Introduction
Urban railways in South Korea have been initiated from the first Seoul subway
line in 1974 and have been operating in Seoul and several metropolitan
cities. The number of passengers using urban railways is increasing and the
railway has played a significant role in public transportation for urban
development. Urban railway is defined as a transportation facility and method
for smooth transportation in the city and includes light rail transit and the
subway as indicated in the law of urban railway (Ministry of Land, 2015).
Risk management associated with safety is a fundamental focus in railway
operations. It has been integrated into global safety management systems of
railways (Berrado et al., 2010) and developed to allow a rapid risk
assessment using a common risk score matrix (Braband, 2012). As roadbed
settlements exceed the allowable limits, it may result in track irregularity
and derailments of trains, causing heavy loss of life. Therefore, risk
management tools are developed to deal with track safety by controlling and
reducing the risk of derailments (Zarembski and Palese, 2006). In this study,
methods to secure the stability of roadbeds have been examined using
numerical analysis.
Numerical analyses have been widely used for risk assessment. Numerical
analyses using three-dimensional geotechnical codes were carried out to
predict the subsidence area and its interaction with buildings (Castellanza
et al., 2015), and a three-dimensional groundwater flow model for risk
evaluation was developed to be an effective management strategy (Ashfaque et
al., 2017). The coupling of numerical models and monitoring data contributes
to undertaking efficient risk reduction policies (Bozzano et al., 2013).
Especially using FLAC, which is a finite-difference numerical code
specialized in the area of geotechnical engineering, numerical computations
to simulate the influence of rainfall (Pisani et al., 2010), both acoustic
emission (AE) activities at AE sensor locations of the Kannagawa cavern (Cai
et al., 2007) and a comprehensive pump test at Sellafield (Hakami, 2001),
showed good agreement with field monitoring results. In this study,
FLAC3D, which is a three-dimensional finite-difference numerical
code especially specialized in the area of geotechnical engineering, is
adopted for numerical analysis.
Ground subsidence near subways:
(a) Seokchon subway station, (b) Bakchon subway station,
(c) Samseongjungang subway station, (d) Janghanpyeong
subway station in South Korea, (e) Texas in the US,
(f) Fukuoka in Japan, (g) Ottawa in Canada and
(h) Guangzhou in China.
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Research on stability assessment and reinforcement of railway roadbeds has
been actively carried out, but the effect of the cavity adjacent to urban
railways on roadbed behavior has rarely been studied. In recent years, the
number of accidents induced by cavities larger than 2 m in diameter has
increased, especially in highly populated cities in South Korea. Ground subsidence near
subways due to self-weight and/or surcharge loading was around 60 % (Lee
and Kang, 2014). Changes in groundwater levels (GWLs) may cause increased
occurrences of ground subsidence because the lowering of GWLs leads to ground
settlement (J. H. Lee et al., 2015). GWL influences both ground settlement
and stability of underground structures. Deep excavation of the ground
adjacent to urban railways has a significant influence on the allowable
tensile strength of underground structures (Lee at al., 2017). If large
underground cavities are located at nearby roadbeds, there is a high
potential of ground subsidence.
Ground subsidence (Fig. 1) in South Korea occurred at nearby urban railways
most recently (Kyunghang Times, 2016a). The ground subsidence (Fig. 1a)
occurred with a cavity with a depth of 5 m, width of 8 m, and length of
80 m near the Seokchon subway station in Seoul. The accident was induced by
inappropriate deep excavation near the subway. The ground subsidence
(Fig. 1b) was caused by the leakage of a water pipeline with a large-scale
cavity with a depth of 21 m, width of 11 m, and length of 12 m near
Bakchon subway station in Incheon (Newshankuk, 2016). The ground subsidence
(Fig. 1c) occurred near Samseongjungang subway station. Six cavities were
found almost simultaneously in Seoul (Kyunghang Times, 2016b). A small-scale
cavity with a depth of 2.2 m (Fig. 1d) occurred near Janghanpyeong subway
station in Seoul, but the cause of this accident has not been clarified. The
accident was assumed to be caused by inappropriate construction near the
subway extension.
Ground subsidence with a cavity with a depth of 3.6 m (Fig. 1e) occurred as
the replacement work of a sewage pipeline was carried out at Texas in the US
(Wikitree, 2016). Ground subsidence with a cavity with a width of 15 m
(Fig. 1f) occurred as tunnel excavation work for a subway extension was
carried out at Fukuoka in Japan (Chosun Ilbo, 2016). Ground subsidence with a
cavity with a width of 25 m (Fig. 1g) occurred as a 50 m tunnel excavation
near the light rail transit was carried out at Ottawa in Canada (Yonhap news,
2016). Ground subsidence with a cavity with a depth of 10 m (Fig. 1h)
occurred as subway construction was carried out near Guangzhou in China (Sisa
China, 2016). Ground subsidence with large-scale cavities in urban areas is
highly correlated with the undiscerned development of urban areas, abuse of
groundwater and inappropriate underground construction.
A total of 80 % of the ground subsidence occurring from 2010 until the
beginning of 2014 in Seoul was induced by aged pipelines for water and sewage
(Oh et al., 2015) since 48 % and 30 % of sewage pipelines in Seoul
were constructed more than 30 and 50 years ago, respectively. Aged pipelines
for water and sewage could cause numerous cavities in the near future (Segye
Ilbo, 2016).
As a cavity exists at the center of the railway track in the box structures
of urban railways, its influence on box structures and roadbed settlements
has been examined to observe the effects of cavities adjacent to the roadbeds
of urban railways (S. J. Lee et al., 2015). A method to establish a database
was proposed to prevent and manage the disasters (Choi et al., 2007).
As a cavity exists adjacent to the roadbed, in this study, a
three-dimensional numerical analysis using FLAC3D is carried out to
assess both roadbed stability and risk level with respect to the distance
between the center of the roadbed and the center of the cavity, diameter of
the cavity, and GWLs.
Numerical analysis
The FLAC3D details given in this work are briefly
described in the following sections by paraphrasing from those of Itasca
Consulting Group (2002).
Theoretical background of FLAC<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="normal">D</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>
Configuration of the railway roadbed and cavity.
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FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) is
a numerical modeling software for advanced geotechnical analysis of soil,
rock, groundwater, and ground support in three dimensions. FLAC is used for
analysis, testing, and design by geotechnical, civil, and mining engineers
(Itasca Consulting Group Inc., 2002). It is designed to accommodate any kind
of geotechnical engineering project that requires continuum analysis. The
mechanics of the medium are derived from general principles (definition of
strain, laws of motion), and the use of constitutive equations defining the
idealized material. The resulting mathematical expression is a set of partial
differential equations, relating mechanical (stress) and kinematic (strain
rate, velocity) variables, which are to be solved for particular geometries
and properties, given specific boundary and initial conditions. An important
aspect of the model is the inclusion of the equations of motion, although
FLAC3D is primarily concerned with the state of stress and
deformation of the medium near the state of equilibrium. Application of the
continuum form of the momentum principle yields Cauchy's
equation of motion:
σij,j+ρbi=ρ(dvi/dt),
where σ is the symmetric stress tensor, ρ is the mass per unit
volume of the medium, [b] is the body force per unit mass, and dv/dt is the material derivative of the velocity. These laws govern,
in the mathematical model, the motion of an elementary volume of the medium
from the forces applied to it. Note that in the case of static equilibrium
of the medium, the acceleration dv/dt is zero, and Eq. (1)
reduces to the partial differential equation of equilibrium:
σij,j+ρbi=0.
Configuration of the train load.
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Physical properties of soil, rail, PC sleeper and the rail
pad.
Soil type
Height
Unit weight
Elastic
Poisson's
Cohesion
Friction
Coefficient of
Ko
(m)
(kN m-3)
modulus (kPa)
ratio (υ)
(kPa)
angle (∘)
permeability (cm s-1)
Soil
Ballast stone
0.3
19.0
133 900
0.30
–
35
–
0.43
Upper roadbed
1.5
18.0
81 600
0.20
3.0
32
–
0.47
Lower roadbed
1.5
18.0
51 000
0.30
10.0
30
–
0.50
Land fill
1.5
17.0
30 000
0.35
5.0
24
1.0×10-3
0.59
Silty clay
1.5
17.0
20 000
0.35
5.0
25
5.0×10-4
0.58
Weathered soil I
15.0
19.0
75 000
0.33
10.0
30
1.0×10-4
0.50
Weathered soil II
15.0
19.0
70 000
0.33
10.0
33
1.0×10-4
0.46
Weathered rock
7.0
20.0
110 000
0.31
60.0
42
1.0×10-5
0.33
Area
Unit weight
Elastic
Moment of inertia
(mm2)
(kN m-3)
modulus (kPa)
(m4)
IXX
IYY
KS60 rail
7,741
77.5
21000×104
30820×10-9
5120×10-9
Length
Width
Height
Interval between
(m)
(m)
(m)
sleepers (m)
PC sleeper
2.45
0.28
0.20
0.58
Thickness
Unit weight
Vertical spring coefficient
(mm)
(kN m-3)
of rail pad (kPa)
Rail pad
5
11.5
15.3×107
Settlement of clay and sand backfill with respect to the distance
from earth retaining walls: (a) settlement of backfill and
(b) prediction of settlement.
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Conditions for numerical analysis
The Mohr–Coulomb failure model has been used for the analysis (Itasca
Consulting Group Inc., 2002, 2016). Since there are various causes and sizes
of the cavities of ground subsidence occurring near urban railways, it is
very difficult to simulate the process of cavity generation. A circular
cavity below the ground surface has been modeled with respect to diameters
(D) of 4–10 m, which is selected by historical events as described in the
previous section. Distances of 15–25 m from the cavity to the center of the
roadbed and various GWLs are arbitrarily selected for roadbed settlement
influenced by the given size of the cavity. The analysis is performed based
on the configuration of the analysis (Fig. 2). As shown in the figure, roller
supports prevent normal translations but are capable of tangential
translations and/or rotations. There is a single linear reaction force either
vertically or horizontally.
An embankment consists of the lower roadbed, upper roadbed and gravel
ballast. The roadbed width at the bottom of the ballast is 8 m. The widths of
its bottom and top are 5.1 and 3.3 m, respectively, and its slope is 1 : 1.8.
In situ soil consists of reclaimed soil, silty clay, weathered soil and
weathered rock. Its physical properties listed in Table 1 are obtained from
lab experiments of soil sampled at a construction site.
KS60 rail and prestressed concrete (PC) sleeper commonly used in gravel
ballast have been used for the numerical analysis. A rail pad, which is
widely used to minimize vibration and impact loading during train operation,
is made of ethylene vinyl acetate (EVA). However, in this study, a
thermoplastic polyurethane (TPU) rail pad, which is more economical and has
higher tensile strength has been used for the numerical analysis. Its
properties are listed in Table 1. The beam element is used for the rail and
rail pad.
Vertical displacement contour of the roadbed at a distance of 20 m
between the center of the roadbed and the center of the cavity = 20 m with
respect to diameter of the cavity: (a) diameter = 8 m and
(b) diameter = 10 m.
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Roadbed settlement with respect to the distance between roadbed and
cavity: (a) diameter = 4 m, (b) diameter = 6 m,
(c) diameter = 8 m and (d) diameter = 10 m.
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An axial load of the urban railway train (16 t) is applied for the numerical
analysis. The effective loading is estimated by multiplying 1.2 with half of
the axial load considering a wheel loading increment of 20 % and a
marginal safety of deficiency of the cant. Dynamic loading to reflect the
dynamic impact ratio (Fig. 3) was estimated by multiplying 1.2 with the
effective loading (Ministry of Land, 2015).
In general, an allowable settlement of 10 mm has been recommended in South
Korea. The vibratory loading induces a loose state in the gravel, and
frequent repairs of ballasts are required. Therefore, an allowable
settlement of 2.5 mm is used to attain additional marginal safety
considering the compressive displacement of both the rail pad and ballasts,
settlement of rail, ride quality, and both water inflow and cracks in the
pavement surface of roadbeds (Jeon, 2014).
Results and discussion
Roadbed settlement
The ground settlement in the backfill area due to the excavation work has
been estimated (Kojima et al., 2005; Kung et al., 2009; Ou et al., 2013) and
its effect on responses of adjacent buildings has been investigated (Lin et
al., 2017; Sabzi and Fakher, 2015; Schuster et al., 2009). Clough and
O'Rourke (1990) have proposed the method to estimate settlement in clay and
sandy soils for in situ wall systems using field measurement data and finite
element analysis (Fig. 4). H, d, δvm and δ
represent an excavation depth, a distance from the wall, the maximum
settlement and a settlement with respect to the distance, respectively. The
settlements tend to average about 0.15 % H. δvm
occurs in the middle of excavation depth near the wall and a settlement
linearly decreases as d increases. Little settlement occurs as d=2H.
Empirical correlations of settlement with d proposed by Bowels (1998) and
Peck (1969) were similar to the one proposed by Clough and O'Rourke (1990).
Bowels (1998) suggested that the settlements tend to average about
0.13 %–0.18 % H. The magnitude of settlements is influenced by the
ground stiffness, the wall stiffness and support spacing. In this study,
although ground is not fully excavated and also there are no wall systems,
the settlement resulting from stress release in ground similarly occurs.
The contours of ground settlement are presented for how the roadbed (Fig. 5)
is influenced by a cavity adjacent to the urban railways. The contours of
ground settlement are presented for cavities with diameters of 8 and 10 m at a distance of 20 m between the center of the roadbed and
the center of the cavity. As shown in the figures, ground settlement
increases as the diameter of the cavity increases. As a cavity is generated
on the right side of the roadbed, the right end of the roadbed is
significantly settled down.
The analysis results (Fig. 6) are presented for cavities with diameters of 4–10 m. As the variation from 15 to 20 m in the distances between the center
of the roadbed and the center of the cavity is applied to the 10 m cavity,
roadbed settlements are calculated with respect to various diameters of the
cavity. The cavity with a diameter of 10 m at a distance of 20 m has little
influence on the roadbed. However, as the diameter of the cavity at the
same distance exceeds 10 m, the roadbed settlement exceeds the allowable
value. As cavities with diameters of 8 and 6 m are generated, at distances
less than 18 and 15 m, where d is close to or less than 2H (2D), the roadbed settlement may
exceed the allowable settlement, resulting in an accident.
Regression analysis of roadbed settlements with respect to the
diameter of the cavity and distance between the roadbed and the cavity.
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Vertical displacement contours of the roadbed for a cavity with a
diameter of 8 m, at the roadbed-to-cavity distance of 25 m:
(a) GWL: ground surface and (b) GWL =-8 m.
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Roadbed settlement with respect to the groundwater level:
(a) diameter of the cavity = 4 m and distance of roadbed from
the center of the cavity = 20 m, (b) diameter of the
cavity = 6 m and distance of the roadbed from the center of
cavity = 20 m, (c) diameter of the cavity = 8 m and
distance of the roadbed from the center of cavity = 25 m, and
(d) diameter of the cavity = 10 m and the distance of the
roadbed from the center of the cavity = 25 m.
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Roadbed settlement increases as the diameter (D) of the cavity increases and
the distance (d) between the roadbed and the cavity decreases. Therefore, in
this study, the roadbed settlement is examined with respect to D normalized
by d (Fig. 7). The regression analyses results show medium to high
correlations of r2=0.72. As D/d is greater than 0.2 and less than
0.3, the roadbed settlement is approximately 5 mm. A
database of measurement sensors should be established for real-time
monitoring of the roadbed, structures and groundwater to prevent disasters
in advance. As D/d exceeds 0.35, the roadbed settlement substantially
increases and is greater than 10 mm. Since it may result in highly probable
traffic accident, train operation should be stopped and the roadbed should
be reinforced or repaired.
The risk level has been estimated by the occurrence of roadbed settlements.
The risk level has been defined
by the value of the roadbed settlements relative to the allowable settlement.
The risk level is defined as safe (not problematic for both ride quality and
track repair), caution (not problematic for track repair), warning (between
caution and danger) and danger (highly probable traffic accident) as a
settlement is equal to or less than 2.5 mm, greater than 2.5 mm and equal
to or less than 4 mm, greater than 4 mm and equal to or less than 9 mm,
and greater than 9 mm, respectively.
Effects of groundwater level
In this study, the effects of GWL on the roadbed settlement are examined and
the GWL is lowered until the allowable settlement value of the
roadbed is satisfied. The maximum distance between the roadbed and the cavity
for the analysis is determined as the maximum value for the satisfied
allowable settlement with no groundwater conditions. A stability assessment
of the roadbed has been carried out at the distance of 20 m for both 4 and
6 m diameter cavities and at 25 m for both the 8 and 10 m diameter
cavities.
The contours of ground settlement (Fig. 8) are presented to examine the
GWL effects in the case of the 8 m diameter cavity
located at a distance of 25 m from the roadbed to cavity. The contours of
ground settlement are presented with GWL on the ground surface and 20 m
below it (Fig. 8a and b). The settlement of the roadbed is
highly subject to GWLs.
Risk level of the roadbed with respect to the diameter of the cavity
and the distance between the roadbed and the cavity for the groundwater
condition. Safety (settlement ≤2.5 mm), caution
(2.5 mm < settlement ≤4.0 mm), warning
(4.0 mm < settlement ≤9.0 mm) and danger
(9.0 mm < settlement).
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The roadbed settlement (Fig. 9) is highly influenced by groundwater. Ground
settlement for 4 and 6 m diameter cavities located at a distance of 20 m
from the roadbed (Fig. 9a and b) satisfies the allowable value for
GWL = -4 and -12 m, respectively. The ground settlement for 8 and
10 m diameter cavities located at a distance of 25 m from the center of the
roadbed (Fig. 9c and d) has substantially decreased as the GWL is 8 and 15 m
below the ground surface, respectively, and satisfies the allowable value as
its level is 18 and 22 m below the ground surface, respectively. This
indicates that a roadbed settlement is highly influenced by GWLs to an extent
greater than even the influence of the size of the cavity.
Risk level assessment of roadbed
Roadbed settlements induced by the cavity near urban railways have been
estimated with respect to the GWL, distance between the
roadbed and cavity, and size of the cavity. As listed in Table 2, the
roadbed settlement increases as the size of the cavity increases and the
cavity is located close to the roadbed. As listed in Table 2, the roadbed
settlement for no groundwater conditions is less than the allowable value,
whereas it is in extreme danger when groundwater is present. When it is in
the status of danger, train operation should be stopped and the roadbed
should be reinforced or repaired. When it is in the status of caution or
warning, a database of measurement sensors for urban railways should be
established for real-time monitoring of the roadbed, structures and
groundwater for disaster prevention.
Conclusions
The number of occurrences of ground subsidence induced by a leakage of aged
pipelines for water and sewage in urban areas resulting in various sizes of
cavity near the urban railway in Seoul has been found to increase and
it may cause roadbed settlement to exceed the allowable value. A
large-scale cavity is rarely found, but if it is close to the roadbed, the
roadbed is highly influenced by the cavity and may cause train derailment.
In this study, numerical analyses are carried out to estimate roadbed
stability and its risk level associated with various GWLs and sizes of
cavities. The analysis results show that roadbed settlement increases as the
diameter (D) of the cavity increases and the distance (d) between the
roadbed and the cavity decreases. The regression analysis results show that,
as D/d is greater than 0.2 and less than 0.3, a database of measurement
sensors should be established for real-time monitoring of the roadbed,
structures and groundwater to prevent disasters in advance. As D/d exceeds
0.35, the roadbed settlement, which substantially increases and is in the
status of danger, may result in highly probable traffic accidents. Therefore,
train operation should be stopped and the roadbed should be reinforced or
repaired. The effects of GWL on the roadbed settlement are examined at the
distance of 20 m for both 4 and 6 m diameter cavities and at 25 m for both
8 and 10 m diameter cavities. Ground settlement for 4 and 6 m diameter
cavities located at a distance of 20 m from the roadbed satisfies the
allowable value for GWL = -4 and -12 m, respectively. The ground
settlement for 8 and 10 m diameter cavities located at a distance of 25 m
from the center of the roadbed has substantially decreased as GWL is 8 and
15 m below the ground surface, respectively, and satisfies the allowable
value as its level is 18 and 22 m below the ground surface, respectively.
This indicates that roadbed settlement is highly influenced by GWLs to an
extent greater than even the influence of the size of the cavity.