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Model uncertainty of various settlement estimation methods in shallow tunnels excavation; case study: Qom subway tunnel
Accepted Manuscript Model uncertainty of various settlement estimation methods in shallow tunnels excavation; case study: Qom subway tunnel
Amir Khademian, Hamed Abdollahi, Raheb Bagherpour, Lohrasb Faramarzi PII:
S1464-343X(17)30319-9
DOI:
10.1016/j.jafrearsci.2017.08.003
Reference:
AES 2985
To appear in:
Journal of African Earth Sciences
Received Date:
15 July 2014
Revised Date:
06 August 2017
Accepted Date:
08 August 2017
Please cite this article as: Amir Khademian, Hamed Abdollahi, Raheb Bagherpour, Lohrasb Faramarzi, Model uncertainty of various settlement estimation methods in shallow tunnels excavation; case study: Qom subway tunnel, Journal of African Earth Sciences (2017), doi: 10.1016 /j.jafrearsci.2017.08.003
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Model uncertainty of various settlement estimation methods in shallow tunnels excavation; case study: Qom subway tunnel
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Amir Khademian1, Hamed Abdollahi1, Raheb Bagherpour1*, Lohrasb Faramarzi1
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1. Department of Mining Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran * Corresponding author, [email protected]: +983133915118
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Abstract
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In addition to the numerous planning and executive challenges, underground excavation in
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urban areas is always followed by certain destructive effects especially on the ground surface;
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ground settlement is the most important of these effects for which estimation there exist
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different empirical, analytical and numerical methods. Since geotechnical models are
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associated with considerable model uncertainty, this study characterised the model
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uncertainty of settlement estimation models through a systematic comparison between model
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predictions and past performance data derived from instrumentation. To do so, the amount of
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surface settlement induced by excavation of the Qom subway tunnel was estimated via
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empirical (Peck), analytical (Loganathan and Poulos) and numerical (FDM) methods; the
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resulting maximum settlement value of each model were 1.86, 2.02 and 1.52 cm,
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respectively. The comparison of these predicted amounts with the actual data from
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instrumentation was employed to specify the uncertainty of each model. The numerical
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model outcomes, with a relative error of 3.8 %, best matched the reality and the analytical
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method, with a relative error of 27.8 %, yielded the highest level of model uncertainty.
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Keywords: Settlement, Model Uncertainty, Instrumentation, Tunnel Excavation, Qom
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Subway, Iran.
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1. Introduction
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The most fundamental reaction of loose ground against any tunnelling activities is the soil
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movement toward the opening. Accordingly, underground excavations in urban areas are
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always followed by some destructive effects, the most important of which are settlement and
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surface building damages. Understanding the ruling principles, estimating and controlling
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these effects are, therefore, a significant part of underground projects in urban areas.
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The adverse consequences of shallow tunnel excavation have been discussed by many
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geotechnical researchers and tunnelling engineers since last decades. Researchers have
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adopted various approaches and methods to estimate tunnelling induced settlement in urban
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areas. These methods are classified into three broad categories of empirical, analytical and
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numerical:
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Empirical methods: The empirical model for predicting the tunnelling induced subsidence
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was first suggested by Litwiniszyn (1956). Using a stochastic model, he represented the
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ground by a material composed of numerous equi-sized spheres in three-dimensions or discs
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in two-dimensions. Later on, Peck (1969) simplified this stochastic solution using the normal
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probability curve or Gaussian curve to determine the surface settlement distribution. His
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solution was based on two (2) basic parameters of volume loss (VL) and settlement trough
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width (i). Although this empirical approach was supported by many researchers, some
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modifications were made, which rendered the Peck solution the strongest and most widely
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used empirical model for predicting transverse and longitudinal surface settlement (Attewell
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and Woodman, 1982; Cording and Hansmire, 1975; Mair and Taylor, 1993; O'reilly and
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New, 1982).
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Analytical methods: Many researchers attempted to calculate ground stress and movement,
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analytically, by describing methods based on closed form solutions. This process started with
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Mindlin’s tunnel problem, in which he introduced the expressions for the tangential stresses
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at the boundary of circular opening and the free surface (Mindlin, 1940). Sagaseta (1987)
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presented a two-dimensional analysis of ground deformations to obtain the strain field in an
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initially isotropic and homogeneous incompressible medium (i.e., extending the strain path
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method of Baligh (1985) by introducing a stress-free ground surface). Verruijt and Booker
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(1996) first modified an approximate method suggested by Sagaseta (1987) to provide a
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solution for ground loss not only regarding the undrained case with Poisson's ratio equal to
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0.5, but also for arbitrary values of Poisson's ratio, and the effect of ovalization as well.
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Loganathan and Poulos (1999) modified the solution given by Verruijt and Booker (1996)
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and neglected the distortion component that results in a narrower surface settlement trough.
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They defined the equivalent ground loss ε0 with respect to the gap parameter g proposed by
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Lee et al. (1992) and Loganathan and Poulos (1998). Additionally, Pinto (1999) introduced
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the relative distortion ratio of the tunnel and extended the analytical solution to describe both
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surface troughs and lateral deformations.
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Numerical methods: Numerical modelling analyses offer considerable possibilities for the
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modelling of many aspects of tunnelling. It is evident that the development of ground
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movements caused by tunnelling is three-dimensional; however, due to the high cost and the
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lengthy process associated with this analysis, simplified 2D procedures are often adopted.
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Finite difference and finite element methods are the most widely used numerical methods for
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estimating the surface settlement.
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Among the researchers who employed the finite element method (FEM) are De la Fuente and
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Oteo (1996) who presented a model based on the finite element analysis which provides a
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rapid and facile assessment of the longitudinal settlement trough. Oteo and Sagaseta (1996), 3
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based on the experiments in Madrid and Karakas subway, presented and used certain finite
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element models to predict the settlements successfully. Liu et al. (2008), through finite
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element analysis and Tunnel3D and ABAQUS software, studied the effect of tunnel
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excavation on support system in a neighbouring tunnel in Australia. They concluded that the
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impact of tunnel excavation on the support system of a neighbouring tunnel strongly depends
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on how the two tunnels are positioned. Using finite element 3D Huang et al. (2009) presented
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a simple analytical solution to study the effect of subway tunnel excavation on the amount of
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settlement at the columns of a bridge. Mirhabibi and Soroush (2012) studied the effect of the
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surface settlement on the neighbouring buildings in Line 1 of Shiraz subway. They
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investigated the effect of different parameters like tunnel depth, the distance between the
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centres of the tunnels, and weight and width of the buildings.
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As mentioned earlier, some researchers used the finite difference method in their studies.
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Wang et al. (2000), using the corrected models of Gauss based on FLAC software and the
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finite difference method, presented the diagram of the surface settlement due to tunnel
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excavations in loose soil; they further formulated the settlement induced by the excavation of
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two other parallel tunnels. Melis et al. (2002), via finite difference method and FLAC3D
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software, attempted to predict the profile of the settlement triggered by shield tunnelling of
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Madrid subway. They studied the constitutive models of elastic and Mohr-Coulomb to
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predict the settlement over various distances. Using the finite difference method, Kucuk et al.
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(2009), showed that following the chemical injection around the tunnel, the amount of water
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leaking into the tunnel decreased, thereby reducing the amount of surface settlement from 25
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mm to 1.5-2 mm.
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An overview of these studies reveals that there are two important fields in settlement analysis
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not fully dealt with, the first being the investigation of settlement induced by NATM
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tunnelling in loose grounds. This study primarily aimed to estimate the amount of surface 4
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settlement induced by Line A of Qom subway excavated by NATM tunnelling method
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between Vali-Asr and Baghiatallah stations.
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On the other hand, each method has its strengths and weaknesses, and certainly, none of them
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do fully comply with reality. The ability of a model to estimate the reality (model realization)
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is a key criterion as regards the selection of the best method. This issue is referred as the
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model uncertainty of various settlement prediction models in the literature, which is the
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second overlooked issue in the mentioned studies. However, certain researchers noticed this
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issue during their studies. Darabi et al. (2012) for instance studied the settlement in Line 3 of
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Tehran subway and compared the results of the numerical method with artificial neural
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networks which were very similar to each other.
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In fact, all geotechnical models are, more often than not, associated with considerable
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amounts of model uncertainty and settlement estimation models are no exception. Therefore,
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the objective of the present research was to characterise the model uncertainty of
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geotechnical models introduced for settlement estimation through a systematic comparison
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between model predictions and instrumentation data pertaining to the ground surface. During
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such a comparison, model input parameters (such as soil strength properties) may also be
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uncertain. To avoid uncertain input parameters, they were modified and verified by back
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analysis based on extensometers data in the tunnel, hence the fact that input parameters can
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be assumed certain.
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2. Field characteristics
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Line A of Qom subway is 14700 m long and it has 14 stations starting at Jamkaran (A1),
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covering different stations like Baghiatallah, Shahid Motahari and ending at Ghale-Kamkar
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station (A14). Figure 1 illustrates the route of Line A as well as its stations. This line was 5
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designed to be excavated by both conventional and mechanised methods. This tunnel is
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expected to be excavated by NATM tunnelling method between Jamkaran (A1) and Vali-Asr
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(A3) stations (3800 m), with a horseshoe-shaped profile, while it will be constructed with
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mechanized excavation (TBM) from Vali-Asr (A3) to Ghale-Kamkar (A14) stations (10900
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m).
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Figure 1. A location map of the Qom Tunnel showing Line A route and stations
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From a geological point of view, Line A of Qom subway is located in a sedimentary plain.
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The northwest parts of these sediments have different shapes and dimensions like silt, clay
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and pebbles of around 10 cm in dimension. There are also some huge round boulders formed
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of different sedimentary, igneous, and metamorphic materials typical of the Sanandaj-Sirjan
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zone. In the excavation extending from Baghiatallah to Vali-Asr stations, sediments are often
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from silt and clay types. Since the terrain slope of Qom plain is toward the southeast,
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flooding waters continuously moved the sediments to farther distances, inducing thick
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sediments in southeast regions.
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3. Settlement estimation
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In general, excavation of tunnels releases a mass of soil and changes the stress situation
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around the tunnel. The release of the soil mass results in certain displacements toward the
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underground space, which can be divided into vertical and horizontal components. The
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former component induces settlement while the latter creates the stressing manner of the
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surface. Both components can create new stresses on the surface (Strokova, 2009). Settlement
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can threaten the stability of the tunnel, yet in urban areas, especially in residential parts,
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settlement becomes much more important due to its potential role in inducing different levels
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of damage to nearby buildings. To preclude massive damages due to tunnel excavation, the
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amount of settlement must be predicted (Kim et al., 2001). As mentioned earlier, all the
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solutions introduced for the estimation of settlement can be classified into numerical,
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analytical and empirical categories. In the following, the amount of surface settlement
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induced by the excavation of Line A of Qom subway through NATM tunnelling method will
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be estimated via each category:
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3.1. Numerical method
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Certain parts of Qom subway were excavated based on NATM method conducted on the
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upper and lower parts (Figure 2). For better execution and results as well as more effective
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control over the soil reaction, circle cutting method was also employed in this section of the
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subway.
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In the circle cutting method, excavation was done in the upper and lower parts. Because the
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soil is weak, it is necessary to prepare pre-support elements in the upper part. As Figure 2
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shows, the excavation sequences begin with part 1. Subsequently, the primary support system
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is set, including a layer of elementary shotcrete, micromesh and lattice girders. The same
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executive steps follow the excavation of part 2 and other parts until the completion of the
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whole section. Because of the loose conditions of the soil and its low cohesion in Qom
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subway tunnel and the step by step excavation method, each advancing step was 70 cm long
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(SCE, 2012).
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Figure 2. Excavation sequences and supporting steps (SCE, 2012)
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This study made use of three-dimensional finite difference code for settlement estimation.
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Despite some complications, the main advantage of a 3D analysis of NATM tunnelling over
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mechanized TBM tunnelling is that there is no need for simulating the complex movement of
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the shield. In the first step of numerical modelling, the geometry of the model was created
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according to Figure 3. The dimensions of the model were determined such that borders would
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not influence model responses. The distance of tunnel crown and axis to the ground surface
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were 12 and 16.5 meters, respectively. The model was 70 m long, 80 m wide, and 40 m high.
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The support system used in this model was a combination of shotcrete and lattice girders. The
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strength properties of shotcrete are shown in Table 1.
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Figure 3. Geometry of numerical model Table 1. Strength properties of shotcrete property value Passion ratio 0.15 Elasticity modulus(kg/cm2) 20 Compressive strength(MPa) 16 Density(kg/m3) 2000
183 184
In the studied region, QF1 and QC2 were the two types of soil structure. Hence two different
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layers are considered in the numerical model. The first layer (QF1) was extended from the
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surface to a depth of 25 m, with a density of 1700 kg/m3, while the second layer (QC2) was
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extended from the depth 25 m to the bottom of the model, with a density of 1900 kg/m3. QF1
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layer is mainly formed of clay silt and a slight amount of sand while more than 50% of its
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particles pass through a #200 sieve and its plasticity index (PI) is low. QC2 layer is mainly
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comprised of clay with a little sand, and more than 50 % of its particles passing through a
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#200 sieve and its plasticity index (PI) is more than QF1.
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The Mohr-Coulomb model was adopted as the constitutive model for analysis. Different
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strength characteristics of the soil layers including Young's modulus, cohesion, friction angle,
194
and K were previously verified through a back analysis process by Ghasemzadeh (2013)
195
based on convergence extensometer data, which are reported in Table 2.
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ACCEPTED MANUSCRIPT 196 Soil layer QF1 QC2
Table 2. Strength properties of soil layers Elastic modulus Cohesion Friction angle
Density
(kg/cm2)
(MPa)
(degree)
(kg/m3)
25 30
0.2 0.3
30 35
1700 1900
197 198
The modelling results were obtained after running the numerical model in several stages.
199
Figure 4 shows the vertical stress contours (Szz) as a result of tunnel excavation. Registering
200
the history of vertical displacement at the model surface provides the surface settlement
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values. Accordingly, the transverse and longitudinal sections of surface settlement caused by
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tunnel excavation were obtained and are shown in Figures 5 and 6, respectively. The
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maximum amount of surface settlement, rightly located just above the tunnel axis is 1.52 cm.
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Figure 4. Vertical stress contours around the tunnel
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Figure 5. Transverse settlement trough
208 209
Figure 6. Longitudinal profile of surface settlement
210 211
3.2. Analytical method
212 213
Among the different analytical methods proposed for settlement prediction, Loganathan &
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Poulos model gives the most acceptable estimates. This model is the first to consider that the
215
elastoplastic movement of the soil at the tunnel face is more oval-shaped (Figure 7b) than
216
radial uniform movement (Figure 7a) (Loganathan and Poulos, 1998). The most important
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parameter when utilising this method is the gap (g) parameter, which indirectly represents the
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convergence of tunnel walls. Other such parameters as geometrical characteristics are
219
requisites for the estimation of settlement via this model.
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Figure 7. Circular and oval ground deformation patterns around a tunnel section (Loganathan and Poulos, 1999)
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Although Loganathan & Poulos model is essentially employed in mechanized tunnelling by
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TBM, it can also be employed for settlement prediction induced by NATM excavation
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method. By calculating the amount of gap in a numerical software and substituting it and
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other needed parameters in Equation 1, the amount of maximum surface settlement is
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obtained as follows:
U Z 0
H (1 ) 1.38 x 2 2 ( 4 gR g ) exp 2 2 2 H X ( H cot R)
(1)
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Where H (tunnel depth) equals 12.5 m, ν (Poisson's ratio of soil) is 0.3, R (tunnel radius) is 4.9 m, g
231
(gap parameter at the crown) is 15.32 mm, β is 45
232
substituting these values in Equation 1, the surface settlement values are achieved, and the maximum
233
amount of settlement equals 2.02 cm.
234
2
and x varies between [-40, 40] m. By
3.3. Empirical method
235 236
Peck’s model, primarily introduced in 1969, is an empirical model most widely used in
237
predicting tunnelling induced surface settlement. Over the following years, various
238
modifications to this basic method were suggested, the best outcome of which is summarized
239
in Equations 2 and 3 (also used in this study). In all empirical models, there is a key 12
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parameter named volume loss (VL), obtained, in the present paper, through the use of the
241
result pertaining to the numerical software.
x2 S S max . exp 2 2i S max
(2)
0.313VL D 2 i
(3)
242 243
Table 3 illustrates the amounts of other parameters required in Equations 2 and 3. By the
244
substitution of these parameters in the equations, the surface settlement values for different
245
distances from the tunnel axis are obtained; the maximum amount of settlement equals 1.86
246
cm.
247
Table 3. Amount of parameters in the empirical equation
Parameter Volume loss (VL) Tunnel diameter (D) Trough width parameter (i) 248
Amount 1% 9.8 m 6.8 m
4. Model uncertainty analysis
249 250
The uncertainties that are dealt with in geotechnical engineering fall under two major
251
categories of aleatory and epistemic. Aleatory uncertainty represents the natural randomness
252
of a variable, while lack of knowledge causes epistemic uncertainty. Epistemic uncertainty is
253
divided into two major sub-categories: Parameter uncertainty and model uncertainty (Figure
254
8). Parameter uncertainty is attributed to the lack of certain data, which results from the
255
inaccuracy in assessing parameter values. Model uncertainty has to do with the degree to
256
which a chosen mathematical model accurately mimics reality (Baecher and Christian, 2005;
257
Griffiths and Fenton, 2007). In other words, the uncertainty in the prediction of unknown
258
values (model outcome) depends on both the structural uncertainty (model uncertainty) and
259
input data uncertainty (Draper, 1995). 13
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Figure 8. Categories of geotechnical uncertainties
262 263
Each prediction model has to be simple in terms of mathematical operations, and it must
264
predict reality. Due to their assumptions and simplification, the design tools use just a few
265
key parameters. Each of the neglected key parameters generates noise (uncertainty) in the
266
model. The source of uncertainty in design tools is their imperfect assumptions and various
267
degrees of simplification in the model. The main reason model uncertainty is focused on is
268
that it is large, and in certain cases, it can be reduced (Griffiths and Fenton, 2007).
269
Geotechnical models introduced for settlement estimation are no exception to the rule above.
270
They have their own assumptions, simplifications and limitations which generate uncertainty
271
in their results. Model uncertainty can only be quantified by comparison with either more
272
involved models that exhibit a closer representation of nature or the data collected from the
273
field or the laboratory (Ditlevsen, 1983). The objective of the present study is to quantify the
274
model uncertainty of different settlement prediction approaches via their comparison with the
275
model results and the exact data obtained in the field. To this end, the settlement trough and
276
maximum settlement estimated by the empirical, analytical and numerical method are
277
compared with that of exact instrumentation data (1.58 cm) which are shown in Figure 9.
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ACCEPTED MANUSCRIPT Distances to tunnel axis (m) -40
-30
-20
-10
0
10
20
30
40
0
Displacement (cm)
-0.5 -1 -1.5 -2 -2.5
278 279
Analytical
Empirical
Numerical
Exact data
Figure 9. Comparison of analytical, empirical and numerical methods with the exact data
280 281
The uncertainty of each model can be simply quantified by calculating the relative error of
282
each model in the estimation of the settlement, derived from Equation 4:
Re lative Error
Model estimate Exact amount Exact amount
(4)
283 284
According to Equation 4, the relative error values of each estimation method are reported in
285
Table 4 along with the maximum settlement values.
286
Table 4. Maximum settlement and relative error of each method Analysis method Settlement amount (cm) Relative error (%) Numerical method
1.52
3.8
Analytical method
2.02
27.8
Empirical method
1.86
17.7
287 288
As stated earlier, the relative error values of each model represent its uncertainty amount. It
289
can, therefore, be understood from Table 4 that the numerical model, with the relative error of
290
3.8 %, has the least uncertainty while the highest uncertainty belongs to the analytical model 15
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with the relative error of 27.8 %. The numerical method results are very close to those of
292
exact instrumentation, rendering it a reliable design tool for settlement estimation. Analytical
293
method results, on the other hand, are far from the exact data, hence an undesirable model for
294
settlement estimation. The empirical model, with a relative error of 17.7%, stands in the
295
middle of the spectrum with its slightly accurate and reliable results. Numerical modelling, it
296
can be concluded, is the best and most precise approach for the estimation of tunnelling
297
induced surface settlement.
298
Besides, it is possible to deem numerical modelling as an optimistic approach to settlement
299
estimation as it underestimates the maximum settlement value. On the contrary, since
300
analytical and empirical methods overestimate the maximum settlement value, they are
301
considered as conservative approaches. In addition, the comparison of settlement troughs in
302
Figure 9 shows that empirical methods predict a narrow settlement trough, while the
303
numerical method predicts the widest one. However, in all three models, the settlement
304
trough width (i) is approximately 8 m.
305
5. Conclusion
306 307
In this study, the model uncertainty of geotechnical models used in settlement estimation was
308
characterized
309
instrumentation data. In this regard, settlement trough and maximum settlement, caused by
310
NATM tunnelling in Line A of Qom subway, were estimated by empirical, analytical and
311
numerical models and compared with the actual measured data. This approach entailed the
312
following conclusions:
through
a
systematic
comparison
16
between
model
predictions
and
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- Geotechnical models introduced for settlement estimation have their assumptions,
314
simplifications and limitations, hence the uncertainty in their results. A model uncertainty
315
analysis is, therefore, essential for the settlement estimation models.
316
- The maximum amount of surface settlement derived from numerical, empirical, analytical
317
methods and from instrumentation data are 1.52, 1.86, 2.02 and 1.58 cm, respectively.
318
- The numerical model has the lowest level of model uncertainty (closest to reality) in
319
estimating the tunnelling-induced surface settlement, rendering it the most precise approach
320
for the estimation of surface settlement.
321
- The analytical method has the highest level of model uncertainty which makes it an
322
undesirable model for settlement estimation. The empirical model shows a moderate
323
performance in this respect.
324
- In comparing the settlement trough estimated by each model, it becomes clear that empirical
325
methods predict a narrow settlement trough while the numerical method predicts a wide
326
settlement trough.
327
Acknowledgement
328 329
We would like to show our gratitude to all reviewers for sharing their valuable comments and
330
insights during this research, which led to valuable improvements in our study.
331
References
332 333 334 335 336 337
Attewell, P., Woodman, J., 1982. Predicting the dynamics of ground settlement and its derivitives caused by tunnelling in soil. Ground engineering 15. Baecher, G.B., Christian, J.T., 2005. Reliability and statistics in geotechnical engineering. John Wiley & Sons. Baligh, M.M., 1985. Strain path method. Journal of Geotechnical Engineering 111, 1108-1136. Cording, E.J., Hansmire, W., 1975. Displacements around soft ground tunnels.
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Darabi, A., Ahangari, K., Noorzad, A., Arab, A., 2012. Subsidence estimation utilizing various approaches–A case study: Tehran No. 3 subway line. Tunnelling and Underground Space Technology 31, 117-127. De la Fuente, P., Oteo, C., 1996. Theoretical research on the subsidence originated by the underground construction in urban areas, Proceedings of the Danube International Symposium, Rumania. Ditlevsen, O., 1983. Model uncertainty in structural reliability. Structural safety 1, 73-86. Draper, D., 1995. Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society. Series B (Methodological), 45-97. Ghasemzadeh, J., 2013. Back analysis and determination of Line A of Qom subway parameters in order to evaluation of supporting system, Department of Mining Engineering. Isfahan University of Technology, Isfahan. Griffiths, D.V., Fenton, G.A., 2007. Probabilistic methods in geotechnical engineering. Springer Science & Business Media. Huang, M., Zhang, C., Li, Z., 2009. A simplified analysis method for the influence of tunneling on grouped piles. Tunnelling and Underground Space Technology 24, 410-422. Kim, C.Y., Bae, G., Hong, S., Park, C., Moon, H., Shin, H., 2001. Neural network based prediction of ground surface settlements due to tunnelling. Computers and Geotechnics 28, 517-547. Kucuk, K., Genis, M., Onargan, T., Aksoy, C., Guney, A., Altındağ, R., 2009. Chemical injection to prevent building damage induced by ground water drainage from shallow tunnels. International Journal of Rock Mechanics and Mining Sciences 46, 1136-1143. Lee, K., Rowe, R.K., Lo, K., 1992. Subsidence owing to tunnelling. I. Estimating the gap parameter. Canadian Geotechnical Journal 29, 929-940. Litwiniszyn, J., 1956. Application of the equation of stochastic processes to mechanics of loose bodies. Arch. Mech. Stos 8, 393-411. Liu, H., Small, J., Carter, J., 2008. Full 3D modelling for effects of tunnelling on existing support systems in the Sydney region. Tunnelling and Underground Space Technology 23, 399-420. Loganathan, N., Poulos, H., 1998. Analytical prediction for tunneling-induced ground movements in clays. Journal of Geotechnical and Geoenvironmental Engineering. Loganathan, N., Poulos, H., 1999. Tunneling induced ground deformations and their effects on adjacent piles, Tenth Austr. Alian. Tunneling Conference. Melbourne:[sn]. Mair , R., Taylor, R., 1993. Prediction of clay behaviour around tunnels using plasticity solutions, Predictive Soil Mechanics: Proceedings of the Wroth Memorial Symposium Held at St. Catherine's College, Oxford, 27-29 July 1992. Thomas Telford, p. 449. Melis, M., Medina, L., Rodríguez, J.M., 2002. Prediction and analysis of subsidence induced by shield tunnelling in the Madrid Metro extension. Canadian Geotechnical Journal 39, 1273-1287. Mindlin, R.D., 1940. Stress distribution around a tunnel. Transactions of the American Society of Civil Engineers 195, 1117-1140. Mirhabibi, A., Soroush, A., 2012. Effects of surface buildings on twin tunnelling-induced ground settlements. Tunnelling and Underground Space Technology 29, 40-51. O'reilly, M., New, B., 1982. Settlements above tunnels in the United Kingdom-their magnitude and prediction. Oteo, C., Sagaseta, C., 1996. Some Spanish experiences on measurement and evaluation of ground displacements around urban tunnels. Geotechnical Aspects of Underground Construction in Soft Ground, 631-736. Peck, R.B., 1969. Deep excavations and tunnelling in soft ground, Proc. 7th int. conf. on SMFE, pp. 225-290. Pinto, F., 1999. Analytical methods to interpret ground deformations due to soft ground tunneling. Massachusetts Institute of Technology. Sagaseta, C., 1987. Analysis of undraind soil deformation due to ground loss. Geotechnique 37, 301320. SCE, 2012. characteristics of Line A of Qom subway project. Sahel Consultant Engineers, Tehran. Strokova, L., 2009. Numerical model of surface subsidence during subway tunneling. Soil Mechanics and Foundation Engineering 46, 117-119.
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Verruijt, A., Booker, J., 1996. Surface settlements due to deformation of a tunnel in an elastic half plane. Geotechnique, 753-756. Wang, Z., Sampaco, K., Fischer, G., Kucker, M., Godlewski, P., Robinson, R., 2000. Models for predicting surface settlements due to soft ground tunneling, North American Tunneling 2000.
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Highlights:
Settlement estimation models are associated with high model uncertainties. Model uncertainty of empirical, analytical and numerical approaches are studied. Maximum predicted settlement of employed models are 1.86, 2.02 and 1.52 cm. Numerical and analytical models have lowest and highest model uncertainties. Numerical modeling is the best design tool for surface settlement estimation.
Amir Khademian, Hamed Abdollahi, Raheb Bagherpour, Lohrasb Faramarzi PII:
S1464-343X(17)30319-9
DOI:
10.1016/j.jafrearsci.2017.08.003
Reference:
AES 2985
To appear in:
Journal of African Earth Sciences
Received Date:
15 July 2014
Revised Date:
06 August 2017
Accepted Date:
08 August 2017
Please cite this article as: Amir Khademian, Hamed Abdollahi, Raheb Bagherpour, Lohrasb Faramarzi, Model uncertainty of various settlement estimation methods in shallow tunnels excavation; case study: Qom subway tunnel, Journal of African Earth Sciences (2017), doi: 10.1016 /j.jafrearsci.2017.08.003
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT 1
Model uncertainty of various settlement estimation methods in shallow tunnels excavation; case study: Qom subway tunnel
2 3
Amir Khademian1, Hamed Abdollahi1, Raheb Bagherpour1*, Lohrasb Faramarzi1
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1. Department of Mining Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran * Corresponding author, [email protected]: +983133915118
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Abstract
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In addition to the numerous planning and executive challenges, underground excavation in
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urban areas is always followed by certain destructive effects especially on the ground surface;
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ground settlement is the most important of these effects for which estimation there exist
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different empirical, analytical and numerical methods. Since geotechnical models are
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associated with considerable model uncertainty, this study characterised the model
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uncertainty of settlement estimation models through a systematic comparison between model
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predictions and past performance data derived from instrumentation. To do so, the amount of
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surface settlement induced by excavation of the Qom subway tunnel was estimated via
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empirical (Peck), analytical (Loganathan and Poulos) and numerical (FDM) methods; the
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resulting maximum settlement value of each model were 1.86, 2.02 and 1.52 cm,
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respectively. The comparison of these predicted amounts with the actual data from
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instrumentation was employed to specify the uncertainty of each model. The numerical
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model outcomes, with a relative error of 3.8 %, best matched the reality and the analytical
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method, with a relative error of 27.8 %, yielded the highest level of model uncertainty.
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Keywords: Settlement, Model Uncertainty, Instrumentation, Tunnel Excavation, Qom
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Subway, Iran.
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1. Introduction
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The most fundamental reaction of loose ground against any tunnelling activities is the soil
29
movement toward the opening. Accordingly, underground excavations in urban areas are
30
always followed by some destructive effects, the most important of which are settlement and
31
surface building damages. Understanding the ruling principles, estimating and controlling
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these effects are, therefore, a significant part of underground projects in urban areas.
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The adverse consequences of shallow tunnel excavation have been discussed by many
34
geotechnical researchers and tunnelling engineers since last decades. Researchers have
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adopted various approaches and methods to estimate tunnelling induced settlement in urban
36
areas. These methods are classified into three broad categories of empirical, analytical and
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numerical:
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Empirical methods: The empirical model for predicting the tunnelling induced subsidence
39
was first suggested by Litwiniszyn (1956). Using a stochastic model, he represented the
40
ground by a material composed of numerous equi-sized spheres in three-dimensions or discs
41
in two-dimensions. Later on, Peck (1969) simplified this stochastic solution using the normal
42
probability curve or Gaussian curve to determine the surface settlement distribution. His
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solution was based on two (2) basic parameters of volume loss (VL) and settlement trough
44
width (i). Although this empirical approach was supported by many researchers, some
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modifications were made, which rendered the Peck solution the strongest and most widely
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used empirical model for predicting transverse and longitudinal surface settlement (Attewell
47
and Woodman, 1982; Cording and Hansmire, 1975; Mair and Taylor, 1993; O'reilly and
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New, 1982).
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Analytical methods: Many researchers attempted to calculate ground stress and movement,
50
analytically, by describing methods based on closed form solutions. This process started with
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Mindlin’s tunnel problem, in which he introduced the expressions for the tangential stresses
52
at the boundary of circular opening and the free surface (Mindlin, 1940). Sagaseta (1987)
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presented a two-dimensional analysis of ground deformations to obtain the strain field in an
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initially isotropic and homogeneous incompressible medium (i.e., extending the strain path
55
method of Baligh (1985) by introducing a stress-free ground surface). Verruijt and Booker
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(1996) first modified an approximate method suggested by Sagaseta (1987) to provide a
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solution for ground loss not only regarding the undrained case with Poisson's ratio equal to
58
0.5, but also for arbitrary values of Poisson's ratio, and the effect of ovalization as well.
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Loganathan and Poulos (1999) modified the solution given by Verruijt and Booker (1996)
60
and neglected the distortion component that results in a narrower surface settlement trough.
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They defined the equivalent ground loss ε0 with respect to the gap parameter g proposed by
62
Lee et al. (1992) and Loganathan and Poulos (1998). Additionally, Pinto (1999) introduced
63
the relative distortion ratio of the tunnel and extended the analytical solution to describe both
64
surface troughs and lateral deformations.
65
Numerical methods: Numerical modelling analyses offer considerable possibilities for the
66
modelling of many aspects of tunnelling. It is evident that the development of ground
67
movements caused by tunnelling is three-dimensional; however, due to the high cost and the
68
lengthy process associated with this analysis, simplified 2D procedures are often adopted.
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Finite difference and finite element methods are the most widely used numerical methods for
70
estimating the surface settlement.
71
Among the researchers who employed the finite element method (FEM) are De la Fuente and
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Oteo (1996) who presented a model based on the finite element analysis which provides a
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rapid and facile assessment of the longitudinal settlement trough. Oteo and Sagaseta (1996), 3
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based on the experiments in Madrid and Karakas subway, presented and used certain finite
75
element models to predict the settlements successfully. Liu et al. (2008), through finite
76
element analysis and Tunnel3D and ABAQUS software, studied the effect of tunnel
77
excavation on support system in a neighbouring tunnel in Australia. They concluded that the
78
impact of tunnel excavation on the support system of a neighbouring tunnel strongly depends
79
on how the two tunnels are positioned. Using finite element 3D Huang et al. (2009) presented
80
a simple analytical solution to study the effect of subway tunnel excavation on the amount of
81
settlement at the columns of a bridge. Mirhabibi and Soroush (2012) studied the effect of the
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surface settlement on the neighbouring buildings in Line 1 of Shiraz subway. They
83
investigated the effect of different parameters like tunnel depth, the distance between the
84
centres of the tunnels, and weight and width of the buildings.
85
As mentioned earlier, some researchers used the finite difference method in their studies.
86
Wang et al. (2000), using the corrected models of Gauss based on FLAC software and the
87
finite difference method, presented the diagram of the surface settlement due to tunnel
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excavations in loose soil; they further formulated the settlement induced by the excavation of
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two other parallel tunnels. Melis et al. (2002), via finite difference method and FLAC3D
90
software, attempted to predict the profile of the settlement triggered by shield tunnelling of
91
Madrid subway. They studied the constitutive models of elastic and Mohr-Coulomb to
92
predict the settlement over various distances. Using the finite difference method, Kucuk et al.
93
(2009), showed that following the chemical injection around the tunnel, the amount of water
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leaking into the tunnel decreased, thereby reducing the amount of surface settlement from 25
95
mm to 1.5-2 mm.
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An overview of these studies reveals that there are two important fields in settlement analysis
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not fully dealt with, the first being the investigation of settlement induced by NATM
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tunnelling in loose grounds. This study primarily aimed to estimate the amount of surface 4
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settlement induced by Line A of Qom subway excavated by NATM tunnelling method
100
between Vali-Asr and Baghiatallah stations.
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On the other hand, each method has its strengths and weaknesses, and certainly, none of them
102
do fully comply with reality. The ability of a model to estimate the reality (model realization)
103
is a key criterion as regards the selection of the best method. This issue is referred as the
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model uncertainty of various settlement prediction models in the literature, which is the
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second overlooked issue in the mentioned studies. However, certain researchers noticed this
106
issue during their studies. Darabi et al. (2012) for instance studied the settlement in Line 3 of
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Tehran subway and compared the results of the numerical method with artificial neural
108
networks which were very similar to each other.
109
In fact, all geotechnical models are, more often than not, associated with considerable
110
amounts of model uncertainty and settlement estimation models are no exception. Therefore,
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the objective of the present research was to characterise the model uncertainty of
112
geotechnical models introduced for settlement estimation through a systematic comparison
113
between model predictions and instrumentation data pertaining to the ground surface. During
114
such a comparison, model input parameters (such as soil strength properties) may also be
115
uncertain. To avoid uncertain input parameters, they were modified and verified by back
116
analysis based on extensometers data in the tunnel, hence the fact that input parameters can
117
be assumed certain.
118
2. Field characteristics
119 120
Line A of Qom subway is 14700 m long and it has 14 stations starting at Jamkaran (A1),
121
covering different stations like Baghiatallah, Shahid Motahari and ending at Ghale-Kamkar
122
station (A14). Figure 1 illustrates the route of Line A as well as its stations. This line was 5
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designed to be excavated by both conventional and mechanised methods. This tunnel is
124
expected to be excavated by NATM tunnelling method between Jamkaran (A1) and Vali-Asr
125
(A3) stations (3800 m), with a horseshoe-shaped profile, while it will be constructed with
126
mechanized excavation (TBM) from Vali-Asr (A3) to Ghale-Kamkar (A14) stations (10900
127
m).
128 129
Figure 1. A location map of the Qom Tunnel showing Line A route and stations
130 131
From a geological point of view, Line A of Qom subway is located in a sedimentary plain.
132
The northwest parts of these sediments have different shapes and dimensions like silt, clay
133
and pebbles of around 10 cm in dimension. There are also some huge round boulders formed
134
of different sedimentary, igneous, and metamorphic materials typical of the Sanandaj-Sirjan
135
zone. In the excavation extending from Baghiatallah to Vali-Asr stations, sediments are often
136
from silt and clay types. Since the terrain slope of Qom plain is toward the southeast,
137
flooding waters continuously moved the sediments to farther distances, inducing thick
138
sediments in southeast regions.
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3. Settlement estimation
140 141
In general, excavation of tunnels releases a mass of soil and changes the stress situation
142
around the tunnel. The release of the soil mass results in certain displacements toward the
143
underground space, which can be divided into vertical and horizontal components. The
144
former component induces settlement while the latter creates the stressing manner of the
145
surface. Both components can create new stresses on the surface (Strokova, 2009). Settlement
146
can threaten the stability of the tunnel, yet in urban areas, especially in residential parts,
147
settlement becomes much more important due to its potential role in inducing different levels
148
of damage to nearby buildings. To preclude massive damages due to tunnel excavation, the
149
amount of settlement must be predicted (Kim et al., 2001). As mentioned earlier, all the
150
solutions introduced for the estimation of settlement can be classified into numerical,
151
analytical and empirical categories. In the following, the amount of surface settlement
152
induced by the excavation of Line A of Qom subway through NATM tunnelling method will
153
be estimated via each category:
154
3.1. Numerical method
155 156
Certain parts of Qom subway were excavated based on NATM method conducted on the
157
upper and lower parts (Figure 2). For better execution and results as well as more effective
158
control over the soil reaction, circle cutting method was also employed in this section of the
159
subway.
160
In the circle cutting method, excavation was done in the upper and lower parts. Because the
161
soil is weak, it is necessary to prepare pre-support elements in the upper part. As Figure 2
162
shows, the excavation sequences begin with part 1. Subsequently, the primary support system
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is set, including a layer of elementary shotcrete, micromesh and lattice girders. The same
164
executive steps follow the excavation of part 2 and other parts until the completion of the
165
whole section. Because of the loose conditions of the soil and its low cohesion in Qom
166
subway tunnel and the step by step excavation method, each advancing step was 70 cm long
167
(SCE, 2012).
168 169
Figure 2. Excavation sequences and supporting steps (SCE, 2012)
170 171
This study made use of three-dimensional finite difference code for settlement estimation.
172
Despite some complications, the main advantage of a 3D analysis of NATM tunnelling over
173
mechanized TBM tunnelling is that there is no need for simulating the complex movement of
174
the shield. In the first step of numerical modelling, the geometry of the model was created
175
according to Figure 3. The dimensions of the model were determined such that borders would
176
not influence model responses. The distance of tunnel crown and axis to the ground surface
177
were 12 and 16.5 meters, respectively. The model was 70 m long, 80 m wide, and 40 m high.
178
The support system used in this model was a combination of shotcrete and lattice girders. The
179
strength properties of shotcrete are shown in Table 1.
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180 181 182
Figure 3. Geometry of numerical model Table 1. Strength properties of shotcrete property value Passion ratio 0.15 Elasticity modulus(kg/cm2) 20 Compressive strength(MPa) 16 Density(kg/m3) 2000
183 184
In the studied region, QF1 and QC2 were the two types of soil structure. Hence two different
185
layers are considered in the numerical model. The first layer (QF1) was extended from the
186
surface to a depth of 25 m, with a density of 1700 kg/m3, while the second layer (QC2) was
187
extended from the depth 25 m to the bottom of the model, with a density of 1900 kg/m3. QF1
188
layer is mainly formed of clay silt and a slight amount of sand while more than 50% of its
189
particles pass through a #200 sieve and its plasticity index (PI) is low. QC2 layer is mainly
190
comprised of clay with a little sand, and more than 50 % of its particles passing through a
191
#200 sieve and its plasticity index (PI) is more than QF1.
192
The Mohr-Coulomb model was adopted as the constitutive model for analysis. Different
193
strength characteristics of the soil layers including Young's modulus, cohesion, friction angle,
194
and K were previously verified through a back analysis process by Ghasemzadeh (2013)
195
based on convergence extensometer data, which are reported in Table 2.
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ACCEPTED MANUSCRIPT 196 Soil layer QF1 QC2
Table 2. Strength properties of soil layers Elastic modulus Cohesion Friction angle
Density
(kg/cm2)
(MPa)
(degree)
(kg/m3)
25 30
0.2 0.3
30 35
1700 1900
197 198
The modelling results were obtained after running the numerical model in several stages.
199
Figure 4 shows the vertical stress contours (Szz) as a result of tunnel excavation. Registering
200
the history of vertical displacement at the model surface provides the surface settlement
201
values. Accordingly, the transverse and longitudinal sections of surface settlement caused by
202
tunnel excavation were obtained and are shown in Figures 5 and 6, respectively. The
203
maximum amount of surface settlement, rightly located just above the tunnel axis is 1.52 cm.
204 205
Figure 4. Vertical stress contours around the tunnel
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206 207
Figure 5. Transverse settlement trough
208 209
Figure 6. Longitudinal profile of surface settlement
210 211
3.2. Analytical method
212 213
Among the different analytical methods proposed for settlement prediction, Loganathan &
214
Poulos model gives the most acceptable estimates. This model is the first to consider that the
215
elastoplastic movement of the soil at the tunnel face is more oval-shaped (Figure 7b) than
216
radial uniform movement (Figure 7a) (Loganathan and Poulos, 1998). The most important
217
parameter when utilising this method is the gap (g) parameter, which indirectly represents the
218
convergence of tunnel walls. Other such parameters as geometrical characteristics are
219
requisites for the estimation of settlement via this model.
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220 221 222
Figure 7. Circular and oval ground deformation patterns around a tunnel section (Loganathan and Poulos, 1999)
223 224
Although Loganathan & Poulos model is essentially employed in mechanized tunnelling by
225
TBM, it can also be employed for settlement prediction induced by NATM excavation
226
method. By calculating the amount of gap in a numerical software and substituting it and
227
other needed parameters in Equation 1, the amount of maximum surface settlement is
228
obtained as follows:
U Z 0
H (1 ) 1.38 x 2 2 ( 4 gR g ) exp 2 2 2 H X ( H cot R)
(1)
229 230
Where H (tunnel depth) equals 12.5 m, ν (Poisson's ratio of soil) is 0.3, R (tunnel radius) is 4.9 m, g
231
(gap parameter at the crown) is 15.32 mm, β is 45
232
substituting these values in Equation 1, the surface settlement values are achieved, and the maximum
233
amount of settlement equals 2.02 cm.
234
2
and x varies between [-40, 40] m. By
3.3. Empirical method
235 236
Peck’s model, primarily introduced in 1969, is an empirical model most widely used in
237
predicting tunnelling induced surface settlement. Over the following years, various
238
modifications to this basic method were suggested, the best outcome of which is summarized
239
in Equations 2 and 3 (also used in this study). In all empirical models, there is a key 12
ACCEPTED MANUSCRIPT 240
parameter named volume loss (VL), obtained, in the present paper, through the use of the
241
result pertaining to the numerical software.
x2 S S max . exp 2 2i S max
(2)
0.313VL D 2 i
(3)
242 243
Table 3 illustrates the amounts of other parameters required in Equations 2 and 3. By the
244
substitution of these parameters in the equations, the surface settlement values for different
245
distances from the tunnel axis are obtained; the maximum amount of settlement equals 1.86
246
cm.
247
Table 3. Amount of parameters in the empirical equation
Parameter Volume loss (VL) Tunnel diameter (D) Trough width parameter (i) 248
Amount 1% 9.8 m 6.8 m
4. Model uncertainty analysis
249 250
The uncertainties that are dealt with in geotechnical engineering fall under two major
251
categories of aleatory and epistemic. Aleatory uncertainty represents the natural randomness
252
of a variable, while lack of knowledge causes epistemic uncertainty. Epistemic uncertainty is
253
divided into two major sub-categories: Parameter uncertainty and model uncertainty (Figure
254
8). Parameter uncertainty is attributed to the lack of certain data, which results from the
255
inaccuracy in assessing parameter values. Model uncertainty has to do with the degree to
256
which a chosen mathematical model accurately mimics reality (Baecher and Christian, 2005;
257
Griffiths and Fenton, 2007). In other words, the uncertainty in the prediction of unknown
258
values (model outcome) depends on both the structural uncertainty (model uncertainty) and
259
input data uncertainty (Draper, 1995). 13
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260 261
Figure 8. Categories of geotechnical uncertainties
262 263
Each prediction model has to be simple in terms of mathematical operations, and it must
264
predict reality. Due to their assumptions and simplification, the design tools use just a few
265
key parameters. Each of the neglected key parameters generates noise (uncertainty) in the
266
model. The source of uncertainty in design tools is their imperfect assumptions and various
267
degrees of simplification in the model. The main reason model uncertainty is focused on is
268
that it is large, and in certain cases, it can be reduced (Griffiths and Fenton, 2007).
269
Geotechnical models introduced for settlement estimation are no exception to the rule above.
270
They have their own assumptions, simplifications and limitations which generate uncertainty
271
in their results. Model uncertainty can only be quantified by comparison with either more
272
involved models that exhibit a closer representation of nature or the data collected from the
273
field or the laboratory (Ditlevsen, 1983). The objective of the present study is to quantify the
274
model uncertainty of different settlement prediction approaches via their comparison with the
275
model results and the exact data obtained in the field. To this end, the settlement trough and
276
maximum settlement estimated by the empirical, analytical and numerical method are
277
compared with that of exact instrumentation data (1.58 cm) which are shown in Figure 9.
14
ACCEPTED MANUSCRIPT Distances to tunnel axis (m) -40
-30
-20
-10
0
10
20
30
40
0
Displacement (cm)
-0.5 -1 -1.5 -2 -2.5
278 279
Analytical
Empirical
Numerical
Exact data
Figure 9. Comparison of analytical, empirical and numerical methods with the exact data
280 281
The uncertainty of each model can be simply quantified by calculating the relative error of
282
each model in the estimation of the settlement, derived from Equation 4:
Re lative Error
Model estimate Exact amount Exact amount
(4)
283 284
According to Equation 4, the relative error values of each estimation method are reported in
285
Table 4 along with the maximum settlement values.
286
Table 4. Maximum settlement and relative error of each method Analysis method Settlement amount (cm) Relative error (%) Numerical method
1.52
3.8
Analytical method
2.02
27.8
Empirical method
1.86
17.7
287 288
As stated earlier, the relative error values of each model represent its uncertainty amount. It
289
can, therefore, be understood from Table 4 that the numerical model, with the relative error of
290
3.8 %, has the least uncertainty while the highest uncertainty belongs to the analytical model 15
ACCEPTED MANUSCRIPT 291
with the relative error of 27.8 %. The numerical method results are very close to those of
292
exact instrumentation, rendering it a reliable design tool for settlement estimation. Analytical
293
method results, on the other hand, are far from the exact data, hence an undesirable model for
294
settlement estimation. The empirical model, with a relative error of 17.7%, stands in the
295
middle of the spectrum with its slightly accurate and reliable results. Numerical modelling, it
296
can be concluded, is the best and most precise approach for the estimation of tunnelling
297
induced surface settlement.
298
Besides, it is possible to deem numerical modelling as an optimistic approach to settlement
299
estimation as it underestimates the maximum settlement value. On the contrary, since
300
analytical and empirical methods overestimate the maximum settlement value, they are
301
considered as conservative approaches. In addition, the comparison of settlement troughs in
302
Figure 9 shows that empirical methods predict a narrow settlement trough, while the
303
numerical method predicts the widest one. However, in all three models, the settlement
304
trough width (i) is approximately 8 m.
305
5. Conclusion
306 307
In this study, the model uncertainty of geotechnical models used in settlement estimation was
308
characterized
309
instrumentation data. In this regard, settlement trough and maximum settlement, caused by
310
NATM tunnelling in Line A of Qom subway, were estimated by empirical, analytical and
311
numerical models and compared with the actual measured data. This approach entailed the
312
following conclusions:
through
a
systematic
comparison
16
between
model
predictions
and
ACCEPTED MANUSCRIPT 313
- Geotechnical models introduced for settlement estimation have their assumptions,
314
simplifications and limitations, hence the uncertainty in their results. A model uncertainty
315
analysis is, therefore, essential for the settlement estimation models.
316
- The maximum amount of surface settlement derived from numerical, empirical, analytical
317
methods and from instrumentation data are 1.52, 1.86, 2.02 and 1.58 cm, respectively.
318
- The numerical model has the lowest level of model uncertainty (closest to reality) in
319
estimating the tunnelling-induced surface settlement, rendering it the most precise approach
320
for the estimation of surface settlement.
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- The analytical method has the highest level of model uncertainty which makes it an
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undesirable model for settlement estimation. The empirical model shows a moderate
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performance in this respect.
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- In comparing the settlement trough estimated by each model, it becomes clear that empirical
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methods predict a narrow settlement trough while the numerical method predicts a wide
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settlement trough.
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Acknowledgement
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We would like to show our gratitude to all reviewers for sharing their valuable comments and
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insights during this research, which led to valuable improvements in our study.
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References
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Verruijt, A., Booker, J., 1996. Surface settlements due to deformation of a tunnel in an elastic half plane. Geotechnique, 753-756. Wang, Z., Sampaco, K., Fischer, G., Kucker, M., Godlewski, P., Robinson, R., 2000. Models for predicting surface settlements due to soft ground tunneling, North American Tunneling 2000.
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Highlights:
Settlement estimation models are associated with high model uncertainties. Model uncertainty of empirical, analytical and numerical approaches are studied. Maximum predicted settlement of employed models are 1.86, 2.02 and 1.52 cm. Numerical and analytical models have lowest and highest model uncertainties. Numerical modeling is the best design tool for surface settlement estimation.