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

Numerical Simulation of Mechanized Tunnelling as Part of an Integrated Optimization Platform for Tunnelling Design

G. Meschke, F. Nagel, J. Stascheit Institute for Structural Mechanics, Ruhr-University Bochum, Germany

M. Stavropoulou, G. Exadaktylos Dept. of Mineral Resources Eng., Technical University of Crete, Chania, Greece

Keywords: Mechanised Tunnelling, Finite Element Method, Tunnelling Design, Optimization

ABSTRACT: Mechanised tunnelling is characterised by a number of interacting components relevant for the ex-cavation process (the soil including groundwater, the TBM, the linings, the support at the cutting face and the tail void) and by a staged process of excavation and lining erection. This imposes a considerable challenge for real-istic modelling of the tunnelling process. The paper addresses recent advances in computational modelling of shield tunnelling. It is shown, how a three-dimensional finite element model, which is able to adequately repre-sent the aforementioned components and their interactions, may be used for reliable predictions of the interac-tions between the excavation process and the soil within the design stage as well as in the construction stage. The paper also highlights the role of numerical simulations in the context of an integrated optimization Platform for Tunnelling (IOPT) currently being developed within the European research project “Technology Innovation in Underground Construction” (TUNCONSTRUCT). Since for more or less similar ground conditions different de-signs are often used and the selection of construction methods is often biased by personal experience, this plat-form shall finally constitute a decision support system providing a systematic guidance through the complete process of the design of machine-driven tunnels.

1 Introduction

Shield tunnelling allows for tunnel advances in a wide range of geological environments including difficult condi-tions such as high ground water pressures, soft soils or small cover depths. It is characterised by a relatively complex construction process and complex interactions between the ground, the supporting measures at the face and the tail void and the tunnel boring machine (TBM) (Maidl et al, 1996) in particular in sensitive urban ar-eas. Safe and cost- and time-efficient mechanized tunnel construction, demands for the reliable determination of the expected time-variant settlements, the stresses and deformations in the lining, the ground and the shield tail, prognoses of possible critical conditions and other design-relevant parameters. Wrong decisions in the planning stage of tunnels concerning, e.g. the tunnel alignment of tunnel, the excavation method or the support design may lead to problems during construction and service and to cost and time overruns. Due to the relatively sparse knowledge of ground conditions, determined from a limited number of exploration sites, the parameters underly-ing the design process are characterized by a high degree of uncertainty. Furthermore, no clear procedures exist how (the limited) geological information is transferred to numerical models and how appropriate design tools shall be selected. Currently, the various aspects involved in the tunnel design are considered more or less sepa-rately, yielding designs which may be strongly biased by the experience of the designing engineer. In the frame-work of the European Integrated Project “Technology Innovation in Underground Construction” (TUNCON-STRUCT) efforts are made to develop a decision support system denoted as ”Integrated Optimization Platform for Tunnelling”, (IOPT) in which geological and geostatistical models, numerical simulation, knowledge-based systems and risk analysis are being combined to assist the engineer during the complete process of tunnelling design. The proposed concept of virtual underground construction (VUC), connected to IOPT via web-based services, will allow the virtual testing of different design scenarios considering a broad variety of geological con-ditions and different excavation methods. A prerequisite for the acceptance of sophisticated models for realistic three-dimensional simulation models of tunnel construction in engineering practice are robust and efficient algorithms accompanied by user-friendly model generation and visualization tools and computing capacities at affordable costs. The development of a numerical simulation model for mechanized tunnelling, which is capable to realistically represent all involved components and their interactions is a central component within this design support platform for underground

440

construction. Although the continuous increase of efficiency of modern computer technology and the consider-able progress in computational structural mechanics have stimulated the development of numerical simulation models in tunnelling since the early 1980’s, compared to the larger number of models developed in the context of NATM tunnelling (see, e.g. (Beer, 2003) and references therein for an overview on recent advances), only a relatively small number of fully three-dimensional numerical models is existing for shield tunnelling due to its considerably more complex nature, see, e.g. (Bernat and Cambou, 1998; Abu-Farsakh and Voyiadjis, 1999; Abu-Krisha, 1998; Komiya et al, 1999; Kastner and Maghazi, 2000). A relatively comprehensive three-dimensional finite element model for simulations of shield-driven tunnels in soft, water saturated soil has been recently proposed in (Kasper and Meschke, 2004). It has successfully been used for systematic studies of inter-actions in mechanised tunnelling (Kasper and Meschke, 2004; Kasper and Meschke, 2006). This model is the basis for the development of a new three-dimensional model for mechanised tunnelling, using a more advanced, flexible software architecture. Within TUNCONSTRUCT the model is characterized by the realistic consideration of the construction process involving all relevant components and construction processes, an automatic model generator (Stascheit et al, 2007) and a three-phase model for soils to represent face support by means of com-pressed air in addition to general partially saturated conditions (Nagel, Stascheit and Meschke, 2007). By means of this model, the effect of various interactions between these components and relevant target values, such as surface settlements, can be analysed. This paper describes the main ingredients of this simulation model for shield tunnelling and its integration within the decision support system IOPT and presents selected numerical results to demonstrate the predictive capabilities of the model.

2 Decision Support System for Underground Construction

Simulation models(NATM and shield tunnelling, lining systems, cutting tools)

Material Models (shotcrete, soft and cemented

soils, isotropic and jointed rocks)

Expert system

DataMining

Geo-technical data

Geologicalblock model

Simulation-basedlook-up tables

Expertknowledge

data

Underground Construction Information System (UCIS)

RuleBase

Integrated Optimization Platform IOPT

Figure 1: Main components of the Decision Support System IOPT for tunnelling

The decision support system IOPT is characterized by a collection of independent software modules related to different aspects and stages of the design process: geological geostatistical and material models to establish a realistic ground model, numerical simulation software for drill and blast and for mechanized tunnelling, respec-tively, tools for sensitivity analysis and parameter identification for the realistic modelling of the various interac-tions between the shield machine, the support measures, the lining and the surrounding soil, knowledge-based and expert systems associated with ground classification used in the pre-design and design phase, respectively, and cost and risk analysis models. These modules are coordinated via IOPT to assist the engineer during the complete process of tunnelling design. Figure 1 shows the main software components interacting with each other via a data base denoted as underground construction information system UCIS.

2.1 Computer-Assisted Design Process

To this end, all relevant steps of the design process, starting from the establishment of the geological model, en-compassing the definition of alignments, cross sections, geotechnical sections, performing a pre-design of pos-sible construction methods, iteratively generating the final design to the evaluation of time and costs and finally, assigning residual risks along with respective mitigation measures will be considered. Figure 2 contains a sche-matic illustration of the main stages of the computer assisted design process in tunnelling using IOPT.

441

For each variant of alignment

Divide complete tunnel intohomogeneous sections

For each homogeneous section

Determine ground behaviour

Select possible construction methods

For each possible construction method

Perform predesign

Select reasonable (combinations of)methods for entire project

For each reasonable combination

Determine System behaviour

Iteratively improve design

Assess time, cost, and risk

Suggest alignment variants

Check selection of homogeneous regionsAnd cross sections

Assess results, check failure category

Check construction methods, define(ranges of) parameters

Assess and adapt predesign

Assessment and adaption of selection

Check results

Assess and adapt design

User: provide criteria, assess results

Major stages of design User intervention

Figure 2: Schematic overview over the main stages of the design process as considered within the Integrated Optimisation System for Tunnelling (IOPT)

After each stage, the user is expected to check and, if necessary, to modify the results from the design support system. The flow of decisions taken during the design process is based on an expert system, which processes rules generated from expert knowledge, regulations, and rules extracted by data mining procedures from a pro-ject data base established within TUNCONSTRUCT (Lehner and Hartmann, 2007). IOPT controls the flow of in-formation and, in particular, the invocation of simulation models, connected to IOPT via internet, by means of a web-service controller (VUC data provider). All data are stored within a central data repository (UCIS) according to a unified product data model established for underground construction (Chmelina and Maierhofer, 2007).

2.2 Virtual Underground Construction as part of the Decision Support System IOPT

Within IOPT, the finite element model ekate, specifically designed for shield tunnelling in partially and fully satu-rated soil conditions will be integrated. The proposed concept of IOPT will allow the virtual testing of different de-sign scenarios considering a broad variety of geological conditions and different excavation methods. As far as the integration of simulation models into IOPT is concerned, the flow of data and information from the geological model towards the set-up of the simulation model involves several strongly interconnected components (see Figure 3). Theses components accomplish the following tasks required for the aforementioned integration:

o Reliable determination of all model parameters based on site data and, if this is not sufficient, from measured data from geologically similar rocks stored in a rock laboratory data base

o Provision of guidance to select the most suitable constitutive model for a given geological situation considering the available quantity and quality of measured site data

o Establish reliable and consistent procedures for the up-scaling of intact rock parameters to respective rock mass parameters

o Consideration of the statistical scatter of the rock mass properties by means of a geostatistical model (Stavropoulou et al, 2007).

o User-friendly sensitivity shell that allows for the determination of sensitivities of a chosen target value (e.g. maximum settlements) with respect to various model-, steering- and machine related parameters.

442

Geological model

• Lithology• bore hole data (E, c, j …)• joint spacing, RMR…• virgin stresses?

Lab test data base

Layer 23Layer 24

Layer 25Layer 23Layer 24

Layer 25

Underground Construction Information System - Data base

Kriging inter-polation per geo-technical layer

Geostatistical model

XY

Z

Model advisior

Suggests suitablemodel for soft soils, cemented soils,jointed rocks

Simulation models

• D&B tunnelling: BEFE++

• Shield tunnelling: ekateekate

ORIG. CAM-CLAY

MOD. CAM-CLAY

CASM

UN-SATURATED

CEMENTED

DOUBLE HARDENING

ORIG. CAM-CLAY

MOD. CAM-CLAY

CASM

UN-SATURATED

CEMENTED

DOUBLE HARDENING

Figure 3. Integration of geological, geostatistical, constitutive and simulation models with IOPT

3 Geostatistical modelling

The coupling of the 3D geostatistical-geological model of the rock mass with a 3D numerical model is envisaged to be a unique tool in underground excavation design and construction optimization. The geological information condensed to longitudinal sections, plan and cross-sections in CAD form is transformed into a 3D geological model. The conceptual geological volumes are exported in ACIS format in the GID pre-processor model for sub-sequent straightforward implementation into ekate. Finally the 3D geological discretized models are created in which a given geological material is assigned to each grid cell (e.g. Figure 4).

(a)

(b)

Figure 4. Example application of Line 9 Barcelona Metro, Singuerlin-Esglesia section: (a)Geological model in

ACIS format, and (b) discretised geological model on a mesh with tetrahedral elements and lithological data as-signed to grid points

The next step is to assign to each element apart from the lithology, the parameters needed by the selected con-stitutive model of each distinct lithological unit. The simplest way to do this is to use RMR, Q or GSI rock mass quality indices to derive a single constant damage state parameter for isotropic rock mass or a constant damage vector for anisotropic ones. Hence, the interpolation/extrapolation of RMR spatial data from boreholes should be performed and the predictions should be assigned at the 3D grid specified by the X,Y,Z coordinates of the

443

nodes. This task may be performed either by virtue of KRIGSTAT code or by a subroutine attached directly on the ekate code. In KRIGSTAT the basic geostatistical procedures have been implemented (Stavropoulou et al., 2007) to interpolate fields of model parameters over the defined study area. It assumes that the expected value

)(ˆkXZ of variable Z – in this case Z stands for RMR - at location Xk can be interpolated as follows:

1

ˆ ( ) ( )m

k i ii

Z X Z Xλ=

=∑ (1)

where Z(Xi) represents the known value of variable Z at point Xi; λi is the interpolation weight function, which de-pends on the interpolation method; and m is the total number of points used in the interpolation. Kriging estima-tions are found by minimizing the variance of estimation. Kriging uses a semivariogram for the interpolation be-tween spatial points. In the case of isotropic conditions and statistical homogeneity, the experimental semivariogram is

[ ]2

1

1ˆ( ) ( ) ( )

2

n

i

h Z X Z X hn

γ=

= − +∑ (2)

where n is the total number of observations separated by the distance h. In practice, Equation 2 is evaluated for evenly spaced values of h using a lag tolerance ∆h, and n is the number of points falling between h- �∆h and h+∆h. A typical semivariogram characteristic of a stationary random field saturates to a constant value (i.e., sill) for a distance called range. The range represents the distance beyond which there is no correlation between spatial points. In theory, γ(h)= 0 when h = 0. However, the semivariogram often exhibits a nugget effect at very small lag distance, which reflects usually measurement errors. Experimental semivariograms can be fitted using spherical, exponential or Gaussian models etc as it is illustrated in Fig. 5a. Based on an isotropic variogram, or-dinary Kriging determines the coefficients

iλ by solving the following system of 1+n equations:

)(ˆ)(ˆ1

ikij

n

ji hh γβγλ =+∑

=

ni ,,2,1 L= and 11

=∑=

n

iiλ (3)

where β is a LAGRANGE multiplier. The isotropic variogram of Equation 2 can be generalized for anisotropic

cases when data depend not only on distance but also on direction:

[ ]( )

2

1

1ˆ( ) ( ) ( )

2 ( )

k

i ii

Z Zk

γ=

= + −∑h

h x h xh

(4)

where h is the vector that separates point xi and xk; )(hk is the number of pairs of variables at distance h apart.

In practice, anisotropic semivariograms are determined by partitioning data in directional bins. Anisotropy is de-tected when the range or sill changes significantly with direction. Geostatistics is useful for understanding the distribution of model parameters in the study area, and to build parameter fields from other parameter fields, e.g., rock mass strength and deformability from RMR, Q or GSI data. The present analysis assesses the error of spatial interpolation using the minimum error variance. In the case of ordinary Kriging, the estimated interpola-tion error at location x0 is the standard deviation of the error estimate

20 0

1

( ) ( )n

OK i ii

x x xσ λ γ β=

= − −∑ (5)

where n, xi, λi and β are defined as in Equations 1 and 3. An example of Kriging predictions of RMR values in a pre-specified grid for the L9 project is displayed in Figure 5b.

444

Figure 5. (a) Main window of KRIGSTAT with the statistical and semi-variogram analyses as well as the borehole RMR data in the model; (b) Kriging estimations of the RMR distribution in the granodiorite formation GR1 tran-

sected by the Line 9 Barcelona Metro (Singuerlin-Esglesia section).

4 Numerical Simulation model for Shield tunnelling

This Section is concerned with a numerical simulation model (ekate) developed in the framework of TUN-CONSTRUCT for the simulation of shield driven tunnels. The model is characterized by the realistic considera-tion of the construction process involving all relevant components, an automatic model generator and a three-phase model for soils to represent face support by means of compressed air in addition to general partially satu-rated conditions.

4.1 Model components

Within the ekate simulation model the shield machine, the hydraulic jacks and the segmented lining are con-sidered as separate components. The shield machine is modelled as a three dimensional deformable body con-nected via frictional contact to the surrounding soil (see Figure 6) Its deformability is considered by a (simplified) modelling of its main load-bearing components (the shield skin, the diving wall and the bulk-head). The shield machine interacts with the soil via its conical skin and the heading face support. The heading face support is considered by equivalent boundary conditions on the soil where, depending on the type of support, fluid flow or capillary pressures and/or displacements or stresses may be prescribed. This also allows consideration of the filter cake both during driving and still stand phases (Kasper and Meschke, 2004). Contact between the shield skin and the soil is accomplished by means of a surface-to-surface contact formulation in the framework of the geometrically nonlinear (Laursen, 2002). Consideration of large deformations may be relevant for analyses of TBM tunnelling in squeezing ground conditions. The annular gap between lining and soil elements and its grout-ing is modelled by two-phase grout elements considering hydration-dependent material properties of the cemen-titious grouting material.

445

The hydraulic jacks advancing the machine are represented by truss elements tied between the lining and the shield machine. In order to realistically model the movement of the TBM and its interaction with the soil, to avoid drift off course of the TBM and to simulate curved tunnel advances an automatic steering algorithm to control the individual jack thrusts similar to the one proposed in (Kasper and Meschke, 2004) is implemented to keep the TBM on the designed alignment path. The simulation of the tunnel advance is performed in a step-by-step procedure by prescribing stretches of the truss elements and deactivating elements in front of the cutting face. After each TBM advance, the excavation at the cutting face, the tail void grouting and the erection of a new lining ring during standstill are taken into account by rezoning the finite element mesh at the cutting face, transferring all variables from the old to the new mesh and adjusting all boundary conditions to the new situation. The segmentation of the tunnel lining is currently not considered in the model. It will be, however, considered on a structural level by a modification of the structural stiffness according to (Blom, 2002).

4.2 Automatic model generation

A sophisticated Finite Element model for shield tunnelling requires considerable effort for the generation of a suitable discretized model. This includes the modelling of the surrounding ground considering the (often rather complex) geological situation on a scale of several hundred meters and the modelling of construction measures such as the shield machine, the lining system and the tail void grouting on a scale of centimetres to meters. To manage the complexity involved in the generation of such a model in space and time effectively an automatic modeller has been developed (Stascheit et al, 2007) as part of the Design Support System IOPT. The main ob-jective of the ekate modeller software is to allow for an automatic generation and execution of shield tunnelling simulations that are invoked autonomously by IOPT via web service. In this context the following tasks have to be performed:

o Acquisition of geometry and geology information o Acquisition of input parameters (e.g. alignment, cross section, machine type, material parameters for

soil, grout and linings) o Generation of the simulation model o Execution of the numerical simulation o Transmission of results o Notification of the remote client on the status of simulation

The modeller is designed such that these tasks are performed reliably, robust and fail-safe. As the client soft-ware (IOPT) will run on a remote system, the I/O and notification procedures are carried out by means of a web-service. The simulation process is controlled through a Python script that can be changed even during runtime. This allows for a high degree of flexibility and adaptability to specific needs. More details on the implementation of the modeller can be found in (Stascheit et al, 2007). The ground topology is directly imported from a Computer Aided Design (CAD) model containing the geological and geotechnical information. The spatial distribution of soil parameters within each of the individual geotechni-cal domains is generated by the geostatistical model presented in section 3 directly linked to the modeller (see Figure 7). Once the ground model has been established, the initial stress state is computed and applied to the simulation model. The tunnel alignment and the relevant machine and driving parameters are read from the data base. Subsequently, the 3D tunnel geometry together with all model components and the different phases of the advancement of the tunnel construction are generated automatically.

446

Figure 7. Automatic generation of numerical models for shield tunnelling: From the geological map to the Finite

Element model

An example for a model with a curved alignment and several geotechnical layers is shown in Figure 8a. A de-tailed view of the shield and the hydraulic jacks is given in Figure 8b. The Finite Element mesh automatically generated by the developed modeller is shown in Figure 8c.

Figure 8. Components of the numerical model for shield tunnelling: a) the complete model consisting of geo-technical layers, lining and shield machine; b) details of TBM and hydraulic jacks; c) Discretized numerical

model for shield tunnelling

4.3 Modelling of partially saturated soils

For simulations of shield tunnelling, two-phase formulations of partially saturated soils, where only the water pressure w

p and the soil displacements su are considered as independent variables and the separate consid-

eration of the air phase within the soil is neglected, are, in general, sufficient (Coussy, 1995). A three phase for-mulation, however, is required in cases, where compressed air is used to prevent water inflow. This becomes evidently important for the simulation of compressed air shields and for simulations of maintenance interven-tions, where the repair of the cutting wheel is performed under compressed air conditions. Such simulations are required for prognoses of possible blow-out failure of the soil in the vicinity of the tunnel face. In the proposed finite element model for shield tunnelling, a three phase model for partially saturated soil is for-mulated within the framework of the Theory of Porous Media (TPM) (Coussy, 1995; Lewis and Schrefler, 1998; Ehlers et al, 1989) considering large deformations to allow applications also in highly deformable, squeezing ground conditions. According to this model, the soil consists of the solid soil skeleton (solid phase) and water and air (fluid phases) filling the pore space of the soil. The TPM describes processes and interactions between phases at the micro-level of the porous material on a macroscopic level using averaging principles. Each phase

is associated with its own state of motion and is represented via its volume fraction α

n and via the degree of

447

saturation βS for the two fluid phases ( β =w[ater], a[ir]):

ββ

βnS

dv

dvn == . (10)

The state of the three-phase material is described by three balance equations: The overall momentum balance of the mixture

0gσ =+ ρdiv , (11)

where σσσσ denotes the overall CAUCHY stress tensor and ρ denotes the averaged density of the mixture, and two balance equations of the two fluid phases (assuming isothermal conditions and neglecting phase changes):

( ) ββρββρβ

vdiv0 nSDt

nSs

D+= . (12)

The stress-strain relation of the soil skeleton is formulated in terms of effective stresses sσ̂ according to

BISHOP’s formulation for three phase continua

( ) ( )( )βχ σσσσsσ −+−= aw

Saˆ . (13)

with βσ as the fluid (β =w) and the gas pressure (β =a), respectively. In general, the BISHOP parameter χ is a

function of the soil depending on the water saturation. In the proposed model the BISHOP parameter is assumed

to be equal to the degree of water saturation w

S . The air phase is treated as an ideal gas, using a linear relation

between pressure and density according to BOYLE-MARRIOT’s law. The water content of the pore volume w

S is described by the soil characteristic curve according to VAN GENUCHTEN (van Genuchten and Nielsen, 1985) (see

Figure 9). The fluid flow s

vβ~ is described in terms of DARCY’s law

( )gs

vβρβ

βγ

ββ −−= p

kgrad~ , (14)

where the permeabilities β

k are given by the product of its intrinsic permeability 0k and the relative permeabil-

ity βrelk (

βS ), which is a function of the saturation according to (van Genuchten and Nielsen, 1985).

Figure 9. Capillary effects in partially saturated soil (left), computed relation between saturation-and capillary

pressure according to VAN GENUCHTEN (right)

For the modelling of the matrix behaviour of non-, fully and partially saturated soft non-cohesive, cohesive and cemented soils a hierarchical library of various constitutive models is being established and will be implemented into ekate. The central model for soft soils is the so-called Clay and Sand Model (CASM) (CASM, 1998). The CASM model is a unified critical state model for both Clays and Sands and is based on the parameter state con-cept introduced by Been and Jefferies (Been and Jefferies, 1985). The state parameter, accounting for the effect of both void ratio and pressure, proves to be of fundamental importance in modelling the behaviour of sands and overconsolidated clays. This model reduces to the Original and the Modified Cam Clay model (Wood, 1990; Borja, 1991) with an adequate choice of parameters.

448

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

Partially saturated conditions are accounted for by including the suction pc in the formulation of the yield- and loading function

with p0 as the hardening parameter governing the hardening and softening behaviour of the soil. Dilatancy is controlled by means of a non-associative flow rule. The multiphase model employed for the soil also allows for the consideration of the flow and pressure conditions at the tunnel face supported by slurry. Currently, two limiting conditions are considered in the existing shield tun-nelling model (Kasper and Meschke, 2004) In Case 1, the slurry infiltrates the soil, but does not form a filter cake. The face support pressure is transferred to the soil skeleton only by the flow resistance of the slurry in the pores of the soil. In Case 2, the slurry forms an impermeable filter cake without infiltration. The face support pressure is transferred to the soil by the filter cake.

Figure 10. a) Illustration of the tail void grouting, b) Assumed time-dependent material properties of the grout

The material behaviour of the hydrating grouting suspension in the tail void is also modelled as a fully saturated material with a hydrating matrix phase, taking into account the fluid interaction between the grout and the soil and the dissipation of the grouting pressure behind the TBM. The grouting pressure is applied via pore pressure boundary conditions on the grout element nodes at the shield tail. Considering the time-dependent stiffness and permeability of the matrix material of the cementitious grout, using a formulation proposed by (Meschke, 1996; Meschke et al, 1996), see Figure 10, the initial pressurised fluid state of the grout and its hardening characteris-tics during hydration are taken into account.

5 Numerical applications of the simulation model for mechanised tunnelling

This section contains selected results of the numerical simulation model for shield tunnelling to provide an over-view on its capabilities with regards to predictions of the influence of selected design parameters on the settle-ments such as the grouting pressure and the hydration characteristics of the grout (Subsections 5.1-5.2) and simulations of air and water flow in the soil resulting from compressed air interventions (Subsection 5.3). Within IOPT, the computation of sensitivities of the tunnel-soil-system with respect to design-relevant parameters such as steering parameters (e.g. face support pressure, grouting pressure), model parameters for the soil and hard-ening characteristics of the grout, machine-related parameters (e.g. taper, length of TBM, trailer weight) and to-pology-related parameters (e.g. cover depth). constitutes a prerequisite for the assessment of suitable ranges of model parameters and the determination of machine- and steering-related parameters. It should be noted, that the analysis results reported in Subsections 5.1 and 5.2 have been obtained with a previous version (Kasper and Meschke, 2004; 2006) of the model currently being developed.

5.1 Influence of the grouting pressure and hydration characteristics of the grout on the settlements

In what follows, selected numerical studies concerning the influence of the grouting material and grouting pres-sure on the predicted settlements are summarized. For more detailed studies of the influence of other parame-ters we refer to (Kasper and Meschke, 2006a). Without reference to a specific project, the construction of a shal-low tunnel driven with a hydro-shield in homogeneous, soft cohesive soil, modelled by the modified Cam-Clay model, is simulated. The tunnel is characterized by a diameter D of 6.3 m and a cover depth of 1.5 D. The ground water table is assumed to be at the ground surface. Details of the model parameters are contained in (Kasper and Meschke, 2004). The taper of the TBM is assumed as 6 cm difference in diameter between the front and the tail.

( ) ,0,,ˆ0 ≤ppf c

sσσσσ

449

00.1

9

-0.5 401.3 3 10

6

4

2

0

- 2

- 4

Settle

ment

(cm)

D a y s ( l o g . )

S i m u l a t i o n o ft h e t u n n e l d r i v e

C o n s o l i d a t i o np h a s e

200

p g = 1 2 0 k N / m 2

p g = 1 5 0 k N / m 2

p g = 1 8 0 k N / m 2

F a c e i sp a s s i n g

T a i l i sp a s s i n g

1 1 0 1 3 0 1 5 0 1 7 00

1

3

G r o u t i n g p r e s s u r e p g ( k N / m 2 )Ma

ximum

settle

ment

(cm)

2

4

a ) b )1 9 0

A

Figure 11. Computed surface settlements in point A of the monitoring section for different grouting pressures. Figure 11 shows that the grouting pressure in the tail void considerably affects the surface settlements behind the TBM. An increased grouting pressure of pg=180 kN/m2 causes a noticeable decrease of the computed sur-face settlements in point A after the TBM has passed the monitoring section. In case of a low grouting pressure of pg=120 kN/m2 considerably larger immediate settlements behind the TBM can be observed followed by a slight long-term decrease of the settlements during the consolidation phase.

Figure 12. a) Measured evolution of the Young's moduli of shotcrete (Hellmich, 1999) and grouting materials (ETAC); b) different time-dependent Young's moduli of the tail void grout

To obtain an insight in the effect of the early age stiffness of the grouting material on the final settlements, three different scenarios for the hydration characteristics of the grouting material according to Figure 12 are investi-gated. A fast temporal increase of the early age stiffness reduces the soil deformations into the tail void. As a consequence, smaller surface settlements are predicted by the simulations based on a fast hydration character-istics of the grouting material see Figure 13. A settlement reduction for increased stiffness of the grout has also been determined in (Inokuma and Fujimoto, 1996). The reduced stress release and upward deformation of the soil into the freshly grouted tail void at the invert behind the TBM causes a significant increase of the lining pres-sure at the invert and to a relatively large increase of the bending moment in the tunnel lining while the change

450

of the ring normal force remains small (Kasper and Meschke, 2006).

6

4

2

0

- 2

- 4

Settle

ment

(cm)

S i m u l a t i o n o ft h e t u n n e l d r i v e

C o n s o l i d a t i o np h a s e

F a c e i sp a s s i n g

T a i l i sp a s s i n g

3 . 0

Maxim

um se

ttleme

nt (cm

)2 . 0

a ) b )

00.1

9

-0.5 401.3 3 10

D a y s ( l o g . ) 200

E ( 1 ) = 5 . 0 . 1 0 5 k N / m 2

E ( 1 ) = 6 . 5 . 1 0 5 k N / m 2

E ( 1 ) = 8 . 0 . 1 0 5 k N / m 2

4 . 1 0 5 5 . 1 0 5 9 . 1 0 5

Y o u n g ' s m o d u l u s E ( 1 ) ( k N / m 2 )6 . 1 0 5 7 . 1 0 5 8 . 1 0 5

A

2 . 5

Figure 13. Computed surface settlements in point A of the monitoring section for different early age hydration characteristics of the grout material.

5.2 Numerical simulation of compressed air intervention

The simulation model for shield tunnelling together with the three-phase model for the soil is applied to the nu-merical analysis of a compressed air intervention of a hydro-shield TBM with 10 m diameter and 15 m overbur-den. Such interventions may be necessary in mechanised tunnelling in fully or partially saturated conditions if the excavation chamber has to be accessed by the working staff to repair or exchange the cutting tools. In this case, the supporting fluid is temporarily replaced by compressed air. In the present numerical analysis the sur-rounding soil has been modelled, for simplicity, as an elastic material permeable for both water and air. Consid-eration of a more realistic elasto-plastic model for clay and sand (Yu, 1998) is currently being implemented into ekate. The ground water level is assumed at the level of the ground surface. The following material parameters have been used for the soil: density ρ� = 2000kg/m3, YOUNG’s modulus E= 5250kN/m2, POISSON’s ratio ν = 0.45 and porosity 20%. The initial permeability for air flow and water is assumed as k0=14.4cm/h and 144.0cm/h, re-spectively. The soil characteristic curve is defined by an air entry pressure of pb

r= 3kN/m2, n= 2.5 and m= 0.4. The initial pressure of the supporting liquid at the tunnel face is assumed equal to the undisturbed pore water pressure. Upon start of the compressed air intervention, a constant air pressure of 253.4kN/m2 is applied at the face. Due to the pressure gradient within the air phase in front of the tunnel face, flowing air starts to fill the pore space by displacing the pore water. A partially saturated zone is evolving in front of the heading face, which is continuously extending during the compressed air intervention. In the vicinity of the cutting face a nearly unsatu-rated zone is evolving (see Figure 14).

451

Figure 14. Numerical analysis of compressed air intervention: Evolution of regions of full saturation (left) and of nearly unsaturated conditions (water content of less than 20%) (middle) at different stages of the com-pressed air intervention: right: distribution of the air pressure 8 hours after start of the compressed air inter-vention

6 Concluding remarks

The paper has addressed the role of geostatistical modelling and a new three dimensional finite element model for the simulation of mechanised tunnel construction as components of a decision support system (IOPT) for tunnelling design currently being developed within the Integrated European research project TUNCONSTRUCT. From the geostatistical model, a spatial distribution of geotechnical parameters within each of the geotechnical sections is obtained. In case of heterogeneous rocks, also up-scaling of the intact rock parameters is provided. borehole data are spatially distributed The numerical simulation model for mechanized tunnelling model takes into account partially and fully saturated soils, the TBM, the hydraulic jacks, the tunnel lining and the tail void grout as separate components. It allows for highly automated numerical simulations of the step-by-step tunnel advance and the installation of the lining. By means of a three-phase finite element formulation for partially satu-rated soils and for the grout injected into the tail void the effect of the groundwater and the grouting are ade-quately taken into account. This model is also able to predict settlements and possible soil failure in compressed air interventions. Selected results of numerical parametric studies have been presented to demonstrate the abil-ity of the model to provide information on the various interactions in shield tunnelling. This type of sensitivity studies will be also used to enhance the reliability of the rule base implemented within IOPT in cases where pro-ject data and expert knowledge do not provide sufficiently reliable information on interdependencies in mecha-nised tunnelling. Since the construction-relevant components and construction phases are considered, the model will also be employed for numerical analyses simultaneously to the second construction process.

7 Acknowledgements

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

References

1. A.A.M. Abu-Krisha. Numerical Modelling of TBM Tunnelling in Consolidated Clay. PhD thesis, University of Innsbruck (1998).

2. M. Y. Abu-Farsakh and G. Z. Voyiadjis. Computational model for the simulation of the shield tunneling process in cohesive soils. International Journal for Numerical and Analytical Methods in Geomechanics, 23(1):23 – 44, 1 (1999).

3. K. Been and M.G. Jefferies. A state parameter for sands. Geotechnique, 35(2):99–112, (1985).

452

4. G. Beer: Numerical Simulation in Tunnelling, Springer (2003).

5. S. Bernat and B. Cambou. Soil - structure interaction in shield tunnelling in soft soil. Computers and Geo-technics, 22(3/4):221–242, (1998).

6. C.B.M. Blom. Design philosophy of concrete linings for tunnels in soft soils. PhD thesis, Delft University, (2002).

7. R.I. Borja. One-step and linear multistep methods for nonlinear consolidation. Computermethods in applied mechanics and engineering, 85:239,272, (1991).

8. K. Chmelina and A. Maierhofer. Development of an underground construction information system in the eu research project tunconstruct. In J. Eberhardsteiner, G. Beer, C. Hellmich, H.A. Mang, G. Meschke, and W. Schubert, editors, Computational Modelling in Tunnelling, 2007, CD-ROM Proceedings of the ECCOMAS Thematic Conference on Computational Methods in Tunnelling (EURO:TUN) (2007)

9. J. Chung and G.M. Hulbert: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-alpha method, Journal of Applied Mechanics, Vol. 60, pp. 371 – 375 (1993)

10. O. Coussy. Mechanics of Porous Continua. John Wiley & Sons, Chichester, (1995).

11. D. Dias, R. Kastner and M. Maghazi. Three dimensional simulation of slurry shield tunnelling. In O. Kusa-kabe, K. Fujita, and Y. Miyazaki, editors, Geotechnical Aspects of Underground Construction in Soft Ground, pages 351–356, Balkema, Rotterdam, (2000).

12. W. Ehlers: Poröse Medien, ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Technical report, Universität Gesamthochschule Essen, (1989).

13. ETAC Ground Injection, Information brochure, Nieuwegein, The Netherlands

14. G. Exadaktylos and M. Stavropoulou. A Specific Upscaling Theory of Rock Mass Parameters Exhibiting Spatial Variability: Analytical relations and computational scheme. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, in print (2008).

15. C. Hellmich: Shotcrete as Part of the New Austrian Tunneling Method: From Thermochemomechanical Material Modeling to Structural Analysis and Safety Assessment of Tunnels, PhD Thesis, Vienny University of Technology (1999)

16. E. Hoek and E.T. Brown. Practical estimates of rock mass strength. International Journal of Rock Mechanics Mining Science, 34(8) (1997) , p. 1165–86

17. A. Inokuma and A. Fujimoto. An improvement of FEM analysis in ground settlement prediction in shield tunnelling. In Mair R.J. and Taylor R.N, editors, Geotechnical Aspects of Underground Construction in Soft Ground, pages i537–542. Balkema (1996).

18. T. Kasper and G. Meschke. A 3D finite element simulation model for TBM tunnelling in soft ground. Interna-tional Journal for Numerical and Analytical Methods in Geomechanics, 28:1441–1460 (2004).

19. T. Kasper and G. Meschke. On the influence of face pressure, grouting pressure and TBM design in soft ground tunnelling. Tunnelling and Underground Space Technology, 21(2):160–171 (2006).

20. T. Kasper and G. Meschke. A numerical study on the effect of soil and grout material properties and cover depth in shield tunnelling. Computers & Geotechnics, 33(4–5), 234–247 (2006)

21. K. Komiya, K. Soga, H. Akagi, T. Hagiwara, and M.D. Bolton. Finite element modelling of excavation and advancement processes of a shield tunnelling machine. Soils and Foundations, 39(3):37 – 52, 6 (1999).

22. T.A. Laursen: Computational Contact and Impact Mechanics, Springer (2002).

23. K.H. Lehner and D. Hartmann. Using knowledge based fuzzy logic components in the design of under-ground engineering structures. In J. Eberhardsteiner, G. Beer, C. Hellmich, H.A. Mang, G. Meschke, and W. Schubert, editors, Computational Modelling in Tunnelling, 2007, CD-ROM Proceedings of the ECCOMAS Thematic Conference on Computational Methods in Tunnelling (EURO:TUN) (2007)

24. J. Lemaitre. A Course on Damage Mechanics. Springer-Verlag, Berlin (1992)

25. R.W. Lewis and B.A. Schrefler. The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. John Wiley & Sons, Chichester (1998).

26. B. Maidl, M. Herrenknecht and L. Anheuser: Mechanised Shield Tunnelling, Ernst und Sohn, Berlin (1996)

27. G. Meschke. Consideration of aging of shotcrete in the context of a 3D viscoplastic material model. Interna-tional Journal for Numerical Methods in Engineering, 39:3123–3143 (1996).

453

28. G. Meschke, Ch. Kropik, and H.A. Mang. Numerical analyses of tunnel linings by means of a viscoplastic material model for shotcrete. International Journal for Numerical Methods in Engineering, 39:3145–3162 (1996)

29. F. Nagel, J. Stascheit and G. Meschke. A numerical simulation model for shield tunnelling with compressed air support. Felsbau, submitted for publication

30. J. Stascheit, F. Nagel, G. Meschke, M. Stavropoulou and G. Exadakytlos. An automatic modeller for finite element simulations of shield tunnelling. In J. Eberhardsteiner, G. Beer, C. Hellmich, H.A. Mang, G. Meschke, and W. Schubert, editors, Computational Modelling in Tunnelling, 2007, CD-ROM Proceedings of the ECCOMAS Thematic Conference on Computational Methods in Tunnelling (EURO:TUN) (2007)

31. M. Stavropoulou, G. Exadaktylos, and G. Saratsis. A combined three-dimensional geological-geostatistical-numerical model of underground excavations in rock. Rock Mechanics and Rock Engineering, 40 (3) (2007), p. 213–243

32. M.Th. van Genuchten, D.R. Nielsen: On describing and predicting the hydraulic properties of unsaturated soils. Annales Geophysicae 3, Vol. 5,pp 615–628 (1985)

33. D.M. Wood. Soil Behaviour and Critical State Soil Mechanis. Cambridge University Press, Cambridge (1990)

34. H.S. Yu: CASM: A unified state parameter model for clay and sand. International Journal of Numerical and Analytical Methods in Geomechanics, 22, p. 621 (1998)

454