1 INTRODUCTION

Nowadays geotechnical engineers are more and more often confronted with sites, which are already constructed, which require an accurate definition of the initial state and present a geometrical complex-ity, which necessitates three-dimensional modeling.

Geotechnical engineering is characterized by highly nonlinear mechanics, in multiphase media, with complex initial states, involving complicated geometry. Soil and rock often require the use of multi-surface plasticity models; they also exhibit in-compressible or dilating behaviors, which are known to generate numerical problems. Generic and robust initial state, stability, and load driver algorithms are therefore needed.

Advances in numerical software for geo-mechanics have been achieved recently, as a result of concurrent progress in different domains: in-creased computer performance, advances in software engineering, unifying theoretical formulations for soil and rock mechanics, and progress in constitutive and numerical modeling.

We present, hereunder, a unified approach to soil and rock mechanics in two-phase media. Material models for soil and rock plasticity, finite element technology related to incompressible and dilatant behavior, and finite element implementation in Z_Soil.PC, are briefly discussed. Finally, illustra-tions from real life situations are shown.

2. MATERIAL MODELS 2.1 Yield criteria for isotropic and layered media

The most commonly used material models are all available in Z_Soil.PC. This includes Mohr-

Coulomb, Rankine, Drucker-Prager, Von Mises, Duncan-Chang, Hoek-Brown and Cap models. The most versatile yield criterion available is a generic three-parameter plasticity criterion proposed in Menétrey & Willam (1995), from which several classical models can be derived by specialization; it is adopted herein as yield criterion, in particular but not exclusively, for matrix failure in layered media. The yield surface is formulated as follows:

( ) [ ] ( )[ ]F , , A 2 mB r ,e C 1 0ξ ρ θ ρ ρ θ ξ= + + − = (1)

A, B, C, and m are parameters, function of ft, the uniaxial tensile strength, fc, the uniaxial compres-sive strength and e, (0.5<e<0.55), the exentricity of the criterion. ξ and ρ are stress invariants, and θ is Lode’s angle, which do not need to be specified. The criterion can be specialized to several of the classical criteria, as illustrated in table 1.

Table 1: Menétrey-Willam (M-W) parameters specializations

Alternative definitions of the parameters are possi-ble: in terms of C, the soil cohesion and φ, the fric-tion angle, or in terms of Drucker-Prager material parameters.

Three-dimensional numerical simulation of underground works, in engineering practice, with Z_Soil.PC

Th. Zimmermann ba, ,A.Truty ca, , K.Podles ca, , A.Urbanski ca, a. Zace Services Ltd, Software engineering, 1015-Lausanne, Switzerland, info@zace.com b. ENAC-LSC, Swiss Federal Institute of Technology, 1015-Lausanne-EPFL, Switzerland

c. Cracow Institute of Technology, Cracow, Poland

with the collaboration of ENAC-LMS, Swiss Federal Institute of Technology, 1015-Lausanne-EPFL, Switzerland Bonnard&Gardel Ingénieurs conseils SA, Lausanne, Switzerland, ComSA Ingénieurs conseils SA , Renens Switzerland De Cérenville Géotechnique SA, Ecublens, Switzerland, CSD Ingénieurs conseils SA, Lausanne, Switzerland Emch+Berger AG, Bern, Switzerland, GEOS Ingénieurs conseils SA, Geneva, Switzerland GVH Ingénieurs conseils SA, Tramelan, Switzerland, Schneller, Ritz,u. Partner AG, Ingenieurbüro, Brig, Switzerland Stucky Ingénieurs conseils SA, Renens, Switzerland ABSTRACT: Three-dimensional finite element analyses of underground works, in soil or rock, on PC, are becoming more popular in geotechnical practice. In this paper, we present selected aspects of constitutive and numerical modeling, and finite element technology and implementation, in Z_Soil.PC. Real life case studies illustrate the discussion.

2.2 Multilaminate model Layered media require even more advanced mod-

els, like the one described in Truty & al. (1997), and Z_Soil (2003), adapted from Zienkiewicz & Pande (1977) and Sharma & Pande (1988).

Up to three weakness plane orientations, which remain fixed in space, can be introduced in the pro-posed model. Each is characterized by a cohesion Ci, a friction angle φi and a dilation (non-associated) angle ψi, like any Coulomb material. A tensile cut-off can also be specified, with fti the maximum ten-sile stress. This leads to a multisurface plasticity problem which requires plasticity conditions to be simultaneously fulfilled, with respect to all surfaces, by any stress state in the material.

3 ELEMENT TECHNOLOGY

3.1 Locking and “classical” remedies The problem of element performance in finite ele-ment computations of elasto-plastic media exhibiting incompressible or dilating behavior has been inves-tigated intensively in recent years, with the aim of developing low order elements which do not lock. Early approaches to overcome locking due to in-compressibility used reduced selective integration, mean dilation (Nagtegaal & al. 1974), and later on the B-bar approach (Hughes 1980). More recent ap-proaches adopted mixed formulations, derived from the Hu-Washizu variational principle, and enhanced strain approximations; this led to the so-called En-hanced Assumed Strain approach (EAS) (Simo & Rifai 1990, Taylor & al. 1976). Unfortunately, this method does not apply to many well-known finite elements (like linear triangles in 2D or linear tetra-hedrons in 3D) and, moreover, it requires the spe-cific design of the enhanced part of the strain field for each element separately. Yet another approach is advocated in Z_Soil.PC. It is based on a mixed con-tinuous displacement-pressure formulation, and complements the Galerkin scheme by least-squares terms, which enhance its stability; the advantages of this formulation over earlier ones is discussed at length in Commend (2001) Truty & Zimmermann (1997), Truty (2001 &2002), Zimmermann & Commend (2001) and references therein.

4 FINITE ELEMENT IMPLEMENTATION IN Z_SOIL.PC

With recent achievements in computer science, finite element technology and graphical environments, the foundations were set for the development of highly interactive, domain specific, computer environ-ments, dedicated to professional geotechnicians. The program Z_Soil is such an environment. Illustrations of computations with the Z_Soil program system are

shown below. Noteworthy features of the environ-ment are initial state simulation including hydraulic and thermal conditions, fully coupled transient analysis in two-phase partially saturated media, with excavation and construction stages, continuous safety assessment using a (c-φ) reduction algorithm and extensions thereof. Soil-structure interaction is properly accounted for by means of a frictional con-tact formulation. Elasto-plastic truss and cable ele-ments, and nonlinear layered beam and shell ele-ments which can account for reinforced concrete modeling are available. Recent features include moisture migration analysis and allow identification of early–age cracking in concrete. 5 APPLICATIONS

Several constructions analyzed with Z_Soil.PC are shown below and the potential of the program is demonstrated through several case studies including a natural cave, a tunnel system and a large excava-tion.

Figure 1 . Railway bridge in Vinslöv, Sweden. Investigation of actions for reconstruction (Eng.: PEAB Grundteknik, Sweden)

Figure 2. Railway bridge in Vinslöv, Sweden. Calculated total settlements after erosion has occurred. The bridge is loaded with macadam and train traffic( Analysis by PEAB Grundtek-nik, Sweden, U.Ekdahl)

Figure 3. Large slope stability analysis in the Swiss pre-alps, displacement intensity map. (Analysis by Com-SA ingénieurs conseils SA, Switzerland, http://www.com-sa.ch) Figure 4. Tehri hydropower installation, India. Mesh of cavern system. (Analysis by USEC- MSUCE, Moscow, S Yufin) Figure 5. Tehri hydropower installation, India. Stress intensi-ties map. (Analysis by USEC- MSUCE, Moscow, S.Yufin)

Figure 6. Shahid Rajaee dam, Iran (Eng.: Stucky ingénieurs conseils SA, Switzerland). Figure 7. Shahid Rajaee dam, Iran. Simulation of construction stages (Analysis by Stucky ingénieurs conseils SA, J.-L.Sarf) Figure 8. Monolithe of Expo02 in Morat, Switzerland (Arch. J.Nouvel, Paris, Eng.: Emch+Berger Eng. AG, Bern) Figure 13. Monolithe of Expo02 in Morat, Switzerland (Arch. J.Nouvel, Paris, Eng. Emch+Berger Eng. AG, Bern Figure 9. Floating Monolithe of Expo02. Stress intensities map of anchoring system (Analysis by Emch+Berger Eng. AG, Bern, Ph. Menetrey)

5.1 Stability analysis of a natural cave (Analysis by GVH Consulting Eng. SA, Tramelan, Switzerland, Bisetti & al. 2000)

A decision of the authorities of the canton of Jura, in Switzerland, to investigate the possibility of rehabili-tating the caves of the former lime mines of Saint Ursanne as a convention and concert hall required a complete safety reassessment of the caves, which is described below. The age of the caves indicates that overall stability is not questionable; local instabili-ties are however identifiable on inspection. These local instabilities are related to weakness planes in the rock structure and indicate that chunks of rock could be mobilized in local failure mechanisms. A safety assessment study was conducted by visual in-spection and numerical simulation with finite ele-ment code Z_Soil.PC, comparing results obtained using different modeling and constitutive assump-tions.

5.1.1 Contact interfaces Contact interfaces are needed for this analysis. Con-tact elements implement a Mohr-Coulomb type con-stitutive behavior with a tensile cut-off. They can accommodate opening discontinuities. In the elastic range, penalty stiffnesses are evaluated from adja-cent elements in order to implement appropriate normal and tangential behavior. Figure 10. 3D mesh

5.1.2 Model 1 The mesh and dimensions are defined in Figures 10 and 11. The initial state of stress is defined by Equa-tion 2 (with σy the vertical stress).

yyzxy Ky σσσσγσ ⋅=⋅==⋅= 43.0; 0 (2)

The rock matrix material is initially isotropic and elastic, later elasto-plastic. Discontinuities are ne-glected. This model serves as a reference for later computations. Results are shown in the form of iso-surfaces on a 3D view and in sections B-B and C-C. Figures 12 to14 show horizontal stresses. Figure 15 shows the failure mode.

Figure 11. 2D section A-A. Figure 12. 3D upside-down view of horizontal stresses (σx).

Figure 13. 2D section B-B of horizontal stresses (σx). Figure 14 : 3D upside-down view of horizontal stresses (σz).

4.64e+022.30e+02-4.3e+00-2.4e+02-4.7e+02-7.1e+02-9.4e+02-1.2e+03-1.4e+03-1.6e+03

σ zz traction max = 470 kN/m2

SECTION C -

XZ

Y

2.61e+027.41e+01-1.1e+02-3.0e+02-4.9e+02-6.8e+02-8.6e+02-1.0e+03-1.2e+03-1.4e+03

3.15e+029.62e+01-1.2e+02-3.4e+02-5.6e+02-7.8e+02-1.0e+03-1.2e+03-1.4e+03-1.7e+03

XX

Z

Y

σ xx traction max = 320 kN/m2

SECTION B -

75 m

80 m

N

SECTION C - C

SECTION B - B

8 m

35 m

SECTION A - A

A thick plate type behavior is clearly identifiable from the tensile stresses present at the cave's roof. Tensile stresses are of the same order of magnitude in both horizontal directions and remain far below the tensile strength. The massif shows no initial plas-tification. The failure mode is obtained from a stabil-ity analysis( C-tanφ reduction algorithm), and yields a safety factor of 24, corresponding to the collapse of the pillars.

Figure 15. Failure mode.

5.1.3 Model 2 Mesh and initial state remain the same. The rock matrix is initially isotropic and elastic, later elasto-plastic.

Figure 16. Horizontal stratigraphic discontinuities.

Figure 17. 2D section B-B of horizontal stresses (σx)

Figure 18. Failure mode.

Horizontal stratigraphic discontinuities are intro-duced via contact elements. Their geometry and po-sition are illustrated in Figure 16.

Comparison of results from models 1 and 2 are presented in a similar manner, they call for the fol-lowing remarks: the plate behavior of the calcareous layers is easily identifiable in Figure 17. At each joint, traction stresses appear at the lower edge, which, however, remain below tensile strength.

The massif again shows no initial plastification. Failure occurs with a safety factor of 9 and the asso-ciated mechanism corresponds to a separation of the first layer at the cavity's ceiling (Fig. 18).

5.1.4 Model 3 Mesh and initial state remain unchanged. Strati-graphic discontinuities are introduced via contact elements, as in model 2. Two families of tectonic discontinuities are introduced via a multilaminate material. Both are vertical and parallel to sections B-B and C-C (Fig 29).

Figure 19. Tectonic discontinuities direction (section A-A).

5.53e+023.16e+027.88e+01-1.6e+02-4.0e+02-6.3e+02-8.7e+02-1.1e+03-1.3e+03-1.6e+03

8 m

35 m

(2+3

+5+1

0+15

)

stra

tigra

phic

dis

cont

inui

ties

1.62e+011.44e+011.26e+011.08e+018.99e+007.19e+005.39e+003.60e+001.80e+000.00e+00FAILURE OF

SUPPORTING PILLARS

5.48e-034.87e-034.26e-033.65e-033.05e-032.44e-031.83e-031.22e-036.09e-040.00e+00

separation of the first layer at the cavity's roof

75 m

80 m

N

SECTION B - B

SECTION C - C tectonic discontinuities:direction of family 1

tectonic discontinuities:direction of family 2

Figure 16. 2D section B-B of horizontal stresses (σx). Figure 20. 2D section B-B of horizontal stresses (σx) Results call for the following comments: the plate behavior of calcareous layers is recognizable as in model 2. However, horizontal stresses are influenced by the presence of tectonic joints and reach the strength values in most exposed zones (Fig.20). Plastification of the massif is identifiable in the cen-tral roof area. Failure corresponds to a collapse of the roof plate with separation of all layers above the cavity (Fig. 21). A safety factor of 4 is computed.

Figure 21. Failure mode (section C-C).

5.1.5 Conclusion The analyses show that the safety of the massif con-sidered as a homogeneous Hoek-Brown type mate-rial is high. Taking discontinuities into account re-duces the safety factor significantly. Two types of models were used in the simulation of discontinui-ties in this analysis: contact elements and multilami-nate material. Both support the introduction of fail-ure characteristics with preferential directions. Contact elements also withstand the opening of dis-continuities, they require meshes which match the contact surfaces, making parametric studies difficult. It appears in the present study that such elements are perfectly appropriate for the simulation of horizontal stratigraphic discontinuities. Multilaminate material is better suited for the simulation of densely distrib-uted discontinuities. These limitations are sometimes incompatible with the simulation of the actual geol-ogy. In the particular case of a dense distribution of microcracks, coupled with a strong confinement, this type of model appears to be the most appropriate for the simulation of families of discontinuities.

In the first performed analysis stratigraphic and tec-tonic discontinuities are ignored, the medium is as-sumed to be of Hoek-Brown type, characterised by tensile and compressive strength. The analysis re-sults in failure of the supporting pillars, with an as-sociated safety factor of about 24.

In the second analysis, stratigraphic discontinui-ties are modelled explicitely with appropriate mesh-ing. Results indicate the separation of a surface layer in the cave's ceiling, with an associated safety factor of about 9. In the third analysis, stratigraphic discontinuities are modeled explicitely with contact elements and tectonic discontinuities are modeled via lamina. Depending on material data and geome-try of discontinuities, a collapse of the roof plate with separation of all layers above the cavity or a global shear failure of the roof plate is observed. An estimated critical safety factor of 4 is found.

These different analyses made it possible to iden-tify the relative influence of different rock character-istics in the safety assessment and the most critical potential failure mechanisms; precise rehabilitation measures could be proposed to the site owner. The analysis illustrates the important role that elasto-plastic numerical simulations can play in a reliable safety evaluation of natural caves in layered media.

5.1 Tunnel in urban environment (Truty & al. 2002) The case of a complex underground tunnel system, in urban environment, is analyzed next. The goal of the simulation is to identify surface settlements in-duced by a multi-stage excavation/construction se-quence, associated with the enlargement and modifi-cation of an existing tunnel system. The difficulties to overcome are: a complex 3D geometry, account-ing properly for a complex initial state, and model-ing of an arch-pipes-parasol system, among others. A wide range of options available in finite element software Z_SOIL 3D are illustrated by the example.

The analyzed tunnel system, embedded at about 10m underground, consists initially of two existing circular tunnels with a diameter of 4m each. A rela-tively large building is already constructed on the surface above the considered system and therefore a careful estimation of surface settlements is neces-sary. The numerical simulation of the proposed ex-cavation/construction works is rigorously modeled with a 3D finite element model according to the as-sumed time schedule and applied technology, which will be shortly described below.

The final geometry of the tunnel system is shown in Fig. 22. The old tunnel in both, left and right, branches is enlarged in a zone located between the sections A-A and B-B and the cross-section geome-try is designed as a set of circular segments with variable radii and centers; the most interesting part is the tunnel junction.

1.41e-021.25e-021.09e-029.38e-037.81e-036.25e-034.69e-033.13e-031.56e-030.00e+00

2.20e+022.28e+01-1.7e+02-3.7e+02-5.7e+02-7.6e+02-9.6e+02-1.2e+03-1.4e+03-1.6e+03

Figure 22. New tunneling system with junctions The excavation/construction scheme, the same for both left (LB) and right (RB) tunnel branches, con-sists of several steps, illustrated in the accompanying figures. The procedure starts with the installation of a special arch support system (ARCH), which is in-stalled above the planned elevation of the new enlarged tunnel and consists of 15 m long circular pipes, which are driven into the underlying soil at some inclination angle, in two layers. After installa-tion of the ARCH support system, the first 10m of the old tunnel and soil, between the old tunnel and the new one, are excavated and the new lining is placed, consisting of a reinforced concrete shell, 40 cm thick, as shown in Fig. 23. These steps are re-peated until the new tunnel passes approximately 60% of the distance between sections A-A and B-B (see Fig. 22). The excavation procedure consists here of 10 steps, the whole section being excavated simultaneously.

Figure 23. Enlargement and ARCH installation In further steps another excavation procedure is ap-plied due to significantly larger tunnel dimensions. First the existing tunnel is fully filled with concrete and then a temporary pilot gallery, protected first by an ARCH system, is excavated and then strength-ened by a concrete shell. The procedure is such that first ARCH pipes are driven, then excavation takes

place and a new pilot gallery lining, inside the exca-vated part, is installed. These steps are shown in Figure 24.

Figure 24. Excavation of pilot gallery

After stabilization of the deformation, the tunnel will be successively enlarged up to its design dimen-sions, first by an excavation of the crown and then, when the crown excavation front is at least 12m away from the front of the pilot gallery, by an exca-vation of the invert fill ( Fig. 25).

The crown is excavated in 6 steps and the upper part of the enlarged tunnel is successively protected with a 40 cm thick reinforced shell. The invert fill is excavated also in 6 steps with the condition that the minimum distance between excavation front of crown and the invert fill cannot be less than 12m. The shell closure is made of a 40 cm thick rein-forced shell built in two steps corresponding to the excavation of crown and the invert fill.

Figure25. Excavation of the invert fill In subsequent excavation steps the new bifurcating tunnel is excavated and, simultaneously, the con-crete lining is installed; in the end, the remaining part of the existing tunnel, previously filled with concrete, is reopened, reaching the stage shown in Fig. 22. The same excavation/construction procedure is applied to both branches of the tunnel system.

This complex problem shows a large variety of the problems encountered by the analyst during genera-tion of the model. The key issue is a 3D finite ele-ment mesh, which should fit assumed geometry up to required level of accuracy and which has to take into account the presence of the excava-tion/construction fronts of assumed geometry. In or-der to increase computational efficiency, low order 3D elements are applied and mostly, if only possi-ble, eight-node bricks. For these elements the effect of volumetric locking can easily be overcome if BBAR or Enhanced Assumed Strain or Stabilized approaches are applied; all are available within the Z_SOIL 3D environment. This point is important as standard low order bricks would exhibit substantial locking effects, which would lead to an overestima-tion of the limit loads, the safety factors and an un-derestimation of the settlements.

The next aspect is the proper modeling of the tun-nel lining behavior. In the considered case we as-sume that the lining behavior is represented by MITC Q4 shell elements and the stress-strain rela-tion, for the further purpose of dimensioning, is as-sumed to be linearly elastic. The last point is ques-tionable as the excavation/construction time schedule indicates that an effect of concrete aging should be included. This is possible within Z_SOIL by the application of the so-called “aging concrete” material model, which reproduces stiffness evolution in time and creeping/relaxation phenomena as well. If needed, it is also possible to apply explicitly an elastic modulus varying in time, but such an ap-proach may result in stress-resultant oscillations.

In this example we do not include an effect of soil-structure interaction between tunnel and neighboring soil, although contact can be easily in-corporated into the model by the application of a Coulomb friction law and an augmented Lagrangian approach, both options being available in Z_Soil.

In in most complex numerical calculations it is not possible to include all effects, like soil nonlinearity, contact, consolidation, creep, seepage etc., from the beginning, as analysis of results can be very difficult and the analyst cannot easily identify which effect is dominant. Usually we start with an elastic calcula-tion and then, step-by-step, we add additional phe-nomena and significant constitutive nonlinearties. Such a hierarchical analysis serves as a base for proper understanding of the analyzed problem and may detect potential user mistakes made in data preparation.

Proper representation of the excava-tion/construction process, corresponding to the as-sumed time schedule, plays a significant role as far as result accuracy is concerned. For this reason, in Z_SOIL, with every finite element, we can associate a so-called existence function attribute which indi-cates at which time the element becomes active and

when it is deleted. This option is of primary impor-tance in tunneling software and therefore, in Z_SOIL 3D mesh generators, we have a wide collec-tion of methods which simplify this process by ap-plication of Import/Export to/from Excel files; in addition, robust object selection tools are available. In the case considered, an arch pipe system is mod-eled with the aid of 3D Timoshenko beam elements, which are embedded within solid elements by means of so called kinematic constraints. It is obvious that we cannot analyse all the local interaction effects be-tween soil and steel pipes, as this happens on a smaller scale as compared with dimensions of the structure, but we can roughly represent the stiffness of this support system assuming that pipes continu-ously deform with the neighboring soil. In such a case, it is possible, in the Z_SOIL environment, to impose a continuity condition by imposing appropri-ate constraints via a penalty formulation.

The tunnel system is embedded in an over-consolidated clay layer with an in situ Ko coefficient equal to K0=1. As we do not know the initial state after construction of the existing two tunnels we have to compute it. Within Z_SOIL.PC, there exists a special, incremental, predictor-corrector procedure to evaluate the initial state. The assumption is that, for actual external forces applied earlier to the sys-tem and gravity, we determine initial stresses corre-sponding to an undeformed state by incremental su-perposition of loads and corresponding initial stresses, completed by K0 confinement effects. The over-consolidated clay layer is represented by an elasto-plastic Mohr-Coulomb model which re-produces only a few major features of soil behavior. The assumed values of material properties are as folows: E=80000 kPa, ν=0.3, c=30 kPa, φ =200, ψ=00. A more comprehensive material model, like Cap or Duncan-Chang, also available in Z_SOIL.PC, could be used here too, but would re-quire a definitely larger set of material properties.

In this example we assume that concrete behaves as a linearly elastic material with a constant Young modulus. As we have already mentioned, this as-sumption is questionable and further analyses with an “aging concrete” material model should be car-ried out. The analysis with this more sophisticated model is, however, more costly, as each time step generated by an excavation/construction event, must be split at least in 4 to 5 steps in order to achieve a certain level of accuracy in the stress integration process.

The whole computation was carried out in about 70 excavation/construction steps. The final settle-ments of the surface due to tunneling are shown in Fig.26. We can see that for the given material prop-erties the maximum vertical displacement is about 7 mm.

Fig.26. Settlements at final stage of tunneling The example described here shows that the analysis of complex tunneling problems in complex urban ar-eas can be successfully carried out using modern numerical software designed for PC platforms. 5.3 Simulation of earthworks and retaining system for a large excavation (Analysis by De Cérenville Géotechnique SA and Com-SA Ing. Conseils SA, Geiser et al., 2002) 5.3.1 Model In the neighborhood of Geneva, the construction of a watch production centre has been planned. The pro-ject involves the execution of a large excavation in soft and saturated clays. It concerns a 145 x 165 m soil surface with a maximum excavation depth of about – 20 m. The designed retaining system is composed of a slurry wall braced at its top. The bracing leans on a 130 m diameter circular rein-forced concrete beam supported by piles linked with a buried circular internal slurry wall located at the excavation’s bottom (Figure 27).

Figure 27: Excavation during the earthworks. A 3D numerical simulation has been conducted in order to control and optimise all the components in-teracting in the project. A similar case (large dimen-sions, similar soil conditions and retaining system) constructed in the 1970’s has been used as a real-scale test in order to precise the soil parameters and

the hydro-mechanical behaviour with the help of a back analysis (Fig. 28).

Standard methodology :

Problem data Lab tests

Numerical model prediction

Methodology adopted in this project :

Problem data Lab tests

Numerical model prediction

Data Lab

Numerical model

Observations during the

construction

Tuning

Real-scale test: Grand Casino

Standard methodology :

Problem data Lab tests

Numerical model prediction

Methodology adopted in this project :

Problem data Lab tests

Numerical model prediction

Data Lab

Numerical model

Observations during the

construction

Tuning

Real-scale test: Grand Casino

Figure 28: Methodology comparison. In the actual project, the soils consist mainly of soft and compressible silty clay and silty clay loam, over a thick compact Wurmian moraine. Based on the geotechnical study, six principal layers were sche-matically defined. It was immediately observed, that an "advanced" constitutive law (here a Cap model) was essential to describe correctly the fined-grained soils. The parametric study emphasized also the in-fluence of the compressibility parameter λ on the observed displacements.

The change in pore-water pressure was observed to be the main factor influencing the general behav-ior in this project. As the soil permeabilities are low, the hydraulic conditions remain transient during the construction. For a one year long excavation, the pore-water pressure looses about 25 to 30 % of its initial value. After reproducing these time-effects on a 2D model, a "pseudo-transient" model was devel-oped for the 3D approach, in order to avoid days-long calculations with a time dependent problem.

The soil is modelled with about 10’000 8-nodes brick elements. The EAS (enhanced assumed strains) finite element technology is selected in order to prevent these elements to lock volumetrically. Structural elements (Figure 29) can be divided into three sub-categories: slurry walls and mat founda-tions are modelled with thin shells (Mindlin-Reissner hypothesis), while 2-nodes trusses are used to introduce supporting piles and bracing. Finally, the circular reinforced concrete beam and the exter-nal slurry wall stiffener are introduced as Ti-moshenko beam elements.

An initial state analysis is conducted first in order to start with a non-zero stress field in equilibrium as-sociated with a zero displacement field. After that, twelve construction and excavation steps take place as follows: first, the superficial soil layer is removed (3 meters deep), followed by the construction of the slurry walls and their supporting structure (circular beam, stiffener, pre-stressed bracing). The actual ex-cavation can then begin, divided in four main zones. In each of the zones about half of the soil is re-moved, then the mat foundation is placed, and then

the other part of the soil is excavated along with the construction of technical galleries (Figure 30).

Stiffener

Supportingslurry walls

Secondarymat foundation

Prestressedbracing

Angle bracing

Circular reinforced concrete beam

Sheet-pile wall

Technical galleriesmat foundation

Slurry wall

Mat foundation

Externalslurry wall

Supporting piles

Circularslurry wall

Stiffener

Supportingslurry walls

Secondarymat foundation

Prestressedbracing

Angle bracing

Circular reinforced concrete beam

Sheet-pile wall

Technical galleriesmat foundation

Slurry wall

Mat foundation

Externalslurry wall

Supporting piles

Circularslurry wall

Figure 29: Structural elements static system.

+0.50 m

-3.05 m

-8.00 m

-13.20 m

-18.80 m

stiffener

externalslurry wall

circular slurry wall

circular beam

pilesmat foundation

galleries bottom

1

2

bracing

-21.75 m

-23.45 m

Zone 1Zone 2 Zone 2

Zone 3 Zone 4

+0.50 m

-3.05 m

-8.00 m

-13.20 m

-18.80 m

stiffener

externalslurry wall

circular slurry wall

circular beam

pilesmat foundation

galleries bottom

1

2

bracing

-21.75 m

-23.45 m

+0.50 m

-3.05 m

-8.00 m

-13.20 m

-18.80 m

stiffener

externalslurry wall

circular slurry wall

circular beam

pilesmat foundation

galleries bottom

1

2

bracing

-21.75 m

-23.45 m

Zone 1Zone 2 Zone 2

Zone 3 Zone 4

Figure 30: Excavation stages. The external slurry wall is reinforced by counterforts in the execution project. Introducing each counter-fort into the global 3D mesh would have been too tedious. An auxiliary analysis has therefore been conducted on a smaller part of the wall in order to estimate the influence of the absence of the counter-forts. Results show that settlements are overesti-mated by 20 to 30 % when modelling the wall with thin shells; the general behavior of the retaining sys-tem is however correctly reproduced. 5.3.2 Results The vertical displacements after the first excavation step are depicted in Figure 31. The maximal settle-ment at this time is located near the excavation and reaches 4 cm. Figure 32 illustrates the settlements around the excavation (and also the swelling of the subgrade) at the end of the earthworks. A maximal settlement of about 7 cm is predicted 30 m behind the external slurry wall.

A cut parallel to the northern wall crossing the ex-cavation at the middle of the side walls shows the predicted deformation of the system at the end of the earthworks (Figure 33). There is a 5 cm horizontal displacement at the bottom of the external slurry wall.

Figure 31: Vertical displacements after the first excavation step

Figure 32: Settlements at the end of the earthworks

Initial position of the external slurry wall Initial position of the circular slurry wallInitial position of the external slurry wall Initial position of the circular slurry wall

Figure 33: Horizontal displacement color maps and deformed mesh Figure 34 shows the predicted distribution of the pore-water pressures behind the external slurry wall with losses of about 25 to 30 % of the initial hydro-static pressures. As in situ measurements are now available, they are also represented, highlighting a good correlation with the predicted values.

-25

-20

-15

-10

-5

0050100150200250

Pore-water pressure (kPa)

Dep

th (m

)

Hydrostatic pressure 3D pseudo-transient FE model 2D transient FE model Observation (GADZ, 29.05.02)

Figure 34: Pore-water pressure behind the external slurry wall. An integrated parametric analysis, backed with the experience of the constructors, helps the project en-gineers optimize the costs of the structure supporting the opening, in the sense that it gives them a qualita-tive analysis on the effective participation of any structural element to the excavation stability. It can be noticed in particular that the influence of the two supporting slurry walls linking the external and the circular walls on forces and displacements is little, as shown in Figure 35.

5 cm

Initial position

Deformation withsupporting walls

Deformation withoutsupporting walls

Supporting walls

5 cm5 cm

Initial position

Deformation withsupporting walls

Deformation withoutsupporting walls

Supporting walls

Figure 35: Comparison of the slurry walls deformation at the end of the excavation, with or without the supporting walls. Horizontal cross-section at the galleries’ bottom level. Another parametric study on the circular buried slurry wall has been conducted in order to check the influence of the concrete quality (Figure 36).

This excavation is currently under construction, and the first set of in situ measures (inclinometers, pore-pressure cells, optical fibers) have just been analyzed. Of course, modifications have occurred; in particular the excavation steps have been changed. A new calculation incorporating better the reality would be necessary, to allow a rigorous comparison. However, in Figure 37, the predicted deformations of the external slurry wall are compared with the ac-tual observations. A rather good agreement can be found between the two curves, in particular in the order of magnitude of the displacements.

The main discrepancies between prediction and measure can be explained in the following way:

Figure 36: Horizontal membrane force in the circular wall. Comparison between E = 2e7 (up) and E = 1e7 kN/m2 (down).

2 cm

Undeformed position

Field measure

Prediction

Not fully excavated yet

4 cm

Undeformed position

Field measure

Prediction

Not fully excavated yet

Figure 37: Horizontal displacement of the wall, prediction vs. field measure at two depths: -3.1 m (up), -19.3 m (down). - on the one hand at y = -3.1 m, the predicted upper

displacement is too small at the middle of the wall. This is due to the fact that, in the numerical simula-tion, the foundation mat was activated before the last excavation phase. However, in the reality, this area is not as stiff as initially planned. - on the other hand, at y = -19.3 m, the predicted displacement is larger than the field measure (bot-tom of Figure 37). But this part of the excavation has

not been finished yet, and additional deformations are expected.

The pore water pressures have also been measured on the field and the “pseudo-transient” computation has shown to be efficient (Figure 37).

To conclude, this example shows the importance of having complete initial data at hand for a 3D nu-merical simulation. The use of a real-scale test is also shown to be very useful in order to calibrate the parameters influencing most of the simulations, in particular the pore-water pressure decrease and the soil compressibilities leading to the necessity to choose an adapted constitutive law (Cap model). The time-consuming aspect of 3D numerical simula-tions can be reduced in conducting different parallel studies (influence of the counterforts, pseudo-transient calculation, no interface elements).

The comparison with in situ measures has vali-dated the a priori predictions.

6 CONCLUDING REMARKS

Nowadays, user-friendly object-oriented environ-ments installed on powerful PCs allow three-dimensional nonlinear analyses to be performed in a matter of a few hours. Reliable single-surface and multi-surface plastic models are available for the analysis of complex soil and rock materials. Generic algorithmic approaches are available for the initial state, time dependent and stability analyses, which allow a global assessment of the essential aspects of the mechanical behavior of a site before, during, and after constructions takes place.

Stabilized weak formulations make it possible to overcome locking phenomena associated with an in-compressible or a dilating behavior, typical of geo-materials. The same approach appears to stabilize pressure oscillations typical of consolidation prob-lems, and to overcome the associated minimal time step size condition(Vermeer & al. 1980).

Together, these improvements permit a unified approach to geomechanical problems, which will soon or already does have an influence on geome-chanical engineering practice (Z_Soil 2003).

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Commend S. 2001. Stabilized finite elements in geomechanics. PhD dissertation 2391. Swiss Federal Institute of Technol-ogy (EPFL).

Geiser F., Commend S., Crisinel J. 2002. Numerical simulation of earthworks and retaining system for a large excavation. Proc. CST 2002 Conf., Prague.

Hughes T.J.R. 1980. Generalization of selective Integration Procedures to Anisotropic and Nonlinear Media. IJNME 15: 1413-1418.

Menétrey Ph. & Willam K.J.1995. A triaxial failure criterion for concrete and its generalization . ACI Structural Journal 92(3): 311-318.

Nagtegaal J.C., Parks D.M. & J.R. Rice J.R. 1974. On Numeri-cally Accurate Finite Element Solutions in the Fully Plastic Range. CMAME 4: 153-178.

Sharma K.G. & Pande G.N. 1988. Stability of rock masses re-inforced by passive, fully-grouted rock bolts. I.J. Rock Mech. Min. Sci. & Geomech. Abstr.25, No 5: 273-285.

Simo J.C. & Rifai M.S. 1990. A class of mixed assumed strain methods and method of incompatible modes. IJNME 29: 1595-1638.

Taylor R.L., Beresford P.J. & E.L.Wilson 1976. A Noncon-forming Element for Stress Analysis. IJNME 10: 1211-1219.

Truty A., Zimmermann Th., Commend S., Urbanski A., & Li Y. 1997. Numerical simulation of stability and failure in elastoplastic layered media. In Jian-Xin Yuan(ed), Com-puters Methods and Advances in Geomechanics (IACMAG 97) 1: 353-358.

Truty A. & Zimmermann Th. 1997. A robust formulation for FE-analysis of elastoplastic media. In Pande & Pietruszc-zak, Numerical Models in Geomechanics NUMOG VI): 381-386.

Truty A. 2001. A Galerkin/Least-squares finite element formu-lation for consolidation. IJNME 52:763-786.

Truty A. 2002. On certain classes of mixed and stabilized mixed finite element formulations for single and two-phase geomaterials. Habilitation thesis, Cracow University of Technology.

Truty A., Zimmermann Th. 2002. Tunneling in urban area: a case study. Proc. 2nd Int.Conf. on Soil Structure Interac-tion in Urban Civil Engineering, Zurich.

Vermeer P. A. & A. Verruijt 1980. An accuracy condition for consolidation by finite elements.IJNME 5: 1-14.

Zienkiewicz O.C. & Pande G.N. 1977. Time dependent multi-laminate model of rocks. Int. J. Num. & Anal. Meth. In Ge-omech. 1: 219-247.

Zimmermann Th., Commend S. 2001. Stabilized finite ele-ments. Applications in geomechanics. In S.Valliappan, N.Khalili(eds.)Proc. 1st Asian-Pacific Congress on Compu-tational Mechanics, Sidney, Australia, 2001. Oxford: El-sevier Science.

Z_Soil 2003. V6 User manual. Zace Services Ltd Report 1985-2003, Lausanne: Elmepress, http://www.zace.com