Predicting non-linear ground movements

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Predicting non-linear ground movements

• Malcolm Bolton
• Cambridge University, UK

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What is the aim?

• Single calculation to verify safety and
  serviceability.
• Direct non-linear ground displacement calculation
  based on a bare minimum of soil element data,
  without using constitutive equations or FEA.
• Mobilisable Strength Design (MSD) offered as an
  improvement to Limit State Design (LSD) in that
  it deals properly with serviceability.
• Focus construction-induced displacements in
  clay.
• We will show 2 examples
• rigid pads / rafts under vertical loading
• multi-propped excavations

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Mobilisable Strength Design (MSD)

• MSD defines a local zone of finite plastic
  deformation.
• The ideal location of a representative element is
  selected at the centroid of the plastic zone.
• Stresses are derived from plastic equilibrium.
• Stress-strain data is treated as a curve of
  plastic soil strength mobilised as strains
  develop.
• Strains are deduced from raw stress-strain data.
• Ground displacements are obtained by entering
  strains back into the plastic deformation
  mechanism.

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Example 1 circular (square) footing on clay

• Focus on undrained settlement under load.
• Use Prandtls plane strain geometry to select the
  plastic zone of deformation.
• Select a kinematically admissible displacement
  field.
• Use plastic work equation to find equilibrium
  stress factor (familiar as bearing capacity
  factor).
• Use plastic displacement field to find compatible
  strain factor (unfamiliar, to be explained).
• Convert triaxial stress-strain curve, using the
  two factors, into a foundation load-settlement
  curve.

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Plastic deformation mechanism
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Stresses and strains for circular footing
?
?
(5.69)
Nc5.81
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Design procedure
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Relation to a triaxial test
Foundation stress smob Nc cmob 5.7
cmob
Triaxial deviator stress qmob 2 cmob
smob/2.85
Foundation distortion d/D g / 1.33
Triaxial axial strain ea 2/3 g
0.9 d/D
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Validation by non-linear FEA
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Soil model SDMCCBolton M.D., Dasari G.R. and
Britto A.M. (1994)
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Soil profile around the representative element
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Soil displacements by FEA
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MSD versus FEA
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More FE validation BRICK model
Many soil profiles and realistic stress-strain
curves have been checked, all with the same high
quality of fit.
? or q (kPa)
?/D or ?q ()
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Why does it work so well?

• Soil stress-strain curves resemble power curves
  over the significant range (see Bolton Whittle,
  1999) with shear strain roughly proportional to
  the square of shear stress.
• So the significant deformation zone is close to
  the perturbing boundary stress.
• And the equation t / tref (g / gref)b is
  self-similar at all stress levels, ensuring that
  the deformation mechanism at small strains is
  identical to that at large strains.

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Field validation Kinnegar test
Lehane (2003) Stiff square pad footing treated
here as a circle of diameter 2.26m
Kinnegar site
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Kinnegar soil profile
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Normalised stress-strain behaviour
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MSD predictions for Kinnegar
Also predicts Jardines Bothkennar test rather
well, and matches Arups observations of large
rafts on London Clay.
But most field tests are not accompanied by the
necessary stress-strain data from a shallow
sample. This is a lesson well taught by MSD
methodology.
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Example 2 ground movements around braced
excavations
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Stability calculations
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Incremental displacements
(Incremental displacement profile after ORourke
1993)
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Comparison of incremental displacement profile
between field data and cosine function (after
ORourke 1993)
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Plastic deformation mechanism
L?S
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Wavelength L free-end condition
L ?S ? 2
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Wavelength L fixed-end condition

• L aS
• 1

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Wavelength L intermediate end condition
s
1 lt ? lt2 L S 2 S
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Estimation of the mobilised shear strength
? cmob/cu
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Assumption of a mobilisation ratio
Shear strength
cu
cmob?cu
Depth
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Calculation procedure for bulging movements
?s
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Surface settlement
     
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Effect of cantilever movement
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Plastic deformation mechanism for cantilever
retaining walls
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Permissible stress field
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Mobilised strength versus excavation depth for
cantilever retaining walls
Cmob/?D
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Calculation procedure for cantilever retaining
walls
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Whittles data of Boston Blue Clay
t / s' log scale
t / s' log scale
g log scale
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FE validationcomparing with Hashash and Whittle
(1996)
Boston blue clay
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Stability calculations for braced excavations
props placed at 2.5m intervals to failure at
excavation depth Hf
Boston blue clay
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Case history Boston Post Office Square Garage
(Whittle et al. 1993)

• The 1400 car parking underground garage was
  constructed with seven levels of below-grade
  structure in the heart of the downtown financial
  district of Boston in late 1980s. The garage
  occupies a plan area of 6880 m2.

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Boston Post Office Square Garage
Measured and predicted displacements
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Measured and predicted settlements
Boston Post Office Square Garage
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Braced excavation in Singapore soft clay

• The sub-structure consists of a two-level
  basement in soft marine clay surrounded by
  Gairnill Garden (a 12 storey residential block of
  flats), Scotts Road and Cairnhill Road.
• The excavation was 110m by 70 m.
• The depth of excavation varies from 6.4m to 7.5m.
  
• The sheetpile wall was supported by three levels
  of bolted struts.
• The vertical spacing varies from 1.4m to 1.8m.
• The sheetpile lengths range from 12m to 24m.

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Soil profile at Moe Building
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Stress-strain response of Singapore Soft Marine
Clay (after Wong and Broms 1989)
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Measured and predicted displacements
Singapore soft marine clay
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Measured and predicted displacements
Singapore soft marine clay
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Conclusions

• Raw stress-strain data from a triaxial test on a
  representative sample taken from a selected
  location in the plastic zone of influence can be
  used directly to predict displacements. No need
  for constitutive laws or parameters.
• Plastic deformation mechanisms with distributed
  plastic strains can provide a unified solution
  for design problems. This application can satisfy
  approximately both safety and serviceability
  requirements and can predict stresses and
  displacements under working conditions without
  the need for FE analysis.

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The future

• Extend MSD to predict consolidation settlements
  from drained / creep stages carried out during
  the representative element or pressuremeter test.
• Verify using centrifuge model tests on
  foundations with long-term PIV monitoring
  providing ground strain contours at 0.01
  intervals.
• Attempt to extend to sand, referenced to
  pressuremeter test rebound loops.

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Thank you for inviting me!