Transcript Plan of Stata Center

Predicting non-linear ground movements
Malcolm Bolton
Cambridge University, UK
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
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.
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.
Plastic deformation mechanism
u,r
D

u u v
 
0
r r z
(u , v)  f ( r , z ,

D
)
v,z
Stresses and strains for circular footing


cmob

 mob  Nc cmob
 2c
u
1 dVol   dA

 

A


Energy _ dissipated
Work _ done
Vol
Nc=5.81 (5.69)
 dVol


Vol
  1.33

D
Design procedure
0.3D
cmob
cmob
 mob  Nc cmob


 = Mc  /D

Relation to a triaxial test
Foundation stress
mob  Nc cmob  5.7 cmob
Triaxial deviator stress qmob  2 cmob  mob/2.85
Foundation distortion
/D   / 1.33
Triaxial axial strain
a  2/3 
 0.9 /D
q
OR
mob/2.85
a OR 0.9 /D
Validation by non-linear FEA
Soil model: SDMCC
Bolton M.D., Dasari G.R. and Britto A.M. (1994)
G
Gmax=Ap’n1OCRm1
G=Bp’n2OCRm2 qb2
MCC flow rule
Very small
strains
Small Strains
Large Strains
q~10-5
q~10-2
lnq
Soil profile around the
representative element
Soil displacements by FEA
MSD versus FEA
More FE validation: BRICK model
or qprofiles and realistic stress-strain curves have been
Many soil
(kPa)
checked, all with the same high quality of fit.
/D or q
(%)
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 = ( / ref)b is self-similar at all
stress levels, ensuring that the deformation mechanism
at “small” strains is identical to that at “large” strains.
Field validation: Kinnegar test
Lehane (2003)
Kinnegar site
Stiff square pad footing
treated here as a circle
of diameter 2.26m
Kinnegar soil profile
Normalised stress-strain behaviour
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
(Triaxial compression data)
taught by MSD methodology.
(Triaxial extension data)
Example 2: ground movements around
braced excavations
Stability calculations
Nc 
H
cu
Incremental displacements
Supports
y
max
L
Soil excavated to cause max

1
/max
0
 max
y/L
2y 

 1  cos(
)
L 

1
(Incremental displacement profile after O’Rourke 1993)
Comparison of incremental displacement profile between field
data and cosine function (after O’Rourke 1993)
Plastic deformation mechanism
s
 s  2
m
L
L=S
Wavelength L: free-end condition
s
s
L = S
=2
Wavelength L: fixed-end condition
s
s
L = S
=1
Wavelength L: intermediate end condition
s
s
1 <  <2
L=S~2S
Estimation of the mobilised shear strength
b = cmob/cu
D  b  cu s dV
W   vdV
W  D
 vdV

b
 c  dV
u s
Assumption of a mobilisation ratio
Shear strength
cu
cmob=bcu
Depth
Calculation procedure for bulging
movements
b
b
cmob
cu
s
  vdV
 c  dV
u s
s  2
m
L
Surface settlement
MSD
Effect of cantilever movement
Plastic deformation mechanism for
cantilever retaining walls

H
D
s
45
s=2
Permissible stress field
H
a
p
v
2cu
2cu
Limiting pressures in
undrained conditions
D
p
a
a
p
a=v -2cmob
p=v+2cmob
Mobilised strength versus excavation
depth for cantilever retaining walls
Cmob/D
Calculation procedure for cantilever
retaining walls
H
D
cmob
p
a
a
p
a=v -2cmob
p=v+2cmob
s

H
s
D
s=2
t / '
log scale
Whittle’s data
of Boston Blue
Clay
t / '
log scale
% log scale
FE validation
comparing with Hashash and Whittle (1996)
Boston blue clay
Stability calculations for braced excavations – props
placed at 2.5m intervals to failure at excavation depth Hf
Wall
length
L
(m)
(1)
FE analysis
(Hashash and
Whittle 1996)
Hf
(m)
(2)
Numerical limit analyses (Ukritchon, 1998)
Average isotropic
strength
cu/vo’= 0.21
Hf —lower
bound
(m)
(3)
Peak anisotropic
strength,
cu/vo’= 0.17–0.34
Hf —upper Hf —lower Hf —upper
bound
bound
bound
(m)
(m)
(m)
(4)
(5)
(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
Boston blue clay
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.
Measured and predicted displacements
Boston Post Office Square Garage
Measured and predicted settlements
Boston Post Office Square Garage
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.
Soil profile at Moe Building
Stress-strain response of Singapore Soft
Marine Clay (after Wong and Broms 1989)
q
q max
a(%)
Measured and predicted displacements
Singapore soft marine clay
Measured and predicted displacements
Singapore soft marine clay
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.
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.
Thank you for inviting me!