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-TwoDimensionalModeltoAssesstheSoilBehavioraroundTunnel(BaghdadMetro).

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AqeelAL-Adili

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1

Two Dimensional Model to Assess the Soil Behavior Around Tunnel lining (Baghdad Metro)

AQEEL SHAKIR Al-ADILI Building and Construction Engineering department, University of Technology, Baghdad ,Iraq, e-mail; aqeeladili@hotmail.com

ABSTRACT

The project of Baghdad metro represents one of the important transporting projects in Iraq,

and the city of Baghdad may be regarded as an example of a modern city built on alluvial plain

deposits and may be encountered in other cities with similar soil behaviours. This paper aimed to

build 2-D model based on finite elements numerical approach (PLAXIS) in order to study the soil

behavior around tunnel in different soil types for tunnel boring method (TBM). The main objectives

of this study are to assess the stresses and strain redistribution around tunnel opening and ground

displacement (settlements).

This research has been carried out by taken 9 different sites chosen along the proposed

Baghdad Metro project to apply this study technique (one of these locations is under Tigris River).

The displacements of soil clusters and the differential settlement for the foundations of buildings

near and above of the tunnel lining for the studied locations have a different rates, depending on soil

types and properties, phreatic level, and tunnel depth. The stresses distribution which result from

tunnel construction in the most of the locations, concentrated around tunnel body, as well as the

beneath structures foundation. The calculations and analysis concludes that the studied locations will

not have serious problems of settlements and deformation with respects to the tunnel boring method.

Key words: Tunnel – Soft soil displacement – PLAXIS modelling – strain distribution – settlement.

1- INTRODUCTION:

Baghdad city is located in the Mesopotamian alluvial plain between latitudes 33°14' - 33°25' N

and longitudes 44°31'-44°17'E. The general altitude ranges between 30.5 and 34.85 m.a.s.l. The

Tigris river divides the city into a right (Karkh) and left (Risafa) sections. The area is characterized

by a arid to semi arid climate with dry hot summers and cold winters, the mean annual rainfall is

about 150 mm.

The project of Baghdad metro represents one of the important transporting projects in Iraq.

This project proposed since 1978. Soil investigations were carried out and the design criteria were

planned, nevertheless, the project not constructed yet. Many problems in this project were raised due

to the behavior of Baghdad soil, with alluvial deposits in origin (non – homogenous), high water

table, presence of organic matters, large fill strata, and sulfated soil (Al-Siaede,1997). The project

comprises 32 km of metro path, which is made up of two lines meets at central interchange –

Kulafaá street (Khulani sq. SO1). Thus, forming four routes A to D (Fig.1). The proposed lines will

2

have 10 m diameter tunnel with invert levels between 10 – to 25 m below ground level

(BRTA,1980).

This paper aimed to build 2-D model based on finite elements numerical approach in order to

study the soil behavior around tunnel in different soil types for tunnel boring method (TBM)

methods. These machines are used in unstable ground conditions where the face requires support at

all times; this principally applies to permeable ground below the water table (i.e. mainly sands or

mixtures of sands, silts and clays) or soft clays (Mair and Taylor, 1997).

The main objectives of this study are to assess the: stresses redistribution around tunnel

opening; stress variation (effective and total), strain distributions, and ground settlement and

differential settlements above the tunnel for structures and soil surface. Nine sites have been chosen

along the proposed Baghdad Metro project to apply this study techniques (one of these locations is

under Tigris river),(Fig.-1).

2. SOIL PROFILE DESCRIPTION:

Al-Adili,1998, described Baghdad soil properties as alluvial origin and are generally consists

of fill material (Recent stratum) with variable thickness ranging from 0.5 to 4 m, which is essentially

cohesive in nature. This is generally underlain by cohesive strata, clay, silty clay or clayey silt, with

sand lenses in some places. At depths of more than 7-8 m, the sediments are generally sandy. The

recent strata are essentially cohesive, except beneath the river where it is granular, and has

completely replaced the cohesive stratum.

The granular stratum, generally comprised of medium dense to dense silty medium sand,

which is sometimes slightly gravely to gravely fine, and the maximum depth achieved being about

60 m. ( BRTA,198). Table-1, shows the soil profiles of the 9 studied locations.

The soil is relatively saline as a result of high gypsum and salt contents of the parent

formations from which the sediments were derived and the dry climate and long periods of

cultivation. Chlorides and sulphates are the predominant types of salts. The soil of Baghdad showed

a wide range of variation in grain size distribution.

Table-1: Soil profiles of the study locations for tunnel model.

Locations Soil profile Tunnel

depth (m)

Distance between

foundation and tunnel (m)

W.T

(m)

S1 Fill= 2m

Soft soil =7m

Sandy soil=3m

6.5 3 -2.5

S2 Fill=4m

Silty clay=5m

Silty sand=4m

12 5 -4

3

S3 Fill=1m

Silty clay=4m

Clayey silty sand=6m

8 7 -2.5

S4 Fill=1m

Silty clay=7m

Clayey silty sand=3m

9 8 -1.5

S5 Fill=2m

Clayey silt=2m

Sandy clayey silt=4m

6 7 -2

S6 Fill=3.5m

Clay=5m

Clayey sand=2.5m

7 5 -2.5

S7 Fill=1m

Clay=2.5m

Clayey silt=3.5m

Sandy silt=2

Clayey silty sand=3m

5 8 -2

S8 Fill=2m

Silty clay=3m

Clayey sandy silt=3m

6.5 7 -

2.25

S9 Fill=2

Clayey silt=4m

Silty sandy clay=2m

Silty sand=3m

4 8 -2.5

3.NUMIRECAL MODEL ANALYSIS :

3-1. Methodology :

Finite element (FE) analysis offers considerable possibilities of modeling many aspects of

bored tunnel construction. Many 2-D analysis are based on the ground reaction curve concept,

sometimes referred to as the Convergence-Confinement method (CCM), as shown in

Fig.-2(Peck,1969; Mair and Taylor, 1997).

4

Figure-1: Baghdad Metro routing and study locations( BRTA,1980).

Fig.-2: Application to 2D F.E. analysis of principle of CCM.

5

Three dimensional effects are approximated by reducing a proportion of the stresses

imposed by the soil to excavated acting on the tunnel boundary, and then installing the tunnel lining.

This can be simplified by considering the radial stresses applied to the tunnel boundary, r , this can

be expressed as;

r = ( 1 - λ ) o ------------------ 1

Where, o is the initial ground stress prior to tunneling, and λ is an unloading parameter (0<

λ < 1). The stress removed from the soil prior to installation of the lining is λo, and correspondingly

the stress applied to the installed lining is (1 - λ) o, (Mair and Taylor, 1997). As the stress is

removed from the tunnel boundary, radial displacements occur which are equivalent to volume loss

Vl. The resulting volume loss is related to the reduction in stress, λo.

The numerical approach which used in this research, is 2-D finite element special purpose

computer package PLAXIS-8 (Brinkgrev,2002).

The real situations may be modeled either by plane strain or an axisymmetric model. The

static deformation and static equilibrium of continuum of a soil body can be formulated as:

LT + p = 0 ---------------- 2

This equation relates the spatial derivatives of the six stress components, assembled in

vectors p . LT is the transpose of a differential operator, in addition to the equilibrium equation, the

kinematics relation can be formulated as:

= L u ----------------- 3

This equation expresses the six strain components, assembled in vectors as the spatial

derivatives of the three displacement components, assembled in vector u. The link between eq.1 and

eq.2 is formed by a constitutive relation representing the material behavior which can be represented

as :

= M ---------------- 4

The analysis of Baghdad metro model, based on plain strain with Mohr – Coulomb model to

simulate the behavior of soil and continua, with drained conditions to simulate the soil conditions

and to assess the settlements on long term, as well as, the plastic deformation analysis. These criteria

will figure the accurate prediction of final situation. Furthermore, the theory of ground water flow in

porous medium can be described by Darcy’s law, considering steady flow in applying model on

Baghdad soils).

3-2. Analysis of tunnel model and concepts:

The most important concepts in tunneling studies is the distributions of stresses and strains of

soils around tunnel lining, as well as, settlements and/or ground displacement. When a circular

tunnel is driven in any ground, the initial ground stresses (vertical and horizontal) will be changed to

new stresses components named radial and tangential stresses, (Obert and Duval,1967). The radial

and tangential stress components, for each soil state coincide with the principal total stresses:

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t = v and r =h at the spring line (tunnel axis level), and

t = h and r = v at the invert and crown of tunnel ( floor and roof).

Wong and Kaiser,(1987) used the finite element method to study the stress redistribution

around the circular tunnels in 2-D models. They found that the yielding initiation will be started

when the stress differences (t - r) exceeds the shear strength of the soil. While the yield locations

around tunnel depends on the initial ground stresses (v,h) and the ground stress ratio Ko. They used

relation between stress ratio Ko, and the Rankine´s effective earth pressure coefficient Ka, to estimate

the initial state of soil as below;

When Ka > Ko , the soil is plastic while when

Ka < Ko , the soil is elastic .

Table –2 below, shows that Baghdad soil is considering elastic states in all 9 locations studies.

Table- 2: Some of Baghdad geotechnical parameters .

Locations

Ko

Ka

τ (kN/m

2)

Tunnel

depth (H)

State

SOI

0.6

0.25

400

25 Elastic

AO2

0.6

0.25

138

10

Elastic

A14

0.6

0.25

270

16.5

Elastic

A24

1.5

0.35

275

16.5

Elastic

BO6

1.5

0.30

229

20

Elastic

CO2

1.5

0.35

300

20.5

Elastic

CO8 1.5 0.39 112 10 Elastic

C2O 0.6 0.25 255 15 Elastic

DO6 0.6 0.25 260 16.5 Elastic

The construction of bored tunnels in soft ground inevitably causes ground movements

(settlements or subsidence). The prediction of ground movements and the assessment of the potential

effects on the infrastructure is therefore an essential aspect of the planning, design and construction

of a tunneling project in the urban environment (Mair and Taylor, 1997).

Settlements and displacements due to tunneling construct , have different kinds, such as;

surface (immediate settlement), subsurface, horizontal, longitudinal settlements as well as post –

construction settlements (long term settlements), (Mair and Taylor,1997).

Peck (1969), and subsequently authors, have shown that the transverse settlements trough

immediately following tunnel construction is well – described by a Gaussian distribution curve as:

Sv = Smax exp(-y2/2i

2 ) ----------------- 1

Where; Sv = Settlement

7

Smax = maximum settlement on the tunnel center-line

y= horizontal distance from the tunnel center-line

i= horizontal distance from the tunnel center-line to the point of

inflexion of the settlement trough .

The volume of the surface settlement trough (per meter length of tunnel), Vs, can be

evaluated by integrating eq. 1 to give;

Vs = √2π i Smax ------------------------- 2

The volume loss (ground loss Vt), is the amount of ground lost in the region close to the

tunnel. When tunneling under drained conditions Vs less than Vt because of dilation, while ground

movements usually occur under undrained (constant volume) conditions, in which case Vs = Vt (Mair

and Taylor, 1997). Whatever the soil type, it is convenient to express the volume loss in terms of the

volume of the surface settlement trough, Vs, expressed as a percentage fraction, Vl , of the excavated

area of the tunnel, i.e. for a circular tunnel ;

Vs = Vl (π D2 / 4 ) --------------------- 3

Horizontal movements could cause damage to structures and underground services. O’Reilly

and New(1991), proposed that, for tunnels in clays, ground displacement vectors are directed

towards the tunnel axis, this leads to the simple relation ; Sh = ( y / zo ) Sy ----------------------- 4

This assumption leads to the distribution of surface horizontal ground movement given by ;

Sh / Shmax =1.65 ( y /i ) exp ( -y2 / 2 i

2 ) ------------------ 5

The theoretical maximum horizontal movement, Shmax, occurs at the point of inflexion of the

settlement trough and is equal to 0.6 K Smax.

Subsurface settlement profiles developed and how they relate to surface settlement trough,

becoming increasingly important in the urban environment (Mair and Taylor,1997; Burland,2001).

Moreover, in the urban area, there may be cases where a structure close to or directly above the

tunnel center-line might experience more damage from the progressive longitudinal settlement

trough generated ahead of the tunnel face, than from the final transverse settlement profile after the

tunnel face has passed beneath the structure (Mair and Taylor, 1997), they concluded that the

longitudinal settlement trough having the form of the cumulative probability curve, but it has only

been validated for tunnels in clays.

Long term settlement (post–construction settlement), tends to cause wider settlement trough,

and can be significant, particularly in the case of tunnels in soft, compressible clays (Mair and

Tylor,1997). These arise from changes of pore pressures (and hence effective stresses) following

construction of the tunnel, and take the form of increasing settlements (sometimes referred to as

consolidation settlements) but generally with very little increase in the horizontal component of the

ground movements.

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4. RESULTS AND DISCUSSION:

In urban areas, it is essential to protect pre-existing structures and underground conduits from

damage during tunneling. To accomplish this, it is necessary to predict the influence of tunneling on

neighboring structures. Predicting of ground stress and deformation behavior (immediate settlements

after tunnel constructions) has been carried out by numerical analysis, based on 2-D FM package

PLAXIS Ver.8. Fig.-3, illustrate tunnel analysis model which considers in this calculations represent

the typical model (SO1). Table-3, shows the soil parameters for the model data.

Fig.-3: Typical Model of the soil section and tunnel lining in PLAXIS calculations (not to scale).

Table-3: Soil properties as input data in the typical model (lab test results).

Parameters Granular soil Soft soil Fill material

Unit weight dry(kN/m3) 18 16 16

Unit weight saturated(kN/m3) 20 18 20

Permeability-h (m/day) 0.5 0.0001 1

Permeability-v(m/day) 0.5 0.0001 1

Young modulus(kPa) 10000 2000 4000

Poisson’s ratio 0.33 0.3 0.3

Cohesions (kN/m2) 1 5 1

(degree) Friction angle 30 25 30

4.1. GROUND DISPLACEMENT AND SETTLEMENTS:

Analysis of 9 different locations along Baghdad metro routs have showed wide range with

displacements (settlement) of the structures (with raft foundation) above tunnel lining, ranging from

54 mm for location BO6 to 126 mm for the location C2O. Figure-4 and Figure-5 illustrates the total

12 m

4 m

B = 10m

Foundation=25 kPa

Soft soil(clayey silty soil)

L1=5m

Fill soil

8 m Granular soil

Load weight-=25 kN/m2

Tunnel lining (D=10m) 9

W.T.

L2=3L1(m)

9

displacement for soil profiles around and above tunnel lining (foundation exist) for the typical

location (SO1). However, the differential settlements of buildings took a place depending on loads

and pressures of the buildings (structures), ranging from 6 mm on location CO2 up to 19 mm on

location A14, as simulated in this model (Fig.6). The differential settlement is due to tunnel lining,

and it shows maximum settlement in the adjacent edge of structures to tunnel lining, Table-4 showed

the results of differential settlements. However, the study showed that the percentage of differential

settlement were within allowable limits (Bowels,1996), and considers with not high failure effects.

The major factors influencing the development of post-construction settlement above tunnel are as

follows:

i. The magnitude and distribution of excess pore pressure, ∆u, generated by construction

tunnel .

ii. The compressibility and permeability of the soil.

iii. The pore pressure boundary conditions, particularity the permeability of the tunnel lining

relative to the permeability of the soil.

iv. The initial pore pressure distribution in the ground prior to tunnel

construction.(Burland,2001 ) .

Figure-4; The deformed mesh and displacement of the soil and foundation,(SO1).

10

Figure-5; Shows the total displacement (directions and magnitude) on the soil

profile above and around tunnel lining.

Figure-6; Illustrate the differential settlement which occurred in foundation above

tunnel lining.

Mair and Taylor,(1997), mentioned from three case histories, involved tunnel construction

methods (TBM) there was very significant face support. This caused appreciable positive excess

pore pressure to be generated, and in all three cases dissipation of these excess pore pressure resulted

in post-construction settlement troughs very similar to the classical Gaussian curve associated with

short-term settlement ( assuming i = 0.5 zo) .

11

Table - 4: The settlement of the structures existing above tunnel lining due to tunnel

constriction.

Locations

Total

displacement(mm)

Settlement

(mm)

Differential

Settlement(mm)

Bending

Moment

(kNm/m)

Shear strain

%

SO1

86.5

24

8

512

13.5

AO2

105

30

18

15

5.5

A14

104

30.5

19

12

5.7

A24

78

17

8.5

335

2.6

BO6

54

17.5

10

283

11.4

CO2

79

15

7

362

2.3

COS

102

30

18.5

20

6

C2O

126

79

17.5

11

7.3

DO6

88

30

9

502

13

4.2. STRESS AND STRAIN ASSESSMENTS:

The assessment of degree of structures (Buildings) damage can be a highly subjective and

motive matter. The deformation of structures such as cracking in masonry and concrete walls, and

finishes, due to strain which resultant from tunneling is very important and could be large scale

phenomena. Kuwahara, et al.,(1997), explained that the magnitude of strains developed is different,

reflecting the different soil conditions, construction and grouting methods adopted at a particular

site, the patterns of strain distribution are similar to each other. Namely, tensile strains develop

above the tunnel crown during “tail void settlement “, and these tensile strains decay with the

distance from the tunnel center towards ground surface. Strains at the side of tunnel show

compressive. The initial tensile strain above the tunnel crown turn to compressive strains during

“subsequent settlement“. The strains at the side of the tunnel remain compressive with an increase in

magnitude. The results of this calculation showed that the effective stresses distribution after tunnel

construction (volume loss) and drying the lining (pore water pressure =zero), are concentrated

mainly around tunnel lining and under buildings foundation in the locations SO1, C2O, and DO6

(Fig.-7 and Fig.-8), while the other studied locations showed less concentration and amount

(intensity) around tunnel and under foundations. The arching occurring around tunnel reduces the

stresses acting on the tunnel lining (Brinkgreve, 2002).

12

Figure-7; Shows the effective stresses in the soil profile due to tunnel lining,(SO1).

Figure-8; Shows the total stresses in the soil profile due to tunnel lining,(SO1).

The deformations behaviour and trends of the soil could be observed and concluded from

incremental strain and plastic point resultant from this model. Figure-9, illustrate that location SO1

(typical model) have less tension areas of the soil, especially around tunnel lining, while the rest

study locations showed wide areas of tension soil body (plasticity and mobility) around tunnel lining

13

and near foundation of structures. Furthermore, the deformation and strains (total and volumetric

strains) of soil skeleton due to tunnel construction are concentrated around tunnel lining with high

intensity as well as at the far end of foundation of the structures (buildings) (Figures-10 and 11).

Locations SOI, DO6, and BO6 showed high intensity of strain around tunnel but with low to

medium percentages, while locations A14, AO2, COS, and A24 showed less intensity strains around

and under foundation but with high percentages

Figure-9: The plastic point analysis for the soil cluster (SO1 location).

Figure-10; Shows the total strain in the soil profile due to tunnel lining.

14

Figure-11; Shows the volumetric strain in the soil profile due to tunnel lining.(shading scale)

5. CONCLUSION:

This paper has been carried out to investigate the behaviour and properties of soil around and

above tunnel after construction, the research have been concluded the followings;

1. The present study demonstrates a successful application of PLAXIS in analyzing the soil

properties and any existing foundations around tunnel lining. A simulation of this new

situation (displacement and deformations) has concluded a suitable and rational result to

investigate the tunnels (Baghdad metro) construction effects.

2. The displacements of soil clusters near foundations of the tunnel lining of the 9 studied

locations have a different rates ranging from 54 to 126 mm. This displacement depends on

many factors such as soil profile, soil properties, and the horizontal and vertical distance

from the tunnel centre.

3. Stresses distribution which results from this model have been showed in the most of the

locations concentrated around tunnel body, as well as the strain effects the soil clusters

around lining of the tunnel.

4. The research approved that the studied locations will not have serious problems of

settlements and deformation with respects to the tunnel boring method. It has found that the

most deformation clusters are near and around tunnel lining, and in fewer rates near surface

soils.

5. This study also prevailed that must have precaution for the foundation above the centre of

tunnel lining like in the location of intersection of the metro routings and beneath the Tigris

river.

15

REFERENCES

Al-Adili,A.S. (1998), Geotechnical Evaluation of Baghdad Soil Subsidence and their Treatments ,

Ph.D. Thesis , Univ. of Baghdad , 150 p .

Al-Siaede,R.S.(1997), The Analytical model for Geotechnical Problems Around Tunnels, Ph.D.

thesis, Univ. of Baghdad, 142 p.

Brinkgreve,R.B.J. (2002), Delft university of Technology and PLAX1S b.v.-8, Netherlands.

BRTA,(1980), Baghdad Metro, Modified Studies and Preliminary Design. Tech. report. NCCL.

Iraq.

Bowles, J. (1996), Foundation Analysis and Design, 5th

ed., MeGraw-Hill inc., N.Y., 1175 p.

Burland, J.B. (2001), Subsidence due to Tunnelling and its Effect on buildings, Proceeding of the

15th

int. conference of soil mechanics and foundation eng., Turkey, pp. 2399 - 2402 .

Kuwahara,H.,Yamazaki,T. and Kusakabe,O.(1997),Ground Deformation Mechanism of Shield

tunnelling due to Tail void formation in soft Clay, Proceeding of the 14th

int. conference of soil

mechanics and foundation eng.. Germany, pp. 1457-1460.

Mair,RJ. and Taylor,R.N. (1997), Bored Tunnelling in the Urban Environment, Proceeding of the

14th

int. conference of soil mechanics and foundation engineering, Germany, pp.2353- 2380.

Peck,R.B. (1969), Deep Excavation and Tunnelling in Soft Ground, State of the art report, 7th

ICSMFE, pp. 225 - 290.

Obert,L. and Duval,W. (1967), Rock mechanics and the design of structures in rock. John Wiley

and sons , Inc. ,USA.

O'reilly.M.P. and New,B.M. (1991),Tunneling induced ground movements; predicting their

magnitude and effects. In Proc.l4th

int. conf. on ground movements.

Wong,R. and Kaiser,P.(1986), Ground Behavior near Soft Ground Tunnels. Prec. int. cong. on

large under ground, Italy , pp. 942 - 951.