comparing numerical alternatives to model jet grouting in tunnels

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Comparing Numerical Alternatives to

Model Jet Grouting in Tunnels

M. Barla*, J. Bzowka**

* Department of Structural, Building and Geotechnical Engineering,

Politecnico di Torino, Italy

** Silesian University of Technology, Department of Geotechnics,

Gliwice, Poland

ABSTRACTThe paper deals with the numerical modelling of jet grouting in tunnels by the Finite Element

Method. Three different FEM approaches to reproduce the grouted umbrella are compared.

Reference is made to the case study of the Aescher tunnel, excavated in Switzerland.Considerations and suggestions, useful at the modelling stage, are given based on the results

obtained.

KEYWORDS: Jet grouting, tunnelling, numerical modelling

INTRODUCTION

Jet grouting was developed in Japan in the mid-1960s. The original developments and studieswere conducted around 1965 by the Yamakado brothers. The Chemical Churning Pile (CCP)

method originally developed by Nakanishi and co-workers used chemical grouts as the jetting

medium.

By 1972, the CCP group in Japan developed the “Jumbo Special Pile” (JSP) method using

compressed air as an envelope around the grout jet to give column diameters of 80 to 200 cm.Meanwhile, a “Jet Grout Pile” (JGP) method was being simultaneously developed by another

independent group, and JSP and JGP merged around 1980 into the “Jumbo Jet Special Grout”

(JSG) method. The major rival group, headed by Yahiro had also developed in 1970 the “Jet

Grout” (JG) method (Xanthakos et al., 1994).

At present date, the jet grouting method is currently applied in a number of engineering

construction environments (Brill et al. 2003). This includes also tunnels where jet-grouting is

usually used to create a reinforced umbrella, ahead of the tunnel face, to protect excavation (e.g.Bruce et al. 1987, Mussger et al. 1987, Barla et al. 1988, Pelizza & Peila 1993, Barla 1997). Jet

grouting can also be used to improve soil characteristics at the foundations of the steel sets. It isundoubtedly that jet grouting proved to be a very effective measure in specific ground conditions

(shallow tunnels, weak ground, conventional excavation method) but, as a matter of fact, a number

of arguments related to numerical modelling of the effect of the reinforced columns still remain

unclear.

This paper deals with the numerical modelling of jet grouting in tunnels by the Finite Element

Method. Three different FEM approaches to reproduce the grouted umbrella, commonly adopted

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in practice at the design analysis stage, will be compared. Reference will be made to the case study

of the Aescher tunnel (Coulter & Martin 2006), excavated in Switzerland. The scope of this paper

is to discuss the merits and the drawbacks of the different approaches and not that of best backanalyse the tunnel behaviour. Therefore, simplifications are introduced in the numerical simulation

scheme.

THE AESCHER TUNNEL

General overview

The case study of the Aescher tunnel (Figure 1 and 2) is an interesting application of jetgrouting in tunnels, well described in the geotechnical literature (Coulter 2004, Coulter & Martin

2006).

The Aescher tunnel consists of two parallel, two-lane highway tunnels (Bazel and Luzern)

excavated through rock and soft ground under a maximum cover of 70 m. The Basel tunnel lies to

the north of the Luzern tunnel, carrying traffic in the direction of Basel (northwest), while the

Luzern tunnel carries traffic in the southeast direction, towards Luzern. The Basel and the Luzerntunnels are respectively 2055 m and 2090 m. The distance between the two tunnel centerlines is

32 m. The tunnels were constructed by the conventional method, comprising a top-heading (75 m2)

and a subsequent bench excavation (81 m2). The schematic cross section is shown in Figure 3.



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Figure 1: Aescher tunnel plan view (a) and geological longitudinal section (b) (Coulter &

Martin 2006)



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Figure 2: Aescher tunnel East portal (Coulter & Martin 2006)

Geological-geostructural context

The general stratigraphy is described by Coulter & Martin (2006) as a thin fluvial deposit

overlying glacial moraine. The fluvial deposit consisted of a cohesionless fine silty sand strata, up

to approximately 10 m thickness, with a unit weight of 19 kN/m3 and a friction angle equal to 30°.

Ground water was present in this deposit, perched on top of the glacial moraine.

The glacial moraine consists of a brown clayey sand and silt, with gravel and isolated

boulders. The moraine was observed to be dry during the geological investigation and the

excavation of the tunnel, although a few water bearing lenses of silty sand and gravel were present.

The properties of the moraine, given by Coulter & Martin (2006), are:

- elastic modulus: 80 MPa,

- unit weight: 22–23 kN/m3,

- effective cohesion: 5 ÷ 20 kPa,

- effective friction angle: 32° ÷ 35°.

The Molasse bedrock which underlies the moraine changes several times throughout the tunnel

drive. The bedrock consists of layered sandstone, siltstone, marl and clay marl. Typical parametersfor the Molasse used for tunnel design (Coulter & Martin 2006) were;

- elastic modulus: 2 GPa,

- unit weight: 25 kN/m3,

- cohesion: 1 MPa,

- friction angle: 40°.

When the tunnel was excavated into the glacial moraine, the installation of jet grouting

umbrella was used to reduce settlements. The jet-grout umbrella for the Aescher tunnel consistedof 39 columns (Figure 3). The columns had a specified diameter of 600 mm with a spacing of

450 mm, between the boreholes, at the tunnel face, to ensure overlapping columns. The temporary



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support consisted of welded wire mesh and steel lattice griders and 400 mm of shotcrete. The

invert was closed with welded wire mesh and 200 mm of shotcrete.

The cross section of interest in this paper (chainage 1000 m) was excavated at 14.7 m depth, in

the moraine layer.

Figure 3: Cross section of the Aescher tunnel showing the top-heading and bench

excavation sections and the jet-grouting columns (modified from Coulter & Martin 2006)

NUMERICAL MODELLING

Model geometry

A finite element numerical model was set up to reproduce the geometry of the Aescher tunnel.

The Phase2 code (Rocscience 2007) was used to this purpose. Figure 4 shows the mesh

dimensions and the boundary conditions adopted. The mesh is composed by six-noded triangles,with an increased density close to the excavation boundaries and between the tunnel and the

surface. Horizontal displacements are prevented along the vertical boundaries. Rollers are alsoused to prevent vertical displacements at the bottom boundary. No restraints are imposed to the top

boundary.



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Figure 4: Finite element mesh and boundary conditions

Material properties and stress state

An elastic perfectly plastic behaviour with a Mohr-Coulomb failure criteria was considered forthe different soil layers. The geotechnical parameters adopted in the numerical analyses are given

in Table 1 and were derived from the geotechnical characterisation described above.

Preliminary analyses were performed by assuming an elastic perfectly plastic behaviour for the

jet grouting with the parameters listed in Table 1, which considers the evolution of strength andstiffness versus the curing time (Coulter & Martin 2006). These analyses showed that the jet

grouting columns remain in the elastic domain during and after excavation. The tunnel lining wasconsidered elastic with properties given again in Table 1. Gravity loading was activated and a

stress ratio of 0.5 was considered.

Table 1: Mechanical parameters used in the numerical analyses

E

c'

peak

c'

residual '

peak

'

residualσt

[kN/m3] [MPa] [-] [MPa] [MPa] [°] [°] [MPa]

Sand 19 35 0.2 0.015 0.015 30 30 0.020

Moraine 22 80 0.2 0.020 0.020 40 30 0.024

Bedrock 25 2000 0.2 1 1 40 40 1.20

Jet grouting 22 900 0.2 1.3 1.3 35 35 1.86

Tunnel lining 25 30000 0.2 - - - - -

Analysis sequence

The FEM analyses were performed in two stages in order to simulate the construction processof the top heading only. Simplifications were introduced in the numerical simulation scheme, as

already mentioned. The analyses do not consider the correct sequence of installation of the single

jet grouting columns, they have been considered installed all in one single step.

The two different stages are described below and shown in Figure 5:

200 m

40 m36.3 m

6.9 m



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Stage 1: where the in situ state of stress is applied to the model, the jet grout injection is

simulated by accounting for one of the three methods discussed below and the tunnel

heading is excavated. A stress release of 20% is applied at this stage to simulate the 3Deffect, thanks to the staged loading option of Phase2.

Stage 2: where the remaining 80% of stress release is applied together with the installationof the temporary lining.

STAGE 1 STAGE 2

Application of the in situ state of stress to the model,simulation of the jet grout injection and top heading

excavation by applying a stress release of 20%

Installation of the temporary lining together with anadditional 80% of stress release.

Figure 5: Stages of the numerical analyses

In order to simulate the effect of the jet grouting columns, the following three different

methods were considered in the FEM analyses (Figure 6):

1. METHOD A: jet grouting columns are simulated by applying the correspondent material properties to the finite elements belonging to the reinforced arch at the crown. In this case,the geometry of the arch is very simple and continuity of the soilcrete is considered always

effective. The total number of finite elements in the mesh is 3225.

2. METHOD B: the jet-grouting umbrella is simulated by accounting for the original circular

geometry of each column. The interaction and continuity between the columns is effective

within their intersection only. Again the mechanical parameters of soilcrete are applied tothe finite elements belonging to the jet grouting columns. The overall model geometry is

more complicated in this case and the total number of elements increases to 9431.

3. METHOD C: the jet-grouting umbrella effect is simulated by introducing a structural

interface (a standard beam plus two joints). The geometry of the umbrella is not properlyreproduced as its thickness is not considered (it is considered though in the structural

element properties together with stiffness and strength). The structural interface in Phase2

is constituted by three elements: an external joint, a liner and an internal joint. The beam is

connected by the nodes to the finite element mesh and sliding can occur along the joints.

The total number of elements (2401) is significantly reduced with this method.

The three methods above are among those commonly used in practice at the design analysis

stage.



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Figure 6: Three different methods adopted to simulate the consolidated jet grouting arch.

METHOD A

METHOD B

METHOD C



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Analysis results

Results of the numerical analyses performed are described in this paragraph. Since consistent

parameters were adopted in the numerical analyses performed with the three different methods, the

results are compared in order to highlight differences and similarities.

For each method, maximum principal stress, yielded elements and vertical displacements at

the end of Stage 2 are shown in Figure 7. A fundamental aspect concerns the stress redistribution

in the ground occurring after the top heading excavation. Arching effect is generated and stressesare redistributed to the bench, unloading the crown. As shown in Figure 7, yielding occurs at the

corners.

The analyses show the initiation of two shear bands. This is particularly evident for methods B

and C, less for method A. Tensile failure is generated at the foot of the reinforced arch (for methodB also between the single columns). It is important to underline that shear bands are not fully

developed which is a clear indication of the stabilising effect of the jet grouting umbrella, which

limits tunnel convergence.

If the attention is now moved to the effect of tunnelling on the surface (i.e. subsidence),

surface settlements obtained from the numerical models are compared in Figure 8 to the empiricalrelationship by Peck (1969) and to monitoring data.

Maximum principal stress σ1 [MPa]and yielded elements

Vertical displacements [m]

Method

A

Method

B

F ıgure 7 cont ınues on the next page



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Method

C

Figure 7: Maximum principal stress σ1 and yielded elements (left) and vertical

displacements (right) with the three methods at the end of stage 2.

Figure 8: Computed settlements troughs compared to monitoring data.

Monitoring data show a maximum vertical displacement equal to 25 mm. The settlement

under tunnel centreline is well reproduced by all the analyses performed. The best fit is obtained

by Method B, while the other two methods, A and C, show slightly lower or higher valuesrespectively. The small difference between Methods A and B is dependent to the fact that the first

method has a larger area of finite elements belonging to the reinforced material. In the case ofMethod C instead the displacement computed are strongly dependent to the joints parameters of

the structural interface which, in general, are not straight forward to define. At the same time, it is

-80 -40 0 40 80Distance from tunnel centerline [%]

-0.03

-0.02

-0.01

0

V e r t i c a l d i s p

l a c e m e n t [ m ]

Monitoring data

Peck's equation

Method A (Arch)

Method B (Columns)

Method C (Beam)



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clear that Methods A and B suffers from the full bonding (i.e. no relative sliding is possible)

between the finite elements pertaining to the moraine and those of the reinforced soil.

Larger difference is shown in the comparison to the other monitored data, at a given distance

from the tunnel centreline. It is well known that continuum numerical models show limitations in

predicting tunnelling induced settlements and are unable to effectively represent the formation ofthe shear bands which are dependent to the finite element mesh discretization (Zienkiewicz et al.

1995, Sterpi 1999). Being the scope of this paper that of comparing numerical alternatives,

keeping simple the procedure, the Authors did not investigate this point further, adding complexityto the analyses. However this would have allowed to reduce the scattering from the monitoring

data and reduce wideness of the settlement trough.

The numerical models show similar results among them and in fair agreement with the

monitoring data, allowing one to conclude that the geometry of the jet grouting arch does notrepresent a key point when the interest is to determine surface settlements induced by tunnelling at

the design analysis stage. Results from the numerical models A and B are definitely comparable

showing that it is useless to simulate the real geometry of the columns. Method A is to be

preferred being the mesh set up easier and the calculation faster. However, using beam elements

(where the true geometry is not fully considered within the mesh) seems to be more conservativethan adopting finite elements to simulate the reinforced arch and has the drawback of the need to

appropriately define joints parameters.

CONCLUSIONS

The main conclusions of the work performed so far can be summarised as follows:

- jet-grouting remains in the elastic state, in the case of interest;

- the jet-grouting effect can be effectively simulated by the Finite Elements Method in plane

strain conditions by adopting relatively simple methods, even though the problem is clearlythree-dimensional, when the interest is on the prediction of maximum ground settlements;

-

the three jet grouting simulation methods do not show fundamental differences in allowing oneto obtain realistic results, therefore the choice among the available methods should be driven by

consideration over computational time and easiness in meshing.

ACKNOWLEDGEMENTS

The Authors wish to thank G. Ragazzo who performed the numerical analyses described in

this paper.

REFERENCES

1. Barla G., Rabagliati U., Fidato C., Cavalli T. 1988. Observation and monitoring for the

design of stabilization measures by the jet-grouting method at the Valsesia tunnel. Proc.

Gruppo Nazionale di Coordinamento per gli Studi di Ingegneria Geotecnica, Convegno diMonselice. Pp. 93-106.

2. Barla G. 1997. Panel discussion: Tunnelling for Turin railway link. Proceedings of the 14 th

International Conference on Soil Mechanics and Foundation Engineerin, Hamburg, 6-12

September 1997. A.A. Balkema Editor. Vol. 4, pp. 2387-2390.

3. Brill, G.T., Burke, G.K., Ringen, A.R., 2003. A ten year perspective of jetgrouting:

advancements in applications and technology. In: Johnsen, L., Bruce, D.A., Byle, M. (Eds.),Proceedings of the 3rd International Conference – Grouting and Ground Treatment, New



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Orleans, vol. 1 of Geotechnical Special Publication No. 120, American Society of Civil

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9. Pelizza S., Peila D. 1993. Soil and rock reinforcements in tunnelling. Tunnelling andUnderground Space Technology, Volume 8, Issue 3, July 1993, Pages 357-372.

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International Journal for Numerical and Analytical Methods in Geomechanics 23 (13), 1427– 1454.

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Zienkiewicz, O.C., Huang, M., Pastor, M., 1995. Localization problems in plasticity usingfinite element with adaptive remeshing. International Journal for Numerical and Analytical

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