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Analysis of the stand-up time of the tunnel face

R. Schuerch(1)

, G. Anagnostou(1)

(1)ETH Zurich, Switzerland

ABSTRACT: We present a computational method and dimensionless design diagrams for the estimation of the

stand-up time of the tunnel face in a low-permeability, saturated, water-bearing soft ground. The design diagramscover a wide range of typical soft ground parameters and apply to a shallow tunnel whose overburden is equal toone diameter. Under the considered conditions, the time-dependency of the face stability is caused by theconsolidation and excess pore pressure dissipation process in the soil ahead of the face. Consequently, weanalyse the ground response to tunnel excavation by means of hydraulic-mechanically coupled, spatial stressanalyses. This approach is theoretically demanding both with respect to the failure criteria and to the numericalanalysis scheme. The presented results are important from a tunnel engineering point of view, because a shortstand-up time may require the implementation of costly and time-consuming auxiliary measures such as grouting,face reinforcement or ground freezing.

1 Introduction

This paper investigates the time dependent stability of the tunnel face assuming that all time effects

are due to the consolidation process of the ground. This assumption is reasonable for shallow tunnelscrossing water-bearing soils. In the analysed problem, the unsupported tunnel face remains stable

under the undrained conditions prevailing after excavation (short-term), but collapses before reaching

the drained conditions prevailing at steady state (long term). The paper focuses on the transient

conditions between these two extremes. The topic is important for low and medium permeability soils

such as the glacial deposits which are widely present in Central Europe.

The response of the ground to excavation under transient conditions is governed inherently by the

strong interaction between seepage flow and soil deformation. For this reason face collapse cannot be

investigated by the traditional approach based upon a kinematic assumption of the failure mechanism

(e.g. Anagnostou and Kovri, 1994, Davis et al. 1980), but only through a fully coupled hydraulic-

mechanical stress analysis. Due to the complexity of the problem, few works have addressed this

topic: Hfle et al (2009) investigated the stability of the unsupported face during on-going tunnel

excavation, while Ng and Lee (2002) estimated the necessary face reinforcement as a function of theconsolidation time. There is also relatively little research work on the similar problems of delayed

failure of slopes and excavations (e.g. Holt and Griffiths, 1992, Potts et al., 1997, Vaughan and

Walbancke, 1973).

2 Computational model

The numerical analysis is carried out using the FE program Abaqus (Dassault Systmes, 2011).

Figure 1 shows the numerical model. The ground is discretized by 8-node brick elements (C3D8P).

The element size varies from 0.5 m (close to the tunnel face) to 6 m (at the model boundary).

The water table is taken equal to the elevation of the ground surface (Hw= H). No-flow conditions are

imposed at the tunnel wall (which is true for a practically impervious lining) and at the symmetry plane.

The hydraulic potential at the tunnel face is assumed equal to the elevation (seepage face).

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Figure 1. Numerical model

Table 1. Assumed material constants

Unit weightJ' [kN/m3] 10Youngs modulusE [MPa] 20Poissons ratioQ [-] 0.3Angle of internal frictionM' [] 15, 25 or 35Dilatancy angle\' [] 0Cohesionc [kPa] 530Coeff. of lat. pressure K0 [-] 0.5 or 1.0

Permeabilityk [m/s] 10-7

At the far field boundaries, the potential is fixed to its initial value (which is true if there is no draw-

down of the water table). The tunnel lining is simulated in a simplified way by fixing all nodal

displacements at the excavation contour.

The initial stress field corresponds to the overburden pressure at each point. The analyses have been

performed for two values of coefficient of lateral pressure (K0 = 0.5 and 1.0) corresponding to different

degrees of consolidation of the soil.

The ground is modelled as an isotropic, linearly elastic and perfectly plastic material obeying the Mohr-

Coulomb yield criterion. Non-dilatant plastic behaviour is assumed. The Abaqus subroutine UMAT,

which performs the integration of the elasto-plastic incremental equations, is according to Clausen et

al. (2005). Table 1 summarizes the parameters considered in the analysis.

The tunnel face stability under transient conditions is investigated by means of a numerical analysis of

the consolidation process. The analysis starts by simulating the excavation as an undrained process.This is achieved by reducing practically instantaneously (i.e., in very short time intervals) the total face

support pressure from its initial value (horizontal in situ stress) to zero. Atmospheric pressure

conditions at the tunnel face are imposed during the consolidation process.

3 Failure identi fication

Since we wish to study the evolution of face stability over time, the ground parameters are selected

such that the unsupported tunnel face will be stable under undrained conditions, but fail under drained

conditions.

Schuerch and Anagnostou (2012) show that the identification of failure in coupled problems is only

possible by observing and evaluating simultaneously the time-development of the displacements,

volumetric strains and effective stresses at certain control points (points A, B and C in Fig. 4). At theultimate state, re-distribution of the stresses in the ground is no longer possible. At this time the

effective stresses remain constant while the displacements continue to increase.

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-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12

u

[m]

t [h]

-0.05%

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

0 2 4 6 8 10 12

Hvol

[-]

t [h]

Nearly ultimate state

B

A

C

uA,x

uB,x

uA,z

uC,z

uC,x

uB,z

ts

Figure 2. Time development (a) of the displacements (ux,uz) and, (b), of the volumetric s train (Hvol) atpoints A, B and C of Fig. 4 (c=20 kPa, M = 25, K0 = 1.0, other parameters acc. to Table 1)

A constant effective stress field means that the elastic volumetric strains also remain constant. As the

assumed plastic behaviour is non-dilatant, the volumetric strains are equal to elastic ones and,

consequently, they also remain constant at collapse.

Consider, for example, the time development of displacements and volumetric strains for a numerical

example (Fig. 2). According to Figure 2a, the displacements increase rapidly after 9 hours and tend to

infinity at about 11 hours. The rapid evolution of the displacements indicates that the system is

approaching the ultimate state. According to Figure 2b the volumetric strains tend to a constant value

at 10.2 hours. Figure 4 shows that at this time the plastic zone reaches the ground surface. Although

both the extent of the plastic zone and the magnitude of the displacements consistently indicate that

the system approaches the ultimate state at about ts = 10.2 hours, it should be noted that the quality of

the numerical solution decreases close to collapse and that at this time the numerical solution

becomes unstable. For this reason the values do not reach a constant value (Schuerch and

Anagnostou, 2012).

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4 Stand-up time of the tunnel face

The time-dependency of the stability of the tunnel face was investigated by varying systematically the

ground parameters according to Table 1. For dimensional reasons and due to the structure of the

equations underlying consolidation theory, a dimensionless stand-up time can be defined tskE/(J'D2)

which is a function of the normalized cohesion c/(JD) and of the other parameters (, K0, \, Q, H/D,

Hw/H, Jw/J). Note that if the permeability or Youngs modulus is higher by a factor of ten, the stand-uptime will be ten times shorter.

Figure 3 shows the dimensionless stand-up time as a function of the normalized soil cohesion for

three values of the friction angle and for K0 = 0.5 or 1.0. The marked point of every line indicates the

limit of validity of the numerical solution. (For higher values ofc/(JD) the numerical solution becomes

unreliable because tensile stresses develop in the model.) According to Figure 3, the stand-up time

depends strongly on the cohesion and on the friction angle of the ground (cf. Schuerch and

Anagnostou 2013).

It is interesting to note that the stand-up time depends considerably also on the coefficient of lateral

pressure, although this parameter does not have any influence on the safety factor in the uncoupled

problem (Vermeer and Ruse, 2001). Figure 4 shows the contours of the short-term plastic zone (i.e.,

the one developing under undrained conditions) for a coefficient of lateral pressure K0 of 0.5 or 1.0.

ForK0 = 0.5, the plastic zone is more developed toward the surface than forK0 = 1.0. This is becauseunder undrained conditions the shear resistance of the ground depends essentially on the mean initial

stress (Broms and Bennermark, 1967), which is higher in the case of K0 = 1. Consequently, a low

coefficient of lateral pressure is unfavourable with respect to the time-development of stability. At

failure, however, the extent of the plastic zone is very similar for the two values ofK0 (Fig. 5).

5 Application example

Figure 6 shows the stand-up time as function of the permeability for an application example. The

diagram was obtained from the dimensionless design diagram of Figure 3 by means of simple

calculations for given cohesion, unit weight, friction angle, Youngs modulus of the ground and tunnel

diameter (see inset in Fig. 6). According to Figure 6, for a permeability of k = 10-8

m/s, the stand-up

time varies between about 10 hours and 4 days depending on the coefficient of lateral pressure.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.05 0.1 0.15 0.2 0.25 0.3

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.05 0.1 0.15 0.2 0.25 0.3

M' = 35

M' = 25

> @'

'

c

DJ> @

'

'

c

DJ

>

@

2

'st

kE

D

J

>

@

2

'st

kE

D

J

K0 = 0.5 K0 = 1.0

M' = 15

M' = 35

M' = 25

M' = 15

Figure 3. Dimensionless diagrams for the determination o f the stand-up time of the tunnel face (\=0,Q=0.3, H/D=1, Hw/H=1, Jw/J=1)

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6 Closing remarks

The tunnel face may be stable in the short term, but collapse after a certain time period. This happens

more or less rapidly depending on the permeability, the Youngs modulus, the coefficient of lateral

pressure and the effective shear strength parameters of the ground. The stand-up time of the tunnel

face is important in engineering practice, especially in medium- and low-permeability water-bearing

ground. Numerical analyses provide useful indications regarding the stand-up time, but their resultsmay be mesh sensitive. This issue is subject of ongoing research.

7 Acknowledgements

This paper evolved within the framework of the research project "Tunnel face stability and tunnelling

induced settlements under transient conditions". The support given to this project by the Swiss

Tunnelling Society (STS) and the Federal Road Office of Switzerland (FEDRO) is greatly appreciated.

Ground surface

z

x

0 5 10 15 20

A

C

B

K0 = 0.5

K0 = 1.0

Figure 4. Contour o f the shor t-term plastic zone (c=20 kPa, M = 25)Ground surface

0 5 10 15 20

z

x

K0 = 0.5 (ts = 1.1 h)

K0 = 1.0 (ts = 10.2 h)

Figure 5. Contour of the plastic zone at ultimate state (c=20 kPa, M = 25)

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1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06

ts

k [m/s]

1 hr

1 month

1 year

10 years

K0 = 0.5

K0 = 1.0

10 hours

4 days

E' = 20 MPac' = 20 kPaQ= 0.3M' = 25

\ '= 0

J'= 10 kN/m3

D = 10m

H/D= 1

Hw/H= 1Jw /J'= 1

Figure 6. Stand-up time ts of the tunnel face as a function of t he ground permeability k

8 References

Anagnostou, G., Kovri, K., 1994. The face stability of slurry-shield driven tunnels. Tunn Undergr Space Technol(9): 65174.

Broms, B.B., Bennermark, H., 1967. Stability of vertical openings. Journal of the Soil Mechanics and FoundationsDivision 93: 7194.

Clausen, J., Damkilde, L., Andersen, L., 2005. An efficient reurn algorithm for non-associated Mohr-Coulombplasticity. In Proceedings of the Tenth International Conference on Civil, Structural and EnvironmentalEngineering Computing, B. H. V. Topping Ed., Civil-Comp Press. United Kingdom: Stirling.

Dassault Systmes, 2011. Abaqus 6.11, Theory Manual.

Davis, E.H., Gunn, M.J., Mair, R.J., Seneviratne, H.N., 1980. The stability of shallow tunnels and undergroundopenings in cohesive material. Gotechnique (30): 397416.

Hfle, R., Fillibeck, J., Vogt, N., 2009. Time depending stability of tunnel faces. In Proceedings of the 35th ITAAITES General Assembly, Budapest.

Holt, D.A., Griffiths, D.V., 1992. Transient analysis of excavations in soil. Computers and Geotechnics (13): 159174.

Ng, C.W.W., Lee, G.T.K., 2002. A three-dimensional parametric study of the use of soil nails for stabilizing tunnel

faces. Computers and Geotechnics 29: 673697.

Potts, D.M., Kovacevic, N., Vaughan, P.R., 1997. Delayed collapse of cut slopes in stiff clay. Gotechnique (47):953982.

Schuerch, R., Anagnostou, G., 2012. Tunnel face stability under transient conditions: stand-up time in lowpermebility ground. In Proceedings of the 22nd European Young Geotechnical Engineers Conference,Gothenburg.

Schuerch, R., Anagnostou, G., 2013. The influence of the shear strength of the ground on the stand-up time ofthe tunnel face. In Proceedings of the International Symposium on Tunnelling and Underground SpaceConstruction for Sustainable, Seoul.

Vaughan, P.R., Walbancke, H.J., 1973. Pore pressure changes and the delayed failure of cutting slopes inoverconsolidated clay. Gotechnique 23: 531539.

Vermeer, P.A. , Ruse, N., 2001. Die Stabilitt der Tunnelortsbrust in homogenem Baugrund. Geotechnik 24(3):186-193.

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