The deformation of overburden soil induced by thrust faulting and its impact on underground tunnels

(1)

The deformation of overburden soil induced by thrust faulting and

its impact on underground tunnels

Ming-Lang Lin

a

, Chun-Fu Chung

a

, Fu-Shu Jeng

a,

⁎

, Ta-Chun Yao

b

a

Department of Civil Engineering, National Taiwan University, Taiwan

b_{Mohand Associates Inc., Taipei, Taiwan}

Received 10 July 2006; received in revised form 18 March 2007; accepted 27 March 2007 Available online 12 April 2007

Abstract

Overburden soil beds situated above a fault are often deformed by propagation of bedrock thrusting from the fault during large earthquake. The deformed beds formed a triangular shear zone. This coseismic faulting often causes damage to underground tunnels located in the shear zone. The present research studies the deformation behavior of the overburden soil beds and the tunnel, the associated mechanism and the impact on the safety of tunnel linings induced by a large blind thrust slip. Based on sandbox experimental and numerical studies, it is found that results from numerical analysis are in agreement with the sandbox model tests with regard to growths of the shear zones within the soil beds, location of the tunnel in this shear zone and deformations of the tunnel. The potential major shear zone may be bent or bifurcated into two sub-shear zones owing to existence of a tunnel inside the shear zone. Furthermore, the occurrence of back-thrust faulting will threaten the safety of nearby structures. It was also identified that stiffness of the soil and the fault dip angles are among the major factors controlling the configuration of shear zones, the stresses within the soil, and the loads on tunnel linings. Based on the identified mechanisms, the strategies for hazard prevention are accordingly suggested and discussed.

Keywords: Fault-induced damage; Triangular shear zone; Thrust fault; Tunnel; Lining; Segment

1. Introduction

Major earthquakes often induce coseismic ground ruptures, which are the consequence of bedrock thrusting and subsequent propagation of a thrust-fault tip upward to the surface of the ground. Results from trench investigation of fault profiles indicate that a major fault zone may contain several sub-faults within the over-burden soils, which is often referred as“sediments” by geologists, and the fault may continuously slip upon

subsequent major earthquake events (Chen et al., 2004). Coseismic faulting is often accompanied by damage to engineering structures. These fault-induced damages included failures of houses, roadways, railways, bridges, viaducts, dams, tunnels, lifelines, foundations, and piles, etc. (Shearad et al., 1974; Bonilla, 1982; O'Rourke and Palmer, 1996; Prentice and Ponti, 1997; Murbach et al., 1999; Kung et al., 2001; Ulusay et al., 2001; Bray, 2001; Takada et al., 2001; Kelson et al., 2001a,b; Backblom and Munier, 2002; Kawashima, 2002b; Dong et al., 2003; Kontogianni and Stiros, 2003; Sorensen and Meyer, 2003; Cluff et al., 2003; Honegger et al., 2004; Anastasopoulos, 2005; Donmez and Pujol, 2005;

Konagai, 2005; Bray and Kelson, 2006).

⁎ Corresponding author. Tel./fax: +886 2 2364 5734. E-mail address:fsjeng@ntu.edu.tw(F.-S. Jeng).

(2)

Intensive studies of deformational behaviors of over-burden beds induced by faulting have been conducted.

(Roth et al., 1981, 1982; Cole and Lade, 1984; Lade

et al., 1984; Tani et al., 1994; Bray et al., 1994a,b; Lazarte and Bray, 1996; Bray, 2001; Erickson et al., 2001; Johnson and Johnson, 2002; Finch et al., 2003, 2004; Lee and Hamada, 2005; Lin et al., 2005, 2006a;

Hardy and Finch, 2006; Johansson and Konagai, 2006).

Beds of overburden soil deformed by propagation of thrust fault situated underneath comprise severely dis-torted zone (fault zone) within a triangular shear zone. Although one major fault slip surface can be developed, if the slip is large enough, subsidiary faults may also form within the overburden soils. Lin et al. (2006a) explored the processes of thrust faulting within over-burden soil and examined the influences of controls under a range of boundary conditions using physical sandbox models and numerical analysis. A much larger slip, up to 30% of the overburden soil thickness, was conducted in the research to observe consequences induced by such a high degree of distortion. The results revealed that Young's modulus and the dilation angle are the most influential parameters in models. A stiffer E leads to early fault propagation and the occurrence of back-thrusts, and causes more significant discrepancies in the deformation behaviors of models with different scales. A greater dilation angle of the overburden soil leads to a wider fault zone.

In-depth studies on the impact of fault movement on engineering structures based on numerical approaches

(Duncan and Lefebvre, 1973; Kennedy et al., 1977; Wang

and Yeh, 1985; Bray, 1990; Lazarte, 1996; Bray, 2001; Takada et al., 2001; Kawashima, 2002a; Dong et al., 2003; Chung et al., 2005; Anastasopoulos, 2005; Lin

et al., 2005; Karamitros et al., 2007) and experimental

analysis using scale models (Trautmann and O'Rourke, 1985; Trautmann et al., 1985; Burridge et al., 1989; Bray, 1990; Lazarte, 1996; Chung et al., 2005; Lin et al., 2005, 2006b; Johansson and Konagai, 2006; Nahas et al., 2006;

Yilmaz and Paolucci, 2007) have also been carried out.

Table 1presents a summary of results of these studies. In

these studies the main types of faults dealt with are thrust-fault and strike–slip thrust-fault, and the types of structures include tunnels, pipelines, foundations, buildings, dams, and bridges, etc. Both sandy and clayey soils have been studied. The development of major shear zone within the overburden soil is revealed and the mechanism is also discussed. Underground tunnel is the main topic of this study. The reported cases of fault induced tunnel damage include the Wrights Tunnel (San Francisco Earthquake, ML= 7.9, 1906), the Kern County Tunnel (Kern County Earthquake, ML= 7.7, 1952), the Inatori railway tunnel

(Off Izu Oshima Earthquake, ML= 7.0, 1978), the Rokko Tunnel (Kobe Earthquake, Mw= 7.2, 1995), the Outlet Tunnel of Kakkonda hydropower station (Mid-North Iwate Earthquake, Mw= 6.1, 1998), the Outlet Tunnel of Shih-Kang Dam (the Chichi Earthquake, Mw= 7.6, 1999), etc. (Bonilla, 1982; Prentice and Ponti, 1997; Kung et al., 2001; Bray, 2001; Backblom and Munier, 2002;

Konto-gianni and Stiros, 2003; Konagai, 2005). Chung et al.

(2005)andLin et al. (2006b)discussed a case in which

both the soil beds and the shield tunnel within these beds were deformed.

On the basis of these previous studies, the present research attempts to further explore the following issues: (1) The interaction between the growth of a shear zone and the tunnel within the overburden soil; (2) The stress states within soil, and load states on

tunnel linings induced by blind thrusting. An index (danger factor), which has better capability than contours of plastic strain in illustrating the interaction between soil and tunnel, was used to evaluate how far the soil was from a failure state; (3) The influence of local controls (amount of slip, horizontal distance of the tunnel to the fault tip, soil properties) on the interaction between the growth of a shear zone and the tunnel;

(4) The effect of loading induced by faulting on joints in segmental shield tunnel linings are considered in full-scale numerical analysis;

(5) The influences of local controls (location of the tunnel, fault dip angle, soil properties) on loading states;

(6) With the help of axial force–moment diagrams of segmental lining support, identify the parameters that truly relate to the safety of the tunnel lining. 2. Methodology

Full-scale experiment is undeniably the best method in studying the actual deformational behavior of over-burden soil induced by thrust faulting, and its impact on underground tunnels, however such experiment, in reality, is far too costly and difficult to execute. In this research full-scale numerical analysis was adopted. However, to ensure that the numerical model could re-veal reasonable predictions, physical sandbox model experiments, and numerical analyses were adopted. The results of physical sandbox experiments were compared with those produced by numerical analyses so that the correctness of the numerical simulation could be jus-tified. As such, the numerical model, which had been calibrated to ensure its prediction on small-scale model,

111 M.-L. Lin et al. / Engineering Geology 92 (2007) 110–132

(3)

Table 1

Summary of the existing studies for the fault movement on engineering structures Methodology Fault type Overlying stratum/external

action on structure

Type of structure Deformation Soil–structure interaction/ soil/structure behavior Numerical analysis

Duncan and Lefebvre (1973)

Strike–slip faults External force Nuclear power plant Cross-sectional No/elasto-plastic/elastic

Kennedy et al. (1977) Strike–slip faults Beam–spring Buried pipeline Logitudinal Yes/elastic /elasto-plastic

Wang and Yeh (1985) Strike–slip faults Beam–spring Buried pipeline Logitudinal Yes/elastic /elasto-plastic

Bray (1990) Normal/thrust faults

Clay Earth embankments Cross-sectional Yes/elasto-plastic/ elasto-plastic

Lazarte (1996) Strike–slip faults Clay Earth embankments Cross-sectional Yes/elasto-plastic/ elasto-plastic

Takada et al. (2001) Thrust faults Beam–spring Buried pipes Cross-sectional

and logitudinal

Yes/elastic /elasto-plastic

Kawashima (2002a) Thrust faults Beam–spring Bridge foundation Logitudinal Yes/elastic /elasto-plastic

Anastasopoulos (2005) Normal faults Soil Building – Yes/elasto-plastic/elastic

Lin et al. (2005) Thrust faults Sand Tunnel Cross-sectional Yes/elasto-plastic/elastic

Chung et al. (2005) Thrust faults Sand Shield tunnel Cross-sectional Yes/elasto-plastic/elastic

Karamitros et al. (2007) Strike–slip faults Beam–spring Buried pipeline Logitudinal Yes/elasto-plastic/elastic

Yilmaz and Paolucci (2007)

Normal/thrust faults

Undrained soil Foundation Cross-sectional Yes/elasto-plastic/elastic

Model experiment

Burridge et al. (1989) Thrust faults Sand Tunnel Logitudinal –

Trautmann and O'Rourke (1985)

Strike–slip faults Sand Dam – –

Trautmann et al. (1985)

Strike–slip faults Sand Dam – –

Bray (1990) Thrust faults Clay Earth embankments – –

Lazarte (1996) Strike–slip faults Clay Earth embankments – –

Lin et al. (2005) Thrust faults Sand Tunnel Cross-sectional –

Chung et al. (2005) Thrust faults Sand Shield tunnel Cross-sectional –

Lin et al. (2006b) Thrust faults Sand Shield tunnel Cross-sectional –

Nahas et al. (2006) Normal faults Sand Foundation – –

Johansson and Konagai (2006)

Thrust faults Sand Pile; tunnel Logitudinal –

Field studies

Shearad et al. (1974) Normal/thrust faults Soil Dam – –

Bonilla (1982) Normal/thrust faults Soil Pipeline – –

Lazarte et al. (1994) Strike–slip faults Soil Foundation – –

O'Rourke and Palmer (1996)

Strike–slip faults Soil Pipeline Logitudinal –

Prentice and Ponti (1997)

Strike–slip faults Soil Tunnel Logitudinal –

Murbach et al. (1999)

Strike–slip faults Soil Foundation, transmission tower

– –

Bray (2001) Normal/thrust faults Soil Building, Dam,

Bridge

– –

Ulusay et al. (2001) Strike–slip faults Soil Building, bridge, tunnel

– –

Kelson et al. (2001a) Thrust faults Soil Building – –

Kelson et al. (2001b) Thrust faults Soil Building – –

Kung et al. (2001) Thrust faults Soil Dam –

Takada et al. (2001) Thrust faults Soil Buried pipes Cross-sectional

and logitudinal –

Kawashima (2002b) Strike–slip/thrust faults

Soil Bridge foundation – –

(4)

was used to simulate the full-scale model. The simulation results were close to reality as much as possible.

The framework for execution of this research is illustrated inFig. 1. A small, 1:100-scale model was first built both in physical sandbox experiments and numer-ical analyses. The results of the small-scale model ob-tained from both approaches were then compared. This comparison not only justified the validity of the pre-diction but also helped validating the numerical mod-el. The small-scale numerical model was subsequently modified, including input parameters, boundary con-ditions, and others, until its results met well with the experimental results (Step 2 and step 3 inFig. 1).

The established full-scale numerical model was then adopted to simulate the deformational behaviors of the overburden soil as well as that of a hypothetical shield tunnel located within the soil bed when they were subjected to significant thrust-fault sliding triggered by an earthquake (Fig. 1; Steps 4 to 7). The studied fac-tors include the horizontal distance of the tunnel to the fault tip, fault dip angle, and soil properties, etc. (Fig. 1, Step 6). Meanwhile, a danger factor, which is defined as the reciprocal of the conventionally known “safety factor”, was introduced to indicate the stress state of the soil around the shield tunnel (Fig. 1, Step 6). As well, the axial force–moment diagrams are used to evaluate the safety of the lining.

The load states of the tunnel lining were obtained based on the full-scale numerical model and compared to the axial force moment diagrams to evaluate the safety of the lining.

2.1. Physical model— sand box experiments

The dimensions of the sandbox were 100 cm in length, 60 cm in height, and 20 cm in width (Fig. 2). The bottom

of the sandbox was designed to be movable and capable of simulating the movements of a thrust-fault or normal fault sliding by moving the base plate upward or downward. The mobile hanging wall measured 40 cm, and the fixed footwall measured 60 cm. The maximum upward move-ment could be as high as 20 cm. Accompanying the vertical movements, horizontal movements could be si-multaneously applied to simulate fault movements with dip angles ranging from 0 to 90°. A plexiglas wall was installed on one side of the sandbox to facilitate obser-vation of the deformation. The vertical slip rate of the hanging wall was set to be 4.8 × 10− 4m/s and was con-trolled by a motor at a constant sliding speed.

During the sandbox experiment, the thickness of the overburden soil was 20 cm, and the maximum uplift of the hanging wall was 6 cm. The dip angle of the simul-ated thrust fault was mainly 60°. Furthermore, with reference to the hypothetical cross-section configuration of an actual shield tunnel case, a model tunnel of 0.2 cm tunnel thickness was selected with a radius of 3.05 cm. The model tunnel was installed at a depth of 9 cm and with different horizontal distances to the fault tip line at bedrock (e.g. FW2D, a horizontal distance of two times of tunnel diameter from the tip line of the bedrock, FW denotes footwall, HW denotes hanging wall, and D is the diameter of the tunnel).

The overburden stratum was simulated by quartz sand from Vietnam. The particle sizes of the sand ranged from sieve number 40 to 140 and comprised 99% quartz with a very small proportion of feldspar and mica. The sand had a specific weight of 2.65, and maximum and minimum dry density of 1.67 g/cm3and 1.47 g/cm3, respectively. During the experiments, the relative density was con-trolled to be 55%, which represents a medium stiff state for all tests. The quartz sand had a frictional angle of 30° obtained from direct shear tests, and a secant shear

Table 1 (continued )

Methodology Fault type Overlying stratum/external action on structure

Type of structure Deformation Soil–structure interaction/ soil/structure behavior Field studies

Sorensen and Meyer (2003)

Strike–slip faults Soil Pipeline Logitudinal –

Kontogianni and Stiros (2003)

Strike–slip/thrust faults

Soil Tunnel Logitudinal –

Dong et al. (2003) Thrust faults Soil Foundation – –

Honegger et al. (2004) Strike–slip faults Soil Pipeline Logitudinal –

Donmez and Pujol (2005)

Strike–slip faults Soil Building – –

Konagai (2005) Strike–slip/normal faults

Soil Tunnel; foundation Cross-sectional –

Anastasopoulos (2005) Normal faults Soil Building – –

Bray and Kelson (2006)

Strike–slip faults Soil Pipeline; building; Earth structure

Logitudinal –

(5)

modulus G of 0.5 MPa selected from simple shear tests at a relative density of 55% (Table 2). The adopted sand under various stress levels had an almost linear failure envelope, with a cohesion intercept close to zero. The dilation angle of sand was measured as 9°. Since the dilation angle in full-scale model will vary from site to site, a parameter study for dilation angle ranging from 6° to 30° was accordingly conducted.

In selecting a material for the model tunnel, the main concern lay in proper scale-down of the stiffness such that the model tunnel would be not too stiff compared to the stiffness of the soil used in the model. Meanwhile, since the research aimed at studying the deformation behavior, the deformation of the tunnel was intentionally exaggerated such that the deformation could be easily detected and observed. Therefore, besides the relative stiffness ratio between the soil and the tunnel, the

com-pressibility factors (C⁎) and flexibility factors (F⁎) should be considered (Einstein and Schwartz, 1979). With regard to these issues of concern, a carton paper was selected after several tests for the material for the model tunnel. The properties of the carton paper are also summarized inTable 2.

The faulting process during the sandbox experiment was recorded in photographs. Photos recording deforma-tion of the strata were taken from the side of the box

(Fig. 2). The photos were then processed to correct any

distortion. To facilitate observation of the deformation, thin layers of dyed sand were spread in alternation with un-dyed sand at 2 cm intervals, enabling easy recogni-tion of deformarecogni-tion of the sand. As a result, the visible distortion of dyed sand layers served as a clear indicator of the deformation of the overburden induced by blind fault slip and the development of the influenced zone, etc.

(6)

2.2. Numerical model

A finite element method based on the software ABAQUS (Hibbitt et al., 2004), was adopted for the numerical analysis. An elasto-plastic behavior was adopted for soil material. The material model, the Mohr–Coulomb model, which is often used for representing the behavior of geo-materials, was accord-ingly adopted in the numerical analysis.

2.2.1. Small-scale numerical model

The configuration of the numerical model was set to identical dimensions as those used in experiments

(Fig. 3). The model box measured 100 cm in length,

20 cm in height and the hanging wall was 40 cm while the footwall was 60 cm across. Results from the sandbox experiments reveal that the influenced extent of the shear zone approximately is 20 cm wide and 60 cm of footwall in length should be sufficiently long without significant boundary effect. The right boundary could be moved to simulate the movement of the hanging wall

(Fig. 3). The center of the simulated tunnel is situated

at varied horizontal distances from the tip line of the bedrock (Fig. 3).

A roller condition was set for the left and the right boundaries of sand. Friction between sand and the bot-tom of sandbox was employed (a contact pair for inter-face simulation is readily available in ABAQUS). Both conditions of slip allowable and no slip were considered by means of interface between tunnel and surrounding soil. The material properties of sand and tunnel supports

shown inTable 2were used for numerical simulation of the small sandbox model tests.

A fault zone is often produced within the overburden soil, which is a typical result for physical sandbox model tests when the underlying fault slips. For the numeri-cal analysis, the material inside the fault zone, in fact, reached a plastic state. Therefore, the contour of the plastic strain served as a good indicator representing the fault zone within the overburden soil bed. The con-figuration and location of shear zones obtained by the numerical analysis and by the sandbox test were consistent.

Based on the above, the small-scale numerical model including the input parameters, boundary conditions and others was subsequently modified until its results met well with the experimental results.

2.2.2. Full-scale numerical model

Based on the calibrated small-scale model, which compared well to the model experiments, a full-scale model was then established. With a cross-section and configuration corresponding to an actual shield tunnel, the hypothetical full-scale tunnel would be located proximal to the Taipei Fault in the Taipei Metro System

(Chung et al., 2005). A stretch of at least 1000 m of this

designed lane of the underground tunnel would run close to the bedrock fault line and sub-parallel to the fault line with varied distances. Thus it is reasonable to consider the deformation induced by thrust faulting could be approximately in a two-dimensional plane strain con-dition. The deformation of the tunnel lining would be

Fig. 2. Schematic setup of the experimental study in a model scale.

(7)

mainly cross-sectional deformation. The dimensions (L, H, T and D) of the full-scale numerical model were enlarged to 120 m, 20 m, 11 m and 6.1 m, respectively

(Fig. 3). The hanging wall length was 40 m while the

footwall was 80 m. The thickness of the tunnel lining was 0.25 m. Parameters used in the full-scale model are obtained from site investigation (Table 2). The center of the simulated tunnel is located within the shear zone of the fault at FW7D, FW5D, FW3D, FW1D, HW1D, and HW3D (Fig. 3).

The segmental linings were modeled through elastic beam elements in ABAQUS. Before numerical simula-tion of a full-scale hypothetic tunnel model, ABAQUS had first validated as a suitable FEM model tool for tunnel lining. An elastically lined cylindrical tunnel under plane strain conditions in a linearly elastic ground mass was analyzed through ABAQUS. Axial loads, moments, and shear forces within the tunnel lining were obtained. These results were then compared with the analytical solutions derived by Burns and Richard

(1964),Dar and Bates (1974)andEinstein and Schwartz

(1979). Both full-slip and no-slip conditions at the

ground-support interface were considered. The results validated that the segmental linings of tunnel rings could be modeled very well through FEM model under ex-ternal loading conditions.

Subsequently, a numerical simulation of a full-scale tunnel model was built. The in-situ geostatic stresses were modeled firstly, the coefficient for lateral soil pres-sure was taken to be K0= 1−sinϕ. When the equilibrium of in-situ stresses was reached, the soil in the tunnel was then removed and segmental tunnel linings were installed. The segmental tunnel lining are under the loading from the self weight of the segments and the soil formation. This loading condition (the external load-ing condition) also implied that the tunnel openload-ing had been excavated and supported before the loading corre-sponding to the free-field stresses was applied. Only the external loading condition was performed in this study without considering actual excavation unloading condi-tions that occurred during tunneling (Einstein and

Schwartz, 1979). The assumption of external loading

instead of excavation unloading may lead to support forces that are 50%–100% overestimated (Einstein and

Schwartz, 1979).

The hypothetical shield tunnel comprised six circular segments; each of them had a width of 1.0 m, an inner radius of 2.80 m, an outer-radius of 3.05 m and a thickness of 0.25 m (Fig. 4). The segments were coded as Types A, B and K in accordance with the arc-length of the segments (Fig. 4b). Joints between rings were circum-ferential joints. Joints between segments in longitudinal direction were radial joints. A complete circular ring was formed by one Type K, two Type B and three Type A segments. Meanwhile, the K-segment was staggered from ring to ring to avoid a continuous distribution of the joints within longitudinal direction (Fig. 4b). The moment transferred at the joints would be smaller than the moment of the adjacent segment and the numerical model should properly reflect this phenomenon. Accord-ing to the assembly of concrete linAccord-ing in engineerAccord-ing practice, segments of beam elements were selected to

Table 2

Summary of the material properties adopted in this research Parameter Experimental

simulation

Full-scale simulation

Unit

Model tunnel (carton paper)

Es 400 31,800 MPa

νs 0.3 0.2

Model soil (sand) γ (dry unit weight of soil) 15.7 20.0 kN/m3 E 1.29 19 MPa ν 0.3 0.3 c 5 5 kPa ϕ (frictional angle) 30 30 ° ψ (dilation angle) 6 6, 30 ° ko= 1−sinϕ (stress ratio

at rest) 0.50 0.50 Frictional property of interfacesμ=tan (2/3ϕ) μ (soil–rock) 0.36 0.36 μ′ (soil–tunnel) 0.36 0.36 Remark:

The relative stiffness of the ground mass to the tunnel support can be evaluated by two dimensionless parameters, the compressibility ratio, C⁎ and the flexibility ratio, F⁎ (Einstein and Schwartz, 1979). The compressibility ratio, C⁎, is defined as C⁎ = ER(1−ν2s)/EsAs(1−ν2);

The flexibility ratio, F⁎, is defined as F⁎ = ER3₍₁_−ν s 2_)/E

sIs(1−ν2), in

which E, ν, and Es,νs = the elastic constants for the ground and

support; As= the average cross-sectional area of the support per unit

length of tunnel = t × 1; R = the tunnel radius; t = average support thickness; and Is= the moment of inertia of the tunnel support per unit

length of tunnel. The compressibility ratio is a measure of the relative stiffness of the ground support system under an antisymmetric loading condition, i.e. it reflects the flexural stiffness of the system. The flexibility ratio is a measure of the relative stiffness of the ground support system under a uniform or symmetric loading condition, i.e. it reflects the circumferential stiffness of the system. Increasing the values of C⁎ and F⁎ decreases the support thrust and moment and increases the net inward displacement of the tunnel. Since the research aims at studying the deformation behavior, the deformation of the tunnel was intentionally exaggerated such that the deformation could be easily detected and observed. Roughly estimating from Fig. 6 ofEinstein and Schwartz (1979), the dimensionless support displacement of model is about twice of full-scale tunnel.

Model tunnel (Paper): E/Es= 0.003; t/R = 0.068; C⁎ = 0.054;

F⁎ = 141.9.

(8)

comprise a complete ring and one way to deal with the existence of joints was to consider the tunnel lining as a continuous ring with a discounted rigidity of the tunnel lining (Muir Wood, 1975; Lee et al., 2001b; ITA, 2000). In this study, the discounted rigidity is modeled by a reduction by half of the cross-sectional area of the beam elements located at the twelve radial joints of every two rings (Fig. 4c).

When the equilibrium between in-situ stresses and the excavation of tunnel was reached, the up-thrusting

move-ment of the bedrock by the fault was simulated through lifting 2.5 m in accordance with the fault dip angle. The corresponding axial loads and moments within segmen-tal linings were obtained. The relationship between the design axial load capacity and the design flexural capacity of the segments is described as P–M curves. There-fore, the safety of the segmental lining for combined axial load and flexure moment were examined by confirming whether the load points of the lining were located inside the P–M curves, that is, at the side of origin.

Fig. 4. (a) Typical setup of the lining inside a shield tunnel. A complete circular ring was formed by one Type K, two Type B and three Type A segments. The K-segment was staggered from ring to ring to avoid a continuous distribution of the joints within a longitudinal direction. (b) Cross-section of Type A segment with six joints and P–P′ section without joint. (c) Cross-section Type A segment with twelve joints and Q–Q′ section with joint rigidity reduction.

Fig. 3. Illustration of the configuration of the tunnel, thrust fault, and boundary conditions adopted for the numerical study. FW denotes footwall, HW denotes hanging wall, and D is the diameter of the tunnel, e.g. FW2D, a horizontal distance of two times of tunnel diameter from the tip line of the bedrock. 117 M.-L. Lin et al. / Engineering Geology 92 (2007) 110–132

(9)

2.3. Danger factor

The typical output of analyses based on a finite element method includes displacements, strains, and stresses. To indicate how far the material was from a failure state, an additional measure, a danger factor, was also adopted in this research. The danger factor is defined as (Jeng and Huang, 1998):

Df ¼

fðrijÞ

Sðc; /; roctÞ: ð1Þ

Where S(c,ϕ,σoct) is the shear strength of the material and f(σij) is the applied shear stress.

The Mohr–Coulomb strength criterion, which is conventionally used in geotechnical engineering, was also adopted in this research. Based on the Mohr– Coulomb criterion, the danger factor can be expressed in terms of c,ϕ as: Df ¼ ffiffiffiffiffiffiffi 3J2 p Rmcðh; /Þ cþ I1 tan/ ð2Þ Rmcðh; /Þ ¼ 1 ffiffiffi 3 p cos/sin h þ k 3 þ1 3cos h þ k 3 tan/ ð3Þ h ¼1 3cos 1 J_{ffiffiffiffiffiffiffi}3 3J2 p 3 ð4Þ Where I1= (σ11+σ22+σ33)/3 is the first stress invariant; J2 is the second deviatoric stress invariant; J3is the third deviatoric stress invariant.

The danger factor is the reciprocal of the conven-tional factor of safety. This factor is similar to the stress level (SL,Bray et al., 1994b). When Dfis less than one, the material has not reached a failure state, and on the other hand, when Dfequals to or is greater than one, it indicates that the material has failed.

3. Deformation of overburden soil and tunnel — small-scale model

3.1. Sandbox experiment

When the underlying bedrock thrusts upward during faulting activity, the overburden bed on the hanging wall is up-lifted, and a severely distorted zone (fault rupture surface) inside a triangular shear zone is formed be-tween the footwall and the hanging wall (Fig. 5a). This severely distorted zone is often referred to as a “fault

zone” or a “failure zone”, and is considered to be due to the migration of the thrust fault within the bedrock to the ground surface. A detailed sketch of the distortion is also shown in Fig. 5. If the slip is large enough, sub-sidiary faults may also form within the overburden soils. As a fault moves, the fault zone in the overlying over-burden bed extends to area W/H on the ground surface (W denotes the horizontal distance between where the fault moves and the point where the fault emerges on the ground; H is the thickness of the overlying overburden

bed,Fig. 5). In our experiment, we used 60° as the fault

dip angle and two fault zones were developed. The order of fault zones development was from the hanging wall towards the footwall, and affected area W/H on the ground surface was approximately 0.99 (Fig. 5a). The detailed information for the deformation of overburden soil induced by thrust-fault slip was described in Lin et al. (2006a).

Results of the (FW2D) experiment in which the fault dip angle was also 60° (Fig. 6). Three fault zones developed. The order of development of these fault zones is as follows: the first fault zone developed from the tip of the fault to the ground surface, then the second fault zone began to develop downward to-wards the footwall, however, this was hampered and bent by the underground tunnel, and the fault tip of this strand of fault did not extend to the ground surface. The third fault zone developed within the area between the first and the second fault zones. The affected area on the ground surface W/H was ap-proximately 0.75 (Fig. 5b). There was no perceptible deformation or shifting of the tunnel due to ground uplifting. When compared with a site where there was no underground tunnel, it was clearly observed that the affected area on the ground surface W/H was 24% less, but that the soil inside the triangle zone was distorted more severely (Fig. 5a, b).

The results from experiment FW1D where the tun-nel was much closer to the fault zone are shown in

Fig. 5c. As the ground uplift increased during faulting,

fault zones developed in an upward direction. The first fault zone was hampered and bent by the underground tunnel, then it passed directly underneath the tunnel. When development of the first fault zone reached the surface of the ground, the second fault zone started to develop upward toward the hanging wall and then passed above the tunnel. Ground surface measurement indicated that the affected area on the ground surface W/H was approximately 0.98 (Fig. 5c). The tunnel was uplifted, shifted, rotated, and severely distorted. Compared with the case without underground tun-nel, the affected area on the ground surface W/H was

(10)

similar. However, two distinct scarps were present on the ground.

The results of tunnel deformation observation in sequence are presented in Fig. 6. The results showed that when the tunnel was located at FW2D, there was no perceptible shifting or deformation of tunnel af-ter ground uplifting. Where the tunnel was located at FW1D, the tunnel was distinctly shifted with a 3 cm vertical displacement (see also Fig. 5c, the initial position of the tunnel is in red, the position after uplift is in yellow). The triangular shear zone is enlarged in case that the tunnel is located inside the triangular shear zone.

3.2. Comparison between sandbox experiment and numerical analysis

The results from numerical analysis were then compared with the results from the sandbox experiments

(Fig. 7). Fig. 7a compared the zones of plastic shear

strain concentration with the fault zones from the sand-box experiments without underground tunnel. The lo-cations of the plastic shear strain concentration zones correspond to the locations of the fault zones in sandbox experiments with similar ground surface affected areas. When the tunnel was located at FW2D, the develop-ment of concentrated plastic strain zones was limited by

Fig. 5. The deformation and the development of fault zones of the overlying overburden soil, obtained from sandbox experiments. The distance (denoted as W ) is accordingly defined as the horizontal distance between the surface trace and the bedrock fault tip at the start of deformation, as indicated in the insert. The triangular shear zone above the fault tip is also indicated in the insert. The number neighbors on fault rupture strands denoting the development of the faults in sequence. D is the diameter of the tunnel.

(11)

the underground tunnel, and the concentrated plastic strain zones occurred in the footwall at the area between the fault and the tunnel (Fig. 7b). The affected ground surface area was similar to those resulting from sandbox experiments. The distortion of the mesh was severe, indicating that distortion of the soil within the triangle zone was more severe than that of the soil without the tunnel. There was no conspicuous deformation or shift-ing of the tunnel due to ground upliftshift-ing.

In the case where the tunnel was located at FW1D, the first concentrated plastic strain zone developed in an upward direction while the ground was uplift. When the first concentrated plastic strain zone encountered the tunnel, it was hampered and bent by the underground tunnel, then it passed directly underneath the tunnel. The second concentrated plastic strain zone developed up-ward toup-ward the hanging wall; as development of the first concentrated plastic strain zone reached the ground surface, and it passed through the upper-right side of the

tunnel (Fig. 7c). Therefore, there exhibit two fault scarps on the ground. During ground uplift, the tunnel was distinctly shifted with a 3 cm vertical shift. In addition, the tunnel was deformed and rotated due to squeezing during uplifting.

Comparison of the deformations of the tunnel ob-tained both from sandbox experiments and numerical analyses of the FW1D case revealed that both of the deformed tunnels had similar elliptical shapes (Fig. 8, r0 and r are the radius of the tunnel before and after thrusting, respectively). Actually, the deformations of the tunnel in numerical analyses were smaller than those of the sandbox experiments. It might be a result of the elastic assumption of the tunnel lining adopted in numerical analyses. For easy comparison of the cir-cumferential deformation, the elastic modulus of the carton paper had been reduced to one-tenth of the orig-inal value in order to amplify the deformation of the numerical analysis. The apex of the tunnel crown was

Fig. 6. Fault development subjected to varied uplifting in sequence. The right part is a tunnel located 1D from the fault tip; the left part is a tunnel located 2D from the fault tip. D is the diameter of the tunnel. Dotted lines indicate the fault slip surfaces, and white dotted lines indicate the extent of triangular shear zones involved in all stages.

(12)

taken to be 0°, and following clockwise rotations. Com-pressions occurred at 60°–150° and 240°–330°, where the tunnel wall converged. In these compressive zones, the soil moved toward the tunnel lining, the earth pressure acting on the tunnel lining increased and ap-proached passive earth pressure state. Zones located within 240°–330° showing the most distinct compres-sion. This distinct compression zone is quite obvious that the interaction of the soil and tunnel leads to a severer distortion zone in the sandbox model. The research of

Duncan and Lefebvre (1973) with regard to the earth

pressures on structures due to fault movement discussed a similar phenomenon. An idealized picture of surround-ing earth pressures on tunnel induced by fault movement exhibits four principal earth pressure zones, two passive zones and two active zones—each oriented at 45° to the fault movement direction. Thus the structure is subjected to high earth pressure in one direction (the passive direction) and a simultaneous reduction in earth pressure in the orthogonal (active) direction.

The detail of deformation patterns around the tunnel both from sandbox experiments and numerical analyses are further compared (Fig. 9). The location of the dis-placed tunnel and the deformed configuration of the

tunnel obtained from both approaches were almost iden-tical. Meanwhile, the bifurcated shear zones were also revealed by both approaches.Fig. 9shows how the fault bent near the tunnel, with two separate strands of the fault passing on opposite sides of the tunnel. Judging from the size, shape, and distortion of the deformed mesh, two highly compressively deformed areas could be seen in horizontal direction on opposite sides of the tunnel. In these zones, the soil moved toward the tunnel. On the other hand, two highly extensively deformed areas could be seen in a vertical direction on opposite sides of the tunnel. In these zones, the soil moved outward away from the tunnel. The tunnel lining would bear extra bending moment loading under this approximately antisymme-trical loading induced by faulting.

Remarkably, if the material around the tunnel wall was separated allowably from the wall, the numerical analysis indicated that cavities in the invert and the crown could be yielded (Fig. 9a). This phenomenon highlights that the occurrences of cavities should also be of concern in the practical design.

In summary, when the tunnel was situated inside the triangular shear zone (deducing from free-field conditions, i.e. without underground tunnels) the

Fig. 7. The deformation and the development of shear zones of the overburden soil, obtained from numerical analyses (the right parts) and sandbox experiments (the left parts). The light color zone is the plastic zone. D is the diameter of the tunnel.

(13)

overburden soil might develop greater fault zones or even bifurcate during propagation of the bedrock thrust fault, rendering greater deformation and earth pressure on the tunnel. When the tunnel was situated outside the triangular shear zone under free-field, it might be safe.

The study by Lin et al. (2006a) on overburden de-formation behavior due to fault movement indicated that major parameters affecting the fault zone included fault dip angle, Young's module, and angle of dilation.

Fur-thermore, increasing Young's modulus of the geologic formation might possibly lead to development of back-thrust. In this regard, in conducting whole-scale nu-merical analysis in this study, emphasis was placed on several soil parameters. The main purpose lay in unravelling the distributions of danger factors within overburden soils and the distributions of loading states on P–M diagrams of the tunnel linings through varied properties of soil materials.

4. Deformation of overburden strata and tunnel — full-scale numerical model

4.1. Deformation process and failure modes

Fig. 10 illustrates the predicted deformation of an

FW1D case in sequence when the basement is thrust upward in an inclined angle of 60°. The process of deformation is shown from Fig. 10a to d. As in the small-scale model experiments, a bifurcated shear zone occurred, extended to the ground surface, and was fol-lowed by an increase in width (Fig. 10, left parts). The right part ofFig. 10 shows the distributions of danger factors. It indicates that a much wider zone, around the shear zone, and near the ground surface, was close to a failure state with Df exceeding 0.7. Detailed examina-tion of the stress paths of the soil revealed that the soil around the ground surface failed due to tensile stress,

Fig. 8. Comparison of the tunnel deformations obtained by the experimental study and the numerical analyses (case FW1D). D is the diameter of the tunnel. The apex of the tunnel crown was taken to be 0°, and following clockwise rotations as indicated in the inset. r0and r

are the radius of tunnel before and after fault thrusting, respectively.

(14)

and the failure of soil within the shear zone was due to shearing. This result coincides with the observation that tensile cracks often appear on the ground surface, especially near the thrust-fault trace, after coseismic deformation (Lee et al., 2001a, 2004; Chen et al., 2004). 4.2. Effect of tunnel location relative to thrust faulting The location of a tunnel will affect the displacement and the deformation of the ground as well as the de-velopment of a shear zone within the overburden soil stratum.Fig. 11illustrates the influence of tunnel loca-tion on the above-menloca-tioned behavior. When the tunnel is located in the range of the footwall and not very close to the potential shear zone (Fig. 11a, b, and c), the displacement and deformation of the tunnel is relatively insignificant. Meanwhile, the development of the shear zone is not or is only slightly affected by the existence and the location of the tunnel.

When the tunnel is located in the range of the hanging wall and not very close to the potential shear zone (Fig. 11e and f), the tunnel is also insignificantly deformed and the development of the shear zone is only slightly

affected. However, the tunnel is substantially displaced according to the slide direction of the underlying bed-rock. For the two-dimensional analysis (Fig. 11e and f), the stress applied to the lining might not cause it to fail; however, in a three-dimensional sense, it can be foreseen that this large displacement may cause longitudinal de-formation and cause the tunnel to move and to fail along the longitudinal direction (Kennedy et al., 1977; Wang

and Yeh, 1985).

When the tunnel is located near the boundaries between the hanging wall and the footwall and thus inside the shear zone (Fig. 11d), the one potential major fault zone interacts with the existence of the tunnel and causes development of two fault zones, as described in

Figs. 5, 6 and 7.

Remarkably, for the case shown in Fig. 11c, the deformation and displacement of the tunnel is insignif-icantly visible, but the soil around the tunnel is close to failure state (Fig. 11c, right part), and the stress applied to the lining may cause it to fail. Therefore, for such cases, the induced axial force and moment in the lining should be compared to the capacity of the lining to check the soundness of the lining.

Fig. 10. Development of shear zone upon consecutive bedrock slipping (case FW1D). D is the diameter of the tunnel. The left parts are distributions of plastic strain; the right parts are distributions of danger factors.

(15)

4.3. Effect of soil stiffness

When Young's modulus of soil increased from 19 MPa (representing the typical medium stiff soil; the cases shown inFig. 11) to 190 MPa (representing the typical stiff soil), and the resulted deformation is shown inFig. 12. The increase of soil stiffness, when comparing Fig. 12 with Fig. 11, does not seem to affect the displacement and the deformation of the tunnel. For a stiffer soil, the development of the fault zone tends to be wider and toward the footwall, as compared in Figs. 11 and 12. Furthermore, as indi-cated by the right figures (the distributions of danger factors), the zone in which the soil is close to failure

(e.g., Dfexceeding 0.7) is significantly enlarged due to the increase of soil stiffness. Importantly, the soil near the tunnel is closer to a failure state, as depicted inFig. 12 and compared to Fig. 11. As such, the loads and the soundness of the linings require further examination. 4.4. Development of back-thrust in stiff soil

It has been found that an increase in soil stiffness enables the development of back-thrust faulting (Lin

et al., 2006a). Although the left figures inFig. 12do not

show the development of back-thrust faulting, the right figures do indicate the halfway development of back-thrust, when the soil is quite close to a failure state.

Fig. 11. Configurations of shear zones corresponding to various tunnel locations, medium stiff soil. The left parts are distributions of plastic strain; the right parts are distributions of danger factors. D is the diameter of the tunnel.

(16)

The location of the tunnel seems to affect the de-velopment of back-thrust. When the tunnel is located within the shear zone (Fig. 12c), major deformation occurs in the shear zone, which seems to ease the oc-currence of back-thrust, when comparingFig. 12c with

Fig. 12a and b. At the other extreme, if the tunnel

is located in the potential location of the back-thrust

(Fig. 12e), the development of the back-thrust

be-comes more imminent, when compared to other condi-tions (Fig. 12).

4.5. Effect of dilation angle

Although the strength parameter or the deformation modulus of sand could be measured, another parameter,

the dilation angle of plastic flow ruleψ, was difficult to constrain by simple experiments and thus required numerical analysis to evaluate. With the other properties of the sand being the same, the dilation angleψ for the numerical analysis was accordingly determined as 6°, by adjusting the numerical results to have the same W with the free-field experimental results without a tunnel

(Lin et al., 2006a). Since the dilation angle in a full-scale

model will vary from site to site depending on soil type and in-situ state, a parametric study for dilation angle ranging from 30° to 6° was accordingly conducted. The dilation angle of the soil was decreased from 30° to 6°. When comparingFig. 13withFig. 11, a smallerψ leads to a smaller W, a narrower fault zone, a smaller degree of plastic deformation and a lower surface slope of fault

Fig. 12. Configurations of shear zones corresponding to various tunnel locations, stiff soil. The left parts are distributions of plastic strain; the right parts are distributions of danger factors. D is the diameter of the tunnel.

(17)

scarp. An associated flow rule, in which a dilation angle equals a friction angle, was conservatively selected for the base case, since it would lead to a larger shear zone and a higher load on the tunnel lining.

5. Soundness of the lining — full-scale numerical model

Based on the typical configuration of lining used in engineering practice, the corresponding P–M curves (axial load capacity versus moment capacity) for linings with or without joints were calculated and shown in

Fig. 14. Linings, which are assembled by segments and

hence have joints, tend to have less resistance to moment

and axial force due to the existence of joints. The red color curves represented the designed P–M diagram of beam elements with rigidity reduction. The blue color curves represented the designed P–M diagram of beam elements without rigidity reduction. The axial load and moment at various points located within the linings could be obtained from numerical analysis and were also plotted in the figure (Fig. 14) containing P–M curves so that the load state of every beam constituting the whole ring could be compared to the capacity. Hence, it could be identified whether and where the lining would fail or not. When the stress was located to the right of the P–M curve, the load exceeded the capacity and hence the lining failed (Fig. 14). In reality, the lining material

Fig. 13. Configurations of shear zones corresponding to various tunnel locations. The dilation angleψ=6°. The left parts are distributions of plastic strain; the right parts are distributions of danger factors. D is the diameter of the tunnel.

(18)

would yield plastically after reaching the limit state of P–M curve. Therefore, the results of the analysis serve as an indication for the potentiality of failure instead of the actual configuration of failure (Fig. 14).

For a soil with medium stiffness (E = 19 MPa), the lining may fail for cases FW1D, FW3D, and FW5D

(Fig. 14a). Also, for case HW1D, the lining with joints

may fail. In general, it can be seen that greater load will be induced: (1) when the tunnel is closer to the fault tip; and (2) when the tunnel is located inside the triangular shear zone and at downward near hanging wall side rather than at upward hanging wall side.

In the case of HW3D, the tunnel was almost un-affected by thrust faulting, judging from the distributions of danger factors (right part, Fig. 14f). Therefore, the load states of case HW3D can serve as indicators of the initial load states on segmental lining before thrusting. It can be seen that the maximum moment (∼1800 kN m) induced by thrust faulting in case FW1D is about nine times larger than the original value (∼200 kN m) and the maximum axial load (∼1800 kN) induced by thrust faulting in case FW1D is only about two times larger than the original value (∼900 kN). This result conforms that the loading imposed on a lining induced by the

Fig. 14. The P–M curves of the lining and the load states of the lining. A complete circular ring was formed by seventy-four elements. The curves in red color represent load capacity of beam elements with rigidity reduction. The curves in blue color represented load capacity of beam elements without rigidity reduction. Square boxes denoted with cases name plus dotted lines indicate the maximum moments for varied cases, respectively. 127 M.-L. Lin et al. / Engineering Geology 92 (2007) 110–132

(19)

deformed soil around the tunnel is roughly an antisym-metric loading condition (Fig. 8).

For the purpose of understanding the influence of factors, including Young's modulus E, Poison ratio ν, cohesive strength c, frictional angle of soilϕ, fault dip angle α, …, etc., a systematic parametric study was conducted using the inputs summarized inTable 3. 5.1. Effect of soil stiffness

The cases where the soil has medium or higher stiff-ness are compared inFig. 14a and b. Apparently, much higher load was imposed on the lining by the stiffer soil. Overall, for a given amount of thrusting, an increase in

soil stiffness is indeed undesirable from a safety point of view since it not only induces large failure in the soil (including additional back-thrusting) but also in the lining.

5.2. Effect of frictional angle

The cases of soil with lower or higher frictional angles (30° and 40°) are compared inFig. 14a and c. Soil with a greater frictional angle inherently has greater shear strength and hence a“thinner” shear zone will form when this soil is subjected to thrusting. However, comparing

Fig. 14c to a, it indicated that the greater frictional angle

seemed to result in a slightly greater load in the lining for

(20)

tunnels located in the footwall and near the fault (cases FW1D and FW3D) as well as much greater moments for tunnels located in the hanging wall and very close to the fault tip, especially for case HW1D. A possible in-terpretation of such phenomena is that the smaller shear zone represents a larger degree of“strain accommoda-tion” in and around the shear zone, and leads to a greater load on the lining in the near-fault region.

5.3. Effect of fault dip angle

The cases of faults with higher or lower dip angles (60° and 45°) on the loading state are compared in

Fig. 14a and d. The fault dip angle was converted into

the dip angle of the induced shear zone as well, so that the relative distance of the tunnel to the shear zone

would be altered in the meantime. ComparingFig. 14d to a, a flatter dip angle (45° compared to 60°) resulted in a closer distance of the tunnel to the shear zone located within the footwall so that the loads for cases FW1D and FW3D might increase somewhat.

Remarkably, the load state for tunnels located on the hanging wall far away from the fault (cases HW3D and FW7D) also increased. A detailed check found that a flatter fault dip angle situation would lead to develop-ment of back-thrust, so that the loads for tunnels located on the hanging wall would also be influenced. In case of faults with a smaller fault dip angle, tunnels should be relocated farther away from the fault tip line.

5.4. Effect of dilation angle

The cases of soil with lower or higher dilation angles (6° and 30°) on the loading state are compared in

Fig. 14e and a. The soil with a smaller dilation angle (of

6° compared to 30°) resulted in a farther distance of the tunnel to the shear zone in the footwall so that the load states for cases FW1D and FW5D may decrease somewhat.

The influences of other factors, such as Poison ratioν and cohesive strength c, have also been studied and were found to be insignificant.

6. Conclusion and discussion

For underground tunnels sited in various locations, the deformations of overburden soil and tunnel lining by thrust faulting were studied. It was found that the

Fig. 14 (continued ).

Table 3

Summary of the material properties for full-scale numerical analysis Purpose of analyses Control parameter

α (°) E (MPa) υ c (kPa) ϕ (°) ψ (°) Influence of dip angle 45, 60 19 0.4 5 30 30 Influence of Young's modulus 60 19, 190 0.4 5 30 30 Influence of Poisson ratio 60 19 0.3, 0.4 5 30 30 Influence of cohesion 60 19 0.4 5, 50 30 30 Influence of friction angle 60 19 0.4 5 30, 40 30 Influence of dilation angle 60 19 0.4 5 30 6, 30 129 M.-L. Lin et al. / Engineering Geology 92 (2007) 110–132

(21)

development of a shear zone in the soil is influenced by the existence and the location of an underground tunnel. A major or bifurcated fault zone may develop and extend along the slide direction of the thrust fault, and will induce the failure of the lining, especially for tunnels inside the shear zone. Furthermore, the potential oc-currence of a back-thrust shear zone will also signifi-cantly affect the stress in the soil and the load in the lining. The properties of the soil, especially the stiffness, affect the development of shear zones, back-thrusts, and the safety of the lining as well.

Last but not least, the use of a danger factor, which has better capability than contours of plastic strain to illus-trate the interaction between soil and tunnel, is helpful in evaluating how far the soil is away from a failure state. Safety of the segmental linings for combined axial load and flexure moment are examined by confirming that the points of loads are located inside the P–M curves. The influence of local controls (horizontal distance of the tunnel to the fault tip, fault dip, soil properties) on the safety of the tunnel thus can be identified through full-scale numerical analyses.

6.1. Strategy for hazard prevention

Based on the deformation characteristics found in this study, possible strategies for hazard prevention relating to the deformation induced by thrust faulting are as follows:

(1) Provided that the potential shear zone is recog-nizable and the selection of the tunnel location is admissible, the tunnel should be located within the overburden in the footwall rather than in the hanging wall, thus avoiding the uplifting induced longitudinal failure and as much farther from the triangular shear zone as possible. If the tunnel is located in the hanging wall or very close to the shear zone or the back-thrust shear zone, failure is deemed as inevitable;

(2) If the tunnel must be located close to the shear zones, the reduction of soil stiffness around the shear zone can apparently ease the magnitude of lining load and hence increase the safety; and (3) An artificial cavity between the tunnel and the shear

zone can accommodate the deformation induced by fault thrusting, insulate against the passage of formation from the shear zone to the tunnel, de-crease the amount of load induced, and hence prevent the tunnel from failure. This idea is so far possible rather than feasible or practical; further assessments and cautious design are necessary.

Acknowledgements

The research is mainly supported by Moh and Asso-ciates, Inc. and partly supported by the National Science Council of Taiwan, Grant no. NSC-94-2211-E-002-033, and NSC-95-2211-E-002-258. The advice, comments, and help provided by the editor and two anonymous reviewers have significantly strengthened the scientific soundness of this paper. Also, the authors thank Mr. Christopher Fong for his help to improve the paper. Their kind efforts are gratefully acknowledged.

References

Anastasopoulos, I., 2005. Behaviour of foundations over surface fault rupture: analysis of case histories from the Izmit 1999 earthquake. Proceedings of the 16th International Conference on Soil Mechanics and Geotechnical, Osaka, Japan, pp. 2623–2626. Backblom, G., Munier, R., 2002. Effects of earthquakes on the deep

repository for spent fuel in Sweden based on case studies and preliminary model results. SKB Technical Report TR-02-24. Swedish Nuclear Fuel and Waste Management Co, Stockholm Sweden. 110 pp.

Bonilla, M.G., 1982. Evaluation of potential surface faulting and other tectonic deformation. U.S. Geological Survey, Open-File Report 82-732, p. 56.

Bray, J.D., 1990. The effects of tectonic movements on stresses and deformations in Earth embankments. Dissertation doctor of philosophy, University of California, Berkeley.

Bray, J.D., 2001. Developing mitigation measures for the hazards associated with earthquake surface fault rupture. Proceedings of Workshop on Seismic Fault-Induced Failures, Tokyo, pp. 55–80. Bray, J.D., Kelson, K.I., 2006. Observations of surface fault rupture from the 1906 earthquake in the context of current practice. Earthquake Spectra 22 (22), S69–S89.

Bray, J.D., Seed, R.B., Cluff, L.S., Seed, H.B., 1994a. Earthquake fault rupture propagation through soil. Journal of Geotechnical Engineer-ing 120, 543–561.

Bray, J.D., Seed, R.B., Seed, H.B., 1994b. Analysis of earthquake fault ruptures propagation through cohesive soil. Journal of Geotech-nical Engineering 120, 562–580.

Burns, J.Q., Richard, R.M., 1964. Attenuation of stresses for buried cylinders. Proceedings of Symposium on Soil–Structure Interac-tion, Tucson, pp. 378–392.

Burridge, P.B., Scott, R.F., Hall, J.F., 1989. Centrifuge study of faulting effects on tunnel. Journal of Geotechnical Engineering, ASCE 115 (7), 949–967.

Chen, W.S., Lee, K.J., Lee, L.S., Ponti, Daniel J., Prentice, C., Chen, Y.G., Chang, H.C., Lee, Y.H., 2004. Slip rate and recurrence interval of the Chelungpu Fault during the past 1900 years. Quaternary International 167–176.

Chung, C.F., Lin, M.L., Jeng, F.S., Tsai, L.S., Chin, C.T., Chan, S.J., 2005. A case study on the response of shield tunnel near a thrust fault offset. Proceedings of Geotechnical Earthquake Engineering Satellite Conference, Osaka, Japan.

Cluff, L.S., Page, R.A., Slemmons, D.B., Crouse, C.B., 2003. Seismic hazard exposure for the trans-Alaska pipeline. Proceedings of the 6th U.S. Conference and Workshop on Lifeline Earthquake Engineering. Monograph, vol. 25. American Society of Civil

(22)

Engineers, Technical Council on Lifeline Earthquake Engineering, pp. 535–546.

Cole, D.A., Lade, P.V., 1984. Influence zones in alluvium over dip-slip faults. Journal of Geotechnical Engineering 110, 599–615. Dar, S.M., Bates, R.C., 1974. Stresses analysis of hollow cylindrical

inclusions. Journal of the Geotechnical Engineering Division, ASCE 100 (GT2), 123–138.

Dong, J.J., Wang, C.D., Lee, C.T., Liao, J.J., Pan, Y.W., 2003. The influence of surface ruptures on building damage in 1999 Chi-Chi earthquake: a case study in Fengyuan city. Engineering Geology 71, 157–179.

Donmez, C., Pujol, S., 2005. Spatial distribution of damage caused by the 1999 earthquakes in Turkey. Earthquake Spectra 21 (1), 53–69. Duncan, J.M., Lefebvre, G., 1973. Earth pressures on structures due to fault movement. Journal of the Soil Mechanics and Foundations Division, ASCE 99 (SM12), 1153–1163.

Einstein, H.H., Schwartz, C.W., 1979. Simplified analysis for tunnel supports. Journal of the Geotechnical Engineering Division, ASCE GT4, 499–518.

Erickson, S.G., Strayer, L.M., Suppe, J., 2001. Initiation and reactivation of faults during movement over a thrust-fault ramp numerical mechanical models. Journal of Structural Geology 23, 11–23. Finch, E., Hardy, S., Gawthorpe, R.L., 2003. Discrete element modeling

of contractional fault-propagation folding above rigid basement fault blocks. Journal of Structural Geology 25, 515–528.

Finch, E., Hardy, S., Gawthorpe, R.L., 2004. Discrete element modeling of extensional fault-propagation folding above rigid basement fault blocks. Basin Research 16, 489–506.

Hardy, S., Finch, E., 2006. Discrete element modelling of the influence of cover strength on basement-involved fault-propagation folding. Tectonophysics 415, 225–238.

Hibbitt, Karlsson, Sorensen, Inc, 2004. ABAQUS/CAE User's Manual, Version 6.4-3.

Honegger, D.G., Nyman, D.J., Johnson, E.R., Cluff, L.S., Sorensen, S.P., 2004. Trans-Alaska pipeline system performance in the 2002 Denali fault, Alaska, earthquake. Earthquake Spectra 20 (3), 707–738.

I. T. A. Working Group on general approaches to the design of tunnels, 2000. Guidelines for the design of the shield tunnel lining. Tunnelling and Underground Space Technology 15, 303–331. Jeng, F.S., Huang, K.P., 1998. Safety measures for finite element analysis

applied to geotechnical problem. Journal of the Chinese Institute of Civil and Hydraulic Engineering 10 (2), 279–289 (In Chinese). Johansson, J., Konagai, K., 2006. Fault induced permanent ground

deformations—an experimental comparison of wet and dry soil and implications for buried structures. Soil Dynamics and Earthquake Engineering 26, 45–53.

Johnson, K.M., Johnson, A.M., 2002. Mechanical models of trishear-like folds. Journal of Structural Geology 24, 277–287.

Karamitros, D.K., Bouckovalas, G.D., Kouretzis, G.P., 2007. Stress analysis of buried steel pipelines at strike–slip fault crossings. Soil Dynamics and Earthquake Engineering 27 (3), 200–211. Kawashima, K., 2002a. Damage of a bridge foundation resulting from

fault displacement. Proceeding of Structural Engineers World Congress 2002, Yokohama, Japan, Paper No. T2-8-a-6, 1–8. Kawashima, K., 2002b. Damage of bridges resulting from fault rupture

in the 1999 Kocaeli and Duzce, Turkey earthquakes and the 1999 Chi-Chi, Taiwan earthquake. Proceedings of Structural Engineer-ing and Earthquake EngineerEngineer-ing (Special Issue). JSCE, vol. 19 (2), pp. 179s–197s.

Kelson, K.I., Kang, K.H., Page, W.D., Lee, C.T., Cluff, L.S., 2001a. Representative styles of deformation along the Chelungpu Fault

from the 1999 Chi-Chi (Taiwan) earthquake: geomorphic characteristics and responses of man-made structures. Bulletin of the Seismological Society of America 91 (5), 930–952. Kelson, K.I., Bray, J.D., Cluff, L., Harder, L., Kieffer, S., Lettis, W.,

Page, W., Perkins, W., Rix, G., Roblee, C., Sitar, N., Wells, D., Wright, R., Yashinsky, M., 2001b. Fault-related surface deforma-tion. Earthquake Spectra 17 (S1), 19–36.

Kennedy, R.P., Chow, A.W., Williamson, R.A., 1977. Fault movement effects on buried oil pipeline. Transportation Engineering Journal of ASCE 103 (5), 617–633.

Konagai, K., 2005. Data archives of seismic fault induced damage. Journal of Soil Dynamics and Earthquake Engineering 25, 559–570. Kontogianni, V.A., Stiros, S.C., 2003. Earthquakes and seismic faulting: effects on tunnels. Turkish Journal of Earth Sciences 12, 153–156.

Kung, C.S., Ni, W.P., Chiang, Y.J., 2001. The damage and rehabilitation work of Shih-Kang Dam. Proceedings of Workshop on Seismic Fault-Induced Failures, Tokyo, pp. 33–48.

Lade, P.V., Cole, D.A., Cummings, D., 1984. Multiple failure surfaces over dip-slip faults. Journal of Geotechnical Engineering 110, 616–627.

Lazarte, C.A., 1996. The response of Earth structures to surface fault rupture. Ph.D. Thesis, Department of Civil Engineering, Univ. of California, Berkeley.

Lazarte, C.A., Bray, J.D., 1996. A study of strike–slip faulting using small-scale models. Journal of Geotechnical Testing 19, 118–129. Lazarte, C.A., Bray, J.D., Johnson, A.M., Lemmer, R.E., 1994. Surface breakage of the 1992 Landers Earthquake and its effects on structures. Bulletin of the Seismological Society of America 84 (3), 547–561.

Lee, W.J., Hamada, M., 2005. An experimental study on earthquake fault rupture propagation through a sandy soil deposit. Journal of Structure Engineering and Earthquake Engineering, JSCE 22, 1s–13s. Lee, J.C., Chen, Y.G., Sieh, K., Muller, K., Chen, W.S., Chu, H.T.,

Chan, Y.C., Rubin, C., Yeats, R., 2001a. A vertical exposure of the 1999 surface rupture of the Chelungpu fault at Wufeng, western Taiwan: structural and paleoseismic implications for an active thrust fault. Bulletin of the Seismological Society of America 91 (5), 914–929.

Lee, K.M., Hou, X.Y., Ge1, X.W., Tang, Y., 2001b. An analytical solution for a jointed shield-driven tunnel lining. Journal of Numerical and Analytical Methods in Geomechanics 25, 365–390. Lee, J.C., Rubin, M.C., Mueller, K., Chen, Y.G., Chan, Y.C., Sieh, K., Chu, H.T., Chen, W.S., 2004. Quantitative analysis of movement along an earthquake thrust scarp: a case study of a vertical exposure of the 1999 surface rupture of the Chelungpu fault at Wufeng, western Taiwan. Journal of Asian Earthquake Science 23, 263–273. Lin, M.L., Jeng, F.S., Wang, H.J., Wang, C.P., Chung, C.F., Yao, Daniel, Chan, S.J., 2005. Response of soil and a submerged tunnel during a thrust fault offset based on model experiment and numerical analysis. Proceedings of ASME Pressure Vessels and Piping Division Conference, Denver, Colorado USA. Paper No. PVP2005-71179.

Lin, M.L., Chung, C.F., Jeng, F.S., 2006a. Deformation of overburden soil induced by thrust fault slip. Engineering Geology 88, 70–89. Lin, M.L., Jeng, F.S., Huang, T.H., Chung, C.F., Lee, H.W., 2006b. A study on the damage degree of shield tunnels submerged in overburden soil during the thrust fault offset. Proceedings of PVP2006 ASME Pressure Vessels and Piping Division Conference, Vancouver, BC, Canada. Paper No. PVP2006-ICPV11-93345. Murbach, D., Rockwell, T.K., Bray, J.D., 1999. The relationship of

foundation deformation to surface and near-surface faulting 131 M.-L. Lin et al. / Engineering Geology 92 (2007) 110–132

(23)

resulting from the 1992 Landers earthquake. Earthquake Spectra 15 (1), 121–144.

Muir Wood, A.M., 1975. The circular tunnel in elastic ground. Geo-technique 25, 115–127.

Nahas, A.El., Bransby, M.F., Davies, M.C.R., 2006. Interaction between normal fault rupture and rigid strong raft. Proceeding of International Conference on Physical Modelling in Geotechnics, Hong Kong, August 2006, pp. 337–342.

O'Rourke, T.D., Palmer, M.C., 1996. Earthquake performance of gas transmission pipelines. Earthquake Spectra 12 (3), 493–527. Prentice, C.S., Ponti, D.J., 1997. Coseismic deformation of the Wrights

tunnel during the 1906 San Francisco earthquake: a key to under-standing 1906 fault slip and 1989 surface ruptures in the southern Santa Cruz Mountains. Journal of Geophysical Research 102(B1), 635–648.

Roth, W.H., Scott, R.F., Austin, I., 1981. Centrifuge modeling of fault propagation through alluvial soils. Geophysical Research Letters 8 (6), 561–564.

Roth, W.H., Sweet, J., Goodman, R.E., 1982. Numerical and physical modeling of flexural slip phenomena and potential for fault move-ment. Rock Mechanics. Supplementum 12, 27–64.

Shearad, J.L., Cluff, L.S., Allen, C.R., 1974. Potentially active faults in the dam foundation. Geotechnique 24 (3), 367–428.

Sorensen, P.S., Meyer, J.K., 2003. Effect of the Denali Fault rupture on the Trans-Alaska Pipeline. Proceeding of the 6th US, Conference and Workshop on the Lifeline Earthquake Engineering. Monograph,

vol. 25. American Society of Civil Engineers, Technical Council on Lifeline Earthquake Engineering, pp. 547–555.

Takada, S., Hassani, N., Fukuda, K., 2001. A new proposal for simplified design of buried steel pipes crossing active faults. Earthquake Engineering and Structural Dynamics 30, 1243–1257. Tani, K., Ueta, K., Onizuka, N., 1994. Scale effect of Quaternary ground deformation observed in model tests of vertical fault. Proceeding of 29th Japan National Conference on SMFE, Japan, pp. 1359–1362 (In Japanese).

Trautmann, C.H., O'Rourke, T.D., 1985. Lateral force-displacement response of buried pipe. Journal of Geotechnical Engineering 111 (9), 1077–1092.

Trautmann, C.H., O'Rourke, T.D., Kulhawy, F.H., 1985. Uplift force-displacement response of buried pipe. Journal of Geotechnical Engineering 111 (9), 1061–1076.

Ulusay, R., Aydan, R., Hamada, M., 2001. The behaviour of structure built on active fault zones: examples from the recent earthquakes of Turkey. Proceeding of Workshop on Seismic Fault-Induced Failures, Tokyo, pp. 1–26.

Wang, L.R.L., Yeh, Y., 1985. A refined seismic analysis and design of buried pipeline for fault movement. Earthquake Engineering and Structural Dynamics 13, 75–96.

Yilmaz, M.T., Paolucci, R., 2007. Earthquake fault rupture–shallow foundation interaction in undrained soils: a simplified analytical approach. Earthquake Engineering and Structural Dynamics 36 (1), 101–118.