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. rrodriguez@prointec.es

José Estaire Gepp. Professor, Geotechnical laboratory, CEDEX. Jose.Estaire@cedex.es

Marta Estefanía López Sierra. Geological and geotechnical department project manager, Icyfsa. mlopez@icyfsa.com

Juan Tebar Molinero. Construction manager, ADIF. jtebar@adif.es

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

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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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105

120

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150

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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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