Numerical Study On 3D Effect and Practical Design in Shield Tunneling
Numerical Study On 3D Effect and Practical Design in Shield Tunneling
Numerical Study On 3D Effect and Practical Design in Shield Tunneling
com
ScienceDirect
Underground Space 4 (2019) 201–209
www.elsevier.com/locate/undsp
Received 21 May 2018; received in revised form 27 August 2018; accepted 11 January 2019
Available online 27 March 2019
Abstract
In practice, different design methods are used in solving geotechnical problems depending on the type of issue such as the tunneling,
braced excavation, or bearing capacity of a foundation, that is, the basic mechanism of the design method differs depending on the prob-
lems even for the same ground. A numerical analysis using the finite element method has recently become familiar owing to an improved
computing performance; however, it is not widely used in the design of geotechnical problems including tunnel excavation owing to the
reliability of the constitutive model of the ground material. If a constitutive model of soils can properly express the properties of the
ground material, a numerical analysis will play a vital role in solving the geotechnical problems. In this paper, the current state of a
numerical analysis and its applicability in tunnel design are discussed. Herein, the simulation of the ground behavior during tunnel exca-
vation is carried out using sandy and clay ground parameters for shallow and deep tunnel excavations. This paper is mainly focused on
the effects of tunnel excavation under three-dimensional (3D) conditions, as well as the current design method. Non-linear 2D and 3D
finite element analyses have been conducted, in which the elastoplastic sub-loading tij model has been used as a constitutive model of the
soil. The performance and acceptability of the constitutive model have already been proven to reproduce the results of various model
tests on different geotechnical problems such as the tunneling, braced excavation, and bearing capacity of a foundation, as well as
the measured field data. It was found that a 2D finite element analysis where the rate of stress release is considered, can be used for
the prediction of the ground deformation and surface settlement; however, it does not provide rational information in the prediction
of tunnel lining forces such as the stress, bending moment, and axial force, which emphasize the necessity of a 3D analysis with a proper
construction process in a tunnel design.
Ó 2019 Tongji University and Tongji University Press. Production and hosting by Elsevier B.V. on behalf of Owner. This is an open access article
under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
https://doi.org/10.1016/j.undsp.2019.01.002
2467-9674/Ó 2019 Tongji University and Tongji University Press. Production and hosting by Elsevier B.V. on behalf of Owner.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
202 H.Md. Shahin et al. / Underground Space 4 (2019) 201–209
(Peck, 1969), assuming a given volume loss from the tun- are modified to predict a deformation of the ground during
neling. In certain cases, an elastic finite element analysis the subsequent construction process using in-situ measured
is used to predict the surface settlement troughs that occur data obtained from preceding construction work.
from the tunneling. However, an elastic analysis cannot In this paper, the current use of numerical analysis in
take into consideration various features of the soil, includ- tunnel design is discussed. The subloading tij model has
ing a nonlinearity and dilatancy. As a result, a practical been used as a constitutive model in such analyses, and
elastic analysis is often used for a crude estimation of the the validity and reliability of the model have been demon-
ground deformation. In a traditional design method, the strated in previous studies (Shahin, Nakai, Hinokio,
parameters of the elastic analysis are revised by fitting the Kurimoto, & Sada, 2004; Shahin, Nakai, Hinokio, &
results with the field data. Usually, the range of influence Yamaguchi, 2004; Shahin et al., 2011) and field results
is overestimated in an elastic finite element analysis, which (Konda, Nagaya, Hashimoto, Shahin, & Nakai, 2013) of
is not limited to the tunnel problem but also other geotech- tunnel excavation problems. Using the subloading tij
nical problems such as a braced excavation. Shahin, Nakai, model, Shahin, Nakai, Hinokio, Kurimoto, et al. (2004)
Zhang, Kikumoto, and Nakahara (2011) showed that an showed that such numerical simulations properly repro-
elastic analysis produces wider surface settlement profiles duce the influence of the excavation sequence in a tunnel
than the experimental results. Because there is no yield construction as compared to the laboratory results
point in a linear elastic model, it cannot express a deforma- obtained from two-dimensional (2D) physical models.
tion that occurs locally. In addition, in elastic analyses, the The results of numerical analyses showed that the constitu-
distributions of the shear strain for varying distances from tive model can precisely reproduce the observed patterns of
the tunnel invert toward the bottom boundary (Shahin surface settlement and earth pressure under 2D conditions,
et al., 2011). including the effects of the existing building load on the
In practice, different design methods are used depending tunnel excavation, as demonstrated by Nakai, Shahin,
on the type of problem, such as the tunneling, braced exca- Hinokio, Sada, and Sung (2005) and Shahin et al. (2011).
vation, or bearing capacity of a foundation, etc. It is some- Sung, Shahin, Nakai, Hinokio, and Yamamoto (2006)
what unfortunate that the basic mechanism of the design showed the capability of the constitutive model to predict
method used in geotechnical engineering differs depending the general patterns of the ground behavior in model tests
on the problem, even for the same ground. Although a with existing piled and raft foundations.
numerical analysis using the finite element method has
become familiar with improvements in the capacity of per- 2 Material properties of sand and clay used in the simulations
sonal computers and their lower costs, such an analysis has
yet to be widely applied to the design of geotechnical prob- Regardless of the tunnel excavation problem, the behav-
lems including a tunnel excavation owing to the reliability ior of the ground largely depends on the material proper-
of the constitutive model of the ground material. There- ties of the ground. Herein, the stress–strain relationships
fore, if a constitutive model that can properly express the of sandy ground (Toyoura sand) and clay ground (Fuji-
properties of the ground material and be used for practical mori clay) are first described. The subloading tij model
applications is developed, the numerical analysis will play a was used as a constitutive model for both sand and clay.
vital role in a tunnel design. During the past decade, con- Detailed features of the model are given in Nakai and
siderable improvements were made in the use of numerical Hinokio (2004) and Nakai (2012), some of which are sum-
methods to simulate a tunnel excavation (Amorosi, marized below:
Boldini, & Falcone, 2014; Augarde & Burd, 2001; Conti,
Viggiani, & Perugini, 2014; Mroueh & Shahrour, 2002), (1) The model can explain the behavior of soil, from the
although many studies still use simple constitutive models, negative dilatancy (volumetric compression during
such as linear elastic or elastic perfectly plastic Mohr– shearing) of normally consolidated clay and loose
Coulomb models. Although strain-hardening type nonlin- sand to the positive dilatancy (volumetric expansion)
ear elastoplastic models such as the Cam clay model are of over-consolidated clay and dense sand using the
used at the research level, in practice they are applied as same material parameters and model framework.
a back-end support for existing design methods. As a result, the soil behavior, from a low stress level
In urban areas, however, many excavations are con- as with a model test, to the stress level in the field,
ducted using tunnels within the vicinity of existing struc- can be described using the same material
tures and tunnels. In these cases, how the deformation of parameters.
the ground, including the existing structure, is controlled (2) To obtain reliable results in the analysis of 3D
and how the safety of the tunnel excavation is ensured problems, it is necessary to express the influence of
are questionable. The same questions are also applicable the intermediate principal stress uniquely (from the
in a braced excavation. In response to the current demands, triaxial compression condition to the plane strain
the current design method is unable to provide persuasive and triaxial extension conditions). This model can
answers. Therefore, in practice, the material parameters describe the 3D behavior using material parameters
used in a finite element analysis (mainly an elastic analysis) obtained under triaxial compression conditions.
H.Md. Shahin et al. / Underground Space 4 (2019) 201–209 203
(3) The model can explain the influence of the stress-path can easily be obtained from traditional laboratory tests.
dependency of the plastic flow. Figure 1 shows (a) the characteristics of sand under a
triaxial compression condition (stress–strain-dilatancy rela-
Model parameters for sand and clay are shown in tionship) with a varying relative density (Dr) and (b) the
Table 1. The parameters are fundamentally the same as relation between the internal friction angle and relative
those of the Cam clay model except for parameter a, which density obtained from the diagram in (a). Figure 2(b) is
influences the density and confining pressure. Parameter b used for a conventional tunneling design. Figure 2 shows
represents the shape of the yield surface. These parameters the characteristics of triaxial compression ((a) the
Table 1
Parameters used in subloading tij model for sand and clay.
Parameter Notation Value Remarks
Sand Clay
Compression index k 0.070 0.104 Same parameters
Swelling index j 0.004 0.010 as Cam-clay model
5
Reference void ratio on normally consolidation line at p = 98 kPa and N 1.10 0.922
q = 0 kPa
Critical state stress ratio Rcs = (r1/r3)cs(comp.) Rcs 3.20 3.20
Poisson’s ratio me 0.20 0.20
Shape of yield surface (same as original Cam clay at b = 1) b 1.50 1.50 —
Influence of density and confining pressure a 30 500
(a) Stress–strain-dilatancy curves (b) Internal friction angle vs. relative density
Fig. 1. Simulations of drained triaxial compression tests on sand used in the analyses.
0 0
0.02 0.02
Sand, Dr=78%
Settlement (m)
Sand, Dr=20%
Settlement (m)
tunnel diameter. Figures 4 and 5 show the settlement Figs. 4–8 that the settlement troughs for the stress release
profiles (half section from the tunnel center) of sand of 40%~50% in the 2D analyses nearly correspond to the
and clay grounds, respectively. In the figures, both 2D case in which the lining is set up at 2 m behind the exca-
and 3D analyses are shown for different rates of stress vation face in the 3D analysis for both soil conditions of
release under 2D conditions, and for different locations Dr = 20% and Dr = 78% in sandy ground (Figs. 4 and 6).
of the lining from the excavation face under 3D condi- From the 3D analysis on the soft clay ground
tions. Figures 6 and 7 show the surface settlement at (OCR = 2.0) shown in Fig. 5, it is also understood that
the center (maximum surface settlement) for sand and an early lining is particularly important under such soil
clay, respectively. In these figures, the left vertical axes conditions. In clay ground, the settlement corresponding
represent the rate of stress release for the 2D conditions, to a stress release of 35%~40% in a 2D analysis is
and the right vertical axes represent the position of exca- close to the lining setup after 2 m in the 3D analysis in
vation face for the 3D conditions. It can be seen from the same ground (Figs. 5 and 7). These results also
0
0
0.25
0.02
Clay, OCR=2.0
Settlement (m)
Clay, OCR=8.0
Settlement (m)
0.5
2D: Lining at 3D: Interval 2D: Lining at 3D: Interval
stress release of segment 0.04 stress release of segment
0.75 20% installation 20% installation
35% 2.0 m 35% 2.0 m
40% 4.0 m 0.06 40% 4.0 m
1 50% 6.0 m 50% 6.0 m
60% 8.0 m 60% 8.0 m
1.25 0.08
0 8 16 24 32 40 48 0 8 16 24 32 40 48
Distance from tunnel (m) Distance from tunnel (m)
(a) For OC
CR=2.0 (b) For OCR =8.0
settlement are 1.128 and 0.368 m for relative densities of Fig. 13. Surface settlement profiles at the time of the lining, completion of
20% and 78%, respectively. When the rate of the stress the excavation, and after complete dissipation of excess pore water
release is set to 20% (early lining), the subsidence of the pressure (D/B = 1.0).
208 H.Md. Shahin et al. / Underground Space 4 (2019) 201–209
S cale: 300 kN
Fiel d Field
Analysis Analysis
desig n design
(a) Lining at 40% stress release (b) Lining at 20% stress release
Fig. 16. Axial force on lining from analysis and field design (clay,
OCR = 2.0, D/B = 1.0).
From the viewpoint of a numerical analysis, the tunnel conference on computational methods in tunnelling and subsurface
engineering, Germany, April (pp. 191–202).
excavation problem is not a special problem and is instead Mroueh, H., & Shahrour, I. (2002). Three-dimensional finite element
a boundary value problem that can be solved in the same analysis of the interaction between tunneling and pile foundations.
way as several other geotechnical problems. However, to International Journal for Numerical and analytical Methods in Geome-
chanics, 26(3), 217–230.
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needs to be formulated in the simulation technique. It can applications. Boca Raton London New York: CRC Press.
be stated that, if the mechanical properties of the ground Nakai, T., & Hinokio, M. (2004). A simple elastoplastic model for
normally and over consolidated soils with unified material parameters.
material and the construction process are treated properly, Soils and Foundations, 44(2), 53–70.
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Peck, R. B. (1969). Deep excavations and tunnelling in soft ground. In
Acknowledgements Proceedings of the 7th international conference on soil mechanics and
foundation engineering, Mexico City (pp. 225–290).
Shahin, H. M., Nakai, T., Hinokio, M., Kurimoto, T., & Sada, T. (2004).
The authors acknowledge the financial support of the Influence of surface loads and construction sequence on ground
Advanced Construction Technology Center (ACTEC), response due to tunnelling. Soils and Foundation, 44(2), 71–84.
Shahin, H. M., Nakai, T., Hinokio, M., & Yamaguchi, D. (2004). 3D
Japan for a portion of the numerical simulation. effects on earth pressure and displacements during tunnel excavation.
Soils and Foundations, 44(5), 37–49.
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ground behavior due to shield excavation. In 3rd International