Computers and Geotechnics 33 (2006) 234–247

www.elsevier.com/locate/compgeo

A numerical study of the effect of soil and grout material properties

and cover depth in shield tunnelling
Thomas Kasper a, Günther Meschke b,*

a
COWI A/S, Parallelvej 2, 2800 Kongens Lyngby, Denmark
b
Institute for Structural Mechanics, Ruhr University Bochum, Universitätsstraße 150, 44780 Bochum, Germany

Received 17 October 2005; received in revised form 17 March 2006; accepted 22 April 2006
Available online 12 July 2006

Abstract

For shield-driven tunnels, the influence of the soil and grout material properties and of the cover depth on the surface settlements, the
loading and deformation of the tunnel lining and the steering of the TBM is investigated numerically. To this end, comparative numerical
simulations of a mechanised tunnel advance in homogeneous, overconsolidated, soft, cohesive soil below the ground water table are per-
formed and sensitivities are evaluated. The advancement of the step-by-step tunnel construction process is modelled using a three-dimen-
sional finite element model, which takes into account all relevant components of shield tunnelling. The material behaviour of the
saturated soil and the tail void grout is modelled by a two-field finite element formulation in conjunction with an elasto-plastic Cam-Clay
model for the soil and a hydration-dependent constitutive model for the grout. The analyses provide valuable information with regard to
the significance of the investigated parameters and demonstrate the complexity of the various interactions in shield tunnelling.
 2006 Elsevier Ltd. All rights reserved.

Keywords: Shield tunnelling; Finite element method; Parametric studies; Sensitivities; Soft soil; Consolidation; Grouting

1. Introduction of information. However, it is sometimes difficult to

clearly identify correlations between key parameters from
Shield tunnelling has become a well-established tunnel measurement data due to the varying conditions of the
construction method in various ground conditions. It is measurements and the resulting large scatter. If realistic
characterised by relatively complex interactions between numerical models are used, simulations represent a useful
the soil, the tunnel boring machine (TBM), the hydraulic tool to identify and quantify such correlations. Several
jacks, the tunnel lining and the tail void grout [24]. A numerical models for shield tunnelling characterised by
detailed insight into the influence of relevant parameters different degrees of idealisation and simplification have
such as the design and operation of the TBM, different been developed in the past. First approaches were pro-
construction details and the material characteristics of posed within a two-dimensional context, among others
the soil and the tail void grout is of vital importance in [2,5,13]. If the inherent 3D character of all phenomena
for an optimised design and a successful construction of in shield tunnelling should be considered realistically,
shield-driven tunnels. Such a more detailed insight can more sophisticated 3D models have to be used (see e.g.
be obtained by tests, e.g. [8,22,30,33], by data mining of the models developed in [3,11,21,26,27] among many oth-
existing measurements and project data, e.g. [23,31, ers). The ground behaviour and, in particular, its interac-
34,35], and by numerical simulations. Tests, site measure- tion with the TBM are major factors influencing the
ments and project data are valuable and reliable sources tunnelling process. Simplified two-dimensional numerical
studies in [1] and the two- and three-dimensional numer-
*
Corresponding author. Tel.: +49 234 3229051; fax: +49 234 3214149. ical studies in [3] and [26] investigate the influence of dif-
E-mail address: guenther.meschke@sd.rub.de (G. Meschke). ferent parameters such as the face pressure, the grouting

0266-352X/$ - see front matter  2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compgeo.2006.04.004
 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247 235

pressure, the material characteristics of the soil and the formulation is applied between the shield skin and the
cover depth of the tunnel. However, the frictional contact soil based on Mohr–Coulomb friction with a friction
between the soil and the shield skin and the steering coefficient of 0.2. This takes into account the relative dis-
behaviour of the TBM are not considered in these placements between the shield skin and the soil and the
models. resulting shear stresses in the soil. In order to model
An approach to simulate shield-driven tunnel advances the movement of the TBM and its interaction with the
in soft, water saturated soil by means of an automated soil realistically, to avoid drift off course and to model
three-dimensional finite element model was proposed curved tunnel advances, an automatic steering algorithm
recently in [18]. Since all relevant components and their to control the individual jack thrusts has been developed.
interactions are taken into account and the step-by-step The step-by-step excavation process is modelled by
tunnel advance is explicitly modelled, it allows for realistic repeated rezoning of the finite element mesh at the cut-
simulations and case studies of shield tunnelling below the ting face and repeated insertion of finite elements repre-
ground water table. This paper presents several paramet- senting the tunnel lining and the tail void grout,
ric studies concerning the effect of the ground behaviour, respectively. Furthermore, the boundary conditions for
the behaviour of the tail void grout and the cover depth the face support and the grouting pressure as well as
for a tunnel advance in homogeneous, soft, cohesive soil. the position of the loads representing the back-up trailer
First, a short overview of the investigated tunnel advance are adjusted to the progress of the simulated tunnel
and the finite element model is given in Section 2. The advance. The elements of the grout are directly connected
results of systematic sensitivity studies contained in Sec- to the elements of the tunnel lining on the inner side and
tion 3 will show the influence of the investigated parame- the soil on the outer side. All components are loaded
ters, e.g. on the computed surface settlements, the steering with their self-weight. The segmentation of the tunnel lin-
of the TBM and the deformation and loading of the tun- ing is not considered in the model. In reality, the segmen-
nel lining. tation introduces quite a complex structural behaviour of
the lining resulting in local stresses which can be repro-
2. Finite element modelling of a tunnel advance in soft soil duced only by very detailed modelling procedures (see
e.g. [7,9]) not feasible within the framework of the pro-
The investigated tunnel advance and the different posed 3D model of the whole tunnel. The concrete lining
aspects of the finite element model are described in detail is therefore modelled in a simplified way as a continuous,
in [18]. Hence, only a short description of the finite ele- isotropic, elastic tube with a stiffness of E = 3.15 · 107
ment model is provided in this section. The investigated kN/m2 and m = 0.2.
tunnel has a diameter of D = 6.3 m and a cover depth Fig. 1(b) shows a complete view of the finite element
of 1.5D. It is assumed to be driven by means of a hydro- model used for the simulation of 48 m tunnel advance.
shield in homogeneous, overconsolidated, soft, cohesive The long-term consolidation is taken into account by addi-
soil below the ground water table. Fig. 1(a) shows the dif- tional time steps after completion of the tunnel advance.
ferent components of the finite element model. Neglecting The material behaviour of the water-saturated soil and
the deformations of the shield skin, the TBM is modelled the tail void grout is modelled by a coupled u  pw two-
as a rigid contact body. The length and weight of the field finite element formulation using 20-node brick
shield are assumed as 4.9 m and 4000 kN, respectively. elements with quadratic approximations of the displace-
The TBM is pushed forward by length changes of the ments u and linear approximations of the pore pressure
truss elements representing the hydraulic jacks. A contact pw. The two-field formulation allows to take into account

(a) (b)

Fig. 1. (a) Representation of the different shield tunnelling components in the model and (b) finite element mesh for the simulation of 48 m tunnel advance
with a cover depth of 1.5D and location of the chosen monitoring section for the evaluation of the simulation results.
236 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247

the ground water, the grouting pressure and the fluid account the anisotropy of natural soil deposits and small
interaction between the soil and the slurry at the cutting strain stiffness behaviour, which has been found relevant
face and between the grout and the soil around the tail for realistic predictions of tunnelling induced settlement
void. Neglecting the anisotropy of natural soil deposits, troughs, e.g. in [4]. The overestimation of the soil
an isotropic elasto-plastic Cam-Clay model with an algo- strength for stress paths above the Critical State Line
rithmic implementation as proposed in [10] is used to and for some stress path directions in the deviatoric plane
describe the relationship between the strains and the effec- due to the circular yield surface are further relevant defi-
tive stresses of the soil skeleton. The model incorporates ciencies of the applied Cam-Clay model [14]. However,
a nonlinear elastic law with the tangential bulk and shear the purpose of this paper is the investigation of sensitiv-
moduli depending linearly on the effective hydrostatic ities by means of parametric studies, concentrating on dif-
pressure p 0 while the Poisson ratio is assumed to be con- ferences in the results for different parameters rather than
stant. Fig. 2 shows the yield surface of the Cam-Clay absolute values of the results. Therefore, the deficiencies
model, which represents an ellipse in the p 0 –q-diagram in the soil modelling are considered as being acceptable.
and an ellipsoid in the space of effective principal stresses. The following soil parameters have been used: a compres-
The model predicts hardening with contractant plastic sion index k = 0.05, a swelling index j = 0.01, a Poisson
strains for stress paths below the Critical State Line ratio m = 0.35, a slope of the Critical State Line M =
and softening with dilatant plastic strains for stress paths 1.0, a permeability k = 1 · 107 m/s and a saturated unit
above the Critical State Line [36]. The Cam-Clay model weight cs = 18 kN/m3. The assumed preconsolidation
as a simple elasto-plastic material model for clayey soils pressure in the basic case of 120 kN/m2 at the ground
is chosen as a prototype in the presented parametric surface increasing by 6 kN/m2 per metre depth (cp.
studies. Although it covers the basic observations of the Fig. 9) corresponds to a preload of the soil of approx.
behaviour of isotropically consolidated clay in conven- 120 kN/m2 and results in overconsolidation ratios
tional triaxial and oedometer tests, it does not take into OCR = pc/p 0 of 2.4–3.2 at the depth of the tunnel. The

Fig. 2. Yield surface of the Cam-Clay model applied for soft, cohesive soils.

(a) (b)

Fig. 3. (a) Measured evolution of the Young’s moduli of shotcrete and grouting materials [15,12] and (b) different time-dependent Young’s moduli of the
tail void grout as applied in the simulations in Section 3.4.
 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247 237

initial stress state of the soil has been modelled in a sim-

plified way with a constant coefficient of earth pressure at
rest K0 = 0.54 in all presented analyses irrespective of the
overconsolidation ratio. Although this does not represent
the correct K0 primarily in the upper part of the soil body
with high values of OCR, it is a reasonable estimate at
the depth of the tunnel in all cases in this paper and is
therefore considered suitable for the purpose of the para-
metric studies.
The tail void grout is described as an elastic, fully
saturated porous material. This mode of representation
allows for the modelling of fluid flow within the tail void
and of the infiltration of fluid grout into the surrounding
ground. Pore pressure boundary conditions are applied at
Fig. 4. Initial yield surfaces of the Cam-Clay model for different slopes of
the grout element nodes along the shield tail to model the the Critical State Line M / friction angles u 0 (shown for the soil at the level
initial isotropic pressure of the grout. This pressure is of the tunnel axis).
assumed to vary linearly with height with a gradient of
10 kN/m2/m and has a chosen value at the level of the
tunnel axis of 150 kN/m2. The hydration of the grout is mations become significantly larger for smaller friction
taken into account by applying a time-dependent angles due to the smaller initial yield surfaces (cp.
Young’s modulus and a time-dependent permeability, Fig. 4). As a consequence, larger surface settlements are
while the Poisson ratio is assumed to be constant (0.3). predicted by the simulations (Fig. 5(a)). According to
Fig. 3(a) shows measurement data of the stiffness evolu- Fig. 5(b), the relationship between the friction angle and
tion of two different cementitious materials. The mathe- the maximum surface settlement is strongly nonlinear.
matical description and algorithmic implementation of Due to the larger plastic deformations of the soil along
the stiffness evolution of the grout follows a suggestion the invert for u 0 = 20.7, a larger tilt angle of the TBM
in [28] and [29]. The function E(t) is shown in Fig. 3(b) is necessary to keep the prescribed driving path
with different ratios of E(1)/E(28) as used in Section 3.4. (Fig. 6(b)). Furthermore, Fig. 6(a) shows that the neces-
For the investigated tunnel advance the influence of the sary tilt angle is marginally underestimated by the applied
face and grouting pressure as well as the TBM design has automatic steering algorithm for the jack thrusts. Accord-
been studied in [19,20]. Available measurement data, e.g. ing to Fig. 7(a)–(c), an increase of the radial loading of
in [13,31,35] confirm the determined effect of the face and the tunnel lining and an increase of the ring normal force
grouting pressure on the ground deformations. In the fol- is predicted for smaller friction angles while a slight de-
lowing sections of this paper, the effect of the yield charac- crease of the bending moment can be observed. No signif-
teristics and permeability of the soil, the stiffness evolution icant influence of the friction angle on the upward
of the grout and the cover depth of the tunnel is studied. A movement of the tunnel lining behind the TBM is pre-
comprehensive description of the model and a detailed dicted by the simulations (Fig. 7(d)). The measurement
analysis of the simulation results are contained in [17]. data from different tunnels shown in Fig. 8 have been ta-
ken from the literature and show general agreement with
3. Parametric studies the results of the finite element model. The computed set-
tlements in Fig. 5(a) are in the same order of magnitude
3.1. Friction angle of the soil as observed in an EPB shield tunnel project in soft, cohe-
sive soil in San Francisco (Fig. 8(a)) and show similar
For triaxial compression stress paths, the slope of the trends as the corresponding FE results for this project ob-
Critical State Line M is related to the friction angle u 0 tained in [2]. The simulations presented in [19] reproduced
according to the possibility of temporary heave ahead of the shield for
high face pressure as observed in Fig. 8(a). The back-cal-
M ¼ 6 sin u0 =ð3  sin u0 Þ ð1Þ
culated ring normal force and bending moment of the Bo-
Three different values according to Fig. 4 are used for the tlek Rail Tunnel in the Netherlands shown in Fig. 8(b)
parametric study. It was shown in [18] that the weight of and (c) have the same general characteristics as the com-
the TBM and the frictional interaction of the soil with the puted forces in Fig. 7(b) and (c). The irregular shape of
tapered shield skin cause a considerable hydrostatic stress the ring normal force in Fig. 8(b) might be attributed to
increase in the soil in the vicinity of the invert and a con- the influence of the segmentation of the lining. The mag-
siderable deviatoric stress increase in the vicinity of the nitude of the forces at the Botlek Rail Tunnel is larger
springline and the invert. These stress changes in the soil due to the larger overburden and the larger tunnel diam-
are accompanied by plastic deformations, softening at the eter. The simulation model predicts uplift movements of
springline and hardening at the invert. The plastic defor- the tunnel lining behind the TBM (Fig. 7(d)) which are
238 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247

(a) (b)

Fig. 5. Computed surface settlements in point A of the monitoring section for different friction angles of the soil.

(a) (b)

Fig. 6. Computed TBM movement during the tunnel advance for different friction angles of the soil: (a) vertical deviation and (b) tilt angle.

also observed in practice, e.g. at the Sophia Rail Tunnel overconsolidation a slight increase of the necessary tilt
(Fig. 8(d)). angle a of the TBM during the tunnel advance is predicted
(Fig. 11(b)). According to Fig. 12(a), a decrease of the
3.2. Degree of overconsolidation of the soil overconsolidation causes a small increase of the computed
lining pressure, which results in a slight increase of the ring
In order to determine the influence of the degree of over- normal force (Fig. 12(b)). The bending moment in the
consolidation, three different initial preconsolidation pres- cross-section of the lining remains almost unchanged
sures pc,0 in the soil are assumed according to Fig. 9(a). (Fig. 12(c)). A smaller uplift of the tunnel lining is com-
Fig. 9(b) shows the corresponding overconsolidation ratios puted for a smaller overconsolidation of the soil
OCR = pc/p 0 . As a reference, the initial yield surfaces for (Fig. 12(d)).
the soil at the level of the tunnel axis are depicted in
Fig. 9(c). 3.3. Permeability of the soil
Similar to the effect of a decrease of the friction angle
also a reduction of the overconsolidation causes larger Fig. 13 shows that the computed surface settlements are
plastic deformations of the soil in the vicinity of the shield almost identical for values of the permeability of the soil
machine and therefore leads to an increase of the computed chosen as kS = 1 · 107 m/s and kS = 1 · 108 m/s, whereas
surface settlements (Fig. 10). Again, the relationship larger long-term settlements are computed for kS =
between the overconsolidation and the maximum com- 1 · 106 m/s. As is illustrated in Fig. 16, the face support
puted surface settlement is nonlinear. The trend of increas- and the grouting of the tail void cause excess pore pressures
ing settlements with decreasing overconsolidation has also in the soil ahead of the cutting face and in the vicinity of the
been found in [1]. Within the analysed bandwidth of the tunnel behind the TBM. The taper of the shield skin induces
 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247 239

(a) (b)

(c) (d)

Fig. 7. (a) Computed lining pressure in the monitoring section at time t = 1, (b) normal force in the monitoring section at t = 1, (c) bending moment in
the monitoring section at t = 1 and (d) uplift of the tunnel lining in the monitoring section for different friction angles of the soil.

(a) (b)

(c) (d)

Fig. 8. (a) Measured surface settlements above an EPB shield tunnel in San Francisco in soft, cohesive soil and computed settlements using a finite element
model [2], (b) and (c) ring normal force and bending moment determined from strain measurements at the Botlek Rail Tunnel in the Netherlands [7] and
(d) measured uplift movement of the tunnel lining behind the shield machine at the Sophia Rail Tunnel in the Netherlands [6].
240 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247

(a) (b) (c)

Fig. 9. (a) Assumed initial preconsolidation pressures over depth, (b) corresponding overconsolidation ratios and (c) initial yield surfaces at the level of the
tunnel axis.

(a) (b)

Fig. 10. Computed surface settlements in point A of the monitoring section for different degrees of overconsolidation of the soil.

(a) (b)

Fig. 11. Computed TBM movement during the tunnel advance for different degrees of overconsolidation of the soil: (a) vertical deviation and (b) tilt
angle.

deformations of the soil, which lead to a relatively large, below the tunnel in the less permeable soil. The dissipation
temporary decrease of the pore pressures along the shield of these reduced pore pressures causes a long-term uplift of
skin in the less permeable soil. Furthermore, the buoyancy the tunnel lining (Fig. 15(d)) and, consequently, smaller sur-
of the tunnel lining causes a decrease of the pore pressure face settlements during the consolidation phase (Fig. 13(a)).
 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247 241

(a) (b)

(c) (d)

Fig. 12. (a) Computed lining pressure in the monitoring section at time t = 1, (b) normal force in the monitoring section at t = 1, (c) bending moment in
the monitoring section at t = 1 and (d) uplift of the tunnel lining in the monitoring section for different degrees of overconsolidation of the soil.

(a) (b)

Fig. 13. Computed surface settlements in point A of the monitoring section for different permeabilities of the soil.

For kS = 1 · 106 m/s only increased pore pressures can be 3.4. Hydration characteristics of the grout
observed in the vicinity of the tunnel. The dissipation of
these increased pore pressures during the consolidation The early age stiffness and strength development of
phase leads to a long-term settlement of the tunnel lining the grout is expected to be important, whereas the final
(Fig. 15(d)) and, consequently, to additional settlements at stiffness and strength characteristics are expected to be
the ground surface (Fig. 13(a)). According to Fig. 14, the of minor importance provided that the grout reaches
influence of the permeability of the soil on the steering of similar or higher values than the surrounding ground.
the shield machine is small. Likewise, only small changes In the following parametric study three different
of the lining pressure, the ring normal force and the bending hydration characteristics characterised by different evolu-
moment can be observed for different permeabilities of the tions of the early age stiffness according to Fig. 3(b) are
soil (Fig. 15(a)–(c)). investigated.
242 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247

(a) (b)

Fig. 14. Computed TBM movement during the tunnel advance for different permeabilities of the soil: (a) vertical deviation and (b) tilt angle.

(a) (b)

(c) (d)

Fig. 15. (a) Computed lining pressure in the monitoring section at time t = 1, (b) normal force in the monitoring section at t = 1, (c) bending moment in
the monitoring section at t = 1 and (d) uplift of the tunnel lining in the monitoring section for different permeabilities of the soil.

A fast temporal increase of the early age stiffness reduces behind the TBM causes a significant increase of the lining
the soil deformations into the tail void. As a consequence, pressure at the invert (see Fig. 18(a)). This leads to a rela-
smaller surface settlements are predicted by the simulations tively large increase of the bending moment in the tunnel
based on a fast hydration characteristics of the grouting lining (Fig. 18(c)) while the change of the ring normal force
material (Fig. 17). A settlement reduction for increased remains small (Fig. 18(b)). The smaller stress release of the
stiffness of the grout has also been determined in [16]. soil directly behind the TBM at the invert is connected with
The reduced stress release and upward deformation of an increase of the uplift of the tunnel further behind the
the soil into the freshly grouted tail void at the invert TBM for a more rapid hydration of the grout material
 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247 243

[kN/m2]
Fig. 16. Computed excess pore pressure in the soil at the end of the tunnel advance for kS = 1 · 106 m/s and kS = 1 · 107 m/s.

(a) (b)

Fig. 17. Computed surface settlements in point A of the monitoring section for different early age hydration characteristics of the grout material.

(a) (b)

(c) (d)

Fig. 18. (a) Computed lining pressure in the monitoring section at time t = 1, (b) normal force in the monitoring section at t = 1, (c) bending moment in the
monitoring section at t = 1 and (d) uplift of the tunnel lining in the monitoring section for different early age hydration characteristics of the grout material.
244 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247

(Fig. 18(d)). As expected, no appreciable change of the tions of the two deeper tunnels are depicted in Fig. 19. It
steering behaviour of the TBM has been observed for dif- is shown in Section 3.2 that the overconsolidation has a sig-
ferent temporal evolutions of the grout stiffness. nificant influence on the investigated results. In order to
eliminate its effect in the analysis of the cover depth, the ini-
3.5. Cover depth of the tunnel tial values of the preconsolidation pressures have been
adapted according to Fig. 20(a) such that nearly equal
Three different cover depths (1.5D, 2.25D and 3D) are overconsolidation ratios OCR are obtained at the different
analysed. The finite element meshes used for the simula- levels of the three tunnels (Fig. 20(b)). The slurry pressure

(a) (b)

Fig. 19. Finite element meshes for the tunnelling simulations with a cover depth of 2.25D (a) and 3.0D (b).

(a) (b)

Fig. 20. (a) Assumed initial preconsolidation pressures over depth and (b) corresponding overconsolidation ratios for the different cover depths of the
tunnel.

(a) (b)

Fig. 21. Computed surface settlements in point A of the monitoring section for different cover depths of the tunnel.
 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247 245

and the grouting pressure have also been adapted to the

depth of the tunnel according to the increase of the earth
and ground water pressure with depth. Figs. 21 and 22
show that for increasing cover depths the settlement trough
begins further ahead of the TBM, becomes wider, less steep
and less deep. This corresponds well with field observa-
tions. From a large amount of measurement data the
relationship
i ¼ Kz ð2Þ
between the distance i of the inflection point of the sur-
face settlement trough from the centreline and the depth
of the tunnel z was established in [32,25]. The best fit
for K was found to be 0.5 for cohesive soils. The inflec-
Fig. 22. Computed transverse profile of the final surface settlements in the tion points calculated from (2) with K = 0.5 are also
monitoring section for different cover depths of the tunnel. Inflection
points according to Eq. (2).
shown in Fig. 22. They correspond well with the com-

(a) (b)

Fig. 23. Computed TBM movement during the tunnel advance for different cover depths of the tunnel: (a) vertical deviation and (b) tilt angle.

(a) (b)

(c) (d)

Fig. 24. (a) Computed lining pressure in the monitoring section at time t = 1, (b) normal force in the monitoring section at t = 1, (c) bending moment in
the monitoring section at t = 1 and (d) uplift of the tunnel lining in the monitoring section for different cover depths of the tunnel.
246 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247

puted settlement troughs. Due to the increasing stiffness consolidation was obtained. A more rapid hydration
of the soil with increasing depth smaller tilt angles of of the grout material leads to a slight reduction of the
the TBM during the tunnel advance are necessary to keep surface settlements compared to a more slow hydration
the prescribed driving path (Fig. 23). According to characteristics. The cover depth not only influences the
Fig. 24(a)–(c), the cover depth is the most important fac- depth of the settlement trough, but also its size and
tor influencing the radial loading of the lining and the shape.
corresponding normal force and bending moment in the  The friction angle of the soil has a relatively strong influ-
cross-section of the lining. The lining pressure and the ence on the steering behaviour of the TBM. The smaller
ring force considerably increase with increasing cover the friction angle, the larger is the required tilt angle of
depth. Furthermore, the location of the maximum of the TBM. While the influence of the overconsolidation
the ring force is shifted from the invert towards the and the permeability on the necessary tilt of the TBM
springline. Since the difference between the lining pressure was found to be less significant and the stiffness evolu-
at the crown and at the invert on the one hand and the tion of the grout was found to be irrelevant, a relatively
lining pressure at the springline on the other hand in- strong influence of the cover depth resulting from the
creases, also a relatively large increase of the bending mo- increasing stiffness of the soil with increasing depth
ment can be observed. Due to the increased pressure in has been detected.
the excavation chamber and the increased friction along  As expected, the cover depth of the tunnel is the most
the shield skin a significant increase can also be observed important factor concerning the loading of the lining.
for the jack forces and, consequently, for the axial loading The computed ring normal force and bending moment
of the tunnel lining: the computed sum of the jack forces in the cross-section and the axial force resulting from
during the tunnel advance is 8.5 MN, 11.6 MN and 14.6 the jack forces considerably increase with the depth of
MN for cover depths of 1.5D, 2.25D and 3D. It should be the tunnel. As far as the soil properties are concerned,
pointed out that the influence of the other investigated larger maximum normal forces are predicted for smaller
parameters on the jack forces can be neglected. According friction angles and overconsolidation ratios. The influ-
to Fig. 24(d), the uplift of the tunnel behind the TBM be- ence of the permeability is less significant. The hydration
comes smaller for deeper tunnels due to the increasing characteristics of the tail void grout, however, affects the
stiffness of the soil and of the soil cover with increasing bending stresses in the lining. The faster the hydration,
depth. the larger is the maximum final bending moment in
the lining.
4. Conclusions

A three-dimensional finite element model for shield

Acknowledgement
tunnelling was used for parametric studies to analyse
the influence of different material parameters of the soil,
The financial support of this work by the German Na-
the stiffness development of the tail void grout and the
tional Science Foundation (DFG) under contract ME
influence of the cover depth for a shield-driven tunnel
1848/4 is gratefully acknowledged by the authors.
advance in homogeneous, soft, cohesive soil below the
ground water table. The finite element model takes into References
account all relevant shield tunnelling components and
realistically simulates the step-by-step tunnel advance. [1] Abu-Farsakh MY, Tumay MT. Finite element analysis of ground
Hence, this model allows for detailed and systematic response due to tunnel excavation in soils. In: Fernandez G, Bauer R,
numerical investigations of the various interactions editors. Geo-engineering for underground facilities. ASCE Geotech-
involved in shield tunnelling. The results and conclusions nical Special Publication No. 90. American Society of Civil Engineers;
1999. p. 514–25.
drawn from the numerical sensitivity studies are summa- [2] Abu-Farsakh MY, Voyiadjis GZ. Computational model for the
rised separately with respect to the surface settlements, simulation of the shield tunneling process in cohesive soils. Int J
the steering behaviour of the TBM and the loading of Numer Anal Met Geomech 1999;23(1):23–44.
the lining as follows: [3] Abu-Krisha AAM. Numerical modelling of TBM tunnelling in
consolidated clay. PhD Thesis, University of Innsbruck; 1998.
[4] Addenbrooke TI, Potts DM, Puzrin AM. The influence of pre-failure
 The strength characteristics and the overconsolidation soil stiffness on the numerical analysis of tunnel construction.
ratio of the soil are major factors influencing the soil Géotechnique 1997;47(3):693–712.
deformations in the vicinity of the shield machine and [5] Bernat S, Cambou B. Soil–structure interaction in shield tunnelling in
therefore have a considerable influence on the surface soft soil. Comput Geotech 1998;22(3/4):221–42.
settlements. The settlements increase nonlinearly for [6] Bezuijen A, Talmon AM. Grout properties and their influence on
back fill grouting. In: Bakker KJ, Bezuijen A, Broere W, Kwast EA,
decreasing values of the friction angle and the overcon- editors. Geotechnical aspects of underground construction in soft
solidation ratio. Only for soils with a higher permeabil- ground. Amsterdam: Balkema; 2005. p. 187–93.
ity an influence of the soil permeability on the [7] Blom CBM. Design philosophy of concrete linings for tunnels in soft
settlements leading to larger final settlements after full soils. PhD Thesis, Delft University; 2002.
 T. Kasper, G. Meschke / Computers and Geotechnics 33 (2006) 234–247 247

[8] Blom CBM, van Oosterhout GPC. Full-scale laboratory tests on a [23] Lee KM, Ji HW, Shen CK, Liu JH, Bai TH. Ground response to the
segmented lining, summary report. Delft University; 2001. construction of Shanghai metro tunnel-line 2. Soils Foundations
[9] Blom CBM, van der Horst EJ, Jovanovic PS. Three-dimensional 1999;39(3):113–34.
structural analyses of the shield-driven ‘‘Green Heart’’ tunnel of the [24] Maidl B, Herrenknecht M, Anheuser L. Mechanised shield tunnel-
high-speed line south. Tunn Undergr Space Technol ling. Berlin: Ernst und Sohn; 1996.
1999;14(2):217–24. [25] Mair RJ, Taylor RN, Bracegirdle A. Subsurface settlement profiles
[10] Borja RI. Cam-clay plasticity, part II: implicit integration of above tunnels in clays. Géotechnique 1993;43(2):315–20.
constitutive equation based on a nonlinear elastic stress predictor. [26] Mansour MAM. Three-dimensional numerical modelling of hydro-
Comp Met Appl Mech Eng 1991;88:225–40. shield tunnelling. PhD Thesis, University of Innsbruck; 1996.
[11] Dias D, Kastner R, Maghazi M. Three-dimensional simulation of [27] Melis M, Medina L, Rodriguez JM. Prediction and analysis of
slurry shield tunnelling. In: Kusakabe O, Fujita K, Miyazaki Y, subsidence induced by shield tunnelling in the Madrid Metro
editors. Geotechnical aspects of underground construction in soft extension. Can Geotech J 2002;39:1273–87.
ground. Amsterdam: Balkema; 2000. p. 351–6. [28] Meschke G. Consideration of aging of shotcrete in the context of a 3D
[12] Etac Grout Injection. Information brochure. Nieuwegein, viscoplastic material model. Int J Num Meth Eng 1996;39:3123–43.
Netherlands. [29] Meschke G, Kropik C, Mang HA. Numerical analyses of tunnel
[13] Finno RJ, Clough GW. Evaluation of soil response to EPB shield linings by means of a viscoplastic material model for shotcrete. Int J
tunneling. J Geotech Eng 1985;111(2):155–73. Num Meth Eng 1996;39:3145–62.
[14] Gens A, Potts DM. Critical state models in computational geome- [30] Nomoto T, Imamura S, Hagiwara T, Kusakabe O, Fujii N. Shield
chanics. Eng Comput 1988;5:178–97. tunnel construction in centrifuge. J Geotech Geoenviron Eng
[15] Hellmich C. Shotcrete as part of the New Austrian tunneling method: 1999;125:289–300.
from thermochemomechanical material modeling to structural anal- [31] Oota H, Nishizawa K, Hashimoto T, Nagaya J. Prediction of shield
ysis and safety assessment of tunnels. PhD Thesis, Technical tunnelling influences on ground deformation based on the construc-
University Vienna; 1999. tion process. In: Bakker KJ, Bezuijen A, Broere W, Kwast EA,
[16] Inokuma A, Fujimoto A. An improvement of FEM analysis in editors. Geotechnical aspects of underground construction in soft
ground settlement prediction in shield tunnelling. In: Mair RJ, Taylor ground. Amsterdam: Balkema; 2005. p. 275–81.
RN, editors. Geotechnical aspects of underground construction in [32] O’Reilly MP, New BM. Settlements above tunnels in the United
soft ground. Amsterdam: Balkema; 1996. p. 537–42. Kingdom - their magnitude and prediction. In: Jones MJ, editor.
[17] Kasper T. Finite Elemente Simulation maschineller Tunnelvortriebe Tunnelling ’82. IMM; 1982. p. 173–81.
in wassergesättigtem Lockergestein. PhD Thesis, Ruhr University [33] Schreyer J, Winselmann D. Eignungsprüfungen für die Tübbingaus-
Bochum; 2004 [in German]. kleidung der 4. Röhre Elbtunnel - Ergebnisse der Großversuche
[18] Kasper T, Meschke G. A 3D finite element simulation model for (Suitability tests for the lining of the 4th Elbe tunnel tube – results of
TBM tunnelling in soft ground. Int J Numer Anal Meth Geomech large scale tests). Tunnel 2000;1:34–44.
2004;28:1441–60. [34] Shirlaw JN, Ong JCW, Osborne NH, Tan CG. The relationship
[19] Kasper T, Meschke G. On the influence of face pressure, grouting between face pressure and immediate settlement due to tunnelling for
pressure and TBM design in soft ground tunnelling. Tunn Undergr the North East Line, Singapore. In: Kastner R, Emeriault F, Dias D,
Space Technol 2006;21(2):160–71. Guilloux A, editors. Geotechnical aspects of underground construc-
[20] Kasper T, Meschke G. Parametric studies for shield tunnelling in soft tion in soft ground. Spécifique; 2002. p. 311–6.
soils. In: Bakker KJ, Bezuijen A, Broere W, Kwast EA, editors. [35] Wongsaroj J, Borghi FX, Soga K, Mair RJ, Sugiyama T, Hagiwara
Geotechnical aspects of underground construction in soft ground. T, Bowers KH. Effect of TBM driving parameters on ground surface
Amsterdam: Balkema; 2005. p. 543–9. movements: channel tunnel rail link contract 220. In: Bakker KJ,
[21] Komiya K, Soga K, Akagi H, Hagiwara T, Bolton MD. Finite Bezuijen A, Broere W, Kwast EA, editors. Geotechnical aspects of
element modelling of excavation and advancement processes of a underground construction in soft ground. Amsterdam: Balkema;
shield tunnelling machine. Soils Foundations 1999;39(3):37–52. 2005. p. 335–41.
[22] Koyama Y, Sato Y, Okano N, Shimizu M. Back-fill grouting model [36] Wood DM. Soil behaviour and critical state soil mechanics.
test for shield tunnel. Quart Rep RTRI 1998;39:35–9. Cambridge: Cambridge University Press; 1990.