predicting non-linear ground movements
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Predicting non-linear ground movements. Malcolm Bolton Cambridge University, UK. What is the aim?. Single calculation to verify safety and serviceability. - PowerPoint PPT PresentationTRANSCRIPT
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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 Prandtl’s 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
0
z
v
r
u
r
u
D
u,r
v,z
),,(),(D
zrfvu
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mobcmob cN
cmob
doneWork
A
dissipatedEnergy
Vol
u dAdVolc
__
12
Nc=5.81(5.69)
Vol
dVol
D
33.1
Stresses and strains for circular footing
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Design procedure
mobcmob cN
cmob
= Mc /D
0.3D
cmob
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Relation to a triaxial test
Foundation stressmob Nc cmob 5.7 cmob
Triaxial deviator stressqmob 2 cmob mob/2.85 Foundation distortionD
Triaxial axial strainaD
q
OR
mob/2.85
a OR 0.9 /D
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Validation by non-linear FEA
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Gmax=Ap’n1OCRm1
G=Bp’n2OCRm2 qb2
MCC flow rule
lnq
G
Very small strains Small Strains
Large Strains
q~10-5 q~10-2
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
/D or q
(%)
or q(kPa)
Many soil profiles and realistic stress-strain curves have been checked, all with the same high quality of fit.
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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 / ref = ( / ref)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
Kinnegar site
Lehane (2003)
Stiff square pad footing treated here as a circle of diameter 2.26m
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Kinnegar soil profile
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Normalised stress-strain behaviour
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(Triaxial compression data)(Triaxial extension data)
MSD predictions for Kinnegar
Also predicts Jardine’s Bothkennar test rather well, and matches Arup’s 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
uc c
HN
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maxSoil excavated to cause max
y
Incremental displacements
1
1
0
/max
y/L
)
2cos(1
max L
y
Supports
L
(Incremental displacement profile after O’Rourke 1993)
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Comparison of incremental displacement profile between field data and cosine function (after O’Rourke 1993)
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s
L=S
Plastic deformation mechanism
Lm
s
2
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s
s
L = S
= 2
Wavelength L: free-end condition
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L = S
= 1
s
s
Wavelength L: fixed-end condition
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s
1 < <2
L = S ~ 2 S
s
Wavelength L: intermediate end condition
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dVcD su
dVvW
DW
dVc
dVv
su
Estimation of the mobilised shear strength
= cmob/cu
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Shear strength
cu
Depth
cmob=cu
Assumption of a mobilisation ratio
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Calculation procedure for bulging movements
s
u
mob
c
c
dVc
dVv
su
Lm
s
2
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Surface settlement
MSD
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Effect of cantilever movement
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Plastic deformation mechanism for cantilever retaining walls
H
D45
s=2
s
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Permissible stress field
a
a
p
p
a=v -2cmob p=v+2cmob
D
H
2cu 2cu
pa v
Limiting pressures in undrained conditions
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Cmob/D
Mobilised strength versus excavation depth for cantilever retaining walls
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Calculation procedure for cantilever retaining walls
a
a
p
p
a=v -2cmob p=v+2cmob
D
H
s
mobc
H
D
s=2
s
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'log scale
'log scale
log scale
Whittle’s data of Boston Blue
Clay
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FE validationcomparing with Hashash and Whittle (1996)
Boston blue clay
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Numerical limit analyses (Ukritchon, 1998)
Average isotropic strength
cu/vo’= 0.21
Peak anisotropic strength,
cu/vo’= 0.17–0.34
Wall length
L
(m)
(1)
FE analysis (Hashash and Whittle 1996)
Hf (m)
(2)
Hf —lower bound
(m) (3)
Hf —upper bound
(m) (4)
Hf —lower bound
(m) (5)
Hf —upper bound
(m) (6)
MSD Hf
(m)
(7)
12.5 10-12.5 - - - - 10
20 15.0–17.5 18.5 19 20 20 15.0
40 22.5–25.0 24.5 29.5 35.5 39 27.5
60 30-32.5 27.5 34.0 46.5 56.5 40
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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Measured and predicted displacements
Boston Post Office Square Garage
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Boston Post Office Square Garage
Measured and predicted settlements
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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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maxq
q
a(%)
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!