Plaxis Bulletin...PLAXIS 3D is described by some early users. In addition to another interesting article by PLAXIS users, this bulletin also describes some recent and future activities.

Title

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

Editorial

Issue 29 / Spring 2011

Plaxis Bulletin

Pag

e 14

Table of Contents

Pag

e 4

Pag

e 6

Pag

e 10

ColophonAny correspondence regarding the Plaxis Bulletin can be sent by e-mail to:

[email protected]

or by regular mail to:

Plaxis Bulletinc/o Annelies VogelezangP.O. Box 5722600 AN DelftThe Netherlands

The Plaxis Bulletin is a publication of Plaxis bv and is distributed worldwide among Plaxis subscribers

Editorial board:Wout BroereRonald BrinkgreveErwin BeerninkArny Lengkeek

Design: Jori van den Munckhof

For information about PLAXIS software contact your local agent or Plaxis main office:

Plaxis bvP.O. Box 5722600 AN DelftThe Netherlands

[email protected]

Tel: +31 (0)15 251 7720Fax: +31 (0)15 257 3107

» The Plaxis Bulletin is the combined magazine of Plaxis bv and the Plaxis users association (NL). The bulletin focuses on the use of the finite element method in geotechnical engineering practise and includes articles on the practical application of the PLAXIS programs, case studies and backgrounds on the models implemented in PLAXIS.

The bulletin offers a platform where users of PLAXIS can share ideas and experiences with each other. The editors welcome submission of papers for the Plaxis Bulletin that fall in any of these categories.

The manuscript should preferably be submitted in an electronic format, formatted as plain text without formatting. It should include the title of the paper, the name(s) of the authors and contact information (preferably e-mail) for the corresponding author(s). The main body of the article should be divided into appropriate sections and, if necessary, subsections. If any references are used, they should be listed at the end of the article. The author should ensure that the article is written clearly for ease of reading.

In case figures are used in the text, it should be indicated where they should be placed approximately in the text. The figures themselves have to be supplied separately from the text in a vector based format (eps,ai). If photographs or ‘scanned’ figures are used the author should ensure that they have a resolution of at least 300 dpi or a minimum of 3 mega pixels. The use of colour in figures and photographs is encouraged, as the Plaxis bulletin is printed in full-colour.

03 Editorial

04 New Developments

05 PLAXIS Expert Services Update

06 Effect of Anisotropy on Ten sile Stresses at the Bottom of a Base Course in Flexible Pavements

10 3D Finite Elements Analysis of a Deep Excavation in Monaco

14 Recent Activities

mailto:bulletin%40plaxis.nl?subject=Plaxis%20Bulletinmailto:info%40plaxis.nl?subject=Info%20request%20PLAXIS%20softwarehttp://www.plaxis.nl

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

Editorial

» Since the release of the new PLAXIS 3D program last summer, more than 300 licenses have been sold. It seems that many users have been waiting for an easy-to-use true three-dimensional modelling environment for their complex geotechnical applications, and that PLAXIS 3D accommodates their requirements.

In this bulletin a first practical application using PLAXIS 3D is described by some early users. In addition to another interesting article by PLAXIS users, this bulletin also describes some recent and future activities. In fact, the list of activities is growing, in line with the steady growth of the Plaxis organization itself, which enables us to serve you even better. For more information see the end of this bulletin.

The first user’s contribution involves a study on the effect of anisotropy on tensile stresses in a granular base for flexible pavements using an axi-symmetric finite element model. Anisotropic stiffness in the granular base was modelled using the elastic part of the Jointed Rock model. Different anisotropic stiffness properties were used to investigate the influence on the tensile stresses. It was concluded that anisotropy can lead to a reduction in the tensile stress in the granular 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

detailed description of the complex situation and shows some interesting model sections, including a global view of all the anchors. It was concluded that the new PLAXIS 3D program is quite capable and efficient to model this complex situation and was able to produce satisfactory results.

In addition to the contributions by PLAXIS users, the New Developments column describes a new ‘dimension’ which the Plaxis research team is working on: the modelling of thermal flow and thermo-hydro-mechanical coupling. This enables temperature to be taken into account in the analysis of soil behaviour and soil-structure interaction. The bulletin also describes the positive experiences of a company with a dedicated in-house training course in the framework of PLAXIS Expert Services.

All together we trust to have composed another interesting bulletin for you. Do not hesitate to send us your comments or contact the corresponding author in case you like to discuss some items. We wish you an interesting reading experience and look forward to receiving your contributions for future issues of the Plaxis Bulletin.

The Editors

Editorial

http://www.plaxis.nl

4 Plaxis Bulletin l Spring 2011 l www.plaxis.nl

where temperature could play a role, and it would be convenient if you could take this into account within your PLAXIS analysis.

The development of THM coupling is still a research project. At the moment we are working on a 2D research version and later this year we will make a full 3D implementation. However, it will take some time before this feature will become available in future PLAXIS versions. Nevertheless, by moving into this new ‘dimension’ we are confident to provide you with the right tools to solve your future geo-engineering challenges as well.

New Developments

»A further step is now taken by adding temperature as a degree-of-freedom in the finite element calculations and considering thermal flow in the soil as a result of temperature differences. The first aim is simply to calculate a change of the temperature distribution in the soil by thermal flow and diffusion, and to impose this on a mechanical model of the soil structure with the purpose to calculate thermal expansion or shrinkage (using the thermal expansion coefficients of the respective materials). In this case, thermal flow and deformations are semi-coupled. Another situation to be considered is the effect that temperature differences may cause 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.

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 tunnels and excavations.

• Stability of slopes considering precipitation and evaporation using temperature-dependent water retention curves.

• Geotechnical engineering in permafrost areas.• Efficiency and sustainability of geothermal en-

ergy systems (borehole heat exchangers, heat/cold storage, energy piles)

Not all these examples are as complicated as the term ‘THM coupling’ would suggest. Not in all cases a full coupling is necessary. We will implement simplified calculation options to avoid unnecessary complexity. If you think about it, you may find an example from your own experience

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.

Ronald Brinkgreve, Plaxis bv

Figure 1. Temperature distribution from THM Analysis



»TPS had several people requiring training on the modeling of deep excavations using PLAXIS 2D and more particularly in the case of propped cantilever retaining walls. The intention of TPS was to give a number of their geotechnical and civil engineering graduates a course with a balance between an overview of PLAXIS 2D and its modeling capabilities together with a worked example requiring practical hands-on computer analyses of a current project using the PLAXIS software. In this context, typical soil model and design parameters for a section of propped secant piled wall taken from a recent project design was provided.

Proposed Course ScheduleThe first part of this course (morning session) was organized with fundamental lectures on PLAXIS 2D features and on the use of the software in the most relevant aspects involved in deep excavations modeling. The morning session was split in two parts: Morning Session Part I:• Introduction to PLAXIS 2D

• Input program• Calculation facilities• Output program

• Geometry and Mesh Selection• Overview of Soil Material Models in Plaxis

Morning Session Part II:• Initial Stresses Definition in Plaxis• Modeling Deep Excavation in Plaxis

• Structural elements• Dewatering• Interaction soil-structure

The afternoon session was focusing on practical applications and organized around relevant hands-on exercises as follows:• Practical application I: Dry excavation using a

tied back wall• Practical application II: Settlement due to tun-

nel construction• Worked example: Modeling of a propped

retaining wall with PLAXIS• Comparison with WALLAP.

ConclusionsUpon request Plaxis has provided high-level technical assistance in setting up a one-day practical training course which has been customized to TPS specific requirements. PLAXIS Expert Services has boosted TPS’s analytical skills in the field of deep excavations and increased their productivity resulting in a faster return on their software utilization and investment.

“Excellent course run by a very knowledgeable Plaxis representative. There was a good blend of theory which was augmented by a workshop where we were talked through a worked example. Highly recommended for anyone looking for an introduction to PLAXIS and FE modelling”

The CompanyTPS (part of the Carillion Group) is a team of professional engineers, architects, project managers and consultants. Their extensive range of engineering skills and specialist knowledge enables them to provide professional expertise across all aspects of the construction industry. TPS provides comprehensive integrated services to a wide client base including government, local authority and private sector businesses.

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.

Jon Holliday, TPS Consult

PLAXIS Expert Services Update

“Highly recommended for anyone looking for an introduction to PLAXIS and FE modelling”

TPS has a proven track record of meeting tough challenge and finding cost-effective solutions to complex technical problems throughout the project life cycle, backed by quality, health and safety, and environmental management system certification.

Customer Quotes“An extremely useful introduction to PLAXIS 2D with a course tailored to suit our requirements. The presentations were concise and well delivered with plenty of opportunity for questions and discussion. The course tailored by Plaxis also provided a hands-on practical workshop assisted by a very knowledgeable and helpful Plaxis representative.”



Many studies have used anisotropic models coupled with non-linear behavior (stress-dependent stiffness) for the base course when analyzing pavements. Herein, the effects of anisotropy alone are studied assuming a constant stiffness in the base course until it yields. This was achieved using the Jointed Rock model in PLAXIS.

The Jointed Rock ModelThe Jointed Rock model is a cross-anisotropic, elastic, perfectly-plastic model, especially meant to simulate the behavior of stratified and jointed

rock layers. In this model, two angles define the plane of sliding as shown in Figure 1: the dip (α1 )and strike (α2 ). For a pavement system with a base course that is cross-anisotropic with a vertical axis of symmetry, α1 0= and α2 = 90°.

Using the Jointed Rock model, the stress-strain curve for the base course is linear (stiffness not sensitive to stress level) until the yield point is reached.


» Studies by Tutumluer (1995) and Tutumluer and Thompson (1997) have shown that tensile stresses can be reduced or eliminated by treating the base course as anisotropic rather than isotropic. According to Kim et al. (2005) anisotropy naturally occurs in unbound materials due to preferred orientation and arrangement of aggregates as a result of their physical properties (gradation and shape) and compaction forces.

A truly anisotropic elastic material requires the specification of 21 independent parameters or 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.

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 subgrade. 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).

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

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



The stress-strain behavior in the elastic range can be completely described using the following five parameters:

E1 = Young’s modulus in the horizontal directionE2 = Young’s modulus in the vertical directionν1 = Poisson’s ratio for straining in the horizontal direction due to stress acting also in a horizontal but orthogonal directionν 2 = Poisson’s ratio for straining in the horizontal direction due to stress acting in a vertical directionG2 = Shear modulus in the vertical direction

For a cross-anisotropic material, strains are related to stresses through the compliance matrix as follows:

(Eq. 1)

εε

εγ

γ

γ

ν ν

νx

y

z

xy

yz

xz

E E E

E

=

− −

−

10 0 0

11

2

2

1

1

2

2 EE E

E E E

G

G

E

2

2

2

1

1

2

2 1

2

2

1

1

0 0 0

10 0 0

0 0 01

0 0

0 0 0 01

0

0 0 0 0 02 1

−

− −

+

ν

ν ν

ν( )

σσ

στ

τ

τ

x

y

z

xy

yz

xz

In the plastic range, the Mohr-Coulomb parameters c and φ along with the dilatancy angle, ψ , and tensile strength govern the material’s behavior.

In the Jointed Rock model, sliding is only permitted in three different directions, one of which corresponds to the direction of elastic anisotropy. In PLAXIS, a warning message is issued when the Jointed Rock model is used in an axi-symmetric analysis. This is because a dip

greater than 0 will mean that the sliding plane is conical rather than planar. However, a dip of zero can theoretically be analyzed axi-symmetrically. To verify this, two identical axi-symmetric runs were made in PLAXIS with the base course modeled as an isotropic material using both the Mohr-Coulomb and Jointed Rock

(E = E1 = E2, ν = ν1= ν 2, G G

E2(1 )2

= =+ν )

models. Both gave identical results indicating that the Jointed Rock model can be used in an axi-symmetric analysis when the dip is 0.

The Graham and Houlsby Simplification for Cross-AnisotropyBy defining a new parameter, α , Graham and Houlsby (1983) reduced the number of constants from five to three for a cross-anisotropic material. The three parameters, modified Young’s modulus, E*, modified Poisson’s ratio, ν ∗, and anisotropy factor, α , are defined as follows:

(Eq. 2)E E∗ = 2

(Eq. 3)ν ν∗ = 1

(Eq. 4)α 2 12

=EE

The other three parameters E1, ν 2 and G2, are dependent on parameters E2, ν 2, and α as shown below:

(Eq. 5)E E12

2= α

(Eq. 6)α2 1

2

=EE

(Eq. 7)GE

22

12 1=

+α

ν( )

The compliance matrix can now be re-expressed in terms of E*, ν ∗ and α as follows:

(Eq. 8)

εε

εγ

γ

γ

ανα

να

ναx

y

z

xy

yz

xz

E

=

− −

−

1

10 0 02 2

*

* *

*

11 0 0 0

10 0 0

0 0 02 1

0 0

0 0 0 02 1

0

0 0 0 0 02 1

2 2

−

− −

+

+

να

να

να α

να

να

*

* *

*

*

( )

( )

( ++

να

σσ

στ

τ

τ

* )2

x

y

z

xy

yz

xz

For a material that is isotropic, α = 1. For a material that is stiffer in the vertical direction, α < 1 and α > 1 when the material is stiffer in the horizontal direction. Since the compacted base course is likely to be stiffer in the vertical direction, it follows that 0 < α < 1. Linear elastic isotropic materials cannot have a Poisson’s ratio > 0.5. However, Poisson’s ratio for a linear, elastic, anisotropic material can exceed 0.5. In the Jointed Rock model, a value of Poisson’s ratio > 0.5 cannot be input in PLAXIS. This limits the lower bound value of α that can be studied herein.

AnalysisA 3-layer axi-symmetric flexible pavement system as shown in Fig. 2 was used in this study. A single wheel load that is circular in plan with a radius of 254 mm and having a uniform pressure of 690 kPa was applied on the top of the pavement. The asphalt layer and subgrade were assumed to be homogeneous and isotropic. The asphalt layer was treated as a linear elastic material while a Mohr-Coulomb model was used to describe the subgrade. Rigid interface elements were assumed between layers.



EffEct of Anisotropy on tEnsilE strEssEs At thE Bottom of A BAsE coursE in flExiBlE pAvEmEnts

Table 1: Summary of parameters in PLAXIS analysis

Figure 3: Variation of maximum tensile stress at the bottom of the unbound base course with respect to α assuming ν1 = 0.3

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 exceed 0.5 in PLAXIS.

ResultsWhen 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. The maximum horizontal tensile stress (σ x x− max) 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 from 1 to 0.9. Thereafter, σ x x− maxdecreases with increasing α indicating that by considering anisotropy in the base course, tensile stresses do reduce. However, σ x x− max does not reduce to zero in this set of calculations.

To reduce σ x x− max further:

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

Model Prameters

Description Asphalt Layer Unbound Granular Base Subgrade

Material Model Linear Elastic Jointed Rock Model Mohr-Coulomb

Material Type Drained Drained Drained

γunsat = kNm3Moist unit weight 24.7 16.0 14.9

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

ν1 Poisson’s ratio for a cross-anisotropic material N/A 0.3 N/A

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

ν 2Poisson’s ratio for a

cross-anisotropic material N/A Calculated (Eq. 6) N/A

G2 (MPa)Shear Modulus for a

cross-anisotropic material N/A Calculated (Eq. 7) N/A

c (kPa) Cohesion N/A 0.01 0.01

φ (º) Friction 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

Figure 2: Flexible pavement section analyzed




2. other factors such as stress/strain dependent modulus and the effects of overconsolidation on K0 should be considered in pavement analysis.

Another observation of note from Fig. 3 is that the results are relatively insensitive to the value of E2 for this set of parameters analyzed.

Summary and ConclusionsThe influence of the anisotropy factor (α ) on the horizontal tensile stresses generated in unbound base course layers in flexible pavements was analyzed using the Jointed Rock model in PLAXIS. A non-stress sensitive cross-anisotropic model was assumed for the base course using five constants. By defining an anisotropy factor, α , the number of elastic parameters reduces from five to three. The results show that anisotropy can lead to a reduction in the tensile stress in the unbound base layer. However, the value of α is constrained in this study because PLAXIS does not allow the user to specify a value of ν 2 greater than 0.5 when in fact, a Poisson’s ratio > 0.5 is admissible with anisotropic materials. The Jointed Rock model can become more versatile if this limitation is removed in PLAXIS.

It is well known that the behavior of unbound granular layers is not linear and the resilient modulus (or Young’s modulus) is highly dependent on the stress state. If stiffness nonlinearity (stress-sensitive stiffness) can be incorporated in a cross-anisotropic constitutive model, the modification can prove beneficial to both the geotechnical and pavement engineering community.

Reference• Graham, J., Houlsby, G.T., 1983. Anisotropic

Elasticity of a Natural Clay. Geotechnique 33, No. 2, pp. 165-180.

• Kim, S.H., Little, D.N., Masad, E., Lytton, R.L., 2005. Estimation of Level of Anisotropy in Un-bound Granular Layers Considering Aggregate Physical Properties. The International Journal of Pavement Engineering, Vol. 6, No. 4, pp. 217-227, Taylor & Francis.

• Love, A.E.H., 1927. A Treatise on the Mathemati-cal Theory of Elasticity, 4th edition. Cambridge University Press.

• Masad, S., Little, D., Masad, E., 2006. Analysis of Flexible Pavement Response and Performance Using Isotropic and Anisotropic Material Prop-erties. Journal of Transportation Engineering, Vol. 132, No. 4, pp. 342-349, ASCE.

• Plaxis (2005). PLAXIS 2D: Reference Manual, Version 8.2, Plaxis bv, Delft, The Netherlands.

• Tutumluer, E., 1995. Predicting Behavior of Flexible Pavements with Granular Bases. PhD Dissertation, Georgia Institute of Technology, Atlanta, GA.

• Tutumluer, E., Thompson, M.R., 1997. Aniso-tropic Modeling of Granular Bases in Flexible Pavements. Transportation Research Record 1577, pp. 18-26, TRB, National Research Board, National Research Council, Washington, D.C.



»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

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.

3D Finite Element Analysis of a Deep Excavation in MonacoMarie Porquet, Alain Guilloux and Samy Chakroun, TerrasolRichard Witasse, Plaxis bv

Figure 1: Top view of the modeled area



new retaining walls built during the works) and to describe the general behavior of the school structure. PLAXIS 3D 2010 has been used for this calculation.

Underground ConstructionOur calculation focused on a local model (only part of the entire project) including the different new retaining structures set up near the middle school. Thus we restricted the model to the neighborhood of the new retaining wall, including the existing wall and the new wall, the middle school, and a part of the excavation pit.The soils located uphill the middle school and the excavation were taken into account for initial stresses calculation, without modelling the other existing buildings. The soils located uphill the excavation were deactivated afterward to shorten the calculation time (cf. Figure 1).

Geotechnical profileThe three soil layers encountered on the construction site are the following: superficial colluviums lying over Marls and Calcareous Marls,

with a local Limestone layer located downhill the model. All these layers are tilted.Given the complexity of the different layers, the definition of 28 boreholes was necessary to fully describe the soil model. We used the Mohr-Coulomb model for all soil layers: as a previous model of the excavation was realized using the Mohr-Coulomb model, which is accetable when dealing with rock, we kept using it to be able to compare the results of both models. The soil properties are described in Table 1.

Structural ElementsThe model includes the existing retaining structures, which are:• The old 16 m high anchored wall (from 87 NGM

to 71 NGM) associated to the middle school, made of reinforced concrete;

• The T-shaped reinforced concrete walls of the existing terraces uphill the school;

The model also includes the walls of the new retaining structures, which are:• A soldier-pile wall with 10 piles (Ø 1000 mm)

Table 1: Soil properties

Loading (kN/m3) E(kPa) c’(kPa) (º) (º)

Screes 20 0.101E6 0.30 10 30 0

MCM 24 1.218E6 0.30 30 32 0

Limestone 24 1.600E6 0.30 70 38 0

φ ψν

Unloading (kN/m3) E(kPa) c’(kPa) (º) (º)

Screes 20 0.111E6 0.43 10 30 0

MCM 24 1.336E6 0.43 30 32 0

Limestone 24 1.816E6 0.30 70 38 0

φ ψν

γunsat

γunsat

of variable height (26 m to 14 m, from max. 100 NGM to min. 74 NGM), made of shotcrete and reinforced concrete;

• A soldier-micropile wall with 4 micropiles (Ø 280 mm) approximately 9 m high (from 87 NGM to min. 78 NGM), made of shotcrete;

• A 48 m deep diaphragm wall (from 74 NGM to 26.4 NGM), with 10 m embedment below the raft of the underground structures.

Those retaining structures include piles, micropiles, shotcrete and reinforced concrete, and prestressed anchors with various inclinations. Besides, the floors of the tower basements are built while the excavation goes on, from 73 NGM to 36.8 NGM.

Some structural simplifications were necessary while building the model. The three main simplifications are the following:• The main simplification was that only a part

of the excavation has been introduced in our model. In order to take into account the interaction with the other part, a surface of zero prescribed displacements was defined in the center of the excavation, and only the South half of the excavation and the floors was modeled (using the project symmetry).

• The middle school building structure was not modeled: only the building load was taken into account. Besides, the foundations (piles) of the middle school were not modeled but the building load was applied at the piles tip level (64 NGM).

• The existing wall of the middle school (M1) consists of an anchored wall. Only the anchors placed near the excavation (approximately 30 m) were modeled. The wall part most distant from the excavation pit (which does not have much influence on the works) was modeled by a plate with prescribed displacements.



Plates e (m) (kN/m3) E (kPa)

Middle School (M1) 0.60 25 20E6 0.25

M6_wall 0.30* 25 20E6 0.25

M6_foot 0.40* 25 20E6 0.25

Shotcrete 0.20 24 25E6 0.25

Reinforced concrete 0.40 25 25E6 0.25

Diaphragm wall 0.82 25 30E6 0.25

Floors Variable 25 35E6 0.25

γ ν

Beams dfor (m) Atot (m2) dext (m) dint (m) Aa (m

2) Ab (m2) γ (kN/m3) E (kPa) E (m4)

Micropiles 0.28 0.062 0.22 0.17 0.0137 0.048 70 194E6 6.7E-5

Piles 1.00 0.785 - - - - 25 30.0E6 4.9E-2


Table 2: Plate properties Table 4: Beam properties

Anchored part

Type E(GN/m2) γ(kN/m3) A(mm2) d(m) Tskin(kN/m)7T15Eb 194E6 70 980 0.035 70

7T15MMC 194E6 70 980 0.035 112

9T15Eb 194E6 70 1260 0.040 70

9T15MMC 194E6 70 1260 0.040 112

7T13MMC 194E6 70 651 0.029 112

10T13MMC 194E6 70 930 0.034 112

12T13MMC 194E6 70 116 0.038 112

13T13MMC 194E6 70 1209 0.039 112

Anchors Free part

Structure Type E (GN/m2) A (mm2) EA (kN)

Soldier pile wall

Dywidag φ 36mm 194 1018 197.47E

3

7T15 194 980 190.12E3

9T15 194 1260 244.44E3

Middle school

existing wall M1

7T13 194 651 126.29E3

10T13 194 950 180.42E3

12T13 194 1116 216.50E3

13T13 194 1209 234.55E3

Table 3: Anchor properties

Figure 2: Global view of all the plates

Figure 3: Global view of all the anchors

Finally, the structural elements used in the model (cf. Figure 2 and Figure 3, page 12) are the following: 6 existing (anchored) walls, 2 new soldier pile walls, the diaphragm wall around the excavation, 13 floors inside the excavation, 15 piles and 140 anchors.

The material properties for the structural elements are presented in Table 2 to Table 4.

Model and mesh propertiesThe final model dimensions are the following:• 165 m long in the East-West direction;• 130 m wide in the North-South direction;• Levels from 130 NGM to 10 NGM.

It includes approximately 137,700 elements with an average size of 5 m, and approximately 198,740 nodes (cf. Figure 4).

Loads and Boundary ConditionsInitial stressesThe stresses initialization is performed during the initial calculation phase, using gravity loading with all soil clusters activated.

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.

Applied overloadsA structural overload of 150 kPa is applied at the base of the school piles (at 64 NGM), which corresponds to a distributed load of 15 kPa by floor for a building composed of a ground floor and 9 floors (cf. Figure 5).

Hydraulic conditionsWe considered for the present calculation that drains are introduced behind the retaining structures: thus the water level was assumed to be lowered below the structures and was therefore not considered in the current model.

Boundary conditions: displacementsDuring the initial phase, the boundary conditions are the Plaxis standard boundary conditions:• Zero prescribed displacements along the x axe

on the yz borders;• Zero prescribed displacements along the y axe

on the xz borders;• Zero prescribed displacements along the x, y

and z axes on the model base.

During the calculation, after deactivation of the soil clusters located uphill and North to the

excavation, additional surfaces of prescribed displacements have been defined:• Zero prescribed displacements along the y-axis

on the East-West plan placed uphill the middle school, to retain the grounds;

• Zero prescribed displacements along the x-axis on the North-South plan uphill the excavation, to retain the grounds to be excavated;

• Zero prescribed displacements along the x, y and z axis on the plan oriented North East-South West, placed at the center of the excavation, enforcing symmetry conditions.

Staged ConstructionTo model the whole construction process, 43 calculation phases were necessary: the initial phase (0) to calculate the initial stresses, phase 1 to deactivate some of the soil clusters, and after that, two calculation phases for each excavation phase (one to deactivate the excavated grounds, and one to activate the retaining structures).

Main ResultsThe whole project lasted 2 month. We needed 7 weeks to create the definitive model and to define all the calculation phases, 2 weeks to



The final results were totally satisfying, and our conclusion about using PLAXIS 3D 2010 is very positive. Using the command line feature proved to be a highly useful tool: we could not have achieved the whole meshing and the calculations as quickly as we did without that tool.

The results post-processing in terms of displacements and loads has been achieved rather rapidly thanks to the Output tools (many display options and ability to select part of the structures only).


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

achieve the calculations, and 1 week to analyze the model results. Given the high number of elements and calculation phases, the whole calculation required almost 12 hours to be completed.

The model results show that the new retaining structures should guarantee the stability of the excavation as well as the one of the school building. The total displacements of the new retaining structures do not exceed 5 mm in the present simulation. The Figure 6 shows a model global view with total displacements.

ConclusionComparing 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.



Recent Activities

PLAXIS ConnectPLAXIS Connect is a new licence updating tool, which is automatically installed together with our latest software. The new tool can be used for any 2010 version software and onwards.

With the new tool, updating your licence has become even easier. Simply place your CodeMeter licence key in the computer, open PLAXIS Connect and click to update your licence. The program will automatically search our server for an update. It can’t get any simpler than that.

Besides this, the new program can also be used to validate your installed software and keep it up to date. Furthermore it will warn you when updates are available, and show you the latest news about our products and services.

Watch the instructional movie, and find out how simple it is. Look on our site in the FAQ’s section for the FAQ about PLAXIS Connect: www.plaxis.nl/faq

PLAXIS IntroductoryAt the time we are printing this bulletin we are also finalising our new PLAXIS Introductory.

Containing the 2010 versions of our PLAXIS 2D and PLAXIS 3D software, this new Introductory will be a movie driven introductory. This contains many movies on the workflow of the new programs, on tutorials, but also to explain in detail important features.

One of the new features in some of these movies is the spoken comments. Besides this, in the movies

you can also experience first hand the usage of PLAXIS 2D 2010 and PLAXIS 3D 2010.

The software packages on the introductory are limited editions but you can use them to learn about the program and even perform real analysis on simplified situations.

Furthermore a special Student Version will be made of the introductory. The student version will include a student guide, and is intended for student as free software to learn the basics of 2D and 3D modelling in geotechnical engineering.

Visit our site www.plaxis.nl to order your free copy of the introductory.



Plaxis Asia-PacificSince the 1st of March 2011 the Plaxis Asia office in Singapore has been renamed into Plaxis AsiaPac Pte Ltd. To strengthen the activities already being carried out under the name of Plaxis Asia, the office has been registered as a legal entity and a 100% daughter company of Plaxis bv.

At the same time the Plaxis AsiaPac team will expand with 2 new people. Besides our existing colleagues at Plaxis AsiaPac, Eddy Tan and William Cheang, we will be joined by new staff; Joseph Wong and Xing Cheng Lin.

Recent EventsIn January Plaxis presented itself at the 90th Annual meeting of the Transportation Research Board (TRB) held in Washington, D.C., at the

Marriott Wardman Park, Omni Shoreham, and Washington Hilton hotels. As in recent years, the program has been attracting more than 10,000 transportation professionals from around the world. The TRB annual meeting program covers all transportation modes (road, rail and air), with more than 4,000 presentations in nearly 650 sessions and workshops addressing topics of interest to policy makers, administrators, practitioners, researchers, and representatives of government, industry, and academic institutions. More than 85 sessions and workshops addressed the spotlight theme for 2011: Transportation, Livability, and Economic Development in a Changing World. Following the successful annual EPUM in November 2010 in Germany and DPUM early this year in the Netherlands we proudly organized the

1st BPUM. This first edition of the Belgium Plaxis Users Meeting did attract more than 30 Plaxis professionals from Belgium companies. This first event was hosted by Besix in Brussels and had nice presentations on the use of PLAXIS 2D and PLAXIS 3D.

In February the Dutch Plaxis User Association (PGV) organised a workshop on 2 subjects. The workshop started with the exposure of the new PLAXIS VIP interoperable features. The participants learned about the do’s and don’ts in importing geometry from AutoCad and other CAE software in PLAXIS 2D 2010 and PLAXIS 3D 2010 (see figures 1 & 2). The second part of the workshop focused on the modelling of an embankment and especially on the differences between 2D and 3D modelling.

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


Title

16 Jalan Kilang Timor#05-08 Redhill Forum

159308 Singapore

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The Netherlands

www.plaxis.nlTel +31 (0)15 2517 720Fax +31 (0)15 2573 107

Plaxis AsiaPac Pte LtdSingapore

Tel +65 6325 4191

Plaxis bvDelftechpark 53

2628 XJ Delft

March 13 - 16, 2011Geo-Frontiers 2011Dallas, TX, USA

March 21 - 24, 2011Advanced Course on Computational GeotechnicsSchiphol, The Netherlands

April 7, 2011Singapore Plaxis Users MeetingSingapore

April 7 - 9, 2011Standard Course on Computational GeotechnicsRio de Janeiro, Brazil

April 13 – 15, 2011Applicazione del Metodo degli Elementi Finiti Nell’Ingegneria GeotecnicaGenova, Italy

April 21, 2011Malaysian Plaxis Users MeetingKuala Lumpur, Malaysia

May 2 – 5, 2011Curso de Geotecnia ComputacionalQuerétaro, Mexico

May 10 - 11, 2011Plaxis SeminarBangkok, Thailand

May 16 - 18, 2011Advanced Course on Computational GeotechnicsIstanbul, Turkey

May 23 – 27, 201114th ARC on Soild mechanics & Geotechnical EngineeringHong Kong, China

June 5 - 8, 20112011 International Bridge ConferencePittsburg, PA, USA

June 8 - 9, 2011Plaxis SeminarSeoul, South Korea

June 16 – 18, 2011TC 28 IS Roma 2011Rome, Italy

June 21 – 23, 2011Standard Course on Computational GeotechnicsManchester, United Kingdom

June 22 - 24, 2011Standard Course on Computational GeotechnicsShanghai, China

July 6 - 8, 2011Advanced Course on Computational GeotechnicsSingapore

August 16 – 19, 2011Standard Course on Computational Geotechnics & DynamicsVancouver, Canada

August 29 – September 1, 2011Standard Course on Computational GeotechnicsGothenburg, Sweden

August 31 – September 2, 2011Advanced Course on Computational GeotechnicsManchester, United Kingdom

September 5 - 7, 2011European Young Geotechncal Engineers ConferenceRotterdam, The Netherlands

September 13 - 19, 2011XV European Conference on Soil Mechnics & Geotechnical EngineeringAthens, Greece

September 2011Standard Course on Computational GeotechnicsChennai, India

October 18 - 21, 201136th Annual Conference on Deep FoundationsBoston, MA, USA

November 16 – 18, 2011European Plaxis Users MeetingKarlsruhe, Germany

November 22 - 25, 2011Advanced Course on Computational GeotechnicsHong Kong, China

November 22 - 25, 2011Standard Course on Computational GeotechnicsParis, France

November 2011Advanced Course on Computational GeotechnicsGold Coast, Australia

November 2011Asia-Pacific Plaxis Users MeetingGold Coast, Australia

Activities 2011

Plaxis Bulletin...PLAXIS 3D is described by some early users. In addition to another interesting article by PLAXIS users, this bulletin also describes some recent and future activities.

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