Title

Plaxis Bulletin Issue 29 / Spring 2011

Editorial

Effect of Anisotropy on Tensile Stresses at the Bottom of a Base Course in Flexible Pavements

3D Finite Element Analysis of a Deep Excavation in Monaco Colophon Jori van den Munckhof den van Jori Design: Lengkeek Arny Beernink Erwin Brinkgreve Ronald Broere Wout board: Editorial subscribers Plaxis among worldwide distributed is and bv Plaxis of apublication is Bulletin Plaxis The Table of Contents engineering practise and includes articles on the the on articles includes and practise engineering geotechnical in method element finite the of use the on focuses bulletin The (NL). association » as the Plaxis bulletin is printed in full-colour. full-colour. in printed is bulletin Plaxis the as encouraged, is photographs and figures in colour of use The pixels. 3mega of aminimum or dpi 300 least at of aresolution have they that ensure should author the used are figures ‘scanned’ or photographs If (eps,ai). format based a vector in text the from separately supplied be to have themselves figures The text. the in approximately placed be should they where indicated be should it text, the in used are figures case In reading. of ease for clearly written is article the that ensure should author The article. the of end the at listed be should they used, are references any If subsections. necessary, if and, sections appropriate into divided be should article the of body main The author(s). corresponding the for e-mail) (preferably information contact and authors the of name(s) the paper, the of title the include should It formatting. without text plain as formatted format, electronic an in submitted be preferably should manuscript The categories. these of any in fall that Bulletin Plaxis the for papers of submission welcome editors The other. each with experiences and ideas share can PLAXIS of users where aplatform offers bulletin The PLAXIS. in implemented models the on backgrounds and studies case programs, PLAXIS the of application practical magazine of Plaxis bv and the Plaxis users users Plaxis the and bv Plaxis of magazine combined the is Bulletin Plaxis The The Netherlands The Delft AN 2600 P.O. 572 Box Vogelezang Annelies c/o Bulletin Plaxis to: mail regular by or [email protected] to: e-mail by sent be can Bulletin Plaxis the regarding correspondence Any

Page 14 Page 10 Page 6 Page 4 14 10 06 05 04 03 Fax: +31 3107 257 (0)15 Fax: Tel: +31 251 (0)15 7720 www.plaxis.nl [email protected] Netherlands The Delft AN 2600 P.O. 572 Box bv Plaxis office: main Plaxis or agent local your contact PLAXIS about information For Recent Activities Recent Monaco Excavation in of aDeep Analysis Finite Elements 3D Pavements Flexible in Course a Base sile Stresses of the Bottom at ofAnisotropy Ten on Effect Update Services Expert PLAXIS New Developments Editorial

Editorial

Editorial

Since the release of the new PLAXIS 3D detailed description of the complex situation and program last summer, more than 300 shows some interesting model sections, including licenses have been sold. It seems that many a global view of all the anchors. It was concluded »users have been waiting for an easy-to-use true that the new PLAXIS 3D program is quite capable three-dimensional modelling environment for and efficient to model this complex situation and their complex geotechnical applications, and that was able to produce satisfactory results. PLAXIS 3D accommodates their requirements. In addition to the contributions by PLAXIS In this bulletin a first practical application using users, the New Developments column describes PLAXIS 3D is described by some early users. In a new ‘dimension’ which the Plaxis research addition to another interesting article by PLAXIS team is working on: the modelling of thermal users, this bulletin also describes some recent flow and thermo-hydro-mechanical coupling. and future activities. In fact, the list of activities This enables temperature to be taken into is growing, in line with the steady growth of the account in the analysis of behaviour and Plaxis organization itself, which enables us to serve soil-structure interaction. The bulletin also you even better. For more information see the end describes the positive experiences of a company of this bulletin. with a dedicated in-house training course in the framework of PLAXIS Expert Services. The first user’s contribution involves a study on the effect of anisotropy on tensile stresses in a All together we trust to have composed another granular base for flexible pavements using an interesting bulletin for you. Do not hesitate to send axi-symmetric finite element model. Anisotropic us your comments or contact the corresponding stiffness in the granular base was modelled author in case you like to discuss some items. We using the elastic part of the Jointed Rock model. wish you an interesting reading experience and Different anisotropic stiffness properties were look forward to receiving your contributions for used to investigate the influence on the tensile future issues of the Plaxis Bulletin. stresses. It was concluded that anisotropy can lead to a reduction in the tensile stress in the granular The Editors base layer. A recommendation was given to allow for a wider range of Poisson’s ratios to be selected for anisotropic materials.

The second user’s contribution, as mentioned before, involves a three-dimensional finite element model of a deep excavation with adjacent buildings in Monaco, with the purpose to analyse the deformations as a result of the excavation process. The excavation is retained by diaphragm walls which are supported by several rows of anchors in different directions. The article gives a

www.plaxis.nl l Spring 2011 l Plaxis Bulletin 3 New Developments

Ronald Brinkgreve, Plaxis bv

The full coupling between deformations and changes of pore pressures as a result of undrained loading and/or changes in hydraulic conditions, has become available with the release of PLAXIS 2D 2010, last autumn. The new Advanced calculation mode allows for complex flow-deformation analyses to be performed, taking into account unsaturated soil conditions.

A further step is now taken by adding • Stability of slopes considering precipitation where temperature could play a role, and it would temperature as a degree-of-freedom in and evaporation using temperature-dependent be convenient if you could take this into account the finite element calculations and considering water retention curves. within your PLAXIS analysis. »thermal flow in the soil as a result of temperature • in areas. differences. The first aim is simply to calculate • Efficiency and sustainability of geothermal en- The development of THM coupling is still a a change of the temperature distribution in the ergy systems ( heat exchangers, heat/ research project. At the moment we are working soil by thermal flow and diffusion, and to impose cold storage, energy piles) on a 2D research version and later this year we will this on a mechanical model of the soil structure make a full 3D implementation. However, it will with the purpose to calculate thermal expansion Not all these examples are as complicated as take some time before this feature will become or shrinkage (using the thermal expansion the term ‘THM coupling’ would suggest. Not available in future PLAXIS versions. Nevertheless, coefficients of the respective materials). In this in all cases a full coupling is necessary. We will by moving into this new ‘dimension’ we are case, thermal flow and deformations are semi- implement simplified calculation options to avoid confident to provide you with the right tools to coupled. Another situation to be considered is unnecessary complexity. If you think about it, you solve your future geo-engineering challenges as the effect that temperature differences may cause may find an example from your own experience . convective groundwater flow to occur, whereas the groundwater itself will carry heat (advection) and will change the temperature distribution of the ground. Here, a full coupling between thermal flow and groundwater flow is required. The ultimate goal is to include a full coupling between thermal effects, hydraulic effects and mechanical effects, including phase transition of the pore medium (ice « water « vapour). This so-called thermo-hydro- mechanical (THM) coupling allows for very special situations to be analysed, such as the sustainability of nuclear waste deposits in underground repositories. Figure 1. Temperature distribution from THM Analysis Considering more common civil engineering applications, there are several examples in which temperature and the coupling with the mechanical behaviour plays an important role, such as: • Cyclic loading effects on soil-structure inter- action as a result of day/night temperature changes. • Soil freezing as a mitigation method to stabilize and excavations.

4 Plaxis Bulletin l Spring 2011 l www.plaxis.nl PLAXIS Expert Services Update

Jon Holliday, TPS Consult

Plaxis was contracted by TPS Consult to provide in-house PLAXIS 2D course program with special emphasis on deep excavation modeling for both their geotechnical and structural engineers. Thanks to PLAXIS Expert Services, a one-day tailored course program exactly matching TPS requirements has been implemented.

TPS had several people requiring training The afternoon session was focusing on practical “Excellent course run by a very knowledgeable on the modeling of deep excavations using applications and organized around relevant Plaxis representative. There was a good blend PLAXIS 2D and more particularly in the case of hands-on exercises as follows: of theory which was augmented by a workshop »propped cantilever retaining walls. The intention • Practical application I: Dry excavation using a where we were talked through a worked example. of TPS was to give a number of their geotechnical tied back wall Highly recommended for anyone looking for an and civil engineering graduates a course with a • Practical application II: Settlement due to tun- introduction to PLAXIS and FE modelling” balance between an overview of PLAXIS 2D and nel construction its modeling capabilities together with a worked • Worked example: Modeling of a propped The Company example requiring practical hands-on computer with PLAXIS TPS (part of the Carillion Group) is a team of analyses of a current project using the PLAXIS • Comparison with WALLAP. professional engineers, architects, project software. In this context, typical soil model and managers and consultants. Their extensive range design parameters for a section of propped Conclusions of engineering skills and specialist knowledge secant piled wall taken from a recent project Upon request Plaxis has provided high-level enables them to provide professional expertise design was provided. technical assistance in setting up a one-day across all aspects of the construction industry. practical training course which has been TPS provides comprehensive integrated services Proposed Course Schedule customized to TPS specific requirements. PLAXIS to a wide client base including government, local The first part of this course (morning session) was Expert Services has boosted TPS’s analytical skills authority and private sector businesses. organized with fundamental lectures on PLAXIS in the field of deep excavations and increased 2D features and on the use of the software in their productivity resulting in a faster return on the most relevant aspects involved in deep their software utilization and investment. excavations modeling. The morning session was split in two parts: “Highly recommended for anyone looking for an Morning Session Part I: • Introduction to PLAXIS 2D introduction to PLAXIS and FE modelling” • Input program • Calculation facilities • Output program Customer Quotes TPS has a proven track record of meeting tough • Geometry and Mesh Selection “An extremely useful introduction to PLAXIS 2D challenge and finding cost-effective solutions • Overview of Soil Material Models in Plaxis with a course tailored to suit our requirements. to complex technical problems throughout the The presentations were concise and well delivered project life cycle, backed by quality, health and Morning Session Part II: with plenty of opportunity for questions and safety, and environmental management system • Initial Stresses Definition in Plaxis discussion. The course tailored by Plaxis also certification. • Modeling Deep Excavation in Plaxis provided a hands-on practical workshop assisted • Structural elements by a very knowledgeable and helpful Plaxis • Dewatering representative.” • Interaction soil-structure

www.plaxis.nl l Spring 2011 l Plaxis Bulletin 5 Effect of Anisotropy on Tensile Stresses at the Bottom of a Base Course in Flexible Pavements

Amir H. Mohammadipour, Phillip S.K. Ooi and A. Ricardo Archilla, Department of Civil and Environmental Engineering, University of Hawaii at Manoa, Honolulu, Hawaii, USA

The role of an aggregate base course layer in a flexible pavement system is to distribute loads to a stress level that can be sustained by the underlying . When a pavement is analyzed as a layered, isotropic elastic system, it is not uncommon to see tensile stresses at the bottom of the base course layer upon application of a wheel load. Tensile stresses cannot be sustained by unbound granular materials since they have little or no tensile strength. Because these tensile stresses are generally known to be either unrealistic or overpredicted, using such an analysis can lead to pavement designs that have lower total permanent deformation or rutting (unconservative) and higher fatigue cracking prediction in the asphalt layer (over- conservative).

Studies by Tutumluer (1995) and Tutumluer Many studies have used anisotropic models rock layers. In this model, two angles define the and Thompson (1997) have shown that coupled with non-linear behavior (stress- plane of sliding as shown in Figure 1: the dip (α ) 1 tensile stresses can be reduced or eliminated by dependent stiffness) for the base course when and strike (α2 ). For a pavement system with a »treating the base course as anisotropic rather analyzing pavements. Herein, the effects of base course that is cross-anisotropic with a vertical than isotropic. According to Kim et al. (2005) anisotropy alone are studied assuming a constant axis of symmetry, α and = 90°. 1 = 0 α2 anisotropy naturally occurs in unbound materials stiffness in the base course until it yields. This was due to preferred orientation and arrangement of achieved using the Jointed Rock model in PLAXIS. Using the Jointed Rock model, the stress-strain aggregates as a result of their physical properties curve for the base course is linear (stiffness not (gradation and shape) and compaction forces. The Jointed Rock Model sensitive to stress level) until the yield point is The Jointed Rock model is a cross-anisotropic, reached. A truly anisotropic elastic material requires the elastic, perfectly-plastic model, especially meant specification of 21 independent parameters or to simulate the behavior of stratified and jointed elastic compliance coefficients to completely define the three-dimensional stress-strain relationships (Love 1927). Since obtaining all 21 constants is impractical and since anisotropy is generally thought to occur in more limited forms (e.g.; transverse isotropy or cross-anisotropy whereby the material possesses a vertical axis of symmetry such that its properties are independent upon rotation about that axis), the base course can be idealized to be cross-anisotropic. Love (1927) showed that the behavior of a cross-anisotropic material may be described by five parameters. However, Graham and Houlsby (1983) made a significant contribution when they developed a way to represent cross-anisotropy using only 3 parameters; i.e.; one more than for an isotropic

linear elastic material. Figure. 1. Dip (α1) and strike (α2) as defined in PLAXIS (2005)

6 Plaxis Bulletin l Spring 2011 l www.plaxis.nl The stress-strain behavior in the elastic range can greater than 0 will mean that the sliding plane is The compliance matrix can now be re-expressed be completely described using the following five conical rather than planar. However, a dip of zero in terms of E*, ν ∗ and α as follows: parameters: can theoretically be analyzed axi-symmetrically. To verify this, two identical axi-symmetric runs (Eq. 8) E = Young’s modulus in the horizontal direction were made in PLAXIS with the base course  1 ν **ν  1 − − 0 0 0 E = Young’s modulus in the vertical direction modeled as an isotropic material using both  2 2  2  α α α  ν = Poisson’s ratio for straining in the horizontal the Mohr-Coulomb and Jointed Rock  ν * ν *  1 ε  − 1 − 0 0 0 σ  x  α α  x direction due to stress acting also in a horizontal E       ε y ** σ y GG=2 =    ν ν 1    but orthogonal direction (E = E1 = E2, ν = ν1= ν , ) − − 0 0 0 2 2(1+ν )    2 2    ε z 1 α α α σ z ν = Poisson’s ratio for straining in the horizontal   =   2 *  *  γ xy  E 2() 1+ν τ xy  direction due to stress acting in a vertical direction models. Both gave identical results indicating  0 0 0 0 0  γ   α  τ   yz   yz  G2 = Shear modulus in the vertical direction that the Jointed Rock model can be used in an  *  γ   2() 1+ν  τ  axi-symmetric analysis when the dip is 0.  xz  0 0 0 0 0  xz   α    For a cross-anisotropic material, strains are related 2( 1+ν * )  0 0 0 0 0  to stresses through the compliance matrix as The Graham and Houlsby Simplification for  α 2  follows: Cross-Anisotropy By defining a new parameter, α , Graham and Houlsby (1983) reduced the number of constants For a material that is isotropic, α = 1. For a  1 ν ν  −2 − 1 0 0 0 (Eq. 1) from five to three for a cross-anisotropic material. material that is stiffer in the vertical direction,  EE E   1 2 1  The three parameters, modified Young’s modulus, α < 1 and α > 1 when the material is stiffer in the * ∗  ν 2 1 ν 2  E , modified Poisson’s ratio, ν , and anisotropy horizontal direction. Since the compacted base − − 0 0 0  ε x  E EEE σ x  factor, , are defined as follows: course is likely to be stiffer in the vertical direction,    2 2 2    α ε y σ y it follows that 0 < α < 1.    ν1 ν 2 1    − − 0 0 0  ∗ ε  EE E σ  EE= 2 (Eq. 2)  z  =  1 2 1   z  γ  1  τ Linear elastic isotropic materials cannot have a  xy  0 0 0 0 0  xy  ∗       ν= ν1 (Eq. 3) Poisson’s ratio > 0.5. However, Poisson’s ratio for a γ G2 τ  yz     yz  linear, elastic, anisotropic material can exceed 0.5. γ   1  τ  E  xz   0 0 0 0 0   xz  α 2 = 1 (Eq. 4) In the Jointed Rock model, a value of Poisson’s  G2  E2 ratio > 0.5 cannot be input in PLAXIS. This limits  2() 1+ν   0 0 0 0 0 1  the lower bound value of α that can be studied  E1  The other three parameters E1, ν 2 and G2, are herein. dependent on parameters E , ν , and as shown 2 2 α below: Analysis In the plastic range, the Mohr-Coulomb A 3-layer axi-symmetric flexible pavement system 2 parameters c and φ along with the dilatancy angle, EE1 = α 2 (Eq. 5) as shown in Fig. 2 was used in this study. A single ψ , and tensile strength govern the material’s wheel load that is circular in plan with a radius behavior. of 254 mm and having a uniform pressure of 690 2 E1 α = (Eq. 6) kPa was applied on the top of the pavement. The E In the Jointed Rock model, sliding is only 2 asphalt layer and subgrade were assumed to be permitted in three different directions, one of αE homogeneous and isotropic. The asphalt layer = 2 which corresponds to the direction of elastic G2 (Eq. 7) was treated as a linear elastic material while a 2() 1+ν1 anisotropy. In PLAXIS, a warning message is Mohr-Coulomb model was used to describe the issued when the Jointed Rock model is used in subgrade. Rigid interface elements were assumed an axi-symmetric analysis. This is because a dip between layers.

www.plaxis.nl l Spring 2011 l Plaxis Bulletin 7 Effect of Anisotropy on Tensile Stresses at the Bottom of a Base Course in Flexible Pavements

Description Asphalt Layer Unbound Granular Base Subgrade

Model Prameters Material Model Linear Elastic Jointed Rock Model Mohr-Coulomb

Material Type Drained Drained Drained

γ unsat = kN Moist unit weight 24.7 16.0 14.9 m3 E (MPa) Young’s Modulus 1,724 N/A 41.4

ν Poisson’s Ratio 0.35 N/A 0.33

E1 (MPa) Horizontal Young’s Modulus N/A Calculated (Eq. 5) N/A

Poisson’s ratio for a ν N/A 0.3 N/A 1 cross-anisotropic material

E2 (MPa) Vertical Young’s Modulus N/A 103 to 310 N/A

Poisson’s ratio for a N/A Calculated (Eq. 6) N/A ν 2 cross-anisotropic material

Shear Modulus for a G (MPa) N/A Calculated (Eq. 7) N/A 2 cross-anisotropic material

c (kPa) N/A 0.01 0.01

φ (º) Angle N/A 45 30

ψ (º) Dilantancy Angle N/A 15 0

K0 At-rest earth pressure coefficient 1.0 0.29 0.5

Table 1: Summary of parameters in PLAXIS analysis

Table 1 summarizes the model parameters used in the analysis. A total of 45 runs were conducted

using different values of E2 (103, 207 and 310 MPa), ν1(0.2, 0.25 and 0.3), and α (1.0, 0.9, 0.8, 0.7 and

0.6). Only the results for ν1 = 0.3 are presented.

For ν1 = 0.3, the anisotropy factor, α , according

to Eq. 6 must be greater than 0.6 since ν 2 cannot Figure 2: Flexible pavement exceed 0.5 in PLAXIS. section analyzed

Results When a wheel load in the form of a circular surface traction is applied at the centerline of the axi-symmetric geometry, the bottom of the base course elongates or experiences tensile strains. σ − The maximum horizontal tensile stress ( x xmax) was found to always occur directly below the edge of the circular load. Fig. 3 illustrates the variation of maximum tensile stress at the bottom of the base course with anisotropy factor (α ) for different

values of E2. It increases initially when α decreases σ − from 1 to 0.9. Thereafter, x xmaxdecreases with increasing α indicating that by considering anisotropy in the base course, tensile stresses do reduce. However, σ x− x does not reduce to zero max Figure 3: Variation of in this set of calculations. maximum tensile stress at the bottom of the unbound σ − To reduce x xmax further: base course with respect to α assuming ν1 = 0.3 1. α should not be constrained to 0.6 or greater. Values of α for a variety of aggregate types and properties in the granular base course have been reported to be between 0.17 and 0.46 (Tutumluer and Thompson 1997; Masad et al. 2006); or

8 Plaxis Bulletin l Spring 2011 l www.plaxis.nl Effect of Anisotropy on Tensile Stresses at the Bottom of a Base Course in Flexible Pavements

2. other factors such as stress/strain dependent Reference modulus and the effects of overconsolidation on • Graham, J., Houlsby, G.T., 1983. Anisotropic

K0 should be considered in pavement analysis. Elasticity of a Natural . Geotechnique 33, No. 2, pp. 165-180. Another observation of note from Fig. 3 is that the results are relatively insensitive to the value of E2 • Kim, S.H., Little, D.N., Masad, E., Lytton, R.L., for this set of parameters analyzed. 2005. Estimation of Level of Anisotropy in Un- bound Granular Layers Considering Aggregate Summary and Conclusions Physical Properties. The International Journal The influence of the anisotropy factor (α ) on the of Pavement Engineering, Vol. 6, No. 4, pp. 217- horizontal tensile stresses generated in unbound 227, Taylor & Francis. base course layers in flexible pavements was analyzed using the Jointed Rock model in PLAXIS. • Love, A.E.H., 1927. A Treatise on the Mathemati- A non-stress sensitive cross-anisotropic model was cal Theory of Elasticity, 4th edition. Cambridge assumed for the base course using five constants. University Press. By defining an anisotropy factor, α , the number of elastic parameters reduces from five to three. • Masad, S., Little, D., Masad, E., 2006. Analysis of The results show that anisotropy can lead to a Flexible Pavement Response and Performance reduction in the tensile stress in the unbound Using Isotropic and Anisotropic Material Prop- base layer. However, the value of α is constrained erties. Journal of Transportation Engineering, in this study because PLAXIS does not allow the Vol. 132, No. 4, pp. 342-349, ASCE. user to specify a value of ν 2 greater than 0.5 when in fact, a Poisson’s ratio > 0.5 is admissible with • Plaxis (2005). PLAXIS 2D: Reference Manual, anisotropic materials. The Jointed Rock model Version 8.2, Plaxis bv, Delft, The Netherlands. can become more versatile if this limitation is removed in PLAXIS. • Tutumluer, E., 1995. Predicting Behavior of Flexible Pavements with Granular Bases. PhD It is well known that the behavior of unbound Dissertation, Georgia Institute of Technology, granular layers is not linear and the resilient Atlanta, GA. modulus (or Young’s modulus) is highly dependent on the stress state. If stiffness nonlinearity (stress- • Tutumluer, E., Thompson, M.R., 1997. Aniso- sensitive stiffness) can be incorporated in a cross- tropic Modeling of Granular Bases in Flexible anisotropic constitutive model, the modification Pavements. Transportation Research Record can prove beneficial to both the geotechnical and 1577, pp. 18-26, TRB, National Research Board, pavement engineering community. National Research Council, Washington, D.C.

www.plaxis.nl l Spring 2011 l Plaxis Bulletin 9 3D Finite Element Analysis of a Deep Excavation in Monaco

Marie Porquet, Alain Guilloux and Samy Chakroun, Terrasol Richard Witasse, Plaxis bv

The Odéon tower project in Monaco is exceptional, both by its height, 160m, the tallest building in Monaco, and the depth of the excavation required, planned to reach about 70m. TERRASOL was entrusted with geotechnical consultancy on the soil testing, foundations, etc, but also and mostly with the implementation of a 3D finite elements model to analyze notably the influence of excavations on the surrounding buildings.

The Odeon project consists in the construction of a high-rise building (160 m) in Monaco, with approximately »10 basement levels, located on a steep slope hillside (from 130 NGM to 67.5 NGM). The ground level is assumed to be placed at 67 NGM. The retaining structures to be built around the excavation are the following: • A 15 m high soldier-micropile wall (from 114 NGM to approximately 94 NGM); • A 20 m high soldier-pile wall (from 94 NGM to approximately 74 NGM); • A 38 m deep diaphragm wall, used for the basement excavation, from 74 NGM to approximately 36 NGM.

The soldier-micropile and the soldier-pile walls are temporary structures, whereas the diaphragm wall is permanent. The diaphragm wall will be supported by the parking floors (construction based on the “up and down” method). The superstructure will be resting on the peripheral diaphragm wall (including buttresses) and on localized diaphragm walls inside the excavation.

Several buildings already exist around the excavation, one of them being a middle school located nearby the diaphragm wall and associated to older retaining structures (an anchored wall).

The aim of our work was to determine the horizontal and vertical displacements of the various retaining walls around the middle school (the existing anchored wall of the school and the

Figure 1: Top view of the modeled area

10 Plaxis Bulletin l Spring 2011 l www.plaxis.nl of variable height (26 m to 14 m, from max. Loading γ unsa t (kN/m3) E(kPa) ν c’(kPa) φ (º) ψ (º) 100 NGM to min. 74 NGM), made of shotcrete Screes 20 0.101E6 0.30 10 30 0 and reinforced concrete; • A soldier-micropile wall with 4 micropiles (Ø MCM 24 1.218E6 0.30 30 32 0 280 mm) approximately 9 m high (from 87 NGM to min. 78 NGM), made of shotcrete; Limestone 24 1.600E6 0.30 70 38 0 • A 48 m deep diaphragm wall (from 74 NGM to 26.4 NGM), with 10 m embedment below the γ Unloading unsa t (kN/m3) E(kPa) ν c’(kPa) φ (º) ψ (º) raft of the underground structures.

Screes 20 0.111E6 0.43 10 30 0 Those retaining structures include piles, MCM 24 1.336E6 0.43 30 32 0 micropiles, shotcrete and reinforced concrete, and prestressed anchors with various inclinations. Limestone 24 1.816E6 0.30 70 38 0 Besides, the floors of the tower basements are built while the excavation goes on, from 73 NGM Table 1: Soil properties to 36.8 NGM.

Some structural simplifications were necessary new retaining walls built during the works) and with a local Limestone layer located downhill the while building the model. The three main to describe the general behavior of the school model. All these layers are tilted. simplifications are the following: structure. PLAXIS 3D 2010 has been used for this Given the complexity of the different layers, the • The main simplification was that only a part calculation. definition of 28 was necessary to fully of the excavation has been introduced in describe the soil model. We used the Mohr- our model. In order to take into account the Underground Construction Coulomb model for all soil layers: as a previous interaction with the other part, a surface of Our calculation focused on a local model (only model of the excavation was realized using the zero prescribed displacements was defined part of the entire project) including the different Mohr-Coulomb model, which is accetable when in the center of the excavation, and only the new retaining structures set up near the middle dealing with rock, we kept using it to be able South half of the excavation and the floors was school. Thus we restricted the model to the to compare the results of both models. The soil modeled (using the project symmetry). neighborhood of the new retaining wall, including properties are described in Table 1. • The middle school building structure was not the existing wall and the new wall, the middle modeled: only the building load was taken into school, and a part of the excavation pit. Structural Elements account. Besides, the foundations (piles) of The located uphill the middle school and The model includes the existing retaining the middle school were not modeled but the the excavation were taken into account for initial structures, which are: building load was applied at the piles tip level stresses calculation, without modelling the other • The old 16 m high anchored wall (from 87 NGM (64 NGM). existing buildings. The soils located uphill the to 71 NGM) associated to the middle school, • The existing wall of the middle school (M1) excavation were deactivated afterward to shorten made of reinforced concrete; consists of an anchored wall. Only the anchors the calculation time (cf. Figure 1). • The T-shaped reinforced concrete walls of the placed near the excavation (approximately existing terraces uphill the school; 30 m) were modeled. The wall part most distant Geotechnical profile from the excavation pit (which does not have The three soil layers encountered on the The model also includes the walls of the new much influence on the works) was modeled by a construction site are the following: superficial retaining structures, which are: plate with prescribed displacements. colluviums lying over Marls and Calcareous Marls, • A soldier-pile wall with 10 piles (Ø 1000 mm)

www.plaxis.nl l Spring 2011 l Plaxis Bulletin 11 3D Finite Element Analysis of a Deep Excavation in Monaco

Finally, the structural elements used in the Applied overloads excavation, additional surfaces of prescribed model (cf. Figure 2 and Figure 3, page 12) are A structural overload of 150 kPa is applied at displacements have been defined: the following: 6 existing (anchored) walls, 2 new the base of the school piles (at 64 NGM), which • Zero prescribed displacements along the y-axis soldier pile walls, the diaphragm wall around the corresponds to a distributed load of 15 kPa by on the East-West plan placed uphill the middle excavation, 13 floors inside the excavation, 15 piles floor for a building composed of a ground floor school, to retain the grounds; and 140 anchors. and 9 floors (cf. Figure 5). • Zero prescribed displacements along the x-axis on the North-South plan uphill the excavation, The material properties for the structural elements Hydraulic conditions to retain the grounds to be excavated; are presented in Table 2 to Table 4. We considered for the present calculation that • Zero prescribed displacements along the drains are introduced behind the retaining x, y and z axis on the plan oriented North Model and mesh properties structures: thus the water level was assumed to be East-South West, placed at the center of the The final model dimensions are the following: lowered below the structures and was therefore excavation, enforcing symmetry conditions. • 165 m long in the East-West direction; not considered in the current model. • 130 m wide in the North-South direction; Staged Construction • Levels from 130 NGM to 10 NGM. Boundary conditions: displacements To model the whole construction process, During the initial phase, the boundary conditions 43 calculation phases were necessary: the initial It includes approximately 137,700 elements are the Plaxis standard boundary conditions: phase (0) to calculate the initial stresses, phase 1 with an average size of 5 m, and approximately • Zero prescribed displacements along the x axe to deactivate some of the soil clusters, and after 198,740 nodes (cf. Figure 4). on the yz borders; that, two calculation phases for each excavation • Zero prescribed displacements along the y axe phase (one to deactivate the excavated grounds, Loads and Boundary Conditions on the xz borders; and one to activate the retaining structures). Initial stresses • Zero prescribed displacements along the x, y The stresses initialization is performed during the and z axes on the model base. Main Results initial calculation phase, using gravity loading with The whole project lasted 2 month. We needed all soil clusters activated. During the calculation, after deactivation of 7 weeks to create the definitive model and to the soil clusters located uphill and North to the define all the calculation phases, 2 weeks to In the next phase, once the initial stresses state was reached, the soils located uphill and North to the excavation were deactivated to enable the staged construction calculations.

Figure 3: Global view of all the anchors

Anchors Free part Anchored part

Structure Type E (GN/m2) A (mm2) EA (kN) Type E(GN/m2) 3 A(mm2) d(m) T (kN/m) γ(kN/m ) skin Dywidag 194 1018 197.47E3 7T15Eb 194E6 70 980 0.035 70 36mm Figure 2: Global view of all the plates φ Soldier 7T15MMC 194E6 70 980 0.035 112 pile wall 7T15 194 980 190.12E3

9T15 194 1260 244.44E3 9T15Eb 194E6 70 1260 0.040 70 9T15MMC 194E6 70 1260 0.040 112 Plates e (m) γ (kN/m3) E (kPa) ν 7T13 194 651 126.29E3 Middle School Middle 7T13MMC 194E6 70 651 0.029 112 0.60 25 20E6 0.25 10T13 194 950 180.42E3 (M1) school existing 12T13 194 1116 216.50E3 10T13MMC 194E6 70 930 0.034 112 M6_wall 0.30* 25 20E6 0.25 wall M1 13T13 194 1209 234.55E3 12T13MMC 194E6 70 116 0.038 112 M6_foot 0.40* 25 20E6 0.25 13T13MMC 194E6 70 1209 0.039 112 Shotcrete 0.20 24 25E6 0.25 Table 3: Anchor properties

Reinforced 0.40 25 25E6 0.25 concrete Beams d (m) A (m2) d (m) d (m) A (m2) A (m2) (kN/m3) E (kPa) E (m4) for tot ext int a b γ Diaphragm 0.82 25 30E6 0.25 wall Micropiles 0.28 0.062 0.22 0.17 0.0137 0.048 70 194E6 6.7E-5

Floors Variable 25 35E6 0.25 Piles 1.00 0.785 - - - - 25 30.0E6 4.9E-2

Table 2: Plate properties Table 4: Beam properties

12 Plaxis Bulletin l Spring 2011 l www.plaxis.nl 3D Finite Element Analysis of a Deep Excavation in Monaco

achieve the calculations, and 1 week to analyze the The final results were totally satisfying, and our model results. Given the high number of elements conclusion about using PLAXIS 3D 2010 is very and calculation phases, the whole calculation positive. Using the command line feature proved required almost 12 hours to be completed. to be a highly useful tool: we could not have achieved the whole meshing and the calculations The model results show that the new retaining as quickly as we did without that tool. structures should guarantee the stability of the excavation as well as the one of the school The results post-processing in terms of building. The total displacements of the new displacements and loads has been achieved rather retaining structures do not exceed 5 mm in the rapidly thanks to the Output tools (many display present simulation. The Figure 6 shows a model options and ability to select part of the structures global view with total displacements. only).

Conclusion Comparing the final results with those of the previous model, the displacements were similar. This demonstrates that the simplifications which have been made for this local model were acceptable. The PLAXIS results also showed that the total displacements were acceptable for the structures: according to the calculations, the new retaining structures have been safely designed. These results will be used during construction works to check that the in-situ displacements do not exceed the maximum calculated ones.

This project required a 3D model with high geometrical complexity and many calculation phases. However, the model construction has been relatively easy (given the various structural elements that had to be modeled): once we got familiar with all PLAXIS 3D commands, especially creating copies of a selection, it became quite fast to define the various structural elements. The most time consuming operations were those related to mesh generation due to the complexity of the model.

Figure 4: Global view of the final model

Figure 6: Global view of the final results (total displacement)

Figure 5: Top view of the middle school structural overload

www.plaxis.nl l Spring 2011 l Plaxis Bulletin 13 Recent Activities

PLAXIS Connect Watch the instructional movie, and find out how you can also experience first hand the usage of PLAXIS Connect is a new licence updating tool, simple it is. Look on our site in the FAQ’s section PLAXIS 2D 2010 and PLAXIS 3D 2010. which is automatically installed together with our for the FAQ about PLAXIS Connect: www.plaxis. latest software. The new tool can be used for any nl/faq The software packages on the introductory are 2010 version software and onwards. limited editions but you can use them to learn PLAXIS Introductory about the program and even perform real analysis With the new tool, updating your licence has At the time we are printing this bulletin we are also on simplified situations. become even easier. Simply place your CodeMeter finalising our new PLAXIS Introductory. licence key in the computer, open PLAXIS Connect Furthermore a special Student Version will be and click to update your licence. The program will Containing the 2010 versions of our PLAXIS 2D and made of the introductory. The student version automatically search our server for an update. It PLAXIS 3D software, this new Introductory will be will include a student guide, and is intended for can’t get any simpler than that. a movie driven introductory. This contains many student as free software to learn the basics of 2D movies on the workflow of the new programs, on and 3D modelling in geotechnical engineering. Besides this, the new program can also be used to tutorials, but also to explain in detail important validate your installed software and keep it up to features. Visit our site www.plaxis.nl to order your free copy date. Furthermore it will warn you when updates of the introductory. are available, and show you the latest news about One of the new features in some of these movies is our products and services. the spoken comments. Besides this, in the movies

14 Plaxis Bulletin l Spring 2011 l www.plaxis.nl Plaxis Asia-Pacific Marriott Wardman Park, Omni Shoreham, and 1st BPUM. This first edition of the Belgium Plaxis Since the 1st of March 2011 the Plaxis Asia office in Washington Hilton hotels. As in recent years, the Users Meeting did attract more than 30 Plaxis Singapore has been renamed into Plaxis AsiaPac program has been attracting more than 10,000 professionals from Belgium companies. This first Pte Ltd. To strengthen the activities already being transportation professionals from around the event was hosted by Besix in Brussels and had carried out under the name of Plaxis Asia, the world. The TRB annual meeting program covers all nice presentations on the use of PLAXIS 2D and office has been registered as a legal entity and a transportation modes (, rail and air), with more PLAXIS 3D. 100% daughter company of Plaxis bv. than 4,000 presentations in nearly 650 sessions and workshops addressing topics of interest In February the Dutch Plaxis User Association At the same time the Plaxis AsiaPac team will to policy makers, administrators, practitioners, (PGV) organised a workshop on 2 subjects. expand with 2 new people. Besides our existing researchers, and representatives of government, The workshop started with the exposure of the colleagues at Plaxis AsiaPac, Eddy Tan and William industry, and academic institutions. More than 85 new PLAXIS VIP interoperable features. The Cheang, we will be joined by new staff; Joseph sessions and workshops addressed the spotlight participants learned about the do’s and don’ts Wong and Xing Cheng Lin. theme for 2011: Transportation, Livability, and in importing geometry from AutoCad and other Economic Development in a Changing World. CAE software in PLAXIS 2D 2010 and PLAXIS Recent Events 3D 2010 (see figures 1 & 2). The second part of In January Plaxis presented itself at the 90th Following the successful annual EPUM in the workshop focused on the modelling of an Annual meeting of the Transportation Research November 2010 in Germany and DPUM early this and especially on the differences Board (TRB) held in Washington, D.C., at the year in the Netherlands we proudly organized the between 2D and 3D modelling.

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Figure 1: Drawing in AutoCAD Figure 2: Import of AutoCAD file in PLAXIS 2D 2010

www.plaxis.nl l Spring 2011 l Plaxis Bulletin 15 Title

Activities 2011

March 13 - 16, 2011 June 5 - 8, 2011 September 13 - 19, 2011 Geo-Frontiers 2011 2011 International Bridge Conference XV European Conference on Soil Mechnics & Dallas, TX, USA Pittsburg, PA, USA Geotechnical Engineering Athens, Greece March 21 - 24, 2011 June 8 - 9, 2011 Advanced Course on Computational Geotechnics Plaxis Seminar September 2011 Schiphol, The Netherlands Seoul, South Korea Standard Course on Computational Geotechnics Chennai, India April 7, 2011 June 16 – 18, 2011 Singapore Plaxis Users Meeting TC 28 IS Roma 2011 October 18 - 21, 2011 Singapore Rome, Italy 36th Annual Conference on Deep Foundations Boston, MA, USA April 7 - 9, 2011 June 21 – 23, 2011 Standard Course on Computational Geotechnics Standard Course on Computational Geotechnics November 16 – 18, 2011 Rio de Janeiro, Brazil Manchester, United Kingdom European Plaxis Users Meeting Karlsruhe, Germany April 13 – 15, 2011 June 22 - 24, 2011 Applicazione del Metodo degli Elementi Finiti Standard Course on Computational Geotechnics November 22 - 25, 2011 Nell’Ingegneria Geotecnica Shanghai, China Advanced Course on Computational Geotechnics Genova, Italy Hong Kong, China July 6 - 8, 2011 April 21, 2011 Advanced Course on Computational Geotechnics November 22 - 25, 2011 Malaysian Plaxis Users Meeting Singapore Standard Course on Computational Geotechnics Kuala Lumpur, Malaysia Paris, France August 16 – 19, 2011 May 2 – 5, 2011 Standard Course on Computational Geotechnics November 2011 Curso de Geotecnia Computacional & Dynamics Advanced Course on Computational Geotechnics Querétaro, Mexico Vancouver, Canada Gold Coast, Australia

May 10 - 11, 2011 August 29 – September 1, 2011 November 2011 Plaxis Seminar Standard Course on Computational Geotechnics Asia-Pacific Plaxis Users Meeting Bangkok, Thailand Gothenburg, Sweden Gold Coast, Australia

May 16 - 18, 2011 August 31 – September 2, 2011 Advanced Course on Computational Geotechnics Advanced Course on Computational Geotechnics Istanbul, Turkey Manchester, United Kingdom

May 23 – 27, 2011 September 5 - 7, 2011 14th ARC on Soild mechanics & Geotechnical European Young Geotechncal Engineers Engineering Conference Hong Kong, China Rotterdam, The Netherlands

Plaxis bv P.O. Box 572 www.plaxis.nl Plaxis AsiaPac Pte Ltd 16 Jalan Kilang Timor Delftechpark 53 2600 AN Delft Tel +31 (0)15 2517 720 Singapore #05-08 Redhill Forum 2628 XJ Delft The Netherlands Fax +31 (0)15 2573 107 Tel +65 6325 4191 159308 Singapore