PLAXIS P LAXIS Nº 12 - JUNE 2002 Editorial Some time has passed since the appearance of our last bulletin no 11, but the PLAXIS team did not sit still. Not only was a new director appointed for PLAXIS B.V. which will be introduced further on, also a number of other new team-members have come to work for PLAXIS. The Plaxis-team has extended with four new people in order to improve the capability to accommodate for the demand on new plaxis developments. The Plaxis-team consist of 14 people. In the next bulletin, we will briefly introduce them to you. New Developments which will be discussed in the contribution by Dr Brinkgreve, the head of our development team. He will discuss further developments such as for the release of Plaxis Version 8, the progress on the PLAX-flow program and the other 3D developments. With respect to PLAXIS 2D, Version 8 is due to be expected after the summer holidays, as Beta testing of this new program is underway, and the users in our regular PLAXIS course in Noordwijkerhout in January and also the attendants of the advanced course have had some opportunity to experience this new program. In his regular column Prof. Vermeer will discuss the use of soil parameters and especially parameter estimation. Not always is it possible to do a direct test for a parameter. Or sometimes in a pre-design stage there is only limited information of the soil stratification. In that case it is often very convenient to have some correlations between different soil-parameters in order to be able to proceed with a geotechnical design. In this issue Prof. Vermeer discusses Oedometer stiffness of Soft Soils. In addition to the aforementioned, Prof. Schweiger who also is a regular contributor to our bulletin discusses the relation between Skemptons pore pressure parameters A and B and the performance of the Hardening Soil model. Furthermore we are fortunate to have new contributions with respect to Benchmarking; two contributions on benchmarking are presented here, one on Shield tunnelling and another on excavations. Again we are glad to have a number of practical applications; Among which are a contribution by Dr. Gysi, on a multi-anchored retaining wall, and another one by Mr. Cheang from Singapore on a complicated retaining wall with Jack-In Anchors. Finally in the Users Forum it is shown how a more complicated 3D situation of a Retaining wall with anchors is practically modelled with PLAXIS 2D. Editorial Staff: Martin de Kant, Plaxis Users Association (NL) Marco Hutteman, Plaxis Users Association (NL) Peter Brand, Plaxis B.V. Scientific Committee: Prof. Pieter Vermeer, Stuttgart University Dr. Ronald Brinkgreve, Plaxis bv 1 Bulletin of the PLAXIS Users Association (NL) Plaxis bulletin Plaxis B.V. P.O. Box 572 2600 AN Delft The Netherlands E-mail: [email protected]IN THIS ISSUE: Editorial 1 Column Vermeer 2 New developments 4 Note on pore pressure 6 Benchmarking I 9 Benchmarking II 12 Recent Activities 13 Plaxis practice I 14 Plaxis practice II 17 Users forum 22 Some Geometries 22 Agenda 24
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PLAXIS
PLAXIS
PLAXIS
PLAXIS Nº 12 - JUNE 2002
Editorial
Some time has passed since the appearance
of our last bulletin no 11, but the PLAXIS
team did not sit still. Not only was a new
director appointed for PLAXIS B.V. which
will be introduced further on, also a
number of other new team-members have
come to work for PLAXIS. The Plaxis-team
has extended with four new people in
order to improve the capability to
accommodate for the demand on new
plaxis developments. The Plaxis-team
consist of 14 people. In the next bulletin,
we will briefly introduce them to you.
New Developments which will be discussed in
the contribution by Dr Brinkgreve, the head of
our development team. He will discuss further
developments such as for the release of Plaxis
Version 8, the progress on the PLAX-flow
program and the other 3D developments. With
respect to PLAXIS 2D, Version 8 is due to be
expected after the summer holidays, as Beta
testing of this new program is underway, and
the users in our regular PLAXIS course in
Noordwijkerhout in January and also the
attendants of the advanced course have had
some opportunity to experience this new
program.
In his regular column Prof. Vermeer will discuss
the use of soil parameters and especially
parameter estimation. Not always is it possible
to do a direct test for a parameter. Or sometimes
in a pre-design stage there is only limited
information of the soil stratification. In that case
it is often very convenient to have some
correlations between different soil-parameters
in order to be able to proceed with a
geotechnical design. In this issue Prof. Vermeer
discusses Oedometer stiffness of Soft Soils.
In addition to the aforementioned, Prof.
Schweiger who also is a regular contributor to
our bulletin discusses the relation between
Skemptons pore pressure parameters A and B
and the performance of the Hardening Soil
model.
Furthermore we are fortunate to have new
contributions with respect to Benchmarking;
two contributions on benchmarking are
presented here, one on Shield tunnelling and
another on excavations.
Again we are glad to have a number of practical
applications; Among which are a contribution
by Dr. Gysi, on a multi-anchored retaining wall,
and another one by Mr. Cheang from
Singapore on a complicated retaining wall with
Jack-In Anchors.
Finally in the Users Forum it is shown how a
more complicated 3D situation of a Retaining
wall with anchors is practically modelled with
PLAXIS 2D.
Editorial Staff:
Martin de Kant, Plaxis Users Association (NL)
Marco Hutteman, Plaxis Users Association (NL)
Peter Brand, Plaxis B.V.
Scientific Committee:
Prof. Pieter Vermeer, Stuttgart University
Dr. Ronald Brinkgreve, Plaxis bv
1
Bulletin of thePLAXISUsers Association (NL)
Plaxis bulletinPlaxis B.V.P.O. Box 5722600 AN DelftThe NetherlandsE-mail:[email protected]
IN THIS ISSUE:
Editorial 1
Column Vermeer 2
New developments 4
Note on pore pressure 6
Benchmarking I 9
Benchmarking II 12
Recent Activities 13
Plaxis practice I 14
Plaxis practice II 17
Users forum 22
Some Geometries 22
Agenda 24
PLAXIS
PLAXIS
Fig. 1: Atterberg limits of 21
different soils that weretested by Engel
Column Vermeer
ON THE OEDOMETER STIFFNESS
OF SOFT SOILS
For normally consolidated fine-grained
soils, we have the logarithmic compression
law, �e = Cc �log�’, where De is the change
of the void ratio, Cc the compression index
and �’ the vertical effectivestress in one-
dimensional compression. The compression
index Cc is measured in oedometer tests,
together with other stiffness related
parameters such as the swelling index and
the preconsolidation stress. In this column
I will discuss correlations for the
compression index Cc.
It should be realized that Terzaghi and other
founding fathers of Soil Mechanics lived in the
10-log-paper period and their findings have to
be reformulated for use in computer codes.
Hence, we have to change from a 10-log to a
natural logarithm in order to obtain the
reformulated law,
�e = - � �ln�’, where �= Cc �ln10. On top of
this it is convenient to use strain instead of
void ratio, which leads to the compression law,
where �� = �* �ln�’, �* = ��(1+e) and �� is a
finite strain increment. I will address Cc, as well
as the modified compression index �* and in
addition the oedometer modulus Eoed.
One of the best-known geotechnical
correlations reads Cc� 0.9 (wL - 0.1), where wL
is the liquid limit. For details, the reader is
referred to the book by Terzaghi and Peck
(1967). Wroth and Wood (1978) proposed the
seemingly different correlation Cc� 1.35IP,
where IP is the plasticity index. In reality the
two correlations are virtually identical, as the
plasticity index can usually be approximated as
IP � 0.73 (wL - 0.1). Indeed, with the exception
of sandy silts, data for IP and wL tend to be on
a straight line that is parallel to the so-called
A-line in Casagrande’s plasticity chart (see
Fig. 1). On using the Ip-wL correlation, the
Terzaghi-Peck correlation reads Cc � 1.23IP,
which is very close to the finding of Cc � 1.35IPby Wroth and Wood. Considering the large
amount of evidence on the correlations,
Cc � 1.35IP and IP � 0.73 (wL - 0.1), I conclude
that we may use both
Cc � 1.35IP and Cc � wL - 0.1 (1)
The latter one is only slightly different from
the earlier one by Terzaghi and Peck and to my
judgement also slightly better. Let us now
address the modified compression index �* as
used in all advanced Plaxis models. The
relationship between the traditional
compression index Cc and the modified one
�* is expressed by the equation
�*=Cc �
Cc(2)
(1+e) In10 4.6
The approximation follows for e=1. In general
it is crude to assume e�1, but it works within
the context of the correlations for soft soils.
In combination with the correlations for Cc it
leads to:
�* � 0.3lp and �* � 0.2(wL- 0.1) (3)
For a direct assessment of these correlations,
we will consider data by Engel (2001). This
database contains modified compression
indices for 21 different clays and silts, with a
liquid limit ranging from 0.2 up to 1.1 and a
plasticity index between 0.03 and 0.7, as can
2
PLAXIS
PLAXIS be seen in Fig. 1. Engel’s data for �* leads to
Figures 2 and 3. From Fig. 2 it can be
concluded that the correlation
�* � 0.3lp has some shortcomings. A close
inspection shows that it is nice for clays with
plasticity indices above the A-line in
Casagrande’s plasticity chart, but not for silts
with Ip below the A-line. To include such silts
one could better use the correlation,
�* � 0.2(wL- 0.1) as demonstrated in Fig. 3. On
plotting �* as a function of the liquid limit, as
done in Fig. 3, it is immediately clear that there
is an extremely nice correlation.
It should also be recalled that the correlation
�* � 0.2(wL- 0.1) is not only supported by
Engel’s database, but that it is also fully in line
with the work of Wroth & Wood as well as
Terzaghi & Peck on correlations for Cc.
Let us now consider the oedometer stiffness.
To this end the logarithmic compression law
�� = �* . �ln�’ can be written in the differential
form d�/dln� = �* and one obtains
d�’/ d� = �’/� The tangent stiffness in
oedometer-compression, also refered to as
the constrained modulus, is thus proportional
to stress. Hence, Eoed =�'/�*, where Eoed is also
denoted as M or Es, depending on conventions
in different countries. This linear stress
dependency of soil stiffness is nice for fine-
grained NC-soils, but not for coarse-grained
ones. Therefore Ohde (1939) and Janbu (1963)
proposed a generalisation of the form:
Eoed = Eoed (�'/Pref)m with Pref = 100kPa (4)
where m is an empirical exponent. This
equation reduces to the linear stress
dependency of soil stiffness for m=1.
In the special case of m=1, one thus obtains
the logarithmic compression law for fine-
grained NC-soils. For coarse grained soils, much
lower exponents of about m=0.5 are reported
by Janbu (1963), Von Soos (2001) and other
researchers.
The above power law of Ohde, Janbu and Von
Soos has been incorporated into the Hardening
Soil Model of the Plaxis code. Here it should be
noted that the above authors define
Eoed = v . Pref, where v is a so-called modulus
number. Instead of the dimensionless modulus
number, the Hardening Soil Model involves
Eoed as an input parameter, i.e. the constrained
modulus at a reference stress of
�’= pref = 100kPa. For the coming Version 8 of
the Plaxis code, we have also considered the
use of alternative input parameters. Instead of
Eoed , we have discussed the modulus number
1/�* as well as the modified compression index
itself, as it yields
�* Pref / Eoed (5)
In fact, this simple relationship between the
oedometer stiffness and the modified
compression index triggered our thinking on
alternative input parameters. Finally we decided
3
Fig. 2:Compression indices asmeasured by Engel as a
function of Ip
ref
ref
ref
ref
ref
Fig. 3:Compression indices
correlate nicely with theliquid limit
PLAXIS
PLAXIS to go one step further and use the traditional
compression index Cc by implementing the
equations:
Eoed = Pref
= (1+e) ln10
. Pref (6)�* Cc
Within the new Version 8, users will have the
choice between the input of Eoed and the
alternative of Cc. Similarly, the so-called swelling
index Cs will be used as an alternative input
parameter for the unloading-reloading stiffness
Eur. On inputting Cc one also has to prescribe
a value for the void ratio.
Here, a default value of e=1 will be introduced.
This will make the Hardening Soil Model easier
to use in the field of soft soil engineering.
P.A. Vermeer, Stuttgart University
REFERENCES:
Engel, J., Procedures for the Selection of
Soil Parameters (in German), Habilitation study,
Department of Civil Engineering, Technical
University of Dresden, 2001, 188 p.
Janbu, N., "Soil Compressibility as Determined
by Oedometer and Triaxial Tests", Proceedings
3rd European Conference on Soil Mechanics
and Foundation Engineering, Vol. 1,
Wiesbaden, 1963, pp. 19-25.
Ohde, J. , "On the Stress Distribution in the
Ground" (in German), Bauingenieur, Vol. 20, No.
33/34, 1939, pp. 451-459.
Terzaghi, K. and Peck, R. B., "Soil Mechanics in
Engineering Practice", 2nd Ed, John Wiley and
Sons, New York, 1967, 729 p.
Soos von, P., "Properties of Soil and Rock" (in
German), Grundbautaschenbuch, Vol. 1, 6th
Ed., Ernst & Sohn, Berlin, 2001, pp. 117-201
Wroth, C. P. and Wood, D. M. , "The Correlation
of Index Properties with Some Basic
Engineering Properties of Soils", Canadian
Geotechnical Journal, Vol. 15, No. 2, 1987, pp.
137-145.
New Developments
In a few months, Plaxis version 8 will be
released. This new 2D program is one of the
results of a recently finished two-years
project on Plaxis developments. Another
results of this project is the 3D Tunnel
program, which was released last year. In
this bulletin some new features of Plaxis
version 8 will be mentioned. The new
features are divided into three groups:
Modeling features, calculation options and
user friendliness.
MODELING FEATURES
Plaxis (2D) version 8 has several new features
for the modeling of tunnels and underground
structures. Some of these features were
already implemented in the 3D tunnel
program, such as:
- Extended tunnel designer, including thick
tunnel linings and tunnel shapes composed
of arcs, lines and corners.
- Application of user-defined (pore) pressure
distribution in soil clusters to simulate grout
injection.
- Application of volume strain in soil clusters
to simulate soil volume loss or
compensation grouting.
- Jointed Rock model
Other new modeling features are aimed at
the modeling of soil, structures and soil
structure interaction:
4
ref
PLAXIS
PLAXIS - Input of Skempton's B-factor for partially
undrained soil behavior.
- Hinges and rotation springs to model beam
connections that are not fully rigid.
- Separate maximum anchor forces
distinction between extension and
compression).
- De-activation of interface elements to
temporarily avoid soil-structure interaction
or impermeability.
- Special option to create drains and wells for
a groundwater flow calculation.
CALCULATION OPTIONS
Regarding the new calculation options, most
new features are in fact improvements of
'inconsistencies' from previous versions.
Examples of such improvements are:
- Staged Construction can be used as loading
input in a Consolidation analysis.
- A Consolidation analysis can be executed as
an Updated Mesh calculation.
- In an Updated Mesh calculation, the update
of water pressures with respect to the
deformed position of elements and stress
points can be included. In this way, the
settlement of soil under a continuous
phreatic level can be simulated accurately.
- Loads can be applied in Staged
Construction, which enables a combination
of construction and loading in the same
calculation phase. The need to use
multipliers to apply loading has decreased.
This makes the definition of calculation
phases more logical and it enhances the
flexibility to use different load combinations.
- Preview (picture) of defined calculation
phase in a separate calculations tab sheet.
- Improved robustness of steady-state
groundwater flow calculations. Simplified
input of groundwater head boundary
conditions based on general phreatic level.
In addition, a separate program for transient
groundwater flow is planned to be released
at the end of 2002.
USER FRIENDLINESS
Many new features in the framework of 'user
friendliness' are based on users' suggestions
from the past. Examples of these features are:
- Reflection of input data and applied loads
in the output program.
- Report generation, for a complete
documentation of a project (including input
data and applied loads).
- Complete output of stresses (effective, total,
water), presented both as principal stresses,
cartesian stresses;
also available in cross sections and in the
Curves program.
- Equivalent force in cross-section plots of
normal stresses.
- Force envelopes, showing the maximum
values of structural forces over all
proceeding calculation phases.
- Scale bar of plotted quantities in the output
program.
- Color plots plotted as bitmaps rather than
meta-files. This avoids the loss of colors
when importing these plots in other
software.
- Parameters in material data sets can be
viewed (not modified) in Staged
Construction.
- User-defined material data set colors.
A special feature that is available in Version 8 is
the user-defined soil models option. This
feature enables users to include self-
programmed soil models in the calculations.
Although this option is most interesting for
researchers and scientists at universities and
research institutes, it may also be interesting
for practical engineers to benefit from this
work. In the future, validated and well-
documented user-defined soil models may
become available via the Internet. More
information on this feature will be placed on
our web site www.plaxis.nl.
Registered Plaxis users will be informed when
the new version 8 is available; they can benefit
from the reduced upgrade prices. Meanwhile,
new developments continue. More and more
developments are devoted to 3D modeling. We
will keep you informed in future bulletins.
Ronald Brinkgreve, PLAXIS BV
5
PLAXIS
PLAXIS NOTE ON PORE
PRESSURE
SOME REMARKS ON PORE PRESSURE
PARAMETERS A AND B IN UNDRAINED
ANALYSES WITH THE HARDENING SOIL
MODEL
In undrained analyses Skempton’s pore
pressure parameters A and B (Skempton,
1954) are frequently used to estimate
excess pore pressures. If we consider triaxial
conditions, Skempton’s equation reads
�u = B [ ��3 + A ( ��1 - ��3 ) ]
where ��1 and ��3 are changes in total minor
and major principal stresses respectively. For
fully saturated conditions, assuming pore water
being incompressible, B is 1.0. Furthermore,
for elastic behaviour of the soil skeleton, A
turns out to be 1/3.
A frequently asked question in PLAXIS courses
is “What pore pressure parameters A and B does
PLAXIS use”, if an undrained analysis is
performed in terms of effective stresses setting
the material type to undrained? The answer is
“You don’t know”, except for the trivial cases
of elastic or elastic-perfectly plastic behaviour.