predicting non-linear ground movements malcolm bolton cambridge university, uk

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Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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Page 1: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Predicting non-linear ground movements

Malcolm Bolton

Cambridge University, UK

Page 2: 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

Page 3: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 4: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 5: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Plastic deformation mechanism

0

z

v

r

u

r

u

D

u,r

v,z

),,(),(D

zrfvu

Page 6: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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

Page 7: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Design procedure

mobcmob cN

cmob

= Mc /D

0.3D

cmob

Page 8: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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

Page 9: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Validation by non-linear FEA

Page 10: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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)

Page 11: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK
Page 12: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Soil profile around the representative element

Page 13: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Soil displacements by FEA

Page 14: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

MSD versus FEA

Page 15: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 16: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 17: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Field validation: Kinnegar test

Kinnegar site

Lehane (2003)

Stiff square pad footing treated here as a circle of diameter 2.26m

Page 18: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Kinnegar soil profile

Page 19: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Normalised stress-strain behaviour

Page 20: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

(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.

Page 21: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Example 2: ground movements around braced excavations

Page 22: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Stability calculations

uc c

HN

Page 23: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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)

Page 24: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Comparison of incremental displacement profile between field data and cosine function (after O’Rourke 1993)

Page 25: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

s

L=S

Plastic deformation mechanism

Lm

s

2

Page 26: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

s

s

L = S

= 2

Wavelength L: free-end condition

Page 27: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

L = S

= 1

s

s

Wavelength L: fixed-end condition

Page 28: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

s

1 < <2

L = S ~ 2 S

s

Wavelength L: intermediate end condition

Page 29: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

dVcD su

dVvW

DW

dVc

dVv

su

Estimation of the mobilised shear strength

= cmob/cu

Page 30: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Shear strength

cu

Depth

cmob=cu

Assumption of a mobilisation ratio

Page 31: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Calculation procedure for bulging movements

s

u

mob

c

c

dVc

dVv

su

Lm

s

2

Page 32: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Surface settlement

   

MSD

Page 33: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Effect of cantilever movement

Page 34: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Plastic deformation mechanism for cantilever retaining walls

H

D45

s=2

s

Page 35: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Permissible stress field

a

a

p

p

a=v -2cmob p=v+2cmob

D

H

2cu 2cu

pa v

Limiting pressures in undrained conditions

Page 36: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Cmob/D

Mobilised strength versus excavation depth for cantilever retaining walls

Page 37: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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

Page 38: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

'log scale

'log scale

log scale

Whittle’s data of Boston Blue

Clay

Page 39: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

FE validationcomparing with Hashash and Whittle (1996)

Boston blue clay

Page 40: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

  

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

Page 41: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 42: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK
Page 43: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Measured and predicted displacements

Boston Post Office Square Garage

Page 44: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Boston Post Office Square Garage

Measured and predicted settlements

Page 45: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 46: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Soil profile at Moe Building

Page 47: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

maxq

q

a(%)

Stress-strain response of Singapore Soft Marine Clay (after Wong and Broms 1989)

Page 48: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Measured and predicted displacements

Singapore soft marine clay

Page 49: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Measured and predicted displacements

Singapore soft marine clay

Page 50: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 51: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

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.

Page 52: Predicting non-linear ground movements Malcolm Bolton Cambridge University, UK

Thank you for inviting me!