SETTLEMENT TROUGH DUE TO TUNNELING IN COHESIVE GROUND

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Indian Geotechnical Journal, 41(2), 2011, 64-75

Abstract: Surface settlements of soil due to tunneling are caused by stress relief and subsidencedue to movement of support by excavation. In this paper, the shape of settlement trough causedby tunneling in cohesive ground is investigated by different approaches; namely, analyticalsolutions, empirical solutions and numerical solution by the finite element method. The width ofsettlement trough was obtained through the finite element method by establishing the change inthe slope of the computed settlement profile. The results show that the finite element methodoverpredicted the settlement trough width compared with the results of Peck for soft and stiff claybut there is an excellent agreement with Rankin's estimation. The results show that there is a goodagreement between the complex variable analysis for z/D=1.5, while using z/D = 2 and 3, thecurve diverges in the region far away from the center of the tunnel.

Key words

Tunnel, clay, finite elements, settlement, complex variable

SETTLEMENT TROUGH DUE TO TUNNELING IN COHESIVE GROUND

Mohammed Y. Fattah1, Kais T. Shlash2 and Nahla M. Salim3

1 Assistant Professor, University of Technology , Baghdad, Iraq, Email: [email protected]

2 Professor, University of Technology , Baghdad, Iraq

3 Assistant Professor, University of Technology , Baghdad, Iraq

Introduction

The construction of a tunnel usually leads to some surface disturbance, particularly settlement. These effects are often of little importance to green field sites (i.e. those without structures), but where structures are present, significant damage can result. Continuous research and advancement in technology towards tunneling work will inevitably lead to safer and both economically and environmentally efficient construction process. Besides obtaining field data to formulate empirical relationships of ground deformation, a major difficulty is the inconsistency of soil condition and applicability of the empirical formulas to different types of soil. The available analytical solutions are not sufficient to include complex ground conditions and hence a comprehensive analytical solution coupled with numerical modelling is necessary to model the effect of surface settlement due to soft ground tunneling.

Soft ground may consist of cohesive or cohesionless material. Sites used as case histories are frequently classified as one of these two types, although in reality no site ever fits this definition exactly. Previous researchers have recognized a difference in ground movements due to tunneling in two types of materials, with movements in cohesionless ground appearing to be restricted to a narrower region above the tunnel than in cohesive soils.

This paper discusses different approaches in predicting the settlement. Reanalysis of the problem which was adopted by Chow (1994) is done to understand tunneling. In addition, this paper deals with analytical methods used to analyze the problem of tunnels or cavities in soft ground.

Surface Settlement

There are two main causes for surface movements of soil due to tunneling:

1. The stress relief mechanism causes an upward movement of soil. This is because, when soil is removed from the ground, there is a reduction in soil weight.

2. Subsidence due to the removal of support due to excavation: This causes a downward movement due to lack of support after the excavation.

Several researchers have studied the patterns of a settlement trough by using four different approaches:

1. Analytical solutions (closed form solutions) which include:

a) Elasticity solution

b) Sagaseta’s solution (Sagaseta, 1987)

c) Modified analytical solution (Verruijt and Booker, 1996).

2. Empirical solutions.

3. Numerical solutions.

4. Physical modelling approaches.

These four approaches in solving problems have their own advantages and limitations.

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Indian Geotechnical Journal, 41(2), 2011

Analytical Solutions

Elasticity Solution

Analytical solution exists for a point load acting beneath the surface of an infinite elastic half space (Poulos and Davis, 1974).

Chow (1994) used this solution to estimate the settlement due to shallow tunneling, the effect of the tunnel face is ignored, and the tunnel is assumed to have infinite length. The unloading of the soil mass due to excavation is modelled as a line load along the tunnel axis. It is not possible to obtain analytically the integral of the point load solution (i.e. the solution for a line load), so relative differences in vertical displacement are derived which cancel the insoluble part of the integral. The surface settlement over the tunnel, δz is then calculated as the settlement relative to some distance point on the surface which will in practice experience negligible settlement (Augard, 1997):

)(8 22

22

zxGzD

z +−=

γδ (1)

where, D is the tunnel diameter, γ is the unit weight of soil, G is the shear modulus of soil, x is the horizontal distance from tunnel’s centre, and z is the depth measured from tunnel’s centre.

Sagaseta’s Method

Sagaseta (1987) suggested that in problems where the boundary conditions are only in terms of displacements, and only displacements are required for the solution, it is possible to eliminate the stresses from the governing equations and work in terms of strain for simple soil models. Example of this problem is the determination of the displacement field in an isotropic homogeneous incompressible soil when some material is extracted from it at shallow depth and the surrounding soil completely fills the void left by the extraction. Shallow tunneling in elastic homogeneous soil can be regarded as this type of problem, where the extracted material is defined by ground loss.

The advantage of Sagaseta’s method is that the strain field obtained is independent of soil stiffness, and is valid for incompressible material even for fluid. Sagaseta showed that closed form solution for soil deformed due to ground loss (such as in tunnel excavation) can be obtained. Chow (1994) used this approach to derive the solution for vertical displacement at the surface as:

)(4 22

22

zxGzD

z +−=

γδ (2)

The theoretical solutions provided by Sagaseta (1987), which other authors modified to predict soft ground deformations due to tunneling, is essentially based on incompressible soils. Hence, it might not accurately predict the deformations in soft ground. Elastic solutions are more applicable for hard rock conditions.

Complex Variable Solution

Verruijt and Booker (1996) modified analytical equations for estimation of surface settlement using complex variable method. They considered Mindlin’s problem of circular cavity in an elastic half plane loaded by gravity. The characteristics of this problem are that the stresses and strains due to the removal of the material inside a circular cavity are to be determined, with the stresses at infinity being determined by the action of gravity. This problem was solved by using complex variable method with a conformal mapping of the region in the z-plane. Statement of Mindlin’s Problem

The problem is first be defined by giving all the relevant equations and the boundary conditions. The problem is solved by superposition of the three partial solutions. These solutions are:

The first partial solution represents the stresses due to gravity in the half plane z<0, without the cavity. This is a simple elementary solution.

⎪⎭

⎪⎬

⎫

===

0..

.

0

xz

x

z

zKz

τγσ

γσ (3)

where Ko is the coefficient of lateral stress at rest.

In Mindlin’s problem, only the values Ko =0, Ko =1 and Ko = ν (1−ν) are considered in which ν is Poisson’s ratio. Verruijt and Booker (2000) used the coefficient Ko as an independent parameter determined by the geological history. The surface tractions along the cavity boundary can be related to the stresses. So the surface tractions in this case are found to be:

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z

x (4)

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SETTLEMENT TROUGH DUE TO TUNNELING IN COHESIVE GROUND Mohammed Y. Fattah, Kais T. Shlash and Nahla M. Salim

The program Modf-CRISP is used in modelling tunneling considering different soil models, as follows:

1. Linear elastic.

2. Nonlinear elastic.

3. Elastic- perfectly plastic.

Table 1 Soil properties for London clay (Chow, 1994)

Property Value

Shear modulus, G (kPa) 33557

Poisson's ratio, ν 0.495

Unit weight of the soil, γ (kN/m3) 20

Oteo and Sagaseta (1982) found that the bottom rigid base has the most significant effect on the predicted settlements. When the depth of the rigid base below tunnel axis, Hd, increases, the settlements decrease, resulting in surface heave for a value of Hd/D>7. Hence in the present study, the depth of the bottom base of the mesh has been chosen accordingly.

Computer Program

tunnel axis. Values of z of 7.5 m, 10 m, and 15 m areused. The first analysis is carried out for short termmovement, undrained conditions; where the volumetricstrain is zero. It follows that the value of undrained bulkmodulus must be infinite, and Poisson’s ratio equals0.5. In finite element analysis, it is not possible to usean infinite undrained bulk modulus. To approximateundrained conditions, a value of Poisson’s ratio of0.495 is used. The soil stiffness is assumed to vary withdepth according to the following equation:

)( zzmEE −+= oo (8)

Where E is Young’s modulus, E0 is the initialYoung's modulus at datum elevation, m is the rate ofincrease of Young's modulus with depth, z0 is the depthof tunnel axis, and z is the depth to the point of interest.

Mechanism of Short-Term Settlement Response

Analytical approaches often require theidentification of non-dimensional group of the importantparameters influencing a problem. One such group isthe stability number N, which is defined by Broms andBennermark (1967) as:

u

Tz

SN

)( σσ −= (9)

Where σz is the overburden pressure at thetunnel axis, σΤ is the tunnel support pressure or internalpressure (if any), and Su is the undrained shear strengthof clay. If σΤ =0 then N will be equal to σz /Su or γ z /Su.,where z = C+D, C is the depth of tunnel’s crown. Threevalues of Su /γ z are used in the present analyses. Thevalues of Su /γ z and their corresponding Su for each z /Dare given in Table 2. These values are presented inTables 3 and 4. The analyses were carried out usinghomogeneous elastic analysis and homogeneous elasticperfectly plastic analysis.

Presentation of Results

Linear Elastic Analysis

The results obtained for three different depths ofthe tunnel (z /D = 1.5, 2 and 3) using the program Modf-CRISP are shown in Figure 3, and presented indimensionless form as δ G / γ D2 versus x/D. Heave isnoticed for z/D =1.5, 2 and 3. This is because themovement of the soil is upward due to relief effect ofexcavated soil in a purely elastic homogeneous medium.As x/D increases, the upward movement of the soildecreases, this is because that the soil is remote fromconcentration of loading. These results conform withChow (1994) as illustrated in Figure 4.

Modf-CRISP allows elements to be removed tosimulate excavation and elements to be added tosimulate construction. The implied loading for boththese cases are automatically calculated by theprogram. When performing a non-linear analysisinvolving excavation or construction, Modf-CRISP allowsthe effect of element removal or addition to be spreadover several increments in an "incremental block". Anincrement block is just a series of ordinary incrementsgrouped together in the input data for the program.Element stiffness is always added or removed in the firstincrement of block, but the associated loads aredistributed over all the increments in the block.When a tunnel is excavated, unloading and stiffnessreduction occur simultaneously. The first results fromremoval of material having self weight. The secondoccurs because the ground structure is altered. Tomodel the first of these processes, loads are applied tothe mesh remaining after excavation. The secondprocess is modeled by excluding the stiffness of eachelement excavated from the calculation of structurestiffness.

Linear Elastic and Elastic-Plastic Models

The analyses are divided into two categories:elastic and elastic plastic. The analyses are carried outfor homogeneous soil and soil with properties varyingwith depth. For each soil type, an analysis is made forthree values of z, the depth below the surface of the

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Table 2 Values of Su used for different depths of tunnel analysis

N 3.33 2.5 2.0

)./( zSu γ

0.3 0.4 0.5

C / D 1.0 1.5 2.5 1.0 1.5 2.5 1.0 1.5 2.5

z (m) 7.5 10 15 7.5 10 15 7.5 10 15

z / D 1.5 2.0 3.0 1.5 2.0 3.0 1.5 2.0 3.0

Su (kPa) 45 60 75 60 80 100 90 120 150

Table 3 Soil properties used for linear elastic model (from Chow, 1994)

Homogeneous Non homogenous

z (m) 7.5 10 15 7.5 10 15

z / D 1.5 2.0 3.0 1.5 2.0 3.0

G0 (kPa) 33557 33557 33557 0 0 0

m (kPa/m) 0 0 0 3355.7 3355.7 3355.7

Su0 (kPa) 100 100 100 100 100 100

Reference* 1.5eh 2eh 3eh 1.5en 2en 3en

*e = elastic, n = non homogeneous, h = homogeneous

Table 4 Soil properties used for elastic, perfectly plastic homogeneous analysis (from Chow, 1994)

Homogeneous

z (m) 7.5 10 15

z / D 1.5 2.0 3.0

G0 (kPa) 33557 33557 33557

m (kPa/m) 0 0 0

Su0 (kPa) 45 60 90 60 80 100 90 120 150

Su / γ z 0.3 0.4 0.5 0.3 0.4 0.5 0.3 0.4 0.5

Reference* 1.5 ph3 1.5 ph4 1.5 ph5 2 ph3 2 ph4 2 ph5 3 ph3 3 ph4 3 ph5

*e = elastic, n = non homogeneous, h = homogeneous, p = plastic

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Fig. 3 Surface displacement for elastic-homogeneous soil model predicted by the finite element method for different z/D ratios.

Fig. 4 Comparison of the analysis results with Chow's results for different z/D ratios using elastic homogeneous model

Figures 5, 6 and 7 show a comparison of the surface settlement predicted by different analytical methods. The results show that there is a good agreement between the complex variable analysis and the finite element for z/D = 1.5, while using z/D = 2 and 3, the curves diverge in the region far away from the center of the tunnel, but the behaviour is similar to that of the curve using complex variable method. A good agreement with elastic and Sagaseta's solution is shown in the region far away from the center of the tunnel while heave can be noticed in the region near the center of tunnel using the finite element analysis.

A comparison between the results of the finite element method and the complex variable method is clearly shown in Figure 8 for a z/D value of 1.5. It is observed that the maximum horizontal movement tends to be towards the tunnel as z/D decreases in the complex variable method while the maximum horizontal movement moves away from the center of the tunnel as z/D decreases in the finite element method.

Elastic Non-Homogeneous Soil Model

Modf-CRISP provides a non-homogeneous model in which the material properties can vary with depth. This method is used in the present work, dimensionless plot of δ G / γ D2 against x/D is shown in Figure 9. The results show that settlements are predicted for z/D = 2 and 3 while heave can be noticed for z/D = 1.5.

Elastic-plastic Analysis

The dimensionless settlement profile obtained using elastic-plastic homogeneous soil is shown in Figure 10, corresponding to a constant value of Su / γ z of 0.3. It is observed that for Su / γ z =0.3, settlements are obtained above the tunnel for z/D = 2 and 3 (2ph3, 3ph3) while heave can be obtained at z/D = 1.5. Increasing Su / γ z to 0.4 caused heave when z/D = 2 and 3, while settlement is noticed at z/D =1.5. Further increase in Su / γ z to 0.5 caused heave to be obtained for three values of z (1.5 ph5, 2 ph5, 3 ph5).

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 5 10 15 20 25 30 35 40 45 X / D

Nor

mal

ized

Mov

emen

t1.5eh2eh3eh

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 5 10 15 20 25 30 35 40 45X / D

Nor

mal

ized

Mov

emen

t

Z/D=1.5 eh present workZ/D=1.5 eh Chow (1994)Z/D=3 eh present workZ/D=3 eh Chow (1994)

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Fig. 5 Comparison between different approaches in predicting the surface settlement (z / D = 1.5)

Fig. 6 Comparison between different approaches in predicting the surface settlement (z/D = 2)

Fig. 7 Comparison between different approaches in predicting the surface settlement (z/D = 3)

-5

-4

-3

-2

-1

0

1

2

3

4

0 25 50 75 100 125 150 175 200 225X (m)

Surfa

ce s

ettle

men

t (m

m)

Finite Element AnalysisComplex Variable SolutionElastic SolutionSagaseta Solution

-4

-3

-2

-1

0

1

2

0 25 50 75 100 125 150 175 200 225

X (m)

Sur

face

Set

tlem

ent (

mm

)

Finite Element AnalysisComplex Variable AnalysisElastic SolutionSagaseta Solution

-4

-3

-2

-1

0

1

2

0 50 100 150 200 250 300

X (m)

Nor

mal

ized

Mov

emen

t

Finite Element AnalysisComplex Variable Solution Elastic SolutionSagaseta Solution

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Fig. 8 Comparison of the surface settlement obtained by the finite element method with complex variable results (z/D =1.5)

Fig. 9 Surface displacement predicted by the finite element method using elastic nonhomogeneous soil model for different z/D ratios and Su / γ z=0.3

Fig. 10 Surface displacement using elastic-plastic homogeneous soil model predicted by the finite element method for different z/D ratios and Su / γ z=0.3

-1

-0.8

-0.6

-0.4

-0.2

0

0 50 100 150 200 250 300x (m)

Hor

izon

tal m

ovem

ent (

mm

)

Finite Element AnalysisComplex Variable Solution

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 5 10 15 20 25 30 35 40 45X / D

Nor

mal

ized

Mov

emen

t Z/D=1.5en

Z/D=2.0en

Z/D=3.0en

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 4 8 12 16 20 24 28 32 36 40 44

X/D

Nor

mal

ized

Mov

emen

t

1.5ph32ph33ph3

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Trough Width Parameter (i) As explained previously, the trough width

parameter i describes the width of settlement trough. In transverse settlement profile, it is defined as the distance of the point of inflection (i.e. the point of maximum slope) from the tunnel center line as shown in Figure 1.

To evaluate the width of the settlement trough, i, there are two methods:

1. Using linear regression to obtain the gradient of the plot of ln δ/δmax versus x2 for each settlement profile, the value of the gradient is equal to -1/(2 i2)

2. Establishing the change in the slope of the computed settlement profile.

The first method assumes that the predicted settlement profiles follow the shape of an error function curve:

( )22max 2/lnln ix−= δδ

( )( )22max 2/exp ix−= δδ (10)

Taking natural log for the above equation gives:

( )22max 2/lnln ix−= δδ (11)

By plotting ln δ/δmax versus x2, the gradient obtained would be equal to -1/(2 i2), and the value of i can be evaluated. The disadvantage of this method lies in the assumption made for the shape of the predicted settlement trough.

Although field investigations carried out by Peck (1969) showed that surface settlements in tunneling problems could fit with this type of probability function, computed settlements did not necessarily produce results that could be represented by this type of probability function. This is due to the fact that the data from field investigations were usually obtained in a region comparatively close to the tunnel (e.g. < 20 m).

The predicted value of i becomes inaccurate since it is obtained from the gradient of ln δ/δmax

versus x2 plot, and is taken as the best fit line for the total horizontal width of the finite element mesh (200 m in this case).The second method was achieved by establishing the point where the change in the slope of the settlement profile from positive to negative occurs.

Since the computed settlement profile was plotted by joining the vertical displacement of each node on the surface of the mesh using straight lines, therefore the change in the slope of the settlement profiles were represented by a change in the gradient. This method considers the whole range of x and it is more reliable than the first method.

The second method was used and plots of i / D against z/D are presented in Figure 11. The results are obtained from Peck's field investigation for the values of i / D for the range of values for z/D (1.5 to 3) for soft to stiff clays and the results are also obtained using different equations to estimate the settlement trough width (i). The results reveal that the finite element analysis overpredicts the settlement trough width (i). This may be due to the plastic behaviour of the soil.

Elastic analysis was carried out with C/D >3 to represent a deep tunnel behaviour with σh = σv and unit weight of soil taken as 20 kN/m3. The settlement trough obtained in the analysis is compared with different analyses explained early. A good agreement is obtained between the finite element analysis and elastic analysis.

The surface settlement values calculated using different approaches are shown in Figure 12. The conclusion drawn is that there is a good agreement between the finite element results and the elastic solution in the region near to the center of the tunnel, but the settlement trough is wider than Peck's solution and narrower than Sagaseta’s elastic solution. The estimation of the settlement trough (i) for deep tunnel using different approaches is listed in Table 5.

The results show that there is a good agreement with Rankin (1988), O'Reilly and New (1982) but there is an approximately 36 % difference from Peck's estimation. This difference is due to the fact that Peck used the probability function in the estimation of i which may not necessarily fit with the present results.

Figure 13 shows the horizontal surface displacement obtained from the finite element results and empirical (Gaussian) solution (equation 11). Here, the Gaussian model prediction is based on the assumption that the vectors of ground movement are oriented towards the tunnel axis (O'Reilly and New, 1982). For the tunnel model, both the form (allowing for the trough being too wide) and the magnitude of maximum movement are similar to the Gaussian model.

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Fig. 11 Plot of i/D against z / D using different methods in estimation of the settlement trough width (i)

Fig. 12 Surface settlement obtained from different approaches (deep tunnel) mz 300 = , diameter = 4 m.

Fig. 13 Horizontal movement using different approaches for deep tunnel mz 300 = , diameter = 4 m.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5 3 3.5

Z / D

i / D

CRISP (pn3)Stiff Clay (Peck)Soft Clay (Peck)O'Reilly and New (1982)Atkinson and Potts (1977)Leach (1986)

-6

-5

-4

-3

-2

-1

0-150 -100 -50 0 50 100 150

X / D

Sur

face

Set

tlem

ent (

mm

)

Finite elements (CRISP)Peck, 1969Poulos and Davis, 1980Sagaseta Solution

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

-125 -100 -75 -50 -25 0 25 50 75 100 125X (m)

Hor

izon

tal

Mov

emen

t (m

m)

Finite Elements (CRISP) O'Reilly and New,1982

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Gunn, M. (1993): The Prediction of Surface SettlementProfiles Due to Tunneling, Predictive Soil Mechanics,Proc. Worth Mem. Symp., Thomas Telford, London. , pp.304-316.

O'Reilly, M. P. and New, B. M., (1982): Settlements aboveTunnels in the UK-Their Magnitude and Prediction,Tunneling, 82, pp. 173-181.

Oteo, C.S. and Sagaseta, C., (1982): Prediction ofSettlements Due to Underground Openings, ProceedingInternational Symposium Numerical Method inGeomechanics Zurich, Balema, pp. 653-659.

Peck, R. B. (1969): Deep Excavations and Tunneling in SoftGround, Proceeding of the 7th internationalConference on Soil Mechanics and FoundationEngineering, state of the Art volume, Mexico pp. 225-290.

Poulos, H. G. and Davis, E.H. (1974): Elastic Solutions forSoil and Rock Mechanics, John Wiley and Sons, NewYork.

Rankin, W. (1988): Ground Movements Resulting fromUrban Tunneling, Prediction and Effects, Proc. 23rd

conf. of the Eng. Group of the Geological Society,London Geological Society, pp. 79-92.

Sagaseta, C., (1987): Analysis of Undrained SoilDeformation Due to Ground Loss, Geotechnique, 37 (3),pp. 301-320.

Salim, N. M. N., (2006): Time-Dependent Analysis ofTunnels in Clays Using the Finite Element Method, Ph.D.thesis, University of Technology, Iraq.

Tan, W.L. and Ranjith, P.G., (2003): Numerical Analysis ofPipe Roof Reinforcement in Soft Ground Tunneling,

Proceeding of the 16th

International Conference onEngineering Mechanics, July 16-18 2003, University ofWashington, Seattle.

Verruijt, A. and Booker, J.R., (1996): Surface SettlementsDue to Deformation of a Tunnel in an Elastic Half-plane, Geotechnique, London, England, 46 (4), pp. 753-756.

Verruijt, A. and Booker, J.R., (2000): Complex VariableSolution of Mindlin's Problem of an Excavated Tunnel,in “Developments in Theoretical Geomechanics”, A.A.Balkema, Rotterdam, the Netherlands, pp. 3–22.

Table 5 Estimation of the settlement trough width (i) using different approaches.

i (m)

z (m) D (m) Finite Elements (Present study)

Peck (1969)

O'Reilly and New (1982)

Rankin (1988)

30 4 15 9.48 12.69 15

Conclusions

This paper tries to estimate the surfacesettlement due to tunneling. The surface settlementswere estimated using different methods, analytical,empirical and the finite elements. The conclusionsdrawn from this analysis are as follows:

• In elastic homogeneous medium, the upwardmovement of the soil is due to relief effect of theexcavated soil above the tunnel but this movementdecreases as x/D increases. This is because the soilis remote from concentration of loading.

• The results show that there is a good agreementbetween the complex variable analysis for z/D=1.5,References

• While using z/D = 2 and 3, the curve diverges in theregion far away from the center of the tunnel.

• The finite element method overpredicted thesettlement trough width i compared with the resultsof Peck for soft and stiff clay but there is anexcellent agreement with Rankin's estimation.

References

Augard, C. E., (1997): Numerical Modeling of TunnelingProcesses for Assessment of Damage to Building, Ph.D.thesis, University of Oxford.

Broms, B. B. and Bennermark, H., (1967): Stability of Clayat Vertical Openings, Journal of Soil Mechanics andFoundations Division, ASCE, 93 (1), pp. 71-95.

Broms, B. B. and Bennermark, H., (1967): Stability of Clayat Vertical Openings, Journal of Soil Mechanics andFoundations Division, ASCE, 93 (1), pp. 71-95.

Chow, L. (1994): Prediction of Surface Settlement Due toTunneling in Soft Ground, M.Sc. thesis, University ofOxford.

Cording, E.J. and Hansmire, W.H., (1975): Displacementaround Soft Ground Tunnels, General Report: SessionIV, Tunnels in Soil" Precedings 5th PanamericanCongress on Soil Mechanics and FoundationEngineering, pp. 571-632.

Fujita, K. (1982): Prediction of Surface Settlements Causedby Shield Tunneling, Proceedings of the InternationalConference on Soil Mechanics, vol.1, pp. 239-246.,Mexico City, Mexico.

SETTLEMENT TROUGH DUE TO TUNNELING IN COHESIVE GROUND

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