Case reportVolume 7 - Issue 4 - March 2019DOI: 10.19080/CERJ.2019.07.555720

Civil Eng Res JCopyright © All rights are reserved by Hao Feng

Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel

Hao Feng*Shanghai Civil Engineering Co., Ltd. of CREC, China

Submission: February 05, 2019; Published: March 22, 2019

*Corresponding author: Hao Feng, Shanghai Civil Engineering Co., Ltd. of CREC, China

IntroductionThe prediction and calculation methods of surface settlement

have been extensively studied over the years. Peck and Schmidt (1969) first proposed the empirical formula using the Gaussian function to predict surface settlement:

2

2exp22

lx

V xSiiπ

= −

(1)

(Figure 1)

where xS is the ground settlement at position x; x is the hor-

izontal distance from the tunnel centerline to position x; lV is the

volume of ground loss; and i is the horizontal distance from the tunnel centerline to the inflection point of the internal half settle-ment curve.

Many scholars have revised Peck’s empirical formula to ex-pand its practical applications. In addition to the empirical formu-la for calculating the surface settlement, the stochastic medium theory method is considered to be an effective method for accu-rately predicting the surface movement and deformation caused by underground mining [1]. In addition, the ground subsidence field measurement method and the laboratory test method have been widely used [2]. With the development of computing ability, numerical simulation has been widely used to study the stratum disturbance of soft soil caused by the shield excavation of a tun-nel and the curved segment of a tunnel. However, there is no set-tlement calculation method for curved tunnels in the literature. Based on field measurements from shielding subway tunnels lo-cated in Southeast Asia, using regression modeling of measured

data and mathematical simulation, the relationship between the uneven distribution of jacking thrust and the mechanics of dis-symmetrical settlement are discussed, and a method of calculat-ing the dissymmetrical settlement profile is proposed.

Predicting Surface Settlement Induced by Excavation of a Curved Tunnel

Surface settlement induced by curved tunnelingMeng [3] numerically simulated the ground settlement over a

shield tunnel with an alignment radius of 450m at a depth of 16m using ANSYS software. The surface settlement profile was repre-sented in his paper, as shown in Figure 1. The surface settlement profile in Figure 1 is not as symmetric as a Gaussian curve. The maximum settlement occurs near the tunnel longitudinal axis, slightly forward to the inside of the curve. Ground upheaval takes place on the outside of the curve, while this does not happen on the inside of the curve. Ground on the inside of the curve subsides more than that on the outside when comparing points along the cross section that are equal distances from the tunnel centerline. This indicates that the half settlement trough on the inside of the curve will be wider than its equivalent on the outside.

Formulation of predicting surface settlement induced by curved tunneling

From the numerical results of Meng [3], it can be inferred that function is not suitable for predicting the ground settlement in-duced by curved tunneling [4]. Therefore, it is reasonable to mod-

Civil Eng Res J 7(4): CERJ.MS.ID.555720 (2019) 00105

Abstract

Surface settlement is a natural phenomenon of ground disturbance in subway tunnel construction. Dissymmetrical surface settlement profiles are observed when shielding in a curved tunnel, but these observations are quite different from the predictions of typical formulae which indicate a symmetrical surface settlement profile in straight tunnels. Based on the field measurements from shielding subway tunnels in soft ground located in Southeast Asia, the relation of the uneven distribution of jacking thrust and the mechanics of dissymmetrical settlement are discussed, and the method of calculating the dissymmetrical settlement profile is proposed in this study. The methods proposed in this article can be used to properly predict the surface settlement induced by a single curved tunnel in similar geological and construction conditions. The results also provide a reference set of shield construction parameters.

Keywords: Curved Tunnel; Uneven settlement; Construction; Mass Rapid Transit

How to cite this article: Hao Feng, Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel. Civil Eng Res J. 2019; 7(4): 555720. DOI: 10.19080/CERJ.2019.07.555720.

00106

Civil Engineering Research Journal

ify function by considering the alignment radius to get a better prediction of the settlement induced by curved tunneling [4]. To

predict the surface settlement at the excavation face, the following assumptions can be made:

Figure 1: The surface settlement profile.

A. The maximum settlement occurs above the axis of tunnel, and

B. The surface settlement curve can be treated as two half settlement curves along the sides of the tunnel’s longitudinal axis, both of which can be represented by Gaussian functions with different coefficients.

Based on these assumptions, the surface settlement trough induced by curved tunneling can be depicted as Figure 2. The for-mulation for calculating curved tunneling induced ground settle-ment would be expressed as follows:

2

2

2

2

exp , 0 ,22

exp , 022

i

iix

o

oo

V x xii

SV x x

ii

π

π

− ≥ = − < (2)

where x is the horizontal distance from the tunnel centerline; Vi and Vo are the volume of ground loss on the inside and outside of a curved tunnel; and ii and io are the horizontal distance from the tunnel centerline to the inflection point of the half settlement curve on the inside and outside, respectively.

Figure 2: curved tunneling.

How to cite this article: Hao Feng, Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel. Civil Eng Res J. 2019; 7(4): 555720. DOI: 10.19080/CERJ.2019.07.555720.

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Demonstration of Proposed FormulationIn order to demonstrate the formulation of curved tunneling

induced settlement prediction, expressed as Equation (1), the first

phase Mass Rapid Transit (MRT) project in Kuala Lumpur, which has several curved portions with different alignment radii, was chosen to validate the proposed method.

Project profile

Figure 3: Geological drilling results.

The first phase MRT project in Kuala Lumpur consists of shielding construction. The tunnel runs from Semantan north portal through KL sentral to Parsa seni. The 2,716m long tunnel was built by an earth pressure balanced tunnel boring machine. It is buried at a depth of 13.2m. The shield machine with an articu-lation device has an outer diameter of 6,630mm. The lining ring is 5.8m in inner diameter, 275mm in thickness, and 1.4m in width. The hydraulic jacks of the shield are divided into four groups: the upper, lower, external, and internal groups. The average drilling speed of the shield machine was 6 rings per day.

Engineering geological conditionAs indicated by the geological drilling results shown in Figure

3, the tunnel is mainly located in the Kenny Hill residual soil. The weathered Kenny Hill is approximately class IV with its joints fully developed. It is of complicated and diversified geological struc-ture with mixed soft and hard stratum, containing many mixtures

of soil and rock or interlayers of soil and gravel layers. There is highly weathered quartz rock, phyllite, mudstone, etc. The under-ground water level is 2.62 to 24.77m above the tunnel crown. The permeability coefficient of the formation is about 1.0 × 10−6 to 5.0 × 10−5m/s. The earth pressure balanced tunnel boring machine passes through mainly sandy silt and gravelly silt. The geological condition of each observation surface is shown Table 1.

Measurement of ground settlementPlan of measurement: Several settlement observation sec-

tions had been arranged along the tunnel alignment. Ground set-tlement markers were installed along the observation sections. The ground settlement was measured from 10 days before the shield cutter reached the observation section to 30 days after the shield’s tail passed through the observation sections. The mea-surement was conducted at least once a day.

Table 1: Soil properties.

Soil Type Poisson’s Ratio V Unit Weight (γ)kN/m3 Cohesion (c’)/KPa Inner Friction Angle(φ’)/° Young’s Modulus(E)/MPa

Sandy Silt 0.35 18.5 5 28 56

Quartzite 0.15 20 10 32 280

Figure 4: Measurement of ground settlement.

How to cite this article: Hao Feng, Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel. Civil Eng Res J. 2019; 7(4): 555720. DOI: 10.19080/CERJ.2019.07.555720.

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As shown in Figure 4, four representative observation sections in the curved portion were adopted in this paper. The chainage of the four observation sections are SB CH 1+448, SB CH 1+518, SB CH 1+960, and SB CH 2+400, the alignment radii of which are 500m, 400m, 700m, and 300m, respectively.

Results of measurement: The settlement measurements on the arrival of the cutter of the shield machine have been collected. The observed ground settlement points are shown in Table 2. The observed surface settlement curves at all the observation sections are plotted in Figure 5. In Figure 5, the x value is the horizontal distance from the centerline of the tunnel, and a positive x val-ue indicates the internal of curved alignment; the z value is the ground settlement. Surface upheaval occurs much more frequent-

ly on the external of curved alignment than on the internal of curved alignment. The subsided ground on the internal of curved alignment outranges that on the internal. As shown in Figure 5a, the width of subsided ground on the internal of curved alignment is about 17.0m, which is much larger than around 6.5m on the external of curved alignment Figure 5bc. It can be inferred from Figure 5 that the maximum surface settlement always occurs over the centerline of the north tunnel. On average, the maximum set-tlement tends to grow as the radius of alignment decreases. Fur-thermore, the settlement on the internal of curved alignment is often larger than that on the external when comparing points with the same distance from the centerline. The ground settlement at x = 6.5m is −6.19mm, which is much larger than 0 mm at x = −6.5 m (see Figure 5d).

Figure 5a: Results of measurement.

Figure 5b: Results of measurement.

Jacking thrust: The jacking thrust of the shield is equipped with 22 cylinders, which are divided into groups A, B, C, and D.

Groups A and C are distributed symmetrically on the left and right sides of the shield as shown in Figure 6.

How to cite this article: Hao Feng, Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel. Civil Eng Res J. 2019; 7(4): 555720. DOI: 10.19080/CERJ.2019.07.555720.

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Figure 5c: Results of measurement.

Figure 5d: Results of measurement.

Figure 6: Distributed symmetrically on the left and right sides of the shield.

How to cite this article: Hao Feng, Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel. Civil Eng Res J. 2019; 7(4): 555720. DOI: 10.19080/CERJ.2019.07.555720.

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Table 2 : Observed ground settlement points.

Observed Sections Observed ground Settlement Points x(m) Observed Sections

SB CH 1+448(R=500m)

GSM 1451 6.5

SB CH1+518(R=400m)

GSM 1452 0

GSM 1453 -6.5

GSM 1454 -13

GSM 1455 -16.5

GSM 1456 -18

GSM 1457 -19

GSM 1521 50

GSM 1522 6.5

GSM 1523 0

GSM 1524 -6.5

GSM 1525 -13

GSM 1526 -16.5

GSM 1527 -24

GSM 1528 -31

SB CH 2+400 (R=300m)

GSM 2450 30

SB CH1+960(R=700m)

GSM 2451 3.5

GSM 2452 0

GSM 2433 -6.5

GSM 2434 -13

GSM 2435 -16

GSM 2436 -19.5

GSM 2437 -27

GSM 1961 50

GSM 1962 0

GSM 1963 -6.5

GSM 1964 -13

GSM 1965 -21

GSM 1966 -24

GSM 1967 -34

Table 3: The jacking thrust of group A(Jo) and C(Ji).

Observed Sections Jo / MPa Ji / MPa Jo/Ji

SB CH 1+448 6.44 2.22 0.29

SB CH 1+518 8.05 2.07 0.39

SB CH 1+960 7.92 4.7 0.17

SB CH 2+400 14.7 2.41 0.61

It was observed that the jacking force of group A on the out-side of the curve was greater than that of group C on the inside of the curve when the earth pressure balanced tunnel boring ma-chine reached the observation sections. During the research, the jacking force of the earth pressure balanced tunnel boring ma-chine was recorded. The jacking forces Jo and Ji and their ratio (Jo/ Ji) for jacking groups A and C are shown in Table 3.

Analysis of the measurements

Regression fitting calculation: The observed surface settle-

ments presented in Figure 5 are fitted by Equation (2), as shown in Figure 7. The fitted curve is highly consistent with the in-situ data, and the goodness of fit with the observed surface settle-ments points in-situ is 0.99, 0.96, 0.97, and 0.99, indicating that Equation (2) is applicable for this project.

Relationship between surface settlement and jacking thrust: As the radius of curved alignment varies, both the area and the shape of the surface settlement trough, as well as the un-even jacking thrust of the shield machine, will change accordingly. The variables for ground loss volume per meter Vi and VO were mathematically integrated with Origin software on both halves of the fitted settlement curves in Figure 8. Then, the volume of ground loss per meter on the outside and inside of the curved alignment, Vi and VO, are correspondingly obtained (Table 4). The relationship between Vi /VO and Jo/Ji is fitted by Equation (3), as shown in Figure 8.

How to cite this article: Hao Feng, Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel. Civil Eng Res J. 2019; 7(4): 555720. DOI: 10.19080/CERJ.2019.07.555720.

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/ ( / ) .i o o iV V k J J b= + (3)

Here, Vi and VO are the volume of ground loss on the outside and inside of the curve, respectively; k and b are 0.44 and 0.64,

and the goodness of fit is 0.95. The total ground loss volume Vl is the sum of Vi and VO, as follow:

i o lV V V+ = (4)

Figure 7: Regression fitting calculation.

Figure 8: Relationship between surface settlement and jacking thrust.

Table 4: The volume of ground loss per meter on the external and in-ternal.

Observed Sections Vi/ m·mm VO/ m·mm Vi/ VO

SB CH 1+448 35 14.5 2.41

SB CH 1+518 100 30 3.33

SB CH 1+960 101 75 1.35

SB CH 2+400 109 26 4.23

As a result, with the total ground loss volume Vl and the jack-ing forces Jo/Ji in-situ, we can obtain the ground loss volume Vi and VO through Equations (3) and (4), and then predict surface settlement Sx using formula (2) [5-18].

ConclusionThe following conclusions were drawn based on the mea-

sured settlements:

The prediction method of the surface settlement above the curved portion of a single shield tunnel was obtained and ex-pressed as the following formula:

2

2

2

2

exp , 0 ,22

exp , 022

i

iix

o

oo

V x xii

SV x x

ii

π

π

− ≥ = − <

(2)

The proposed method predicted settlement with a maximum error of 4%.

How to cite this article: Hao Feng, Analysis and Prediction of Uneven Settlement due to a Curved Shield Metro Tunnel. Civil Eng Res J. 2019; 7(4): 555720. DOI: 10.19080/CERJ.2019.07.555720.

00112

Civil Engineering Research Journal

The relationship between uneven surface settlement and jack-ing force in this project was obtained (radius of curved alignment is more than 300m in this case) and expressed as the following equation: / ( / )i o O iV V k J J b= • + (3)

i o lV V V+ = (4)

The ratios of Vi /VO and Jo/Ji have a positive relationship.

It was demonstrated that curved tunnel settlement can be de-scribed with the Formula and Equation in conclusions (1) and (2), and thus surface settlement can be calculated.

The settlement prediction formula in this paper is mainly giv-en for the specific geological condition, which is Kenny Hill resid-ual soil, at an alignment radius of more than 300m. Theoretically, extensive research should be conducted under other geological conditions, alignment radii, and construction conditions to fur-ther test the applicability of the proposed formulae.

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