3D Numerical Simulation of Heading Face Support in PartiallySaturated Soils for Shield Tunnelling

7/30/2019 3D Numerical Simulation of Heading Face Support in PartiallySaturated Soils for Shield Tunnelling

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The 12th International Conference ofInternational Association for Computer Methods and Advances in Geomechanics (IACMAG)1-6 October, 2008Goa, India

3D Numerical Simulation of Heading Face Support in PartiallySaturated Soils for Shield Tunnelling

Felix Nagel, J anosch Stascheit, Gnther MeschkeRuhr University Bochum, Germany

Keywords: Finite Element Method, Shield Tunnelling, Theory of Porous Media, Partially Saturated Soil

ABSTRACT: This paper is concerned with the modelling of the cutting face support within a 3D-simulation model forshield tunnelling. While two-phase formulations for partially saturated soils are, in general, sufficient for numericalanalysis in tunnelling, a three phase formulation is required in cases, where compressed air is used to prevent waterinflow. This technique is frequently used in compressed air shields and in case of maintenance interventions, where

the repair of the cutting wheel is performed under compressed air conditions. In the presentation, a three phase modelfor partially saturated soil is formulated within the framework of the Theory of Porous Media and the effective stressconcept considering large deformations. The soil skeleton, the pore water and the pore air are considered as separatephases. The constitutive relations are described via the soil characteristic curve, relative permeabilities and the stressstrain relation for the soil skeleton. The paper also gives an overview on different possibilities of modelling of headingface support with such a model. Selected results from simulations of heading face support by means of compressedair in shield tunnelling are presented. These analyses demonstrate the capability of the presented model to describethe main time variant effects of two phase flow in partially saturated soils during mechanized tunnelling.

1 Introduction

In mechanized tunnelling surface settlements ahead, along and behind the TBM, resulting from interactions betweenthe face support, the conical TBM, the tail void grouting and the lining with the surrounding partially or fully saturatedsoil, may occur and have to be controlled by the appropriate choice of support measures. Since, in particular in urban

areas with sensitive existing infrastructure severe restrictions concerning the tolerable tunnelling-induced surfacesettlements are set by regulations, reliable prognoses of these settlements are an indispensable prerequisite for thedesign and a valuable tool for decisions to be made during the construction of mechanized tunnelling.

The representation of these interactions within a numerical model requires, besides the realistic representation of allrelevant components involved in shield tunnelling (the lining, the tail void grouting, the hydraulic jacks and the differenttypes of face support) a sufficiently realistic model for the fully or partially saturated soil. Whereas for the support bymeans of a support liquid or earth slurry a two phase soil model is generally sufficient even in the case of partiallysaturated soils, a three phase model considering compressed air as a separate phase has to be used if the facesupport by means of compressed air should be simulated numerically.

Only a relatively few number of simulation models for mechanized tunnelling have been proposed that allow for adetailed consideration of the shield supported tunnel construction as a time dependent problem (Komiya et al., 1999,Abu-Krisha, 1998. Kasper and Meschke, 2004). A relatively comprehensive and automated three-dimensional FE-model for simulations of shield-driven tunnels in soft, water saturated soil proposed by Kasper and Meschke, 2004 hasbeen successfully employed for the investigation of various design and process parameters (Kasper and Meschke,2005, 2006). Coupled numerical models for the simultaneous flow of air and water in partially saturated soil within theTheory of Porous Media (Bluhm and de Boer, 1997; Ehlers and Bluhm, 2002; Ehlers, 1996; Lewis and Schrefler,1999) is a topic of pertinent research in computational geomechanics (see, e.g. Ehlers and Graf, 2002, Sanavia et al.,2002). Applications of three phase models for the analysis of heading face support by means of compressed air withmulti-phase soil models have been performed by (ttl, 2003). The influence of interactions between supporting liquidand the pore water on the stability of the soil in front of the heading face was examined by measurements andanalytical models (Bezuijen et al., 2001, Broere 2002).

However, no numerical model seems to exist that combines both the realistic simulation of the construction processwith an advanced, fully coupled triphasic soil model capable to take into account the space and time variant

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interactions between the heading face support and the pore fluids on the soil deformations during tunnel advance. Inthe framework of the European Integrated Project TUNCONSTRUCT (URL: http//:www.tunconstruct.org) a finiteelement model (ekate) based on the object-oriented FE-code KRATOS (Dadvand et al., 2002) is being developed forthe simulation of shield driven tunnels as a part of an Integrated Design Support (Meschke et al., 2007).This model ischaracterized by a realistic consideration of the construction process in mechanized tunnelling involving all relevantcomponents and their complex interactions (Nagel, Stascheit and Meschke, 2008). It has been supplemented with anautomatic model generator allowing for a user-friendly generation of the simulation model (Stascheit, Nagel and

Meschke, 2007). Consideration of large deformations, which may be relevant for analyses of TBM tunnelling insqueezing ground conditions, are taken into account in the model.

In this paper, the three-phase soil model, implemented within the above described simulation model, and thecapabilities of this model to simulate heading face support in hydro and EPB shield tunnelling are presented. Thepaper is organized as follows: Section 2 describes the underlying theory of partially saturated soils. Section 3addresses consideration of different types of heading face support within this model. The applicability of the model fornumerical simulation of heading face support is demonstrated in Section 4.

2 Three-phase soil model for partially saturated soils

2.1 Partially saturated soil as a triphasic material

Partially saturated soil consists of three phases: the solid soil skeleton and the fluid phases water and air movingthrough the connected pore structure of the soil. In the context of engineering problems the exact geometry of the porevolume and the interactions of the phases within this pore volume are unknown and of minor interest. An up-scalingprocedure is required to describe the microstructural processes in terms of averaged quantities on a macroscopicscale. In the proposed model the Theory of Porous Media (TPM) (Bluhm and de Boer, 1997, Schrefler and Simoni,1988) is used. Within the TPM each phase has its own state of motion (see Figure 1) and is represented via its

volume fraction n and for the fluid phases(=w[ater], a[ir])via the degree of saturationS of the pore volume:

== nSdv

dvn (1)

For the fluid phases their motion within the pore volume is expressed in terms of the velocity sv relative to the soilskeleton, which leads in an integral form to the well known DARCY velocity

ss nS~ = vv (2)

Figure 1: Independent motion of the soil constituents soil skeleton, water and air

By averaging the states and interactions of the phases and their mixture using the TPM the problem can be expressed

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on a macroscopic scale by its governing balance equations. Considering geometrically nonlinear continuummechanics the pore volume can be derived from the mass balance of the soil as a function of the soil skeleton

displacements su as

( ) ( ) sen11n 0s uu div= (3)

The three phase model is characterized by balance equations for each of the phases expressed in terms of the actual

(deformed) configuration: the overall momentum balance of the mixture

0g =+div (4)where denotes the overall CAUCHY stress tensor of the mixtureandthe averaged density of the mixture and thebalance equations of the fluid phases, assuming isothermal conditions and neglecting phase interchange:

( ) += vdivnSDt

nSD0

s

. (5)

In the model air is treated as a compressible and water as an incompressible fluid. The primary variables of the modelare chosen to be the two fluid pressures and the soil skeleton displacements. The stress-strain relation of the soil

skeleton is formulated in terms of effective stresses s according to BISHOPs formulation (Bishop, 1956) for threephase continua

( ) ( )( )+= s awa S , (6)considering the stress states of the fluids. In general, the BISHOP parameter is a material function of the soildepending on the water saturation. Within the presented model the BISHOP parameter is assumed to be equal to thewater saturation wS . This is a common assumption and holds for a wide range of soils. The air phase is treated as anideal gas, using a linear relation between pressure and density after BOYLE-MARRIOTs law. The water content of thepore volume wS is described by the soil characteristic curve after VAN GENUCHTEN (van Genuchten and Nielson, 1985)(see Figure 2) as

mn

b

r

cw

min

w

max

w

min

w

p

p1)SS(SS

++= , (7)

where wSmax (wSmin ) are upper (lower) limits of the water saturation and

b

rp , m and n are model parameters.cp

indicates the pressure difference between water and air, also denoted as capillary pressure. Due to capillary effectswater is able to rise within the pore tubes against an air pressure. For a negative or low capillary pressure the watercan stay in all pores; with rising capillary pressure, however, the water can only exist in the smaller capillaries. Hence,the saturation decreases.

Figure 2. Pressure dependent saturation of the pore volume after VAN GENUCHTEN (van Genuchten and Nielson, 1985)(left), comparison of calculated saturation-dependent relative permeabilities and measurements (Mualem, 1976) (right)

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The fluid flow sv~ is described in terms of DARCYs law

( )gv s

= p

kgrad~ , (8)

where the permeability

k of the soil is given by the product of its intrinsic permeability 0k and a relative permeabilityrelk .

relk as a function of the saturation, which is equal to one if only the fluid fills the whole pore volume and

decreases for partially saturated case. This function is derived directly from the soil characteristic curve. For the flow ofthe water phase, w

relk is obtained as (Mualem, 1976)

( )2

m

m1

eew

rel S11Sk

= , (9)

withww

wwe

SS

SSS

minmax

min

= (10)

see Figure 2.

2.2 Computational Aspects

To allow for the modular implementation of different material models for soil in a large deformation context the spectraldecomposition of the deformation tensor was used (Simo, 1992; Simo and Meschke 1993). In the context of the finiteelement formulation of the model, the balance equations (4,5) are transformed to their corresponding weak forms anddiscretized in space and time. For the spatial discretization quadratic LAGRANGEan shape functions are used for thedisplacement field and linear approximations for the gaseous and liquid pressure while for the temporal integration themidpoint rule is adopted. The solution of the highly nonlinear discretized three-phase problem is based on NEWTONsmethod together with a consistently linearized tangent matrix. For further details of the triphasic formulation for soilsand its implementation see (Nagel, Stascheit and Meschke, 2007). The proposed model has been implemented intothe Finite Element software package ekate. This software, which is specifically designed for numerical simulations ofmechanized tunnelling is based upon the finite element kernel KRATOS. The triphasic model has passed validation by

means of the simulation of THERZAGHIs consolidation problem and the back-analysis of dewatering of a sand columntested in laboratory (Liakopolous, 1965).

3 Numerical modelling of heading face support

For shield supported tunnel advance in a closed mode the heading face beneath the groundwater level may besupported by one of the following support measures; (i) support by an earth slurry, (ii) a bentonite suspension or (iii) bymeans of compressed air. While in earth slurry shields the pressure of the slurry is directly transmitted onto the soilgrains, hydro or compressed air shields are characterized by the application of flow forces of the infiltrating supportfluid. The lower the permeability of the soil in front of the heading face the higher is the flow force, or in other wordsthe pressure gradient of the infiltrating support liquid, and the more effectively is the support pressure transmitted ontothe soil grains (see Figure 3). This effect is, to a large extent, attributed to the existence of a filter cake consisting of amaterial with a very low permeability sealing the heading face. In case of tunnelling with bentonite support this filtercake automatically evolves due to the infiltration of the bentonite suspension into the soil pores. In case ofcompressed air support during repair interventions such a filter cake may persist from an earlier bentonite support.

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Figure 3. Heading face support by means of a supporting fluid (air or bentonite suspension): pressure gradient andpressures on the soil for a support without filter cake (left) and with filter cake (right)

Due to the macroscopic nature of the three-phase formulation of the soil model, the micromechanical supportmechanism can not be taken directly into account. Within FE-simulations for the prediction of surface settlements dueto tunnel advance the heading face support therefore has to be modelled via adequate boundary conditions at the

heading face. While for mechanical support prescribed displacements and for earth pressure support a prescribedarea loading at the heading face is the adequate representation of the support mechanism, the question of adequateboundary condition is more difficult to answer for liquid or compressed air support, since these conditions depend onthe existence of a filter cake. If a perfect filter cake seals the heading face, the supporting liquid acts on animpermeable membrane and the prescription of a corresponding distributed load covers this situation (Kasper andMeschke, 2004, Kasper and Meschke 2006). However, the assumption that a perfect filter cake seals the heading faceis not valid in general.

For a slurry shield it could be shown that a filter cake builds up only for down time of the machine, whereas for theadvancement phase of the machine the evolving filter cake is excavated faster than the bentonite infiltrates into thesoil pores (Bezuijen et al., 2001). This has been corroborated by numerical analyses (Kasper and Meschke, 2004). Inthis case fluid pressures at the heading face should be prescribed. The supporting fluid flows into the pore volume andaffects the effective stresses and pore water pressures of the surrounding soil. The disturbance of the hydrostaticground water pressure by the slurry face support has been measured during the construction of the 2ndHeinenoordtunnel (Bakker et al., 1999). It was observed that the fluid flow due to heading face support resulted in

excess pore pressures within a distance of up to 3 times of the tunnel diameter in front of the heading face (Bezuijenet al., 2001). These excess pore pressures have a profound influence on the face stability (Broere, 2002) and theminimum required support may be considerably larger than for the standard case assuming a hydrostatic porepressure. This holds, in particular, also for compressed air interventions, where the filter cake may become ineffectivedue to the air flow drying the filter cake. A sufficiently realistic 3D-FEM model should be capable to describe theseeffects of heading face support and to consider these influences of the flow of the supporting medium on the state ofthe groundwater in the vicinity of the tunnel face. The soil model presented above allows for the consideration of theseeffects by the application of support liquid pressures at the heading face. In the following benchmark analyses thecapabilities of the model to account for a change in the pore liquid pressure distributions will be demonstrated for thecase of a compressed air support without filter cake.

4 Numerical Examples

A compressed air intervention of a tunnel with 10m diameter and 15m overburden has been simulated by means of

the proposed simulation model. Such an intervention may be conducted for a hydro shield if the excavation chamberhas to be entered by the working staff for a repair of the cutting tools. In such a situation the support fluid is beingreplaced temporarily by compressed air. Computations have been performed for 8 hours of compressed air support fortwo different types of soils. The following results show the influence of the support on the pore fluids for a soft soil withhigh permeability and one with low permeability with respect to water and air flow.

Within the simulation the surrounding soil has been modelled as an elastic material permeable for both water and air.The ground water level has been assumed at the ground surface. Besides the permeabilities against water and airflow the material parameters of the soil have been chosen as: density=2000 kg/m3, YOUNGs modulus E=5250kN/m2, POISSONs ratio= 0.45.The porosity of the soil is assumed as 20%. The soil characteristic curve is given byan air entry pressure of brp = 3kN/m

2, n=2.5 and m=0.4, which is corresponds to a sharp transition from the fullysaturated to the unsaturated case. The simulation started with an initial support liquid pressure equal to the

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undisturbed pore water pressure. During compressed air intervention, this prescribed water pressure at the headingface has been replaced by a constant air pressure of 253.4kN/m2.

4.1 Heading face support by means of compressed air in a soil with high permeability

Figure 4: Compressed air support in a soil with high permeability. Saturation of the pore volume with water after 8h(left), isolines for a pore air pressure of 220 kN/m2 (centre), isolines for a pore water pressure of 210kN/m2 (right)

The numerical analysis has been performed for a soil with an initial permeability for air flow of 14.4 cm/h and for waterflow of 144.0 cm/h. Due to the applied air pressure at the heading face air flows into the pore volume by replacing thepore water. A partially saturated zone establishes in front of the heading face which extends during the compressed airintervention up to a size of approximately 1 D in front of the tunnel face (see Figure 4). It can be observed that anunsaturated or nearly unsaturated zone evolves the longer the intervention lasts. Due to air inflow an air pressuredistribution within the soil volume establishes which affects the soil deformations within the partially saturated zoneand the water in the vicinity of the tunnel face. The zone of excess pore pressures extents up to 1.5 D in front of thetunnel face. Due to the high permeability of the soil this excess water pressure reached its maximum shortly after thebeginning of the intervention and dissipates again fast afterwards (see Figure 4).

4.2 Heading face support by means of compressed air in a soil with low permeability

Figure 5: Compressed air support in a soil with low permeability. Saturation of the pore volume with water after 8h(left), isolines for a pore air pressure of 220 kN/m2 (centre), isolines for a pore water pressure of 210kN/m2 (right)

For the second example the initial permeability of the soil has been assumed as ~100 times larger compared to theprevious example (0.12 cm/h for air flow of and 1.58 cm/h for water flow). The inflow of air and the low permeability ofthe soil against an air flow results in a comparably smaller unsaturated zone in the vicinity of the tunnel. A zone ofexcess pore water pressure extending ~1 D in front of the heading face is observed. In contrast to the previousexample, however, this excess pore water pressure does not dissipate fast but remains during the complete duration

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of the compressed air intervention (see Figure 5).

5 Conclusions

A numerical simulation model for partially saturated soils has been presented in the context of a 3D simulation model(ekate) for numerical simulations of shield tunnelling. The proposed formulation of the soil within the framework of theTheory of Porous Media in conjunction with the simulation model allows consideration of different types of heading

face support by taking into account the interaction of the support liquid and the pore water of the surrounding soil. Inparticular, the triphasic coupled formulation of partially saturated soils offers the possibility to simulate the applicationof compressed air as a supporting medium at the tunnel face. This may be relevant in case of repair interventionsduring mechanized tunnelling in fully or partially saturated soils. Numerical benchmark analyses of a compressed airintervention in tunnel have demonstrated that the proposed model covers the main effects connected with theinteractions between the face support and the groundwater. Further extensions of the model will include the effect ofthe changing filter cake during the construction phases with consideration of driving and still-stand phases. The modelis designed as a part of an Integrated Design Support System currently being developed in the framework of theEuropean Research project TUNCONSTRUCT. Results from numerical analyses employing the presented simulationmodel may be used within the design and construction process for the assessment of the soil stability in front of theheading face, for the prediction of settlements due to the construction process and for the determination of designacting on the tunnelling machine and the lining and the amount of compressed air needed to conduct the interventionin case of compressed air interventions.

6 Acknowledgements

This work has been supported by the European Commission within the Integrated Project TUNCONSTRUCT(IP011817-2). Co-funding to the first two authors was also provided by the Ruhr University Research-School funded bythe DFG in the framework of the Excellence Initiative. This support is gratefully acknowledged.

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3D Numerical Simulation of Heading Face Support in PartiallySaturated Soils for Shield Tunnelling