Tunnelling Jan 2004

NUMERICAL MODELLING OF BUILDING REPONSE TO

TUNNELLINGTowards a new damage assessment method

A presentation describing a DPhil Thesis in progressJohn Pickhaver

University of OxfordDepartment of Engineering Science

Homes at risk after gardens disappear into hole above rail link 10.02.03

Rail tunnel firm ignored subsidence warnings, say residents 10.02.03

Hole swallows gardens as rail link rattles East End 10.02.03

Tunnelling - In the Headlines


LONDON GETS THAT SINKING FEELING 11.3.2003

Some of Britain's best known landmarks could be at risk of sinking caused by the Jubilee Line Extension and other tunnelling beneath the capital, according to new Satellite images taken over the last five years. A European Space Agency satellite has been taking pictures of London once every 35 days over the last five years. Nigel Press, chairman of NPA Satellite, who are the British distributors of data from the satellite, said: "The damage is probably continuing. These projects will have caused structural cracks and other damage. We know there are some people who have cracks in buildings on the line of the Jubilee line. There are definitely problems."


SUBSIDENCE DAMAGE in SANTA MONICA 7.9.1996

In a scene reminiscent of problems previously witnessed along Hollywood Boulevard, three CahuengaPass property owners are reporting cracks in the floors, walls and ceilings of homes directly above the route of Metro Rail subway tunneling in the Santa Monica Mountains. Excavation experts say that gaps left in tunnel walls by digging machines and not completely packed eventually fill with dirt falling from above. The settlement can take weeks, months or even years to work its way to the surface. Experts say that if the dirt that slips away was supporting a building, walls can shift, buckle or crack.

Overview

Tunnelling background : the benefits and potentially damaging effects

Current damage assessment methods

Objectives of the current research project

Description of the current research project

Conclusion

Tunnelling background

Underground construction will continue to grow as a means of providing transport and other infrastructure due to increasing population pressures and the diminishing amount of surface space

Tunnels involve lengthy planning, scoping and cost benefit phases and carry significant political risk

Tunnels are costly projects. Urban tunnels cost on average £50million per kilometer.

Assessing the impact of tunnel projects on existing buildings in urban environments is thus extremely important

Tunnel constructionHard Rock Tunnel construction:Cross City Tunnel, Sydney Australia

Above: A roadheader excavating in sandstone. Right: Installing rockbolts to support the tunnel crown.

Tunnel construction cont…

Soft Ground Tunnel Construction – the focus of this research

Bulkhead

Screw conveyor driving motor

Belt conveyor

Erector

Gate jack

Shield jacks Cutter frame

Cutter face

Cutter driving motorScrew conveyor Tail seal

Above: Earth Pressure Balance Shieldat the front of a soft ground tunnelboring machine

Below: A completed concrete lined tunnel

Current tunnelling projectsTunnelling continues to be an important area as evidenced by the number of current and planned projects worldwide.

Projects include theChannel Tunnel Rail Link in London

Plan and Section including St Pancrasand Stratford stations

Reproduced from the 1:250 000 ‘Routemaster’ series map by permission of the Ordnance Survey on behalf of the Controller of Her Majesty’s Stationery Office. © Crown Copyright AL850292

London St PancrasInternational and Domestic Station

Stratford International and Domestic Station

Proposed tunnelling projectsCross Rail, London

Proposed Bond Street station layout

Proposed tunnelling projectsCross Rail, London

The surface above the proposed Bond Street station showing thelarge number of potentially affected buildings

Effects of Tunnelling

When we tunnel in soft soil, ground movements are caused by soil filling the ground loss associated with tunnel construction

Ground or volume loss includes radial and face movements.

SHIELD LOSS TAIL LOSSFACE LOSS

TunnellingDirection

TunnellingShield

Tunnel Lining

Effects of TunnellingThis ground loss manifests itself as settlements on the surface which typically exhibit a Gaussian settlement profile at greenfield sites.

SURFACE PROFILE due toground movements

(vertical scale exaggerated)Hogging Sagging

SURFACE BUILDING

TUNNEL

Tunnel Induced Ground MovementsSurface settlement trough in three dimensions

Damage to structuresSurface settlements can cause damage to buildings sited in the settlement trough

Damage can include tilting of the complete building…

Damage to structures

…significant structural damage…

…or most commonly cracking of the façade.

Recent Tunnel subsidence eventsAn example of tunnel induced damage: Lavender Street Stratford,

February 2003 - Channel Tunnel Rail Link, London

Recent Tunnel subsidence eventsBlackheath Hill, Greenwich, UK April 2002 – (Old chalk workings)

Damage prevention measures

Design: Tunnel alignment and depth – the further away, the less damage

Construction method – Choice of best boring machine type to minimise volume loss

Construction workmanship – the more accurate the boring machine control the less settlement

Compensation grouting - Used to ‘reinflate’ subsided ground

All these methods require prior assessment of potential damage to buildings

y

z

SmaxS i

Damage assessment methods

Three stages in a damage assessmentStage 1: PreliminaryGreenfield gaussian displacement quantified and applied to all buildings above the tunnel alignment

Zo = Depth to tunnel axis Ko = trough width parameterKo a function of soil type ranging from 0.2 (dry granular) to 0.4 (stiff clay) and 0.7 (soft silty clay)

2

2

i2y

maxv eSS−

= i = K z0

Stage 1 damage assessment cont…

Apply greenfield displacement to buildings and calculate Max slope (θ) and Max settlementBuildings with θ >1/500 and maximum settlement greater than 10mm are deemed at risk and subject to Stage 2 assessment

Other buildings deemed at negligible riskConservative as neglects stiffness/weight of building and soil-structure interaction

Damage assessment methods cont…

Stage 2: Tensile strains within the at risk buildings are considered

Building considered as weightless elastic beam following greenfield ground displacements and maximum tensile strain calculated

Assumption that the building follows the greenfield displacements found to be overly conservative as shown on the following slide. The actual Mansion House building settled much less than was predicted due to tunnelling. This was due to the interaction of the structure’s stiffness and weight with the soil movements.


Mansion House Settlement (From Frischman et al, 1994)

An improved assessment method (Potts and Addenbrooke, 1997) includes stiffness of building in 2D to modify tensile strains from greenfield analysis


Calculated Tensile Strain converted to potential damage category using charts

Damage assessed as category 3 or greater subject to Stage 3 assessment to give accurate idea of potential damage and opportunity for protective measures

>0.3Severe to very severe

4 to 5

0.15-0.3Moderate3

0.075-0.15Slight2

0.05-0.075Very slight 1

0-0.05Negligible0

Tensile strainNormal degree of severity

Category of damage

Damage assessment methods cont…

Stage 3: Further detailed investigations

Finite element methods would be used at this stage

Full numerical models of buildings including tunnel, soil and structure are analysed

Many developments have been completed in this area with a significant programme of work here at Oxford addressing gaps in current practice

3D numerical models at Oxford

Areas of research at Oxford include:

Soil model - Nested yield surface failure model for overconsolidated clay soil

Masonry modelling – appropriate constitutive models

Tunnel construction modelling including tunnel lining and staged construction

Improved numerical methods

Use of supercomputer to speed up run times

Results of tunnel construction simulations show the effect of the building modifying ground movements and the effect of the soil-structure interaction on the damage to the buildingDamage predicted using 3D FE models differs from the semi-empirical stage 2 predictions and those including the building stiffness in only two dimensions – it is much more realistic3D FE models are more complex and time consuming however, with significant computer resources requiredThe aim of this project is to make 3D FE analyses more simple and quick and therefore more widely useable

3D numerical models at Oxford

Aims of current projectSimplified 3D modelling – The aim is to replace full buildings in 3D models with a representative series of ground beams. This is commonly done in 2D but not in 3D.

Three phases:1. Analysis of facades and ground beams in two dimensions to ensure

beams have appropriate properties2. Use of ground beams in three dimensions to model buildings3. Case study verification against real life tunnelling projects

Full building

Simplified beams connected to model the building

Description of current project

PHASE 1

Beams used to represent buildings are traditionally simply given the same dimensions as building façade and the same material properties

Aim: Determine properties to give beams to represent the façade so they respond to ground movements in a similar way

Method: Numerical analysis of masonry building facades subjected to imposed ground displacements

Based on idea that ground sees only base reaction, not full structure

Phase 1 AnalysisApply a displacement to the base of façadeAnalyse base reaction for a range of facadesFactors influencing response of façade include:

Overall dimensionsMaterialAmount of openingsDirection of ground movements (hogging or sagging)

L

andDirection of imposeddisplacement for hogging

H

sagging

Amount of openings, façade material and dimensions all varied

Phase 1 Analysis

18.7500.75 – 7.5Gaussian displacement

G6(check analysis)

18.7500.75 – 7.5Imposed displacement

A4

No openings0.75 – 7.5Imposed displacement

A2

Masonry (no tension)


A7


A5


A3

No openings0.75 – 7.5Imposed displacement

A1

Linear Elastic

Amount of openings as % of façade area

Length/HeightRatio range

TypeAnalysisFamily

Façade Material

Phase 1 Analysis20m

8m

L/H = 2.5

Material Properties: Elastic : E = 10,000MPa, v = 0.2, G = 4166MPaMasonry: E = 10,000MPa, v = 0.2, c = 10kPa (residual tensile strength), Et= 0.01kPa (residual stiffness)

Phase 1 AnalysisDisplacements applied at base chosen to give convenient stress at façade base and zero area under curve

Expression for parabolic load q:

Derive expression for displacement y:

Potential for short deep ‘beams’ to be required, therefore shearterms included in displacement expression

Extent of building, l

Stress ‘q’ at façade base

x

wo

w’

l/2

( )'w

l4xlxw

q 2o −

−=

( )( ) ( )2

22o432234

2o

AGl2lxxwlxllxlx4x2

EIl180lxxw)x(y −

−−−+−−

=

Phase 1 Results

Define stiffness K to be the stress divided by the displacement at the midpoint:

Derive theoretical beam stiffness Kbeam for beam of length L, and properties, A, I, E, G using expression for displacement at the midpoint gives:

)2/l(ywK o=

( ) ( )AGCL

EICL

1

CAG

LwCEI

LwwK

22

14

2

2o

1

4o

o

+=

+=

= Kbeam

Phase 1 Results

Present results in terms of NORMALISED STIFFNESS (NS)

Normalised stiffness (NS) = K/Kbeam

If façade does simply act like a beam NS = 1.0

Results following show plot of normalised stiffness against L/H ratio for different families of façade by percentage of windows (elastic only)

Phase 1 Results

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0L/H

Nor

mal

ised

Stif

fnes

s Ra

tio

K/K

beam

1A1Xss - No windows1A3Xss - 18% windows1A5Xss - 9% windows1A7Xss - 6% windows

Phase 1 Results

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0L/H

Nor

mal

ised

Stif

fnes

s Ra

tio

K/K

beam

1A1Xss - No windows1A3Xss - 18% windows1A5Xss - 9% windows1A7Xss - 6% windows

L/Hcrit

Phase 1

Development of procedures to determine properties for an equivalent deep beam to represent a façadeLet stiffness of such a beam be Kmodel:

Aim is now to determine values of A* and I* from the geometry of any given façade such that Kmodelapproximates K from FE analysesTwo procedures, both common for region L/H>L/Hcrit

G*ACL

*EICL

1elmodK2

21

4

+=

Phase 1Part A SHEAR

From (a) Shear Strain:

Vertical Displacement:

F

L

Vs

Aγ

(a)

AGF

GLVs ===

τγ

AGFLVs =

Phase 1From (b) with a window and vertical sections:

For the equivalent deep beam let:

Such that:

Thus:

3

L

Vs

A3A2A1F

21

(b)

+++=

n

n

2

2

1

1s A

L...AL

AL

GFV

G*AFLVs =

+++=

n

n

2

2

1

1

AL...

AL

AL

GF

G*AFL

∑=

= n

1i AiLi

L*A

Phase 1Part B BENDING

For plain wall (a):

For beam with openings take horizontal strips as in (b) each of height hi, area Ai, and distance to NA bi

Calculate effective height hi’: hi’ = Ai/L

L

NA

hiH

LAi

bi

(b)(a)

12thI

3

=

Phase 1

For strip with windows second moment of area Ii is thus:

The effective second moment of area for an equivalent deep beam is then given by:

23

bi'.hi.t12

'thiIi +=

∑=

=n

1iIi*I

Phase 1These procedures give A* and I* for L/H>L/HcritFor L/H<L/Hcrit two methods consideredMethod 1: Linear Depression

Method 2: Limiting Height

Hlim equal to L/3, above which façade material is ignored

×

=

∑=

Hcrit/LH/L

AiLi

L*A n

1i

×= ∑

= Hcrit/LH/L)Ii(*I

n

1i

∑=

=

n

1i limAiLi

L*A ∑=

=n

1ilimIi*I

Phase 1

h1

h2

h3

h5

h4

w1 w4 w5 w6 w7 w8 w9 w10 w11w2 w3

Example of determining beam properties A* and I* from the geometry of a facade

A = 8m2, A* = 4.848m2 and I=42.67m4, I* = 29.716m4Kmodel = 691 and Kfe = 676

Phase 1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Length/Height

Nor

mal

ised

Stif

fnes

s R

atio

Observed - No windows Observed - 19% windows

Predicted - No windows Predicted - 19% windows

Proposed (predicted) ground beam and observed FE façade response to ground movement showing good agreement


PHASE 2

Three dimensional simulations of tunnelling, comparing full building models and simplified models

1. 2D beams developed in phase 1 implemented into OXFEM, an in house FE program

2. 2D beams developed in phase 1 joined together to model buildings in 3D analysis using OXFEM

Phase 2

Difference between formulation of Bernoulli-Euler beams (bending only) and Timoshenkobeams (bending and shear, shown at right)

Shape functions derived for a 2 node Timoshenko beam element – extra shear terms

These beams were then implemented into OXFEM

Implementation of Timoshenko Beams into OXFEM

Phase 2Beams implemented: 2 node, 6 degree of freedom beam.

u1, w1, θ1

u2, w2, θ2

−−−−

−−

=

22

22

3

L4L6L2L6L612L612

L2L6L4L6L612L612

LEIK

+−−−−−−−+

−

=

22

22

3

L)4(L6L)2(L6L612L612

L)2(L6L)4(L6L612L612

LEIK

εε

εε

3LEIa = 2kAGL

EI12=ε

Bending only (no axial terms) Bending and Shear (no axial terms)

ε+=

1aK

Phase 2

Testing of Timoshenko beams in OXFEM

Apply same displacements to beam and full façade

Compare response of each:

Phase 2

Stress at Bottom 1A13ssbeams20x8 - No windows

-8000

-6000

-4000

-2000

0

2000

4000

0 2 4 6 8 10 12 14 16 18 20

Position

Stre

ss (N

/m2)

Facade ModelTheoryBeam ModelPoly. (Facade Model)

Phase 2

Stress at Bottom 1A33ssbeams20x8 -18%windows

-8000

-6000

-4000

-2000

0

2000

4000

0 2 4 6 8 10 12 14 16 18 20

Position

Stre

ss (N

/m2)

ModelTheoryBeam ModelPoly. (Model)

Phase 2

3D analyses

2D beams developed in phase 1 and now implemented and tested in OXFEM are joined to model buildings in 3D analyses using OXFEM

Schedule of analyses:

Phase 2

Masonry Beams2OMBMasonry Full building2OMF

Elastic Beams2OEBElastic Full building2OEF

SIMPLIFIED BUILDINGFULL BUILDING

OBLIQUE

Masonry Beams2SMBMasonry Full building2SMF

Elastic Beams2SEBElastic Full building2SEF

SIMPLIFIED BUILDINGFULL BUILDING

SYMMETRIC

Phase 2Symmetric Analysis – Typical FE mesh

Phase 2

100m

50m

60m

Oblique Analysis – Typical wireframe layout

Phase 2

50m

100m

10m

5m

Oblique Analysis – Typical wireframe layout (elevation)

Phase 2

60m20m

10m

100m

Oblique Analysis – Typical wireframe layout (plan)


PHASE 3Case studies with Jubilee Line data from LondonCase study data collected by Imperial CollegeAim to replicate real soil-structure interaction problem with the new simplified 3D finite element procedures

Phase 3Plan of case study site in Berdmonsey, London showing

two Jubilee Line tunnels running beneath three

masonry structures

Phase 3

Simplified models of buildings

Lambeth group soil

10m deep 4.85m diameter tunnel

Schematic of simplified 3D model of case study site

Project AchievementsSimplified finite element method, retaining important aspects – could be used in Stage 2 assessments thus increasing accuracy at that stage

Means by which parametric study could be undertaken to develop a 3D hand method for assessment – more accurate than current 2D hand methods

Modelling of multiple buildings simultaneously now possible or multiple simple beam buildings can be placed around a full model of at risk structure, again increasing the accuracy of the full system modelled

Conclusions

A simplified method of modelling buildings for use in three dimensional numerical simulations of tunnellingis being developed.

Efficient inclusion of full three dimensional effects in the prediction of tunnel induced damage is thus possible.

This will acilitate ease of project assessment and planning for urban tunnelling projects including choice of tunnel alignment, construction methods and the contractual environment.

NUMERICAL MODELLING OF SETTLEMENT DAMAGE DUE TO

TUNNELLINGTowards a new damage assessment method

A presentation describing a DPhil Thesis in progress John Pickhaver

University of OxfordDepartment of Engineering Science

Documents

Tunnelling Jan 2004