10 - ground movements

16/05/2012

1

GM 1 Design Issues for Tunnels

Requirements for tunnelling The first requirement for tunnelling is that the tunnel is able to be built:

- advancing the hole safely; - maintaining the integrity of the opening both temporarily and permanently.

A second requirement is that tunnel construction does not damage adjacent or overlying buildings or utilities:

- preferred the techniques reducing the disturbance of the surrounding ground.

A third requirement is that it is capable of withstanding the external loads during its lifetime. The actual stresses in the permanent lining are determined prevalently:

- by the details of the method of construction; - by the sequence of the construction events; - by the behaviour of the surrounding soil during the construction period.

Ground Movements

GM 2 Ground Movements

The primary components of ground movement associated with shield tunnelling in soft ground are:

Sources of ground movement around the excavation

1. deformation of the ground towards the face resulting from stress relief;

2. radial ground movements due to the passage of the shield, possibly due to an overcutting edge (bead) used to help steeering combined with any tendency of the machine to pitch, yaw and roll (when trying to maintain the alignment);

3. tail void due to the existence of a gap between the tailskin of the shield and the lining;

4. deflection of the tunnel lining as it starts to take the ground loading;

5. time dependent consolidation in fine grained soils or creep.

(Mair & Taylor, 1997; Cording,1991)

In case of excavation without a shield ( e.g. NATM) the sources 1, 4 and 5 are present.

16/05/2012

2


It is important wih open face tunelling method For TBMs with pressurised face, such ad EPB Shield sor Slurry Shields, is negligible, provided a good control.

Stress relief at the face

ground loss at front

shield

permanent lining

backfill injections

Over-pressurization at the face can lead to outward movements heave at ground surface.

This component is in part due to the tapered shape of the shield. It can increases if there is difficulty in keeping the right alignment of the shield (for instance in curve) or if there is a need to tilt the shield slightly up to prevent it from diving (pitching).

Radial ground movements

pitch angle

taper

Tail void

The effect of tail void can be minimized by immediate grouting.


It is usually small compared to the other components, once the ring has been competed.

Deflection of the tunnel lining

Consolidation

It can be important for soft soil. It results from the fact that the construction process changes the stress regime locally around the tunnel. The dissipation of the pore pressure changes induced by the undrained excavation is a primary source of time-dependent settlement.

Another source of delayed settlement may be the change of pore pressures due to a draining effect of the tunnel in case of permeable lining.

Creep may be a further cause of delayed settlement.

16/05/2012

3


Surface trough

v

u w

y

z

H=z o

w max x

trough extent

For shallow tunnels in soft ground, these movements affect the ground surface, producing a settlement trough . This is particularly relevant in urban areas.

Importance of assessing ground movements to optimize the tunnel technique or to adopt measures to prevent or control them.

Semi-empirical methods, based on a large collection of measurements from case studies, are a simpler and reliable alternative to numerical methods:

allow a rapid initial estimate of ground displacements; provide a conservative risk assessment of potential damage to structures; for flexible structures such as long masonry walls at the ground surface, interaction effects may bevery low realistic results from empirical methods.

GM 6 Empirical Method

Peck (1969) and Schmidt (1969) first established that the greenfield profile in the transverse section of the tunnel is well described by a Gaussian distribution curve.

Transverse profile of settlements

x/i -3 -2 -1 0 1 2 3

-1.0

-0.5

w/w max

inflection point

w = wmax Hexp(-x2/2i2)

By integrating the curve, the volume of the settlement through (per metre lenght of tunnel) is:

maxS wi2V Selecting the values of: Vs and i

16/05/2012

4

Empirical Method

Case Study

Measured settlements along the cross section of Naples Metro Line 1 First Tunnel

(Bilotta et al. 2005)

GM 7


According to Attewell an Woodman (1982) and Attewell et al. (1986) the profile of settlements in longitudinal direction can be represented by the Cumulative Gaussian Distribution function (or complementary error function)

Longitudinal profile of settlements

y/iy

-3 -2 -1 0 1 2 3

0.5

1.0 w/w max

yymax i2

y

2

1

i2

y

2

1

w

werfcerf1

Such a profile is close to that which can be caused by an unsupported cavity.

16/05/2012

5


Depending on the kind of ground and excavation technique the source of ground movement can be further back from the face and this leads to a profile of settlements which complies with a translation of the cumulative curve.

Longitudinal profile of settlements

y/i

-3 -2 -1 0 1 2 3

0.5

1.0

w/w max

w = w max F(y/ i )

0.2

0.4

closed shield (e.g. sand or soft clay)

open shield (e.g. stiff clay)

Although it is a common assumption that iy=ix=i, many experimental measurements show that iy is generally higher than ix.

-2

0

2

4

6

8

10

12

14

16

-40 -30 -20 -10 0 10 20

distance from the tunnel face (m)

wm

ax (

mm

)

L13

L15

L17

L19

L21 L23

Empirical Method


Case Study

Measured settlements in the longitudinal section of Naples Metro Line 1 First Tunnel

GM 10

16/05/2012

6


Clough & Smith (1981)

Estimating the trough width parameter i

10

n 0.8

D

z2K

D

2in

o

K = 0.5

1 2 3 5

z o / D

1

10

2

3

5

0.5

2 i / D

z o

i

D

Sand above the groundwater

Sand below the groundwater

Clay

Sand above the groundwater

Soft Clay

Stiff Clay

OReilly and New (1982) oKzi

(n = 1)

K = 0.6 to 0.7

K = 0.4 to 0.5

K = 0.2 to 0.3

The parameter is largely independent of the tunnel construction technique.

If C/D>1


Estimating the trough width parameter for layered ground

Tunnels are often constructed in ground which comprises layers of coarse and fine graded soils. Selby (1988) and New and O Reilly (1991) suggested that in this case the trough width parameter can be estimated as:

ii

izKi

Field observations of surface settlement profiles of stratified soils where sand is overlain by a clay layer indicate wider profiles than would be obtained if the tunnel were only in sand (according to the equation). Less evidence is available of sand overlying clay, where the narrowing predicted by the equation has not been observed (e.g. Grant and Taylor, 1996).

16/05/2012

7


Volume loss

The volume of the settlement trough, VS, must be estimated. This value will depends on the ground movement components caused by the excavation. They occur mainly around tunnels during construction GROUND LOSS or VOLUME LOSS, VL.

Volume loss is usually referred to as a percentage of the excavated volume of tunnel, VT: V (%) = VL/VTH100

If the excavation occur in undrained conditions, such as in clay, the volume of the ground above the tunnel does not change and it can be assumed: VS = VL

For over consolidated clays, Dimmock and Mair (2007) propose: V (%) = 0.23 e 4.8LF (for LF 0.2) where LF=N/Nc


In coarse grained soils the excavation is performed in drained condition. Hence, volumetric strain may occur.

Deformation field between the excavation and the ground surface

1 0

0 3

1

-1 -2 -4

-0.5

0

Shear strain (%)

Volume strain (%) + dilatancy

3

1

1

16/05/2012

8

Coarse-grained soils

(Attewell , 1977)

Volume loss in drained conditions

Empirical Method

In coarse grained soils the volume of the settlement trough VS is generally lower than the volume loss VL, due to dilatancy.

Suggested trough parameters

Empirical Method

The selection of the volume loss value is based on engineering judgement and experience from previous project in similar ground.

ground excavation parameter K volume of trough technique (i = KHzo) VS (%)

stiff clay open shield 0.4-0.5 0.5-3.0 (1-2) NATM/SCL 0.5-1.5

glacial deposit open shield 0.5-0.6 2.0-2.5 compressed air TBM 1.0-1.3

soft silty clay compressed air TBM 0.6-0.7 2.0-10 (su=10-40kPa)

sand above GW 0.2-0.3 1.0-5.0

sand below GW STMs/EPBs 0.4-0.5 1.0-10 VS 0.5% (ITA/AITES, 2007)

16/05/2012

9

Mixed face conditions or discontinuities

Empirical Method

For TBM excavation in complex conditions a matrix approach for assessing the trough parameters has been proposed by Chiriotti et al. (2001). According to the Authors, in the table VL=1% is assumed as a reference value for homogeneous conditions (soil-like material), mainly depending on ground loss around the shield. Should this value be changed, all the rest have to be changed accordingly.


Trough width below the ground surface

In urban areas there is often the need to estimate the settlements below the ground surface. Gaussian profile can also reasonably approximate the subsurface settlement profiles, provided that the narrowing of the settlement trough with depth is well modelled.

z)K(zi o

According to Mair et al. (1993), the parameter K is not constant with depth, to get a more realistic wider subsurface trough at depth. For clay they propose:

0

0

zz1

zz10.3250.175K

Moh et al. (1996) have proposed a slightly different formulation for i(z):

m

0

0

0.8

0

z

zz

D

z

2

Dzi

with m=0.4 for silty sand and m=0.8 for silty clay (in the latter case it corresponds to substitute (z0-z) to z0 in the expression by Clough & Schmidt, 1981)

16/05/2012

10


Horizontal displacements

In the transverse direction to the tunnel construction, the surface (and subsurface) horizontal displacements can be estimated by various assumptions. The simplest is to assume that the ground movement are radial, i.e. directed toward the tunnel axis.

0z

xwu

2

2

x

2imax

0 0

x xu(x) w(x) w exp

z z

max u(x) occurs at x=i


Horizontal strains

Simply by derivation of the horizontal displacements the horizontal strain can be calculated.

No strain point occurs at x=i

h

d(x) u(x)

dx

16/05/2012

11


Horizontal displacements

Based on experimental evidences, Taylor (1995) proposed that the vector of displacement does not point to the tunnel axis but to a point below the tunnel axis.

w

z 0.325

0.1751

xu

0


Long term settlements

Hurrel (1984) proposed that the long term settlement can be calculated by superimposing to the short term settlement, two consolidation troughs centered at the sides of the tunnel axis. He proposed an empirical formula to evaluate the long term settlement as a function of the short term settlement and the overload factor N.

The maximum settlement may be 2 to 4 times larger than the short term. The width parameter may be 1 to 2.5 times larger. Work in this area is still continuing (e.g. Wongsaroj et al. 2007)

16/05/2012

12

Empirical Method

Multiple tunnels

Measured settlements along the cross section of Naples Metro Line 1 First and Second Tunnel


According to Hansmire & Cording, 1985, interaction between two tunnel excavation occurs when the distance between the two tunnel axes is about two diameters, as in this case.

GM 23

Empirical Method

Limit of the empirical method

GM 24

The empirical method for predicting ground movements induced by tunnelling is generally suitable for:

greenfield conditions;

single tunnels of multiple tunnels without interaction;

homogeneous ground conditions;

in clay, undrained conditions (not reliable for consolidation settlements post construction).

A further limitation of the empirical method is that good judgement is required in the selection of an appropriate value ov volume loss.

However the method has a particular high practical value in cases where previous tunnelling in similar ground conditions and with similar construction techniques has been performed.

16/05/2012

13

The method by Sagaseta (1987) is based on the elastic solutions, assuming =0.5.

a

Sagasetas Method GM 25

Real case

Surface

Sink

Step 1 Infinite medium

Surface (ignored)

Sink

Step 2 Image Sink/ Source

Step 3 Surfaces Stresses

Solution = 1 + 2(a) + 3(a) = 1 + 2(b) + 3(b) = Real Problem

(a) Negative image (paved surface)

(b) Positive image (suspended surface)

Surface(ignored)

Sink Sink

Sink image

Surface (ignored)

Source image

s = 0 t = 0

s = s o t = t o

s = - s o t = t o

s = s o t = - t o

2 t o

2 s o

(a) (b)

If the soil is incompressible (no volume change, e.g. undrained conditions) v=0, regardless the constitutive model.

If for any reason the direction of the displacement vector is known at each point, this equation, with the appropiate boundary conditions, is sufficient to determine the dispalcement field.

Concentrated ground loss

The basic case considers the action of a point sink which extracts a finite volume of soil at some depth h below the top surface.

Displacement field due to a sink

For plane strain n=2

For 3D conditions n=3

rr

r

Step 1 + Step 2(a) (paved surface) Step 3(a)

(Cerrutis solution)


Procedure to work out the solution

16/05/2012

14


Displacements at ground surface in trasverse section

D is the tunnel diameter

h is the tunnel axis depth

V is the volume loss, to be determined (on empirical basis or in correlation with overload factor N)

22

2

22

2

hx

h

4

DV'w

hx

x

4

DV'u


Displacements at ground surface in longitudinal direction

22222

2

222

2

22222

2

hyx

y1

hx

h

4

DV'w

hyx

1

4

DV'v

hyx

y1

hx

x

4

DV'u

As the main interest is the movement at the ground surface, the ground loss can be concentrated at the tunnel axis.

16/05/2012

15


Caracas Metro. Profile of calculated and measured displacements at surface (Oteo & Sagaseta, 1982)

San Francisco (plastic clay): development of surface settlements

(weathered scists)

Case histories and calculations limit of the method

Although the ratio between the horizontal and vertical displacements is similar to what can be obtained by the empirical method, the width of the settlement through is much higher than the real.

limit of trivial linear elastic analysis

Verruijt and Bookers Method GM 30

Compressible ground and Ovalization

Verruijt and Booker (1996) extend the solution of Sagaseta by considering the ground compressible (0.5) and taking into account ovalisation (the latter through a parameter )

222

222

22

20z

)h(x

)hh(x

2

D

hx

h)(1D w

/2V'

The total area of the settlement trough is found by integrating the equation:

For =0.5 it corresponds to Sagasetas. Otherwise the area is larger than ground loss.

2D2

V')(1A

settlement due to ovalization

settlement due to ground loss

ovalization ground loss

Although ovalisation of the tunnel may be an explanation for the rather narrow settlement troughs usually observed in practice, it does not seem an important issue for e.g. TBM excavation.

16/05/2012

16

pGGAP

GAP Parameter GM 31

The GAP parameter to simulate the undrained loss of ground

Lo and Rowe (1982), Rowe and Kack (1983) and Lee et al. (1992) proposed an approach to define the undrained ground loss based on a GAP parameter.

*3Dp uGGAP

The method is based on the results of a 3D FE analysis on an elastic perfectly plastic soil: Eu/su =200 to 800, =20 kN/m

3, H/D=1.5 to 4.

The method can be used to predict the ground loss to be used in 2D FE analyses or with empirical correlations.

uGGAP *3Dp

GAP Parameter GM 32

Physical gap Gp

The physical gap represents the geometric clearance between the outer skin of the shield and the lining. It is cmposed of the thickness of the tail, , and the clearance required for the installation of the lining inside the shield, :

2Gp

16/05/2012

17

GAP Parameter GM 33

Equivalent 3D ground loss at the tunnel face

The tunnel heading face loss can be simulated in a plane strain analysis by increasing the maximum allowable radial displacement at the tunnel crown.

2

2*3D

x

x2f a

2

ua

kaV

Assuming the step of advanced x=2a and the a uniform front inward displacement (k=1): 2

u x*3D

The displacement x was calculated in the 3D analyses and represented as:

Twvox

o

x

uKa

E

aP

E

ss

'

GAP Parameter GM 34

Ground losses over the shield

This corresponds to the volume of soil that is displaced in excess to the diameter of the cutting shield.

The main source of such a radial component of displacement are the alignement problems encountered when steering the shield, e.g. the excess pitch: pitch L

Any other irregular motion (e.g. yawing) is source of similar ground loss

the overcutting problem is primarily related to workmanship and cannot be precisely determined prior to construction

On the basis of 3D analyses of unlined tunnels (overcutting can be considered a temporary unlined excavation over the shield) the Authors assume:

PG0.6

If the shield is tapered or a bead is provided to reduce friction during advance, an extra gap of width t is created, then:

tG0.6 P

16/05/2012

18

Loganathan and Poulos Method GM 35

Ground loss

Loganathan and Poulos (1998) redifined the ground loss with respect to the GAP parameter.

Equivalent undrained ground loss around the tunnel:

2

2

2

2

04R

GAPRGAP4

R

R2

GAPR

The non-uniform radial movement around the tunnel influences the deformation pattern of the surrounding soil. Hence, the contribution to the equivalent ground loss at the tunnel boundary is not constant in the ground, but at any point (x,z) it can defined as:

22 zx ee DA0x,z CB

The constants A and B are derived assuming that 75% of the ground loss occurs on the upper tunnel arch and is cumulative of the deformation in a wedge of soil reaching the ground surface.

The constant C and D are derived assuming that the component of ground loss due to the horizontal movement at a distance x and a depth H is 50% of that at surface.


Surface settlements

the solution by Verruijt and Booker (1996) was modified, also neglecting the long term ovalization :

2

2

2

2

2

2

x,zH

0.69z

RH

1.38xexp

4R

g4gRSince

GAPg

22

2

2

2

2

2

0zxH

HD 1

RH

1.38xexp

4R

g4gRw

It follows that the trough width i reads:

0.9

2R

H1.15

R

i

Such a value is somewhat higher than that estimated by the empirical relationships proposed by Clough and Shmidt (1981) and Mair et al. (1981). However the settlement trough is narrower than that by Sagaseta (1987) or Verruijt and Booker (1996).

16/05/2012

19


Subsurface settlements and horizontal displacements

Case Study: Thunder Bay Tunnel (Ontario)

222

22

2222

2

2

2

2

2

2

2

Hzx

Hzx2z

Hzx

Hz43

Hzx

H-z

4

D

H

0.69z

RH

1.38xexp

4R

g4gRw

2222222

2

2

2

2

2

2

2

Hzx

Hz4z

Hzx43

Hzx

1x

4

D

H

0.69z

RH

1.38xexp

4R

g4gRu

1

Numerical Methods GM 38

The benefits of the numerical methods ove analytical or closed form solutions are (Potts and Zdravkovic (2001):

simulate the construction sequence;

deal with complex ground conditions;

model realistic soil behaviour;

handle complex hydraulic conditions;

deal with ground treatment;

account for adjacent sevices and structures;

simulate intermediate and long-term conditions;

deal with multiple tunnels.

General issues

Although tunnelling is a three-dimensional problem, 2D analyses are stil very common.

There are a number of ways to represent a three-dimensional phenomenon (e.g. 3D arching) in a 2D plane strain analysis.

16/05/2012

20


A predefined void is introduced into the finite element mesh that represents the total volume loss expected.

The gap is greatest at te crown of the tunnel and zero at the invert (Rowe et al. 1983)

GAP method

This is the most suitable method for tunnels excavated without a shield (e.g. NATM).

The proportion of unloading of the ground before the installation of the lining construction is prescribed: the volume loss is a predicted value.

The parameter (Panet and Guenot, 1982) is used to define stress release.

Convergence-confinement method


It is similar to the convergence-confinement method: the expected volume loss at the end of construction is prescribed. The support pressure at the tunnel boundary is reduced in increments and the generated volume loss can be monitored. Once the prescribed value is reached the lining is installed. Further deformation may occur depending on the lining stiffness.

Volume loss control method

It was developed for NATM tunelling by Swoboda (1979). The method involves reducing the ground stiffness in the heading by a certain amount. The lining is installed before the modellede excavation is complete. This method can cope with crown and invert construction or side drifts.

Progressive softening method

16/05/2012

21


When modelling the process of tunnelling to predict the displacement field induced by the excavation, the choice of the constitutive law for soil is very important.

In particular the following features of the stress-strain behaviour of soil should be taken into account:

non-linearity;

anisotropy of the elastic matrix;

small strain stiffness;

recent stress history.

Important issues

D = 4.5 m @ real scale

(Cam Clay)

(Lee & Rowe, 1989)


Anisotropy of the elastic matrix

The ratio Eh/Ev has a small influence

Cross-anisotropic elastic matrix:

Eh, Ev, vh, hh, Gvh

vh/hv= Ev/Eh

Ghh = Eh/2(1+hh)

Settlement prediction is very sensitive to Gvh

16/05/2012

22

(Addenbrooke et al, 1997)

Model J4 (Jardine et al., 1986) and Model L4 (Burland e Puzrin, 1996): both are elastic non-linear isotropic perfectly plastic models. Both are able to model stiffness decay with the strain level.

Non linearity + Anisotropy

Non-linearity

AJ4: model J4 + anisotropic elastic matrix AJ4i Gvh as measured by lab tests AJ4ii considerably lower than lab tests


Anisotropy vs non linearity of the elastic matrix

(Mair, 1993)

Model 3-SKH (Stallebrass, 1990) is able to account for the dependency of stiffness on the strain level and the recent stress history (cf. different relative position of bubbles in the stress space). Very different settlement pattern are predicted, depending on the assumed recent stress history.


Influence of recent stress history (Jovicic, 1994)

16/05/2012

23

(a)

(b)

(c)

Anisotropic linear

elastic pre-yield model

Isotropic non-linear





Influence of the primary stress state (Addenbrooke et al, 1997)

The effect of the ratio K0 can be such to hide the combined effect of anisotropy and non-linearity of the elastic matrix.

(a)

(b)

(c)

Anisotropic linear






Ko = 0.5

Ko = 1.5

For instance, to model 3D stress rearrangement around the heading in a 2D analysis, in a OC soil the initial K0 may be arbitrarily reduced around the tunnel cavity.

Effects of tunnelling on structures GM 46

Deformation pattern of buildings due to tunnelling in soft ground

The impact of ground movements on structures depends on the size, shape and material of the structure, as well as its position relative to tunnel.

Short buildings tend to rise the forward settlement wave. They experience tilt as a rigid body, not sagging or hogging.

A stiff long building experiences progessive deformation and differential settlements as far as the tunnel heading advances.

A long building may sag or hog across the transverse settlement trough, depending on its relative position to the tunnel axis.

(Attewell, 1995)

16/05/2012

24


Effects of tunnelling on piled foundations

Studies on both small scale models and full-sale field monitoring indicated that there are zones of influence that affect the pile in different ways depending on their relative position to the tunnel.

Piles settle more than ground surface in zone A, less in zone C, of the same amount as ground in zone B.

Piles in zone A experience a considerable reduction in their base loads during tunnelling.

(a) Settlement s, relative settlement s, rotation , angular strain ;

(b) Relative deflection and deflection ratio /L;

(c) tilt and relative rotation (or angular distorsion) .


Definitions of the foundation movements

The average horizontal strain h is defined as the change of length L over the length L

(Burland and Wroth, 1974)

16/05/2012

25


Relevant building dimensions

The height H is taken from the foundation level to the eaves (i.e. the roof is usually ignored).

The building can be divided in two parts, each at a side of the point of inflection of the settlement profile at the foudation level.

The length of the building is not considered beyond the practical limit of the settlement trough (for a single tunnel it can be taken as 2.5 i).

In calculation of building strain, the building span length is defined as the length of building in a hogging or sagging zone (Lh or Ls).

0.5B

(Potts & Addenbrooke, 1997)


Effect of the building stiffness on the settlement profile

Potts & Addenbrooke (1997) carried out a parametric study of the influence of building stiffness on ground movemnts induced by tunnelling using FE analyses with a non-linear elastic-plastic soil model.

The building was represented by an equivalent beam with EA and EI.

The axial stffness * and bending stiffness * are defined as:

4ss

B)(0.5EEI/*

B)(0.5EEA/*

16/05/2012

26

(Potts & Addenbrooke, 1997)


Modification factors

On the basis of their study, Potts & Addenbrooke (1997) proposed modification factors for deflection ratio DR (or /L) in sagging and hogging.

Similar charts were produced for h.

4s B)(0.5EEI/*

The inherent stiffness of the building is often such that its foundations will interact with the supporting ground, tending to reduce both the deflection ratio and the horizontal strains.


Relative stiffness parameters for masonry load bearing walls

The building can be modelled by an elastic beam located on the ground surface. It has a Youngs modulus E, a second moment of area I and cross sectional area A. The length of the beam, L, is assumed equal to the full length of the building faade, B. The height of the beam is H, its thickness t.

4swallswall

B)(0.5E/EI*

B)(0.5E/EA*

12

HtI

3

wall

HtAwall

Hence:

In hogging, due to the inability of the masonry in the upper part of the wall to withstand significant tensile stresses, the neutral axis is likely to be nearer to the foundations (Mair et al, 1996). Dimmock and Mair (2008) suggest therefore to estimate the relative bending stiffness in hogging by considering the foundation only (thickness d) as opposed to the full height of the faade, H.

12

dtI

3

foundation

16/05/2012

27

(Franzius, 2003)


Relative stiffness parameters for framed structures

The building can be modelled by an elastic beam located on the ground surface. It has a Youngs modulus E, a second moment of area I and cross sectional area A. Assume a concrete frame structure consisting of a certain number of storeys. m storeys m+1 slabs

4sbuildingsbuilding

B)(0.5E/EI*

B)(0.5E/EA*

The second moment of area for the equivalent single beam can be calculated using the parallel axis theorem (Timoshenko, 1955) assuming the neutral axis to be at the mid-height of the building (smooth base).

12

1tI

3slab

slab

1tA slabslab

1m

1

2mslabslabcbuilding hAIEEI

Where hm is the distance between the building neutral axis and the slab neutral axis.

The axial stiffness is given by:

slabcbuilding AE1mEA

Hence:


Relative stiffness parameters for masonry faades with openings (Pickhaver, 2006)

This approach assumes appropriate bending and shear stiffness for the beam considering openings, by investigation of geometric properties A and I. It differs from the approach of Burland and Wroth (1974) who note that differing amounts of openings may be allowed for by manipulation of the ratio E/G directly. This approach (Pickhaver, 2006) results in a better assessment of equivalent stiffness when the percentage of opening is high and dominates the behaviour. Determination of appropriate effective values, A and I from the geometry of any given faade A from consideration of shear:

n vertical strips of net cross section Ai and length Li

I from consideration of bending:

n horizontal strips of height hj and thickness t. bj is the distance to the neutral axis

n

1ii

i

A

L

LA*

n

1j

2jj

3j bht

12

htI*

G*A

FLVs

16/05/2012

28


Case study 1: Elizabeth House (Mair & Taylor, 2001)

The EB and The WB tunnels (5.6 m diameter) were constructed with NATM. Then a 5.6 m-diameter crossover tunnel was constructed connecting the two running tunnels. It was located beneath the Elizabeth House. The largest span of the excavation was 12.4 m.

The largest eccentricity of the building to the tunnel is e/B1 but it reduces rapidly in a north-east direction along the building.



The building can be modelled as follows: HB = 12*3.5+1.4 = 43.4 m B = 18 m ILB slab = 1.4

3/12 = 0.23 m4/m I slab =0.3

3/12 = 2.3H10-3 m4/m

Assume (EI)building=E Islab (i.e. neglect infill walls contribution) Take Econcrete = 23 Gpa (EI)building = 23H106 (13H2.3H10-3 + 0.23) = 23H106H0.26 6 H106 kN/m

Tunnel axis depth 23 m below LB floor slab i.e. approx. 30 m bgl. At 18.5 m bgl E0.01% 180 MPa Taking into account only LB, B and ground floor slab: Considering e/B 0.4:

13

43

6

m105910180

106*

28.1910180

0.3)2(1.41023*

3

6

0.2M

0.2MDRhog

DRsag

In a transverse direction the building behaves almost rigidly, with negligible /L.

16/05/2012

29



In longitudinal direction: Assume B = 50 m Considering e=20m, e/B 0.4:

15

43

6

m1082510180

106*

10.12510180

0.3)2(1.41023*

3

6

1M

0.8MDRhog

DRsag

In a longitudinal direction the building behaves almost perfectly flexibly.


As the building was relatively flexible in longitudinal direction, it tent to follow the greenfield profile of settlement .

Influence of the building stiffness on the settlement trough

Jubilee Line Extension: settlements of Elizabeth House

(Standing, 2001)

16/05/2012

30

Estimate height of load-bearing brickworks walls to be 9 m. Assume B = 39 m. Assume foundations are strip footings founded at approx. 1.5 m bgl. Depth of tunnel axis is 17 m bgl. At z = 10 m, E0.01% 200MPa E for masonry lies between 5 and 10 GPa: take 7.5 GPa.


Case study 2: Neptune House (Mair & Taylor, 2001)

The EB and The WB tunnels were constructed by EPB (5.03 m OD). They passed under a group of masonry buildings among which the Neptune House, a 3-storey building, 39 m 8 m in plan. Both tunnels were approx. perpendicular to its long dimension.

The building behaves rigidly for any value of e/B.

12

43

63

m106119.51020012

107.591*

.

e/B any for

0.2M

0.2MDRhog

DRsag

31719.510200

107.591*

3

6

.


Since the building is relatively stiff it changes the settlement trough, showing a rigid deformation.

Influence of building stiffness on the settlement trough

sett

lem

ent

(mm

)

distance from 5031 (m)

greenfield prediction

stiff building

measured 26.07.96

Jubilee Line Extension: settlements of Neptune House

(Mair, 2001)

16/05/2012

31


Cracking of a simple beam in bending and in shear (Burland & Wroth, 1974)

The building is represented by a rectangular beam of length L and height H. The problem is to calculate the tensile strains in the beam for a given deflected shape of the building foundations and so obtain the sagging or hogging ratio /L at which cracking is initiated. Little can be said about the distribution of strains within the beam unless its mode of deformation is known: two extreme modes are bending only about a neutral axis at the centre and shearing only. In bending only, the maximum tensile strain occurs in the bottom extreme fibre, which is where cracking will initiate. For shear only, the maximum tensile strains are inclined at 45, initiating diagonal cracking.


(Burland et al., 1977)

This classification provides 6 classes, on the basis of the ease of repairing plaster and brickwork or masonry walls.

Classification of visible damage to walls

categories 0, 1 & 2 relate to aesthetic damage;

categories 3 & 4 relate to serviceability damage;

category 5 represents damage affecting stability.

Most buildings experience a certain amount of cracking, often unrelated to foundation movement, which can be dealt with during routine maintenance and decoration. If an assessment of risk of damage due to ground movement is to be made, the classification of damage is key.

16/05/2012

32



Class 1 -2 (very slight or slight) Fine cracks which are easily treated during normal decoration / Cracks easy filled

Class 3 (moderate) Some brickwork requires replacing above and below windows



Class 4 (severe) Some loss of bearing in beams. Replacing sections of walls, especially over windows

Class 5 (very severe) Instability, complete rebuilding required

16/05/2012

33

Timoshenko (1957) gives the expression for the total mid-span deflection of a centrally loaded beam having both bending and shear stiffness as:


Relationship between (/L) and

Where E is Youngs modulus, G is the shear modulus, I is the second moment of area and P is the point load. The equation can be re-written in terms of the deflection ratio /L and the maximum extreme fibre strain bmax as follows:

where t is the distance of the neutral axis from the edge of the beam in tension. Similarly, for the maximum diagonal strain dmax, it becomes:

Similar expressions are obtained for the case of a uniformly distributed load. Therefore, the maximum tensile strains are much more sensitive to the value of /L than to the distribution of loading.

HGL

18EI1

48EI

PL

2

3

maxb,G

E

2tLH

3I

12t

L

L

maxd,

2

E

G

18I

HL1

L

maxb,G

E

2tLH

3I

12t

L

L

maxd,

2

E

G

18I

HL1

L

Rectangular isotropic beams with the neutral axis at the bottom edge


Relationship between (/L)/lim and L/H By setting max = lim, the two equations define the limiting values of /L for the deflection of simple beams. In general, both modes of deformation will occur simultaneously and it is necessary to calculate both bending and diagonal tensile strains to check which type is limiting L/H, E/G, position of neutral axis

16/05/2012

34


Relationship between category of damage and limiting tensile strain

(Boscardin & Cording, 1989)

Boscardin and Cording (1989) introduced two important advances: 1. The influence of horizontal ground strain h was added to the beam model of Burland and

Wroth by simple superposition. They then developed an interaction diagram relating angular distortion (2/L) and h for different categories of damage.

This interaction diagram strictly relates only to L/H = 1 for a hogging mode of deformation

Category of Degree Limiting tensile damage of severity strain, lim (%) 0 negligible 0 - 0.05 1 very slight 0.05 - 0.075 2 slight 0.075 - 0.15 3 moderate 0.15 - 0.3 4-5 severe to very severe > 0.3


Relationship between category of damage and limiting tensile strain

(Boscardin & Cording, 1989)

2. From their work it is possible to assign a range of values of limiting tensile strain lim to

the different categories of damage defined by Burland et al (1977). This may introduce a serviceability approach.

16/05/2012

35


Superimposition of the horizontal ground strain

It is assumed that the deflected beam is subjected to uniform extension over its full depth. The resultant extreme fibre strain br is given by:

In the shearing region, the resultant diagonal tensile strain dr can be evaluated using the Mohrs circle of strain.

The value of dr is then given by:

where is Poissons ratio. The maximum tensile strain is the greater of br and dr. Thus, for a beam of length L and height H, the maximum value of tensile strain max for a given value of /L and h can be computed in terms of t, E/G and . This value of max can then be to assess the potential associated damage.

hmaxb,br

2maxd,

2hhdr

2

2

1

2

1

h h-

/2

maxd,dr

/L= 0 h=lim

shear bending


(Burland, 1997) Superimposition of the horizontal ground strain

bending + shear

As h increases towards the value of lim, the limiting values of /L for a given L/H reduce linearly, becoming zero when h = lim.

As h increases, the limiting values of /L decrease non-linearly at an increasing rate towards zero.

16/05/2012

36

L/H=1


Relationship of damage category to deflection ratio and horizontal tensile strain for hogging

By adopting the values of lim associated with the various categories of damage (serviceability approach), an interaction diagram can be developed showing the relationship between /L and h for a particular value of L/H.


Relationship of damage category to deflection ratio and horizontal tensile strain for hogging

(Pickhaver, 2006)

To determine the deflection ratio (/L) to apply to each faade to achieve a level of damage, interaction charts for each value of L/H for the masonry faades can be produced using the same approach as Burland (1997).

16/05/2012

37


Evaluation of risk of damage to buildings due to subsidence (Burland, 1995)

Preliminary assessment It is based on a consideration of both maximum slope and maximum settlement of the ground surface at the location of each building. According to Rankin (1988), a building experiencing

maximum slope of 1/500 settlement of less than 10 mm

has negligible risk of any damage. By drawing contours of ground surface settlement along the route of the proposed tunnel and its associated excavations it is possible to eliminate all buildings having negligible risk.

Since in calculating the tensile strains, the building is assumed to have no stiffness so that it conforms to the greenfield site subsidence trough, this approach is usually still very conservative.



Second-stage assessment After having identified those buildings along the route requiring further study, in a second-stage assessment the faade of a building is represented by a simple beam whose foundations are assumed to follow the displacements of the ground in accordance with the greenfield. The maximum resultant tensile strains are calculated, if necessary partitioning the building, and the corresponding potential category of damage, or level of risk, is then obtained.

16/05/2012

38



Second-stage assessment with relative stiffness approach The inherent stiffness of the building can be considered at this stage by making use of the charts by Addebroke and Potts (1997), obtaining more realistic predictions.



Detailed evaluation Detailed evaluation is carried out on those buildings that, as a result of the second-stage assessment, are classified as being at risk of category 3 damage or greater. Because each case is different and has to be treated on its own merits it is not possible to lay down detailed guidelines and procedures. Particular attention should be paid to the previous movements experienced by the structure for different causes, as they may reduce the tolerance of the building to future movements .

16/05/2012

39

Protective Measures GM 77

Types of protective measures

Various methods are used to protect both surface and subsurface structures from the effects of ground movements generated by tunnelling. First of all: make sure that the structure is outside the zone of significant ground movements. Consideration of ground movements within the design process can influence the location and layout of stations and tunnels. Tunnel alignment design is therefore considered to be a form of protective measure.

Another method of reducing the impact of ground movements on an overlying structure is specifying the tunnel construction sequence.

Once the geometry of the stations and tunnels is fixed and the potential damage assessment has identified the need for protective measures, the available protective measures can be considered in three categories:

In-tunnel measures: actions taken from within the tunnel during its construction;

Ground treatment measures: methods for improving the engineering response of the ground;

Structural measures: methods increasing the capacity of the structure to resist/accommodate ground movements.


In-Tunnel measures

Reduce at source the magnitude of movements or distortions attributable to volume loss.

In general, where the ground is capable of supporting itself during excavation, advantage is taken of this property by tunnelling in open-face conditions. There is then the possibility of undertaking measures to reduce movements from within the tunnel, which include:

face support measures; excavation in parts; pilot tunnels; barrel vaulting; mechanical pre-cutting .

16/05/2012

40

(Maiorano e Viggiani, 2003)

Line 1 Naples Underground

Excavation of a chamber in pyroclastic soil where two running tunnels converge.

Above there is a 3-storey building.

The chamber roof is about 20 m deep.

Actions:

pilot tunnel;

jet-grouting forepoles;

chemical and grout injections in radial longitudinal directions.


In-Tunnel measures

ground improvement;

compensation grouting;

ground reinforcement.

permeation grouting soil compaction soil replacement freezing ...


Ground treatment methods

Improve the mechanical behaviour of the ground (stiffness).

16/05/2012

41


Compensation Grouting It is defined in the current practice as the introduction of a medium to high viscosity particulate suspension into the ground between a subsurface excavation and a structure, in order to negate or reduce the settlement of the structure due to ongoing excavation (Littlejohn, 2003).

Corrective compensation grouting It is triggered when a threshold value of settlement or distortion of the structure is measured. Concurrent compensation grouting It is be adopted during the excavation following a pre-determined plan to limit the occurring settlement or distortion to a given value. Sometimes, a pre-treatment grouting (cement or chemical injections) is adopted to stiffen the soil and set up the fracture system before the actual compensation.

Careful positioning Observational approach


Tube--Manchettes (TAMs)

Tubes with ports at regular intervals along them are installed and grouted into drillholes.

The grout is injected by inserting a probe into the tube and isolating the port to be injected by inflating packers at either side of the injection nozzle and then applying sufficient pressure to open the port and initiate flow into the ground.

The ports comprise four holes spaced equally around the circumference of the tube and usually covered with a rubber sleeve (the manchette).

16/05/2012

42


Compensation Grouting

Compaction grouting is obtained with sand and silt mortar using large diameter grout tubes and consists in a series of injected bulbs. The term compaction grouting originally was adopted to improve the strength and stiffness of the ground by compaction. However, it has become associated with the controlled injection of a mortar to create an expanding bulb, which displaces loose granular soils.

v

vv

Fracture grouting is obtained by hydro-fracturing the soil with relatively fluid grout injected from tubes--manchettes (TAMs). It forms a sheet of grout frequently only 12 mm in thickness, the extent of which is limited only by the volume of grout injected.

The grouting techniques need to minimise the extent to which grout can penetrate or permeate into the soil structure since filling voids within the ground will not generate displacements.

Fine-grained cohesive soils penetration does not occur, Granular soils a wide range of grout mixes will penetrate the soil.

Actions:

grouting between the excavation and the building.

sLIM: 40 mm

this was exceeded due to dewatering;

(/L)LIM : 1/1000

the deflection ratio of the structure was contained below the permitted value.

(Pototschnik, 1992)

Vienna Underground. A station (30 m wide, 8 m high) was excavated by NATM 12 m beneath a 5-storey building in silty clay.



16/05/2012

43

(Harris, 2003)



Actions:

pre-treament grouting

fracture grouting

Tilt control

Pre-treatment was needed in a layer of gravel to make effective the following fracture grouting.

5 shafts

363 TAMs (10470 m)

27550 injections (2052 m3 grout)

Monitoring

London Underground. Fracture grouting was performed at various locations along the 15.5 km of mainly twin 4.4 m internal diameter tunnels

Westminster Station of Jubilee Line Extension close to the Big Ben.

by stiffening ground by acting as a barrier between the source of the movement and the structure


Ground Reinforcement

Inclusions between the tunnel and the structures to be protected can be used to reduce their movements:

diaphragm walls line of piles

damage to building

16/05/2012

44

Shanghai Observatory. The ancient astronomical observatory, about 50 m high, needed to be protected from the excavation of a shield tunnel with 11 m diameter and 20 m axis depth, passing about 15 m away from the building foundation .

(Chen et al., 1998)


Ground Reinforcement

Actions:

root piles wall to reduce tilt.

Piles about 30 m deep (20 cm diameter), constructed 14 m away from the tunnel axis and capped by a reinforced concrete beam. This beam was tied at its edges by tension cables which extended to the rear of the observatory and was anchored to blocks founded on additional root piles.

assessed tilt: 0.5 to 110-2

measured tilt: 10-3

1.5

10.1

29.1

2 m

10 m

8 m

45

3.6

m

D=8m

Actions:

wall-type jet-grouting reinforcement to reduce the building settlements.

maximum measured settlement in the nearby untreated zones: 10 to 12 mm

maximum measured settlement : ~ 2 mm

(Sola et al., 2003)

Madrid Metrosur.


Ground Reinforcement: barriers

Sola et al. (2003) report: 5 cases of jet-grouting portals, 6 cases of jet-grouting walls, 4 cases of inverted-V treatments which were undertaken along two lines of the Madrid underground.

16/05/2012

45


Ground Reinforcement: barriers

Actions:

two close rows of adjacent jet-grouting columns to reduce settlements. (70 cm spacing between rows, 90 cm spacing between columns in the row).

maximum predicted settlement beneath the building: 7 to 10 cm

maximum measured settlement beneath the building: ~ 5 mm (Oteo et al., 1999)

Madrid French Institute.

A tunnel (8.4 m diameter, 14-15 m axis depth) was excavated by using an EPB shield partly in sand and partly in the overlying 1018 m fill cover. The building of the Institute was only 8-9 m away from the tunnel axis.

Influence of length

Influence of roughness

Influence of thickness

Influence of location

A wall has to be deepened below the tunnel axis;

The offset of the wall is not influencing its effects

No significant influence of the wall thickness

Smooth walls acts like a strong discontinuity in shear stress transmission, thus reducing noticeably ground movements behind them;


Ground Reinforcement: diaphragm wall as a barrier

ThickThin

(Bilotta, 2008)

Small scale (centrifuge) tests and FE analysis shown the influence of several parameter on the effectiveness of a diaphragm wall.

d

t

wEXC

d

t

wEXC

(scale factor N=160)

16/05/2012

46

Influence of weight The wall weight must be limited


Ground Reinforcement: diaphragm wall as a barrier

Provided that the ground loss during the construction is controlled, a diaphragm wall can be effective in reducing settlements, depending mainly on its length, weight and roughness.

The analyses have also shown that it can be effective in reducing horizontal displacements, depending mainly on its roughness and length.

0

0

T

TC

LFs s

s s

+25%

(Bilotta & Taylor, 2005)


-35

-30

-25

-20

-15

-10

-5

0

-40 -20 0 20 40

distance from tunnel axis (m)

se

ttle

me

nt (m

m)

greenfield

s/b=12

s/b=6

s/b=3

continous wall

(Bilotta & Russo, 2011)

pile spacing

Ground Reinforcement: line of piles as a barrier

d

t

wEXC

d

t

wEXC

b

16/05/2012

47

Ground Reinforcement: line of piles as a barrier


0.0%

0.1%

0.2%

0.3%

0.4%

0.0% 0.1% 0.2% 0.3% 0.4%

h

/L

L/H=1

L/H=3.33

greenfield

s/b=12

s/b=6

s/b=4

s/b=3

s/b=2

diaphragm wall0 1

2

3

4 & 5

a) V'=1%

0.0%

0.1%

0.2%

0.3%

0.4%

0.0% 0.1% 0.2% 0.3% 0.4%

h

/L

L/H=1

L/H=3.33

greenfield

s/b=12

s/b=6

s/b=4

s/b=3

s/b=2

diaphragm wall0 1

2

3

4 & 5

b) V'=2.5%

(Bilotta & Russo, 2011)

The efficiency of the protective method is dependent on the spacing ratio. loose piles, s/b=12 to s/b=6: low efficiency and no significant benefits by the reduction of the spacing dense piles,s/b =6 to s/b=2: constant increase in efficiency use of rows of closely spaced piles

Effect on potential damage


Structural measures

Structural measures include a range of techniques to reduce the impact of ground movements. They are applied to the structure to be protected. Their mode of operation can be to:

increase the ability of the foundations to resist the predicted movement; stiffen the structure such that it modifies the predicted movement; make the structure less sensitive so that it can accommodate the anticipated movement; control the movement of the structure by isolating it from its foundation.

Examples are: deep underpinning such that the piles extend below the zone of ground movements and thereby reduce the movements of the structure; increasing the tensile capacity of the structure where this is small or unreliable. This is achieved by installing tension elements such as tie bars or ring beams;

Shallow underpinning techniques

16/05/2012

48


Structural measures

Further examples:

installation of jacks within structural elements to enable the movements of the superstructure to be controlled independently of the foundation; planned maintenance (e.g. railway tracks) or contingency measures (such as propping or repair) to be implemented on the basis of observed performance.

Typical layout of structure jacking

10 - ground movements

Documents

ground movements gm

ground surface

soft ground

surrounding ground

ground loading

face ground loss

sources of ground movement

shield tunnelling