PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

Plaxis Bulletinissue 15 / march 2004

Plaxis BVP.O. Box 572

2600 AN Delft

The Netherlands

Tel: + 31 (0)15 2517720

Fax: + 31 (0)15 2573107

Email: info@plaxis.nl

Website: http://www.plaxis.nl

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

SIMULATION OF A SOIL NAIL’S DYNAMIC PULLOUT RESPONSE

Three Dimensional Deformation Analysis of a Deep Excavation

Practical Application of the Soft Soil Creep Model

Activities2004

8 - 10 March 2004 Short course on Computational Geotechnics (German) Stuttgart, Germany

21 - 25 March 2004 International course for Experienced Plaxis Users (English) Noordwijkerhout, The Netherlands

18 - 20 April 2004Plaxis workshop (English) Cairo, Egypt

19 - 23 April 2004International course on Computational Geotechnics(Spanish) Guayaquil, Ecuador

26 - 28 April 2004 Short course on Computational Geotechnics (Italian) Napels, Italy

22 - 27 May 2004ITA-AITES 2004Singapore

8 - 10 June 2004 International course on Computational Geotechnics forExperienced Plaxis Users (English) Boston, Massachusetts USA

11 June 2004 1st North American Plaxis Users Meeting Boston, Massachusetts USA

22 - 24 June 2004International course on Computational Geotechnics(English)Bali, Indonesia

25 June 2004 1st Asian Plaxis Users Meeting Bali, Indonesia

25 June 2004 Geotechnical InnovationsStuttgart, Germany

22 - 24 June 2004 Short course on Computational Geotechnics (English) Manchester, England

25 - 27 August 2004 9th International symposium on numerical models ingeomechanics (English) Ottawa, Canada

28 - 30 August 2004 Short course on Computational Geotechnics (English) Ottawa, Canada

18 - 20 October 2004 Short course on Computational Geotechnics (English)Trondheim, Norway

19 October 2004 Norwegian Plaxis Users MeetingTrondheim, Norway

11 - 12 November 2004 European Plaxis Users MeetingKarlsruhe, Germany

22 - 26 November 2004 15th Southeast Asian Geotechnical Conference (English) Bangkok, Thailand

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Editorial 3

Plaxis Users Inquiry 3

New developments 4

Recent activities 5

Plaxis Practice 6THREE DIMENSIONAL GROUND DEFORMATION ANALYSIS OF DEEP EXCAVATION ADJACENT TO RAILWAYEMBANKMENT IN THE CITY OF ROTTERDAM

Plaxis Practice 10SIMULATION OF SOIL NAIL’S DYNAMICPULLOUT RESPONSE

Plaxis Practice 12WHAT IS THE MECHANICAL IMPACT OFWATER IN GROUND?

Plaxis Tutorial 14PRACTICAL APPLICATION OF THE SOFT SOIL CREEP MODEL

Colophon The Plaxis Bulletin is the combined magazine of Plaxis B.V. and the Plaxis UsersAssociation (NL). The Bulletin focuses on the use of the finite element method in geo-technical engineering practise and includes articles on the practical application of thePlaxis programs, case studies and backgrounds on the models implemented in Plaxis.The Bulletin offers a platform where users of Plaxis can share ideas and experienceswith each other. The editors welcome submission of papers for the Plaxis Bulletin thatfall in any of these categories.

The manuscript should preferably be submitted in an electronic format, formatted asplain text without formatting. It should include the title of the paper, the name(s) of theauthors and contact information (preferably email) for the corresponding author(s). Themain 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 placedapproximately in the text. The figures themselves have to be supplied separately fromthe text in a common graphics format (e.g. tif, gif, png, jpg, wmf, cdr or eps formatsare all acceptable). If bitmaps or scanned figures are used the author should ensurethat they have a resolution of at least 300 dpi at the size they will be printed. The useof colour in figures is encouraged, as the Plaxis Bulletin is printed in full-colour.

Any correspondence regarding the Plaxis Bulletin can be sent by email tobulletin@plaxis.nl

or by regular mail to:

Plaxis Bulletinc/o Dr. W. BroerePO Box 5722600 AN DelftThe Netherlands

The Plaxis Bulletin has a total circulation of 8000 copies and is distributed worldwide.

Editorial Board:

Dr. Wout BroereDr. Ronald BrinkgreveMr. Erwin BeerninkMr. Marco Hutteman

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LAST YEAR A QUESTIONNAIRE WAS SENT BY THE DUTCH

PLAXIS USERS ASSOCIATION, TO PLAXIS USERS, ASKING

THEM ABOUT THEIR DAY TO DAY EXPERIENCE WITH THE

PLAXIS PROGRAMS AND INVITING THEM TO GIVE THEIR VIEW

ON FURTHER DEVELOPMENTS AND EXTENSIONS TO THE

PLAXIS PROGRAMS. THE RESULTS FROM THE INQUIRY ARE

PRESENTED AND DISCUSSED IN THIS ISSUE OF THE

BULLETIN.

Many users remarked that they were unsure about the planned developments forand continous improvement of the 2D version of Plaxis. This topic is discussedin the column New Developments, which focuses this time on the long termdevelopments for Plaxis V8 and its successor Plaxis V9.

The Soft Soil Creep model has been available in Plaxis for several years now, butfrom the users' responses it is clear that the determination of the input param-eters for this model is not always straightforward. The Plaxis Tutorial in this issueexplains how the value of OCR influences the creep behaviour and how this valuecan be estimated if sufficient soil investigation data is lacking.

You will also find the other regular columns in this issue, such as a review ofRecent Activities and a list of upcoming Activities. Although it was intended todiscuss the results of the last Benchmark in this issue, we decided to extend thedeadline for the Benchmark No. 3 until May 16th. We hope that this will allowsufficient time for the people who still want to enter a solution, but did not findthe time until now.

And as always, users can share their experience in Plaxis Practise. This time aninnovative use of the Plaxis 3D Tunnel program is presented, describing theanalysis of a deep excavation for a metro station in Rotterdam. Although theentire project involves bored tunnels, the article focuses on the deep excavationpit instead of the tunnels, and shows how the complex situation can be analysedusing 3D finite element calculations.

We would like to use this opportunity to invite you to contribute to Plaxis Practise.Sharing your experience with Plaxis with other users is what makes this part ofthe Bulletin such a success and we hope to see more contributions for the fol-lowing Bulletins.

Plaxis Users InquirySince the PLAXIS program became available on a commercial basis back in the late1980ties, there has been a strong relation between the users and the Plaxis organiza-tion. This resulted in the founding of the PLAXIS Users Association, which is also repre-sented in the PLAXIS Foundation. Over the years the Plaxis Users Association has con-tributed in the different stages of the development of the program, by feedback to thePlaxis organization on the needs of Dutch geotechnical engineers. Furthermore theUsers Association and the PLAXIS Company work closely together on the publication ofthe PLAXIS Bulletin, a joint initiative. As one of last year’s activities the Dutch PlaxisUsers Association did a poll amongst their members about the use of and the satisfac-tion of the PLAXIS programs.

In this article, the conclusions derived from the questionnaire and the feedback fromthe Plaxis Company are discussed by Dr. Bakker (director of PLAXIS BV) and Mr.Hutteman (Plaxis Users Association).

THE QUESTIONNAIRE

Although the response was below expectation, with 23 fully filled out forms, all majorDutch contractors and consultants did reply. The amount of forms returned on behalf ofthe company was large enough to derive some general conclusions.

Summarized, the main results as evaluated by the Dutch Plaxis users Association were: • Plaxis is mainly used in design, for design purposes and variation analysis. • The type of analysis is mainly for soil-structure interaction; coupled settlement and

stability analyses and foundation engineering.• Further, PLAXIS is widely used with respect to different types of structures.• In addition to that the users have a large demand for background information on lat-

est material models, and examples how to use these models and how to derive thenecessary parameters would be highly appreciated.

• Although the efforts put into the further development of 3D computer codes is under-stood and appreciated, the users emphasize that 2D developments are still veryimportant and demanded for.

• The PLAXIS manuals and specific courses are highly appreciated. In addition to thatthe users would desire to be informed via a) the Bulletin, and b) through additionalworkshops. The further use of the internet to share case studies would be advocat-ed.

• With respect to 2D versus 3D analysis; in practice PLAXIS 3D analysis is not yet wide-ly used. This might be partly due to the complexity of these models. A major shiftfrom 2D to 3D on the short term is not foreseen. In practice the use of 3D analysis isthought to be limited to specific applications, where the complexity would demandthe additional effort.

THE DISCUSSION

Bakker: In general the results are well understood, and coincide with the views andaims that the Plaxis Company strives for. The priority that the users ask for with respectto the use and presumably the further development of the 2D codes is understandable,although we think that the efforts put into 3D developments in past and upcoming yearsare necessary to assure continuity in serving the Plaxis users also for the future.However we understand that the main use of the Plaxis computer codes still is and willbe for a number of years for the application of 2D problems. Therefore we have to finda balance between serving present and future needs of our user group. (E.g. see alsothe issues discussed in the Column on New developments in this issue of the bulletin,which discusses some of these 2D developments still going on)Hutteman: This is seen and some of the developments of the 3D have found its way intothe 2D version of the program. Although we understand that, to serve its continuity thePLAXIS Company must be on the edge of the envelope, the tension between the ongoingconcern in daily GeoEngineering and next generation’s needs should be carefully moni-tored. >>>

Editorial

Benchmark No. 3: Embankment 1Specifications of benchmark no. 3 can be found in Plaxis bulletin issue 14 /September 2003 (www.plaxis.nl > news > plaxis bulletins). Users are kindlyrequested to mail the results to Helmut.Schweiger@tugraz.at. The extendeddeadline is: 16 May 2004. All results will be kept strictly confidential.

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>>> Bakker: In addition to the attention on 2D developments, the users ask for morecommunication and information about the use of present (material) models available,but also about ongoing development. They emphasize the importance of the PLAXISBulletin, as a medium to communicate these issues. Hutteman: This is just one end of this topic; next to this the Dutch users would like tosee more backgrounds on the parameter determination. E.g. type of soil investigationvs. parameters vs. PLAXIS models

Bakker: Apart from the general conclusions looking into more detail to specific state-ments put forward by the users, one remark worth mentioning is that 3D Tunneling isnot specifically more important than other Geotechnical problems, which can be placedinto the perspective that the first 3D computer program that PLAXIS released wasnamed and dedicated to Tunneling. Here it may be put forward that the functionality fortunnel problems in practice is not too much a limitation, which is well understood, by alarge user group of this program. Nevertheless we expect that the new 3D Foundationsprogram to be released shortly will serve a larger user group. Hutteman: Please note that in this bulletin holds an article where the 3D tunnel pro-gram was used in an excavation analysis of a building pit.

Bakker: In addition to that, plans have been developed to widen the applicability of the3D Tunnel program into a more generally applicable program for UndergroundConstruction; i.e. including all the necessary functionality for deep excavations.Therefore a new full 3D mesh-generator is being developed, which will widen the appli-cability of this new program with respect to geometry.Hutteman: As last general remark I would like to stress that although we sometimeswould like to see more small improvements in the existing products (mostly included inthe intermediate internet updates) we fully support the PLAXIS program on its productdevelopments

CALL FOR FURTHER COMMENTS

Since both the Dutch Users Association and the PLAXIS Company would like the inter-national opinion on the present and future developments of the PLAXIS program, wechallenge you to send your comments to either the PLAXIS Company or the PLAXIS UsersAssociation. We value the user’s opinion and we will continue trying to serve the PLAXISusers as best as possible with respect to their needs.

Klaas Jan Bakker Marco HuttemanDirector PLAXIS BV Dutch Plaxis Users Association

New developments

FROM THE REGULAR CONTACTS WITH PLAXIS USERS AT

COURSES, USER MEETINGS AND OTHER OCCASIONS, IT IS

NOTICED THAT QUITE A FEW USERS WONDER TO WHAT

EXTEND 2D DEVELOPMENTS STILL CONTINUE.

In recent years a lot of emphasis in our communication has been put on 3D devel-opments, such that it might give the impression that Plaxis 2D is passé.

However, in this column we like to clarify that this is not the case. In addition tothe 3D developments we do plan and perform further 2D developments toenhance the capabilities of Plaxis 2D, since by far most of the engineering anddesign applications are still 2D.

As with most Plaxis upgrades so far, the new 2D developments (from Version 8towards Version 9) are a balanced mixture between modelling requirements anduser-friendliness; functionality requirements from users on the one hand, andscientific developments that we consider necessary and useful on the long run atthe other hand. Some of these planned developments are described below.

The improvement of soil models to enhance the practical engineering applicabil-ity has been a theme throughout all Plaxis developments. Although some usershave expressed their difficulty in following new developments in soil modelling,others complain that specific aspects of soil behaviour are not yet captured bythe existing models. We see it as a challenge to provide all users with the nec-essary information to be able to benefit from the new developments.

Some of these aspects are:• Strain-dependent stiffness (especially high stiffness at small strains), which

is important for an adequate description of deformations around soil retain-ing structures and tunnels.

• Accumulation of volumetric strain upon cyclic loading, which is important toenhance dynamic analysis, taking into account liquefaction and stability.

• Hysteretic damping during cyclic loading, which relates to the former issue.• Anisotropy of strength and stiffness, which is important for the advanced

modelling of clay and peat.

Hence, there is still a demand for improvement of the models. It is planned forVersion 9 to implement a new model based on kinematic hardening, which cap-tures the first three features mentioned above to a certain extent. The lastfeature, anisotropy, is planned to be included in the Soft Soil Creep model.

Ronald Brinkgreve & Klaas Jan Bakker, Plaxis BV

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Recent activities3DFOUNDATION

The most recent activity is the completion of our latest novelty the 3DFoundation pro-gram. 3DFoundation is designed for the analysis of raft, pile-raft and offshore founda-tions. Large arbitrary 3D soil geometries and meshes can easily be generated by the def-inition of one or more boreholes. Structures or structural parts and piles can be definedindependent of non-horizontal soil stratigraphy by well defined dedicated wizards.Directly following the Experienced Plaxis User Course we organize on March 25 a specialone day course on the new 3DFoundation program. Contact our sales staff atinfo@plaxis.nl for more information on 3DFoundation or the one day course.

PLAXIS STAFF

In October Arjan Bregman joined the Plaxis Sales & Marketing department. His mainactivity is to support the sales department and to assist the marketing manager in hisworldwide marketing campaign. Arjan studied and graduated Industrial Managementat the Haagse Hogeschool. Arjan will furthermore assist Plaxis during trade fairs andsymposia.

Andrei Chesaru studied Civil Engineering and graduated at the TU Delft, specializing ontunneling technology. He also has several years of experience working as part-time pro-grammer. Within Plaxis he will work on the development and maintenance of user-inter-face applications.

USER MEETINGS

Last quarter of 2003 user meetings were organized in Karlsruhe, Delft and Oslo forrespectively the European, Dutch and Norwegian users.With over 50 participants and a good mixture of presentations and fruitful discussiongroups the European Plaxis user meeting in Karlsruhe was very successful.Especially the results of the discussion groups are a challenge for Plaxis to be also stateof the art in geotechnical engineering in the coming decade.

PlaxFlow was the central theme at the Dutch users day. During this day lectures bygroundwater flow experts were combined with the opportunity to learn more aboutPlaxFlow during a workshop.

In continuation of these successful user meetings we scheduled the 1st North AmericanPlaxis users meeting in Boston, Massachusetts on June 11, 2004.

COURSES

After succesfully conducting courses in German, French, Spanish, Portugese and Arabicwe are proud to announce our first short course in Italian. This course will be held from26 till 30 April in Naples. For an extensive overview on course and other upcomingevents see Activities on the back page of this bulletin.

AGENT IN INDIA

Ram Caddsys Pvt Ltd is founded in 1998, Ram is distinguished in the engineering soft-ware arena by the expertise of its personnel and their commitment to bring better qual-ity products and reliable service. Ram aims at providing top quality state-of-the artsoftware for Geotechnical, civil and structural engineering industry. Ram is privately held and headquartered in Chennai, India. Today, Ram has forgedalliance with many software developers, who are leaders in A/E/C industry to markettheir solutions through out South-East Asia and Middle East.Mr. Ram Kumar will be providing technical support on Plaxis software in India. He has var-ied experience in modeling the soil and soil-structure interaction problems. He has workedon the analysis of slope stability, sheeting design, 2D & 3D tunnel modeling, Pile groupanalysis and design, 3D soil structure interaction analysis for various foundations etc.

Another interesting feature in Version 9 will be the possibility to automaticallyperform model parameter variations in order to evaluate the sensitivity of thecomputational results with respect to model parameters. We will create an auto-matic procedure based on the input of an upper and lower bound of certainparameters. This will provide users a bandwidth of results, rather than a singleanswer. This approach will also enable a kind of probabilistic analysis for thosewho are ready to make a next step, but the automatic parameter variation byitself is already a great benefit for most users.

Parameter selection, in general, is probably the most difficult part in any Plaxisanalysis. To support users in the selection of soil models and their parameters,we will implement a facility that enables users to simulate standard soil tests onthe basis of material data sets they entered. This enables the user to review theconsequences of selected parameters in an early stage, and allows for optimisa-tion of parameters for practical problems based on available soil test data. Ofcourse, this should not be the only source of information to be used to selectmodel parameters, but such a facility can be quite helpful, especially when usingadvanced soil models.

In addition to parameter selection, another issue is the way parameters are relat-ed to the topology of the underground. The development of the 3D Foundation pro-gram has further enhanced our methods on 3D modelling of the underground. Theconceptual idea developed could also be used as a basis for the 2D models if wefurther investigate the possibilities to import soil data. It is expected that importof such data might become a new feature in the next upgrade of Plaxis 2D.

Many Plaxis users are nowadays struggling with the use of finite element com-putational results in design codes, such as the new European codes (Euro Code7). Working groups are discussing how to use the finite element method in con-junction with Euro Code 7, but this is still an ongoing discussion. Nevertheless,most proposals seem to converge to a similar method, which is based onstrength reduction (‘phi-c reduction’, as called in Plaxis). We will closely followthe discussions and make the necessary implementations to enable users to fol-low the proposed procedure.

Herewith we trust to have made clear that, in addition to all 3D developments ascommunicated earlier, we do intend to continue developments of the Plaxis 2Dcomputer programs. We recognize that most users will continue to use Plaxis 2Dfor engineering applications. With the improvements as mentioned above, wehope to enhance the capabilities of Plaxis for design purposes in addition to itscapabilities as an analysis tool. We are open to hear further suggestions how thiscan be achieved.

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ABSTRACT

In Rotterdam, the Netherlands, the new RandstadRail underground line is going to bebuilt in the period 2004 - 2008. Approximately two-third of the 3.0 km long Statenwegroute will be constructed using tunnel-boring techniques. The remaining part is built indeep conventional excavations (depth around 20 m), which are also used for line-up anddismantling of the tunnelling equipment. This paper highlights some of the geotechni-cal calculations as performed during the engineering of the excavations near theRotterdam Centraal station railway yard. Special attention has been paid to the grounddeformations of the railway yard embankment that are expected to occur during theexcavation works, as very strict tolerances apply to railtrack position and elevation.Modelling of the excavation geometry for one- and two-dimensional geotechnical calcu-lations revealed that quite a number of simplifications had to be made on followingaspects: surface profile (embankment vs. street elevation), varying distance betweenexcavation and embankment, supporting effect of perpendicular diaphragm walls, moreor less independent behaviour of diaphragm wall sections, etc.. It has therefore beendecided to perform additional three-dimensional computations. The selected software(Plaxis 3D) provided sufficient possibilities to account for all kinds of asymmetry withinthe geometry. Verification of the Plaxis 3D results was done through evaluation of thecalculation results for a one-dimensional geometry by 1D-, 2D- and 3D calculation tools.The results from the 3D calculations show some typical features of soil behaviour, suchas arching effects. The ground deformations on the railway embankment as derived fromthe output data have been used in the official procedures for obtaining permission forworking close to, and partly on, terrain owned by railway company ProRail.

RANDSTADRAIL IN ROTTERDAM

In Rotterdam, the Netherlands, the new RandstadRail underground line is going to bebuilt in the period 2004 - 2008. After completion it will provide connections from thecentre of Rotterdam to the towns and cities in northern direction: a.o. Den Haag andZoetermeer. RandstadRail will be linked to the terminal station of the existing Erasmusunderground line, which is located in the vicinity of the Rotterdam Centraal railwaystation. On October 28, 1999, local authorities have decided on the preferred routingof the RandstadRail line on Rotterdam territory, known as the “Statenwegtracé, vari-ant 2”. Approximately two-third of the 3.0 km long Statenweg route will be construct-ed using tunnel-boring techniques. The remaining part is built in deep conventionalexcavations (depth around 20 m), which are also used for line-up and dismantling ofthe tunnelling equipment. This paper highlights some of the geotechnical aspectsinvolved in the design of the excavations near the Rotterdam Centraal station railwayyard.

EXCAVATIONS NEXT TO RAILWAY EMBANKMENT

Relatively deep excavations are required at the Conradstraat, near Rotterdam Centraalrailway station. Here, the arrival of the tunnel boring machine (TBM) is planned. Thelocation and dimensions of the excavations are mainly determined by limitations relat-ed to tunnelling in soft soil conditions, existing buildings and infrastructure, future con-nection to Erasmus underground line, and general specifications for underground rail-way design (a.o. slope inclination). As illustrated on Figure 1, the excavations will belocated very close to the railway yard. At some points the distance to the nearest rail-

way track is about 5 meters only. Terrain conditions are: Conradstraat street level at NAP-0.3 m, railway yard elevation at NAP +3.0 m. An impression of the local site conditionsis shown on Figure 2 (camera positions as indicated on Figure 1).

Figure 1: General location plan.

Figure 2: Site impression photographs.

Following excavations are described in detail in this paper:

Excavation Length x Excavation Struts Remarks(reference coordinates) Width depth (*)I-west 10.0 m x NAP -19.1 m NAP -2.0 m Submerged(km 0.220 to km 0.230) 20.0 m excavation; water

level @ NAP -0.5 mI-east 30.0 m x NAP -16.8 m NAP -1.0 m Dry excavation(km 0.188 to km 0.220) 17.5 m to NAP -18.3 m NAP -7.5 m

NAP -13.5 m(*) NAP: reference elevation

The retaining wall has been designed as a reinforced concrete diaphragm wall down toNAP -42.5 m with thickness 1.50 m. Additional anchoring is used on the railwayembankment side in order to counteract the ground pressure driving force. Cross sec-tion drawings of the excavations are presented on Figures 3a and 3b.

Plaxis Practice

THREE DIMENSIONAL GROUND DEFORMATION ANALYSIS OF DEEP EXCAVATION ADJACENT

TO RAILWAY EMBANKMENT IN THE CITY OF ROTTERDAM

ir. V.M. Thumann, Rotterdam Public Works Engineering Department, Rotterdam, The Netherlands

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Figure 3a: Cross section a-a.

Figure 3b: Cross section b-b.

GEOTECHNICAL ANALYSES REQUIRED

Special attention has been paid to the ground deformations of the railway yardembankment that are expected to occur during the excavation works, for following rea-sons:1. Obtaining permission for working close to, and partly on, terrain owned by railway

company ProRail;2. Anticipating on remedial levelling activities on the railway yard, as very strict toler-

ances apply to railtrack position and elevation.

Initially, one-dimensional calculations were performed for the structural design of thediaphragm wall. These analyses are not sufficient to determine ground deformations atthe railway tracks on the embankment. Therefore, two-dimensional finite element cal-culations are required to find the ground deformations at varying distance from theretaining wall. In this particular case, additional three-dimensional finite element cal-culations were executed to account for all kinds of asymmetry.

MODELLING OF GEOMETRY

Modelling of the excavation geometry for one- and two-dimensional geotechnicalcalculations revealed that quite a number of simplifications had to be made on fol-

lowing aspects: surface profile (embankment vs. street level), varying distancebetween excavation and embankment, supporting effect of perpendicular diaphragmwalls, more or less independent behaviour of diaphragm wall sections, interactionbetween excavations, etc.. It has been decided to use three-dimensional computa-tions to account for these features. The selected software (Plaxis 3D) provided suf-ficient possibilities for modelling of the geometry; building the model and perform-ing the analyses appeared to be rather time consuming, however. The 3D analysishas been split into two parts denoted ‘c’ and ‘d’ for practical reasons (hardware lim-itations), as shown on Figure 4. The diaphragm wall is assumed to be in place atstart of the calculations. Length of the diaphragm wall sections are 2.9 m and 0.1m. The 0.1 m sections, having very low strength properties, are located between eachpair of 2.9 m sections to simulate the reduced interaction effect between the longerelements.

Figure 4: 3D finite element analyses model geometry.

ROTTERDAM SOIL DATA

General soil conditions at the site, which are typical for the Rotterdam region, are asfollows:

Elevation (NAP m) Water pressure from: to: Origin - Type of soil φ‘ (deg) c’ (kPa) head (NAP m)-0.3 -4.5 fill - sand 25.0 0.0 -1.6(surface)-4.5 -5.5 Holocene - clay 18.0 8.0-5.5 -8.0 Holocene - peat 12.4 10.0-8.0 -17.0 Holocene - clay 16.6 10.0-17.0 -35.0 Pleistocene - sand 27.2 0.0 -2.4-35.0 -37.5 Kedichem - clay 18.0 8.0-37.5 -40.0 Kedichem - sand 26.4 0.0 -2.4-40.0 -41.0 Kedichem - peat 13.0 3.5-41.0 -44.5 Kedichem - loam 24.5 4.0-44.5 -45.0 Kedichem - sand 26.4 0.0 -2.4-45.0 -50.0 Kedichem - loam 24.5 4.0-50.0 .... Kedichem - sand 26.4 0.0 -2.9

The data coming out of the extensive RandstadRail laboratory testing programme havebeen used to determine the required input parameters for the geotechnical calculations.

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Plaxis Practice

1D VERSUS 2D VERSUS 3D ANALYSIS - VERIFICATION OF RESULTS

The one-dimensional analyses as used for the structural design of the diaphragm wallhave been performed using MSheet software. An iterative solution procedure was fol-lowed to account for the dependency of the wall stiffness (reinforced concrete) on thebending moment. For verification of the calculation models, the same one-dimensionalgeometry has been analysed using both Plaxis 2D and Plaxis 3D software. For compar-ison, the horizontal displacements as derived from the MSheet analysis are shown nextto the Plaxis output data in Figure 5a (Plaxis 2D) and Figure 5b (Plaxis 3D). The maxi-mum values as determined from the analyses are as follows:

Analysis Location umax Soil model Software (version)(ref. Fig. 1) (@ elevation)

1-D b - b 63 mm Mohr-Coulomb MSheet (5.4.8.2)(NAP -13.6 m) bi-linear springs

2-D b - b 89 mm ‘Hardening Soil’ Plaxis 2D (8.1.2.109)(NAP -13 m)

2-D b - b 64 mm ‘Hardening Soil’ Plaxis 3D Tunnel (1.2.1.211)(NAP -13 m)

Figure 5a: Model verification - One-dimensional geometry analysis MSheet (1D) vs.Plaxis 2D.

Figure 5b: Model verification - One-dimensional geometry analysis MSheet (1D) vs.Plaxis 3D.

The two-dimensional analyses result in horizontal ground deformations at location b -b (Plaxis 2D: 89 mm and Plaxis 3D: 64 mm) which are in the same order of magnitudecompared to the one-dimensional analysis (MSheet: 63 mm). This gave sufficient con-fidence to proceed with full 3D analysis of the complex asymmetrical geometry. Furtherinterpretation of the three-dimensional analysis results is discussed below.

FULL 3D CALCULATION RESULTS - SPECIAL FEATURES

The horizontal displacements in model x-direction as calculated by the three-dimen-sional Plaxis 3D analyses are shown on Figure 6. Following aspects from the full 3Danalysis results are highlighted:• Consequences of analysis split into part ‘c’ and ‘d’.

It is noted that the displacements towards the edge of the model are affected by theboundary conditions. The influence area of the boundary conditions appears to bedifferent for each analysis, due to the variation of excavation geometry. Careful eval-uation and interpretation of this aspect is very important, as to obtain a reasonablecombination of output data coming from both analysis parts.

• Diaphragm wall behaviour.As intended, each diaphragm wall section along the railway yard is supported onlyby anchors and struts, and does not get any significant support from adjacent sec-tions. As a result, direct support due to presence of the perpendicular wall is limit-ed to just one diaphragm wall section only.

• Arching effect.The arching effect around the excavations is clearly visible on the displacementsplots. Locally, the supporting effect due to the perpendicular diaphragm walls has amajor influence as well.

• Horizontal displacements of diaphragm wall.For comparison, the maximum values as determined from the Plaxis analyses of the2D- and 3D-geometry are as follows:

Analysis Location umax Soil model Software (version)(ref. Fig. 1) (@ elevation)

2-D b - b 64 mm ‘Hardening Soil’ Plaxis 3D Tunnel (1.2.1.211)(NAP -13 m)

3-D b - b 21 mm ‘Hardening Soil’ Plaxis 3D Tunnel (1.2.1.211)(NAP -12 m)

The arching effect is considered to be the main reason for the large reduction of thecalculated horizontal displacements when comparing the outcome of the 2D- and3D-geometry analysis. The three-dimensional analysis of the geometry at location b- b results in horizontal deformations which are 65% less (21 mm vs. 64 mm) thanthe two-dimensional analysis.

• Railtrack deformations.The deformations of the railtrack on the embankment have been derived through pro-cessing of all (!) data points of the Plaxis geometry. The relevant points were foundby selecting those with y-coordinate +3,0 m (embankement surface elevation). Thevertical displacements of these data points have been put on drawing as presentedin Figure 7. Another selection has been made where x-, y- and z-coordinate had tomatch with the railtrack line coordinates. The horizontal deformations perpendicularto the railtrack were calculated from these points as presented on Figure 8.

EPILOGUE

Dutch railway company ProRail is expected to provide a formal statement of no objec-tion to the planned excavation works at the Conradstraat site by november 2003, afterevaluation of technical information including the railway yard embankment deforma-tions as described in this paper. The results of the described geotechnical analyseshave also been used to optimise the funds reservation for the anticipated remedial rail-track levelling works. Start of the building activities is expected before end 2003.Extensive monitoring of railtrack and ground deformations in the vicinity of the build-ing pit will be performed during the excavation works.

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Figure 8: Horizontal railtrack deformations (perpendicular to railtrack axis).Figure 7: Vertical deformations on railway embankment (3D analysis results).

Figure 6: Horizontal deformations around excavation I-west and I-east (3D analysis results; model x-direction).

10

INTRODUCTION

The assessment of an in-situ nail – soil interface resistance and its load displacementcharacteristic are the main design parameters to ensure the stability and serviceabil-ity of a nail reinforced structure. Sufficient field pullout results are required for a safeand economic nailed structure design. However, the number of available pullout testresults are always limited by time. In view of this, an attempt was initiated at theNational University of Singapore to explore the viability of using dynamic pullout testsas an alternative test method to assess the nail’s static pullout behavior, becausedynamic pullout tests appear to be faster than the conventional quasi static pullouttests.Before the prototype physical experiment for a dynamic nail pullout test will be carriedout, a numerical analysis by ‘Plaxis 8.2’ was carried out to numerically understand thenail’s dynamic pullout behavior and to reveal the effect of a different loading duration.Although it is termed as a dynamic pullout test here, the simulated dynamic loadingcharacteristic is similar to a kinetic (Statnamic) pile load test condition with relativewave length > 10 (Holeyman, 1992).

FINITE ELEMENT MODEL AND MATERIAL PROPERTIES

The horizontally oriented soil nail was modeled as a vertical inclusion in the middle ofa soil drum, using the possibilities of the axisymmetry model. The numerical model isshown in Figure 1. For simple comparison between the dynamic and static pullout char-acteristics, uniform soil conditions were assumed. The horizontal boundary was posi-tioned at a distance of 60r (r = nail’s radius) away (Randolph and Wroth, 1978) fromthe axis of symmetry. The upper vertical boundary was placed at 20r from the nail’shead to sufficiently eliminate boundary confinement effects. An absorbent boundarywas placed at the right and bottom boundary to eliminate any spurious reflected waves. Table 1 shows the material types and material properties used in the analysis.

Properties Soil Nail (steel)Material model Mohr Coulomb Linear elasticElastic modulus 10MPa 200GPaPoisson’s ratio 0.3 0.2Unit weight 18 kN/m3 80 kN/m3

Friction angle 36° -Cohesion 0° -Dilation angle 0° -Rinter 0.75 -

Table 1: Material properties

INITIAL STRESS CONDITION

The ground water condition was assumed to be dry. ∑-Mweight was set to zero in the ini-tial stress generation calculation step in order to avoid initial stresses generated bygravity. The initial stress condition was created by imposing load B (Figure 1) at theright boundary in the first step of calculation; creating a uniformly distributed normalstress along the nail’s shaft to simulate the initial stress condition for the actual, hor-izontally, oriented nail. In this calculation step, the absorbent boundary was deleted, theupper and bottom boundaries were vertically fixed, the left boundary was totally fixed

and the right boundary was totally free to allow the imposed load to transfer to the nail’sshaft. Interface elements were turned off in this calculation step.

Figure 1.

Due to the characteristics of the axisymmetry model, the generated normal stress withthe abovementioned method is uniformly distributed on the nail’s perimeter. Althoughthis initial stress condition is different compared to the actual working nail in which thecircumferential normal stress distribution is non-uniform, caused by the difference invertical and horizontal stress, this shortcoming does not cause severe errors becausethe main purpose of this study is to compare the differences between static and dy-namic pullout response of the modeled soil nail under the same conditions.

Figure 2.

DYNAMIC STIFFNESS AND DAMPING COEFFICIENT

According to the Plaxis 8 dynamic manual, radiation (geometry) damping, which willhappen naturally in a numerical calculation, is the dominant damping effect for a sin-gle source problem with an axisymmetric model, and Rayleigh damping can be ignored.This statement agrees with the finding by other researchers such as Chow Y.K. (1981)who concluded that radiation damping is the dominant damping source in pile driving.In order to assess the accuracy of Plaxis 8.2 in the modeling of radiation damping, thedynamic response of a circular soil disk with a massless vibrating shaft at the axis ofsymmetry, as shown in Figure 2, was calculated. A known frequency harmonic load wasimposed on the shaft and the calculated vibration response was measured. Accordingto the dynamic equation of motion as shown below,

Ma + Cv + Ku = F

with M = 0, the dynamic stiffness (K) and damping (C) coefficient can be back-calcu-lated by matching the measured displacement (u) and velocity (v) with the imposed

Plaxis Practice

SIMULATION OF SOIL NAIL’S DYNAMIC PULLOUT RESPONSE

Assoc. Prof. Tan Siew Ann, National University of Singapore & Mr. Ooi Poh Hai, National University of Singapore &Mr. Cheang Wai Lum, National University of Singapore

11

harmonic load (F). Figure 3 shows the back-analyzed stiffness and damping coefficientplotted against a dimensionless frequency, a0, defined as

a0 =rϖVs

With r = the shaft’s radius, ϖ = the circular frequency and Vs = the soil’s distortionstress velocity.The theoretical value for the stiffness and damping coefficient derived by Novak et al(1978) was also plotted in Figure 3 for comparison. It can be concluded that the stiff-ness and damping coefficient simulated by ‘Plaxis 8.2’ agree well with the theoreticalvalue.

Figure 3.

ELEMENT SIZE EFFECT

The effect of element size is crucial for dynamic calculations, especially for lumpedmass finite element codes such as Plaxis. A model with too large element size adverse-ly affects the stress wave propagation. Theoretically, the element size must be as smallas possible but it is impractical to adopt very small elements because it increases thecalculation time dramatically. Deeks and Randolph (1992) have proposed that for ac-curate simulation of stress propagation, the node spacing for a line element must be atleast 1/12 of TL, the length travelled by the rising portion of the imposed load in themedium.

Figure 4.

To assess the optimum element size for a 15-node triangular element, the same meshin Figure 2 was utilized by replacing the harmonic load with a half sine load with a cer-tain loading duration. Figure 4 plots the displacement trace measured at a distance of0.5m from the imposed load for the mesh with a different α ratio, defined as

α =TL

Average Element Size

It was found that the measured displacement trace is identical for 0 > 1.8, thus 2 isproposed as the optimum a value.

Figure 5.

RESULT AND DISCUSSION

Figure 5 shows the load displacement curves calculated by Plaxis 8.2 for a stiff nail100mm in diameter and 5m in length loaded by a half sine load with different loadingdurations. All dynamic loading results fall in the kinetic loading condition with a rela-tive wave length > 10. The numerically simulated static load displacement curve is alsoplotted in this figure for comparison. This figure clearly shows that the differencebetween dynamic and static load displacement curves becomes less with longer load-ing duration.

Figure 6.

Figure 6 shows the dynamic soil response curves, which were derived from Figure 5 bysubtracting the inertia effects. The inertia effect was assumed equal to the nail’s totalmass multiplied by the nail’s head acceleration, considering that only the nail’s headacceleration is measurable in actual field tests. The difference between the soilresponse curve and the static pullout curve is now purely due to the radiation dampingeffect. The effect of an increase in the stiffness coefficient due to dynamic loading isnegligible as shown in Figure 3.

Figure 7 and Figure 8 show the dynamic soil response and static load displacementcurves for a 15m extensible nail, measured respectively at the nail’s head and the nail’stip. Again kinetic loading conditions were ensured. These figures show that the dynam-ic soil response curves are almost similar to the static load displacement curve withinsignificant dynamic effects. This is because a longer loading duration (> 60ms) is re-quired to achieve a kinetic loading condition. The dimensionless frequency, a0, for alonger loading duration will be smaller; and the damping coefficient will also be small-er by referring to Figure 3. As an example, for a loading duration of 100ms, the a0 isequal to 0.03 and the damping coefficient is close to zero (Figure 3).

12

Water pressures play a crucial role in the stability of dikes and excavations. Stabilityand deformation incorporating the actual local pore pressures is based on:

equilibrium: σij,j’ = p,i (1)

and can be obtained by PLAXIS. The pore pressure field is conceived as input, as a con-ditioned volume force. How this field is determined? Figure 1 shows a typical canalembankment near Delft in the Netherlands which conducts the excess water pumpedout of the lowlands, here almost 4 meter under the canal water level.

Figure 1: Stagnant flow in a canal embankment.

The stationary groundwater flow pattern in the geological stratification consisting ofpeat, clay, and sand (top down) can be determined by the porous flow equation:

stat. flow: Kij(p,j + γ z,j),i = 0 (2)

where anisotropy and inhomogeneity are included in the permeability K.Capillarity and infiltration by rain, evaporation or overtopping water determine thedynamics of the groundwater table. Then the permeability K is a function of the mois-ture content θ. This flow field is described by:

unsat. flow: K[θ](p,i),i + γK[θ],z = γθ,t (3)

For example, infiltration on a sloping surface shows a saturated zone on top and a wet-ting front propagating vertically, finally reaching the groundwater table underneath(see fig. 2)

Saturated groundwater flow including storage effects, like fluid compressibility β isformulated by:

compr. flow: Kij(p,j + γ z,j),i = nγβ p,t (4)

The so-called elastic storage, related to the compressibility of the porous medium: α,can be included in a similar manner:

stor. flow: Kij(p,j + γ z,j),i = S p,t (5)

WHAT IS THE MECHANICAL IMPACT OF

Frans Barends, GeoDelft / Delft University of Technology

Plaxis Practice

Figure 7.

Figure 8.

CONCLUSION

In this article, the dynamic pullout test of a single soil nail was simulated using thePlaxis 8.2 dynamic module. At first, the ability of ‘Plaxis 8.2’ to accurately simulate theradiation damping effect of a vibrating shaft with an axisymmetric model was exam-ined, and found to be closely comparable with the theoretical solution. From a series ofparametric studies on the effect of element size, it is recommended that the α ratio (asdefined in this article) should be larger than 2 to ensure the accuracy of stress propa-gation in this lumped mass finite element program. The numerically simulated soil nail’s dynamic pullout behavior has provided convincingresults on the viability of a dynamic pullout test to assess the static pullout behavior ofboth stiff and extensible nails. Generally the dynamic pullout response is stiffer thanthe static pullout response, mainly due to the damping effect (radiation damping). Theincrease in loading duration decreases the damping effect, and consequently the dy-namic pullout response will be closer to the static pullout response. For the simulatedcase, the radiation damping effect is negligible for loading durations > 100ms.

REFERENCES

Chow, Y.K. Dynamic Behavior of Piles. PhD Thesis, University of Manchester. 1981.

Deeks A.J. and M.F. Randolph. Accuracy in Numerical Analysis of Pile Driving Dynamics.In 4th Int. Conf. Application of Stress Wave Theory to Piles, 1992, the Hague, theNetherlands, pp 85-90.

Holeyman, A.E. Keynote lecture: Technolofy of Pile Dynamic Testing. In Proc. 4thApplication of Stress Wave Theory to Piles, September 1992, the Hague, theNetherlands, pp 195-215.

Novak, M., T. Nogami and F. Aboul-Ella. Dynamic Soil Reactions for Plane Strain Case.J. Engineering Mechanics Division, ASCE, vol. 104, pp 953-959. 1978.

Randolph, M.F. and P. Wroth. Analysis of Deformation of Vertically Loaded piles. J.Geotechnical Engineering div., vol. 104, pp 1465-1488. 1978

13

A typical result of the consolidation effect is shown for a dike, suddenly loaded with ahigh river level. The response in the pore pressures after one hour is shown in figure 3.

Figure 3: Two-dimensional consolidation effects.

Two typical effects are distinguished. The first one shows at the clay-sand interface(bottom, rear side) a relatively thin zone of consolidation. There, pore pressures reactmainly vertically and they are strongly attenuated. This phenomenon is important indike design under transient loading. A special simple model for this effect, WATEX, isavailable. The other peculiar effect is an immediate pore pressure increase under thelee side slope. When this was observed in a real dike in 1978 one thought: “Pore pres-sure increase indicates effective stress decrease, and hence, there is a stability prob-lem for the lee slope.” Well, this was one-dimensional thinking! The case is that therisen river water exposes a significant horizontal load on the dike that increases thehorizontal effective stress. The corresponding porosity change causes the pore pressureincrease. Here, the stability of the lee slope is not effected. In this type of problems the phreatic surface and the semi-saturated zone play a sig-nificant role. The recent dike breach at Wilnis and Terbregge, in the Netherlands, in thedry summer of 2003 clearly demonstrate this fact.At present, a semi-coupled combination of PlaxFlow and PLAXIS V8 cannot elucidatesuch phenomena properly. Maybe in near future a full coupling will be available.

Figure 2: Infiltration in a sloping surface.

with a storage: S = nγβ (1+α /nβ). From equation (2), (3), (4), and (5), the pressurefield is obtained, which can be inserted in (1) to obtain the mechanical reaction of thesoil. PlaxFlow is suitable to determine all these types of porous flow fields in a friendlyand extensive manner.Volumetric deformations in soil by loading or creep induce porosity changes and conse-quently pore pressures, particularly noticed in the saturated zone. Consequently thegroundwater flow changes. This interaction is called consolidation. Thus S, like in equa-tion (5), is incomplete, sometimes incorrect. The full groundwater flow is to bedescribed by:

full flow: Kij(p,j + γ z,j),i = γ (nβ p,t + ε,t + cε / t) (6)

In cases with mainly one-dimensional deformation one may simplify ε,t = α p,t andomitting the creep term cε / t makes (6) equal to (5).In general e, representing the volumetric strain, depends on a multi-dimensional soilresponse, stresses and creep, and consolidation is described by (1) and (6), simultane-ously. These equations are coupled by p and e. Such type of problems can be treatedwith models like PLAXIS and DIANA.

WATER IN GROUND?

For more information

on Plaxis 3DFoundation

please contact Mr. Erwin Beernink at info@plaxis.nl

14

The Soft Soil Creep model distinguishes between primary loading and unloading/reload-ing behaviour and in this respect the model is similar to the Hardening Soil and SoftSoil models. In the last two models the distinction is made by means of a cap, i.e. acurved plane in stress space that defines the limit stress state between those twomodes of loading. The position of this cap is initially determined by the preconsolida-tion stress. However, in the Soft Soil Creep model the position of the cap is not onlydetermined by the maximum stress state that has been reached in the past, as is thecase in the other two models, but it is also a function of time.

In the Hardening Soil (HS) and Soft Soil (SS) models there is no time dependency in themodel. The cap expands instantaneously if an increase in the load would cause thestress state to fall outside the current cap. In the Soft Soil Creep (SSC) model this shiftof the cap needs time. If a higher load is applied, the cap will not follow immediately,but will take 1 day to adapt to the new stress state. This value of 1 day is an arbitrarilychosen value used in the model and cannot be varied by the user.

Furthermore, when the cap reaches the applied stress state after one day, it will notstop expanding but continue to expand with a continuously decreasing expansion rate.Any change in the stress state will cause a change in the velocity with which the capexpands; an increase in stress, even when the stress remains below the cap, will causean increased velocity of the cap expansion. Similarly, a decrease of stress will cause adecrease in the velocity of the cap expansion. The cap will, however, always keepexpanding.

It is evident that time is essential for the behaviour of the cap; therefore PlaxisCalculations will give a warning if a project in which the SSC model is used containsphases with a zero time step. Please note that this is a warning that can be ignored insome cases. An example would be a calculation phase where the soil layer that ismodelled with the SSC model is not activated yet.

As mentioned above the expansion velocity of the cap depends on time. This has con-sequences for the determination of the initial stresses as the history of the soil plays amayor role here. Let’s for example assume an embankment was constructed severalmonths ago, consisting of soft soils which strongly exhibit creep behaviour. Presently wewould like to continue construction on top of that embankment.When we construct a model for this case and assume that the subsoil and the embank-ment are both drained this could be easily modelled using time independent soil be-haviour. In that case the embankment could be activated in the first calculation phaseto model the present day situation; whether the embankment was built last week or lastyear is not important then.

However, when the Soft Soil Creep model is used the time that has elapsed since the con-struction of the embankment is important for the construction on top of the embankment. Itwill influence not only the long term displacements but also the short term displacements.If the embankment had been built long ago, it would have had more time to creep. Thiswould mean that the cap would have expanded more. Hence, when loaded, the embankmentwould show a stiffer (reloading) behaviour and less primary loading than if it were built onlya week ago. An older embankment will show less short term settlements. The creep velocitywill always increase due to the construction on top, but a more recently constructedembankment will always creep faster than an embankment that has been constructed longago. As a result the long term settlements due to the last loading stage for a more recentlyconstructed embankment will also be larger than in the case of an older embankment.

This example shows that the construction history is far more important when using theSSC model than it would be when using a time independent model. Of course the entireconstruction history can be modelled also, including the time between the actual con-struction of the embankment and the present day. There are many cases, however,where the in-situ history is not so clear. This is commonly the case when dealing withsoft soil layers that have been undisturbed for centuries, but these soft layers willgreatly influence the deformations of anything built on top.

In order to properly model the creep behaviour two main parameters are needed for theinitial situation at t=0. These are the location of the cap and its expansion velocity.These parameters cannot be entered directly by the user, but must be specified bymeans of the parameters µ* (modified creep index) and the OCR. The change of thecreep rate in time is defined by the combination of parameters λ*, κ* and µ* wherethe modified creep index specifies the creep rate after 1 day. The creep rate for a spe-cific soil is derived from these three parameters (see formula 6.23 in the Plaxis MaterialModels manual) so that the volume change due to creep over a period ∆t equals

This defines the time-dependent creep behaviour, but does not yet define at what creeprate the Plaxis calculation starts. The latter is defined by the OCR. In the SS and HSmodel the OCR is simply the ratio of the maximum stress state ever reached in the past(the preconsolidation stress) and the current stress state. The same holds for the SSCmodel, but in this case the position of the cap is also time dependent. So the correctvalue of the OCR should also take into account the time elapsed since the soil wasformed and started creeping.

By default Plaxis assigns an OCR=1 to all clusters. In the SSC model this would meanthat there has been creep for only one day. As said before, when the stress is increasedbeyond the cap it will take 1 day for the cap to expand to the new stress state, thatmeans to the situation where OCR equals 1. This also means that the Plaxis defaultsare only suited for a newly applied material which will exhibit large creep deformations.This is generally not the case for creep sensitive layers in the subsoil.

Those layers should initially be assigned a proper OCR that represents the history ofthat layer. There are basically two ways to do this. The first possibility is to assign anOCR in Initial Conditions by either double-clicking on a cluster or specifying the OCR inthe table of K0-values before starting the initial stress procedure (K0-procedure). TheOCR can be obtained from proper laboratory tests but these may not always be avail-able. Alternatively it is possible to estimate the OCR for soils where the last load stepwas primary (virgin) loading and the overburden has been constant ever since. In thiscase the OCR can be estimated using:

In this formula ∆t is the time in days that has elapsed since the last primary loading step.Typically this is the time since the material was deposited, and in case of the OCR for anexisting clay or peat layer it could even be a time in days equal to hundreds of years.

Plaxis Tutorial

PRACTICAL APPLICATION OF THE SOFT SOIL CREEP MODEL

Dennis Waterman, Plaxis BV & Wout Broere, Delft University of Technology / Plaxis BV

15

The second possibility to assign a correct OCR value in Plaxis is to leave the OCR equalto 1 in the initial conditions and start the calculation with a plastic nil step. For thisphase set the time interval equal to ∆t. Plaxis will now calculate the stress state duethe creep over that period, which results in a certain OCR. In the second phase of thecalculation the settlements due to the simulation of the creep history must be discard-ed using the “reset displacements to zero” option in Plaxis Calculations.Generally, if ∆t is large the exact value becomes less important, as the OCR dependson natural logarithm of time. It makes a large difference whether soil has been in placefor 10 days or 1 year, but there will be relatively little additional creep between 100years or 200 years.

When generating the initial stresses using the K0-procedure, the influence of the OCRwarrants some extra attention. The initial vertical preconsolidation stress at a certaindepth is calculated, as might be expected, from the effective weight of the soil on topmultiplied by the OCR value that has been entered (σc = OCR . σ'y). When a plot of theOCR values obtained in this way is inspected, it can be noticed that the reported OCRvalues differ slightly from the input value. The reason for this is that the OCR value inPlaxis Output is defined in terms of isotropic stress measures using pp = OCR . peq. Herepp is the isotropic preconsolidation stress and peq is the isotropic equivalent stress state,defined as

The reason for this is that the regular definition of OCR (σc = OCR . σ'y) is not alwaysmeaningful in complex 3D loading situations, whereas the isotopic definition is alwaysvalid.

In order to illustrate this a simple example is given. Define in Plaxis V8 a square of 1x1mwith standard boundary conditions and a distributed load on top.

Define a material data set using the Soft Soil Creep model and the material type set todrained. Other material parameters are given in table 1. Normally one would useundrained material behaviour but to more clearly illustrate creep only drained behav-iour is selected here.

Figure 1: Geometry used in this example.

Parameter Name Value UnitMaterial model Model Soft Soil Creep -Type of material behaviour Type Drained -Unit weight of soil above phreatic level γunsat 17.0 kN/m3

Unit weight of soil below phreatic level γsat 17.0 kN/m3

Modified compression modulus λ* 0.025 -Modified swelling modulus κ* 0.010 -Modified creep modulus µ* 0.001 -Cohesion (constant) cref 1.0 kN/m2

Friction angle φ 28.0 ºDilatancy angle ψ 0.0 º

Table 1: Material parameters

For this case the sample is assumed dry and for initial stresses generation the defaultvalues for K0 and OCR are used. The calculation consists of 5 phases:

1. A load of -100 kPa is applied at the top with time interval zero.2. A staged construction phase with a time interval of 100 days. Use the “reset dis-

placements to zero” option.3. Starting from the initial phase once more add a staged construction phase with a

time interval of 36500 days (100 years). 4. A load of -100 kPa is applied at the top with time interval zero.5. A staged construction phase with a time interval of 100 days. Use the “reset dis-

placements to zero” option.

Start the calculation and ignore the warning about calculation phases with zero timeinterval.

Figure 2 shows a graph of the displacements vs. time for a node in the sample. Theadditional resting time of phase 3 increased the OCR from 1 to approximately 2.4resulting in a stiffer behaviour of the sample as can be seen from the figure.

Figure 2: Time - settlement curve.

-0,050

-0,045

-0,040

-0,035

-0,030

-0,025

-0,020

-0,015

-0,010

-0,005

0,000

0 20 40 60 80 100 120

Time (days)

Uy

(m)

immediate loading

loading after 100 years

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

Plaxis Bulletinissue 15 / march 2004

Plaxis BVP.O. Box 572

2600 AN Delft

The Netherlands

Tel: + 31 (0)15 2517720

Fax: + 31 (0)15 2573107

Email: info@plaxis.nl

Website: http://www.plaxis.nl

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

SIMULATION OF A SOIL NAIL’S DYNAMIC PULLOUT RESPONSE

Three Dimensional Deformation Analysis of a Deep Excavation

Practical Application of the Soft Soil Creep Model

Activities2004

8 - 10 March 2004 Short course on Computational Geotechnics (German) Stuttgart, Germany

21 - 25 March 2004 International course for Experienced Plaxis Users (English) Noordwijkerhout, The Netherlands

18 - 20 April 2004Plaxis workshop (English) Cairo, Egypt

19 - 23 April 2004International course on Computational Geotechnics(Spanish) Guayaquil, Ecuador

26 - 28 April 2004 Short course on Computational Geotechnics (Italian) Napels, Italy

22 - 27 May 2004ITA-AITES 2004Singapore

8 - 10 June 2004 International course on Computational Geotechnics forExperienced Plaxis Users (English) Boston, Massachusetts USA

11 June 2004 1st North American Plaxis Users Meeting Boston, Massachusetts USA

22 - 24 June 2004International course on Computational Geotechnics(English)Bali, Indonesia

25 June 2004 1st Asian Plaxis Users Meeting Bali, Indonesia

25 June 2004 Geotechnical InnovationsStuttgart, Germany

22 - 24 June 2004 Short course on Computational Geotechnics (English) Manchester, England

25 - 27 August 2004 9th International symposium on numerical models ingeomechanics (English) Ottawa, Canada

28 - 30 August 2004 Short course on Computational Geotechnics (English) Ottawa, Canada

18 - 20 October 2004 Short course on Computational Geotechnics (English)Trondheim, Norway

19 October 2004 Norwegian Plaxis Users MeetingTrondheim, Norway

11 - 12 November 2004 European Plaxis Users MeetingKarlsruhe, Germany

22 - 26 November 2004 15th Southeast Asian Geotechnical Conference (English) Bangkok, Thailand