Surface Settlement Induced by Tunnelling

THE UNIVERSITY OF NOTTINGHAM MALAYSIA CAMPUS

Surface Settlement Induced by Tunnelling

by

Yehya Shakeel Siddiqui

4/1/2011

A dissertation submitted in part consideration of the degree of Beng (Honours) in Civil Engineering

Abstract

A parametric study was performed to evaluate the effects of different parameters on surface

settlements above tunnels in cohesive soils. The finite element program PLAXIS 2D was used to carry

out the numerical analysis for a bored tunnel in unsaturated, homogenous sand. The three

parameters that were varied were the tunnel diameter, soil friction angle and the ground loss.

40 different transverse settlement profiles were obtained. Results showed that there was a

substantial increase in surface settlement as the tunnel diameter increased, but the soil friction

angle had an insignificant effect on the surface settlement. Two different values of trough width

parameters were obtained from the graphs and compared with the calculated trough width

parameter. The values coincided for deeper tunnels, but for shallower tunnels the empirical values

deviated from the values obtained from the settlement curves

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Acknowledgements

My years at UNMC have been a unique and special experience. There have been so many people

I have gotten to know and so many things that I have learned, and this especially has made my life at

UNMC a very memorable experience. I would like to express my special thanks to all my friends who

have encouraged me to keep going, especially my friend Yosef Teare, in completing this investigative

project and also in getting through life at UNMC.

Above all I am particularly grateful to Dr.Chan Swee Huat who supervised my research in this

thesis, he provided me with his valuable suggestions and comments despite his very busy schedule.

His very friendly nature was highly appreciated as it permitted me to visit him very frequently and

allowed for us to have friendly discussions at any time of the day.

Finally, I owe my deepest appreciation to my parents. Their prayers have been the greatest thing

I could have asked for and have driven me to thrive in every goal I dream of.

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Table of Contents

Abstract...........................................................................................................................................2

Acknowledgements.........................................................................................................................3

Chapter 1: Introduction...................................................................................................................4

Chapter 2: Literature Review..........................................................................................................4

2.1 Introduction..........................................................................................................................4

2.1.1 Causes............................................................................................................................4

2.2 Stochastic and Empirical Methods........................................................................................4

2.2.1 Litwinniszyn (1956).........................................................................................................4

2.2.2 Peck (1969).....................................................................................................................4

2.2.3 Cording and Hansmire (1972, 1975, 1989).....................................................................4

2.2.4 O’Reilly and New (1982).................................................................................................4

2.2.5 Attewell and Woodman (1982)......................................................................................4

2.3 Laboratory Experiments........................................................................................................4

2.3.1 Atkinson and Potts (1977)..............................................................................................4

2.3.2 Kimura and Mair (1981)..................................................................................................4

2.4 Finite Element and Numerical Methods................................................................................4

2.5 Summary...............................................................................................................................4

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Chapter 3: Plaxis..............................................................................................................................4

3.1 Introduction..........................................................................................................................4

3.2 Material Properties...............................................................................................................4

3.2.1 Mohr-Coulomb...............................................................................................................4

3.2.2 Drained versus Undrained..............................................................................................4

3.2.3 Structural Elements........................................................................................................4

Chapter 4: Analysis..........................................................................................................................4

4.1 Introduction..........................................................................................................................4

4.2 Problem Geometry................................................................................................................4

4.3 Fixities...................................................................................................................................4

4.4 Mesh.....................................................................................................................................4

4.5 Material Properties...............................................................................................................4

4.6 Boundary Conditions.............................................................................................................4

Chapter 5: Model Results................................................................................................................4

Chapter 6: Discussions....................................................................................................................4

6.1 Variation in Diameter............................................................................................................4

6.2 Variation in Soil Friction Angle..............................................................................................4

6.3 Comparison of Trough width parameters.............................................................................4

Chapter 7: Conclusion.....................................................................................................................4

Appendix A......................................................................................................................................4

Appendix B......................................................................................................................................4

References......................................................................................................................................4

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Chapter 1: Introduction

Majority of tunneling activities are conducted in developed locations and it is vital to shield

surface structures from any structural or architectural damage during the process of tunneling. One

of the chief problems during the planning and execution of underground tunnels is to estimate how

much impact the ground movements are going to have on adjacent buildings and utilities.

Aside from the evaluation of stability, the determination of settlements at the surface is one of

the most crucial elements in tunneling. On the other hand, in geotechnical engineering,

deformations of the soil can be predicted with lesser accuracy than stability of the soil structure. This

is due to the fact that the ground has a nonlinear stress-strain relationship; this makes it difficult to

evaluate the stress distribution of the soil.

During the process of excavation, there are changes in the stress state in the ground mass

around the excavation which in turn leads to ground loss. The ground losses and change in stress are

expressed in terms of vertical and horizontal ground movements. These ground movements cause

surface settlements which results in the structures supported by the affected ground to rotate,

translate, deform, distort and possible sustain damage. Consequently, major tasks facing the

engineer and the contractor are the evaluations of the distribution and degree of the ground

movements resulting from the tunnelling process and then consequently having to assess the

tolerance of the structures to the deformations and distortions sustained as a result of the ground

displacements.

In addition to that, utilities must be protected as damage to lines and mains can cause economic

loss and even jeopardize the health and safety of the public. For these reasons ground deformations

during the tunnelling process, generally manifested in the form of surface settlements, became a

major design element.

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Chapter 2: Literature Review

2.1 Introduction

The effects on surface settlements induced by tunnelling provided motive for researchers to

develop new and improved methods for estimating surface settlements as well as settlement

profiles and troughs. Most of the studies done so far were based chiefly on a large quantity of case

studies and evaluated observations. By defining the spatial characteristics of the surface settlement

profiles leads to a greater understanding of which structures will be affected and to what degree.

Ground movements are an unavoidable result of excavating and constructing a tunnel. Tunnel

excavation causes relaxation of in-situ stress, which is only partly constrained by the inclusion of the

tunnel support. It is not possible to create a void instantly and provide an infinitely still lining to fill it

exactly. Hence a certain amount of the ground deformation will take place at the tunnel depth; this

will set off a chain of movements which will result in settlements at the ground surface.

2.1.1 Causes

Settlements are caused mainly due to three components:

1. The immediate settlements caused by the tunnel excavation, which is a function of: stability

of the tunnel face, the time necessary to install the tunnel the rate of tunnel advance, the

time required installing the tunnel lining and in the case involving mechanized tunnelling,

the time required to fill the tail-void. The immediate settlement alongside the tunnel axis

starts at a certain distance in front of the tunnel face and comes to a stop when grout

injection of the tail void has hardened a sufficient amount to counteract any additional radial

displacement.

2. The settlements caused due to deformation of the tunnel lining. This constituent can be

applicable for large diameter tunnels at shallow depth. But, it plays an insignificant role in

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mechanized tunnelling in urban environment, where the loads are well predicted and

excessive deformation can be easily avoided by correctly designing the segmented lining.

3. The long term settlements, due to :

(i) Primary consolidation, this occurs normally in cohesive or compressible soils due the

dissipation of excess pore pressures.

(ii) Secondary consolidation is a form of soil creep which is principally controlled by the

rate upon which the soil skeleton of compressible soils can yield and compress.

The principal methods for estimating ground deformations around tunnel excavations can be

grouped as follows:

Stochastic and empirical methods

Analytical methods

Finite element and numerical methods

Laboratory experiments

2.2 Stochastic and Empirical Methods

Empirically derived relationships are in the form of formulae, which have been based upon field

observations. Empirical methods are widely used; on the other hand predictions of ground

movements based on such methods are inadequate for most practical applications. The

mathematical model for predicting the subsidence of a stochastic medium was first proposed by

Litwiniszyn (1956). Peck (1969) later proposed that the surface settlement distribution could be

determined empirically using the normal probability curve, which has no theoretical basis. Which

resulted in an inverted probability function, empirically derived, used to describe the transverse

settlement trough. The method proposed for estimating the longitudinal settlement trough was

done by Attewell and Woodman (1982) who adopted the stochastic theory.

In reality, ground movements depend on a number of factors such as tunnel geometry and

depth, tunnel construction method, the quality of the workmanship and management and the

behaviour of the soil surrounding the tunnel. As a result the empirical methods are subjected to

these significant limitations.

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2.2.1 Litwinniszyn (1956)

A stochastic process is the counterpart to a deterministic process. Rather than managing only

one possible reality of how the process might evolve in time, in a stochastic process there is some

indeterminacy in its future evolution described by probability distributions. This means that although

the initial condition is known, there are numerous possibilities that the process might go to, but

there are higher possibilities of some occurring and much lower of others.1

According to the stochastic theory the, the total effect of tunneling excavation on the ground

surface is equivalent to the accumulated effects of the innumerable micro-element excavation. In

the stochastic model, the ground is represented by a material composed of numerous equi-sized

spheres in the three-dimensions or discs in two dimensions. By the removal of a sphere a

movements is created at the base of the stacked assemblage. The model elements, acted upon my

gravity alone move according to the laws of probability, which leads to an inverted bell shaped

surface settlement trough in the form of a Gaussian curve.

Litwinniszyn (1956) firstly applied the stochastic medium theory in excavation engineering. From

this model, the settlement trough of normal probability form can be expressed as:

Eq. 2.1

For settlement over a thing tabular opening of width and closure thickness at a depth ,

and are empirical coefficients in the equation and is the vertical coordinate.

1 http://en.wikipedia.org/wiki/Stochastic_process

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http://en.wikipedia.org/wiki/Stochastic_process

Litwinniszyn (1956) recommends and . It is found that settlement curves

calculated from the stochastic model using the and values match up well to those measured

over actual tunnels in clay soils (Attewell, 1978).

2.2.2 Peck (1969)

The most common empirical method to predict ground movements is based on the Gaussian

distribution. Based on information from a range of sources, Peck observed that the settlement

trough over a single tunnel could be represented within reasonable limits by the Gaussian curve.

Peck (1969) mainly simplified the stochastic solution first proposed by Litwinniszyn (1956). The

solution provides an approximation of the settlements that will be expected at laterally varying

distances from the centerline of the tunnel.

Peck (1969) adopted the following expression to describe the settlement component due to

the construction of shield tunneling.

Eq. 2.2

Where is the vertical settlement of a point which is at a distance from the vertical plane

containing the tunnel axis, is the settlement of the point directly above the tunnel, and is a

parameter which defines the width of the settlement trough, as shown in Fig. 2.1. The value of is,

according to the properties of the normal probability curve, equal to .

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Values of have been calculated for tunnels for which reasonably reliable settlement data

are available. They are illustrated in the dimensionless plot of against , (Figure 2.2). The plot

shows trends and relates the results to soil types. As expected the larger the depth of tunnel, the

greater the width of the settlement trough.

Figure 2.1 Gaussian Curve for transverse settlement trough and ground loss

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Figure 2.2 Relation between settlement trough width parameter and tunnel depth for different ground condition

The total volume of the subsidence trough (for the unit length of the tunnel) can be obtained

from the integration of Eq. 2.2 and the result is:

Eq. 2.3

Peck produced a dimensionless plot of the observed width of the settlement profile where

different types of soil areas where compared to the depth of the tunnel axis (Figure 2.3).

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Figure 2.3 Relationship between trough width and tunnel depth (from Peck 1969)

2.2.3 Cording and Hansmire (1972, 1975, 1989)

Cording and Hansmire obtainable a method of estimating surface settlement based on

geometric considerations. In this method, they assumed that the volume of ground loss around the

tunnel opening will equal the volume of the settlement trough at the surface.

They stated that the difference between the volume lost into the tunnel and the volume of the

surface settlement trough is largely due to the compression of the soil at the side of the tunnel and

the volume increase of granular material over the crown.

Cording and Hansmire (1972, 1975, and 1989) where Peck’s successors at the University of

Illinois, they used the properties of the normal distribution curve (by Peck and Schmidt (1969)) as an

expedient method for describing the trough widths of tunnels:

Eq. 2.4

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Where is the vertical settlement of a point which is at a distance from the vertical plane

containing the tunnel axis, is the settlement of the point directly above the tunnel, and is a

parameter which defines the width of the settlement trough.

Figure 2.4 shows that the volume of the settlement trough can be simply defined by the

width ( ) and the maximum displacement ( ). Therefore the volume of the settlement trough

can be calculated as a triangle with base and a height as follows.

Eq. 2.5

Where is the volume of the settlement trough per unit length of the tunnel, is the half

width of the base of the triangle trough, and is the maximum displacement of the trough.

More over their method includes an empirical relationship between the general soil type and the

angle at which the element propagates from the tunnel opening to the surface, . Figure 2.4 and 2.5

relates to the different ground types.

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Figure 2.4 Relation of trough width (from Cording and Hansmire (1975))

Figure 2.5 Relationship between trough width and tunnel depth(from Cording and Hansmire (1975))

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In addition, Cording and Hansmire (1975) stated that some settlement data might not fit the

normal distribution curve, particularly granular soil. The settlement at the centre of the trough did

not continue to increase in proportion to the settlement at the edge of the trough, after the

settlement at the centre became large. Rather as increased, additional settlement was

concentrated just above the tunnel where the zone of high shear strain exists. After that, the

settlement trough no longer fits the normal probability curve and the calculated values of decrease

steadily. When applying the normal distribution curve for predicting surface settlement, one should

know the limitations, especially for cohesionless soil in which localized yield zones rapidly propagate

from the tunnel sidewalls to the surface.

2.2.4 O’Reilly and New (1982)

O’Reilly and New (1982) proposed that surface settlements above tunnels cane be estimated

using empirical methods, an error function curve of the form proposed by Schmidt and Peck (1969).

O'Reilly and New (1982) assumed the radial flow of soil displacement in the direction of the

tunnel axis and that conditions of plane strain constant volume deformation apply. The assumption

is supported by data from field measurements and the results of centrifuge tests on model tunnels

in soft clay. The agreement of radial flow means that the width of the zone deformed ground

decreases linearly with depth below the ground surface. The information available tends to propose

that the flow is directed towards a "sink", close to the invert level of the tunnel, which is located at a

point somewhat beneath the axis level of the tunnel.

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O’Reilly and New (1982) showed that is broadly independent of tunnel construction method

and of tunnel diameter (except for very shallow tunnels where the cover to diameter ratio is less

than one).They proposed that:

Eq. 2.6

Eq. 2.7

where is the trough width parameter at height above tunnel axis and is a parameter that

depends on the soil – about 0.4 for strong clay and sand below water level, 0.7 for soft clay, and 0.2-

0.3 for sand above water level -; and is the tunnel diameter.

Figure 2.6 Soil displacement model around model tunnel in clay (from Mair (1979))

In addition, the result is convincingly reliable with the findings of Fujita (1981) who examined

data from a number of case histories in Japan for numerous tunnels excavated using wide-ranging

techniques such as hand EPB shield, slurry shield, blind shield, and mined shield. Fujita (1981)

established the conclusion of O'Reilly and New (1982) that the width of the surface settlement

profile above tunnels in clays is independent of the construction method used.

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Figure 2.7 Variation in trough width parameters of tunnels in clays

The solution given above is for cohesionless soil and not applicable to granular soil, as the

hypothesis, particle displacement away from the tunnel are directed toward the tunnel axis, is not

supported by laboratory studies (Cording et al. 1976).In addition to that, the assumption of

deformation at constant volume is untenable as some dilation or contraction of granular soils is

almost expected during deformation.

O'Reilly and New (1982) stated that ground movement in cohesionless soils leads to a deep and

narrow settlement trough with high horizontal surface strain when associated with vertical ground

strains in excess of 0.5%. Therefore, the Gaussian curve cannot always precisely approximate this

type of ground movement. These assumptions also match up to the reports presented by Cording

and Hansmire (1975) and Attewell (1978) that, in several case studies particularly in granular

materials, the surface settlement trough cannot suitably be represented by a normal probability

curve.

2.2.5 Attewell and Woodman (1982)

Apart from the transverse settlement profile, the longitudinal profile also plays a vital role in the

tunneling process. In tunneling cases where 3D information is required for settlement, buildings in

the zone of influence may be subjected to twisting and torsional forces, therefore longitudinal

settlements need to be analyzed.

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Attewell and Woodman (1982) examined a number of case histories of tunnel construction in

clays and showed that the cumulative probability curves to be reasonably valid for both, the

longitudinal settlement trough as well as the transverse settlement trough. Attewell and Woodman

(1982) assumed that half of the maximum settlement occurs in the vertical plane of the shield face

and that the point , located far behind the advancing face, has undergone the maximum surface

settlement .

Figure 2.8 Tunnel co-ordinate systems for longitudinal surface settlement (after Attewell and Woodman (1982))

The equation for the settlement is given by Attewell and Woodman as:

Eq. 2.8

Where:

: Surface vertical settlement at a location

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: Distance of the considered point from the tunnel axis

: Longitudinal position of the considered surface point

: Volume of the settlement trough per meter of the tunnel advance

: Initial position or starting section of the tunnel

: Position of the tunnel face

: Trough width parameter

: Integrated normal probability function defined as

Eq. 2.9

:

However this method is only applicable for use in clayey soils because the approach was checked

against data from just one tunneling project, the Jubilee Line Project in London clay.

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2.3 Laboratory Experiments

This method involves the construction of scale models of a tunnel of specific diameter and depth

in varying soil types. With this method the type and magnitude of soil deformation can be analyzed

during the tunnel excavation. Laboratory experiments are an only way to study the actual

mechanism of ground movement and collapse, but it is difficult to simulate the real environment and

the effect of size sensitivity.

2.3.1 Atkinson and Potts (1977)

A centrifuge model for tunneling introduced by Atkinson and Potts (1977), which can be

accelerated to 75g. This enabled the stresses in the soil around the tunnel to be the same as the

stresses around a tunnel 75-times larger accelerated in earth's gravity alone. The tunnel model

illustrated in Figure 2.9 was constructed in two types of soil: overconsolidated clay and dry sand. The

sand was the fraction of Leighton Buzzard sand passing a No. 14 sieve (1.2 mm) and retained on a

No. 25 sieve (0.6 mm) and the clay was kaolin, overconsolidated from slurry to an overconsolidation

ratio of about 4.

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Figure 2.9 Model tunnel tests - boundary conditions and dimensions (after Atkinson and Potts (1977))

The study is primarily concerned with radial ground losses and makes no provision for

movements of ground into the tunnel face normal to the plane of section. Cylindrical tunnels are

driven into the soil using a thin-walled cutter and an internal fluid pressure , applied to the

sidewall through another membrane. The tunnel pressure , is the equal of an excess air at the

tunnel face through construction. Due to the design rigidity, the back and front faces of the box

force a condition of plane strain on the soil. The base is far enough from the tunnel lining so that

there is no influence on the soil behavior around and above the tunnel as this might lead to

inaccurate results.

Two different types of tests have been conducted. In a series of "static tests" under normal

gravitational acceleration, or , were changed slowly so that the pore pressure which was caused

by the increase in the loading was dissipated and the clay was drained. For the tests which were

conducted in sand, the models were accelerated in a large diameter centrifuge which would increase

the stresses due to body-weight forces. Steady accelerations of 75g were applied to induce stresses

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in the model equal to those in corresponding structure 75 times larger than the model. Therefore

the 60 mm diameter tunnel model would have performed in the manner of a 4.5 m diameter tunnel

stressed in the earth's gravitational field. Measurements of local deformations were made by

photographic techniques. In a few of the experiments, thin metal tubes were used to line the tunnel

instead of thin rubber membranes. Strain gauges were also used in order to measure the loads in the

tubes.

Atkinson and Potts (1977) reported that the magnitude of the surface settlement increases as

the crown settles, but the magnitude of for a particular model tunnel depends on:

the depth of tunnel

soil characteristics

presence of a surface surcharge

For model tunnels in sand without surface surcharge loading, Atkinson and Potts (1977) derived

an expression for the point of inflection as:

Eq. 2.11

Where z is the depth to tunnel axis and R is the tunnel radius. For settlement above tunnels in

dense sand and in overconsolidated kaolin, both with surface surcharge loading, the expression is:

Eq. 2.12

2.3.2 Kimura and Mair (1981)

Atkinson and Potts (1977) focused their research on the ground movement behavior in plane

strain tunnel models; whereas Kimura and Mair (1981) used the same experimental techniques, but

they also took into account the 3D problems of a tunnel heading near the ground surface. They

conducted experiments in soft ground to investigate the relationship between the 2D and 3D

models.

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Certain assumptions and a simplified model of a tunnel under construction were created in

order to investigate the influence of parameters affecting tunnel stability and ground movement. For

soft ground tunneling, the unlined heading is represented as shown in Figure 2.10. represents the

tunnel support pressure, is the cover above the crown, is the tunnel diameter and is the

distance from the tunnel face to the structural lining.

Figure 2.10 Tunnel heading in soft ground (after Kimura and Mair (1981))

For the 2D test, the experimental techniques and models were the exact same ones as those

tunnel models which were introduced by Atkinson and Potts (1977). The schematic of the model is

shown in Figure 2.11.However, for tests conducted in the 3D, Kimura and Mair (1981) developed a

semicircular tunnel with the plane of symmetry being an almost frictionless interface between the

clay and the Perspex window. The length of the semi-circular tunnel was lined, in such a way that

only the heading of length was not lined; the ratio was varied from 0 to 3. Kaolin clays with

undrained shear strength of 26 kPa were used all through the test series.

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Figure 2.11 Dimension of 3D test series (after Kimura and Mair (1981))

The 2D test series results showed a complete collapse of the tunnel, causing ground movement

to occur, leading to the subsidence of the ground surface as shown in figure 2.12. Kimura and Mair

(1981) observed that the width of the surface settlement trough to be in good agreement with the

field data collected by Peck (1969). This result also agreed with the model tunnel tests that where

conducted by Atkinson and Potts (1977).

Figure 2.12 Schematic diagram of the failure above the tunnel model

A result from the 3D test series after failure is shown in Figure 2.13, in which the cover-to-

diameter ratio was 1.5 and the length of unlined heading was 0. It can be seen in the figure that

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the soil moved toward to the tunnel face, which resulted in the formation of a sink hole at the

ground surface. This behavior shows the three-dimensional ground movement ahead of the tunnel

face.

Figure 2.13 Schematic diagram of the failure mechanism

In summarize the centrifuge tests conducted on model tunnels revealed how the ground

movement characteristics are affected strongly by the stability of the tunnel. In addition to that,

these results may be helpful to aid the tunnel design and evaluation process based on the

experimental behavior of ground movement

2.4 Finite Element and Numerical Methods

Conventional geotechnical design of tunnels has been carried out using empirical

approaches. Majority of the available design code e.g. Euro Code, British Standard etc. are based on

such approaches. The non-numerical ways of obtaining good predictions of the likely ground

response to tunnelling and the likely loads in a tunnel lining are certainly cheaper and quicker to use.

But they are characteristically uncoupled, that is the loads are determined by one technique (usually

an elastic solution), and movement by another (usually empirical as described in chapter 2.2), the

two not being linked together. In addition to that, the empirical predictions are limited to greenfield

situations, where there is no existing surface or subsurface structure to influence the pattern, or

magnitude of ground displacement. In actual tunnelling, the problem is more complex, involving

numerous parameters which include pore pressure changes, plasticity, lining deformations and

existing structures and utilities.

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The finite element method involves the following steps:

Element discretisation.

Selection of nodal displacements as primary variable.

Derivation of element equations to form global equations.

Formulation of boundary conditions.

Solution of global equations.

The finite element method has been used in numerous engineering fields for over thirty years,

but has only relatively recently been introduced for the analysis of geotechnical problems. This is

mainly because there are many complex issues which are specific to geotechnical engineering and

which have only been determined recently.

The finite element method can:

Simulate the construction sequence

Account for adjacent services and structures

Deal with ground treatment

Deal with complex ground conditions

Model realistic soil behaviour

Handle complex hydraulic conditions

Simulate intermediate and long term conditions

Deal with multiple tunnels

The main limitation of the basic finite element theory is that it is based on the assumption of

linear material behaviour, but soils do not behave in such a manner. Real soil behaviour is highly

non-linear, with both strength and stiffness depending on stress and strain levels.

Currently tunnels are modelled using 2D finite element methods. This is because of their

simplicity and their ability to be carried out fairly quickly and economically. But a 3D model is more

accurate because for 2D FE models, it is not so easy to estimate the stress reduction factors, which is

a fraction of the load effecting on tunnels. With the 3D model, estimation of stress reduction factors

is no longer required as excavation stages can be modeled not only in cross-section but also in the

longitudinal section.

27

For the purpose of performing a 2D plane strain analysis, the components of ground loss are

represented quantitatively in terms of the gap parameter. Therefore, the idea of this technique is to

simplify the spatial ground movements due to tunneling into a plain strain space. In order to convert

from 3D to 2D, the gap parameter needs to be applied to obtain the equivalent volume of ground

movements in the transverse section. Specifically, these effects can be approximately included in a

2D plane strain model by assuming a larger excavated tunnel diameter, with the additional volume

corresponding to the volume of ground lost over the shield.

There are numerous problems involved when only 2D analysis is done. The predicted settlement

trough tends to be wider than the measured settlements, particularly for tunnels in heavily

overconsolidated clays. Also when dealing with 2D analysis, the assumption is made that the end of

the excavation is far away from the tunnel section being analyzed, this makes 2D analysis inadequate

if 3D effect are considered significant.

Numerous boundary conditions are required to model the tunnel construction procedure. The

boundary conditions include:

displacement conditions, which are required to represent the far field conditions or any

symmetry of the problem

surface tractions

construction of structural shell elements

excavation of solid soil elements

hydraulic conditions at the far field boundaries

soil strata interfaces

tunnel lining

Adequate displacement conditions must be prescribed in order to maintain any rigid body

modes, such as translations or rotations of the complete mesh. Analysis of tunneling in drained

granular materials requires careful considerations of the hydraulic boundary condition, both during

and after excavation, whereas excavation in clays is usually rapid enough to be treated as an

undrained process, therefore the tunnel parameter may remain impermeable until after excavation

is complete.

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2.5 Summary

Based on the numerous researches, it can be concluded that the normal probability curve

remains the most suitable method to determine the transverse settlement troughs. For that reason,

in the practical world, it is fitting to use the empirical solution given by Peck (1969) and the

parameter ( ) introduced by O'Reilly and New (1982) to determine the surface settlement trough

induced by tunneling. Nevertheless, the restriction of empirical methods is that they need

knowledge of the maximum surface settlement ( ) which can be obtained from instrumentation

reading only after the shield passes or it can be predicted from estimated ground loss ( ).

Because the maximum settlement depends on five components of ground loss which are; face loss,

over-excavation, pitching, ground disturbance, and tail void, this makes prediction of the magnitude

29

of ground loss exceptionally difficult particularly in the case of EPB tunneling. Therefore, to predict

the surface settlement profile acceptably, one still needs other methods to find out the maximum

settlement, or needs good judgment, which comes only from years of experience, in the selection of

a suitable value of ground loss. This requires taking into consideration numerous aspects of the

process of tunneling such as the ground conditions, tunnel alignment, operation control and

tunneling techniques.

The solution given by Attewell and Woodman (1982), for the longitudinal surface settlement

which assumes that 50% of maximum surface settlement is coincident with the plane of the shield

face, is valid only for open-faced shield. But this assumption is not true in the case of closed-face

shields, as Nomoto et al. (1999) results from the centrifuge tests which simulated the ground

response due to closed-face shield tunneling showed that the settlement in plane of the shield face

was less than .

Even though the prediction of ground movement based on finite element and numerical

methods are useful for representing the general form of the settlement, they also have considerable

limitations. 2D analyses are not realistic enough for modeling three-dimensional behavior of shield

tunneling and therefore can’t get reasonable predictions of the surface settlement trough. Although

3D finite element analyses are used to improve these restrictions, the cost and time necessary for

the full 3D analysis are significantly high. In addition, the 3D models cannot replicate all aspects of

shield tunneling behavior, which is a lot more complex. For this reason, in the practical world, the

use of the finite element method is still comparatively restricted.

The laboratory models verify the solution proposed by Peck (1969) that the surface settlement

trough matches well the normal probability curve. Only the inflection points from the tests are a bit

different. The centrifuge tests on model tunnels done by Kimura and Mair (1981) show how tunnel

stability has a major impact on the ground movement characteristic of the soil. Nevertheless, even

the complicated models are unable to simulate the entire shield tunnelling procedure. Numerous

other factors which have a major contribution to the amount of settlement were not modelled, such

as pitching angle and tail void grouting. Therefore, the physical models can be used only to verify

assumptions and to propose an overall picture of the mechanism of ground movement.

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Chapter 3: Plaxis

3.1 Introduction

In the following analysis, Plaxis 2D was used to conduct a parametric study of the

longitudinal settlement profile for a bored tunnel construction. Plaxis 2D is a robust finite element

software that can handle complicated geometries and complex construction sequences.

3.2 Material Properties

31

3.2.1 Mohr-Coulomb

The model chosen for this analysis was the Mohr-Coulomb model, for a number of

important reasons. Mainly because the model is simple enough which helps keep the computation

times reasonable. The Mohr-Coulomb represents a ‘first-order’ approximation of soil behavior. For

each layer a constant average stiffness is assumed. Due to this assumption computations tend to be

relatively fast and one obtains a first impression of deformations. Secondly, the Mohr-Coulomb

model captures realistic material behavior unlike the linear elastic model. Third, the soft soil model is

not much better than the Mohr-Coulomb for unloading problems such as tunneling; therefore there

are no benefits in its use. The five available input parameters in PLAXIS, that are and for soil

elasticity; and for soil plasticity and as and angle of dilatancy, are well-known to geotechnical

engineers who can easily obtain these data’s from relatively simply and widely used tests, in contrast

to the more advance parameters required for the more sophisticated models.

3.2.2 Drained versus Undrained

The program allows for a drained or an undrained analysis to be done using any of the material

models. As is usually the case in geotechnical engineering design, a fully drained analysis will closely

approximate long-term settlements while the undrained case will simulate the limiting case. In the

following study the soil being studied was sand therefore using drained of undrained will not have a

large effect on the final results.

32

3.2.3 Structural Elements

Plates and shells are can also be implemented into the analysis. Most of them are treated as

linear elastic members as they are made of strong materials such as steel that yield only at very high

stresses. Also, normal stiffness and flexural rigidity are used to define material behavior. The

interfaces between the soil and structural element can also be set, is the interface strength

reduction factor, for rigid ( ) or a reduced strength ( ). For the case where

represents condtions in which the values of interface friction and adhesion are equal to

the internal friction and cohesion of the soil, whereas signifies lower interface values

than the strength parameters of the soil.

Chapter 4: Analysis

4.1 Introduction

33

The chosen problem geometry consists of a tunnel excavated through sand using the bored

tunnel method. The aim of the analysis is to compare the maximum surface settlement by changing

the friction angle of the soil, the ratio of depth/diameter and the volume loss to the surface

settlement trough obtained using empirical methods.

The input parameters for the analysis were chosen arbitrarily. Nevertheless, every effort was

made to ensure that the tunnel dimensions, material properties, and boundary conditions were

close to what might be encountered in the field. Moreover, if the input parameters are accurate, the

modelled behaviour will provide insight into the mechanism that will minimize the damage to

surface structures.

The aim of the analysis is to obtain the inflection point for the different simulations run. The

inflection point is a vital parameter governing the settlement zone. It depends on numerous factors

including the geometry of the tunnel and the ground conditions. Due to the limited number of

boundary conditions available, which mainly include the geometry of the tunnel and the ground

conditions, numerous different methods have been proposed to help determine the trough width

parameter. The fastest and simplest way is to approximate the position of the inflection point at

on a graph of , where the vertical displacement and x is the horizontal distance

from the tunnel axis.

Another method to calculate the inflection point is by equating equations 4.1 and 4.2.

Eq. 4.1

Eq. 4.2

Where is the ground loss, is the volume condition and is the diameter of the tunnel.

The final method used to obtain the trough width parameter in this analysis is by reading the

value of the inflection point from the graph. The three diffrent values of the trough width

34

parameter are then plotted on the graph proposed by Peck (1969), Figure 2.2 which shows the

relation between settlement trough width parameter and tunnel depth.

Using the methods mentioned above an attempt has been devoted to develop charts for

estimating I-values and maximum settlements of tunnel sites.

4.2 Problem Geometry

The model geometry is based on a hypothetical tunnel located on a green field. The soil profile

has been kept simple; homogenous isotropic linear elastic sand above ground water level was used.

The depth of the tunnel has been kept constant throughout the simulations, but the diameter of the

tunnel, the soil friction angle and the ground loss have been varied.

The depth to the centre of the tunnel is 14 m. Figure 4.1 shows the problem geometry.

Figure 4.1 Problem geometry modeled in half-space

Due to symmetry, only the half-space was modeled as shown in figure 4.1. Halving the number

of elements significantly reduces the computational time.

4.3 Fixities

35

Standard fixities were applied to the boundaries of the symmetric half-space as shown in figure

4.2. These fixities consist of:

1) Vertical geometry lines for which the x-coordinate is equal to the lowest of highest x-

coordinate in the model receive a horizontal fixity ( ).

2) Horizontal geometry lines for which the the y-coordinate is equal to the lowest of highest y-

coordinate in the model receive a full fixity ( ).

3) Structural elements that extend to the boundary of the cross-section, just as the top and

bottom of the shield in Figure 4.1, receive a rotation fixity where no rotation is allowed

around the z-axis (longitudinal axis) if at least one of the displacement directions ( )

of that point is fixed. (PLAXIS, 2001).

Figure 4.2 Applied fixities for (a) vertical geometry lines, (b) horizontal geometry lines, and (c)

structural plate at vertical geometry line

36

4.4 Mesh

The 2D mesh was created with a fine element configuration away from the tunnel, but near the

tunnel boundary the mesh was refined to a very fine mesh. The mesh configuration for one of the

tunnels is shown in Figure 4.3.

Figure 4.3 2D mesh

The length of the mesh was increased as the diameter of tunnel increased due to the fact that

the size of the mesh used in a finite element analysis has an important effect on the computed

results. In cases where the mesh size is too small, the fixed boundaries restrict the movement of the

soil, producing incorrect results.

4.5 Material Properties

To bring the behaviour of modelled sand into conformity of with what might be observed in real

soils, the material properties were chosen carefully. They have been listed in the table below.

37

Table 4.1 Material Properties for soil

Mohr-Coulomb 4

Sand

Type Drained

unsat [kN/m³] 17.00

sat [kN/m³] 20.00

kx [m/day] 1.000

ky [m/day] 1.000

einit [-] 1.000

ck [-] 1E15

Eref [kN/m²] 13000.000

[-] 0.300

Gref [kN/m²] 5000.000

Eoed [kN/m²] 17500.000

cref [kN/m²] 1.00

[°] 25/30/35/40

[°] 0.00

Einc [kN/m²/m]

0.00

yref [m] 0.000

cincrement [kN/m²/m]

0.00

Tstr. [kN/m²] 0.00

Rinter. [-] 1.00

Interface

permeability

Neutral

38

Table 4.2 Material Properties for the tunnel lining

No. Identification EA EI w Mp Np

[kN/m] [kNm²/m] [kN/m/m] [-] [kNm/m] [kN/m]

1 Tunnel Lining 1.4E7 1.43E5 8.40 0.15 1E15 1E15

4.6 Boundary Conditions

As mentioned earlier the depth of the tunnel is kept constant during the simulations. The

following parameters are varied:

Diameter of tunnel

Soil friction angle

Ground loss

The third parameter, ground loss is expressed as a percentage of the notional excavated volume

of the tunnel. In general the ground loss is defined as a fraction of the ratio of the surface settlement

trough volume and the tunnel volume per unit length. These ground loss parameters are empirical

and differ for different subsurface environments and tunnel configurations. To simulate ground loss

during the simulation of the Tunnel, a contraction or volume strain can be applied.

In this analysis the ground loss parameter is varied between 1%, 2% and 3%. The Diameter of the

tunnel is varied between 2m, 4m, 6m, 8m and 10m and the soil friction angle is changed from 25˚,

30˚, 35˚ and 40˚. Table 4.3 gives information on the tunnels used in the simulation.

Table 4.2

Tunnel No. Depth (m) Diameter (m) Depth/Diameter

1 14 2 7.00

2 14 4 3.50

3 14 6 2.33

39

4 14 8 1.75

5 14 10 1.40

Chapter 5: Model Results

The results obtained from 1% ground loss were ignored due to the fact that there was a heave in

the soil surface instead of settlement.

The maximum ground settlement obtained from the analysis is directly measured from the

output graphs in the PLAXIS software. The resulting surface settlement curves are plotted with

vertical settlements against the horizontal distance from the tunnel axis corresponding to the

settlements. The trough width parameter for and the observed trough width paramater

are taken from the graphs.

See Appendix Figure A.1 to A.8 for the surface settlement curves.

After the trough width parameters were obtained for all of the different tunnel simulations the

relationship between settlement trough width parameter and tunnel depth were plotted to compare

the results obtained with Peck’s (1969) chart.

refers to the i taken from from the plotted graphs

the refers to the inflection point picked up from the plotted graphs

refers to the i calculated from equations 4.1 and 4.2

refers to the graph plotted by Peck (1969)

See Appendix Figure A.17 to A.24.

40

41

Chapter 6: Discussions

6.1 Variation in Diameter

As expected with a decrease in the depth/diameter ratio there is a substantial increase in the

surface settlement, this is because as the depth/diameter ratio decreases there is a decrease in the

depth of cover.

FIGURE 6.1 Variation in surface settlement

From Figure 6.1 it can be clearly seen that there is an exponential decrease in the surface

settlement as the tunnel diameter decreases. The deformation behaviour around a shallow tunnel is

often characterized by the formation of shear bands which develop from the tunnel shoulder and

sometimes reach the ground surface. Figure 6.2 gives the strain-distribution model derived from the

results of the measured displacements taken from a subway tunnel in Washington D.C. (Cording and

Hansmire (1985).

A possible justification of this deformational can be stated with the help of Figure 6.3. The

region A, which is bounded by the slip plane k-k, can be regarded as potentially unsteady zone which

can dislodge vertically due to the insufficient frictional support along the length of the k-k planes.

The shear band a which has formed along the k-k line separates the region A from the surrounding.

The region adjacent to A, region B, follows the displacement of region A which leads to the

42

formation of a second shear band b. The regions A and B indicate the primary and secondary regions

of deformational behaviour pointed out by Murayam et. al. (1969, 1971). This effect is not seen for

deeper tunnels and for deeper tunnels (C/D>2.5), the observed tunneling impact at the ground

surface is usually restricted (Cording and Hansmire, l975; Leblais and Bochon, 1991; Pantet, 1991).

FIGURE 6.2 Stress distributions around a subway tunnel (after Cording and Hansmire (1985)).

Figure 6.3 Distinctive deformational mechanisms around a shallow tunnel.

43

Figure 6.4 Vertical displacements for φ-25, ground loss 2% and tunnel depth/diameter = 1.4

Figure 6.5 Vertical displacements for φ-25, ground loss 2% and tunnel depth/diameter = 7

From the two figures the difference is evident, for the shallower tunnel in Figure 6.4 the vertical

displacements lines are much denser compared to the deeper tunnel. For the deeper tunnel there

are sub-surface displacements at deeper depths, and as the depth decreases there is substantial

decrease in the vertical displacement of the soil.

44

6.2 Variation in Soil Friction Angle

From the Figure 6.6 it can be seen that the soil friction angle does not seem to have a substantial

effect on the maximum surface settlement.

Figure 6.6 Variation in maximum surface settlement against increasing soil friction angle for

Ground Loss 3 %

For shallower tunnels there seems to be an insignificant no difference in the maximum surface

settlement of the soil, but as the tunnel cover depth increases there is a noticeable increase in the

settlement.

45

Figure 6.7 Surface Settlement Curves for Z/D =7 and Ground Loss 3%

Figure 6.8 Surface Settlement Curves for Z/D = 1.4 and Ground Loss 3%

46

From Figures 6.7 and 6.8 there seems to be only a slight deviation between the surface

settlement curves, thus indicating that the soil friction angle has a very minute effect on the surface

settlement for tunnels with the surface settlement between 0.01m to 0.06m.

6.3 Comparison of Trough width parameters

The main aim of this analysis was to compare the obtained trough width parameters with Pecks’

(1969).

From Figures 5.9 to 5.16 you can see that the deeper tunnels correspond with Pecks’, but slowly

deviate from Peck’s values for shallower tunnels.

Figure 6.9 Relation between settlement trough width parameter and tunnel depth for Φ-40

47

As anticipated, the greater the depth of tunnel, the greater the width of the settlement trough.

The values of the inflection point from the graph and the value from are close to each

other, indicating that gives a good approximation for calculating the trough width

parameter.

The trough width parameter calculated using the empirical formulae do not coincide well for

shallower tunnels. The main reason behind this is because the empirical formulae used to calculate

the trough width parameter assumes a Gaussian curve, but for shallower tunnels the settlement

curve follows a much steeper curve. (See Appendix Figure A.17 to A.24)

Eq. 6.1

Figure 6.10 Surface Settlement Curves for Φ-35, Z/D = 1.4 and Ground Loss 2%

48

Figure 6.12 Comparison of Trough Width Parameter for φ35 and ground loss 2%

Figure 6.10 shows the comparison between the Plaxis Generated surface settlement curve and the

settlement curve calculated from Equation 6.1. There is a clear difference between the two settlement curves,

for shallower tunnels the surface settlement is more complex and doesn’t follow the Gaussian curve.

Furthermore the difference in the trough width parameters can be seen in Figure 6.12, for shallow tunnels

there is a large deviation in the calculated trough width parameter.

49

Chapter 7: Conclusion

Surface settlement profiles were obtained using the finite element program PLAXIS 2D for a

bored tunnel in sand. The friction angle, ground loss and diameter were varied to see how they

might influence the surface settlement and trough width parameter.

1. As was expected the shallower tunnels tend to have a much larger settlement than

deeper tunnels.

2. The soil friction angle does not seem to play a vital role in the surface settlement for

cohesive soil, when the maximum surface settlements are between the ranges of

0.01m to 0.06m.

3. The trough width parameter taken from the graph and the trough width parameter

corresponding to correspond well with each other, indicating that

gives a good approximation of the trough width parameter.

4. The trough width parameter calculated using empirical methods is suitable for

tunnels with but for shallower tunnels with the empirical formula gives

varying values of the trough width parameter due to the difference in the settlement

curves.

The limitation with the empirical method is due to the fact it requires information of the

maximum surface settlement to describe the settlement trough. The possible ways of obtaining the

maximum settlement can be from instrumental readings only after the shield passes or it can be

estimated using the ground loss parameter. But the main problem is that the ground loss parameter

depends on many factors which include geological conditions, operational parameters, and tunnel

geometry, therefore the estimation of the precise ground loss parameter is particularly complicated.

The significance if the input parameters in predicting surface settlement was investigated. It was

found that the ground loss has a more significant effect on surface settlements than the other

factors but that all input parameters play a role.

Finally to conclude, the fact is that the simulation of reality still remains an estimate, which

inevitable involves some numerical and modelling errors. Furthermore, the precision upon which

reality is approximated depends significantly on the knowledge of the user concerning the modelling

50

of the problem, the understanding of the soil models and their boundaries, the choice of model

parameters, and the skill to judge the consistency of the computational results.

51

Appendix A

Table A.1 Results from analysis of φ25

Friction angle 25%

Ground loss 2%

Depth (m) Diameter (m) Depth/DiameterSurface Settlement

(m)

Calculated Trough Width

parameter

Trough Width parameter from

graph (m) corresponding i

14 2 7.00 0.00207922 12.056 12.110 0.00124753 10.10014 4 3.50 0.00710854 14.105 11.090 0.00426512 9.80014 6 2.33 0.01078357 20.920 11.110 0.00647014 12.20014 8 1.75 0.01383775 28.983 9.830 0.00830265 10.36014 10 1.40 0.02403083 26.077 10.530 0.01441850 10.590

Ground loss 3%


(m)


parameter



14 2 7.00 0.00365993 10.273 12.080 0.00219596 12.00014 4 3.50 0.01233623 12.192 11.011 0.00740174 12.20014 6 2.33 0.02515356 13.453 11.110 0.01509213 11.10014 8 1.75 0.03675908 16.366 11.050 0.02205545 11.05014 10 1.40 0.05713479 16.452 10.990 0.03428087 11.000


52

Friction angle 30%

Ground loss 2%


(m)


parameter



14 2 7.00 0.00234092 10.708 12.140 0.00140455 12.13014 4 3.50 0.00865539 11.584 12.387 0.00519324 10.96514 6 2.33 0.01108608 20.350 12.507 0.00665165 13.50014 8 1.75 0.01466543 27.347 11.220 0.00879926 11.10014 10 1.40 0.02679271 23.389 10.510 0.01607563 10.590

Ground loss 3%


(m)


parameter



14 2 7.00 0.00407179 9.234 11.100 0.00244307 11.06514 4 3.50 0.01388222 10.834 11.147 0.00832933 11.15014 6 2.33 0.02582703 13.102 12.300 0.01549622 11.11014 8 1.75 0.03885271 15.484 11.130 0.02331163 11.13014 10 1.40 0.06149900 15.285 12.376 0.03689940 11.300


53

Friction angle 35%

Ground loss 2%

Depth (m) Diameter (m) Depth/Diameter Surface Settlement (m)Calculated

Trough Width parameter



14 2 7.00 0.00272805 9.188 11.060 0.00163683 11.06014 4 3.50 0.01369853 7.319 9.990 0.00821912 9.97814 6 2.33 0.01206541 18.698 9.640 0.00723925 9.70014 8 1.75 0.01612907 24.866 7.800 0.00967744 11.10014 10 1.40 0.02920425 21.458 8.730 0.01752255 10.000

Ground loss 3%





14 2 7.00 0.00420827 8.935 10.680 0.00252496 10.68514 4 3.50 0.01455913 10.330 9.290 0.00873548 10.73014 6 2.33 0.02656609 12.738 9.790 0.01593965 10.10014 8 1.75 0.04102761 14.663 10.670 0.02461657 10.30014 10 1.40 0.06517070 14.423 10.490 0.03910242 10.600


54

Friction angle 40%

55

Ground loss 2%





14 2 7.00 0.00383956 6.528 10.040 0.00230374 9.00014 4 3.50 0.00775537 12.928 9.992 0.00465322 12.33014 6 2.33 0.01277986 17.652 9.670 0.00766792 12.00014 8 1.75 0.01792904 22.369 9.300 0.01075742 10.20014 10 1.40 0.03359109 18.655 8.746 0.02015466 9.300

Ground loss 3%





14 2 7.00 0.00437154 8.601 10.760 0.00262292 10.67014 4 3.50 0.01512545 9.943 10.490 0.00907527 10.49014 6 2.33 0.02766883 12.230 10.070 0.01660130 10.30014 8 1.75 0.04348045 13.836 10.970 0.02608827 10.55014 10 1.40 0.07172888 13.105 10.267 0.04303733 10.100

56

Figure A.1 Surface Settlement Curves for Φ-25 and ground Loss 2%

Figure A.2 Surface Settlement Curves for Φ-25 and ground Loss 3%

57

Figure A.3 Surface Settlement Curves for Φ-30, Ground Loss 2%


58



59



60

Comparisons of Trough Width Parameter

Figure A.9 Comparison of Trough Width Parameter for φ25 and ground loss 2%

.


61



62



63



64

The graphs below are for 2% ground loss:

Figure A.17 Relation between settlement trough width parameter and tunnel depth for Φ-25

65




66

The graphs below are for 3% ground loss:


67


A.23 Relation between settlement trough width parameter and tunnel depth for Φ-35

68

A.24 Relation between settlement trough width parameter and tunnel depth for Φ-40

Appendix B

Project diary

Week 1: 7th- 14th October 2010

Had my first meeting with Dr.Chan Swee Huat: Dr.Chan gave me the topic ‘Surface settlement induced by tunneling’ and I was asked to do a literature review.My second meeting with Dr.Chan: I had to get familiar on how to use Plaxis. During this week I did a few lessons using the tutorial manual but had problems using the software so I could not continue.

Week 2: 14th- 21th October 2010

Third meeting with Dr.Chan: figured out the problem with the software. This week concentrated more on literature review and less on learning how to use the software.

Read the following thesis:

-THREE DIMENSIONAL ANALYSIS OF SURFACE SETTLEMENT IN SOFT GROUND TUNNELING BY JEDEDIAH

DRURY GREENWOOD, BACHELOR OF GEOLOGICAL ENGINEERING, UNIVERSITY OF MINNESOTA, 2001

Chapter 3: Surface Settlements pg 22.

o Different methods for estimating ground deformation around tunnel excavations:

Stochastic and empirical methods. Analytical methods Finite element and numerical methods Laboratory experiments

- SURFACE SETTLEMENT PREDICTIONS FOR ISTANBUL METRO TUNNELS EXCAVATED BY EPB-TBM BY

S.G.ERCELEBI, H.COPUR AND I.OCAK, RECEIVED: 13 JULY 2009 / ACCEPTED: 15 MARCH 2010

What should be looked at before excavation:

o A thorough study of the ground by site investigations should be performed to find out

69

Physical and mechanical properties of the ground existence of underground water deformation characteristics such as stiffness

o Technical parameters:

Tunnel depth and geometry tunnel diameter–line–grade single or double track lines neighboring structures

o Primary reason for ground movements:

convergence of the ground into the tunnel after excavation

o Three settlement prediction approaches for mechanized tunnel excavations:

numerical analysis such as finite element method analytical method semi-theoretical (semi-empirical) method

-ANALYTICAL PREDICTION FOR TUNNELING-INDUCED GROUND MOVEMENTS IN CLAYS, BY N.

LOGANATHANL AND H. G. POULOS,Z FELLOW, ASCE

o The settlements caused by tunneling are often characterized by the term "ground loss," expressed as a percentage of the notional excavated volume of the tunnel.

Ground Loss definition: a percentage of the ratio of the surface settlement trough volume and

the tunnel volume per unit length

o equivalent undrained ground loss Eo is defined with respect to the gap parameter

Gap parameter: magnitude of the equivalent two-dimensional void formed around the tunnel

due to the combined effects of the three-dimensional (3D) elastoplastic ground deformation at the

tunnel face, over excavation of soil around the periphery of the tunnel shield, and the physical gap

that is related to the tunneling machine, shield, and lining geometry.

o Verruijt and Booker (1996) for the estimation of the ground settlement due to a uniform radial ground loss

70

Week 3: 21st - 28th October 2010

No meeting with Dr.Chan was required as I was still getting familiar with the software. I completed tutorial lessons 1, 2 and 3 of Plaxis.

Did not understand the following from the software:

Standard Fixities K0 – Procedure Prescribed Displacements Plastic/Elastic analysis (rigid/flexible footing) Initial effective stress state

Week 3: 28th October- 4th November

Major software error could not continue with tutorial (not much work done this week due to

coursework).

Fourth meeting with Dr.Chan: Very short brief meeting as Dr.Chan had to go for accreditation meeting. Software problem solved.

Week 4: 4th -11th November

Finished tutorial lessons 4 and 5.

Did not understand the following from the software:

Strength reduction factor inter. (pg 48) Dilatancy angle ∑Mstage (pg 55) Undrained river embankment – water level changes

Read the following thesis

71

- SETTLEMENTS AND DAMAGE CAUSED BY CONSTRUCTION-INDUCED VIBRATIONS , BY K. RAINER

MASSARSCH , GEO ENGINEERING AB, BROMMA, SWEDEN

o The propagating waves expose buildings or installations in the ground to repeated distortion cycles (“sagging” as well as “hogging”). This effect is fundamentally a cyclic loading problem and not a “dynamic effect”. Distortion problems can also occur at very slow distortion rates, for example in connection with tunnelling work or as a result of seasonal ground water variations (swelling and shrinking of foundation soil).

-REPRESENTING SETTLEMENT FOR SOFT GROUND TUNNELLING, BY TAKAHIRO AOYAGI (PG1-40)

o Factors Influencing ground movement

Geological conditions Tunnel dimensions Construction methods

o page 16: Research by peck and schmidt

Basic equations

S = vertical settlement of a point

x = distance from vertical plane containing tunnel axis

I = parameter defining width of trough

Contains info on work done by other researchers


Continuation of

-REPRESENTING SETTLEMENT FOR SOFT GROUND TUNNELLING, BY TAKAHIRO AOYAGI (PG 40- )

72

Soft ground tunnelling Magnitude of settlement in cohesionless soil > cohesive soils Settlement trough width cohesionless soils < cohesive soils

Maximum surface settlement (eqn. 3.3)

Prediction of Ground Displacements (pg 49)

-other information regarding DAT not required.

-SURFACE SETTLEMENT PREDICTION FOR ISTANBUL METRO TUNNELS VIA 3D FE AND EMPIRICAL

METHODS, BY S.G. ERCELEBI, H. COPUR, N. BILGIN & C. FERIDUNOGLU ,ISTANBUL TECHNICAL

UNIVERSITY, FACULTY OF MINES, MINING ENG. DEPT., MASLAK, ISTANBUL, TURKEY

CONTAINS NUMEROUS EQUATIONS USED in estimations for surface settlement (pg 165)

Started work on the essay.


Finished tutorial lessons 5 and 6. Completed all the Plaxis tutorials.

Fifth meeting with Dr.Chan: Dr.Chan gave me data that I needed to input into the software for analysis. This included shear strength parameters, depth of tunnel, Poisson’s ratio etc.

Continued work on the essay.

Semester Break : Finished 4000+ words of literature review.


Continued work on literature review, most research was done, only compilation of work needed.

73


Had my first meeting of the semester with Dr.Chan Swee Huat: Dr.Chan read skimmed thru my literature review. We discussed the simulations that we will need to run for my research. Decided on using uniform layer of clay, and the parameters that would be varied during the analysis.


Ran my first simulations with Plaxis, had a few problems regarding certain parameters to input into the system.

Had my second meeting of the semester with Dr.Chan Swee Huat: Dr.Chan explained on how

to choose my parameters for the analysis. These parameters included, and for soil

elasticity; and for soil plasticity and as an angle of dilatancy

Week 4 and Week 5: February 28th -13th March

Ran numerous simulations, then the case of drained and undrained came up.

Had my third meeting of the semester with Dr.Chan Swee Huat: Expalined to him the drained and undrained problem, we then decided to use Sand for the analysis.

Read numerous research papers from the book:

-GEOTECHNICAL ASPECTS OF UNDERGROUND CONSTRUCTION IN SOFT GROUND : INTERNATIONAL

SYMPOSIUM ON GEOTECHNICAL ASPECTS OF UNDERGROUND CONSTRUCTION IN SOFT GROUND

Proved very helpful in my literature review and gave me a deeper insight in the complicated

techniques used for underground construction.

74

Another important book which provided additional information for my literature review was:

-MECHANIZED TUNNELLING IN URBAN AREAS :

Week 6 and Week 7: 14th – 27th March

Ran 60 different simulations on Plaxis. Most of the results matched with each other, but

there were a few errors with my simulations.

Had my fourth meeting of the semester with Dr.Chan Swee Huat: Explained to him the

errors that I had with my analysis, found out the problem, I had made a mistake with the

procedure.

Continued running my simulations.

Week 8 : 28th March– 3rd April

Had my fifth meeting of the semester with Dr.Chan Swee Huat: Showed all my results to Dr.Chan, he agreed that I can continue with my analysis.

Week 9 and Week 10: 4th – 17th April

Started work on my analysis. The plotting of the surface settlement curves was the most tedious

part of the analysis phase. Worked on my report, e-mailed my draft to Dr.Chan who checked it

thoroughly and told on the parts I needed to improve on.

Finished 7000+ words of my report.

Week 11:

75

Continued work on my report, couldn’t meet Dr.Chan during the week as he had work, and

therefore had to meet up with him on a Saturday.

Had my final meeting of the semester with Dr.Chan Swee Huat: Showed him my finally rough draft. He gave me advice on where there was still room for improvement.

Made a few changes to my report, proof read it twice and was ready for printing.

References

Akagi, H. and Komiya, K. (1996). "Finite Element Simulation of Shield Tunnelling Processes in Soft Ground". Proc. Int.Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, London, Balkema, pp. 447-452.

Atkinson, J. H., Brown, E. T., and Pottss, D. M. (1975). "Collapse of Shallow Unlined Tunnels in Dense Sand". Tunnel & Tunnelling, May 1975, pp. 81-87.

Atkinson, J. H. and Pottss, D. M. (1977). "Subsidence above Shallow Tunnels in Soft Ground". Proc. ASCE Geotechnical Engineering Division, Vol. 103, GT 4, pp. 307-325.

Attewell, P. B. and Farmer, I. W. (1974). "Ground Deformations resulting from Shield Tunnelling in London Clay". Canadian Geotech. J., Vol. 1, No. 3, pp. 380-395.

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Surface Settlement Induced by Tunnelling