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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
The 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:
where Sx is the ground settlement at position x; x is the horizontal distance from the tunnel centerline to position x; Vl is the volume of ground loss; and i is the horizontal distance from the tunnel centerline to the inflection point of the internal half settlement curve.
Many scholars have revised Peck’s empirical formula to expand its practical applications. In addition to the empirical formula for calculating the surface settlement, the stochastic medium theory method is considered to be an effective method for accurately predicting the surface movement and deformation caused by underground mining . In addition, the ground subsidence field measurement method and the laboratory test method have been widely used . 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 tunnel and the curved segment of a tunnel. However, there is no settlement calculation method for curved tunnels in the literature. Based on field measurements from shielding subway tunnels located 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 dissymmetrical settlement are discussed, and a method of calculating the dissymmetrical settlement profile is proposed.
Meng  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 represented 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.
From the numerical results of Meng , it can be inferred that function is not suitable for predicting the ground settlement induced by curved tunneling . Therefore, it is reasonable to modify function by considering the alignment radius to get a better prediction of the settlement induced by curved tunneling . To
predict the surface settlement at the excavation face, the following
assumptions can be made:
A. The maximum settlement occurs above the axis of tunnel,
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 formulation
for calculating curved tunneling induced ground settlement
would be expressed as follows:
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.
In 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.
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 articulation
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.
As 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 structure
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 underground
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.
Plan of measurement: Several settlement observation sections
had been arranged along the tunnel alignment. Ground settlement
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 measurement
was conducted at least once a day.
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 value
indicates the internal of curved alignment; the z value is the
ground settlement. Surface upheaval occurs much more frequently
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 settlement
tends to grow as the radius of alignment decreases. Furthermore,
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).
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.
It was observed that the jacking force of group A on the outside
of the curve was greater than that of group C on the inside
of the curve when the earth pressure balanced tunnel boring machine
reached the observation sections. During the research, the
jacking force of the earth pressure balanced tunnel boring machine
was recorded. The jacking forces Jo and Ji and their ratio (Jo/
Ji) for jacking groups A and C are shown in Table 3.
Regression fitting calculation: The observed surface settlements
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 settlements
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 uneven
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.
As a result, with the total ground loss volume Vl and the jacking
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].
The following conclusions were drawn based on the measured
The prediction method of the surface settlement above the
curved portion of a single shield tunnel was obtained and expressed
as the following formula:
The relationship between uneven surface settlement and jacking
force in this project was obtained (radius of curved alignment is
more than 300m in this case) and expressed as the following equation:
The ratios of Vi /VO and Jo/Ji have a positive relationship.
It was demonstrated that curved tunnel settlement can be described
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 given
for the specific geological condition, which is Kenny Hill residual
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 further
test the applicability of the proposed formulae.
Faramarz M, Ali AR, Qasem BC, Erfan RD (2018) Application of petrographic image analysis in assessment of chemical attack in the concrete segments of a tunnel Articles in Press. Scientia Iranica, Iran.