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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICSInt. J. Numer. Anal. Meth. Geomech., 2005; 29:443–471Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nag.421

Numerical modelling of compensation grouting

above shallow tunnels

C. Wisser1,n,y, C. E. Augarde2 and H. J. Burd3

1Mott MacDonald, Formerly Department of Engineering Science, Oxford University, U.K.2School of Engineering, University of Durham, South Road, U.K.

3Department of Engineering Science, Oxford University, U.K.

SUMMARY

This paper describes the development of a numerical model for compensation grouting which is a useful

technique for the protection of surface structures from the potentially damaging movements arising fromtunnel construction. Pipes are inserted into the ground between the tunnel and the overlaying structurefrom an access shaft. Buildings on the surface are instrumented and movements are carefully monitored.Once the deformations exceed a certain Trigger Level, grout is injected into the ground to prevent damage.In the finite element model described here, compensation grouting is modelled by applying an internalpressure to zero-thickness interface elements embedded in the mesh. An ‘observational algorithm’ is used,where the deformations of the surface are monitored and used to control the injection process. Exampleanalyses of compensation grouting are given for three-dimensional tunnel construction underneath agreenfield site. Different strategies are used to control the injection process and their effectiveness inpreventing surface movement is assessed. The numerical model is shown to replicate general behaviourexpected in the field and is capable of modelling the control of ground surface movements at a greenfieldsite. Copyright# 2005 John Wiley & Sons, Ltd.

KEY WORDS: finite elements; compensation grouting; tunnels

1. INTRODUCTION

Compensation grouting (CG) is a technique for controlling ground movements caused by the

construction of shallow tunnels. A liquid grout is pumped into the ground through narrow tubes

(Tubes !aa Manchette or TAMs) between the advancing tunnel and the ground surface.

Movements occur at the tunnel excavation due to various mechanisms of ground loss. The

intention of the grouting is to prevent any significant movements from propagating to the

surface, thus reducing the likelihood of damage to overlying structures. Successful CG requires

detailed monitoring of surface movements in conjunction with careful control of grout injection.

It is also a relatively new procedure; the first published use of CG to control tunnelling

Received 9 February 2004Revised 15 November 2004Copyright# 2005 John Wiley & Sons, Ltd.

yE-mail: [email protected]

Contract/grant sponsor: EPSRC

nCorrespondence to: C. Wisser, Mott MacDonald, St. Anne House, Wellesley Road, Croydon CR9 2UL, U.K.

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settlements in the U.K. appears to have been in 1994 at Waterloo Station, London [1]. The

technique has since come to wider prominence, following its extensive use during the

construction of the Jubilee Line Extension in London where tunnels were driven through

London Clay close to many prestigious buildings. The detailed mechanics of CG are not well

understood. Researchers are now, however, using physical [2] and analytical modelling [3–11] todevelop an improved understanding of the mechanics of CG. An improved understanding has

potential economic benefits; for example, a realistic model could provide predictions of the

effects of a particular scheme of grouting (i.e. the layout of TAMs) and thus suggest alternative

and cheaper arrangements.

This paper describes the development and use of a three-dimensional finite element model of

fracture grouting for tunnelling in overconsolidated clay. In addition to a number of new finite

element procedures, the model also incorporates a range of strategies for controlling the

modelling of grout injection.

2. PREVIOUS NUMERICAL MODELS OF FRACTURE GROUTING

Fracture grouting is a form of compensation grouting in which a low viscosity grout is injected

into the ground under high pressure to form fracture planes along which the grout flows.

Grouting is usually carried out in three stages. Firstly the ground is ‘conditioned’ by injection of

grout until a small movement is observed at the ground surface. This prepares the ground for

the second stage of grouting and ensures that any subsequent injections are immediately

effective. Secondly, grout is injected as the tunnel is advanced (a process referred to as

concurrent grouting). This is controlled by close monitoring of movements of the ground

surface or structures on the surface. A third stage of grouting may be needed some time after

completion of the tunnel to compensate for consolidation settlements.

Most published numerical modelling of compensation grouting is restricted to the second

(concurrent) stage where better understanding of the mechanics could lead to the greatest

economic benefit. Previous research in this area has generally been based either on the use of a‘prescribed strain’ approach to model grout injection or, alternatively, a ‘prescribed pressure’

approach. These two approaches are outlined below.

In a ‘prescribed strain’ approach, grout injection is simulated by imposing appropriate values

of strain on the elements representing the grouted soil. This type of approach is described by

Nicolini and Nova [12] who adopt a set of anisotropic inelastic strains to represent the grout

injection process. This allows the magnitude of the imposed strain to be different in different

directions and also to vary spatially. Also, Nicholson et al. [3] describe a model for fracture

grouting in which a specified volumetric strain is applied to elements at a pre-defined grout level.

Similar procedures are described by Mayer and Kudella [4], Falk and Schweiger [7] and

Schweiger and Falk [8].

In a ‘prescribed pressure’ approach, grout injection is generally modelled by a two-stage

procedure. Firstly, an appropriate numerical scheme is used to represent the effect of thepressure of the liquid grout on the neighbouring soil. This procedure may require the use of

special ‘grout elements’. Secondly, the properties of the grout are changed, once injection is

complete, to simulate the increase in stiffness of the grout as it sets. Two-dimensional numerical

schemes adopting this type of approach, in which line elements are used to model layers of grout

formed by fracture grouting, are described in References [5, 6, 10]. A three-dimensional model

Copyright # 2005 John Wiley & Sons, Ltd. Int. J. Numer. Anal. Meth. Geomech. 2005; 29:443–471

C. WISSER, C. E. AUGARDE AND H. J. BURD444

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employing this approach is described by Soga et al. [2] and Buchet and Van Cotthem [9]. In

these 3D models, based on the finite difference program FLAC3D, the injection process is

modelled by the application of internal pressure to the relevant solid elements. After injection is

complete, the stiffness of these elements is increased to an appropriate value.

These approaches offer two fundamentally different means of modelling grout injectionprocesses. In both cases, it is necessary to specify, at the start of the analysis, certain details

relating to the way in which grout flows into the ground. In a prescribed strain approach, the

extent of the grouting and the magnitude and spatial variation of the imposed strains must be

defined in advance. In the prescribed pressure approach, however, it may be possible to devise

more detailed models to represent the way in which the grout actually flows in the ground; in

this case fewer assumptions need to be made in advance by the analyst. For example, in heavily

overconsolidated clay (such as London Clay), injected grout tends to form thin horizontal

layers. In cases where the vertical stresses vary with position (e.g. beneath a building) grout

would be expected to flow preferentially towards areas of low vertical stress. A prescribed

pressure approach would allow for the possibility of a numerical procedure in which this

preferential flow of grout is modelled [11]. This removes the need for the analyst to specify full

details of the final size and shape of the grouted zone before the analysis starts.In practice, compensation grouting is generally undertaken by pumping a specified volume of

grout into the ground. In a numerical model based on a prescribed strain approach, this volume

is imposed directly on the soil by the specification of an appropriate distribution of strain.

Although in a numerical model based on a prescribed pressure approach the grout injection is

controlled by the application of pressure (and not volume), the possibility does exist of imposing

a specified volume of grout by simply terminating the grout injection process when the volume

of grout injected into the mesh (as indicated by the increase in volume of the ‘grout elements’)

reaches the required value.

Prescribed strain approaches, in general, have the considerable advantage of simplicity in

comparison with prescribed pressure approaches. However, prescribed pressure approaches do

appear to have the advantage that, in principle at least, they are capable of more detailed

modelling of the flow of grout into the ground. In spite of the additional complexity involved,therefore, a prescribed pressure approach is adopted in the analyses described in this paper.

3. PROPOSED MODEL OF GROUT INJECTION

3.1. Background

The grout injection model described in this paper is based on the 3D tunnelling model described

in Reference [13]. The features of this earlier model that are relevant to the current study, are

outlined below.

(a) The soil is assumed to behave in an undrained manner. It is modelled using a multi-

surface elasto-plastic model [14] which captures the small strain non-linearity that istypical of overconsolidated clays such as London Clay. It consists of an arbitrary

number of nested von Mises yield surfaces which form cylinders parallel to the space

diagonal in total principal stress space. The inner surfaces move in stress space according

to a set of linear strain hardening rules. When a stress point reaches a yield surface the

stiffness is reduced (Figure 1) and those yield surfaces in contact with it follow its stress


COMPENSATION GROUTING ABOVE SHALLOW TUNNELS 445

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path (Figure 2). It models the non-linearity of clay at small strains, the effect of the recent

stress history on the current behaviour and the memory loss of the recent stress history,

when all surfaces have become fully re-orientated.

Each yield surface is described by two parameters specifying the size of the surface and

the magnitude of the stiffness reduction as the yield surface is activated. The size of theoutermost surface is fixed and determines the undrained shear strength of the material.

In the calculations described in this paper, the parameters were selected to give a

variation of stiffness with strain that is representative of the behaviour of London Clay.

The resulting variation of the tangent stiffness against shear strain based on the

parameters in Table I is shown in Figure 3. The undrained strength profile is taken from

data for London Clay given by St. John et al. [15]. The undrained shear strength

increases linearly with depth: su ¼ 60 þ 6z kPa; where z is the distance (in m) below the

ground surface. Kim [16] and Ng et al. [17] report that the ratio of small strain shear

Figure 1. Variation of shear stress with shear strain for nested yield surface model [14].

σ1

3

σ2

σ

σ1 σ2

3σ

initial state translated surfaces

outer surface(fixed in stress space)

inner yieldsurfaces

Figure 2. Nested yield surface model [14].



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stiffness to undrained shear strength G0=su for London Clay is about 100–250. However,

Liu [18] reports numerical difficulties when adopting a value of 250. A value of 500 was

therefore used for the analyses in this paper.

(b) The soil is modelled using an unstructured mesh of 10-noded tetrahedral elements. The

analyses were conducted using the finite element program OXFEM [13] which has been

developed at Oxford University, U.K. for the study of problems in geotechnical

engineering. This program deals with non-linear problems using a modified Euler

approach.

It should be noted that in the analyses described by Burd et al. [13] the tunnel was unlined. In

the model described in this paper, however, the tunnel was lined with a thin layer of tetrahedral

continuum elements [11, 19].The procedure to model tunnel installation is as follows:

1. The finite element mesh is generated to include the volume of soil that is removed during

the tunnelling operation and also a thin tube of continuum elements in the location where

the lining is installed.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01

shear strain γ (%)

G / G 0

Figure 3. Variation of tangent shear modulus with strain (triaxial).

Table I. Parameters used for nested yield surface model (for a description of the soil model and itsparameters see Reference [14]).

Gs0 o n su0 m g

3:0 104 kPa 3:0 103 kPa=m 0.49 60 kPa 6 kPa=m 20 kN=m3

Surface c0a g0

a Surface c0a g0

a

1 0.02 0.9 6 0.2 0.32 0.04 0.75 7 0.3 0.153 0.06 0.5 8 0.5 0.054 0.1 0.3 9 0.7 0.0255 0.15 0.2 } } }



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2. Tunnel installation is modelled in incremental lengths. At the start of an installation

increment the properties of the continuum elements representing the appropriate length of

tunnel lining are changed from their initial values (corresponding to soil) to values

appropriate for the modelling of the tunnel lining material.

3. Soil elements within the tunnel lining are removed (using the procedure described byBrown and Booker [20]).

4. A uniform hoop strain is applied to the tunnel liner. This provides a specified reduction in

cross-sectional area of the tunnel and is the means adopted in the analysis to prescribe the

ground loss. Since the imposed hoop strain is uniform this procedure does not generate

bending moments in the liner (although bending moments may be generated in response to

the stresses applied by the surrounding soil)

The liner consists of a contiguous ring. No attempt is made to model the detailed structure of a

segmental lining.

It should be noted that the calculations described in this paper are focussed on the application

of compensation grouting to ‘greenfield site’ conditions. Although preliminary studies have also

been carried out on compensation grouting beneath a surface structure (see Reference [11]) these

studies have served principally to demonstrate that, for the case where a building is present, theproblem of controlling the grout injection process becomes substantially more difficult than is

the case for the greenfield site. This paper is therefore devoted to the study of compensation

grouting processes for the case where a building is absent. However, an assessment of the

preliminary studies conducted by Wisser [11] for the case where a building is present is given in

Section 4.4 of this paper.

The model of compensation grouting described in this paper is concerned entirely with the

immediate (undrained) response of the soil to the injection of grout. It is likely that the injection

of grout will lead to the generation of excess pore-pressures in the neighbouring soil and that the

dissipation of these pore pressures will lead to further soil deformations. The study of these

long-term movements, however, is beyond the scope of the current paper.

3.2. Modelling grout injection

The model of CG described in this paper consists of two separate processes: (a) procedures to

model the injection of grout and (b) procedures to control the grout injection process in

response to movements at the ground surface. This section describes the grout injection model.

Procedures to control the grout injection process are described in Section 3.3.

This paper is concerned entirely with fracture grouting in a heavily overconsolidated clay

(e.g. London Clay). In heavily overconsolidated soils, there is evidence both from site

investigations [21] and laboratory tests [22] that, as a consequence of the horizontal in situ stress

being larger than the vertical in situ stress, the grout opens horizontal fracture planes in the soil.

Grout flows along these fracture planes to form horizontal layers. To model this behaviour,

grout elements are generated in the finite element mesh in horizontal planes in the locations

where grout is assumed to flow. The grout injection procedure is modelled by a prescribedpressure approach as described below. One drawback of the approach used here is that the

extent of the grouting patch has to be defined by the user. A refined model, in which the

interaction between the grout pressure and the in situ stresses in the ground is used to determine

the distance travelled by the grout, is given by Wisser [11]. Further discussion of this advanced

model, however, is beyond the scope of the current paper.



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The grout elements used in the model are based on conventional 12-noded interface elements

as described in Ngo-Tran [23], and as shown in Figure 4. The triangular faces of the grout

elements match the faces of the tetrahedra either side of the grout layer. Values of stiffness are

specified in the normal and the two orthogonal shear directions.

To limit the spatial extent of the grout element panels, the edges of the interface elementscoincident with the edge of the panel must be tied together. This could be achieved by altering

the formulation of these particular edge interface elements to include constraints on element

node pairs along these edges. An alternative approach is used here, where the element edges are

joined together by separate tie elements that implement the constraints directly by coupling the

degrees of freedom of the nodes on the edge. This approach avoids the need for different types of

grout elements, and simplifies mesh generation. Tie elements to join 2D and 3D elements

together have been developed by Houlsby et al. [24] for modelling 2D masonry facades in

tunnelling settlement damage analyses [13]. In the model described in this paper the tie element

formulation was adapted to tie two 3D nodes together to create a patch edge. Further details of

the formulation of these tie elements are given in Reference [11].

The procedure for modelling grout injection, in outline, is as follows:

(a) The initial assignment of high shear and normal stiffness to the grout elements to tie

together the gap into which grout will flow. The stiffness is selected to ensure that any

additional flexibility introduced by the grout elements is minimal.

(b) Modelling of grout injection. This is achieved by reduction of grout element stiffness to

zero and application of an appropriate internal pressure to the grout elements.

(c) Control of the grout pressure by the monitoring of surface movements (see Section 3.3).

(d) Grout cure: an appropriately high stiffness is assigned to the grout elements. This is

achieved by changing the material parameters in a single calculation step.

To achieve Step (b), an incremental grout pressure D p is applied repeatedly to increase the

internal grout pressure p g: Details of this procedure are set out below.

Vertical compressive stresses generally exist in the grout elements as a consequence of the

vertical stresses in the neighbouring soil elements (Figure 5(a)). At the start of the groutinjection analysis, the value of the smallest vertical compressive stress ðszÞmin at any Gauss point

within the grout panel is determined. Clearly, the applied grout pressure must exceed ðszÞmin for

grout to flow into the panel and so the grout pressure, p g0; at the start of the grout injection step

is set to p g0 ¼ ðszÞmin:

1 24

7

9

10

12

z

y

x

3

58

11

10

Figure 4. 12 noded interface element.



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An increment of grout pressure D p is then applied; the applied grout pressure, p g1; at the end

of this first increment is therefore p g1 ¼ p g0 þ D p (see Figure 5(b)). However, the value of incremental grout pressure applied at each individual Gauss point will depend on the value of

the pre-existing vertical stress, as shown in Figure 5(b). At the i th Gauss point, the applied

incremental grout pressure D pi ; is

D pi ¼ p g1 szi for p g1 szi > 0

D pi ¼ 0 for p g1 szi 0ð1Þ

where szi is the vertical stress at the i th Gauss point at the start of the grout increment.

The values of incremental grout pressure are applied in the analysis by the application of

incremental nodal loads, f ; evaluated from

f ¼ Z A

½BTD pi dA ð2Þ

where ½B is the appropriate matrix relating nodal displacements to relative displacement for the

grout element and dA is an element of area. The deformations within the mesh, and the resulting

Gauss point stresses, are computed using conventional finite element techniques. Further

increments D pi are applied using the above procedure until certain measures of movement at the

ground surface fall to acceptable limits.

location

location

(σ z )min

extent of grout panel

σ z


∆ p

(σ z )min

current extent of

σ z

∆ pi

Gauss point i

hydrofracture zone

pg1

location

σ zhydrofracture zone


current extent of

∆ p

pg1

pg2

(a) (b)

(c)

Figure 5. Calculation of grout pressure across a grout panel: (a) initial stresses (compression positive);(b) first grouting increment; and (c) second grouting increment.



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The procedure for modelling the injection of grout in the ground, described above, does not

involve the specification of the volume of grout actually injected into the ground. This is a

consequence of the pressure-controlled approach that is adopted. However, in a practical

analysis, it may be desirable to compute the volume of grout that is required to achieve the

required amount of settlement control. This calculation could be achieved relatively easily byintegrating, over the area of each grout patch, the normal displacements developed in the grout

elements. However, this particular calculation was not carried out in the analyses described in

this paper.

3.3. Grouting Strategies

To control the compensation grouting process the displacement of a set of points on the ground

surface (referred to in this paper as ‘Observation Points’) are monitored. Appropriate values of

grout pressure are then applied (using procedures described in Section 3.2) to control the

movements of these points. For modelling purposes, a set of rules are required to allow

appropriate values of grout pressures to be computed and applied. The set of rules governing the

acceptable limits of movement are referred to in this paper as a ‘Grouting Strategy’.Implementation of an appropriate Grouting Strategy can lead to considerable additional

complexity in the model for the following reasons. Firstly, to ensure that the requirements of the

Grouting Strategy are satisfied, a feedback system needs to be implemented to ensure that the

grout pressure is set to an appropriate value. A second source of complexity arises from the need

to formulate each strategy in a way that leads to a stable and unique numerical algorithm. In

practice, decisions on grout pressures and injection locations are generally made by a ‘panel of

experts’ on the basis of recent data on ground movements. To approach a realistic model, the

combined experience of a ‘panel of experts’ needs to be encapsulated within an appropriate

numerical procedure. This is a far from straightforward procedure.

A Grouting Strategy is a set of rules that compares the parameters derived from movements of

the Observation Points (referred to as ‘Settlement Control Parameters (SCPs)’) with predefined

limits known as Trigger Levels and Target Levels. Possible Settlement Control Parameters are,for example, absolute settlement or deflection ratio. A Trigger Level, TR, is the critical value of

SCP at which grouting should begin. It represents the limit at which the magnitude of the ground

movement is about to become unacceptable. The Target Level, TA, is the parameter value at

which grouting can stop, ground surface movements having been reduced to an acceptable limit.

Each increment of grout injection is applied as a single load step in a non-linear analysis (see

Section 3.2), at the end of which deformations are determined and new values of Settlement

Control Parameters derived. If the Target Level is overshot, this analysis step is automatically

discarded, and a smaller grout pressure increment is applied. The new pressure increment is

determined by linear interpolation between the parameter values at the start and end of the

discarded step. A flow chart for the settlement control algorithm is given in Figure 6. Since it is

difficult to reduce the pressure to the level so that the Settlement Control Parameter exactly

meets the specified Target Level, the user also specifies a tolerance e: Grouting is stopped whenthe observed SCP satisfies: TA e4SCP4TA þ e:

The purpose of compensation grouting usually is to control surface deformations to avoid

damage to buildings. Building damage is commonly classified into six categories, from negligible

to very severe according to visual assessment [25] or by simple elastic analysis assuming the

structure to be a deep beam [26]. These categories of damage can be linked to direct



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measurements of building movements to allow assessment to take place during tunnelling

operation. In many cases, however, these calculations are completed before the start of the

project to estimate values of vertical displacement at certain points in the structure that would

lead to excessive damage. These calculated displacement values may then be treated as

settlement limits that should not be exceeded during construction. One example of this approachoccurred in the Jubilee Line project where a limit of 25 mm was applied to all rail structures [27].

Alternatively, it may be of greater importance to check levels of differential settlement (i.e.

relative movement measured between two points). A common dimensionless measurement of

differential settlement is deflection ratio DR,

DR ¼ D

Lð3Þ

where D is the maximum vertical deflection measured between two points a distance L apart (see

Figure 7). However, it seems that in practice, reported practical procedures in which

compensation grouting is used to limit deflection ratio are less common than those to limit

discrete values of settlement.

Three Grouting Strategies implemented in the numerical model are described below:

Strategy A. Grouting Strategy A uses absolute settlement of the Observation Points as the

Settlement Control Parameter. Trigger Level and Target Level coincide. Grouting is started if

the maximum settlement of all Observation Points exceeds the Trigger Level and continues until

the maximum settlement of all Observation Points reaches the specified Target Level. Note that

Grouting Strategy A only requires that the settlement (i.e. downwards movement) at all

start

groutingnecessary?

apply groutingpressure

calculatedisplacements

calculate newgrouting pressure

target levelmet?

target level

exceeded?

end

yes no

noyes

yes no

Figure 6. Flow chart for grouting calculation.



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Observation Points is less than some specified value. Implementation of this strategy is relatively

straightforward and the algorithm is stable. However, note that the strategy could lead to

unacceptably large values of soil heave being generated.

Strategy B. Strategy B is similar to strategy A although it is designed to control soil heave as

well as soil settlement. Grouting is started if the maximum settlement exceeds the Trigger Leveland continues until either the maximum settlement reaches the lower Target Level (which

coincides with the Trigger Level) or the minimum settlement (equal to the maximum heave)

reaches the upper Target Level. This avoids the possibility of grouting inducing substantial

differential settlements into the structure by generating soil heave.

Strategy C . Strategies A and B use settlement and heave as the SCP, which seems to be

consistent with most current reported site practice. However, discrete measurements of

settlement alone may not always be the best measure of the potential building damage. Strategy

C uses deflection ratio as the Settlement Control Parameter; this parameter may provide a more

direct indication of potential building damage.

To compute appropriate values of deflection ratio, Observation Points must be grouped along

lines on the ground surface corresponding to the building facades. An arrangement for a simplefour-facade building outline is shown in Figure 8. Observation Points, in groups of three,

provide four deflection ratio parameters (DR1 and DR3 for the front and back facades, DR2

and DR4 for the two side facades). The conventional procedure for assessing the likely damage,

outlined for example by Mair et al. [28], considers the part of the building in the sagging region

of the settlement trough separately from the part in the hogging region and is based on the

definition of a sagging ðDRsÞ and hogging ðDRhÞ deflection ratio (Figure 7(a)). This approach

cannot be used directly in this finite element model because it would involve determining the

point of inflection of the settlement curve and adjusting the position of Observation Points

accordingly. Alternatively, a larger number of Observation Points could be used, but this is not

adopted in this paper for the sake of simplicity.

In this model the deflection ratio DR between three fixed Observation Points is determined, as

shown in Figure 7(b). This deflection ratio depends on the position of the Observation Pointsand might not necessarily coincide with the definition used by Burland and Wroth [29] and Mair

et al. [28]. However, this is not regarded as a disadvantage if the Observation Points are sensibly

placed.

An additional parameter, termed AVG, is introduced for Strategy C to take account of the

differing effect an increment of grout injection can have on the ground movement beneath

∆ s

Ls

Lh

∆h

DRh =

∆h

Lh

DRs =

∆s

Ls

DR = ∆ L

∆

L/ 2 L/ 2(a) (b)

Figure 7. Deflection ratio: (a) deflection ratio as defined by Burland and Wroth [29] and Burland et al. [25];and (b) deflection ratio adopted in strategy C.



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different facades. AVG is the mean of the absolute values of the observed deflection ratios, i.e.

AVG ¼

PNDFLi ¼1 jDRi j

NDFLð4Þ

with NDFL the number of the deflection ratios defined by the user

(NDFL would be four for the example shown in Figure 8).

DRi deflection ratio i :This measure is included to allow for cases where grout injection causes one deflection ratio to

increase while the remaining ones are reduced by further grout injection. To illustrate the

importance of AVG, consider the simple building of Figure 8 where further grout injection

would increase one deflection ratio above a Target Level. This could be the point to terminate

grout injection. Alternatively one could continue with the injection, as long as the damage in the

other facades was reduced. In this case further damage in one location is accepted, provided the

overall damage is reduced; this is the approach taken for the research presented here. Anadditional Target Level is therefore the point where AVG begins to rise, indicating a net

increase in damage for the structure as a whole.

Given the Control Parameters DRi and AVG the control algorithm is as follows, where N obs

refers to the number of deflection ratio measurements:

TA ¼ TR

grout ¼ off

for each grouting increment do

for i ¼ 1 to N obs do

if DR i > TL then

grout ¼ on

end if

end forif AVG is increasing then

grout ¼ off

end if

if grout ¼ on then apply grout pressure this step

end for

building

Observation pointDR1

DR3

DR2

back facade

front facade

DR4

Figure 8. Example for Strategy C (plan view of building outline with 6 observations points and 4deflections ratios DR as Settlement Control Parameter).



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4. MODELLING CG FOR TUNNELLING

To illustrate Grouting Strategies A, B and C, several analyses have been carried out using the

mesh shown in Figure 9. The analyses involved the installation of a straight and horizontal

tunnel of length 60 m; diameter 5 m and axis at a depth of 10 m: Due to symmetry, only one half of the problem was modelled. Overconsolidated clay was modelled using the soil model

described in Section 3.1. The soil parameters employed are given in Table I. Prior to excavation,

initial stresses due to the unit weight of soil and K 0 ¼ 1:25 were generated. A list of the analyses

is given in Table II.

vertical faces fixed in direction normal to the face

xy

z

boundary conditions: base fixed

10 m

50 m

60 m60 m

Figure 9. Mesh for example analyses.

Table II. Example analyses.

AnalysisGroutingstrategy

Grout element shear and normalstiffness kGE

ðkN=m3Þ

E1 None No grout elements insertedA1 A 1 105

A2 A 1 106

A3 A 1 107

B1 B 1 106

C1 C 1 106



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Observation Points were placed on the ground surface at the possible location of a surface

structure (Figure 10), although note that a structure was not actually modelled in these example

analyses. Further analyses in which buildings are included, are presented by Wisser [11].

Grouting panels were located half way between the tunnel crown and the overlying structure. In

practice, a grouting zone above a tunnel is usually defined by lines extending at 458

from thetunnel invert [30]. To be consistent with this practice, three grouting panels of dimensions

8:75 m 5 m (denoted 1, 2, 3 in Figure 11) were inserted in the meshes used in these analyses.

Three grouting panels were selected on the initial assumption that this was the minimum

number of independent zones of grouting to provide reasonable control of ground surface

movements. Tunnel excavation and lining installation was carried out in 6 stages, with the

1

6

7

23

4

5

Tunnel

5.0 m 5.0 m

5.0 m

5.0 m

assumed building footprint

front facade

Direction of tunnel construction

C

rear facade

L

Figure 10. Position of the Observation Points (plan view on the ground surface).

direction of tunnelling

12.5 m 12.5 m5.0 m5.0 m

excavation stages

5.0 m 5.0 m

8.75 m

grouting panels5.0 m

building footprint

12.5 m 12.5 m

1 32

Figure 11. Plan view of grouting layout.



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length of one excavation stage being between 5 and 12 :5 m: While it is accepted that these

increments are longer than would be adopted in practice, relatively large increments were

adopted in order to keep the run times to acceptable values.

After each increment of excavation, the tunnel liner was shrunk to simulate a ground loss of

2% (see Section 3.1). The model simulated ground loss principally by allowing radial movementof the soil around the tunnel liner. Face loss is not explicitly modelled. This seems reasonable on

the basis that ground movements around tunnels are conventionally regarded as not being

sensitive to whether the ground loss is associated with the tunnel face, or closure of the soil onto

the lining, or a combination of both. The different stages of each analysis are specified in

Table III.

Figure 12 shows surface contours of settlement for analysis E1 at selected stages of

excavation. It is noticeable that ahead of the tunnel face a small amount of heave is created.

Transverse and longitudinal plots of settlement for this analysis are shown in Figure 13

demonstrating that the magnitude of the heave ahead of the tunnel face is small. The surface

settlement trough is, however, wider and shallower than predicted by the semi-empirical

approach [28], as commonly found for numerical analysis of this problem [31].

4.1. Grouting Strategy A

Strategy A is used in analyses A1–A3. The limit for the maximum settlement is set to 0 mm with

a tolerance of 1mm: The three analyses in this series are used to investigate the influence of

initial grout stiffness on the nature of results in an analysis with grouting, and differ only in the

initial and final stiffness assigned to the grout elements. Inserting grout elements into a mesh

changes its flexibility. The magnitude of this effect depends on the stiffness (normal and shear)

assigned to the grout elements. Before CG can be modelled realistically, a suitable stiffness for

the grout elements has to be selected. If the stiffness is too high, numerical problems caused by

ill-conditioning of the stiffness matrix may occur; if it is too low the soil continuum above the

tunnel axis and ahead of the tunnel face may not be modelled correctly.

Figure 14 shows the vertical movements along the surface above the tunnel axis after eachinjection stage for analyses A1–A3. It is noticeable that significant heaves are induced in all

analyses; this is a consequence of the Grouting Strategy, which places no control on heave

Table III. Stages of the analyses (see Figure 11 for layout).

Analysis stage Task performed

1 Excavation to y ¼ 12:5 m and shrinking of liner2 Excavation to y ¼ 25:0 m and shrinking of liner3n Grouting of panel 14 Excavation to y ¼ 30:0 m and shrinking of liner5n Grouting of panels 1 and 2y

6 Excavation to y ¼ 35:0 m and shrinking of liner7n Grouting of panels 2 and 3y

8 Excavation to y ¼ 47:5 m9n Grouting of panels 310 Excavation to y ¼ 60 m and shrinking of liner

nOnly in analyses A1, A2, A3, B1, C1 where compensation grouting is specified.yGrouting of two panels is dealt with by treating them as a single combined panel.



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magnitude. It should also be noted that the Trigger Level is defined for the Observation Points,which are located between 25 and 35 m along the tunnel axis. Since the Grouting Strategy is

controlled by the Observation Point movements, settlements are allowed to exceed the Trigger

Level away from these locations. While the surface deformations agree very well between the

three analyses outside the grouting zones, differences are noticeable above the activated grouting

panels. However, the results of A2 and A3 are sufficiently close to be assumed that in both cases

0 10 20 300

10

20

30

40

50

60

m

0

2

4

6

8

10

12

excavatedtunnel

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10

20

30

40

50

60

m

0

2

4

68

10

12

14

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10

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50

60

m

0

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6

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14

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60

m

0

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14

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40

50

60

m

0

2

4

68

10

12

14

s e t t l e m e n t s

i n m m

s e t t l e m e n t s

i n m m

s e t t l e m e n t s i n m m




0 10 20 300

10

20

30

40

50

60

m

2

4

6

8

10

12

14

(a) (b)

(c) (d)

(e) (f )

Figure 12. Contour plot of surface settlements for E1: (a) after stage 1; (b) after stage 2; (c) after stage 3;(d) after stage 4; (e) after stage 5; and (f) after stage 6.



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the effect of grout element flexibility on the results is not significant. In view of this a grout

element stiffness of kGE

¼ 1 106

kN=m3

(corresponding to run A2) is adopted for latercalculations.

It is useful to assess the additional flexibility that grout elements introduce, by comparing

their stiffness with the stiffness of the surrounding soil. Under purely compressive stress, a grout

element with a normal stiffness of kGE experiences the same strain magnitude as a layer of

continuum elements with thickness d and a Young’s modulus E where

d ¼ E

kGE ð5Þ

d can be therefore be thought of as a thickness of soil equivalent to the presence of the grout

elements. The ‘equivalent thickness’ for analysis A2 is of 0:12 m; using the Young’s modulus of

the continuum elements at the grout panel depth. This seems sufficiently small to minimise the

additional flexibility induced by the grout elements and was therefore used for all subsequentgrouting analyses.

Figure 15 shows the surface settlements for analysis A2 along the tunnel axis and in the

transverse direction at y ¼ 25:0; 30.0 and 35:0 m ( y is measured along the tunnel axis starting

from the beginning of the tunnel) just before and after the first injection (analysis stages 2

and 3).The Observation Points are marked on the plots. The influence of grout injection

0 10 20 30 40 50 60−5

0

5

10

15

20

distance from tunnel axis [m]

s e t t l e m e n t s [ m m ]

stage 1stage 2

stage 3

stage 4

stage 5

stage 6

0 10 20 30 40 50 60−5

0

5

10

15

20



stage 1 stage 2

stage 3

stage 4

stage 5

stage 6

0 10 20 30 40 50 60−5

0

5

10

15

20


s e t t l e m e n

t s [ m m ]

stage 1stage 2

stage 3stage 4

stage 5

stage 6

0 10 20 30 40 50 60−5

0

5

10

15

distance along tunnel axis [m]

s e t t l e m e n

t s [ m m ]

s t a

g e

1

s t a

g e

2

s t a

g e

3

s t a g

e 4

s t a

g e 5

stage 6

(a) (b)

(c) (d)

Figure 13. Surface deformations for E1: (a) transverse plot at y ¼ 25:0 m; (b) transverse plot at y ¼30:0 m; (c) transverse plot at y ¼ 35:0 m; and (d) along tunnel axis.



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does not extend far beyond the boundaries of a grouting panel and the heave created decreases

very rapidly towards the panel edge. While the injections cause large heave movements of

Observation Points 1, 2, 6 and 7, which are close to the tunnel axis and above grouting panels,the effect on Observation Points 3, 4 and 5 (which are located outside the grouting panels, see

Figures 10 and 11) is in comparison very small. Observation Point 3 is always the last of all

Observation Points to reach the specified Target Level, resulting in considerable heave at other

locations closer to the tunnel axis. The maximum heave increases steadily after each injection

stage. As one panel is grouted after the other, Observation Point 3 moves further away from the

currently activated panel. With increasing distance, the effect of a grout injection on an

Observation Point decreases and hence more injection steps are necessary for point 3 to meet

the specified target. This in turn causes considerable heave of the Observation Points closer

to the activated grouting panel. Also of note is the lack of disturbance behind the tunnelling

face from later injections. The contour plots of the surface deformation after each injection

stage, shown in Figure 16, also illustrate some of the observations described above. In particular

the large amount of heave created and the small zone of influence of the grout injectionsare visible.

These results show that poorly devised Grouting Strategies which are based on minimizing

settlement alone, such as Strategy A, can result in large movements which could cause

significant structural damage. In the case presented here, a considerable amount of unwanted

heave is created and CG would induce more damage than it aims to prevent, if a surface

0 10 20 30 40 50 60−40

−30

−20

−10

0

10

20



1

7

A1A2A3

0 10 20 30 40 50 60−80

−60

−40

−20

0

20



1

7

A1A2A3

0 10 20 30 40 50 60−250

−200

−150

−100

−50

0

50



1

7

A1A2A3

0 10 20 30 40 50 60−600

−400

−200

0

200



1

7 A1A2A3

(a) (b)

(c) (d)

Figure 14. Plot of surface settlements along tunnel axis for different interface stiffness (Grouting StrategyA): (a) after first injection (stage 3); (b) after second injection (stage 5); (c) after third injection (stage 7);

and (d) after fourth injection (stage 9).



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structure were present. The problem is exacerbated by the fact that the spatial arrangement of

grouting panels, involving just three independent regions, is too coarse to achieve satisfactorycontrol. A more detailed scheme, involving a greater number of independent grouting locations

is described by Wisser [11]. Further discussion of this scheme, however, is beyond the scope of

the current paper.

4.2. Grouting Strategy B

The results for strategy A above clearly demonstrate the need to include heave as well as

settlement control in a Grouting Strategy. Such an approach is contained in Grouting Strategy

B and is now demonstrated using the results of analysis B1. The results of analyses A1–A3

indicate that Observation Points away from a grouting panel are little affected by any grouting

in that panel. For this reason only Observation Points above the currently activated panel were

used in the Grouting Strategy algorithm for analysis B1. These are detailed in Table IV.Contour plots of the vertical surface movements after each injection stage (B1 analysis stages

3, 5, 7, 9) are given in Figure 17. As seen in previous analyses, the grouting effect is localised

above the panels.

Longitudinal and transverse plots of the surface vertical movements for analysis B1 are given

in Figures 18–21. Each plot shows the deformations before and after each injection. Since the

0 10 20 30 40 50 60−40

−30

−20

−10

0

10

20



1

7

Stage2Stage3TargetTolerance

0 10 20 30 40 50 60−40

−30

−20

−10

0

10



1

2

3


0 10 20 30 40 50 60−3

−2

−1

0

1

2



4


tolerance interval

0 10 20 30 40 50 60−1.5

−1

−0.5

0

0.5

1

1.5



5

6

7


(a) (b)

(c) (d)

Figure 15. Surface settlements for A2 after stage 2 (before grouting) and stage 3 (after grouting of panel 1):(a) plot along tunnel axis; (b) transverse plot at y ¼ 25:0 m; (c) transverse plot at y ¼ 30:0 m; and

(d) transverse plot at y ¼ 35:0 m:



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Observation Points used by the Grouting Strategy change during the analysis, as different panels

are activated, the Target and Trigger Levels are only marked for the Observation Points whichare currently active. Along the tunnel axis (Figures 18(a), 19(a), 20(a), 21(a)) Observation Points

react strongly to the injection of grout and grouting stops when these points hit the heave Target

Level. On the transverse plots it is noticeable that the termination of grouting occurs before all

the Observation Points have been lifted above the maximum settlement level, due to the

restriction on further heave of points over the tunnel axis. As for previous analyses, grout

0 10 20 300

10

20

30

40

50

60

m

m

−30

−25

−20

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−5

0

5

10

excavatedtunnel

activatedgrouting panel

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10

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m

m

−60

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0

10

0 10 20 300

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50

60

m

m

−200

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0

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10

20

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40

50

60

m

m

−400

−350

−300

−250

−200

−150

−100

−50

0

(a) (b)

(c) (d)

Figure 16. Contour plot of surface settlements (in mm) for A2 after each injection stage: (a) stage 3;(b) stage 5; (c) stage 7; and (d) stage 9.



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0 10 20 300

10

20

30

40

50

60

m

m

−15

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−5

0

5

10

activatedgrouting panel

excavatedtunnel

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30

40

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60

m

m

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0

5

10

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m

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0

5

10

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10

20

30

40

50

60

m

m

−15

−10

−5

0

5

10

(a) (b)

(c) (d)

Figure 17. Contour plot of surface settlements (in mm) for B1 after each injection stage: (a) stage 3;(b) stage 5; (c) stage 7; and (d) stage 9.

Table IV. Observation Points used for different grout-ing panels for analysis B1.

Activatedgrouting panel

Analysisstage

ObservationPoints used

1 3 1, 2, 31 and 2 5 1, 2, 3, 42 and 3 7 4, 5, 6, 73 9 5, 6, 7



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injection in the panels used here has very little effect on Observation Points 3 and 4. Another

observation of the model behaviour which seems to agree with site experience is that oncegrouting has been completed in a panel, and the tunnel is advanced, there is negligible change to

surface movements behind the face (see Figures 20(b), 21(b), 21(c)).

Strategy B avoids the generation of large heaves and therefore represents an improvement on

Strategy A. It cannot, however, ensure that settlements are kept below Target Levels because the

constraints on settlements and heaves conflict.

Maximum settlement and heave cannot be satisfied by as few as three grout panels and one

independent grout pressure. In practice, of course, a large number of grout injection points

would be used, each with independent values of grout pressure. The use of an increased number

of independent grout injection pressures in the model would clearly improve its ability to control

the surface settlements. This would increase considerably the complexity of the control

algorithm used to determine the optimum grout pressures, however, and is beyond the scope of

the current paper.

4.3. Grouting Strategy C

The results of analyses A2 and B1 have shown that control using absolute deflection

measurement may not provide adequate control of building damage, which is the objective of

0 10 20 30 40 50 60−20

−10

0

10

20



1

0 10 20 30 40 50 60−20

−15

−10

−5

0

5

10



1

2

3


0 10 20 30 40 50 60−2

−1

0

1

2


s e t t l e m e n

t s [ m m ]

Stage2Stage3

0 10 20 30 40 50 60−0.5

0

0.5

1


s e t t l e m e n

t s [ m m ]

Stage2Stage3


(a) (b)

(c) (d)

Figure 18. Surface settlements for B1 after stage 2 (before grouting) and stage 3 (after grouting of panel 1):(a) plot along tunnel axis; (b) transverse plot at y ¼ 25:0 m; (c) transverse plot at y ¼ 30:0 m; and




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any CG operation. Better control over building damage may therefore be possible with

Grouting Strategy C which uses deflection ratio instead of absolute movement to control thegrouting. Analysis C1 described below was undertaken to investigate this strategy.

The deflection ratios of the three facades making up the notional building were the SCP for

Grouting Strategy C in analysis C1. Using symmetry (see Figure 22), the deflection ratios were

calculated as follows:

DR1 ¼s1 s3

w

DR2 ¼s4 1

2 ðs3 þ s5Þ

d

DR3 ¼s7 s5

w

ð6Þ

where DR1; DR2; DR3 are the deflection ratios of the notional front, side and rear facadesrespectively (the front facade being the one passed first by the tunnel). s1 to s7 are the settlements

of Observation Points 1–7 (downwards movements correspond to a positive settlement) and

w and d are the width ð20 mÞ and depth ð10 mÞ of the building (see Figure 10). With this

definition a positive deflection ratio corresponds to a sagging mode, and a negative value

corresponds to a hogging mode.

0 10 20 30 40 50 60−20

−10

0

10

20


s e t t l e m e n t s [

m m ]

1 Stage4Stage5TargetTolerance

0 10 20 30 40 50 60−20

−15

−10

−5

0

5



m m ]

1

2

3


0 10 20 30 40 50 60−20

−15

−10

−5

0

5


s e t t l e m e n

t s [ m m ]

4


0 10 20 30 40 50 60−0.5

0

0.5

1

1.5


s e t t l e m e n

t s [ m m ]

Stage4Stage5

(a) (b)

(c) (d)

Figure 19. Surface settlements for B1 after stage 4 (before grouting) and stage 5 (after grouting of panel 1and 2): (a) plot along tunnel axis; (b) transverse plot at y ¼ 25:0 m; (c) transverse plot at y ¼ 30:0 m; and




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In analysis E1 the maximum deflection ratio, as defined by Equation (6) was approximately

0.04% and occurred in stage 4 between Observation Points 7 and 5 ðDR3Þ: This information wasused to set the Target Level for analysis C1, i.e. to limit the maximum deflection ratio to one half

of this value (0.02%).

Values of deflection ratios DR1; DR2 and DR3 during the analysis are plotted in Figure 23.

This figure shows that at the end of stage 2 (i.e. at the start of stage 3) all deflection ratios are

positive (indicating sagging deformations). The deflection ratio of the front facade ðDR1Þ

slightly exceeds the Trigger Level of 0.02% and so grout is injected, in three steps, until DR 1

falls below 0.02% (see Figure 23(a)).

Due to tunnel excavation in the next stage (stage 4) the deflection ratio of the front facade

increases considerably and, at the end of this stage, it reaches a value of 0.038%. Since this

exceeds the Trigger Level of 0.02%, further grout injection is modelled in stage 5 (see Figure

23(b)). This grouting procedure is seen to be effective in reducing DR1 and, the grout injection

terminates when DR1 falls below 0.02%. (Note that in this analysis the final value of DR 1 is0.014%. Although the algorithm ensures that the final deflection ratio is less than the target

value, the finite value of grout pressure increment, D p; means that the values of deflection ratio

may undershoot the target value). The grouting procedure modelled in Stage 5 also has the effect

of increasing, slightly, the deflection ratio in the rear facade DR3: However, this deflection ratio

remains below the Trigger Level of 0.02%.

0 10 20 30 40 50 60−30

−20

−10

0

10

20



1


0 10 20 30 40 50 60−15

−10

−5

0

5



Stage6Stage7

0 10 20 30 40 50 60−20

−15

−10

−5

0

5



4


0 10 20 30 40 50 60−20

−15

−10

−5

0

5

10



5

6

7Stage6Stage7TargetTolerance

(a) (b)

(c) (d)

Figure 20. Surface settlements for B1 after stage 6 (before grouting) and stage 7 (after grouting of panel2 and 3): (a) plot along tunnel axis; (b) transverse plot at y ¼ 25:0 m; (c) transverse plot at y ¼ 30:0 m;

and (d) transverse plot at y ¼ 35:0 m:



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At the end of stage 8 (i.e. at the start of stage 9) it is clear from Figure 23(c) that the deflection

ratio in the rear facade exceeds the exceeds the Trigger Level. This results in a further grout

injection in stage 9 that is seen to reduce the deflection ratio to below the Target Level of 0.02%.

The developments of deflection ratios DR1; DR2 and DR3 during all analyses discussed in

this paper are plotted, with respect to excavated tunnel length, in Figure 24. It is noticeable that

0 10 20 30 40 50 60−20

−10

0

10

20



m m ]

1Stage8Stage9TargetTolerance

0 10 20 30 40 50 60−15

−10

−5

0

5



m m ]

Stage8Stage9

0 10 20 30 40 50 60−20

−15

−10

−5

0

5


s e t t l e m e n

t s [ m m ]

Stage8Stage9

0 10 20 30 40 50 60−20

−15

−10

−5

0

5


s e t t l e m e n

t s [ m m ]

5

6

7


(a) (b)

(c) (d)

Figure 21. Surface settlements for B1 after stage 8 (before grouting) and stage 9 (after grouting of panel 3):(a) plot along tunnel axis; (b) transverse plot at y ¼ 25:0 m; (c) transverse plot at y ¼ 30:0 m; and


symmetry axis

∆

observation point 1

observation point 3

L / 2

Figure 22. Average deflection ratio DR1 of the front facade using symmetry.



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Strategy A (analysis A2) results in large deflection ratios which would induce more damage to a

building rather than prevent it. Limiting the amount of heave with strategy B (analysis B1) leads

to smaller deflection ratios. However, since the deflection ratios at the end of analysis B1 exceed

those of analysis E1 (an analysis with no compensation grouting), grouting also in this case may

increase rather than reduce any damage to a surface structure. More promising is strategy C

(analysis C1) which provides smaller values of deflection ratio, in particular for DR1; than

analysis E1 where no grouting is carried out. This suggests that strategies based on deflection

ratio, rather than absolute deflection, may be more successful in protecting buildings from

tunnelling induced damage.

4.4. Analyses involving a masonry building on the soil surface

Further calculations in which a masonry building is explicitly included in the model are

described by Wisser [11]. In these calculations an attempt was made to use Grouting Strategy C

1 1.5 2 2.5 3

−0.02

−0.01

0

0.01

0.02

step

d e f l e c t i o n r a t i o ( % )

DR1

DR2

DR3

AVGlimit

2 4 6 8 10 12 14 16 18 20−0.02

−0.01

0

0.01

0.02

0.03

0.04

step


DR1

DR2

DR3

AVGlimit

5 10 15 20

−0.02

−0.01

0

0.01

0.02

0.03

0.04

step


DR1

DR2

DR3

AVGlimit

(a)

(b)

(c)

Figure 23. Development of deflection ratio for analysis C1 in grouting stage 3, 5 and 9 (in stage 7 nogrouting because all Target Levels are met). Note: AVG ¼ ðjDR1j þ jDR2j þ jDR3jÞ=3: (a) stage 3;

(b) stage 5; and (c) stage 9.



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to minimize the predicted damage to the building. Although, in this modelling exercise the

grouting operations were able to reduce the values of deflection ratio, the control of

deformations in a building was found to be a substantially more difficult task than that of

controlling deformations at the ground surface when a building is absent. Activation of aparticular grout panel could be used to reduce the deflection ratio in one of the facades, but this

often had the effect of increasing it in other facades. This behaviour seems to be caused by the

building providing a stiff coupling between the Observation Points. It is thought that, in

principle, a numerical model of compensation grouting procedures for the case where a building

is placed on the ground surface could be developed, but this would require rather more than the

−0.40

−0.35

−0.30

−0.25

−0.20−0.15

−0.10

−0.05

0.00

0.05

0.10

tunnel length excavated (m)

d e f l e c t i o n

r a t i o ( % )

E1

A2

B1

C1

−0.035

−0.030

−0.025−0.020

−0.015

−0.010

−0.005

0.000

0.005

0.010



E1

A2

B1

C1

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5



E1

A2

B1

C1

(a)

(b)

(c)

Figure 24. Development of deflection ratio for analysis E1, A2, B1, C1 (in analyses A2,B1, C1 grouting at an excavated tunnel length of 25.0, 30.0, 35.0 and 47:5 m): (a) DR1

(front); (b) DR2 (side); and (c) DR3 (back).



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three independent grout panels and a single independent grout pressure as adopted in this

model. An advanced model of this sort has not yet been attempted.

5. CONCLUSIONS

A three-dimensional numerical model of compensation grouting above a tunnel in over-

consolidated clay has been presented. Various different approaches to controlling the injection

of grout are possible in compensation grouting depending on Control Parameters that are

adopted. Since building damage generally needs to be minimized it appears sensible to adopt a

control strategy based on a parameter that is closely related to accepted measures of damage.

This numerical model has been shown to replicate general behaviour expected from the field.

The model is based on three independent panels to model the grout injection process. This

approach provides a model that is capable of controlling ground surface movements for the case

where a surface building is absent. Equivalent analyses (not reported in detail in this paper)

suggest that a more sophisticated approach involving an increased number of independent grout

panels and a more complex control algorithm, is needed for cases where a building exists at theground surface.

ACKNOWLEDGEMENTS

The first author was supported by an EPSRC studentship during the period of this research. Some of thecalculations presented were performed at the Oxford Supercomputing Centre.

REFERENCES

1. Harris DI, Mair RJ, Love JP, Taylor RN, Henderson TO. Observations of ground and structure movements forcompensation grouting during tunnel construction at Waterloo Station. G !eeotechnique 1994; 44(4):691–713.

2. Soga K, Bolton MD, Au SKA, Komiya K, Hamelin JP, Van Cotthem A, Buchet G, Michel JP. Development of compensation grouting modelling and control system. In Proceedings of the International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground , Kusakabe O, Fujita K, Miyazaki Y (eds), Tokyo, Japan, 19–21July, 1999. Balkema: Rotterdam, 2000; 425–436.

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