plaxis bulletin bulletin comparison of structural elements response in plaxis 3d and sap2000 ... 3d...

Title

Editorial

Issue 35 / Spring 2014

Plaxis Bulletin

Comparison of Structural Elements Response in PLAXIS 3D and SAP2000

Reliability of Quay Walls Using Finite Element Analysis

3D Finite Element Analysis of a Complex Excavation

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Table of contents

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

[email protected]

or by regular mail to:

Plaxis Bulletinc/o Annelies VogelezangPO Box 5722600 AN DelftThe Netherlands

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

Editorial board:Erwin BeerninkRonald BrinkgreveMartin de KantArny 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]: +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.

Editorial03

New Developments04

Recent Activities22


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PLAXIS Expert Services: 3D Modelling of a Building Subjected to Earthquake Loading

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Upcoming Events24

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Cover photo courtesy of CUR 211 (2013). Quay Walls, 2nd edition. Gouda

www.plaxis.nl l Spring issue 2014 l Plaxis Bulletin 3

» 20 years of Plaxis bv has shown countless new features and developments throughout

the years. This has also been the case with the Plaxis Bulletin. Again we have had some changes, namely in the editing staff. We would like to firstly thank Wout Broere for al his years of hard work and help with the Plaxis Bulletin. We are also happy to introduce the newest editor for this magazine, Martin de Kant. Welcome and good luck!

The begining of 2014 was also the begining of quite some new developments at Plaxis. We released the completely restyled PLAXIS 2D AE. Furthermore we are expanding our offices and are happy to announce the opening of the new branch office in Houston TX, U.S.A., Plaxis Americas LLC. You can read all about these and other news in the recent activities column.

Furthermore, in this 35th issue of the Plaxis bulletin, we have again tried to compile interesting articles and useful information for you. In the New Developments column we will discuss some different developed features for applications in rock in PLAXIS software over the last years, with a specific focus on the recent release of the new Swelling Rock Model.

The first user’s article discusses the analysis of the response of a number of structural models subjected to different loading conditions. The goal of such a comparison is the assessment of the structural elements performance in PLAXIS 3D as compared to that obtained by the well-known SAP2000, a widely used code for structural analysis. An overall good match was obtained, as such highlighting the possibility to use the code PLAXIS 3D to perform both structural and geotechnical calculations in soil-structure interaction problems.

The second user’s article takes a more detailed look into the combination of FEM analysis in combination with the Eurocode. Two quay walls were examined to check the applicability of the existing FEM design method of the Dutch Handbook Sheet Pile structures (CUR 166) on quay walls with relieving floor. Differences in partial safety factors are proposed to reach the required reliability index.

The third user’s article describes the development of a comprehensive three-dimensional finite element model for the Stata Center basement excavation (Cambridge, USA) using PLAXIS 3D 2012. The analyses highlight the effects of the 3D excavation and support geometry on wall deflections and show a good agreement with the measured response assuming undrained conditions using the Mohr-Coulomb soil model.

In addition there is a joint presentation about a project where Deltares and Plaxis worked together to set up a 3D non linear dynamic model of a building interacting with the subsoil through its pile foundation, for the assessment of the impact of man-induced earthquakes on infrastructures. Plaxis provided assistance in setting-up the 3D finite element model to evaluate the building’s seismic performance under possible moderate seismic activity.

We wish you an enjoyable reading experience and look forward to receiving your comments on this spring 2014 issue of the Plaxis bulletin.

The Editors

Editorial

4 Plaxis Bulletin l Spring issue 2014 l www.plaxis.nl

References:• Anagnostou, G. (1993). A model for swelling

rock in tunnelling. Rock Mechanics and Rock Engineering 26 (4), 307-331.

• Grob, H. (1972). Schwelldruck im Belchentunnel. Proc. Int. Symp. für Untertagebau, Luzern, 99-119.

• Heidkamp, H. & Katz, C. (2002). Soils with swelling potential - Proposal of a final state formulation within an implicit integration scheme and illustrative FE-calculations. Proc. of the 5th World Congress on Comp. Mec., Vienna, Austria.

• Huder, J. & Amberg, G. (1970). Quellung in Mergel, Opalinuston und Anhydrit. Schweizerische Bauzeitung 43, 975–980.

• Schädlich B., Schweiger H.F., Marcher T. (2013). Numerical Analysis of Swelling Deformations in Tunnelling – A Case Study. Proc. EURO:TUN 2013, 429-436.

• Wittke-Gattermann, P. & Wittke, M. (2004) Computation of Strains and Pressures for Tunnels in Swelling Rocks. Proc. ITA 2004 E14, 1-9.

New Developments

»Specific features that have been developed in the last decade include:

• Hoek-Brown isotropic material model for weathered rock

• Jointed Rock anisotropic material model, also available with Mohr-Coulomb failure criterion

• Swelling Rock model for time-dependent anisotropic swelling of clay- and siltstones

• Embedded piles and embedded pile rows, useable as rock bolts and forepooling elements

• Biot’s pore pressure coefficient, for a proper effective stress calculation considering compressible solid material at high pressure

• New tunnel designer and parametric geometry definition

The latter two features will become available in the upcoming PLAXIS 3D 2014 release.

In the remainder of this article I would like to focus on the Swelling Rock model. This model is available as a user-defined model that can be used to simulate the time-dependent anisotropic swelling of anhydrite and argillaceous rocks. The model was originally implemented by Prof. Thomas Benz of NTNU and further developed by Dr. Bert Schädlich of TUGraz for PLAXIS. The model is based on previous work by Wittke-Gattermann & Wittke (2004), Anagnostou (1993) and Heidkamp & Katz (2002). It accounts for the stress- and time dependency of swelling deformations. The following features are included:• Transverse isotropic elastic stiffness• Elastic-perfectly plastic material behaviour with

Mohr-Coulomb failure criterion.• Three swelling laws, all going back to the idea

formulated by Grob (1972): The Wittke model, the Anagnostou model, and a mixed variant.

The swelling parameters kq, sq0 and hq can be obtained from a so-called Huder-Amberg test (Huder & Amberg, 1970). Details of the model and its parameters are described in a document that is available for PLAXIS users. The model and the document are free of additional charges for VIP users. Interested users may contact our sales department. The model has been validated and applied in a case study of the Pfaendertunnel near Bregrenz, Austria (Schädlich et al, 2013). The results of the case study turned out to give a good match with the measured displacement profile below the tunnel invert. The model can also be used to evaluate the increase in tunnel lining forces as a result of swelling rock and to analyse appropriate mitigating measures.

With the Swelling Rock model and the other features as mentioned above, we trust that you will confidently use PLAXIS in deep underground applications. We welcome your feedback on these features as well as your article on such applications in future Plaxis Bulletins.

Starting as a finite element software package for geo-engineering applications in soft soil, PLAXIS has meanwhile evolved

to cover most geo-materials, ranging from soft soil to rock. This makes PLAXIS a convenient tool to analyse not only

embankments, foundations and excavations at shallow depths, but also applications in the deeper underground, like deep

tunnels and underground openings in hard soils and soft rocks as well as deep mining applications.

Ronald Brinkgreve, Plaxis bv

Grob’s swelling law (left) and the influence of the swelling parameter hq on the time-dependency of the swelling process for a maximum swelling strain of 2% (right)


»The dimension of the FE model is 60m long, 30m wide and 30m deep for a rather simple

5m*5.5m building resting on four 15 m long piles. Only half of the geometry has been modelled due to symmetry conditions. The model contains a total of roughly 36,800 elements and 55,000 nodes (i.e 165,000 dof). Each finite element has 10 nodes.

The soil stratigraphy consists of a relatively soft sand layer up to -1 m, a sandy clay layer from -1 m to -2 m, a medium dense sand layer from -2 m to -3.5 m, a clay layer from -3.5 m to -14 m resting of a rather dense soil layer all the way down to the model base. For the analyses, different stiffness values have been adopted for respectively the static analysis and the dynamic one (the static analysis aiming at modelling the construction sequence of the building under drained situation in order to obtain a realistic state of stresses before running the dynamic analysis for the earthquake loading and for which considerably larger material stiffnesses need to be taken into account).

For the assessment of the impact of man-induced earthquakes on infrastructures, Deltares and Plaxis worked together to

set up a 3D non linear dynamic model of a building interacting with the subsoil through its pile foundation. Plaxis provided

assistance in setting-up the 3D finite element model to evaluate the building’s seismic performance under possible moderate

seismic activity. The main challenge of this project was the rather short time frame within which such FE analyses needed to be

carried out. Thanks to PLAXIS Expert Services, Deltares managed to deliver FEA results in an efficient and timely manner.

Jaap Bijnagte and Mandy Korff, Senior Geotechnical Engineers, Deltares, The Netherlands

PLAXIS Expert Services: 3D Modelling of a Building Subjected to Earthquake Loading

The building has been entirely modelled by means of plate elements (walls, floor, ceiling and supporting beams each with different properties). The piles have been modelled has volume elements surrounded by interface elements for optimum soil-structure interaction modelling. Along their neutral axis, very soft beams have been introduced for the purpose of easing results post-processing in terms of structural forces.

The results of this study were used by Deltares to evaluate the influence of the soil and foundation stiffness on the transfer of the earthquake signal from the subsoil into the structural elements of the building. The impact of the presence of the building was evaluated, as well as the structural integrity of the pile and the connection to the structure. These results will be applied as a starting point for the development of guidelines for the vulnerability assessment of piled buildings in typical soft soil conditions under earthquake loading. PLAXIS Expert Services added value:• Quick start on the job• Set-up of fully optimized & ready to run models• Regular model review • Next business-day advanced technical assistance

About DeltaresDeltares is an independent institute for applied research in the field of water, subsurface and infrastructure. Throughout the world, Deltares works

“Plaxis experts helped us to quickly set up the model and optimize it to run the complex analyses very efficiently. Having his first-hand experience present

in house while discussing the best approach supported our vulnerability assessment team to deliver these state of the art results to our client in time.”

The input motion applied at the model base has been derived from a so-called deconvolution analysis carried out using a companion PLAXIS 1D model for which a target peak ground acceleration along with relevant frequency ranges were already provided and used to generate the input motion at the model base under free-field assumption.

on smart solutions, innovations and applications for people, environment and society focussing mainly on deltas, coastal regions and river basins. Managing these densely populated and vulnerable areas is complex, which is why Deltares works closely with governments, businesses, other research institutes and universities at home and abroad.


Modelling a Spatial Frame with Beams and Columns: Model M1The reference structure of the case study described in this section is a single-bay spatial frame fixed at the base and consisting only of beams and columns all characterised by a section


» The impulse in software technology and computational power of personal computers

has recently offered the possibility to perform fully-3D finite element analyses of complex engineering projects. In particular, in the field of civil engineering it is nowadays feasible to perform the analysis of a soil-structure interaction problem by a unique model, accounting at the same time for both geotechnical and structural issues. The three-dimensional version of the finite element code PLAXIS includes a wider choice of structural elements (such as beams, plates and node-to-node anchors), enhancing its modelling capability at the cost of a deeper structural competence required to the user. This paper provides a contribution on this specific topic, illustrating a number of structural models, where the different structural elements were employed, to investigate and clarify their response under different loading conditions. These models range from simple single-bay spatial frame to multi-storey frame with cross-bracings simulating the presence of infilled panels. All the models are assumed fixed at base, i.e. no foundation systems were considered, in order to focus the attention on the structural response only. The observed behaviour was compared with that obtained analysing the same structure by the finite element code SAP2000, a widely used software for structural analysis. This assessment was useful to highlight some differences in the formulation of the corresponding structural elements in the two codes.

In this paper the response of a number of structural models subjected to different loading conditions is analysed with the

codes PLAXIS 3D and SAP2000. The goal of such a comparison is the assessment of the structural elements performance in

PLAXIS 3D as compared to that obtained by the well-known SAP2000, a widely used code for structural analysis. An overall

good match was obtained, as such highlighting the possibility to use the code PLAXIS 3D to perform both structural and

geotechnical calculations in soil-structure interaction problems.

Gragnano C. G., Fargnoli V., Boldini D. (Corresponding Author), University of Bologna, ItalyAmorosi A., Technical University of Bari, Italy

Figure 1: Spatial frame with beams and columns and global coordinate system

of 30 cm x 30 cm (Fig. 1). The figure illustrates the dimension of the structural elements, the right-handed global reference system (x, y, z) and the local coordinate (s), this latter represented only for beam 2-6 for sake of simplicity.

Unit weight γ (kN/m3) 24

Young's modulus E (GPa) 25

Poisson's ratio ν (-) 0.2

Table 1: Material properties of beams and columns

Figure 2: Three-dimensional view of model M1 under loading conditions C1 (a), C2 (b) and C3 (c)

Unit weight γ (kN/m3) 32.36

Young's modulus E (GPa) 10

Poisson's ratio ν (-) 0.2

Table 2: Material properties of the isotropic floor slab


a rigid contact at the soil-structure interface, thus being appropriate for the modelling of a soil-foundation system much stiffer than the superstructure. On the contrary, a foundation plinth 1 m high and characterised by a square section (1 m x 1 m) was assumed at the base of each column in the PLAXIS 3D analysis, modelled by a two-dimensional plate element. As this code does not allow to perform numerical analyses without including soil elements, a soil volume (12 m x 15 m x 15 m) was defined at the frame base, assuming for it a very rigid behaviour, characterised by a Young’s modulus of 750 GPa and a Poisson’s ratio equal to zero. The response of the model was analysed considering the following loading conditions:• C1 = gravity loads + uniformly distributed

vertical loads equal to 10 kN/m acting on the beams (Fig. 2 a);

• C2 = gravity loads + concentrated vertical loads of 50 kN acting at nodes 3 and 6 (Fig. 2 b);

• C3 = gravity loads + concentrated horizontal loads of 50 kN acting at nodes 3 and 6 (Fig. 2 c).

Numerical analyses were carried out using a finite element mesh of medium density in PLAXIS 3D (i.e. the average size of the finite element is equal to 1.3 m), while adopting the default option in SAP2000. Distributions of shear, bending moment and inflection for beams 6-7 (relative to loading conditions C1 and C3) and 3-7 (for loading condition C2) as calculated by the two codes are shown in Figures 3, 4 and 5. This latter figure also reports the horizontal displacements along x direction of column 1-2 under loading condition C3. It is possible to note that the results calculated by SAP2000 and PLAXIS 3D are fairly coincident in terms of shear, bending moment and inflection,

Figure 3: Model M1: response of beam 6-7 under loading condition C1 in PLAXIS 3D and in SAP2000


In this example, defined model M1, as in the following ones, beams and columns are modelled as one-dimensional elements of frame-type in SAP2000 and beam-type in PLAXIS 3D. This latter element, differently from the frame type, is not able to react to torsional actions. Both elements allow for deflections due to shearing as well as bending.

A linear-elastic constitutive law was adopted for these elements, whose parameters were selected consistently with the assumed reinforced concrete material (Table 1). All the six displacement components were restrained at the base of the model in SAP2000. In an interaction problem, this condition simulates



while the horizontal displacements evaluated for column 1-2 differ in a non-negligible way. Such difference is due to the characteristics of the beam element in PLAXIS 3D which, as anticipated, does not sustain the torsional action induced by loading condition C3 (Fig. 5). This is confirmed by the results of a further analysis, illustrated in Figure 6, identical to the previous one except for the torsional constraint at the column head which was removed in the SAP2000 model: this modification leads to an almost coincident response as obtained by the two codes. Modelling a Floor Slab in a Simple Spatial Frame: Model M2Figure 7 shows a single-bay spatial frame differing from the simple structure of model M1 (Fig. 1) for the presence of a floor slab at the top. A brick-reinforced concrete floor slab is a structural element having a heterogeneous composition (i.e. reinforced concrete and brick) and a different stiffness in the two plane directions (i.e. higher stiffness in the warping direction). It is subjected to a plane stress condition and it is mainly loaded in its out-of-plane direction. The numerical model of this structure (model M2) is coincident to model M1 in terms of beams, columns and constraint conditions at the base. Concerning the floor slab, two different mechanical hypotheses were considered, namely isotropic and anisotropic. This latter allows to reproduce the main characteristic of a floor slab, that is a structural element rigid in its own plane and capable of differentiating the load transferred to the main beams as compared to the secondary ones. The isotropic behaviour was obtained in PLAXIS 3D using a two-dimensional linear-elastic plate element of thickness equal to 25 cm with the material properties listed in Table 2. A two-dimensional shell element with the same geometrical and material properties was selected to model the isotropic floor slab in SAP2000. The presence a floor slab with anisotropic behaviour was represented in SAP2000 without simulating the structural element itself, but just applying the constraint diaphragm to the nodes 2, 3, 6 and 7 (Fig. 7). This constraint, generally used to model structural components which have very high in-plane stiffness, forces the nodes belonging to the plane of the slab to move together in a rigid way. Assuming the warping direction of the floor slab along x-axis and according to the current design practice, the weight of the floor slab was accounted for applying vertical forces to the main beams (in y direction) and to the secondary ones (in x direction) with reference to the influence areas: a load equal to 64.1 kN and 16.8 kN was attributed to the main and secondary beams, respectively. In particular, the first load is equal to half of the floor slab weight (80.9 kN, being the total weight equal to 161.8 kN), reduced of the load (16.8 kN) transferred to the adjacent secondary beams by a floor slab slice 50 cm wide. When modelling the same slab in PLAXIS 3D, an anisotropic elastic model was employed. More specifically, according to the warping direction along x-axis, the Young’s modulus, Ey, and the shear modulus, Gyz, were reduced as compared to those adopted in the isotropic case. The amount

Figure 5: Model M1: response of beam 6-7 and column 1-2 under loading condition C3 in PLAXIS 3D and in SAP2000

Figure 6: Model M1: response of beam 6-7 and column 1-2 under loading condition C3 in PLAXIS 3D and in SAP2000 without torsional constraints at column heads.

Figure 7: Spatial frame with beams, columns and a floor slab

Table 3: Values of the parameters for estimating the equivalent diagonal width, bw

tw (m) 0.3

hw (m) 4

Ew (GPa) 3

Ec (GPa) 25

Ic (m4) 0.000675

θ (°) 45

λw (1/m) 1.351

dw (m) 5.657

bw (m) 0.504



The diagonal elements of the frame were modelled in order to make them equivalent to a building infill panel, adopting a simplified version of a formulation proposed in the literature (Panagiotakos and Fardis, 1996; Fardis, 1997). The width of the cross bracings, bw, was defined with reference to the expression of Mainstone (1971):

(1) where: dw is the diagonal length of the panel, hw is the panel height and the parameter λh is equal to: (2) where Ew and Ec are the Young’s moduli of the infill panel and of the reinforced concrete structural elements surrounding the panel, respectively; θ is the angle formed by the diagonal of the infill panel with respect to the horizontal axis; tw is the panel thickness; Ic is the moment of inertia of the columns adjacent to the infill panel. The values of these parameters are summarised in Table 3. The cross bracings were modelled as weightless one-dimensional elements reacting only to axial stress (denoted as truss elements in SAP2000 and node-to-node anchor elements in PLAXIS 3D), characterised by an axial stiffness equal to K = Ew * bw * tw = 450000 kN. An elastic-plastic constitutive law was selected for the elements to introduce a limit value of the tensile strength equal to zero, aimed at neglecting tensile stresses for the cross bracings. The response of model M3 was assessed by considering the structural elements weight (beams and columns) and a force of 20 kN applied at node 2 along x-axis (loading condition C4). Figure 12 shows a perfect match among the results of the two models in terms of normal stress acting in column 3-4 and diagonal element 2-4; shear, bending moment and inflection in beam 2-3; horizontal displacement in column 3-4. Modelling a Spatial 3-Storey Frame with and without Cross Bracings: Models M4(I) and M4(II) In this section the responses of two 3-storey frame structures subjected to horizontal loads are compared, the structures differing only for the presence of cross bracings (Fig. 13). The inter-storey height is 4 m and the beams length is equal to 4 m in x direction and 5 m in y direction. The numerical models of the open-frame structure and that of the structure with diagonal elements are denoted as M4(I) and M4(II). In the models beams and columns are represented by one-dimensional elements (frames and beams in the two codes) and, for sake of simplicity, the floor slabs are modelled as linear-elastic-isotropic elements of shell-type in SAP2000 and plate-type in PLAXIS 3D. For both models the mechanical properties of columns, beams and floor slabs are those listed in Tables 1 and 2; the usual rigid constraint conditions are assumed at the base of the frames. The equivalent width dw of the cross bracings, modelled as node-to-node anchor and truss elements in PLAXIS 3D and SAP2000 respectively, was defined using Eq. (1) and the same elastic-plastic constitutive law assumed for model M3 was selected in this case. Both models were analysed under gravity loading

of the necessary reduction of the moduli to match the reference results obtained by SAP2000 is equal to 10%, as such the adopted parameters are Ey = 1 GPa; Gyz= 416.7 MPa. The same loading conditions previously analysed for model M1were considered, namely C1 (taking also into account the floor slab weight), C2 and C3. The finite element mesh used for this model in PLAXIS 3D is similar to that defined in model M1; in SAP2000, on the contrary, the mesh of the model with isotropic slab was modified to make it roughly equivalent to that defined in PLAXIS 3D. This expedient is related to the fact that in SAP2000 the load of the floor slab is transferred to the beams in correspondence of the mesh nodes, therefore a similar finite element discretisation is required in order to obtain consistent results by the two different codes. Figures 8, 9 and 10 show the comparison between models M1 and M2 in terms of shear, bending moment and inflection for beam 3-7 under loading conditions C1, C2 and C3, respectively. Figure 10 also shows the horizontal displacements of column 1-2 along x-axis. Results demonstrate the good agreement between the structural responses obtained by the two different numerical codes. In general, it is possible to observe an equivalent response of beam 3-7 under loading conditions C1 and C2 for model M2 too. As expected, the different assumption concerning the behaviour of the floor slab (i.e. isotropic or anisotropic) plays an essential role in the intensity and distribution of shear, bending moment and inflection. In the anisotropic case, the structural element 3-7 is one of two main beams of the floor slab and it results to be more heavily loaded as compared to what observed in the isotropic model, where all the beams were equally loaded per unit of length. On the contrary, the different mechanical hypotheses seem to have a barely relevant influence on the horizontal displacement of the column: this should be due to the fact that in both isotropic and anisotropic cases the relevant shear stiffness Gxy assumes the same value, leading to a similar head restrain acting on the column, therefore resulting in a correspondingly similar displacement pattern. Modelling a 2D-Frame with Diagonal Elements: Model M3The simple structure shown in Figure 11 is a single-bay plane frame with cross bracings. These elements are commonly adopted in numerical studies to account for infill panels (e.g.: Panagiotakos and Fardis, 1996). Those latter, although being non-structural components, significantly contribute to the overall structural response in the in-plane horizontal direction, leading to a generally stiffer behaviour as compared to open-frame ones. In the corresponding numerical model, defined as model M3, the structural elements (i.e. beam and columns) are represented by frames and beams in SAP2000 and PLAXIS 3D, respectively, and are characterised by the material properties listed in Table 1. The base of the frame is constrained as in all the other models.



b h dw h w w= ⋅ ⋅ ⋅−0 175 0 4. ( ) .λ

λθ

hw w

c c w

E tE I h

=⋅ ⋅⋅ ⋅ ⋅

sin( )24

4



Figure 10: Model M2: response of beam 3-7 and column 1-2 under loading condition C3 in PLAXIS 3D and in SAP2000

Figure 11: 2D frame with cross bracings

and horizontal ones acting along x-axis, those latter equal to 20 kN, 40 kN and 60 kN at the first, second and third frame level respectively (loading condition C5) (Fig. 13). A control point position was selected at the top level (node 3.4) as representative of the horizontal displacement of the structure. The horizontal displacement distributions in columns 0.4-1.4, 1.4-2.4, 2.4-3.4 are reported in Figure 14 for the two models. It is worth noting that both codes provide the same results: the maximum horizontal displacement is equal to 8 cm for model M4(I) and about 0.8 cm for model M4(II). The outcome of the analyses clearly highlights the effect of claddings on the overall structural stiffness, although simply accounted for by means of equivalent diagonal elements: in fact, the presence of cross bracings produces a horizontal displacement reduction of an order of magnitude as compared to the reference case where they are not included.

Conclusions In the paper the response of a number of structural models subjected to different loading conditions was analysed by the finite element codes PLAXIS 3D and SAP2000. The main outcomes resulting from the comparison, carried out in terms of stress and displacements, can be summarised as follows:• beams and columns can be modelled with

frame elements in SAP2000 and beam elements in PLAXIS 3D. The main difference in the ele-ment formulations resides in the inability of beam elements to react to torsional actions. In fact, the release of torsional constrains in SAP2000 produces perfectly matching results;

• the floor slab can be modelled in SAP2000 by a shell element or using a diaphragm constraint combined with some additional vertical forces at the top of the columns to simulate the effect of the slab weight. In the first case an isotropic behaviour is obtained, while in the latter a more realistic response is reproduced, as it allows to account for the higher stiffness observed in the warping direction. A plate element is instead available in PLAXIS 3D. The use of an isotropic formulation allows to nicely reproduce the response of the shell element, while an aniso-tropic model should be selected to fit, after a careful calibration of its elastic parameters, the response of the more advanced scheme of SAP2000;

• infill panels can be modelled in a simplified manner as cross bracings, whose characteristics were obtained using the formulation proposed by Mainstone (1971). Truss and node-to-node anchor elements were used respectively in SAP2000 and PLAXIS 3D, leading to perfectly consistent structural responses.

This study should be considered as a preliminary step towards more complex soil-structure interaction problems, which indeed require a good level of confidence in the use of structural elements in 3D analyses with PLAXIS.

AcknowledgementsSpecial thanks to Ph.D. Eng. Francesco Tucci for his helpful support during this research activity.

References 1. M.N. Fardis, 1997. Experimental and numeri-

cal investigations on the seismic response of RC infilled frames and recommendations for code provisions. Report ECOEST-PREC8 No. 6. Prenormative research in support of Eurocode 8.

2. R.J. Mainstone, 1971. On the stiffnesses and strengths of infilles frames. Proc. Inst. Civil. Engineers, iv 7360s: 59-70.

3. T.B. Panagiotakos and M.N. Fardis, 1996. Seismic response of infilled RC frames struc-tures. 11th World Conference on Earthquake Engineering, Acapulco, México, June 23-28. Paper No. 225.



Figure 14: Models M4(I) and M4(II): comparison between horizontal displacements obtained in PLAXIS 3D and in SAP2000 with (on the right) and without (on the left) cross bracings.

Figure 13: Three-dimensional view of the structures and loading distributions with (top) and without (bottom) cross bracings. Each node of the frame is defined through a double number: the first indicates the level it belongs to, while the second is a sequential number.

Figure 12: Model M3: responses of column 3-4, beam 2-3, and diagonal element 2-4 under C4 load condition in PLAXIS 3D and in SAP2000


»During the last two years, CUR committee 183 has worked on the upgrade of the

Dutch Quay Walls handbook (CUR 211), which was published in November 2013. Two of the main elements that are considered in this new edition are the addition of FEM analysis as a method for design, comparable to the description in the Dutch Handbook Sheet Pile Structures (CUR 166), and the calibration of partial safety factors design with FEM. With respect to the actuality of this update it must be remembered that with the new 2nd Maasvlakte and other changes in the Rotterdam harbour area, several quay walls are under construction, such as illustrated in Fig. 1, which configuration was a reference site for the CUR analyses.

One of the arguments for the further introduction of FEM analysis for quay wall design is that for the larger quay walls, relieve platforms are often used under heavy loaded conditions. In that situation

During the last years the Finite Element Method (FEM) is increasingly applied in the design of quay walls. Especially in

case of quay walls with relieving floors and bulk-storage as surcharge load, sub-grade reaction models are limited in their

accuracy of modelling the situation. The Finite Element Method often is the only option to more detailed design calculations

of quay walls. In the recent years the introduction of Eurocode and the increasing use of Finite Element analysis for design

calculations has triggered the update of the CUR Quay walls handbook CUR 211. The latter second edition has recently been

published. In advance of this second edition it was decided to look into more detail into the combination of FEM analysis in

combination with the Eurocode which lead to the study that is described in this article. In order to infer a more fundamental

base for the design method with FEM, two quay walls were examined to check the applicability of the existing FEM design

method of the Dutch Handbook Sheet Pile structures (CUR 166) on quay walls with relieving floor. Furthermore, it was checked

whether the current partial safety factors needed to be adapted. This research is done by performing probabilistic FEM

calculations. The First Order Reliability Method is incorporated in the software Prob2B (Courage & Steenbergen, 2007) to

perform the calculations. It appeared that using the design method of CUR 166 for quay walls with relieving floor leads to an

underestimation of the reliability of the structure. Therefore it is advised to adapt the design method. Furthermore, differences

in partial safety factors are proposed to reach the required reliability index.


Authors: H.J. Wolters, K.J. Bakker and J.G. de Gijt, Delft University of Technology. The Netherlands

Fig. 1: A quay wall under construction at Maasvlakte 2

one must consider that the piles under the relieve platform may bear a part of the horizontal load that is normally taken by the retaining wall. Furthermore, if the load itself is bulk-storage there are limitations to the accuracy of modelling surcharge load with sub-grade reaction models that are normally applied for soil retaining wall design; horizontal components of bulk storage may be difficult to model; see Fig. 2.

The influence of relieve platforms and high surcharge loads on greenfield is one of the reasons to evaluate the design procedures in CUR 166 in the combination with Finite Element analysis, for different failure mechanisms. The method applied in this study is to put Finite Element analysis in a framework of probabilistic analysis. Within this framework, partial safety factors are inferred from the reliability indices and the influence coefficients of the variables of the FEM model, obtained with FORM analysis. This paper presents the method


that is used to obtain the reliability indices and partial safety factors and compares the results from these calculations with the 2003 edition of CUR 211.

Quay Walls and Failure MechanismThe research is done for two different types of quay wall, modelled in Plaxis. To begin with, an anchored sheet-pile with two different sheet-pile lengths (21m and 23m) was analysed. The sheet-pile is anchored 2 m below ground level (ground level is NAP) and has an AZ36-700N profile. The wall is excavated till NAP -12 m and a surcharge load of 30 kN/m2 is present. The upper sand layer reaches till NAP -10 m. Below there is a clay layer till NAP -15 m followed by another sand layer. The soil and structural parameters can be found in the report of Wolters (2012, pp. 83-84). This first configuration was used to check the method.

Secondly, a heavier quay wall with relieving floor was modelled; see Fig. 3. In this article

the main focus is on this second analysis. The model is based on the quay wall from Fig. 1. The quay wall is anchored by a double anchor that must guarantee a top displacement of less than 50 mm. The combi-wall consists of tubular piles with 1420 mm diameter and 18 mm wall thickness. In between the piles there are three sheet-piles with profile AU20. The wall is excavated till NAP -19 m which implies 24 m retaining height. A bollard force of 70 kN/m and a surcharge load of 40 kN/m2 behind the quay wall are taken into account. The level of the top of the quay wall is NAP +5,0 m. The soil configuration is based on Maasvlakte conditions. The upper sand layer reaches till NAP -8,50 m. Below there is a clay layer till NAP -11,0 m, a sand layer till NAP -19,0 m, another clay layer till NAP -22,0 m and Pleistocene sand. The soil and structural parameters can be found in the report of Wolters (2012, pp. 137-138).

The PLAXIS Hardening Soil model was used to model the soil, because this enables a better

description of the unloading behaviour of the soil behind the wall and gives a description of the soil deformations under the relieving platform. In contrast to the normal design procedure, here for the probabilistic analysis, mean values of the parameters where used. Normally, characteristic values would need to be applied, according to the Eurocode. The difference between mean values and characteristic values was discounted for afterwards when partial safety factors where derived.

As a starting point for the analysis the FEM procedures, as described in CUR 166, were taken. The analysed failure mechanisms of these structures are anchor failure in tension (ULS), wall failure in bending (ULS), soil mechanical failure (ULS) and excessive deformations (SLS).For each failure mechanism a reliability function is defined of the form:Z = Resistance(R) – Solicitation (S),which implies that failure is assumed for Z<0. The

Fig. 2: Horizontal shear forces due to bulk-storage, that will increase the anchor force, are difficult to model with sub-grade reaction model Fig. 3: Quay wall with relieve platform, modelled in PLAXIS

Photo courtesy of CUR 211 (2013). Quay Walls, 2nd edition. Gouda



output that is searched for are the reliability index β, linked to the probability of failure (pf = Φ(-β)) and the influence coefficients per variable (αi). As tool for the probabilistic analysis the PLAXIS kernel was linked in with software (i.e. Prob2B (Courage & Steenbergen, 2007)), which controlled the variations that are necessary to derive the influence coefficients αi.

First Order Reliability Method (FORM) & Prob2BThe used probabilistic method FORM is an iterative level II approach, entailing linearization in the design point to derive influence coefficients. Using this method the uncertainty in the output of the analysis can be objectively weighted with the uncertainty in the input parameters discounting these objectively with the variation coefficient of a parameter that is uncertain. The variation coefficient Vi being defined as:

The approach that is applied in Prob2B can be described in different steps:• The calculation starts with a ‘normal’ PLAXIS

calculation using mean parameter values. The parameter values are transformed into standard-normal u-space by the transformation:

• For each stochastic variable an additional calculation is made by increasing the variable by a fraction of the standard deviation. This variation is made in order to check the variables influence on the Z-value. This influence is expressed in the derivative dZ/dx, in which x is a parameter value.

• This derivative is important in the FORM procedure to determine the standard deviation and mean value of Z, which define the reliability index:

• From the derivatives for each variable an influence coefficient, αi, can be determined by: The sum of αi

2 is equal to 1.

• For each parameter a possible design point value can be determined by:

• This procedure is repeated by iterating with the new obtained parameter values instead of the initial mean values. After some iterations, convergence may be found and the design point and corresponding β and αi can be determined. For the failure mechanisms the Z function should approach zero.

This FORM procedure is incorporated in Prob2B. However, not all stochastic parameters can be included. Variations in surcharge loads, water levels and bottom level (dredging depth) need to be made manually. With these manual variations dZ/dx is calculated and from there the uncertainty in those parameters can be incorporated in the reliability index and influence factors can be derived.

Table 1: Example of the output of a FORM calculation

Number of calculations (FORM): 78

β: 2.646

Pf: 4.068*10-3

Parameter (X) V = s / μ Α X* (design point) Unit

Gsilty moderately packed sand 0.3 -0.12 43310 [kPa]

Gpleistocene sand 0.3 0.48 106400 [kPa]

sin(φ)silty moderately packed sand 0.18 0.67 0.48 [-]

sin(φ)pleistocene sand 0.18 0.46 0.38 [-]

γsat,silty moderately packed sand 0.05 -0.30 20.15 [kN/m3]

calc. Z-value

1 170400

78 8110

Fig. 4: Example of a plastic point plot in the design point of wall failure in bending (Red: Mohr-Coulomb point, Green: Hardening point, Blue: Cap and Hardening point)

From the output of Prob2B partial safety factors can be derived using the formulas: (load) and

(resistance),

The coefficients of variation for the soil variables and their correlations with other variables are derived from a database of Rotterdam Public Works, containing 3000 tri-axial tests and added by information from the Dutch national annex to NEN-EN 1997 (former NEN 6740). For the structural variables the prescriptions of the Joint Committee on Structural Safety (2002) are followed.

OutputFor each FORM calculation output is generated by the software. Table 1 is an example of the output for the limit state function of wall failure in bending. The table includes the variation coefficients (input) the influence factors, design point values and the failure probability (reliability index). When implementing the design values a plastic point plot can visualize the failure mechanism.

An example of such a plot is given in Fig. 4. In this plot it can be seen that wall failure occurs due to failure of the soil elements at the lower part of the piles. This soil failure leads to a reduced fixing moment which causes an increase in the maximum

Vii

i

=σµ

ux

ii i

x i

=− µσ ,

βµσ

= = −∑ ∗

∑

z

z

ii

i

udZdu

dZdx

2

αii

i

dZdu

dZdx

=

∑

2

Xi i i x i∗ = −µ α βσ ,

γα βk S

i

i i

VV,

.=

+−

1 1 641

γα βk R

i

i i

VV,

.=

−−

1 1 641



relatively high prescribed target reliability in CUR 211 (Wolters, 2012 pp. 170-174).

For the quay wall with relieving floor the differences are shown in Table 3. The target reliability indices for the lower anchor failure, wall failure and soil mechanical failure are not reached.

Results – Partial Safety FactorsCompared to the method as described in CUR 166 for Sheet Pile walls, for Quay walls with relieving floor the partial safety coefficients need to be adapted. A summary as proposed for CUR 211 for Consequence class 2, i.e. β= 3.8 is indicated in Table 4.

With respect to the analyses as performed, compared to the results based on point variation values of parameters, it appeared to be necessary to include spatial correlation in soil layers in order to derive realistic values of the partial safety factors.

The main consequences with respect to the partial safety factors are:• Theoretically the partial safety factors should

be subdivided in factors per failure mechanism to be checked. For practical purposes one set of safety factors is proposed for all mechanisms that cover the safety that needs to be realized.

• In deviation from the structural mechanisms for the design of walls and anchors, where a factor of 1.25 for soil strength suffices, for soil mechanical stability a higher partial safety factor on the internal angle of friction is necessary, γφ should be increased for this mechanism up to 1.35.

• For practical purposes, in addition to the structural design, stability needs to be checked for a higher value of MSF (in a φ – c reduction procedure). All procedures further in agreement with Eurocode being related to characteristic values of the parameters

• With respect to stiffness, for the structural design, characteristic low values of the soil stiffness need to be applied, however for anchor failure in addition to that a check needs to be done with a partial safety coefficient of 0.4.

• The latter means that for anchor design the results of an analysis with a high characteristic value of soil stiffness needs to be checked.

• The analysis indicates that for the geometrical parameters an additional retaining height and water level difference of 15 cm needs to be taken into account for both variables.

• In engineering practice other uncertainties such as dredging depth are more uncertain and it is advised to account for these small differences by including them in the definition of the design shape of the geometry before doing a Finite Element analysis.

DiscussionThe influence factors combined with failure plots (e.g. see Fig. 4) explain how a failure mechanism occurs. Anchor failure in tension mostly occurs due to exceedance of the soil shear resistance in the layer where the anchor bonding element is positioned, combined with reduction of the passive shear resistance in the lowest sand layer. Sometimes this passive shear resistance is not fully developed due to the higher soil stiffness, which gives the elastic parameters more influence.

β calculated β CUR 211

Anchor failure 4.09 3.828

Wall failure 3.96 3.872

Soil mechanical failure 3.38 4.396

Deformations 2.69 1.800

Table 2: Reliability calculated for the simple Quay wall

Table 4: Partial safety factors with respect to the characteristic values of parameters

Parameter Reliability /Consequence Class

RC2

Angle of internal friction γj’ 1,25

Effective cohesion γc’ 1,25

Density γg 1,0

Surcharge load γF 1,05

Soil Stiffness γE 1,0

Table 3: Reliability calculated for the Quay wall with relieve platform

β calculated β CUR 211

Upper Anchor failure 4.40 3.828

Lower Anchor failure 2.99 3.828

Wall failure 2.65 3.872

Soil mechanical failure 2.78 4.396

Deformations 2.44 1.800

Finally, the uncertainty in anchor parameters can contribute significantly to the anchor failure.

Wall failure is mainly induced due to reduction of the internal angle of friction and therewith the passive shear resistance in the Pleistocene sand layer. The fixing moment is reduced, which causes the bending moment in the wall to increase. The bending moment gets even larger by failure of soil elements in upper layers, which act as an additional load on the wall.

Soil mechanical failure (Fig. 5) is also induced by reduction in passive shear resistance, which implies that this mechanism is correlated with the wall failure mechanism.

ConclusionsFor the anchored sheet-pile the target reliability is well approached for the mechanisms wall failure in bending and anchor failure in tension, when designing according to the FEM design prescriptions of CUR 166. The obtained reliability index for soil mechanical failure is too low, but this is mainly due to the used calculation method.

In case of quay walls with relieving floor, the obtained reliability indices are too low. It is therefore necessary to adapt the FEM design procedure for this more complicated type of quay wall and subsequently to modify the partial safety factors, in order to design the structure with an acceptable failure probability.

Note that the results are obtained for structures in the Maasvlakte area of the Port of Rotterdam. Therefore the conclusions are only valid for those specific circumstances. The applied method of analysing the quay walls by probabilistic FEM calculations, however, can be used for quay walls in different situations.

References1. Courage, W.M.G., Steenbergen, H.M.G.M.

(2007). Prob2B: variables, expressions and Excel Installation and Getting Started. Delft: TNO Built Environment and Geosciences

2. CUR 166 (2008). Handbook Sheet pile structures, 5th edition (in Dutch). Gouda

3. CUR 211 (2003). Handbook Quay Walls, 1st edition. Gouda

4. CUR 211 (2013). Quay Walls, 2nd edition. Gouda5. Joint Committee on Structural Safety (2002).

Probabilistic Model Code. Retrieved on 22 February 2012 from http://www.jcss.byg.dtu.dk

6. Wolters, H.J. (2012). Reliability of Quay Walls. MSc thesis on probabilistic Finite Element calculations of quay walls. Delft: Delft University of Technologymoment in the piles.

Results – reliability indicesThe calculated reliability indices for the different failure mechanisms are compared to the prescribed target reliability indices in the first edition of CUR 211 to see whether the FEM design method of CUR 166 leads to sufficient reliable quay walls. Table 2 shows that this target reliability index is reached for the failure modes anchor failure and wall failure. Furthermore the reliability level is by far reached for the deformations requirement (maximum displacement of 50 mm). However, the obtained reliability for soil mechanical failure is too low. This can be explained to some extent by the applied calculation method, but is also due to the

Fig. 5: Distribution of variation in soil stiffness, (CUR 166)


Title

»The Ray and Maria Stata Center building at MIT (Massachusetts Institute of Technology)

was designed with a basement for underground parking requiring a 12.8m deep excavation. The excavation was supported by a perimeter diaphragm wall that formed part of the permanent structure and extended 14 m into a deep layer of underlying Boston Blue clay. The diaphragm wall was braced by a combination of prestressed tieback anchors, preloaded raker and corner bracing support elements. The control of ground movements was a critical aspect of the subsurface design due to the close proximity of the excavation to the historical MIT Alumni swimming pool building (a meter away from the edge of the excavation).

The complexity of the excavation process and structural supports presented a significant modeling challenge that exceeded the computational capabilities of finite element codes available at the time of construction (in 2001). The predictions of performance were limited to simplified 2D finite element models (plane strain, half sections) that were assumed to generate worst-case scenarios for wall deflections and ground deformations.

The measured performance during the actual excavation exceeded the allowable wall deformations (38mm) prescribed at the start of the project with maximum lateral movements

This article describes the development of a comprehensive three-dimensional finite element model for the Stata Center

basement excavation (Cambridge, USA) using PLAXIS 3D 2012. The project involved a complex sequence of berms, access

ramps and phased construction of the concrete mat foundation. Lateral wall movements and building settlements were closely

monitored throughout construction, while photos from a network of webcams located around the open-plan site provided

a detailed time history of the construction processes. The analyses highlight the effects of the 3D excavation and support

geometry on wall deflections and show a good agreement with the measured response assuming undrained conditions using

the Mohr-Coulomb soil model.


Zhandos Y. Orazalin, Ph.D. Candidate, Department of Civil & Environmental Engineering, Massachusetts Institute of Technology, Cambridge, USAAndrew J. Whittle, Professor of Civil & Environmental Engineering, Massachusetts Institute of Technology, Cambridge, USA

that ranged from 51mm to 89mm and maximum settlements exceeding 50mm. Fortunately, these movements did not cause any noticeable damage to adjacent structures and were eventually deemed acceptable. Nonetheless, the magnitude of these unforeseen movements could have potentially caused more problems.

More comprehensive three-dimensional finite element analyses of the Stata Center basement excavation have been enabled by the recent advances in PLAXIS 3D software including the efficient multicore iterative solving capabilities and geometric data import from CAD files. These analyses showed a good agreement with the measured response assuming undrained

conditions in clay and highlighted the effects of the 3D excavation and support geometry on wall deflections.

Project DescriptionThe site for the MIT Stata Center has a very large rectangular plan area (approx. 100m x 119m), which abuts an existing building along its southern edge (Figure 2). A floating mat foundation system was designed so that the weight of the building is balanced against the weight of the soil extracted from the site. The excavation support system comprises a reinforced 76 cm thick concrete diaphragm wall that is supported through the use of:1. three levels of tiebacks on the west, south, and

Layer Soil Model Top Elevation, m γ, kN/m3 Su, kPa j'ps G/s'vo ν' K0

Fill MC (D)* 6.4 18.9 - 35° 75 0.3 0.5

Organics MC (UD) 3.0 15.7 48 - 150 0.3 0.5

Sand MC (D) 1.2 20.4 - 37° 230 0.3 0.5

BBC (Upper) MC (UD) -3.0 18.4 68 - 61 - 75 0.3 0.8

BBC (Lower) MC (UD) -17.0 19.3 61 - 93 - 75 0.3 0.6

Glacial Till MC (D) -29.0 22.0 - 43° 385 0.3 1.0

Table 1: Soil properties (*D = drained, UD = undrained)


Title

Photo courtesy of http://philip.greenspun.com

Figure 1: Excavation support plan and site view

Figure 2: Subsurface conditions



at the depth of 1.8 m. A typical subsurface profile underlying the Stata Center in the middle of the site would consist of 3.4 m of fill, 1.8 m of organics, 4.3 m of sand, 26 m of clay, and 4.6 m of glacial till (Figure 2). The principal stratum is the marine clay (Boston Blue Clay), which can be sub-divided into an upper overconsolidated clay crust and a lower lighly-overconsolidated unit. The clay has low hydraulic conductivity and is modeled as an Undrained Elastic - Perfectly Plastic (EPP) material with the undrained shear strength that ranges from a minimum value, su = 60kPa at El. -16m to a maximum, su ≈ 90kPa at the base of the clay. The other layers are also represented by the EPP (Mohr-Coulomb) model. Table 1 illustrates soil properties based on the subsurface exploration program.

Model DescriptionThe excavation for the Stata Center has a complex geometry and variety of structural support systems which makes the project challenging to model. However, the uniqueness of this project is that the excavation process was very well

documented - it was constantly photographed, monitored, and described in daily field logs, as well as recorded on webcams located around the construction site. Using these data, it was possible to create a full three-dimensional numerical model of the actual excavation with respect to the time frame of construction sequence.

Olsen (2001) developed a series of 3D geometric models to represent the construction process by reconciling daily field reports, photographs and time-lapse of the project. Figure 4 illustrates the process of converting the geometric information into Phases used in the development of the 3D finite element model. Project data from project drawings were initially used to construct a CAD model of the support system. This information was then used to create a base case model within PLAXIS 3D. The excavated surface geometry is obtained from the models reported by Olsen (2001) that are converted into a set of tetrahedral elements using mesh tessellation operators in the CAD program. These are then imported into Plaxis 3D as soil clusters that represent the excavation

east sides, 2. two levels of corner bracing, and 3. two levels of raker supports on the north side.Tiebacks were installed at an angle of 20 degrees from the horizontal at El. 3 m, El. – 0.3 m, and El. –3 m and preloaded from 498 to 569 kN. Two levels of corner bracing consisting of 91-cm-diameter pipe struts were installed at El. 3 and El. –3 m.

The City of Cambridge prohibited the installation of tiebacks beneath the Vassar Street such that two levels of inclined raker bracing (at El. 3 and El. –3 m) were used along the North side of the excavation. The raker bracing consisted of 91 cm in diameter pipe struts extending from embedded plates in the diaphragm wall to kicker blocks embedded in the concrete mat foundation (Figure 1).

Site Characterization and Soil PropertiesThe site is located at the eastern part of the MIT campus in Cambridge, Massachusetts. The ground surface is approximately level at El. +6 m, and the groundwater table is in the overlying fill

Figure 3: Design of soil clusters to be excavated in several PLAXIS phases



Figure 4: Staged construction mode and output example

Figure 5: Output of the phase “April 25, 2001” in PLAXIS3D (vertical displacements) and corresponding photo of the construction site

process as a series of 36 “staged construction” steps in the finite element model. Figure 5 shows that the resulting finite element model represents a close approximation to the original geometric model.

The overall finite element model extends laterally beyond the footprint of the excavation to a distance of 150-170m in all directions and vertically to the base of the glacial till. The model represents the soil mass using approximately 11200 tetrahedral elements (10-noded) with the second order interpolation of displacements. The calculation time lasted less than 20 hours on an Intel Core i7-3960X Extreme Edition CPU overclocked to 4.0 GHz with 16 GB RAM on a SSD hard drive.

The diaphragm wall is represented by three-dimensional elastic plate elements. The toe of the diaphragm wall does not extend into the underlying rock; therefore, it is free to move within the soil mass. The mat foundation was also modeled using elastic plate elements; tiebacks and corner bracers were represented

as prestressed node-to-node anchors. The free lengths of tiebacks were modeled using node-to-node anchors, and the embedded pile elements represented the grouted part. Each raker comprises a 91 cm diameter steel pipe strut (prestressed node-to-node anchors) that supports the wall and is inclined downward to a kicker block cast into the foundation slab.

The Boston Blue Clay has been modeled assuming undrained conditions using the Mohr-Coulomb model. The layer is subdivided into two units, each with undrained shear strength varying linearly with elevation (i.e., matching the undrained strength profile shown in Figure 2). Since the site surface is assumed to be mainly horizontal, the initial stresses are defined by K0 conditions, and hydrostatic pore pressures, with groundwater table at El. 4.6m. The boundary conditions usedin the model are the Plaxis standard boundary conditions with fixity in the horizontal plane at the basal boundary and zero prescribed lateral displacements along the corresponding axes at the borders.

ResultsA general pattern of measured movements at the center of a wall typically correspond to an initial cantilever movement of approximately 10-20 mm during the excavation to the first tieback support level, as well as 32 mm before the first level of raker support. The movement was fully recovered (except the North Wall) and the wall moved back during pre-stressing the first level of bracing. After the installation of the first level support, the wall rotated at the brace during the excavation progress. At the subsequent bracing, the wall kept moving laterally below the brace location. The maximum movements (June, 2001) measured in the inclinometers range from 51-64 mm at SC-02 (North), SC-04 (East), and SC-10 (West) to about 82 mm at SC-07 (South). The greatest movements were observed within the middle of a tieback supported wall while the smallest movements were recorded by the inclinometers located closer to the corners. In contrast, the North wall, supported by the raker support, showed an opposite pattern with the smallest movements occurring at the center due to the fact that the plan geometry of the North wall consisted of two



planes that intersect at the wall center (Figure 7).

Figure 6 presents comparisons between the computed and measured wall deflections for the 11 inclinometers located around the perimeter (Figure 1) at 4 stages of construction (spanning the period from mid-January to June 2001). The inclinometers can be sub-divided into sections where the wall is supported by tieback anchors (SC-10, SC-08, SC-07, and SC-04), corner bracing (SC-11, SC-09, SC-06, SC-05 and SC-03) and raker supports (SC-02, SC-01).

In general, the patterns of measured wall deflections are very well described by the base case finite element model. The results are within 5-10mm of the measured maximum and toe deflections of the diaphragm wall at the end of construction (Phase 35), with the noted exception of conditions at the NW and NE corners of the site (SC-11, SC-01 and SC-03), where measured maximum wall deflections are 20mm higher than the numerical predictions. The most likely causes influencing the results are the ground loss during construction of the wall panels and lack of preloading of the 2nd level corner bracing prior to final excavation of berms in the NE

corner. Nevertheless, the base case results are in particularly good agreement with wall deflections along the tieback-supported South wall and in close agreement with maximum deflections at the center of the raker-supported North wall.

ConclusionsThe application of a full 3D analysis in PLAXIS 3D 2012 to the Stata Center excavation project has been demonstrated. In order to capture the 3D effects of soil and support system responses from a non-uniform excavation process, complex shapes of soil volumes were extruded based on the photographs and excavation plans using CAD. The non-uniform soil excavation resulted in the three-dimensional effects which were well-captured by the 3D model predictions. The analysis results show a good agreement with the measured data and provide keys to explain many features of the observed performance including the differences in diaphragm wall deformations associated with sections supported by tieback anchors, raker beams and corner bracing. The usage of a relatively simple constitutive soil model (within the undrained conditions) was sufficient due to the overconsolidated state of the marine clay. The study has shown that the full 3D finite

element analysis can be effectively used for such complex excavation projects.

References1. Hewitt, R. D., Haley, M. X., Kinner, E. B. (2003).

Case History of Deep Excavation on an Urban Campus. Proc., 12th Panamerican Conf. on Soil Mechanics and Geotechnical Engineering, Soil Rock America. Boston.

2. Olsen, M. B. (2001). Measured Performance of a Large Excavation on the MIT Campus. SM Thesis, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA.

3. Orazalin, Z. Y. (2012). Three-Dimensional Finite Element Analysis of a Complex Excavation on the MIT Campus. SM Thesis, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA.

4. Orazalin, Z. Y., Whittle, A. J., & Olsen, M. B. (2014) “Three-dimensional analyses of excavation support system for Stata Center basement on MIT campus,” in review ASCE Journal of Geotechnical and Geoenvironmental Engineering.

Figure 6: Lateral wall deflections results



Figure 7: Three-dimensional diaphragm wall displacements

Phase 3: Excavation EL. -6.4m


Phase 3: Excavation EL. +2.4m



Recent activities

Product updates: PLAXIS 2D AEEarly 2014 the PLAXIS 2D Anniversary Edition was released. The user interface of PLAXIS 2D AE has been restyled to follow the flexible and easy to use workflow of the PLAXIS 3D program. In this new graphical user interface the geometric modelling and staged construction is integrated allowing for quick and easy switching between input (geometry) and calculation phases.

Other new and improved features include; Command Line and Commands Runner, borehole wizard for soil modelling, CPT import, Remote Scripting API with python wrapper, Phases Explorer and Phases Window, and much more. Furthermore we also deliver a conversion tool, which proved to be very versatile. In case you run into a conversion issue, please let us know and we will update this conversion tool accordingly.

There are also two new user defined soil models available. The first is an update for the Visco-Elastic Perfectly Plastic Model. It is a simple and robust model which can be used to model time-dependent behaviour (creep and relaxation) of various materials. The second is the new Swelling Rock Model, which can be used to simulate the

time-dependent anisotropic swelling of rocks. In the new developments column at the beginning of this bulletin you can read more about this new model.

A look back: European Plaxis Users MeetingThe European Plaxis Users Meeting 2013 was held in Karlsruhe, Germany. Not only was it the 20th edition of the meeting, Plaxis bv was also celebrating its 20th Anniversary. For this reason we had extra social activities including some food and drinks to commemorate the occasion. We also announced the winners of the master thesis competition. The committee members were Erjona Engin, MSc. (Plaxis bv) Dr. Claire Heaney (Cardiff University), Dr. Bert Schädlich (TU Graz), Dr. Nallathamby Sivasithamparam (NGI), and Dr. Phil Vardon (TU Delft).

The winner was Zhandos Orazalin with his research on the use of 3D FE analyses in PLAXIS 3D to simulate ground deformations, pore pressures, and diaphragm wall deflections. In this issue of the Plaxis Bulletin you can read his article entiteled “3D Finite Element Analysis of a Complex Excavation“. The Runner-up was Christian Elescano with his study on soil ground

improvements by grout injection, comparing solutions obtained with FE and analytical analyses. The Notable prize went to Jasper Sluis for his validation of the 2D embedded pile row feature. His article was already available in the previous 34th edition of the Plaxis Bulletin. You can look back at all our issues of the Plaxis Bulletins over the years on our site at www.plaxis.com/bulletin. The last article by Christian Elescano will be included in an upcoming bulletin, so keep an eye out for it.

All in all it was a great moment to look back at 20 years of Plaxis bv and an even longer history of our software. You can also check out the video on the evolution of PLAXIS software on our website.

Plaxis Americas LLCA big step for our North American operations was the formation of a US based company by Plaxis, Plaxis Americas LLC. This new company makes doing business with Plaxis easier and faster, and underlines the commitment of Plaxis to the North American geotechnical community. Sales and backoffice activities for all US and Canadian clients are now coming from this new Houston based company.


The past fall and winter saw Plaxis exhibit at a variety of national and regional geotechnical events – this illustrates the diverse geotechnical sectors in which Plaxis is being used (e.g. DFI, Dam Safety). At CGS’s GeoMontreal a lot of interest in PLAXIS came from existing and potential users from all across Canada. And more recently, at ASCE’s Geo-Congress, the new PLAXIS 2D AE version was demonstrated to numerous engineers. We’ll continue to visit and exhibit at events across North America in 2014, so check the list of upcoming events at www.plaxis.com/events to see when and where you can meet us in person. We look forward to meet you!

The upcoming months will see two educational opportunities: a standard course in New York in June, and an advanced course in Houston in October. These well-balanced courses are led by a course leader from Plaxis and have in-depth contributions from American professors. And for the first time we are offering early bird discounts

for our North American courses (which stacks with VIP discount) so make sure to register early to get the best price!

News from Plaxis Asia-PacificPlaxis AsiaPac started the year by conducting a series of technical seminars and workshops in Asia.

IndiaIn association with our Indian agent, Ramcaddsys, we conducted a series of lectures on the modelling of Geotechnical problems.

In collaboration with the Civil and Ocean Engineering Departments from IIT-Madras, two seminars were conducted on the 11th and 12th February 2014. The seminars were on the application of PLAXIS 2D and 3D programs. The seminars centered on the modelling of excavations, foundations, tunnelling and earthquake analysis.

In collaboration with Cochin University of Science and Technology (CUSAT) a workshop on the application of PLAXIS 3D was conducted on 14th February 2014.

Finally the 5th Indian PLAXIS Users meeting was held in the city of Kolkata on the 18th of February 2014. The users meeting was well received and was attended by users from all academia and industry. We look forward to be back for the 6th edition of Indian PUM in New Delhi in 2015.

Plaxis AsiaPac and Ramcaddsys will be back in New Delhi for the 4th Indian Advanced Course. It will be held from the 29th to 31st of October 2014 in collaboration with the Indian Institute of Technology, New Delhi.

Hong KongPLAXIS AsiaPac in association with our Hong Kong agent, Solution Research Centre, conducted a series of “Entry” and training workshops in March 2014. This series of modular training workshops offered greater flexibility and allowed our valued users to subscribe to a structured training program. Module HKG 1 on the topic of “Introduction to PLAXIS 2D” was held on 23rd of February. This was followed by Module HKG 3 which is on the topic of Geotechnical Modelling.

We will be back in the second quarter of the year to conduct these modules again with the addition of advanced application modules.

SingaporePLAXIS AsiaPac in association with Norwegian Geotechnical Institute conducted a one-day seminar on Offshore Geotechnical Modelling using FEM on the 1st of April 2014. The seminar was well received and attended by users from the Offshore industry. This is the first of our annual seminar on the subject of Offshore Geotechnics. We look forward to conducting this event in 2015.

Title

April 9, 2014Lancement de la nouvelle interface graphique de PLAXIS 2DParis, France

April 10, 2014Workshop: Introduction à PLAXIS 2D AEParis, France

April 23 - 25, 201427th Central Pennsylvania Geotechnical ConferenceHershey PA, U.S.A.

May 5 - 8, 2014Offshore Technology Conference Houston TX, U.S.A.

June 1 - 4, 201448th ARMA Rock Mechanics SymposiumMinneapolis MN, U.S.A.

June 3, 2014Workshop: Introduction to PLAXIS 3DDelft, The Netherlands

June 4, 2014Workshop: Dynamics in PLAXISDelft, The Netherlands

June 17 - 20, 2014Standard Course on Computational Geotechnics & 3D ModellingNew York, U.S.A.

June 18 - 20, 2014Numerical Methods in Geotechnical EngineeringDelft, The Netherlands

June 22 - 25, 20142014 North American Tunneling ConferenceLos Angeles CA, U.S.A.

June 23 - 26, 2014Standard Course on Computational GeotechnicsManchester, United Kingdom

June 24 - 25, 2014Russian Plaxis Users MeetingSt. Petersburg, Russia

30 June - 3 July, 2014Curso de Geotecnia ComputacionalSantiago de Querétaro, Mexico

July 8 - 10, 2014Journees nationales de geotechnique et de geologie de l’ingenieurBeauvais, France

September 8 - 11, 2014Standard Course on Computational GeotechnicsZurich, Switzerland

September 10 - 13, 2014COBRAMSEG 2014Goiânia, Brasil

September 12, 2014Workshop on Foundations and 3D ModellingZurich, Switzerland

September 21 - 25, 2014Dam Safety 2014San Diego CA, U.S.A.

September 23 - 26, 2014 33. Baugrundtagung Berlin, Germany

September 28 - October 1, 2014GeoRegina 2014Regina, Canada

29 September - 2 October, 2014Advanced Course on Computational GeotechnicsTrondheim, Norway

30 September - 3 October, 2014Standard Course on Computational GeotechnicsBrisbane, Australia

6 - 10 October, 2014Advanced Course on Computational Geotechnics & DynamicsWellington, New Zealand

October 7 - 10, 2014Advanced Course on Computational GeotechnicsHouston TX, U.S.A.

October 13 - 15, 2014AFTES 14th International CongressLyon, France

October 21 - 24, 2014DFI 39th Annual Conference on Deep FoundationsAtlanta GA, U.S.A.

Upcoming Events 2014

16 Jalan Kilang Timor#05-08 Redhill Forum

159308 Singapore

Computerlaan 142628 XK Delft

The Netherlands

Plaxis AsiaPac Pte LtdTel: +65 6325 4191

[email protected]

Plaxis bvTel: +31 (0)15 2517 720

[email protected]

Plaxis Americas LLCTel: +1 (650) 804 [email protected]

2500 Wilcrest Drive, St. 300Houston TX 77042

U.S.A.

www.plaxis.com

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