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Page 1

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

Plaxis Bulletin
issue 16 / october 2004

Plaxis BV
P.O. Box 572

2600 AN Delft

The Netherlands

Tel: + 31 (0)15 2517720

Fax: + 31 (0)15 2573107

Email: [email protected]

Website: http://www.plaxis.nl

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

SPRING CONSTANT AND SOIL-STRUCTURE INTERACTION PROBLEMS

Use of Interface Element for Simulation of

Breccia Resliding on Claystone

Activities
2004

29 - 30 September 2004
Plaxis 2-Day Course for Intermediate users (English)
Petaling Jaya, Selangor Malaysia

5 October 2004
Funderingsdag
Ede, The Netherlands

18 - 20 October 2004
International Course for Experienced Plaxis Users
(English)
Trondheim, Norway

19 October 2004
Norwegian Plaxis users meeting
Trondheim, Norway

11 - 12 November 2004
European Plaxis users meeting,
Karlsruhe, Germany

13 November 2004
Special users meeting on applications of User Defined Soil
Models
Karlsruhe, Germany

17 - 19 November 2004
Pratique éclairée des éléments finis en Géotechnique
(French)
Paris, France

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

2005

4 - 7 January, 2005
Short course on Computational Geotechnics + Dynamics
(English) - New York, USA

17 - 19 January 2005
International course Computational Geotechnics (English)
Noordwijkerhout, The Netherlands

24 - 26 January 2005
Geo-Frontiers - Austin, Texas

February 2005
2-Day Course for Intermediate users (English) - Bali, Indonesia

March 2005
Finite Elementen in der Geotechnik (German)
Stuttgart, Germany

21 - 25 March 2005
International course for Experienced Plaxis Users (English)
Noordwijkerhout, The Netherlands

7 - 12 May 2005
ITA-AITES 2005 - Istanbul, Turkey

13 – 15 May 2005
Short Course for Experienced Plaxis Users (English)
Istanbul, Turkey

15 - 17 June 2005
5th International Symposium on Geotechnical Aspects
of Underground Construction in Soft Ground Amsterdam,
The Netherlands

Page 2

2

Editorial 3

New developments 3

New developments 4
PLAXIS AND EUROCODE 7

Plaxis Benchmark No. 4 4
SINGLE PILE 1

Plaxis Benchmark No. 3 5
EMBANKMENT 1 - RESULTS

Recent activities 7

Plaxis Practice 8
NOTES ON THE APLICATION OF
THE SPRING CONSTANT AND
SOIL-STRUCTURE INTERACTION
PROBLEMS

Plaxis Practice 12
USE OF INTERFACE ELEMENT FOR
SIMULATION OF BRECCIA RESLIDING
ON CLAYSTONE

Plaxis Tutorial 15
PRACTICAL APPLICATION OF
THE SOFT SOIL CREEP MODEL
PART II

Colophon
The Plaxis Bulletin is the combined magazine of Plaxis B.V. and the Plaxis Users
Association (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 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 email) 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 common graphics format (e.g. tif, gif, png, jpg, wmf, cdr or eps formats
are all acceptable). If bitmaps or scanned figures are used the author should ensure
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of 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 to
[email protected]

or by regular mail to:

Plaxis Bulletin
c/o Dr. W. Broere
PO Box 572
2600 AN Delft
The Netherlands

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

Editorial Board:

Dr. Wout Broere
Dr. Ronald Brinkgreve
Mr. Erwin Beernink
Mr. François Mathijssen

Cover photo: Hill slide near Kawhia, NZ

Page 8

8

Plaxis Practice

AGENTS

Plaxis B.V. appointed a third agent in the U.S.A. From May 1st the company GEMSoft
(Geotechnical Engineering Modeling Software) will be an official Plaxis agent for the
U.S.A. GEMSoft is located in the Central part of the U.S.A. with offices in Chicago, IL and
Houston, TX.

The Houston office is headed up by Kenneth E. Tand, and the Chicago office by Erik G.
Funegard. Both Erik and Kenneth have long backgrounds in geotechnical engineering
with a strong focus on the petrochemical industry.

Kenneth holds a Master’s degree in Civil Engineering from the University of Houston and
has been a practicing geotechnical engineer for over 35 years. Ken has been a Plaxis
user for over 10 years and has published several papers on the use of Plaxis to solve
difficult geotechnical problems.

Erik holds a M.Sc. in Civil Engineering from the Royal Institute of Technology in
Stockholm Sweden, as well as an MBA from the University of Chicago. Erik was the
chief geotechnical engineer for a major international oil company for over 10 years with
first-hand experience of the use of advanced analysis techniques to reduce construc-
tion costs.

All three agents can act, as agent for the whole U.S.A. but GemSoft will primarily work in
the central U.S.A. The Plaxis agent for mainly the West part of the U.S.A., C. Felice &
Company, LLC with its headquarter in Kirkland, Washington has been merged with LACHEL
& Associates, Inc. The new firm will be known as LACHEL FELICE & Associates, Inc.
For contact details of GemSoft, Lachel Felice and the long-term Plaxis agent in the East
of U.S.A., GeoComp see our website.

TERRASOL celebrates its 25th anniversary! This event will take place in Paris-La
Défense on September 28th 2004. TERRASOL was founded in 1979, and has regularly
grown up since (more than 30 people today) as a leading geotechnical consulting com-
pany, working in fields like foundations, tunneling, maritime works, excavations, earth-
works, infrastructures, etc.

TERRASOL has always used its geotechnical know-how and expertise to develop and sell
its own software. It became PLAXIS' agent for France in 1998, and now participates in
the PDC program and Plaxis Advisory Board. Its software department also provides serv-
ices like technical support and continuing education.

REVISED WEBSITE

A revised website is launched to disseminate information more transparently. We hope
we have created an informative Website that makes life easier for the Plaxis users and
others. News, product and course information is easy to find and updates are easy to
access.
Any additional suggestions are welcome; please send them to [email protected]

INTRODUCTION

The use of a spring constant for the design and analysis of raft and pile-raft founda-
tions has many limitations, related to the proper estimation of the spring constant
magnitude and the soil structure interaction. Spring constants have been used for
example in the design of a Mass Rapid Transit railway station in an oversea project. The
overview of soil condition on that particular site is as shown in Fig. 1 below.

At this project the spring constant concept was adopted for designing the station raft
foundation. The structural engineer asked for the magnitude of the spring constant
from a young geotechnical engineer, who then gave a coefficient of subgrade reaction
(in kN/m3 ) derived from a plate-loading test. This parameter was later converted into
a foundation coefficient of subgrade reaction, ks, by using the following equation:

Figure 1: SPT vs Depth

where B is the width of the raft foundation.

This last parameter was then applied as a spring constant by multiplying it with the
unit area under the raft foundation (the unit dimension became kN/m). A certified
Professional Engineer then approved the outcome of the raft foundation design for con-
struction. Without prejudice to blame others, it is obviously a mistake! Why it is so? For
B greater than 0.3 m, equation 1 clearly shows that the greater the value of B the small-
er the value of ks. While it is structurally correct that the wider the foundation the more
flexible the foundation is. It does not equally right for the foundation soil. The engineers
had missed the fact that the soil at that area was far from homogeneous.

NOTES ON THE APLICATION OF THE SPRING

GOUW Tjie-Liong, PT Limara, Indonesia

B + 0.3
ks = k 2B (1)

2

Page 9

9

The soil condition shows that, within the influence of the raft foundation, the deeper the
foundation soils the harder they are. This means the deeper soils have greater rigidity
as compared to the layer right below the raft foundation (note: the width of the raft is
around 35 m).

The inappropriate spring constant led to an excessive settlement of the raft. As a result,
in order to reduce the settlement, the center of the raft was strengthened with more
than 20 number of bored piles. Upon reviewing the design, the author proved that the
bored piles were excessive and unnecessary. However, by the time it was found, it was
too late.

The above case shows the application of spring constant without considering the char-
acteristics and the behavior of the underlying soils. And it is also an example of the
existence of ignorance, gaps and weakness in the relation among the structural and
geotechnical engineers. This papers tries to elaborate the underlying principle the
spring constant theory, its limitation and the application of specially made geotechni-
cal software to solve the problem of soil structure interaction.

SPRING CONSTANT - THE THEORETICAL BACKGROUND AND THE
LIMITATION

“What is the spring constant at this particular site?” or “What is the modulus of sub-
grade reaction at this location?” is a common question asked by a structural engineer
to a geotechnical engineer. It is a straightforward question. Unfortunately, it has no
direct, let alone a simple answer.

The concept of spring constant was first introduced by Winckler in 1867. He modeled
flexible foundation, such as raft, to stand on an independent discreet spring elements
or supports. In 1955, Karl Terzaghi, in his paper ‘Evaluation of coefficients of subgrade
reaction’ proposed a method to estimate the magnitude of the spring constants. His
approach, also known as subgrade reaction model, was then became popular and com-
monly used in the design of raft foundation.

Looking back into the origin of this concept (see Fig.2), one can see that the modulus
or the coefficient of subgrade reaction, ks(x), is defined as the foundation pressure, p(x),
divided by the corresponding settlement of the underlying soil, d(x), i.e.:

Figure 2: Subgrade Reaction under a Flexible Foundation

x

C L

z

2b
Slab infinitely long
in y direction

(center line)

Subgrate
Reaction

H

Hard Layer

p(x)
Es, µs

Es, µs are elastic parameters of soil
Es = Young Modulus of Soils
µs = Poisson Ratio of Soils

In other words, the subgrade reaction is no other than the distribution of soil reaction, p(x),
beneath the raft foundation structure against the foundation load. The distribution of the
soil reaction is not linear in shape. This is particularly true when the foundation is sub-
jected to uniform load. In this case, generally, the distribution of the soil reaction in clayey
soils is curving upward, as shown in Fig. 2, with the largest reaction around the edges of
the foundation and the smallest reaction around the center. In sandy soils, the reverse
reaction is seen, i.e. zero on the edges and maximum at the center point. In principle, the
distribution of the soil reactions right beneath the raft foundation depend on the position
of the point under consideration (i.e., the distance of x), the shape of the loading and the
relative rigidity (EI) of the raft foundation structure against the underlying soils.

The Winckler model is a simplified mathematical formulation of an elastic soil model. This
concept does not take into account the fact that the foundation reaction or the soil stress-
es is distributed to the deeper soil layer and forming the so called ‘bulb pressure’. The soil
settlement beneath the foundation is the accumulation of interactions between the soil
stresses and the elastic parameters of the soils at each point inside the bulb pressure zone.
Assuming the soils inside the bulb pressure zone posses are homogeneous, Vesic (1961)
expanded the Winckler model into elastic model and developed the following equation:

The above Vesic’s equation clearly shows that the modulus of subgrade reaction
depends not only on the width of the foundation, B, but also on the elastic parameters
of soils, Es and µs, and on the shape factor of the foundation, Ip.

In the earlier days, for the sake of mathematical simplicity, it is generally simplified
that the spring constant is not a function of the position x (see Fig.2), hence a single
value of spring constant is applied. However, the non-linearity distribution of the soil
reactions right beneath the foundation structure suggests that the so-called modulus
of subgrade reaction, hence the spring constant, is not a unique value. Terzaghi him-
self recognized the limitation of this assumption. Bowles (1997) suggested providing
higher ks at the edges of the raft and smaller ks at the center position.

The above explanations show that there is no discrete value of modulus of subgrade
reaction for a given type of soil Therefore, it does not realistic to ask for a spring con-
stant value without the information on the type and the size of the foundation structure.

In layered soils with different elastic parameters, an equivalent model must be developed
in order to derive a representative modulus of subgrade reaction. To do this the elastic set-
tlement of the layered soils induced by the foundation pressure must first be calculated.
Poulos and Davis, 1974, mathematical formulation can be used to calculate the elastic
settlement of the foundation soils. In a pile raft foundation, to answer the question on the
magnitude of the spring constant, the geotechnical engineer also has either to calculate
the settlement of the pile foundation or derives it from a pile load test result.

Since the modulus of subgrade reaction (spring constant) is needed to calculate the
settlement of the foundation soils, why should one goes to the trouble in providing the
spring constant? The structural engineers asked the spring constant because they want
to feed in the parameter into their computer software. To the author knowledge, as it is
not developed to handle geotechnical problems, the structural engineering software
used in analyzing raft or pile raft foundation cannot handle geotechnical parameters.

CONSTANT AND SOIL-STRUCTURE INTERACTION PROBLEMS

ks (x) =
p(x)
d(x) (2)

ks =
Es

B.Ip. (1-vs
2) (3)

Page 15

15

UNDRAINED BEHAVIOUR

In the previous issue of the Plaxis Bulletin some basic aspects of the Soft Soil Creep
model have been discussed. For simplicity, the soil behaviour was limited to drained
behaviour, so that the influence of the overconsolidation ratio (OCR) and the initial
creep velocity could be shown clearly. However, in the real world soils that exhibit creep
behaviour generally have a low permeability. These soft soils almost always show
undrained behaviour under short term loading. This combination of undrained behav-
iour and creep raises some additional issues that will be discussed here.

In the previous Plaxis Tutorial, a square block of clay was modelled using Soft Soil Creep
(SSC) material, with standard boundary conditions, initial stresses due to its own
weight and no initial excess pore pressures. For the current example, we will change the
material behaviour from drained to undrained, and re-examine its behaviour.

Assume first that it is possible to seal all sides of this block of soil, so that any excess
pore pressures that develop can not drain off and effectively consolidation cannot
occur, but deformation is not hindered. Common clingfoil will do this nicely, as will the
closed consolidation boundaries that are available in Plaxis. Now leave the block of soil
undisturbed for a considerable time period. After for example 10 years, the material will
still be almost undeformed, but has developed significant excess pore pressures inside,
even though no external load was applied.

This development of excess pore pressures in the absence of external loads or defor-
mation is completely logical for a SSC material. Normally, creep behaviour of the soil
causes plastic deformation and, as a result, a decrease in volume. However, as the
material is undrained and there is no possibility to consolidate, volume strains are not
allowed in the model. Therefore, the plastic volume strain that is calculated due to
creep has to be compensated by an elastic volume strain of equal magnitude but oppo-
site direction. As the total volume strain is the sum of the elastic and plastic volume
strains, this results in a nett volume strain equal to zero.

According to Hooke’s law, elastic expansion, a negative elastic compression, leads to a
decrease of the effective stresses. But, since no external load was applied, the total
stresses must remain the same, and a decrease of the effective stresses is only allow-
able if the excess pore pressures increase. It is this mechanism that causes the
observed excess pore pressures. Of course, this mechanism will continuously increase
the excess pore pressures over time, but the creep that drives it will diminish rapidly.
As the creep rate depends on the effective stress level, and the excess pore pressures
decrease the effective stresses in the sample, the creep rate will decrease at an even
higher rate than in the case of a drained material.

The shift of stress from the effective stress part of the total stress to the (excess) pore
pressures is also the cause for the very small deformation that is observed in the Plaxis
model. Even though water is often assumed to be totally incompressible, it is not, and
the increased pore pressures cause a very small volume strain of the pore water, and
thereby of the entire model.

This is, of course, a rather theoretical example. Soil is hardly ever left completely undis-
turbed for 10 years in a situation where consolidation cannot occur. But this example
still shows an important feature of the SSC model: creep behaviour of undrained soils
leads to an increase of excess pore pressures.

Consolidation, on the other hand, deals with the dissipation of excess pore pressures
over time in soils with low permeability and has the opposite effect. The combination of
consolidation and creep in a creep sensitive soil can therefore cause a wide range of
behaviour. The precise behaviour depends on whether creep or consolidation is domi-
nant.

Over time, creep would tend to increase the pore pressures, causing the creep velocity
to decrease and the consolidation velocity to increase. Due to consolidation the pore
pressures will drop again, which causes the consolidation rate to decrease and the
creep rate to increase. This combination of effects is illustrated below.

A simple 1D consolidation test has been performed on four different soil data sets, each
with the same strength and stiffness parameters as listed in the previous Plaxis
Bulletin, but with permeabilities varying between 0.1 m/day and 10-4 m/day. For this
exercise closed consolidation boundaries have been added to the left and right side of
the square soil block, as shown in Figure 1.

Figure 2 shows the excess pore pressure in the middle of the soil sample as a function
of time. After first loading the sample with 100 kPa over a period of 1 day, the excess
pore pressure is 109 kPa in all cases (100 kPa due to the load and 9 kPa due to creep
during the first day). For the highest permeability (0.1 m/day) the excess pore pressures
immediately drop when consolidation starts, whereas for lower permeabilities the excess
pore pressures first increase for a while, until consolidation really becomes the dominant
effect and the excess pore pressures finally decrease. Note that for a permeability of 10-4
m/day the excess pore pressures even rise to a peak value of 130 kPa after 63 days!

Figure 1: Geometry with closed consolidation boundaries

Figure 2: Development of excess pore pressures over time for the various cases

Plaxis Tutorial

PRACTICAL APPLICATION OF THE SOFT SOIL CREEP MODEL – PART II

D. Waterman, Plaxis BV & W. Broere, Delft University of Technology/Plaxis BV

Page 16

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

Plaxis Bulletin
issue 16 / october 2004

Plaxis BV
P.O. Box 572

2600 AN Delft

The Netherlands

Tel: + 31 (0)15 2517720

Fax: + 31 (0)15 2573107

Email: [email protected]

Website: http://www.plaxis.nl

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES

SPRING CONSTANT AND SOIL-STRUCTURE INTERACTION PROBLEMS

Use of Interface Element for Simulation of

Breccia Resliding on Claystone

Activities
2004

29 - 30 September 2004
Plaxis 2-Day Course for Intermediate users (English)
Petaling Jaya, Selangor Malaysia

5 October 2004
Funderingsdag
Ede, The Netherlands

18 - 20 October 2004
International Course for Experienced Plaxis Users
(English)
Trondheim, Norway

19 October 2004
Norwegian Plaxis users meeting
Trondheim, Norway

11 - 12 November 2004
European Plaxis users meeting,
Karlsruhe, Germany

13 November 2004
Special users meeting on applications of User Defined Soil
Models
Karlsruhe, Germany

17 - 19 November 2004
Pratique éclairée des éléments finis en Géotechnique
(French)
Paris, France

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

2005

4 - 7 January, 2005
Short course on Computational Geotechnics + Dynamics
(English) - New York, USA

17 - 19 January 2005
International course Computational Geotechnics (English)
Noordwijkerhout, The Netherlands

24 - 26 January 2005
Geo-Frontiers - Austin, Texas

February 2005
2-Day Course for Intermediate users (English) - Bali, Indonesia

March 2005
Finite Elementen in der Geotechnik (German)
Stuttgart, Germany

21 - 25 March 2005
International course for Experienced Plaxis Users (English)
Noordwijkerhout, The Netherlands

7 - 12 May 2005
ITA-AITES 2005 - Istanbul, Turkey

13 – 15 May 2005
Short Course for Experienced Plaxis Users (English)
Istanbul, Turkey

15 - 17 June 2005
5th International Symposium on Geotechnical Aspects
of Underground Construction in Soft Ground Amsterdam,
The Netherlands

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