A Review on Methods of Predicting Tunneling Induced Ground Settlements S. M. Yahya
Department of Geotechnics & Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia. e-mail:
[email protected]
R. A. Abdullah
Department of Geotechnics & Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia. e-mail:
[email protected]
ABSTRACT The purpose of this review paper is to present the techniques, approaches and methods for assessing the ground settlements induced by tunneling. Tunneling operation poses threat to adjacent structures by creating subsidence, heave, and vibrations which make the structure more vulnerable. With the advent of urbanization and innovative technologies, utilizing underground space is becoming a sustainable practice day by day. The assessment of ground settlement induced by tunneling is significant to policy makers, practitioners and designers associated with tunneling. The versatility of geological strata and condition has led the practice even more challenging. The multidimensional aspects and problems of tunnel applications has made the practice a complex one requiring incorporation of interdisciplinary nature of this study such as geology, civil engineering, mining engineering specially rock engineering and rock mechanics. This paper also addresses the issues regarding various methods, constitutive models, different ground conditions for instance, mixed faced soil and rock interface ground), roles effect of dimensions on analysis and prospects of multi and interdisciplinary roles.
KEYWORDS: Ground settlement, empirical method, analytical method, numerical method, mixed faced ground.
INTRODUCTION The continuously growing development projects in various cities around the world having limited available surface space and now they are relying on underground space such as tunnels. Tunnels are constructed to facilitate rapid transit, water supply, sewerage system and various others facilitates. These tunnels are generally situated in populated cities and constructed in soil or rock or mixed ground. The construction of these underground infrastructures is complex in nature. And the construction will inevitably induce ground settlement due to convergence of the ground after tunnel excavation, which changes the in-situ stress of the ground and disturbing the original condition by stress release (Ocak, 2008). The ground settlement is a significant issue in urban areas because excessive settlements can trigger potential damage to surrounding roads, structures, underground pipelines and facilities and with a view to decreasing this adverse impact, it is essential to analyze, forecast and control the ground settlement that develops during tunnelling process. Therefore, the prediction of ground settlement is of great significance to - 5813 -
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protect these existing structures in urban areas prior to tunnel construction. The information will not only ensure safety but also will work as a tool for decision making in order to avoid excessive settlement by taking take appropriate countermeasures (Wang et al., 2013). Therefore, the careful use of methods for predicting the ground settlements induced by tunnelling is crucial. The scope of this review paper is limited to TBM and NATM tunnelling methods. Different methods are adopted for this prediction and other associated issues regarding the methods are discussed in this paper. This paper deals with short term settlement only. Usually the short-term settlements occur during or after excavation within a certain period of time, assuming that the state of the ground is in the dominant undrained condition (Latif et al., 2013). Long term settlements which include consolidation, creep behaviour and other factors are not within the scope of this paper.
METHODS FOR PREDICTING TUNNELING INDUCED GROUND SETTLEMENTS Currently several methods and approaches are available for estimating and predicting ground movements caused by tunnelling. Generally, study on the prediction of ground settlement has been carried out by these following three methods: • • •
Empirical methods Analytical methods and Numerical methods.
The methods and commonly used computation tools used for numerical methods are shown in Figure 1. The computational tools include only 3D versions. Computational Tool
Method
Empirical Method
Analytical Method
Numerical Method FEM
PLAXIS 3D, ABAQUS,
FDM
FLAC3D
Continuum Model
Discontinuum Model
DEM
3DEC
Figure 1: Different methods for prediction of settlements & computational tools
Empirical Method Empirical method provides the most simple calculation and thus extensively used in practical applications. The most common and widely used empirical method for predicting settlement
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induced by tunnel is the Peck’s formula (Peck, 1969) (Equation 1). This classical empirical method is useful for preliminary estimation and initial idea about surface settlement. The formula is as follows: − y2
(1) Sv (y) = Sv max . e 2i where, Sv (y) is the surface settlement, Sv max is the maximum settlement above tunnel axis, i is 2
the horizontal distance from the tunnel axis to the point of inflection of the settlement trough, y is the horizontal distance from the tunnel axis. Many researches have been conducted involving field investigation and tests regarding estimating i. The estimation of i values by various researchers are shown in Table 1. Name Peck (1969)
Table 1: Recommendation for value of i by various researchers Value of i
i z = R 2R
Comment Based on field observations
n
n=0.1 to 0.8
Atkinson and Potts (1977) = i 0.25 ( z + R )
Based on field observations
In case of loose sand
=i 0.25 (1.5 z + 0.5R ) O’Reilly and New (1982)
In case of dense sand and over consolidated clay
= i 0.43 z + 1.1
In case of cohesive soil
Based on field observations of UK tunnels
= i 0.28 z − 0.1 Mair (1993) Attewell (1977)
Clough and Schimdt (1981)
In case of granuar soil
i = 0.5 z
i z =α R 2R
n
i z =α R 2R
n
α=1 and n=1
Based on field observations worldwide Based on field observations of UK tunnels Based on field observations USA tunnels
α=1 and n=0.8 [Note: Here, z is the depth of tunnel below ground and R is the tunnel radius.] The estimation of maximum settlement can be done by Equation 2 (Mair, 1993). Where, VL is ground loss (ratio of ground loss volume/tunnel volume per meter length) and D is the tunnel diameter.
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S max =
0.313VL D 2 i
(2)
However, the empirical method which is derived from 20 case histories have no theoretical background and assumes the vertical settlement profile in the ground same as the Gaussian distribution. Moreover, this method is limited by few parameters and unable to address complex situations and other parameters which induce settlement. It also does not cover horizontal displacement and do not consider the impact on any structure interaction. Several authors (Chi et al., 2001, González and Sagaseta, 2001) pointed out some important limitation of this method such as inapplicability to various ground conditions, construction techniques, horizontal movements and subsurface settlements. They are not able to provide solution of tunnel with support. Numerical method provides better solution to overcome these problems. However, the empirical method is useful for comparing the results with the numerical method for validation purpose of a model.
Analytical Method Analytical method provides a better solution and advantageous over numerical method because it can take into consideration of various other relevant parameters affecting ground surface settlement. Unlike empirical method, analytical method can address both horizontal vertical displacements. It also provides a better understanding of the inter-relationship between these affecting parameters. Analytical solutions provided by various authors are limited in number. As some initial assumptions are to be made prior to find a solution, these are applicable for specific type of case and condition. Sagaseta (1987) presented a closed-form solution for isotropic and homogeneous incompressible soil due to near-surface ground loss from tunnelling. Verruijt and Booker (1996) presented a generalization of Sagastea’s solution in homogeneous elastic half spaces for the case of ground loss having arbitrary values of Poisson’s ratio which also included the effect of long term tunnel lining deformation or ‘ovalization’. However, the analytical solution of Verrujit and Booker was unable to provide a satisfactory agreement with the measured settlement profile. Later Loganathan and Poulos (1998) attempted to refine Verrujit and Booker’s solution by incorporating ground loss parameter for tunnels in clay. The refined solution provided better results for tunnels in stiff clay but overestimated for tunnels in soft clay. More recently, Chi et al. (2001) extended the equivalent ground loss model of Loganathan and Poulos to clayey and sandy soils and the analytical solution was used to conduct back analyses for 29 cases which were performed using optimization principle to obtain key parameters of influence zone angle and gap parameter that provide the best fit to the measured ground settlement profiles. Bobet (2001) presented an analytical solution for shallow tunnel in saturated ground. Based on method proposed by Bobet (2001), Chou and Bobet (2002) studied short term settlement at the ground surface and found good agreement comparing between predictions and actual observations along with correlation between soil and liner, tunnel geometry, and construction procedure. At the tunnel centreline is the gap parameter was mostly responsible for the maximum surface settlements. The limitation of this analytical solution is that it only gives reasonable predictions for shield driven tunnels in medium to stiff clays, or in soils and soft rocks where plastic deformations around the tunnel are small. And also because the analytical solution is based on the assumption of elasticity, it tends to underpredict maximum soil deformations and overestimate the settlement trough. The analytical solution is derived for a specific type of case
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and problem. Since the ground condition, physical and mechanical properties of soil and rock, also the geometrical properties of tunnel varies from site to site, it is not applicable to all type of case and cannot deal with complex unique different situation which is a limitation of analytical method.
Numerical Method Recently, with the rapid development of computational tools, user-friendliness and ability to solve the complex problems the numerical methods are becoming more popular. Many limitations of empirical methods and analytical methods can be overcome by the numerical method. Apart from geotechnical properties of ground, tunnel geometry and depth the stress-strain condition of both tunnel structure and ground which affect the settlement also rely on the construction process. Numerical method can take into account this construction process called ‘step-by-step’ method (Katzenbach and Breth, 1981, Galli et al., 2004). As shown in Figure 1, the numerical method which constitutes continuum and discontinuum modelling are useful tool for predicting tunnel induced ground settlement. Continnum model includes Finite Element Method (FEM) and FDM (Finite Difference Method) and Discontinnm model include Distinct Element Method (DEM). Li and Zhu (2007) indicated that various factors of affecting ground settlement can be comprehensively considered by the numerical method, which could forecast ground settlement caused by the tunnel excavation accurately. Numerical methods can deal with various soil and rock properties, geometrical properties, complex boundary condition and time dependent calculation. Auto generation of mesh is one of the very useful features of the modelling software and another attractive feature is colourful output of the graph and results. Vafaeian and Mirmirani (2003) reported that the advantage of using the finite element program is that it can be applied to any special cases as well, for example for a layered soil of different density or different elasticity modulus, or non-circular sections. For some cases, authors found numerical analysis useful to estimate the settlement, although unfavourable results were found in some cases. Giving for example, Rowe et al. (1983) found that FEM generally gave good estimates of ground settlements in their analyses of some case histories. Mair (1993) reported that finite element analysis gave poor predictions for surface settlements even with a refined constitutive soil model and found that the surface settlement trough was too wide and shallow compared with those given by the empirical methods and field measurements. A comparative advantages and limitations of these three methods are showed in Table 2.
Table 2: Advantages and limitations of empirical, analytical and numerical methods.
Methods Empirical
Advantages • Very simple calculation • Provide initial idea and estimation of settlement • Useful for comparing results with other methods.
Analytical
• Can address various other parameters • Cover both horizontal and vertical displacement. • Relationship between affecting parameters could be understand. • Applicable to any type of complex
Numerical
Limitations • Consider few parameters • Don’t cover horizontal displacement and subsurface settlement. • Cannot address complex and different ground condition. • Doesn’t include construction techniques. • Limited number of solutions available. • Applicable to specific type of ground condition. •
• Construction of model and analysis is time
Vol. 19 [2014], Bund. T ground and site condition. • Construction process and support can be included. • Cover both horizontal and vertical displacement. • Can address many parameters. • Parametric study possible. • User friendly computational tool available. • Better graphic visualization possible. • Chart and graph can be generated easily. • Auto generation of mesh.
5818 consuming. • May lead to misleading results if user doesn’t have ‘in-depth’ understanding of modeling process and software. • Not easy to verify and validate the results.
Effect of Dimensions on Numerical Methods: 2D vs 3D modeling approaches For simplicity, time constraints and easy understanding of settlement induced by tunnelling, many authors prefer to use two-dimensional (2D) analysis. Besides, 2D analysis is handy for studying parameters affecting ground settlement if there are any significant changes in condition regarding boundary, ground, geometry, meshing. However, the tunnelling process is definitely three-dimensional (3D) process. Therefore, the surface settlement induced by tunnelling also needs to be investigated by 3D analysis. Regardless, it should be noticed that the 3D analysis requires additional efforts and data, therefore, more expensive, yet gives a more reliable and realistic results comparing to 2D analysis. In tunnel modelling the excavation length of the tunnel slice is a significant aspect in 3D analysis whereas in 2D analysis the cross-section of the tunnel through infinite length has to be considered. 3D analysis also provides better visualization and the user get a ‘feel’ about the overall underground structure. There are some significant differences between the 2D and 3D approach. During the tunnelling process a 3D stress-deformation state develops at the heading. The simulating of partial relaxation of stress at the tunnel heading or deformation of the excavated surface at the tunnel heading, which occurs prior to installation of lining plays a significant role in the analysis of stress-strain state in the tunnel along with its surroundings. The three dimensional approach provide a better and adequate analysis by simulating the progress of works, stress changes, and deformations in the vicinity of the tunnel heading. The tunnel construction process is usually simulated in the numerical analysis by the "step-by-step" simulation. The first step is the analysis of the initial or in-situ stress condition in the ground, which is followed by step by step simulation of excavation and support work sequences. During the 2D analysis of tunnel, some assumptions have to be made to consider the partial relaxation of stress at the tunnel heading, i.e. deformations that occur at the tunnel heading prior to installation of lining or support which is also known as plane strain condition. Several methods have so far been proposed in literature for the simulation of tunnel construction using 2D models: stress relief method or convergence confinement method (Panet and Guenot, 1982), stiffness reduction method/softening method (Swoboda, 1979), disk calculation method (Schikora and Ostermeier, 1988), Hypothetical modulus of elasticity (HME) soft lining method, volume loss control method (Potts and Zdravkovic´, 2001) and the gap method (Rowe et al., 1983). Field observations by Finno and Clough (1985) indicated that the ground response during tunnelling is both three-dimensional and time-dependent. An advancing tunnel face creates a complex 3D stress path (Eberhardt, 2001). An investigation by Franzius and Potts (2005) on the
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influence of geometry and dimensions of a 3D finite element model for predicting tunnel-induced surface settlement showed how the vertical boundaries can influence the results. This study explained the prospects of 3D analysis which gives reasonable results if simulated in specific way like increasing the length of incremental tunnel excavation. Also, the results obtained by Lee and Rowe (1990) studying a hypothetical tunnel indicate that the general three-dimensional stress and displacement patterns around a tunnel are very different as compared to those obtained at the plane strain transverse section. The distance required for the ground displacement to reach the plane strain condition will depend on the amount of plasticity developed around the tunnel opening. Vlachopoulos and Diederichs (2014) also noted that tunnelling in yielding ground generates 3D, bullet shaped plastic zone in soft rock. Qureshi et al. (2012) indicated that although there are many simplified modelling solutions available, there are still uncertainties regarding these simplifications. In an attempt to study the soil-structure interaction of buried structures using finite element modelling software MIDAS GTS (Geotechnical and Tunnel Analysis System), both 2D and 3D finite element analysis were performed on the basis of transverse moments and shear forces on same cross sectional horseshoe shaped tunnel under loading of overlaying rocks. Comparing the two results of moments and shear forces in top slab, walls and base slab of both typical sizes of tunnels, it was found that, in 3D finite element analysis of tunnels, the values of forces and moments are less than 2D finite element analysis. Therefore, it can be concluded that, the tunnel designed by using 2D finite element analysis is on the conservative side but uneconomical. Also, when the difference in values of forces and moments are compared between 3D and 2D finite element analyses, it has been found to be more in large sections than small sections. This implies that 3D analysis more accurate and safer than 2D analysis. Maraš-Dragojević (2012) compared settlement cross sections obtained by 2D and 3D finite element analyses of a tunnel for clayey-marly terrain of Belgrade and concluded that both 3D and 2D analyses provide similar cross-sectional profiles of settlement, given that proper assumptions (for example, stress reduction coefficient in this study) has been made in 2D analysis to take into account partial relaxation of stress at the tunnel heading. So, it is evident that either 2D or 3D analysis is acceptable as long as it answers the objective of modelling.
Choice of Model in Numerical Analysis In numerical analysis, several common models have been widely used namely, LinearElastic, Mohr-Coulomb, Drucker-Prager, Modified Cam-Clay Model. Karakus and Fowell (2003) used modified Cam-Clay model to simulate London clay behaviour and to consider settlement due to tunneling process. Mašín (2009) studied the accuracy of the 3D finite element predictions of displacement field induced by tunneling using new Austrian tunnelling method (NATM) in stiff clays with two different constitutive models, one of them being Modified Cam-Clay Model. Lambrughi et al. (2012) studied ground displacements induced by tunnelling comparing Linear Elastic, Mohr–Coulomb model and Modified Cam–Clay model. The study found better fitted results using the Modified Cam– Clay model whereas the Mohr–Coulomb models showed higher fluctuations around measured data. However, Modified Cam-Clay model may allow unrealistically high shear stress and applicable for critical state condition and therefore its scope is limited to theoretical purpose; in case of practical applications like tunnelling it may be misleading. Potts and Zdravkovic (2000) also concluded that use of modified Cam clay model in advanced numerical analysis can be problematic. They indicated that the model was originally developed for triaxial stress and strain conditions and therefore must be extended into generalised stress and strain space for use in numerical analysis. At present there is no universally accepted way of performing this extension and consequently there are many different forms of the model implemented in the various available computer codes. In many of these cases the finer details of
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the model are not documented. Consequently many potential errors are associated with a user’s lack of ‘in depth’ understanding of the constitutive model being employed. Many authors used Mohr-Coulomb criteria in their FE model for prediction of settlements (Migliazza et al., 2009, Huang and Zhou, 2011, Fattah et al., 2013). But the applicability of these models is limited to tunnelling in soft ground. Numerical modelling of tunnels in hard rock or ‘mixed faced ground’ or ‘soil-rock interface ground’ is different because the deformation of surrounding rock in a tunnel is complex due to non-elastic, discontinuous and heterogeneous characteristics of rock. Therefore, the Mohr-Coulomb law is not suitable for a rock mass (Simanjuntak et al. 2012). For unusual conditions, in the numerical analysis models in compliance with rock mechanics need to be incorporated. The predicted behaviour of rock mass as a result of excavation is therefore based on the non-linear yield function given by Hoek-Brown criterion. The use of Hoek-Brown model which incorporates Geological Strength Index (GSI) can provide a reliable and better solution for this type of case. The GSI system and the Hoek-Brown failure criterion were implemented in practical applications of many engineering projects across the world and gave reasonable estimates of the strength of a wide variety of rock masses (Hoek, 2006). However, the Hoek-Brown criterion and GSI chart have to be applied with caution. It is applicable for rock masses which have isotropic behaviour. It is not recommended to assign GSI value in case of rock masses having highly anisotropic mechanical behaviour, for instance, undisturbed slate (Marinos et al., 2005). Marinos et al. (2005) also indicated that it is not appropriate to assign GSI values to excavated faces in strong hard rock having few discontinuities spaced at distances of similar magnitude to the dimensions of the tunnel because in these cases the stability of the tunnel will be governed by the three-dimensional geometry of the intersecting discontinuities and the free faces created by the excavation.
Versatility of Ground: Special case of Mixed Faced Ground Not all sites have homogeneous soft ground. The geology of site is uncertain one. Schmidt (1989) pointed out that, in general, tunnel engineers face difficulties in considering the potential for subsidence, but that enough cases have now been reported to compile an experience-base for better understanding of the this settlement. These cases, however, almost exclusively involve shallow tunnels excavated in soft, unconsolidated soils (Zangerl et al., 2008). Many researchers have emphasized on settlement prediction by tunnelling in soft ground (Lambrughi et al., 2012, Wang et al., 2012, Hajihassani et al. 2013). The special case is the mixed faced ground which needs further comprehensive study. Mixed-face conditions could be characterized by two or more geological formations present simultaneously on the tunnel face (Zhang et al., 2010). Tóth et al. (2013) provided a definition of mixed-faced ground: ‘Mixed-face ground is the ground, where there are two or more geological materials simultaneously present on the tunnel face with significant differences in material properties that influence significantly, (a) penetration rate of the tunnel boring machine (TBM), or (b) operational parameters of the TBM or (c) support system installed behind the TBM.’ There are several cases reported around the world regarding this ground condition. As reported by Klados and Yeoh (2006), the Storm water Management and Road Tunnel (SMART) in Kuala Lumpur, Malaysia provided more experiences in mechanized tunnelling in mixed-face ground condition. The tunnel was constructed in the Kuala Lumpur limestone formation covered with silt and sand. Two 13.26 m diameter slurry shield TBM excavated the tunnel in mixed and karstic conditions. Due to the tropical weathering and the abandoned and refilled tin mines, the surface of the bedrock was extremely irregular. A large section of the tunnel was excavated in
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mixed ground conditions. Zhao et al. (2007) also reported a similar mixed-faced condition with a changing ground from hard rock to mixed face and soft ground (and vice versa) in Kranji Tunnel, Singapore. The ground consisted of granite with different weathering grades (from fresh rock to residual soil). Bai et al. (2013) also stated a case of “combination of soil and rock” strata. As this type of condition is relatively rare and the settlement behaviour induced by tunnelling will be different. More extensive study is thus required in the field incorporating knowledge of rock mechanics and rock engineering as most of the studies emphasized on soil only. Integrative study of rock and soil in tunnel modelling may solve this issue.
PROSPECTS OF MULTI AND INTERDISCIPLINARY APPROACH The modern era of globalization and information technology has made the flow of sharing knowledge and information very easy and quick. The incorporation of multi and interdisciplinary approach in studying tunnel is of great importance to increase efficiency and avoid confusion. Multi and interdisciplinary approach obviously can provide solution practical and new emerging problems associated with tunnelling, variety of geotechnical condition and uncertainties and reduce the communication gap between professionals of various discipline. This will increase effectiveness, efficiency, reliability of real-life challenges. The integrative collaboration of disciplines like geology, mining engineering, rock mechanics and rock engineering, geotechnical engineering is necessary to address wide range of challenges. The help of various other disciplines may be needed but the major role playing subjects are shown in Figure 2. The disciplines shown here are closely related to each other but as they emerged as different mature subjects they are shown separately. Confusion should be avoided between two terms. Multidisciplinary approach means different disciplines working together, each drawing on their disciplinary knowledge and interdisciplinary approach implies integrating knowledge and methods from different disciplines, using a real synthesis of approaches. Geology
Rock Mechanics & Rock Engineering
Integrated Solution
Mining Science & Engineering
Geotechnical Engineering
Figure 2: Various disciplines needed to be collaborated
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Different disciplines have their respective roles and contribution in the theoretical and applied field of knowledge. The knowledge of geology is essential because it deals with the study of solid earth material comprising three types of rocks (igneous, sedimentary and metamorphic) and their structural properties, behaviour, geological mapping. Geotechnical engineering which is a speciality of civil engineering deals with the engineering aspects of all type of construction on or below the ground. Rock mechanics is a broader part of geomechanics (includes both soil and rock mechanics) which is concerned with the mechanical behaviour of rock masses. The experience of mining engineers encountered in underground mining excavations, for instance, rockburst, can also contribute to the integrated knowledge base. Single-discipline approaches usually do not produce comprehensive and successful solutions (Grigg, 2014). So undoubtedly, multi and interdisciplinary approach of these mentioned fields will be able to address not only present existing problems, but also will make the engineers and geologists to become proactive to new changing situations.
CONCLUDING REMARKS The prediction of ground settlements induced by tunnelling is very important task. The methods and approaches need to be chosen and used carefully. Also, deep understanding regarding the various aspects and issues related to these methods is necessary. Improper use can lead to discrepant results and potential hazard if used in decision making. Although the abovementioned methods have their respective pros and cons, practical engineering judgement must be applied according to the context and type of problem case encountered. In this age of advanced computer technology, numerical method can be very useful over other methods if utilized and handled properly. Numerical method needs better user expertise, knowledge and skill in terms of modelling and interpreting with a view to achieving accurate results of settlements induced by tunnelling. Following points can be concluded: •
3D numerical analysis has more advantages than 2D analysis and is recommended. However, 2D analysis can also give better results if appropriate procedures and ground model are used.
•
As most studies were done on tunnelling in soft ground, more comprehensive studies are required for tunnelling in different ground conditions such as rocky ground and mixed faced ground.
•
Appropriate choice of models and associated input data play a significant role in the numerical modelling results. The model should be carefully chosen in such a way that they can represent the relevant ground condition as to get a practical result of settlement. If necessary the model can also be user optimized.
•
Multi and interdisciplinary approach can resolve various issues by creating a bridge of knowledge between various disciplines related to tunnelling. This could benefit both researcher and practitioner by easing the job and contributing more in the knowledge base of tunnel.
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17. Huang, L.-C., and Zhou, C.-Y. (2011) “Simulation of Tunnel Surrounding Rock Mass in Porous Medium with Hydraulic Conductivity Tensor,” In: I. A. Dar and M. A. Dar (Eds.), Earth and Environmental Sciences, 423-434. 18. Karakus, M., and Fowell, R. J. (2003) “Effects of different tunnel face advance excavation on the settlement by FEM,” Tunnelling and Underground Space Technology, 18(5), 513-523. 19. Katzenbach, R., and Breth, H. (1981) “Nonlinear 3-D analysis for NATM in Frankfurt Clay,” Paper presented at the Proceedings of the International Conference on Soil Mechanics and Foundation Engineering, 10th. 20. Klados, G., and Yeoh, H. K. (2006) “Uniqueness of SMART project in the logistic and construction challenges encountered during TBM North and South drive,” Paper presented at the 7th International Congress on Rock Mechanics. 21. Lambrughi, A., Medina Rodríguez, L., and Castellanza, R. (2012) “Development and validation of a 3D numerical model for TBM–EPB mechanised excavations,” Computers and Geotechnics, 40(0), 97-113. 22. Latif, M. F. A., Ismail, M. A. M., Selamat, M. R., and Ng, S. M. (2013) “Effects of Pipe Roof Supports and the Tunnels Excavation on the Ground Settlement,” Electronic Journal of Geotechnical Engineering, 18, 1045-1056. 23. Lee, K. M., and Rowe, R. K. (1990) “Finite element modelling of the three-dimensional ground deformations due to tunnelling in soft cohesive soils: Part I — Method of analysis,” Computers and Geotechnics, 10(2), 87-109. 24. Li, X.-q., and Zhu, C.-c. (2007) “Numerical Analysis on the Ground Settlement Induced by Shield Tunnel Construction,” Journal of Highway and Transportation Research and Development (English Edition), 2(2), 73-79. 25. Loganathan, N. and Poulos, H. (1998) “Analytical prediction for tunneling-induced ground movements in clays,” Journal of Geotechnical and Geoenvironmental Engineering, 124(9), 846-856. 26. Mair, R. J. (1993) “Developments in Geotechnical Engineering Research: Application to Tunnels and Deep Excavation,” Unwin Memorial Lecture 1992, Proceedings of the ICE Civil Engineering, 97, 27-41. 27. Maraš-Dragojević, S. (2012) “Analysis of ground settlement caused by tunnel construction,”. Građevinar, 64(07.), 573-581. 28. Marinos, V., Marinos, P., and Hoek, E. (2005) “The geological strength index: applications and limitations,” Bulletin of Engineering Geology and the Environment, 64(1), 55-65. 29. Mašín, D. (2009) “3D Modeling of an NATM Tunnel in High Clay Using Two Different Constitutive Models,”.Journal of Geotechnical and Geoenvironmental Engineering, 135(9), 1326-1335. 30. Migliazza, M., Chiorboli, M., and Giani, G. P. (2009) “Comparison of analytical method, 3D finite element model with experimental subsidence measurements resulting from the extension of the Milan underground,” Computers and Geotechnics, 36(1–2), 113-124.
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