rak-50 3149 h. l8- soil parameters for mc
TRANSCRIPT
Soil Parameters for Drained and Undrained Analysisand Undrained Analysis
Applied Theory
Dr Minna Karstunen
based on work by Dr H. Burd, University of Oxford
Introduction
• The aim is to discuss the choice of parameters for the Mohr-Coulomb model.
• More advanced soil models may have some advantages over the Mohr-Coulomb model (but require the specification of a larger number of parameters)
• Typical experimental methods currently used to measure • Typical experimental methods currently used to measure the soil parameters are briefly discussed.
• It is also useful, however, to estimate values of soil properties based on previous experience, and on correlations with other soil parameters.
Undrained and Drained Loading
• In carrying out any analysis in geotechnical engineering it is usually necessary to distinguish between drained and undrained loading. and undrained loading.
• The soil may also be partially drained which means that it lies between these two extremes.
Undrained and Drained Loading
• drained analysis appropriate when– permeability is high
– rate of loading is low
– short term behavior is not of interest for problem – short term behavior is not of interest for problem
considered
• undrained analysis appropriate when– permeability is low and rate of loading is high
– short term behavior has to be assessed
Undrained and Drained Loading
Suggestion by Vermeer & Meier (1998)
T < 0.10 (U < 10%) � undrained analysis
T > 0.40 (U > 70%) � drained analysis
tDγ
EkT
2
w
oed====
k = permeability
Eoed = stiffness in 1-d compression
γw = unit weight of water
D = drainage length
t = construction time
T = dimensionless time factor
U = degree of consolidation
Drained Analysis
Drained analysis may be carried out by
using a constitutive model based on
effective stresses in which the material model is specified in terms of drained model is specified in terms of drained parameters.
Modelling Undrained Behavior with
PLAXIS
Method A (analysis in terms of effective stresses):type of material behaviour: undrainedeffective strength parameters (MC: c', ϕ', ψ‘)effective stiffness parameters (MC: E50', ν‘)
Method B (analysis in terms of effective stresses):
Need to be
careful in case
of stiff OC
clays!
Method B (analysis in terms of effective stresses):type of material behaviour: undrainedtotal strength parameters c = cu, ϕ = 0, ψ = 0effective stiffness parameters E50', ν'
Method C (analysis in terms of total stresses):type of material behaviour: drainedtotal strength parameters c = cu, ϕ = 0, ψ = 0total stiffness parameters Eu, νu = 0.495
Mohr Coulomb Model for Drained
and Undrained Analysis
• For drained loading, a total of 5 parameters are
required to specify the Mohr-Coulomb model.
These are; two strength parameters (c' and φ' ),
a dilation angle (ψ) and two elastic parameters.
• For undrained calculations, a separate failure
model based on an undrained shear strength, cu,
is used. Note that cu is not a fundamental
property of the soil; it depends on the stress
level and also the stress history.
Mohr Coulomb Model for Drained
and Undrained Analysis
Drained or
Undrained
(Approach A)
Undrained
(Approach C)(Approach A)
(Approach C)
Mohr Coulomb Model for Drained
and Undrained Analysis
• To analyse a problem using the Mohr-Coulomb
model, appropriate values of the material
parameters must be selected to provide a good
match with the soil being modelled.
• The selection of these parameters is
complicated by the fact that real soil behaviour
often departs considerably from the fundamental
assumptions on which the Mohr-Coulomb model
is based.
The Mohr-Coulomb Model and
Real Soil Behavioura) Most real soils do not exhibit linear elastic behaviour
prior to failure
G/G
[-]
0
1 Retaining walls
Foundations
G/G
[-]
0
1 Retaining walls
Foundations
Shear strain [-]γ
Dynamic methods
Local gauges
Conventional soil testing
Sh
ear
mo
du
lus
G/
10-6
10-5
10-4
10-3
10-2
10-1
0
Tunnels
Foundations
Larger strains
Very
small
strains Small strains
Shear strain [-]γ
Dynamic methods
Local gauges
Conventional soil testing
Sh
ear
mo
du
lus
G/
10-6
10-5
10-4
10-3
10-2
10-1
0
Tunnels
Foundations
Larger strains
Very
small
strains Small strains
The Mohr-Coulomb Model and
Real Soil Behaviour
b) The stiffness of soil tends to increase with increasing stress level. In PLAXIS the stiffness can be specified to increase linearly with depth below
the soil surface.the soil surface.
c) Unloading stiffness differs from stiffness in primary loading
The Mohr-Coulomb Model and
Real Soil Behaviour
Triaxial compression test on a sample of Leighton Buzzard sand
The Mohr-Coulomb Model and
Real Soil Behaviour
d) The friction angle of a sand depends on its density and stress level. The stress level. The choice of φφφφ'
needs careful consideration of these factors.
The Mohr-Coulomb Model and
Real Soil Behaviour
Drained Triaxial Test
Undrained Triaxial Test
Pressuremeter Test
++=
u
uhoLc
GcP ln1σ
The undrained shear strength may be calculated from the limiting cavity
pressure PL (for details see Clarke (1995).
u
For penetration in clays, the
tip resistance qt is given by:
Cone Penetrometer Test
vouktt cNq σ+=
where σvo is the total vertical
stress in the soil at the level of
the cone and Nkt is an empirical
factor, typically in the range of 10
to 20. For further details, see
Lunne et al, (1997).
vouktt
Correlations for Undrained
Shear Strength (cu)Shear Strength (cu)
Undrained Shear Strength from
MC Parameters
++= '
2
1'cot''sin 0
vu
Kcc σφφ
Example: Undrained parameters
from MC
++= '
2
1'cot''sin 0
vu
Kcc σφφ
Example: Undrained parameters
from MC
In this example:
where cuo=4.698 kPa and ρ= 2.326 kPa/m.
zcc uou ρ+=
Example: Undrained parameters
from MC
Note that the correlation is unlikely to give an accurate
shear strength profile for an overconsolidated clay. A
better estimate is obtained with Critical State models.
For an incompressible material, the undrained For an incompressible material, the undrained
Poisson’s ratio would be 0.5 (Method C). However, this
value cannot be used for finite element calculations,
because it would result in an infinite value of bulk
modulus. A suitable value of undrained Poisson’s
ration for use in FE analyses is νu=0.495. In this case,
the appropriate value of undrained Young’s modulus
would be 5537 kPa.
Correlations for su based on
Cam ClayA useful correlation that is based on Cam Clay theory
(and confirmed by the results of laboratory testing) is:
( )µ
σσOCR
cc uu
=
''
where σ’vi is the vertical effective stress at the start of
undrained loading and OCR (the overconsolidation
ratio) is equal to σ’p/ σ’vi, where σ’p is the vertical
(effective) preconsolidation stress.
According to data collected by Muir Wood (1990) µ is
close to 0.8 and (cu/σ’vi)NC lies between 0.1 and 0.35.
σσNCvivi
''
Example
At an OC clay site, the
water table is at the ground
surface.
The preconsolidation
stresses correspond to the stresses correspond to the
application of a vertical
effective stress of 500 kPa
at the ground surface.
Take (cu/σ’vi)NC as 0.2, µ
as 0.8 and the submerged
unit weight of the soil as 8
kPa/m.
cu from Index Tests
PL
PL
ww
wwI
−
−=
)1(1002 LI
uc−
×=
NOTE: This is
remoulded strength
(intact strength can
be much higher)
cu of London Clay
cu of London Clay
Friction and Dilations Angles
for Sandfor Sand
Correlations for Friction Angle
Bolton (1986) proposes a relationship
ψφφ 8.0'' += cv
where φ’cv is the critical state friction angle and ψ is the angle of dilation.
Correlations for Friction Angle
A study by Bolton (1986 and 1987) onpublished sand test data, suggested that themaximum dilation rate of a sand depends ona relative density index IR:a relative density index IR:
kPapforp
II DR 150'1150
'ln5 >−
−=
kPapforII DR 150'15 <−=
minmax
max
ee
eeI D
−
−=
Correlations for Friction Angle
The following correlations were found byBolton to give a good fit to the availabledatabase of test results:
Rcvpeak I5'' =−φφ
Rcvpeak I3'' =−φφ
for plane strain
for triaxial test
For quartz sand, the critical state friction angle φ’cv is approximately 33 degrees.
Correlations for Friction Angle
Determining the relative density of a sand deposit is rather difficult. For
correlations that relate cone resistance to relative density are described in
Lunne et al. 1997.
Estimation of Stiffness
Stiffness of Clay
• Option 1 - Use E50. For problems here relatively large strains are expected (e.g. for foundation bearing capacity and studies of the deformation of soft soil beneath an embankment).
• Option 2 - Use a small strain Young's modulus. If the problem involves the calculation of deformations of stiff problem involves the calculation of deformations of stiff clay under working conditions (e.g. the analysis of the interaction between a tunnel liner and the surrounding ground)
• Option 3 - Use the unloading Young's modulus, Eur. If the problem is dominated by unloading (as may be the case, for example, in an excavation problem)
Measurement of Stiffness in the
Triaxial test
Not accurate for strains below 1%
Measurement of Stiffness in the
Triaxial test
Correlations for Stiffness
Jardine et al. (1984) conducted a series of triaxial tests on a range of soils, using local gauges to measure strains.
Correlations for Stiffness
Jardine et al. (1984)
Correlations for Stiffness
Plate loading tests
by Duncan & by Duncan &
Buchignani (1976).
Data correspond to
strain values of
about 0.1%
Correlations for Stiffness
Data from Termaat, Vermeer and Vergeer (1985) may be used to suggest the following correlation for normally consolidated (Dutch) clay:clay:
P
uu
I
cE
1500050 ≈
Case
Studies
Stiffness profile for
various London clay
site (Matthews et al,
2000, re-plotted by
Simon and Menzies
2000)
Case Studies
Scott et al. (1999)
Stiffness Anisotropy
• Recent studies on natural clays (normally consolidated and overconsolidated) suggest that their stiffness may be anisotropic. Typical data for London clay anisotropic. Typical data for London clay can be found e.g. in Gasparre et al. (2007)
Stiffness of Sands
• Based on data on undrained triaxial testing of sandfs at different densities by Tokheim (1976) and Leahy (1984)Loose sand
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• Atkinson, J.H., Richardson, D. and Stallebrass, S.E. (1990). Effect of recent stress history on the stiffness of overconsolidated soil. Géotechnique 40(4) 531-40.
• Bolton, M.D. (1986). The strength and dilatancy of sands. Géotechnique 36(1), 65-78
• Bolton, M.D. (1987). Discussion on the strength and dilatancy of sands. Géotechnique 37(2), 219-226.
• Burd, H.D. (2007). Soil parameters for drained and undrained analysis. Numerical Methods in Geotechnical Engineering, 12-14 June, 2007, Manchester.
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• Clayton, C.R.I, and Khatrush, S.A. (1986) A new device for measuring local axial strains on triaxial specimens. Géotechnique 36(4) 593-598.
• Clayton, C.R.I., Edwards, A. and Webb, J. (1991). Displacements in London clay during construction. Proc. 10th Int. Conf. on Soil Mech and Fdn. Engng, Florence, 2, 791-796.
• Clayton, C.R.I., Matthews, M.C. and Simons, N.E. (1995). Site Investigation. Blackwell Science.
• Cole, K.W. and Burland, J.B. (1972). Observations of retaining wall movements associated with large excavation. Proc. 5th European Conf. on Soil Mechanics and Foundation Engineering, Madrid, 1,445-453.
• Duncan and Buchignani (1976).
• Gasparre, A., Nishimura, S., Minh, N.A., Coop, M.R. and Jardine, R.J (2007). The stiffness of natural London Clay. Géotechnique 57(1) 33-47 • Gasparre, A., Nishimura, S., Minh, N.A., Coop, M.R. and Jardine, R.J (2007). The stiffness of natural London Clay. Géotechnique 57(1) 33-47
• Gordon, M.A. (1997). Applications of field seismic geophysics to the measurement of geotechnical stiffness parameters. PhD Thesis, University of Surrey, Guildford
• Hope, V.S. (1993). Applications of seismic transmission tomography in civil engineering. PhD Thesis, University of Surrey, Guildford
• Jardine, R.J. , Symes, M.J. and Burland, J.B. (1984). The measurement of soil stiffness in the triaxial apparatus. Géotechnique 34(3) 323-340.
• Leahy, D. (1984). Deformation of dense sand, triaxial testing and modelling. PhD thesis, NTNU, Trondheim.
• Lunne, T., Robertson, P.K. and Powell, J.J.M. (1997) Cone Penetration Testing in Geotechnical Practice. Blackie Academic.
• Mair, R.J. (1993). Developments in geotechnical engineering research: applications to tunnels and deep excavations. Unwin memorial Lecture 1992. Proc. ICE, 3,27-41.
• Matthews, M.C., Clayton, C.R.I., and Own, Y. (2000). The use of field geophysical techniques to determine geotechnical stiffness parameters. Proc. ICE (Geotechnical Engineering),143, 31-42.
• Muir Wood, D.M. (1990). Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press.
• Scott, P., Talby, R. and den Hartog, N. (1999). Queensbury House, London: a case study of the prediction and monitoring of settlements during the construction of a deep excavation. Proc. Int. Symp. Beyond 2000 in Computational Geomechanics, 163-176. A.A. Balkema.
• Simons, N. and Menzies, B. (2000). A short course in foundation engineering. Thomas Telford. 2nd Ed.
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• St. John, H.D., Potts, D.M., Jardine, R.J. and Higgins, K.G. (1993). Prediction and performance of ground response due to construction of a deep basement at 60 Victoria Embankment. Proceedings of the Wroth Memorial Symposium, Oxford, July 1992, 581-608. Thomas Telford.
• Termaat R.J., Vermeer P.A. and Vergeer G.J.H. (1985). Failure by large plastic deformation. Proc. ICSMFE, 4, 2045-2048.
• Tokheim, O. (1976). A model for soil behaviour. PhD thesis, NTNU, Trondheim.
• Wroth, C.P. (1984). The interpretation of in-situ soil tests. 24th Rankine Lecture, Géotechnique, 34(4), 449-89
• Wroth, C.P. (1988). Penetration testing - a more rigorous approach to interpretation. Proc. Of International Conf. on Penetration testing, ISOPT-1, Orlando, 1, 303-311.
Bibliography
• Further information on the topics discussed in this lecture can be found in the following books:
• Simons, N., Menzies, B. and Matthews, M. (2002). A short course in geotechnical site investigation. Thomas Telford investigation. Thomas Telford
• Potts, D.M. and Zdravkovic, L. (2001). Finite element analysis in geotechnical engineering. Application. Thomas Telford
• Loo, B. (2007). Handbook of Geotechnical Investigations and Design Tables. Taylor & Francis.