12 plaxis bulletin
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Plaxis BulletinTRANSCRIPT
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.
In order to investigate this in more detail
undrained triaxial stress paths are investigated
with the Mohr Coulomb model with and
without dilatancy, and with the Hardening Soil
model. In the latter the influence of various
assumptions of E50 and Eoed has been studied.
Soil Parameters
The following parameter sets have been used
and the model number given below is referred
to in the respective diagrams. A consolidation
pressure of 100 kN/m2 has been applied to all
test simulations followed by undrained
shearing of the sample.
Pore Pressure Parameter B
In order to check the value of parameter B in
an undrained PLAXIS analysis a hydrostatic
stress state has been applied after
consolidation. By doing so, the parameter A
does not come into picture and B can be
directly calculated from �u and ��3, when
using undrained behaviour as material type.
PLAXIS does not yield exactly 1.0 because a
slight compressibility of water is allowed for
numerical reasons and therefore a value of
0.987 is obtained for the given parameters for
the Mohr Coulomb model. For the HS model
the value depends slightly on E50 and Eoed, but
also on the power m and changes with loading.
The differences however are in the order of
about 3.0 to 5.0 % for the parameter sets
investigated here. So it is correct to say that
Skempton’s pore pressure parameter B is
approximately 1.0 in PLAXIS, when using
undrained behaviour as material type.
Pore Pressure Parameter A
The value of parameter A is more difficult to
determine. However one can evaluate A from
the results of the numerical simulations and
this has been done for various parameter
combinations for the Hardening Soil model and
the Mohr Coulomb model.
6
Table 1 Parametersets for Hardening
Soil model
Model Number E50ref Eur
ref Eoedref � c ur pref m K0
nc Rf
kN/m2 kN/m2 kN/m2 ° ° kN/m2 - kN/m2 - - -
HS_1 30 000 90 000 30 000 35 0 / 10 0.0 0.2 100 0.75 0.426 0.9
HS_2 50 000 150 000 50 000 35 0 0.0 0.2 100 0.75 0.426 0.9
HS_3 15 000 45 000 15 000 35 0 0.0 0.2 100 0.75 0.426 0.9
HS_4 30 000 90 000 40 000 35 0 0.0 0.2 100 0.75 0.426 0.9
HS_5 30 000 90 000 15 000 35 0 0.0 0.2 100 0.75 0.426 0.9
HS_6 50 000 150 000 30 000 35 0 0.0 0.2 100 0.75 0.426 0.9
Parameters for MC Model: E = 30 000 kN/m2; = 0.2; � = 35°; = 0° and 10°
PLAXIS
PLAXIS Comparison Mohr Coulomb –
Hardening Soil
In this comparison we consider the Mohr
Coulomb criterion and the parameter set 1 for
the Hardening Soil model for dilatant ( = 10°)
and non dilatant ( = 0°) behaviour. The p’-q-
diagramm (Fig. 1) firstly shows that the
effective stress path observed in a typical
undrained triaxial test is only obtained for the
Hardening Soil model because the Mohr
Coulomb model remains in the elastic range
and thus no change in effective mean normal
stress takes place. The well known fact that
dilatant behaviour leads to an increase of
strength in the undrained case is reproduced
by both models in a similar way. It is important
to point out that although the effective
strength parameters are the same for both
models the undrained shear strength is
different due to different effective stress paths
produced by both models, the Hardening Soil
model giving an almost 15% lower value (see
also Fig. 2). The pore pressure vs vertical strain
diagram in Fig. 3 shows the expected increase
of excess pore water pressure followed by a
rapid decrease for the dilatant material
behaviour. It is worth noting that in the case
of the Mohr Coulomb model there is a sharp
transition when the excess pore water pressure
starts to decrease (at the point where the
failure envelope is reached) whereas for the
Hardening Soil model this transition is smooth.
The pore pressure parameter A (Fig. 4) is 1/3
for the non dilatant Mohr Coulomb model (this
is the theoretical value for elastic behaviour)
and is independent of the loading stage and
thus the vertical strain. For the Hardening Soil
model A is not a constant but increases with
deviatoric loading to a final value of approx.
0.44 for this particular parameter set. Of course
the parameter A tends to become negative for
dilatant behaviour.
Hardening Soil – Influence of E50ref and
Eoedref
The reference parameter set is HS_1 of Table
1. Based on this, the reference values of E50
and Eoed have been varied (HS_2 to HS_6). Only
non dilatant material behaviour is considered.
Fig. 5 shows effective stress paths in the p’-q-
space and it is interesting to see that for E50
= Eoed the stress path is the same for all values
of E50 leading to the same undrained shear
strength although the vertical strain (and thus
the shear strain) at failure is different (Fig. 6).
If E50 is different from Eoed, different stress
paths and hence different undrained shear
7
Fig. 1 Stress path in
p’-q-space / MC – HS model
Fig. 2q-�1 - diagram /MC – HS model
Fig. 3 �u-�1 - diagram /
MC – HS model
Fig. 4A-�1 - diagram /MC – HS model
par
amet
er A
exce
ss p
ore
pre
ssu
re [k
N/m
2 ]q
[kN
/m2 ]
q [k
N/m
2 ]
PLAXIS
PLAXIS strengths are predicted. The difference
between HS_4 and HS_5 is more than 30%
which is entirely related to the difference in
Eoed. This is perhaps not so suprising because
Eoed controls much of the volumetric
behaviour which in turn is very important for
the undrained behaviour. However one has to
be aware of the consequences when using
these parameters in boundary value problems.
In Fig. 6 deviatoric stress is plotted against
vertical strain and – unlike in a drained test
where Eoed has only a minor influence on the
q-�1-curve – both parameters have a strong
influence on the results. E50 governs, as
expected, the behaviour at lower deviatoric
stresses but when failure is approached the
influence of Eoed becomes more pronounced.
A very similar picture is obtained when excess
pore pressures are plotted against vertical
strain (Fig. 7). In Fig. 8 the pore pressure
parameter A is plotted against vertical strain
and it follows that for Eoed > E50 (parameter
set HS_4) the pore pressure parameter A is
approx. 0.34, i.e. close to the value for elastic
behaviour. If Eoed < E50 (parameter sets HS_5
and HS_6) the parameter A increases rapidly
with loading, finally reaching a value of
approximately A = 0.6.
Summary
It has been shown that the pore pressure
parameters A and B obtained with PLAXIS from
undrained analysis of triaxial stress paths using
a Mohr Coulomb failure criterion are very close
to the theoretical values given by Skempton
(1954) for elastic material behaviour, i.e. B is
approx. 1.0 and A is 1/3. For more complex soil
behaviour as introduced by the Hardening Soil
model the parameter A is no longer a constant
value but changes with loading and is
dependent in particular on the value of Eoed in
relation to E50. For a given E50 the parameter
A at failure is higher for lower Eoed-values,
which in turn results in lower undrained shear
strength. Eoed < E50 is usually assumed for
normally consolidated clays experiencing high
volumetric strains under compression which
corresponds to a higher value for A in the
undrained case. It is therefore justified to say
that PLAXIS predicts the correct trend, care
however has to be taken when choosing Eoed,
because the influence of this parameter, which
may be difficult to determine accurately for in
situ conditions, is significant and may have a
strong influence on the results when solving
practical boundary value problems under
undrained conditions.
8
Fig. 5 Stress path in
p’-q-space /Hardening Soil
Fig. 6q-�1 - diagram /Hardening Soil
Fig. 7�u-�1 - diagram /
Hardening Soil
Fig. 8A-�1 - diagram /Hardening Soil
par
amet
er A
exce
ss p
ore
pre
ssu
re [k
N/m
2 ]q
[kN
/m2 ]
q [k
N/m
2 ]
PLAXIS
PLAXIS Reference
Skempton, A.W. (1954). The Pore-Pressure
Coefficients A and B. Geotechnique, 4, 143-
147.
H.F. Schweiger
Graz University of Technology
Benchmarking I
PLAXIS BENCHMARK NO.1: SHIELD TUNNEL
1 - RESULTS
Introduction
Unfortunately the response of the PLAXIS
community to the call for solutions for the
first PLAXIS benchmark example was not a
success at all. Probably the example
specified gave the impression of being so
straightforward that everybody would
obtain the same results and thus it would
not be worthwhile to take the time for this
exercise. However, I had distributed the
example on another occasion within a
different group of people dealing with
benchmarking in geotechnics. In the
following I will show the results of this
comparison together with the few PLAXIS
results I have got. As mentioned in the
specification of the problem no names of
authors or programs are given, so I will not
disclose which of the analyses have been
obtained with PLAXIS.
I hope, that the summary of the first
benchmark example provides sufficient
stimulation for taking part in the second call
for solutions for PLAXIS Benchmark No.2,
published in this bulletin, so that we can go
ahead with this section and as awareness for
necessity of validation procedures grow,
proceed to more complex examples. The
specification of Benchmark No.1 is not repeated
here; please refer to the Bulletin No.11.
Results Analysis A – elastic, no lining
Figure 1 shows calculated settlements of the
9
Fig. 1:Surface
settlements -analysis A
Fig. 2: Horizontal
displacements atsurface -analysis A
Fig. 3:Displacements of
slected points -analysis A
Fig. 4:Surface
settlements -analysis B
Fig. 5:Horizontal
displacements atsurface -analysis B
ho
rizo
nta
l dis
pla
cem
ents
[mm
]ve
rtic
al d
isp
lace
men
ts [m
m]
dis
pla
cem
ents
[mm
]h
ori
zon
tal d
isp
lace
men
ts [m
m]
vert
ical
dis
pla
cem
ents
[mm
]
PLAXIS
PLAXIS surface and it follows that even in the elastic
case some scatter in results is observed.
Some of the discrepancies are due to different
boundary conditions. ST5, for example,
restrained vertical and horizontal displacements
at the lateral boundary, others introduced an
elastic spring or a stress boundary condition.
The effect of the lateral boundary is not so
obvious from Figure 1 but becomes more
pronounced when Figure 2, showing the
horizontal displacement at the surface, is
examined. Figure 3 summarizes calculated
values at specific points, namely at the surface,
the crown, the invert and the side wall (for
exact location see specification). A maximum
difference of 10 mm (this is roughly 20%) in
the vertical displacement of point A (at the
surface) is observed and this is by no means
acceptable for an elastic analysis.
Results Analysis B – elastic-perfectly
plastic, no lining
Figures 4 and 5 show settlements and
horizontal displacements at the surface for the
plastic solution with constant undrained shear
strength. In Figure 4 a similar scatter as in
Figure 1 is observed with the exception of ST4,
ST9 and ST10 which show an even larger
deviation from the "mean" of all analyses
submitted. Again ST5 restrained vertical
displacements at the lateral boundary and thus
the settlement is zero here. ST9 used a von-
Mises and not a Tresca failure criterion which
accounts for the difference. The strong
influence of employing a von-Mises criterion
as follows from Figure 4 has been verified by
separate studies. It is emphasized therefore
that a careful choice of the failure criterion is
essential in a non-linear analysis even for a
simple problem as considered here. The
significant variation in predicted horizontal
displacements, mainly governed by the
placement of the lateral boundary condition,
is evident from Figure 5. Figure 6 compares
values for displacements at given points. Taking
the settlement at the surface above the tunnel
axis (point A) the minimum and maximum
value calculated is 76 mm and 159 mm
respectively. Thus differences are - as expected
- significantly larger than in the elastic case but
again not acceptable.
10
Fig. 6:Displacements of
selcted points -analysis B
Fig. 7:Surface
settlements -analysis C
Fig. 8:Horizontal
displacements atsurface analysis C
Fig. 9:Displacements of
selcted points -analysis C
Fig. 10:Normal forces andcontact pressure -
analysis C
no
rmal
fo
rces
[kN
]/co
nta
ct p
ress
ure
[kP
a]d
isp
lace
men
ts [m
m]
ho
rizo
nta
l dis
pla
cem
ents
[mm
]ve
rtic
al d
isp
lace
men
ts [m
m]
dis
pla
cem
ents
[mm
]
PLAXIS
PLAXIS Results Analysis C – elastic-perfectly
plastic, lining and volume loss
Figure 7 plots surface settlements for the
elastic-perfectly plastic analysis with a specified
volume loss of 2% and the wide scatter in
results is indeed not very encouraging. The
significant effect of the vertically and
horizontally restrained boundary condition
used in ST5 is apparent. However in the other
solutions no obvious cause for the differences
could be found except that the lateral
boundary has been placed at different
distances from the symmetry axes and that
the specified volume loss is modelled in
different ways. Figure 8 shows the horizontal
displacements at the surface and a similar
picture as in the previous analyses can be
found. Figure 9 depicts displacements at
selected points. The range of calculated values
for the surface settlement above the tunnel
axis is between 1 and 25 mm and for the
crown settlement between 17 and 45 mm
respectively. The normal forces in the lining
and the contact pressure between soil and
lining do not differ that much (variation is
within 15 and 20% respectively), with the
exception of ST9 who calculated significantly
lower values (Figure 10).
Results with lateral boundary at distance
of 100 m from tunnel axis
Due to the obvious influence of the lateral
boundary conditions a second round of analysis
has been performed asking all authors to redo
the analysis with a lateral boundary at 100 m
distance from the line of symmetry with the
horizontal displacements fixed. As follows from
Figures 11 and 12 which depicts these results
for case A, all results are now within a small
range and thus it has been confirmed that the
discrepancies described from the previous
chapter are entirely caused by the boundary
condition. In addition to finite element results
an analytical solution by Verruijt is included for
comparison. Vertical displacements are in very
good agreement and also horizontal
displacements are acceptable in the area of
interest (i.e. in the vicinity of the tunnel). For
case B similar results are obtained although
some small differences are still present. For case
C the comparison also matches much better
now but some differences remain here and this
is certainly due to the fact that the programs
involved handle the specified volume loss in a
different way.
Comparison undrained – drained
conditions
In order to show that the influence of the
lateral boundary is especially important under
undrained conditions (constant volume) an
11
Fig. 11:Surface
settlementsanalysis A / lateralboundary at 100 m
Fig. 12:Horizontal
displacements atsurface analysis A/ lateral boundary
at 100 m
Fig. 13:Surface
settlementsanalysis A /undrained -
drained
Fig. 14:Horizontal
displacements atsurface analysis A
/ undrained -drained
ho
rizo
nta
l dis
pla
cem
ents
[mm
]ve
rtic
al d
isp
lace
men
ts [m
m]
ho
rizo
nta
l dis
pla
cem
ents
[mm
]ve
rtic
al d
isp
lace
men
ts [m
m]
PLAXIS
PLAXIS
Fig. 1:Geometric data
benchmark excavation
Table 1. Parameters for
sheet pile wall and strut
analysis has been performed for case A with
exactly the same parameters except for
Poisson's ratio, chosen now to correspond to
a drained situation, i.e. deformation under
constant volume is no longer enforced (for
simplicity the difference of Young's module
between drained and undrained conditions has
been neglected). It follows from Figure 13 that
for the drained case the surface settlements
are virtually independent of the distance of the
lateral boundary (results for mesh widths of
50 m and 100 m are shown respectively). The
horizontal displacements (Figure 14) show
some differences of course but in the area of
interest they are negligible in the drained case.
Summary
The outcome of this benchmark example
clearly emphasizes the necessity of performing
these types of exercises in order to improve
the validity of numerical models. Given the
discrepancies in results obtained for this very
simple example much more scatter can be
expected for real boundary value problems.
One of the lessons learned from this example
is that the influence of the boundary
conditions can be much more severe in an
undrained analysis than in a drained one and
whenever possible a careful check should be
made whether or not the placement of the
boundary conditions affects the results one is
interested in. One may argue that this is a trivial
statement, practice however shows that due
to time constraints in projects it is not always
feasible to check the influence of all the
modelling assumptions involved in a numerical
analysis of a boundary value problem. It is one
of the goals of this section to point out
potential pitfalls in certain types of problems
which may not be obvious even to experienced
users and to promote the development of
guidelines for the use of numerical modelling
in geotechnical practice.
Helmut F. Schweiger, Graz University of
Technology
Benchmarking II
PLAXIS BENCHMARK NO. 2: EXCAVATION 1
The second benchmark is an excavation in
front of a sheet pile wall supported by a
strut. Geometry, excavation steps and
location of the water table are given in
Figure 1. Fully drained conditions are
postulated. The soil is assumed to be a
homogeneous layer of medium dense sand
and the parameters for the Hardening Soil
model, the sheet pile wall and the strut are
given in Tables 1 and 2 respectively.
The following computational steps have to be
performed in a plane strain analysis:
- initial phase (K0 = 0.426)
- activation of sheet pile, excavation step 1
to level – 2.0 m
12
�dry �wet E50ref Eur
ref Eoedref � c ur pref m K0
nc Rf Rinter T-Strength
kN/m3 kN/m3 kPa kPa kPa ° ° kPa - kPa - - - - kPa
19.0 20.0 45 000 180 000 45 000 35 5 1.0 0.2 100 0.55 0.426 0.9 0.7 0.0
Table 2. Parameters for HS-model
EA EI W V
kN/m kN2/m kN/m/m -
Sheet pile wall 2.52E6 8064 0.655 0.0
Strut 1.5E6
PLAXIS
PLAXIS
13
- activation of strut at level –1.50 m,
excavation step 2 to level – 4.0 m,
- groundwater lowering inside excavation to
level – 6.0 m
- excavation step 3 to level – 6.0 m
- phi-c-reduction
REQUIRED RESULTS
1. bending moments and lateral deflections of
sheet pile wall (including values given in a
table)
2. surface settlements behind wall (including
values given in a table)
3. strut force
4. factor of safety obtained from phi-c-
reduction for the final excavation step
Note: As far as possible results should be
provided not only in print but also on disk
(preferably EXCEL) or in ASCII-format respectively.
Alternatively, the entire PLAXIS-project may be
provided. Results may also be submitted via e-
mail to the address given below.
Results should be sent no later than
August 1st, 2002 to:
Prof. H.F. Schweiger
Institute for Soil Mechanics and Foundation
Engineering
Computational Geotechnics Group
Graz University of Technology
Rechbauerstr. 12, A-8010 Graz
Tel.: +43 (0)316 – 873-6234
Fax: +43 (0)316 – 873-6232
E-mail: [email protected]
http://www.tu-graz.ac.at/geotechnical_group/
Recent Activities
NEW DIRECTOR OF PLAXIS B.V.
We are pleased to introduce the new
director of PLAXIS BV, Dr. Klaas Jan Bakker.
Dr. Bakker who started the first of February
takes over the chair of Mr. Hutteman, who
temporary occupied the chair on behalf of
MOS Grondmechanica BV.
Since the very beginning Dr. Bakker has been
actively involved in the program(ming) of
PLAXIS and is a key figure in the PLAXIS
network. In his last position he was Head of
Construction and Development at the Tunnel-
engineering department for the Dutch Ministry
of Public Works. Furthermore he is a lecturer
at Delft University of Technology.
COURSES
In 2001 over 400 people attended one of
the 13 Plaxis courses that were held in
several parts of the world. Most of these
courses are held on a regular basis, while
others take place on an single basis.
Regular courses:
Traditionally, we start the year with the standard
International course “Computational
Geotechnics” that takes place during the 3rd
week of January in the Netherlands. The
Experienced users course in the Netherlands
is traditionally organised during the 4th week
of March each year. Besides these standard
courses in the Netherlands, some other regular
courses are held in Germany (March), England
(April), France (Autumn), Singapore (Autumn),
Egypt, and the USA. For the USA the course
schedule is a bit different, as we plan to have
an Experienced users course per two years and
two standard courses in the intermediate
periods. In May, 2002, we had the Experienced
users course in Boston, which was organised
in cooperation with the Massachusetts Institute
of Technology (MIT). For January 2003, a
standard course is scheduled in Berkeley in
PLAXIS
PLAXIS cooperation with the University of California.
For August, 2003, another standard course is
organised in Boulder in cooperation with the
University of Colorado. It is our intention to
repeat this scheme of courses for the Western
hemisphere. For the Asian region, we have
planned a similar schedule that also includes
an experienced users course once every two
years.
Other courses:
Besides the above regular courses, other
courses are organised in different parts of the
world. In the past year, courses were held in
Mexico, Vietnam, Turkey, Malaysia, etc. On the
last page of this bulletin, you can see the
agenda, which lists all scheduled courses and
some other events. Our web-site www.plaxis.nl
on the other hand will always give you the
most up-to-date information.
PLAXIS Practice I
1. Introduction
In Würenlingen (Switzerland), for the
temporary storage of nuclear waste, an
extension of the existing depository was
required. To facilitate this, a 7.5 - 9.0 m deep
excavation was necessary. This bordered
immediately adjacent pre-existing
structures. Furthermore, along one of it‘s
sides there is a route used for the
transportation of nuclear waste.
2. Project
Length of excavation: 98 m
Width of excavation: 33 m
Maximum depth: 9 m
Start of works: Spring 2001
End of construction: Summer 2001
3. Geotechnical conditions
In the Würenlingen area, significant deposits
of the Aare River dominate, which comprises
predominantly gravels and sands. The
groundwater table lies at a depth of ca. 9.5 m
below the surface prior to excavation. The
gravels and sands are known as good
foundation material, with some low apparent
cohesion, allowing for the temporary
construction of vertical cuttings of low height.
4. Construction procedure
Due to space restrictions, a sloped earthworks
profile is not possible. Therefore, it was
concluded to undertake the excavation using
14
Model Behavior �unsat �sat E50ref Eoed
ref m Eurref ur c � Rinter
- kN/m3 kN/m3 kPa kPa - KPa - kPa ° ° -
HS Drained 22.0 22.0 33 000 37 500 0.5 99 000 0.25 1.0 32 6 1.0
Table 1. Soil parameters
Photo 1: Participants in theExperienced users
course, March 2002, theNetherlands.
Photo 2: Plaxis short course,
October 2001, Mexico
Photo 3: Plaxis short course,
November 2001,Vietnam.
PLAXIS
PLAXIS a soil nailing option. Correspondingly, the
excavation had to proceed in benched stages.
Each bench had a height of 1.30 m and a width
of 4.5 to 6.0 m. The free face was immediately
covered with an 18 cm thick layer of shotcrete
and tied back with untensioned soil nails.
The bond strength of the soil nails was
established by pullout tests. Usually the soil
nails are cemented along their full length. For
the pullout tests, however, the bond length
was reduced to between 3.0 and 4.0 m with a
total length of 7.0 m. The individual nails have
a cross-sectional area of 25 mm and yield
strength of 246 kN. During the pullout tests,
it was possible to tension the nails to yield point
without any indication of creep or failure.
In total five benches were necessary to reach
excavation depth. The wall itself is vertical, with
nail spacing of 1.5 m and 1.3 m, horizontal and
vertical respectively. The nails were tightened
three days after installation with a torque key,
to secure a fast seat to the shotcrete. A pre-
tensioning with fully cemented nails is not
sensible (see fig. 1).
5. Calculations
The initial calculations were performed with
the usual statical programs based on beam
theory and limiting equilibrium loading. Due
to the particular safety requirements in
connection with nuclear transport additional
deformation predictions were made. These
calculations were carried out with Plaxis version
7. Geotextile elements were used to model the
nails. Due to the good bonding of the soil nails
proven by the pullout attempts, no reduction
was made for loading transfer along the
geotextile elements.
The calculations were performed with the
following parameters:
� Hardening soil model
� Plane strain with 6 node elements
� 649 elements
� Due to the simple geology, only one soil layer
was used (see table 1)
� Due to good bonding between soil and
shotcrete wall no reduction in interface
friction was made.
� The calculations were performed without
groundwater.
� Shotcrete wall of 18 cm thickness with
reinforced wire mesh, modeled as beam
elements. EA = 5.4 x 106 kN/m, EI =
1.458 x 104 kNm2/m and = 0.2
� Soil nails are modeled as geotextile elements.
EA = 6.87 x 104 kN/m and = 0.
� Results
Final excavation stage
Maximum deformation of shotcrete wall;
17 mm (see fig. 2a and fig. 3).
Maximum horizontal deformation of
shotcrete wall; 14 mm (see fig. 2d).
Maximum force in geotextile element; 49
kN/m, or 73.5 kN per nail (see fig. 4).
Maximum bending moment in shotcrete
wall; 11.5 kNm/m (see fig. 2b).
Maximum axial force in shotcrete wall; -67
kN/m (see fig. 2c).
It must be noted, that the tensile forces in the
geotextile elements at the final excavation
stage did not calculate to zero at the toe of
the nail, as should be in reality. This could be
due to a too wide FE-net around the geotextile
elements, additionally due to the use of only
6-nodes instead of the more precise 15-node
element.
6. Measurement on site
In total, deformation of the excavation was
taken at five stations. Prior to excavation
clinometers were placed ca. 1.0 m behind the
proposed shotcrete wall, with a depth of 7 m
below excavation level. Figure 7 shows the
measured horizontal deformations of two
cross-sections with equal depths (7.2 and 9.0
mm). Figure 6 contains the calculated
horizontal deformations along a vertical line
15
Fig. 1: Typical sectionwith horizontaldisplacements
PLAXIS
PLAXIS 1m behind the shotcrete wall (14.9 mm). A
comparison shows that the calculated
deformations are greater than the measured.
Conspicuous is, that below the excavation base
there is practically no movement measurable.
Plaxis, however, has predicted some 4 mm
deformation. This may be due to an initial
offset or due to stiffer behavior at the bottom
of the excavation.
The maximum measured horizontal
deformation was between 7.2 and 9.0 mm at
the wall head. Plaxis calculated 14.9 mm
horizontal deformation at this point.
If only relative measurements are considered,
assuming that no movement takes place at the
wall toe, then the prediction from Plaxis lays
very close to the actual maximum measured.
The forms of the measured and calculated
deformation curves correspondwell well with
each other.
7. Conclusions
The calculated deformation of the nailed wall
corresponds well with the measured values,
especially if the predicted deformations of
Plaxis below excavation level are not
considered.
The soil parameters used correspond to
conservative average values, evaluated from a
large number of previous sites under similar
conditions. It is plausible that the deformation
parameters are underestimated.
The Plaxis calculation illustrates
comprehensively, that the soil nailing system
(soil-nail-wall) works as an interactive system. It
shows further, that the maximum nail force
does not necessarily act at the nail head, but
according to the distribution of soil movements
may also lie far behind the head of the nail. This
means that displacements are necessarily taking
place before the nail force is activated.
On the one hand, it shows that the shotcrete
wall in vertical alignment is stressed by bending
and compression, and that the wall’s foot
transmits compressive stresses to the soil. On
the other hand, the shotcrete wall in horizontal
alignment is only loaded by bending, whereby
in the absence of lateral restrictions of
deformation there could also be tension. Finally
it is clear to see, that nail head support and
pullout failure should be considered (see fig. 4).
16
Fig. 2:Output in
shotcrete wall
Fig. 3: Deformation of
geotextile
Fig. 4: Axial Forces in
geotextile
Fig. 5:Measured
displacements
Fig. 6:Calculated
displacement
Thanks to prior deformation calculation with
Plaxis and measurement control by clinometer
installation during the construction stage, the
safety of the works in relation to nuclear
transportation could be assessed at all times.
H.J. Gysi, G.Morri, Gysi Leoni Mader AG,
Zürich - Switzerland
� Calculation procedure
Phase 1: Initial stresses, using Mweight = 1.
Phase 2: Live load (5 kN/m2 and 10 kN/m2)
Phase 3: Excavation to top level of
wall (-0.80 m).
Phase 4: First excavation stage,
including shotcrete of wall
and installation of first row
of soil nails (-2.10 m).
Phase 5: Second excavation stage with
shotcrete wall (-3.40 m).
Phase 6: Installation of second row
of soil nails.
Phase 7: Third excavation stage
with shotcrete wall (-4.70 m).
Phase 8: Installation of third row of soil nails.
Phase 9: Fourth excavation stage
with shotcrete wall (-6.00 m).
Phase 10: Installation of fourth row
of soil nails.
Phase 11: Fifth excavation stage
with shotcrete wall (-7.30 m).
Phase 12: Installation of fifth row of soil nails.
PLAXIS Practice II
FINITE ELEMENT MODELLING OF A DEEP
EXCAVATION SUPPORTED BY JACK-IN
ANCHORS
1. INTRODUCTION
A mixed development project that is located
at UEP Subang Jaya, Malaysia consists of three
condominium towers of 33 storeys and a single
20-storey office tower. Due to the huge
demand for parking space, an approximately
three storey deep vehicular parking basement
was required. The deep excavation, through a
filled layer of very loose silty sand and very soft
peaty clay varies from 11m to 13m. Due to the
presence of very soft soil condition and the
fast track requirement of the project,
Contiguous Bored Pile (CBP) walls supported
by soil nails were used to support the
excavation process. This hybrid technique was
envisaged and implemented due to its speed
in construction and the ability of the Jack-in
Anchors1) in supporting excavations in
collapsible soils, high water table and in soft
soils conditions (Cheang et al., 1999 & 2000,
Liew et al, 2000). The use of soil nailing in
excavations and slope stabilisation has gained
wide acceptance in Southeast Asia, specifically
in Malaysia and Singapore due to its
effectiveness and huge economic savings.
Adopting the observational method, numerical
analyses using ‘PLAXIS version 7.11’ a finite
element code were conducted to study the
soil-structure interaction of this relatively new
retaining system. Numerical predictions were
compared with instrumented field readings and
deformation parameters were back analysed
and were used in subsequent prediction of wall
movements in the following excavation stages.
2. SUBSURFACE GEOLOGY
The general subsurface soil profile of the site,
shown in Table 1 consists in the order of
succession of loose clayey SILT, loose to
medium dense Sand followed by firm to hard
clayey SILT. The residual soils (Figure 1) are inter-
layered by 9m thick soft dark peaty CLAY. For
analysis purposes the layers were simplified
PLAXIS
PLAXIS
17
Photo 1: Jack-in Anchor Technique
1) Jack-in Anchor Technique™ is a patentedproduct by Specialist Grouting EngineersSdn. Bhd. Malaysia
PLAXIS
PLAXIS into representative granular non-cohesive and
cohesive material, such as:
3. THE RETAINING SYSTEM
In view of the close proximity of commercial
buildings to the deep excavation, a very stiff
retaining system is required to ensure minimal
ground movements the retained side of the
excavation. Contiguous Bored Pile that acts as
an earth retaining wall during the excavation
works were installed along the perimeter of
the excavation and supported by jack-in
anchors. The retaining wall system consist of
closely spaced 1000mm diameter contiguous
bored piles supported by hollow pipes which
functions as soil nails are installed by hydraulic
jacking using the Jacked-in Soil Anchor
Technology™ as shown in photo 3. Figure 2
illustrates the soil nail supported bored pile wall
system.
18
Photo 2: The Retaining System:Contiguous Bored Pile
Wall Supported by Jack-in Anchors that function
as Soil Nails
Photo 3: Hydraulic Jacking Fig. 2b:
The Retaining System
Fig. 1:Typical Subsurface Profile
Fig. 2a:The Retaining System
DEPTH (m) DESCRIPTION SPT ‘N’ VALUE
LAYER 1 0 to 9 Clayey SILT <12
LAYER 2 9 to 18 Soft Dark Silty CLAY 0
LAYER 3 18 to 27 Medium Dense SAND >18
LAYER 4 27 to 35 Dense SILT >50
Table 1. Soil Layers
PLAXIS
PLAXIS This method has proven to be an efficient and
effective technique for excavation support,
where conventional soil nails and ground
anchors have little success in such difficult soft
soil conditions. Such conditions are sandy
collapsible soil, high water table and in very
soft clayey soils where there is a lack of short-
term pullout resistance.
Relatively, larger movements are required to
mobilise the tensile and passive resistance of
the jacked-in pipes when compared to ground
anchors. However it was anticipated that the
ground settlement at the retained side and
maximum lateral displacement of the wall
using this system would still be within the
required tolerance after engineering
assessment.
4. GEOTECHNICAL INSTRUMENTATION
In view of this relatively new excavation
support technique used for in-situ soft soil
conditions and the close proximity of the
commercial buildings to the deep excavation,
a performance monitoring program was
provided. Firstly, as a safety control. Second,
to refine the numerical analysis using field
measurements obtained at the early stages of
construction and third, to provide an insight
into the possible working mechanisms of the
system.
The geotechnical instrumentation program
consists of 18 vertical inclinometer tubes
located strategically along the perimeter
within the Contiguous Bored Pile wall and 30
optical survey makers (surface settlement
points) near the vicinity of the commercial
buildings. The locations of these instruments
are detailed in Fig. 4 for the inclinometers.
Fig. 5 illustrates the restrained trend of
horizontal displacement of the wall as
measured through inclinometers installed at
the site
5. FINITE ELEMENT MODELLING
EQUIVALENT PLATE MODEL
Equivalence relationships have to be developed
between the 3D structure and 2D numerical
model. Non 2-D member such as soil nails must
be represented with ‘equivalent’ properties that
reflect the spacing between such elements.
Donovan et al. (1984) suggested that properties
of the discrete elements could be distributed
over the distance between the elements in a
19
Fig. 4:GeotechnicalInstruments
Fig. 5:Measures deflection
profile
PLAXIS
PLAXIS uniformly spaced pattern by linear scaling.
Unterreiner et al. (1997) adopted an approach
similar to Al-Hussaini and Johnson (1978) where
an equivalent plate model replaces the discrete
soil-nail elements by a plate extended to full
width and breadth of the retaining wall. Nagao
and Kitamura (1988) converted the properties
of the 3-D discrete elements into an equivalent
composite plate model by taking into account
the properties of the adjacent soil. The two-
dimensional finite element analysis performed
hereafter uses the ‘composite plate model’
approach.
Finite Element Analysis
The finite element analyses were performed
using ‘PLAXIS’ (Brinkgreve and Vermeer, 1998).
The Contiguous Bored Pile wall and steel tubes
were modelled using a linear-elastic Mindlin
plate model (Figure 6). The nails were ‘pinned’
to the CBP wall. The soil-nail soil interface was
modelled using the elastic-perfectly-plastic
model where the Coulomb criterion
distinguishes between the small displacement
elastic behaviour and ‘slipping’ plastic behaviour.
The surrounding soils were modelled using the
Mohr-Coulomb soil model. Table 2 and 3 shows
the properties used for the analyses.
6. COMPARISON OF FIELD INSTRUMENTED
AND PREDICTED DISPLACEMENT READINGS
Measured And Predicted Lateral Deflection
Figure 7 compares the in-situ, predicted and
back analysed lateral deflection of the soil nail
supported wall. The measured lateral deflection
is showing a trend of restrained cantilever and
the jack-in anchors are restraining the
horizontal displacement of the wall. Initial finite
element prediction (Prediction No.1) based on
soil strengths correlated from laboratory
20
Table 2: Soil Properties
Layer 1 Layer 2 Layer 3 Layer 4
E (kN/m2) 34000 9000 30000 200000
�soil (kN/m3) 19 20 20 19
0.25 0.25 0.25 0.25
� 25 0 35 30
C 2 12 2 2
0 0 0 0
Table 3: Nail and Contiguous Bored Pile Wall Properties
ENAIL 2.90E+06 kN/m2
ECONC. 2.00E+07 kN/m2
Figure 7: Lateral Deflection of Soil Nailed
Contiguous Bored Pile Wall
Figure 8: Lateral Deflection of ‘Stiff’ and ‘Flexible’
Soil Nail System
Fig 6: 2-Dimensional finite element mode
PLAXIS
PLAXIS results. Excavation involves mainly the
unloading of adjacent soil, the ground stiffness
is dependent on stress level and wall
movements. These aspects were taken into
account in prediction no.2, the trend is similar
and a better prediction was obtained.
Subsequent finite element runs were made
base on the improved parameters.
7. SOIL-NAIL-SOIL-STRUCTURE
INTERACTION
Lateral Bending Stiffness of Soil Nails
A flexible nail system with a bending stiffness
of 1/220 of the stiff nail system was numerically
simulated. It was hypothesised that if bending
stiffness of the inclusions were insignificant in
the performance of the nail system, there
would be no difference in the lateral
displacement of the wall. However figure 8
shows that bending stiffness is significant, at
least in a soil nail supported embedded wall.
With a stiff nail system, the lateral displacement
was significantly reduced. Figure 9 illustrates
that the influence increases as excavation
proceeds further, this is due to the fact that
larger movements are required to mobilised
lateral bending resistance of the nails.
8. CONCLUSION
The soil-nail-soil-structure interaction of a nailed
wall is complex in nature. Soil nails are subjected
to tension, shear forces and bending moments.
The outcome of this numerical investigation of
a real soil-nailed supported Contiguous Bored
Pile wall in soft residual soils is that nail bending
stiffness has a significant effect as deformation
progresses, at least in this hybrid support
system. Soil-nail lateral resistance is dependent
not only on the relative stiffness and yield
strengths of the soil and nail, but also on the
local lateral displacement across the shear zone.
Due to the hybrid nature of this system, the
results indicated that the relative stiffness of
the nail and wall too governs the development
of bending i.e., lateral resistance of the soil nail.
In soft soils, numerical results indicated greater
bending moments in the nails due to larger wall
deflection. The implication of this study is
additional analysis of different working
mechanisms in various soil types should be
envisaged.
9. REFERENCE
1. Al-Hussaini, M.M., Johnson, L., (1978),
Numerical Analysis of Reinforced Earth Wall,
Proc. Symp. On Earth Reinforcement ASCE
Annual Convention, p.p. 98-126.
2. Brinkgreve, R.B.J., Vermeer, P.A., (1998),
Plaxis- Finite Element Code for Soil and Rock
Analyses- Version 7.11,A.A.Balkema.
3. Cheang, W.L., Tan, S.A., Yong, K.Y., Gue, S.S,,
Aw, H.C., Yu, H.T., Liew, Y.L., (1999), Soil Nailing
of a Deep Excavation in Soft Soil,
Proceedings of the 5Th International
Symposium on Field Measurement in
Geomechanics, Singapore, Balkema.
4. Cheang, W.L., Luo, S.Q., Tan, S.A., Yong, Y.K.,
(2000), Lateral Bending of Soil Nails in an
Excavation, International Conference on
Geotechnical & Geological Engineering,
Australia. ( To be Published)
5. Donovan, K., Pariseau, W.G., and Cepak,
M.,(1984), Finite Element Approach to Cable
Bolting in Steeply Dipping VCR Slopes,
Geomechanics Application in Underground
Hardrock Mining, pp.65-90.New York: Society
of Mining Engineers.
6. Liew, S.S., Tan, Y.C., Chen, C.S., (2000), Design,
Installation and Performance of Jack-In-Pipe
Anchorage System For Temporary Retaining
Structures, International Conference on
Geotechnical & Geological Engineering,
Austraila. ( To be Published)
7. Nagao, A., Kitamura, T., (1988), Filed
Experiment on Reinforced Earth and its
Evaluation Using FEM Analysis, International
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Figure 9: Influence ofNail Stiffness
PLAXIS
PLAXIS Symposium on Theory and Practice of Earth
Reinforcement, Japan, pp.329-334.
8. Unterreiner, P., Benhamida, B., Schlosser, F.,
(1997), Finite Element Modelling Of The
Construction Of A Full-Scale Experimental Soil-
Nailed Wall. French National Research Project
CLOUTERRE, Ground Improvement, p.p. 1-8.
W.L.Cheang, Research Scholar,
E-mail: [email protected],
S.A.Tan, Associate Professor,
E-mail: [email protected],
K.Y.Yong, Professor, Department of Civil
Engineering, National University of
Singapore
Users Forum
BEAM TO PILE PROPERTIES
IN PLAXIS
Properties for anchors are entered per anchor
so : EA = [kN] per anchor
Ls = [m] is spacing centre to centre
Beams and geotextiles are continuous in the
z-direction (perpendicular to the screen).
Therefore, a beam /geotextile will be a
continuous plate/textile in the z-direction. The
properties are entered per meter
in the z-direction EA = [kN/m], EL = [kN/m2/m]
Modelling a row of piles or a row of grout
bodies in the z-direction can be done by
dividing the EAreal and ELreal by
the centre-to-centre distance Ls.
For a beam:
EAreal=Ereal*dreal*breal [kN]
EAplaxis= EAreal/Ls [kN/m]
For a grout body:
EAreal=Ereal*dreal*breal [kN]
EAplaxis= EAreal/Ls [kN/m]
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Fig 1. Partial geometryfor shieldtunnel
project
Some geometries
In the past bulletins, a few articles were related
to experience with the 3D Tunnel program.
Since it’s release last year, the 3D Tunnel
program has been used in practice for some
interesting projects. In the below graphs,
without further explanation you will find a brief
overview of possible projects and geometries.
The printed figures also indicate that the 3D
Tunnel program can deal with projects beyond
tunneling.
PLAXIS
PLAXIS
Fig 4. Partial geometry for anchored retaining wall.
Fig 5. Deformed mesh for interacting tunnels.
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Fig 2. Partialgeometry for pile-
raft foundation
Fig 3.Displacement
contours for shieldtunnel project
PLAXIS
PLAXIS ACTIVITIES
8-10 MAY, 2002
International course for experienced Plaxis users
(English)
Boston, USA
16 MAY, 2002
2nd French Plaxis Users meeting (French)
Paris, France
14-18 OCTOBER, 2002
Short course on Computational Geotechnics
(Arabic, English)
Cairo, Egypt
25-26 OCTOBER, 2002
Short course on Computational Geotechnics
(Portuguese, English)
Sao Paulo, Brazil
7-8 NOVEMBER, 2002
11th European Plaxis Users meeting (English)
Karlsruhe, Germany
18-20 NOVEMBER, 2002
Short course on Computational Geotechnics
(English)
Trondheim, Norway
27-29 NOVEMBER, 2002
Short course on Computational Geotechnics
(French)
‘Pratique des éléments finis en Géotechnique’
Paris, France
6-9 JANUARY, 2003
Short course on Computational Geotechnics &
dynamics (English)
Berkeley, USA
19-22 JANUARY, 2003
Short course on Computational Geotechnics
(English)
Noordwijkerhout, The Netherlands
10-12 MARCH, 2003
Short course on Computational Geotechnics
(German)
Stuttgart, Germany
23-26 MARCH, 2003
International course for experienced Plaxis users
(English)
Noordwijkerhout, The Netherlands
8-10 APRIL, 2003
Short course on Computational Geotechnics
(English)
Manchester, England
28-30 APRIL, 2003
Short course on Computational Geotechnics
(Italian)
Napoli, Italy
31 JULY–2 AUGUST, 2003
Experienced Plaxis users course (English)
Singapore
For more information on these activities
please contact:
PLAXIS bv
P.O. Box 572
2600 AN DELFT
The Netherlands
Tel: +31 15 26 00 450
Fax: +31 15 26 00 451
E-mail: [email protected]
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