm, the resulting gap being 15 cm, Fig. 3.
Fig. 3 Standard cross-section of the tunnel.
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R. Rodríguez Escribano, J. Estaire Gepp, M.E. López Sierra & J. Tebar Molinero
GEOLOGICAL-GEOTECHNICAL
CHARACTERIZATION
The study zone is located in the central-southern part of
Andalusia (south of Spain), geologically corresponding to
the central sector of the External Zones of the mountain
range known as the Cordillera Bética, belonging to the
domain known as “Subbetic Chaotic Complexes” (Middle
Subbetic), within a large olistostrome, though now mostly
covered with outcropping materials corresponding to the
post-orogenic neogene fill sediments of the Granada Basin.
The “Olistostromic unit” corresponds to what in part is
known in the region as the Antequera Trias, also covering
part of the materials that have so far been considered as
Plio-Pleistocene in this sector. Its cartographical distinction
is complicated since its stratigraphy presents a complex
structuring owing to the fact that the elements or masses of
materials which it comprises have been laid down by
gravitational mechanisms.
As a consequence of a large and continual number of
surveys, the geological-geotechnical model has been
produced, going from an initial model with a more
sedimentary concept to a model with a more tectonic
concept, Fig. 4.
Fig. 4 Geological-geotechnical model of the tunnel, and
profile P-1.
Three geological-geotechnical profiles representative of the
model were selected in order to undertake the research
work. This paper sets out solely the most significant case
which corresponds to the profile known as number 1,
located at around kilometre point 502+390, with an
overburden of 57,2 m, and represented by plio-quaternary
materials from the Rio Frío Formation (RFc and RFa),
composed of alternating layers of sands, gravels,
conglomerates and clays.
RESULTS OF THE AUSCULTATION
In the neighbourhood of profile number 1 the results were
obtained using the following instrumentation: convergence
cross-section ring, instrumented ring with total radial
pressure cells and extensometers, rings with piezometers
and measurements from profilometers, in addition to
sections of subsidence in the surface crossing of the A-92
highway by means of marker stones, extensometers and
level gauges. These results are used in this paper for
calibrating and comparing the results of the calculation
models.
In practical experience a loss of cross-section in EPB for a
straight tunnel of around 1% can be expected, of which 0%
takes place in the face, 0,8% in the shield, and 0,2% behind
the tail. This has its repercussions on the available
profilometers, since just the value of soil loss after the
passage of the tunnelling machine has been provided,
Fig. 5.
0
15
30
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105
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165180
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-100 0 100-60 -20 40 80
Displacements (mm)
PROFILE 1, TUNNEL RING SEGMENTS PROFILOMETER No 1.432LEYEND
CONTROL POINTS Fig. 5 Profilometer in the neighbourhood of profile 1, with
the result being a contraction of 0,14% of the area of the
tunnel (positive values indicate an increase in cross-section
and negatives ones a reduction).
STRESS-STRAIN ANALYSIS
Numerical modelling
A 2D numerical model has been produced, using Plaxis 2D
v9, finite element software applying the method of the
“contraction model”, which has allowed the behaviour of
the lining of the tunnel segments to be understood, even
knowing that the problem is clearly three-dimensional.
Pre-process
Definition of the ground
The ground has been introduced by means of what are
known as “constitutive models”, which are mathematical
expressions for modelling the stress-strain of the soil, made
up of constitutive equations having their basis in: principles
of mechanics, laws of physics, experimental evidence and
theoretical principles.
In this work, the following constitutive models have been
used, and a detailed explanation of them can be found in
“Plaxis 2D v9, Reference Manual” [1]: a 1st generation
model, Mohr-Coulomb (MC), a 2nd generation model,
Hardening-Soil-Model (HSM), and a 3rd generation model,
Hardening-Soil-Small-Model (HSsM). Table 1 lists the
geotechnical parameters for calculation.
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EPB tunnel stress-strain behavior numerical modeling, applying different materials constitutive models, Spain
Table 1 Soil parameters for units: RFc and RFa.
Parameter Depth (m) Value Unit
Base parameters, models MC, HSM y HSsM
unsat 22 kN/m3
sat 22 kN/m3
c’ 50 kPa’ 26 º 0 º’ 0,30
E’ = E50ref 0-30
30-40 40-50 >50
50.000 75.000
130.000 250.000
kPa
Additional parameters, models HSM and HSsM
Eoedref 0-30
30-40 40-50 >50
50.000 75.000
130.000 250.000
kPa
Eurref 0-30
30-40 40-50 >50
100.000 150.000 260.000 500.000
kPa
m 0,5
ur 0,2 pref 100 kPak0
nc 0,562 Rf 0,90
Additional parameters, model HSsM
0,7 2·10-4 G0
ref 0-30 30-40 40-50 >50
4,2·104
6,3·104
1,1·105
2,1·105
kPa
Definition of the structures
The definition of the lining for the ring of segments was
made using the “tunnel designer” tool (Plaxis), with the
main parameters being contained in Fig. 6.
Fig. 6 Structural parameters of the lining.
Definition of the contour conditions
The established contour conditions basically amount to
three: vertical edges of the mesh (with movements Ux=0),
horizontal base of the mesh (with movements Ux=Uy=0),
and depth dimensions 3D with width 5D on each side of the
axis (D being the diameter of the tunnel).
Definition of the initial conditions
On the basis of the available information a coefficient of
thrust at rest of k0= 0,75 has been initially established.
Definition of the mesh
In this stage, the geometry of the mesh was proceeded to be
refined, reducing the possible mathematical errors of the
meshing, Fig. 7.
3D
5D
Fig. 7 Mesh of the calculation model for profile 1.
Calculation phases
Three calculation phases have been established: Phase 0,
initial situation, own weight of the ground; Phase 1,
excavation of the tunnel and location of the ring of
segments; Phase 2, contraction of the tunnel lining, using a
value of 1%, on the basis of the analysed information.
Post-process
This final stage displays and processes the calculation
results. Shown in Figs. 8-9 is a comparative example of the
displacements of the lining, where the difference between
constitutive models can be appreciated.
Mohr-Coulomb
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R. Rodríguez Escribano, J. Estaire Gepp, M.E. López Sierra & J. Tebar Molinero
Fig. 8 Total displacements of the lining, MC.
Hardening-Soil-Model
Fig. 9 Total displacements of the lining, HSM.
Analysis of the state of strain
The analysis of the state of strain has been carried out using
the models of Peck (1969) [2] and of Oteo and Sagaseta
(1996) [3] as theoretical models for adjusting the curve, and
the MC, HSM and HSsM models, Fig. 10, as constitutive
models in numerical methods.
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
-110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110
Se
ttle
me
nt
(mm
)
Distance to the left tunnel 1 axis (m) SECTION 502+460
Leveling Benchmarks Peck, 1969. [Terrain F. K=0,5; Soil Loss=1,00%]
Oteo and Sagaseta, 1996, E=93.550 kPa, Subsidence F.=0,7, Terrain F.=1,3 MEF, Mohr-Coulomb (MC)
MEF, Hardening Soil Model (HSM) MEF, Hardening Soil Small Model (HSsM) Fig. 10 Comparative graph of settlement troughs.
Analysis of the state of stress
The analysis of the state of stress was able to be done due to
having instrumented rings with total radial pressure cells in
all of them, thereby comparing the real data recorded with
that obtained by means of numerical methods employing
the three constitutive models already mentioned, those for
MC, HSM and HSsM.
It has been necessary to carry out an additional calculation,
due to adjusting the initial coefficient of rest from k0 of
0,75 to 1,50, since the data recorded by the pressure cells
did not fit in with the numerical results. The explanation
was to be found in the observation of its geological profile
position, where it can be seen how the instrumented ring is
located in a reverse fault zone which meant that the stress
field was inverted, Fig. 11.
CONCLUSIONS
The analysis undertaken has allowed the following
conclusions to be reached:
Tunnel Ring Segments,
No. 1.810, 501+825
PROFILE 1 (502+390, POSITION C13)LEYEND
CPTR FIELD DATA
GEOSTATIONARY
MC
HSM
HSsM
015
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45
60
75
90
105
120
135
150
165180
195
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0 200 400 600 800 1000 1200 1400 1600 1800 2000
Total Radial Pressure (kPa)
K0 = 1,50
PROFILE 1 (502+390, POSITION C13)LEYEND
CPTR FIELD DATA
GEOSTATIONARY
MC
HSM
HSsM
015
30
45
60
75
90
105
120
135
150
165180
195
210
225
240
255
270
285
300
315
330
345
0 200 400 600 800 1000 1200 1400
Total Radial Pressure (kPa)
K0 = 0,75
Fig. 11 Comparative graph of the state of stress.
It is recommended and necessary to have: adequate
knowledge of the geological model; adequate
auscultation in order to be able to calibrate the
theoretical and numerical models; and a comparison of
the results of advanced calculations with simple
analyses.
The hyperbolic constitutive models with hardening
(HSM and HSsM) allow stress-strain results to be
obtained that provide a better fit with the real data,
though the perfect elasto-plastic model (type MC)
would, from the point of view of stress, even obtaining
somewhat conservative results, eliminate risks in the
calculations of linings since all the data on stress that it
has been possible to obtain from auscultation in the
work can be included.
The results obtained applying the HSM and HSsM
models have been very similar, as a consequence of the
fact that the range of strains is located at the limit of
the application of models of small strains.
The excavation process produces a relaxation in the
stress of the ground around the tunnel, which leads to
thrusts that are smaller than in geostationary cases.
REFERENCES
1. PLAXIS 2D v9. (2010), Reference Manual. 2. Peck, R. (1969), Deep excavation and tunneling in Soft
ground. G. Report 7th Int. Symp. On S.M. and F.E.
México. State of the Art. Volume, 225-258.
3. Oteo, C. and Sagaseta, C. (1996), Some Spanish
experience on measurement and evaluation of ground
displacements around urban tunnels. Proc. Int. Sym.
On Geotechnical Aspects of Underground Construction
in Soft Ground. London, 641-646.
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