7 John Burland Paradox of the Gaussian Subsidence Trough

8/18/2019 7 John Burland Paradox of the Gaussian Subsidence Trough

1/40

The Paradox of the Gaussian Subsidence

Trough

John Burland

Imperial College London


2/40

Introduction

• Ever increasing tunnelling in urban areas.

• Impacts of tunnelling induced movements on

buildings and infrastructure growing in importance.• Complex and challenging ground-structure

interaction problems.

• Realistic “soil-like” constitutive models are nowavailable.

• Numerical methods of analysis are advancing at an

immense pace.• We have been very successful in predicting ground

movements around deep excavations and complex

buildings.


3/40

The Palace of Westminster


4/40

Underground car park at the Palace of Westminster


5/40

JLE Station box and tunnels at the Palace of

Westminster


6/40

Queen Elizabeth II Conference Centre


7/40

Queen Elizabeth II Conference Centre

North-South Cross Section


8/40

The Leaning Tower of Pisa


9/40

Comparison between the deduced and computed history of

inclination of the Leaning Tower of Pisa


10/40

Cylindrical tunnel at depth H beneath surface

H


11/40


H


12/40


H


13/40


Existing tunnel

H


14/40

On the face of it we should have the constitutive

models and computational ability to successfully

model ground movements around tunnels

e ave a uge a a ase aga ns w c o va a e

and calibrate such modelling


15/40

Transverse Gaussian settlement trough

s s -yi

=

max exp

2

22


16/40

Case history data for trough width parameter i and tunnel

depth (after Rankin, 1988)

• K = i/H

• K = 0.4 to 0.6 for clayeysoils and residual soils

• K = 0.3 to 0.5 forgranular soils


17/40

Normalised Gaussian settlement trough

The Gaussian settlement trough is usually expressed as:

s very use u o express n norma se orm as:

By plotting this normalised subsidence curve for K varying

from 0.4 to 0.6 we see just how well defined it is


18/40

Normalised Gaussian settlement trough

with K varying from 0.4 to 0.6


19/40

JLE tunnels beneath St James’s Park


20/40

JLE Westbound at St James’s Park

Depth of axis H = 31m; External diameter = 4.85m;

Measured surface volume loss V sl = 3.43%


21/40

The Challenge

Given the volume loss, how well are we ableto predict the shape of the subsidence trough


22/40

Modelling the tunnel excavation process

• The initial stresses are applied within the soil mass.

• The stiffness of the material within the tunnel is thenprogressively reduced until the prescribed volume lossis obtained.

• A lining is then inserted.


23/40


Comparison with non-homogeneous, isotropic non-

linear models. (Addenbrooke, Potts and Puzrin, 1997)


24/40


Comparison with non-homogeneous, anisotropic,

non-linear models. (Addenbrooke, Potts and Puzrin, 1997)


25/40


FE mesh for 3D analysis: non-homogeneous, non-linear,

anisotropic model. (Franzius, Potts and Burland, 2005)


26/40

The influence of K o (Doležalová, 2002)

Ko=0.5 Ko=1.0

Ko=1.5


27/40

To date the response to the challenge is

not encouraging

• Doležalová (2002): “ No satisfactory explanation ofthe discrepancy between the numerical and empirical

prediction of the settlement trough has been

”o a ne

• Franzius, Potts and Burland (2005): “. . . Neither 3D

effects nor elastic soil anisotropy can account for theover-wide settlement curves obtained from FE tunnel

analysis in a high K o regime”


28/40

The Paradox

The paradox lies in the fact that the observedshape of the subsidence trough is remarkably

whereas numerical predictions have proved to

be very sensitive to such variables.


29/40

The work of Verruijt and Booker (1996)

• They obtained closed form solutions by

approximating a tunnel to a “line sink” in an

so rop c, omogeneous e as c a space.

• Their work may show a way forward


30/40

Deformations around a line sink in a half space

(Verruijt and Booker, 1996)

A circle reduces in radius

and translates

A circle becomes an oval and

translates


31/40

Definitions of change of shape of an initial circle

(Verruijt and Booker, 1996)

R

∆r

R

∆

ε = ∆r /R δ = ∆ /R


32/40

Predicted undrained normalised surface settlement

troughs from Verruijt and Booker (1996)

• δ = 0: Radial convergence only

• ε = 0: Ovalisation only

• δ = 1.5.ε: Superposition of radial convergence and ovalisation comparedwith Gaussian curve for K = 0.5.


33/40

Variation of trough width factor K with depth for

subsurface settlement profiles above tunnels inclay (Mair, Taylor and Bracegirdle, 1993)


34/40

Predicted normalised settlement with depth compared with

empirical results obtained by Mair et al (1993)


35/40

What evidence is there for ovalisation or

“squatting” ?


36/40

7ft diameter C.I. lined tunnel in London Clay

Measurement of change in diameter with micrometer tube

(Cooling, 1962)


37/40

7ft diameter C.I.tunnel in London Clay

Diameter changes in newly constructed tunnel in London Clay(Cooling, 1962)


38/40

Horizontal diameter changes in eastbound JLE at

St James’s Park (Nyren, 1998)


39/40


Why, in the presence of high K ostresses, does the ground around

the tunnel squat?

H

Unlike many other problems,

tunnelling involves reducing

support from below

We treat the ground as a

continuum. Are there structural

and fabric effects we are

overlooking?


40/40

We have an intriguing and important

paradox that is in urgent need of resolution

Documents

7 John Burland Paradox of the Gaussian Subsidence Trough