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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
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."
Tunnelling - In the Headlines
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
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
Damage to structuresSurface settlements can cause damage to buildings sited in the settlement trough
Damage can include tilting of the complete building…
Recent Tunnel subsidence eventsAn example of tunnel induced damage: Lavender Street Stratford,
February 2003 - Channel Tunnel Rail Link, London
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.
Stage 2 damage assessment cont…
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
Stage 2 damage assessment cont…
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)
6.2500.75 – 7.5Imposed displacement
A7
9.3750.75 – 7.5Imposed displacement
A5
18.7500.75 – 7.5Imposed displacement
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
Description of current project
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
Description of current project
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.