Centrifuge experiments for shallow tunnels at active reverse fault intersection

Abstract

Tunnels extend in large stretches with continuous lengths of up to hundreds of kilometers which are vulnerable to faulting in earthquake-prone areas. Assessing the interaction of soil and tunnel at an intersection with an active fault during an earthquake can be a beneficial guideline for tunnel design engineers. Here, a series of 4 centrifuge tests are planned and tested on continuous tunnels. Dip-slip surface faulting in reverse mechanism of 60-degree is modeled by a fault simulator box in a quasi-static manner. Failure mechanism, progression and locations of damages to the tunnels are assessed through a gradual increase in Permanent Ground Displacement (PGD). The ground surface deformations and strains, fault surface trace, fault scarp and the sinkhole caused by fault movement are observed here. These ground surface deformations are major threats to stability, safety and serviceability of the structures. According to the observations, the modeled tunnels are vulnerable to reverse fault rupture and but the functionality loss is not abrupt, and the tunnel will be able to tolerate some fault displacements. By monitoring the progress of damage states by increasing PGD, the fragility curves corresponding to each damage state were plotted and interpreted in related figures.

Keywords

reverse fault rupture / continuous tunnel / geotechnical centrifuge / ground surface deformations / fragility curves

Introduction

Surface faulting is the propagation of displacement along a fault in the soil deposits that reaches the ground surface. Surface faulting rupture hazard is recognized as one of the most important causes of damages to different structures in recent earthquakes [¹].

Lifelines expand over a considerable length in a sense that avoiding fault and lifeline intersection is almost impossible [²]. The cause of severe earthquake damage to tunnels usually is due to great ground displacements, like surface faulting. Vibrations without great ground displacement usually cause lower level damages [³].

There exist many studies on tunnel damages from past earthquakes, Indicating that severe damages are caused due to great displacements in surface faulting [⁴–¹⁰]. According to Ref. [⁹], usually underground structures may only be damaged at peak ground acceleration of above \mathrm{2}\mathrm{m}/{\mathrm{s}}^{\mathrm{2}}, while the most observed damages of tunnels corelate to the presence of a fault. Wright tunnel (the United States), subject to 1906 San Francisco earthquake, is one of the first tunnels damaged by faulting where the transverse horizontal offset of 4.5ʹ occurred under the fault. Rock fell from the tunnel ceiling and walls, the timbers broke through flexure and the tunnel was blocked at several locations [¹⁰].

The idea that tunnels are invulnerable to earthquake observed in the past 50 to 100 years is rejected by Ref. [⁷], the Bolu tunnels, Kern County tunnel and Wrights tunnel in specific. They concluded that in active seismic zones, both during the construction and their operating period, faulting is the most important cause of failure.

According to Ref. [⁴] the key points for designing civil-infrastructures near seismic faults is their outlining with respect to the total of 8 tunnels damaged by earthquake faults in Japan, the United States and Turkey consisting of tube train and water conveyance tunnels.

There exist many experimental and numerical studies on the propagation of fault rupture in soil deposits [¹¹–¹⁸]. Some researchers have examined the effects of fault activity on surface structures like building foundations, piles, bridges and dams [¹,¹⁹–²⁷]. The focus of many studies is on fault impact on pipelines [²⁸,²⁹]. Though tunnels are vulnerable to fault activity, research in this area is limited [²,³⁰]. The authors in Ref. [³⁰] conducted the first and only centrifuge physical modeling to assess the interaction of a continuous tunnel at intersection with faults in the occurrence of an earthquake. A scaled aluminum tube is used to model the tunnel. In their study, a centrifuge model is developed to assess the effects of fault displacement of 61 cm in prototype scale on the tunnel. The model tests on segmental tunnel at the intersection with active normal faults are assessed in Ref. [²]. By assessing many centrifuge models, they deduced that segmental tunnels and normal faulting can be modeled in a successful manner. They also reported that failure of segmental tunnels does not occur suddenly and can withstand a certain amount of displacement without complete failure. The focus of other studies in this area, in particular physical modeling, is on assessing the interaction of soil and tunnel parallel to the fault in earthquake [³¹–³⁴]. Avoidance of an intersection is impossible if the tunnel is perpendicular to the fault line, thus, the most severe damage. Somehow, this vital issue has not been a major issue of discussion in this realm.

It is proved that the 1g and Ng experimental methods are able to model fault rupture propagation in soil deposits and assess the faulting effects on different structures, where centrifuge method is more effective because the soil stress level in model and prototype is the same. For computational modeling of fault rupture phenomenon, it is necessary to consider large displacements, damages to the tunnel and crack propagation in tunnel lining. Modeling of such events through conventional numerical methods is not easy, but through the modern methods of computational modeling, its simulation becomes possible [³⁵–³⁷]. Nowadays computational methods are being developed through which fracture modeling and crack propagation in dynamic and quasi-static phenomena have become possible [³⁸–⁴⁴]. These methods are adopted to estimate the cause of failure in such events. Some of the practical computational methods consist of the meshless, local remeshing and phase field modeling. These methods are the new improved approaches for modeling development, growth and evolution of a discrete crack [⁴⁵–⁴⁸].

In case of interaction between tunnels and active faults, the angle of the tunnel and the fault line is of essensse. A tunnel orientation is parallel to the fault or intersects it at an angle up to 90°; in the first case avoiding the fault line is the best solution, and in the second case where the tunnel path is perpendicular to the fault line, avoiding intersections because of their length is impossible, where the fault activity causes the most severe damage. In highway and railway tunnels, faulting causes ground settlement, crack in tunnel lining, soil fall and complete collapse [⁴⁹]. This settlement may change the slope of the route or cause obstruction. Cracking and breaking the tunnel lining will cause water leakage into the tunnel. Faulting imposes a great displacement to the tunnel leading to deformations of the tunnel section, squeezing soil and rocks inside the tunnel thus, complete or partial obstruction.

Designing a lifeline and fault intersection, the only possible approach is to apply an appropriate mitigation strategy. The authors in Ref. [⁵⁰] categorized damage reduction methods in five different approaches of routing and relocating the lifeline, isolation from damaging ground movements, reduction in ground movements, applying high strength materials, and applying flexible materials and joints. The authors in Ref. [⁵¹] claimed that there exist two practical approaches like over-excavation and articulated design reducing tunnel damage at the intersection of the active fault.

Method and materials

Geotechnical centrifuge and scaling laws

In small scale models, the stress level is smaller than the prototype, and the mechanical behavior of soil types depends on the stress level. The premise of centrifuge modeling is to run a test on a {\displaystyle \raisebox{1ex}{$\mathrm{1}$}\!\left/ \!\raisebox{-1ex}{$N$}\right.} scale model of a prototype in the centrifuge enhanced gravity field. The acceleration of gravity increases with the same geometric ratio N [⁵²]. In this study, by considering the available materials, the dimensions of the centrifuge basket, the conventional tunnel diameter and the available centrifuge capacity N = 60 [⁵³]. The dimensions of the model tunnel scale, soil and the dimensions of the prototype are tabulated in Table 1.

Faulting simulator box

Modeling of faulting requires a simulator box one side of which moves relative to the other side and simulates the displacement caused by fault rupture in an earthquake. A centrifuge machine allows the model to be made much smaller than the prototype, but it also creates limitations. The box should be appropriate to model fault displacement, must withstand the desired acceleration (60 g) and its dimensions should be so small that it can be installed in the centrifuge basket. This designed and constructed box shown in Fig. 1, has dimensions of L100 cm × W50 cm × H60 cm, appropriate for modeling soil at L100 cm × W50 cm × H30 cm dimensions. One side of this box is made of plexiglass plate to allow the observation of fault rupture propagation In this simulate, the left side of the box is referred to the hanging wall, and with its motion simulate the fault displacement. The force exerted by a hydraulic jack, with a set of wedges and linear guideways, moves the moving body at a 60-degree angle to the horizon.

Sand type #161 of Firouzkuh and PVA fiber-cement cylinder

Clean sand of is applied for many physical tests worldwide: Toyoura sand in Japan, Nevada sand in the United States and Firouzkuh sand in Iran. For most laboratory researches at the University of Tehran, Firouzkuh #161 sand is used, the mine of which is located in NE Tehran. It is a yellowish clean sand type, uniformly graded and its silt content is less than 1%. This sand’s grading chart is shown in Fig. 2 and its properties are tabulated in Table 2 [²,⁵⁴,⁵⁵].

For each continuous tunnel model, a 6 mm thickness PVA fiber-cement cylinder is applied. The mechanical properties of the cylinder material including compressive strength, tensile strength and elastic modulus are obtained by running a series of tests. The compressive strength is obtained by means of a uniaxial compression test and the flexural strength through a transverse loading test. Load-displacement curve obtained from transverse loading test on 100 mm diameter cylinder is shown in Fig. 3 [⁵⁶–⁶¹]. According to the run tests, the obtained results consist of: compressive strength of 27 MPa, tensile strength of 20 MPa and elasticity modulus of 18 GPa.

Experiment procedure

To assess the behavior of shallow tunnels across a reverse fault during an earthquake, 4 centrifuge experiments are run. The experiments are run by applying the fault displacement in a quasi-static manner, and dynamic effect of faulting is ignored. According to Ref. [⁶²] the compressive response of the fine sand is not sensitive to strain rate. The velocity of applied base displacement shows a 2 mm/s velocity. This method of simulation is adopted in Refs. [⁶³–⁶⁵].

The soil deposits are simulated with and without the tunnel presence. Two different diameters of 100 mm and 150 mm are of concern for tunnel lining of models in these tests, representing the diameters of 6m and 9m at prototype scale, and named as tunnel A and B, respectively. The tunnel is perpendicular to the fault line in order to simulate the most destructive pattern.

The soil is poured into the fault simulator box in 10 layers of 30 mm thick with the same density. During the filling process, the model tunnel is placed inside the box. Because the length of the simulator box is limited, two semi-rigid connections are used for providing suitable boundary conditions. Both ends of the tunnel are connected to the box walls through these connections. To observe the failure lines in soil deposit, dyed sand is applied among every sand layer, Fig. 4. The final surface of the soil is meshed by dyed sand. After placing the fault simulator box in the centrifuge, measuring and imaging instruments are installed on it. Upon the start of centrifuge rotation, sample acceleration increases to 60 g. By keeping this acceleration constant, the bed-rock is moved in a gradual manner, where at each step, the bed-rock, tunnel and soil surface displacements are measured. The soil layer deformation where it touches the plexiglass is photographed, and all occurrences inside the tunnel are photographed by the camera. The whole structure of this model is shown in Fig. 5.

The maximum faulting displacement of the bed-rock is 48mm, which is applied at an angle of 60 degrees to the horizon, making the vertical displacement component 42mm. The physical model is 60 times smaller than the prototype. According to the scaling rules of centrifuge modeling, maximum vertical displacement in the prototype is 2.5m.

Results and discussions

Free field model

To assess the propagation of reverse fault rupture in alluvial deposits, the free field model is placed under a 60-degree angle fault displacement. To actuate faulting displacement, hydraulic jack force is applied by wedges and linear guideways to the hanging wall. The soil deformations in the free field model behind the plexiglass before and after faulting is shown in Fig. 6, where the formation of the shear zone is evident due to soil failure. The rupture propagation path, from the rupture point bedrock to the ground surface, deviates slowly toward the footwall. Fault Movement leads to a severe strain on the ground, which are detectable at a distance about h from each side of the shear zone. The main shear zone is as wide as fault displacement (h). By approaching ground surface, the main shear zone width increases.

Tunnel collapse

To assess the tunnel fault intersection behavior a series of centrifuge tests with different tunnel diameters are run here. The prototype tunnel diameters are 6 m and 9 m. Reverse fault displacements are made in a gradual manner. A schematic view of the tunnel model affected by reverse faulting is shown in Fig. 7 and the damaged tunnel models subject to reverse faulting are shown in Fig. 8.

The tunnel collapse occurs 77 mm from fault rupture point toward the Hanging wall (f=\mathrm{77}\mathrm{m}\mathrm{m}, Fig. 7). As observed in Fig. 7 at final stage of surface faulting, the tunnel section of the hanging wall remains horizontal and the other section gains a slope of 8.6%.

On footwall side, there is a cavity below the tunnel. This cavity is due to tunnel section movement from the damage zone upwards. The cavity is 90 mm long with an 18 mm depth.

Tunnel failure progress

The failure progress of the tunnel at the stages of reverse faulting in model test 1 is shown in Fig. 9. In tunnel model A, the first crack is observed with a vertical displacement of 2.3 mm. As the vertical displacement increases up to 19.8 mm, sudden soil pour is observed which completely blocks it. The displacements continue up to 42 mm.

Sinkhole

Due to soil pour in the tunnel, a massive sinkhole appears on the ground surface, Fig. 7, where the dimensions of the sinkhole are expressed as: w, u, and D_p, which represent dimensions of the sinkhole along the tunnel and perpendicular to it, and its depth, respectively. At the final stage of the test with a 48 €mm Permanent Ground Displacement (PGD), according to the observations, w, u, and D_p are measured as: 130€, 180, and 63€ mm, respectively. The sinkhole area on the ground surface is about {\mathrm{276}\hspace{0.17em}\mathrm{c}\mathrm{m}}^{\mathrm{2}} and the volume of soil poured into the tunnel is about {\mathrm{580}\hspace{0.17em}\mathrm{c}\mathrm{m}}^{\mathrm{3}}. The sinkhole and fault surface trace are shown in the Fig. 10. The fault surface trace, in Fig. 10 is the area with the most relative deformations.

Ground surface deformations and potential hazards for structures

Analysis, estimation, assessment and monitoring of surface displacements resulting from the excavation of tunnels are studied by many researchers because of the threat posed by ground settlement to the safety of buildings and infrastructures [⁶⁶–⁷¹]. However, there exist not many studies on surface displacement due to faulting and its interaction with tunnels. Surface fault rupture causes severe deformation on the ground surface. Some researchers have assessed ground surface deformations due to fault rupture propagation by studying previous faults, and the experimental and numerical modelings thereof. Presence of a tunnel changes the pattern of the rupture propagation and surface deformations.

The tunnel failure and soil falling in the tunnel causes the formation of a massive sinkhole which envelopes buildings and surface structures. Based on the results of the tests run on reverse faulting conditions, in the tunnel damage zone, there is the possibility of formation of a sinkhole, thus construction in such areas should be avoided. A conservative suggestion is that buildings should not be constructed along the tunnel from the fault location at 2D (twice the tunnel diameter length) distance in the hanging wall. In the vicinity of the fault, and the sides of the tunnel, a steep slope will be formed on the ground surface, where, the damage caused by the ground surface deformation must be checked and assure that the structure maintains the expected performance. Otherwise, damage reduction strategies should be adopted or the construction of the structures at such location be stopped. A 3D view of ground surface deformed shape due to reverse faulting in tunnel models is shown in Fig. 11, whereas observed the dangers of surface deformation associated with reverse faulting across a tunnel on structures are evident. The vertical displacement and horizontal relative displacement contours of the ground surface are shown in Figs. 12 and 13, respectively.

In the related available literature, the focus of studies run on displacements is on settlements and their effects on buildings. Ground surface movements especially the non-uniform displacements, can cause excessive deformations and forces thereof as to building damage consisting of architectural and structural damages. Architectural damage is due to little displacements manifested in usual cracks in building components. Severe cracks can interfere with the function of the building. Non-uniform displacements cause secondary stresses in building frames and structural members [⁷²]. Many researchers have determined the amount of permissible angular distortion by considering the effects of settlement on buildings [⁷³–⁷⁷]. The limitations of angular distortion associated with structural damages are proposed by Ref. [⁷⁵].

Longitudinal and lateral profiles of ground surface deformed shape in this centrifuge models are shown in Figs. 14–16, wherein each, the location and dimensions of the sinkhole, ground surface vertical displacements and, slope changes of the ground surface is evident. These profiles are measured at the last stage of faulting and compared with the angular distortion limits in order to determine the severity of structural damages. Here it is found that the values obtained here exceed that of the limitations proposed by Ref. [⁷⁵]. This issue becomes more intense when the presence of a tunnel in some places leads to deformation concentration. Consequently, it is recommended once more to avoid building near the fault locations as much as possible. In faults with a possible displacement of less than 50 cm, a building could be constructed with a distance from the possible sinkhole and the centerline of the tunnel.

Fault rupture propagation

The fault rupture propagation in soil deposits surrounding the tunnel in two conditions: presence of tunnel A and presence of tunnel B is illustrated in Fig. 17, where the shear zone is marked from the bedrock to the ground surface. The shear zone is diverted toward the footwall as it approaches the ground surface. By comparing Fig. 17 with Fig. 6, which shows the fault rupture propagation in the free-field soil, it can be deduced that the width of the shear zone in presence of the tunnel is reduced. An increase in tunnel diameter leads to a reduction in shear zone width and cause it to become more concentrated which in turn would increase soil shear strain.

The vertical displacement of the ground surface adjacent to the plexiglass after faulting is shown in Fig. 18, where the ground surface deformation in the free field model and the tunnel models A and B all are of the same form. This phenomenon indicates that at a slight distance from the tunnel axis, the effects of the tunnel on the fault propagation fades. The most deformation at the ground surface occurs within 50 to 200 mm range, from the fault rupture point. The maximum slope of the ground surface is in the same locality within 30 and 50 percent rate.

Tunnel damage states and fragility curves

Another important issue is the tunnel damage state in fault movements. In the study of PGD, four damage states consisting of: none (\mathrm{D}\mathrm{S}), slight/minor (\mathrm{D}\mathrm{S}), moderate (\mathrm{D}\mathrm{S}), and extensive/complete (\mathrm{D}\mathrm{S}) are defined for tunnels by HAZUS which are evident in these experiments. The progress of damage state in PGD, in test 3, on tunnel B under reverse faulting is shown in Fig. 19. Depending on the damage state in different vertical PGDs in reverse faulting tests, the fragility curves are drawn based on MLE method, Fig. 20. These curves express the probability of exceeding the damage state for different displacements (i.e., probability of exceeding damage state 1, with a displacement of 55 cm, is more than 90%). In case of reverse faulting, in low displacements, the probability of extensive damages and complete tunnel service stoppage is low. The probability of exceeding the damage state 4, despite the vertical displacement of 1 m, is less than 10%. Tunnel slope and damage state variations with an increase in PGD in tunnels with different diameters are shown in Fig. 21. If these two factors of indicative of tunnel performance level, it can be claimed that an increase in tunnel diameter would increase the resistance and decreases the probability of damage due to reverse fault rupture. Due to the fact that the fault rupture acts as a coercive force on a tunnel, the tunnel slope becomes more dependent on the relative displacement of the sides of the fault as shown in Fig. 21 .

Repeatability

In each fault mechanism, propagation of fault rupture in soil deposits and its effects on the tunnel and ground surface are of fundamental similarities. The fault rupture propagation path in soil, sinkhole on the ground, formation of fault trace due to reverse faulting tests, formation of fault scarp and Graben zone in normal faulting tests and their comparisons in different tests with the results of other assessments, indicate the repeatability of these experiments. In addition to all this confirmatory evidence, in Test 1, where a tunnel is modeled in reverse fault rupture at 60g acceleration, is repeated at 50g acceleration. The similarity of the results of this repetition with the aspects of the rupture propagation, the location and severity of the tunnel damage, the mechanism of damage and its effects on ground surface also moreover confirms the repeatability of these experiments.

Conclusions

The findings here are briefed as follow:

1) The physical simulation through centrifuge is a useful tool for modeling reverse fault displacement on tunnels, and it is well-suited to study the interaction of tunnels, soil and active faults.

2) Earthquake fault rupture can cause severe damage to the tunnels in a manner that it suspends their operation but the functionality loss is not abrupt, and the tunnel will be able to tolerate some fault displacements.

3) In designing tunnels, avoid intersect to an active fault as much as possible, otherwise, the effects of fault offset should be of major concern.

4) Fault movement causes great ground displacements which can damage a variety of structures. The failure of a tunnel leads to a massive sinkhole formation on the ground surface that can envelop structures.

5) Reverse fault displacement causes gradually settlement of tunnel, and its slope changes.

6) Slight movement away from tunnel axis will fade the effects of the tunnel on the fault rupture propagation and the rupture will propagate without any tunnel interference in soil deposits.

7) The fragility curves are plotted for different damage states and compared with the curves provided by HAZUS for damage to the tunnels caused by PGDs.

8) The curves obtained for the slight damage state are approximately resemble those of the HAZUS curves.

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