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ARMA 08-093

Numerical Study of Fault Geometrical Effects on Seismic Stability of Large Underground Caverns S. Ardeshiri Department of Civil Eng., Tarbiat Modares University, Tehran, Iran

M. Yazdani Assist. Prof., Department of Civil Eng., Tarbiat Modares University, Tehran, Iran, & Mahab Ghodss Consulting Engineering Co., Tehran 19187-81185, Iran Copyright 2008, ARMA, American Rock Mechanics Association This paper was prepared for presentation at San Francisco 2008, the 42nd US Rock Mechanics Symposium and 2nd U.S.-Canada Rock Mechanics Symposium, held in San Francisco, June 29July 2, 2008. This paper was selected for presentation by an ARMA Technical Program Committee following review of information contained in an abstract submitted earlier by the author(s). Contents of the paper, as presented, have not been reviewed by ARMA and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of ARMA, their officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: Underground facilities built in areas subject to earthquake activity must withstand both static and seismic loading. The seismic stability of large-scale underground caverns, such as underground opening for hydropower house is often affected by faults nearby. In this study, the influence of faults on seismic behavior of underground caverns has been investigated using numerical methods. A parametric study has been carried out to determine the most critical situation of a single fault crossing cavern section with the strike parallel to cavern axis. For such a purpose several cases of faults having different dips and different intersection points with cavern wall were considered. For each case a dynamic nonlinear analysis was performed under an earthquake ground motion applied on bedrock. To assess the seismic effects on stability of cavern, two quantities related to rock mass response, the maximum values of area of plastic zone around underground opening and vertical displacement in cavern roof are selected to be extracted from analyses. The results indicate that the most critical dip angle for a single fault crossing cavern section is ranged between 30˚ to 50˚. In addition, the most critical situation of fault causing large vertical displacement is the case in which the fault intersects the cavern roof.

1. INTRODUCTION Historically, underground facilities have experienced a lower rate of damage than surface structures. Nevertheless, some underground structures have experienced significant damage in recent large earthquakes, including the 1995 Kobe, Japan earthquake, the 1999 Chi-Chi, Taiwan earthquake and the 1999 Kocaeli, Turkey earthquake. Discontinuity is one of the major features of rock as a construction material. Joints, faults and bedding planes exist inherently in most rocks and affect stability of rock structures. Many static and seismic instabilities of underground caverns ascribed to the influence of faults located nearby. Brekke and Selmer Olsen (1996) concluded in a survey of factors causing failures of underground excavations in Norway, that faults are often a major cause of failures. In particular in recent years, many reports on fault-induced

problems considering the stability of underground caverns have become a pivotal issue that engineers and researchers are facing in the current time [1]. However, finding a theoretical solution to survey the stability of underground cavern is beyond the bounds of possibility. In order to construct an economical and reliable support system, it is essential to have a better knowledge of the faultinduced behavior of underground excavations considering the stability aspects. Underground structures have characteristics that make their individual seismic behavior in comparison to most surface structures, most notably their complete enclosure in soil or rock, and their significant length (i.e. tunnels). The design of underground facilities to resist seismic loading, thus has aspects that are very different from the seismic design of surface structures. So using numerical method for investigation of seismic behavior of large-scale underground caverns is inevitable [2].

A significant number of methods have been developed and extensively applied for these problems. However, a convenient method must be problem oriented. With the extensive application of numerical methods in geomechanics, particularly a variety of joint models introduction in FEM and FDM (Goodman et al., 1968; Desai et al., 1984; Beer and Poulsen, 1994), a thorough assessment of this kind of fault-related problem can be realized [3]. Based on these considerations, the main objective of this work oriented to assess the effects of faults on the induced plastic zones and displacement redistribution after exposure to earthquake forces, around underground openings. In addition, the attention was focused on evaluating the effects of mechanical properties of faults on the stability of caverns considering the location and the dip of the fault. The result can offer a preliminarily guidance to understanding the operation of caverns faced to earthquake forces, so it can helps engineers to have a suitable support design. In this paper by applying an explicit finite difference program (FLAC2D) and using interface element, the effect of earthquake on a large underground cavern with finding the most critical situation of a single fault crossing cavern section, were investigated. 2. FAULTS AND MODELING METHOD Faults are the commonly encountered large geological discontinuities in hard rock masses. Most severe underground instabilities are found to be closely associated with the faults presence nearby. Y.H.Hao and R.Azzam research on effect of fault on stability of large-scale underground caverns in static conditions has shown that faults affect the stability of underground structure by the tendency of increasing the plastic zones, displacements and causing both asymmetrically distributed in the rock masses adjacent to the excavation. In the past several decades, different types of joint elements have been proposed for simulating rock joints or faults in rock mechanics (Goodman et al 1968, Pande et al. 1979, Desai et al. 1984, Griffiths 1985). These joint elements were then widely developed to model joints and interfaces in engineering applications and for investigation purposes. Schweiger, (1990) used the thin-layer joint element model to assay the fault thickness and stiffness effects on underground tunnel stability. Lei et al. (1995) applied a contact-friction interface

element to survey the fault influence on the stress redistribution and lining moment and normal force of lining. Steindorfer, (1998) used the ratio of longitudinal to vertical displacement to evaluate the effect of fault zones in the process of tunnel excavation [1]. However, in this paper an interface element to simulate fault behaviors is used. Additional information about the details of this model could be achieved in FLAC2D code manual. LM

Gridpoint ks

S

LO

N T kn

Side A O Side B

M LN

P

Zone

Fig. 1. Fault model. The interface represented by side A and side B, which are connected by normal (kn) and shear (ks) stiffness springs. (S=slider, T=tensile strength and Ln=length associate with grid-point N)

In this model, faults or joints in nature are represented as normal and shear springs with normal and tangential stiffness (Kn and Ks, respectively) between two planes, which may contact one another (Figure 1.). The model can explain main fault characteristics such as slipping, opening and compression behavior. It can also describe the fact that the fault exhibits zero tension in the normal direction and follows Coulomb's friction law for shear. FLAC2D code is a two-dimensional explicit finite difference program using time-marching technique procedures at very small steps. The interface is divided into many differential elements. The incremental relative displacement vector at the contact point is resolved into the normal and shear directions and the total normal (Fn) and shear (Fs) forces are determinable using the following equations: Fn( t + Δt ) = Fn( t ) − K n ΔU n(t + Δt / 2) L Fs( t + Δt ) = Fs( t ) − K s ΔU s( t + Δt / 2 ) L

Also expressed in matrix form as:

(1)

⎧ΔFn ⎫ ⎡ K n ⎬=⎢ ⎨ ⎩ ΔFs ⎭ ⎣ 0

0 ⎤ ⎧ ΔU n L ⎫ ⋅⎨ ⎬ K s ⎥⎦ ⎩ ΔU s L ⎭

(2)

Where the stiffness, kn and ks, have the units of [stress/displacement]. L is the segment length of the interface element; ΔUn is the displacement increment of the interface element in the normal direction, and ΔUs is displacement increment of a segment of interface element in the tangential direction. The status of fault can be determined by the following criterions: (a) Tensile yield condition: Ft=σt-t where σt is the tensile stress acting on the fault and t is the tensile strength of the fault. If Ft ≥ 0, then the interface break, and the shear and normal forces are set to zero. Normally, the tensile strength of faults is zero.

boundaries are fixed on horizontal direction and zero displacement condition is applied on the base of the model. The effect of overlying rock weight is applied on the model top boundary by a normal stress. It is noted that adopting displacement boundary conditions on the vertical boundaries of the model rather than the stress boundary condition is the premise of obtaining ideal numerical results for fault-related problem (Hao and R.Azzam, 2005). A fault with different dips is supposed to run through the rock mass in the vicinity of the cavern or intersect the cavern. It is also further assumed that the fault strike is parallel or nearly parallel to the alignment of the cavern such that a plane strain state can be applied. This case is well recognized to be most unfavorable for the stability of underground caverns (Hoek and Brown, 1982).

5 MPa

(b) Shear yield condition: The status of shear stress condition along faults can be determined by Mohr-Coulomb shearstrength criterion. 20 m

Fs max =cl+Fn tanφ

If the criterion is satisfied (i.e., if |Fs| ≥ Fs max), then Fs=Fs max, with the sign of shear preserved. 3. PHYSICAL CONDITIONS

MODEL

AND

30 m

2

240 m

1

Where c is cohesion along the interface, l is effective contact length and φ is friction angle of interface.

3 4

BOUNDARY

To evaluate the effect of a fault on seismic stability of underground openings, a typical model as shown in Figure 2, is chosen. The underground opening considered in this model is a representative of many hydroelectric schemes such as the underground power houses and surge chambers. Its cross-section has an arch-profile crown shape of tall sidewall with dimensions of 20 m wide and 30 m high. In order to avoid from unfavorable effects of the model boundaries on the results, the size of model in each direction is taken eight times of the cavern dimension. The fault is also extended far enough from the excavation and the displacements of fault ends at the model borders are approximated to the states of remote rock masses. In static case, vertical

α

160 m Fig. 2. A model of cavern crossed by a single fault assumed with various locations in cavern perimeter (cases1, 2, 3 and 4).

As shown in Fig. 2, four possible fault locations with respect to the cavern were considered in this investigation. For the convenience of discussion case 1 is denoted where the fault passes by tangency of the cavern roof. Case 2, the fault intersects the middle of the left sidewall. Case 3, the fault cuts cavern crown and through the centre of the bottom

surface. Case 4, the fault emerges out in the near of heel of the cavern sidewall. For all the cases, the fault dips are assumed to be in the range from 20º to 80º and the mechanical properties of rock mass and fault are consistent.

3.2. Model considerations under dynamic loads Hayashi et al. (1973) gave the relation between the elastic modulus in dynamic Ed and the elastic modulus in static Es as following: E d = (1.3 ~ 1.7) E s

3.1. Model considerations under static loads Throughout this present study, the underground cavern is assumed to be at a depth of 300 m under the ground. The in-situ stress in the model prior to cavern excavation is considered to be due to the weight of rock masses at rest. The vertical stress varies linearly with depth and the horizontal stress is calculated by σh=k0σv, where k0 is the ratio between the horizontal and vertical stresses. Intact rock in the present model is considered as an elastic–perfectly plastic material that follows Mohr– Coulomb failure criterion. Slip failure of the fault is also governed by the Mohr–Coulomb criterion. Selection of the input parameters for this analysis is mainly based on the following considerations. The data specified for the rock mass and the fault should make the model to reveal fully unfavorable aspects of the effects of fault and these data should also be the true reflection of their some characteristics in reality. Therefore, the elastic modulus of the rock mass is assigned to 20 GPa, the internal friction angle is fixed in the neighborhood of 35º and its tensile strength and cohesion are no high. These specified geotechnical parameters basically represent the type of sparse jointed rock masses having low-medium strength in nature. Since the emphasis of this analysis is to discuss the effects of some important fault parameters, only fault stiffness, tensile strength and cohesion are needed to specify. This analysis is intended to study a type of weak fault that have a weathered, persistent and smooth surface without any tensile strength and cohesion and thin thickness. Therefore, shear dilation, strain hardening and softening of fault are neglected in the model. It should be noted that the interests in this paper are placed on the comparative analysis of the effect of different fault parameters rather than absolute prediction of a practical case. The aboveneglected properties of the fault have no influence on the general discussion of the problem. The selected geotechnical parameters for the rock mass and fault represent a stable model under static conditions.

(3)

The value of Ed is obtained by the in-situ dynamic loading test, and the Poisson’s ratio νd is 0.2~0.3. Price et al. (1969) explained that the tensile strength will increase about up to 1.5 times that of the static value at the time of quick loading. The mechanical properties of rock mass and fault used in the present research under static and dynamic conditions are listed in Table 1. Table 1. Input parameters of rock mass and fault for the numerical modeling Material properties Density ρ (kg/m3) Internal friction angle φ Cohesion c (MPa) Poisson ratio Normal stiffness kn (GPa/m) Shear stiffness ks (GPa/m Es (GPa) Ed (GPa) Tensile strength σt (KPa)

Rock mass 2600 35 2 0.2

Fault 24 0 20 2

20 25 1.7

The boundary conditions used in the dynamic analysis are illustrated in Figure 3. Quiet boundaries were used on all outside boundaries of model. These boundaries prevent reflection of outgoing seismic waves back into the model. Quiet boundaries were combined with free-field boundaries on the vertical outside boundaries that prevent distortion of vertically propagating plane waves along the boundaries. Dynamic loading was applied at the bottom of model, as propagating vertically upwards [4].

and maximum vertical displacement of the underground cavern induced by earthquake loading. These quantities are obtained for different fault dips, Peak Ground Accelerations (PGA.

Fig. 3. FLAC2D model boundary conditions for dynamic simulation.

The record of accelerogram of 1999 Kocaeli, Turkey earthquake with magnitude of 7.4 in scale of Richter (Fig. 4) has been used.

Fig. 4. Acceleration Record of Kocaeli earthquake.

4.1. Area of plastic zone Figures 5 to 8 illustrate the variation of plastic area extent in surrounding rock mass versus fault dips for different PGA in each location for intersection of fault with cavern periphery. All results are obtained for k0=1 and frictional angle of fault φ=24º. It can be seen that the fault-induced area of rock mass plastic zone around underground cavern is dependent on the fault dip. In addition, the maximum of plastic area in each fault location such as roof, wall and floor is occurred at different fault dips. However, the maximum plastic areas are obtained for dips ranging from 30º to 50º. For example in the case of fault in roof (fig. 5), the critical dip is 40º. When the fault intersects the wall of cavern in the middle point (fig. 6), this critical dip is 80º for PGA of less than 0.2g and 50º for larger PGAs. If the fault crosses the cavern floor at its center (fig. 7), the most critical dip is obtained at 50º. In the case of fault in lower corner of cavern in floor, it is occurred at 30º.

4. NUMERICAL RESULTS AND DISCUSSION The effect of earthquake on underground opening depends on various parameters including peak acceleration, magnitude and duration of earthquake, the relative rigidity between underground opening and ground and in-situ stress state as well. Furthermore, for underground caverns crossed by a single fault, some other parameters such as intersection of fault with cross section and mechanical properties of fault can be effective on the stability. In this section the effects of fault orientation and the location of its intersection with cavern perimeter as well as the PGA of earthquake loading are studied on seismic stability of cavern. In order to quantify the stability of cavern, two indices of the extended plastic area in rock mass and the maximum vertical displacement in tunnel roof have been adopted. The obtained results are discussed below based on the quantitative evaluation of the area of plastic zones

Fig. 5. Variation of plastic area extent versus fault dip for different PGA in case 1: fault intersects cavern roof (k0=1; φ=24º).

Fig. 9 summarizes the plastic area in the rock mass varied with the fault dips for different fault locations. It is interesting to note that the pattern of variation for rock mass plastic area against fault dip is generally similar between case 1 and case 3 and also between case 2 and case 4. The fault in case 4 locations is seemed to be the most unfavorable for the stability of cavern in terms of the area of induced plastic zones in rock mass.

Fig. 6. Variation of plastic area extent versus fault dip for different PGA in case 2: fault intersects left cavern wall in the middle point and also the roof (k0=1; φ=24º).

Fig. 9. Variation of plastic area extent versus fault dip for PGA=0.15g in cases 1 to 4 (k0=1; φ=24º).

Fig. 7. Variation of plastic area extent versus fault dip for different PGA in case 3: fault intersects cavern floor in the middle point and also right cavern wall (k0=1; φ=24º).

Fig. 8. Variation of plastic area extent versus fault dip for different PGA in case 4: fault intersects cavern floor in the corner point (k0=1; φ=24º).

4.2. Maximum vertical displacement Figures 10 to 13 exhibit the variation of maximum rock mass vertical displacement against fault dips for different PGA in each fault location crossed the cavern periphery. All results are obtained for k0=1 and frictional angle of fault φ=24º. The presented values are related to displacement induced by earthquake loading at its final moment of excitation and are independent from initial displacement produced by in-situ stresses. It is obvious that the maximum vertical displacement is occurred in cavern roof. The results show the high effects of fault dip and fault location on cavern roof displacements. However, the maximum roof settlement is obtained for fault dips between 40° to 50°.

Fig. 10. Variation of maximum vertical displacement of roof versus fault dip for different PGA in case 1: fault intersects cavern roof (k0=1; φ=24º).

Fig. 13. Variation of maximum vertical displacement of roof versus fault dip for different PGA in case 4: fault intersects cavern floor in the corner point (k0=1; φ=24º).

Comparing the amounts of vertical displacements shown in these figures indicates that case 1 in which fault intersects the cavern roof is most critical situation for fault location in terms of earthquakeinduced deformations. For example, the maximum vertical displacement of roof for most critical fault dip and PGA of 0.15g, is obtained 270 mm in case 1 (fig. 10) which is about 20 times larger than that in other cases with the same conditions. Figure 14 presents the extent of failure zone in surrounding rock mass for case 1 in which a tensile failure is observed adjacent to the intersection of fault with cavern roof. Fig. 11. Variation of maximum vertical displacement of roof versus fault dip for different PGA in case 2: fault intersects left cavern wall in the middle point and also the roof (k0=1; φ=24º).

Fig. 12. Variation of maximum vertical displacement of roof versus fault dip for different PGA in case 3: fault intersects cavern floor in the middle point and also right cavern wall (k0=1; φ=24º).

Fig. 14. Tensile Failure on rock mass around Underground cavern for case 1, fault dip=40º, PGA=0.15g, (k0=1; φ=24º).

5. CONCLUSION In this paper, FLAC2D numerical solution is presented for evaluating the effects of faults on the behavior of rock mass failure and deformation around the large-scale underground openings under seismic loads. Numerical analysis indicates that the influence of a fault to the underground cavern stability is different from its inherent properties. Same as static conditions, fault influences the seismic stability of large-scale underground caverns by the tendency of increasing the plastic zones and displacement and causing these two components to distribute asymmetric in the rock masses. This is strongly dependent of the fault dips, fault locations. Fault dip in relation to the underground cavern is proved to be an important factor on defining behavior of caverns face to earthquake forces. Based on the result of this investigation, it can be concluded that fault with dip nearly 40º to 50º are most critical. When a fault crossed cavern section, it can result to creating sharp edges on cavern section. Faced to earthquake waves these sharp edges would set on tensile failure. However these kinds of damage on cavern section are local and supplying the sufficient flexibility would be providing the required resistance against seismic loads.

ACKNOWLEDGEMENT The study was sponsored by the Iran water resources management co. REFERENCES 1.

Y.H. Hao, R. Azzam. 2001. Analysis of fault effects on the stability of large underground caverns. In ISRM Symposium 2nd Asian Rock Mechanics Symposium, Peking, Frontiers of Rock Mechanics and Sustainable Development in the 21st Century 2001, 529 – 533. Rotterdam: Balkema.

2.

Hashash, Y.M.A., Hook, J.J., Schmidt, B., Yao, J.I. 2001. Seismic design and analysis of underground structures. Tunneling and Underground Space Technology Res. 16, 247–293.

3.

Hao Y.H., R. Azzam. 2005. The plastic zones and displacements around underground openings in rock masses containing a fault. Tunneling and Underground Space Technology Res. 20, 49–61.

4.

M.C. Pakbaz, A. Yareevand, 2005. 2-D analysis of circular tunnel against earthquake loading. Tunneling and Underground Space Technology Res. 20, 411–417.

5.

FLAC2D, User's Manual. Itasca Consulting Group, Inc.

6.

S. Ardeshiri, 2008. Influence of discontinuities on seismic behavior of large underground caverns, M.S. Thesis, University of Tarbiat Modarres, Tehran, IRAN.

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B. Damjanac, M. B, M. L, D. K, J. L. 2007. Mechanical degradation of emplacement drifts at Yucca Mountain—A modeling case study Part II: Lithophysal rock. International Journal of Rock Mechanics & Mining Sciences Res. 44, 368–399.