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An approach to assessing the hydraulic conductivity disturbance in fractured rocks around the Syueshan tunnel, Taiwan
Tunnelling and Underground Space Technology 24 (2009) 222–230
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Review
An approach to assessing the hydraulic conductivity disturbance in fractured rocks around the Syueshan tunnel, Taiwan Hung-I Lin, Cheng-Haw Lee * Department of Resources Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 14 February 2008 Received in revised form 22 June 2008 Accepted 24 June 2008 Available online 15 August 2008 Keywords: Fractured rock Seepage UDEC Syueshan tunnel Hydraulic conductivity
a b s t r a c t The Syueshan tunnel, a long and recently completed tunnel in Taiwan, suffered many collapses due to huge groundwater surges during excavation. Thus, variations in hydrological conditions in fractured rocks after excavation have become a topic of interest in the field. A proposed model has been developed to predict the disturbance of hydraulic conductivity caused by excavating around the Syueshan tunnel in fractured rocks. The closure of fractures is assumed to be the sole factor that causes hydraulic conductivity changes, and a hyperbolic relation between normal stress and closure is introduced instead of using a linear relation in this estimation. The magnitude and range of disturbed hydraulic conductivity are straightforwardly evaluated by coupling the models of the redistributed stress, stress-dependent closure and the cubic law. A computer program, UDEC (Universal Distinct Element Code), is used to estimate the relation between normal stress, closure, and the disturbed stress after excavation. Linking the model of redistribution stresses and closure, the variation of apertures in the excavation’s disturbance zone can be obtained and the change of hydraulic conductivity estimated by the cubic law. Results show that the effect of the fracture parameters on the permeability changes and the redistributed stresses is the principal cause of hydraulic conductivity changes. Furthermore, large increases in tangential stresses result in the closure of fractures, so that excavation is not the immediate cause of groundwater surges. In addition, reductions in radial and increases in tangential hydraulic conductivity form a permeable excavation disturbance zone around the tunnel. This axial channel would become a diversion of regional groundwater, causing the huge seepage at the intersection of the fractured zone. Ó 2008 Elsevier Ltd. All rights reserved.
Contents 1. 2.
3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integrated model development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Stress-dependent closure of aperture in fractured rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Redistributed stresses after excavating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Disturbed hydraulic conductivity around tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Deformation of a single fracture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Stress-dependent hydraulic conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Aperture closure in fractured rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Stress after excavating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. Initial aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4. Radius of tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
* Corresponding author. Tel.: +886 62757575; fax: +886 62380421. E-mail address: [email protected] (C.-H. Lee). 0886-7798/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2008.06.003
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1. Introduction The Syueshan tunnel, the fourth longest in the world, is located in the northeast of Taiwan (Fig. 1) and finally opened to the public on June 16, 2006 after a 15-year construction. The tunnel is 12.9km long and penetrates through the Syueshan Mountain Range, encountering many complicated geological conditions along the tunnel alignment, where there are several folds and faults. There were 42 collapses in the pilot tunnel and 48 collapses in the main tunnel during construction, and the major causes were the seepage of groundwater. There were many times when the TBM, tunnel boring machine, was badly buried in major collapses after huge groundwater surges (TANEEB, 1999). Even at the time of writing, six months after opening, there are groundwater leakages in many sections of the tunnel. There are not only caused by the fractured zones or faults, but also by the disturbance zone caused by the excavation process. The Syueshan tunnel passes through several stratums, including Fangchiao, Makang, Tatungshan, Tsuku, Kankou, and Szenleng
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Sandstone, and major geological structures, including the Yingtzulai Syn-cline fold, Taotiaotzu Syncline fold, Shihtsao fault, Shihpai fault, Paling fault, Shanghsin fault, and the Chingyin fault, from west to east as shown in Fig. 2, and there are five major faults during the last 3 km in the east end of the tunnel. Moreover, this area is located on the Szenleng sandstone, which is part of Eocene formation series. The color of this sandstone is mainly gray to white, occasionally dark gray, and is formed of quartzite particles which range in size from fine to medium grains. The Szeleng Sandstone mainly consists of slightly metamorphosed quartzitic sandstone and argillite, occasionally interbedded with carbonaceous shale. Quartzitic sandstone appears in relatively thick layers, whereas the thickness of the interbedding layer, argillite or carbonaceous shale, varies from a few millimeters to a few meters (Cheng and Chang, 1998; Tseng et al., 2001; Liu et al., 2005). Szenleng sandstone is sturdy because its major component is quartz, and thus it is hard, brittle, and abrasive. Thus, Szenleng sandstone causes a lot of wear to TBM drilling bits and disc cutters. In addition, this area is located in the north-eastern part of the
Fig. 1. Location of Syueshan tunnel.
Fig. 2. Geological profile of the Shueshan tunnel (after Tseng et al., 2001).
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Table 1 Parameters of rock mass and fractures (TANEEB, 1990, 1991, 1997, 1999) Parameters of rock mass Bulk modulus Rock density Shear modulus Cohesion Friction angle Tensile strength Normal stiffness Shear stiffness
1.36 108 Pa 2600 kg/m3 0.89 108 Pa 1.085 107 Pa 30° 3.319 106 Pa 19.68 MPa/m 5.68 MPa/m
Parameters of fractures on cross-section Orientation Space Initial aperture
59°, 84° 10 m 0.2 mm
Shui-Shan mountains, which is strongly influenced by the Okinawa Trough expansion. In turn, many previously unrecorded strike slip faults were observed along this tunnel, and the five major normal faults cross this tunnel conduce to many fractured zones. It means that the rock mass at the east portal section of the Shueshan tunnel is highly fractured, especially in the fault zones. During the excavation of the pilot tunnel, the TBM was buried 13 times because of collapses and groundwater leakage. The most series damage occurred in the 10th collapses, when it took 221 days to dig out the TBM. In order to find out the reason of this groundwater gush problem, there were many geological investigations and field experiments in the Szenleng sandstone. Therefore, the 10th TBM burial is chosen to be one case. On the other hand, to compare with a different tunnel depth, the 7th TBM burial is chosen as the second case. These two cases are both located in Szeleng sandstone and the difference between them is the depth and the initial stress; the depth of case 1 is 185 m and that of case 2 is 330 m. The mechanical parameters of rock mass and fractures were obtained from both the route selection study report (TANEEB, 1990, 1991) and in the report on the water gush problem (TANEEB, 1997, 1999), and are shown in Table 1. Based on the parameters, a proposed model has been provided to consider the influence of effective stress redistribution induced by excavation and the related variance of hydraulic conductivity after cylindrical opening in a fractured rock mass. 2. Integrated model development The integrated model is developed to estimate the stressdependent closure of fractures and changes in hydraulic conductivity around the tunnel due to excavation. The disturbance of these openings is mainly because the destruction of the rock structure leads to variation in the stresses, and these changes lead to the deformation and displacement of rock mass. In addition to the mechanical problems, these alterations in fractures also result in new hydraulic properties. The condition of loading and unloading is the major factor in fracture aperture closure in rock mass, and these fractures are the main passages of groundwater. There are three major steps necessary in order to estimate the stress-dependent closure and hydraulic conductivity due to excavation. The flow chart is described in following and shown in Fig. 3. 2.1. Stress-dependent closure of aperture in fractured rocks The relationship between closure and stress was often assumed to be linear in both the continuum (Pusch, 1989; Bai and Elsworth, 1993; Liu et al., 1999; Cai and Kaiser, 2005) and discrete approaches (Goodman and Shi, 1985; Jing et al., 2001). However, Goodman (1976) contains the results of some simple tests to propose a hyperbolic relation between normal stress and normal
Fig. 3. Flow chart for determining the stress-dependent hydraulic conductivity in fractured rocks.
closure. When loading is applied on fractures, a few contacts on the fractures wall would deform at first, and fissure occurs or breaks, then more contacts increase the stiffness. The hyperbolic relation is different from the linear one, but the actual relation is difficult to determine in fractured rocks and it is hardly worth obtaining the deformation of each fracture. In this paper, the representative hyperbolic normal stress–closure curve of the specific fractured rock model is acquired by the program, UDEC (Universal Distinct Element Code). 2.2. Redistributed stresses after excavating Assuming that the change in fracture apertures in the rock mass follows hyperbolic curve, and the hydraulic conductivity variation is solely dependent on the aperture, the disturbance caused by excavating can be estimated by considering the redistributed stresses (Ivars, 2006; Li, 2006). In contrast to the linear relationship, the hyperbolic one is a more practical and serviceable approach. In order to estimate the variation of aperture closure, the UDEC computer program is also applied to evaluate the redistribution stresses after excavation. By linking the variation of stress and relation between normal stress and closure, the spatial closure is obtained. 2.3. Disturbed hydraulic conductivity around tunnel Based on the former result, we assume that the matrix is impermeable and the anisotropic hydraulic conductivity of fractured rocks is dependent on the orientation and closure of fractures. The disturbed hydraulic conductivity around the tunnel is estimated by the aperture of fractures and the cubic law (Witherspoon et al., 1980), which is an idealized flow along an open fracture in terms of the flow between a pair of smooth parallel plates. 2.4. Deformation of a single fracture The hydraulic conductivity of a single fracture is governed by several factors, such as aperture, roughness and filler, and it is difficult to measure. To be simplified, an equivalent hydraulic aper-
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ture b, assumed to be in parallel fracture and with the properties of the fluid, is used to describe the capability of fluid conductivity in real fractures (Witherspoon et al., 1980).
Kf ¼
qw gb2 12l
ð1Þ
where Kf is the hydraulic conductivity of the fracture, qw is the density of water, g is the gravitational acceleration, and l is the kinematic viscosity. Meanwhile, a discontinuity subjected to increases in normal stress and shear stress exhibits local normal displacements and shear displacements, which may be expected to depend on the geometry, strength, deformability, and other mechanical properties of the rock matrix and fractures. Goodman (1976) contains the results of some simple tests which find that fracture closure increases with stress but approximates to a limit to propose the following hyperbolic relation between normal stress rn and normal displacement Dv
rn ¼ rni þ Rrni
t Dv Dv < Dvmax Dvmax Dv
ð2Þ
where rni is the initial seating pressure such that Dr = rn rni, Dvmax is the maximum normal displacement produced by rn increased from the specified seating pressure, and parameters R and t are determined experimentally. However, sometimes even though the parameters R and t are fitted by Dr and Dv, the maximum closure, Dvmax, is difficult to obtain in experiments. Bandis et al. (1983) investigated the suitability of Eq. (2) for modeling a compression test on the unweathered fractures to identify certain limitations in the hyperbolic relation. They proposed an alternative expression that gives the normal stress rn for a specific small initial seating stress rni as follows
rn rni ¼
Dv a bDv
ð3Þ
where a and b are constant parameters. As shown in Fig. 4, in contrast to the loading curve, the unloading stress–opening curves are also hyperbolic, but the hysteresis effect means that the opening would not reach the initiation, and the first, second and third cycles are each of similar shapes. In tunnel excavation, the fractures open and apertures increase when unloading. However, in a multiple regression analysis, Bandis et al. (1983) found the maximum closure Dvmax could be estimated from the compressive strength rd of the rock as follows
Dvmax R
rd
S
ei
ð4Þ
where ei is the initial aperture and in mm, rd is in MPa, and the empirical parameters R and S are as tabulated above. Because the unloading curve is difficultly obtainable, we assumed that the ratio of unloading and loading closure is constant and the maximum closure reduces as a result of hysteresis effect. This ratio is assumed as the maximum closure ratio of the 2nd and 1st circles. That is written as
0:65 rd 0:03 eu 4:46 ei rd ¼ 0:68 ¼ 0:52 el ei rd 8:57 e
ð5Þ
Fig. 4. Static diagram of normal stresses rn versus discontinuity closure Dv for unweathered discontinuities in a range of rock types for three loading cycles; experimental data points omitted (after Bandis et al., 1983).
2.5. Stress-dependent hydraulic conductivity In fractured rocks, the hydraulic conductivity of the matrix is much lower than for the fractures. The fluid flow in the matrix can be neglected and a rock mass be assumed to possess n families of plane, parallel and constant width fractures with different orientations and densities. Following Castillo (1972), the flux, Q, across the segment can be defined as
Q¼
n X bi ABðV i NÞ si i¼1
ð6Þ
where bi and si are fracture aperture and spacing, respectively; A is the segment length; B is the thickness (perpendicular to the section); Vi is the fluid velocity vector in the fractures; and N is the normal vector. If the medium is continuous, VN, the velocity in the direction of N, could be written as
V¼
Q AB
ð7Þ
Combining Eqs. (6) and (7) gives rise to
Q¼
n X bi V i cos ai si i¼1
ð8Þ
where ai is the angle between the direction of N and the strike of the fractures. Applying Darcy’s law, we obtain
V ¼ K N rh V i ¼ K i rh cos ai
ð9Þ ð10Þ
i
where eu is unloading closure increment after the maximum closure, el is the closure when loading. The unit of both the aperture is mm. To integrate Eq. (3) with Eq. (5), the loading and unloading curves could be obtained by a set of normal stress and closure data.
where h is the total head and Ki is the hydraulic conductivity in the i direction. Substituting Eqs. (9) and (10) into Eq. (8) yields (Liu et al., 1999)
KN ¼
n X bi K i cos2 ai si i¼1
ð11Þ
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Fig. 6. Normal stress versus fracture closure on loading and unloading (data from Table 1).
Fig. 5. The model assumes an applied loading of rN and two fractures with initial aperture of b1 = b2 = 0.2 mm.
Table 2 Empirical parameters in Eq. (4) (Bandis et al., 1983) Parameter
Cycle 1
Cycle 2
Cycle 3
R S
8.57 0.68
4.46 0.65
6.41 0.72
When loading or unloading is applied in fractured rocks, aperture change is the major factor which induces the variation in hydraulic conductivity. The aperture variation is dependent upon the loading or unloading caused by excavation. An example is tested with two fractures, as shown in Fig. 5, by assuming that the relation between normal stress rn and closure follows Eq. (3) with constant a = 15 and b = 10. The hysteresis ratio is according to Eq. (5) and the parameters in Table 2, where the initial aperture is 0.2 mm and the uniaxial compressive strength of the intact rock is 150 MPa. The result of the relation between normal stress and aperture is shown in Fig. 6. The closure of each fracture could be determined in two samples with h = 30° and h = 90° when loading. And integrate the cubic law to the closure, the stress dependent hydraulic conductivity is shown in Fig. 7a and b. Both he figures show the apparent equivalent continuous hydraulic conductivity of rocks with two fractures in different angles, and the aperture and hydraulic conductivity of each fracture decreased when loading applied. In this two figures, aperture closure while stress is applied makes the hydraulic conductivity decrease and the other factor is the orientation of fractures. Because the closure is dependent on the normal stress, closure and variance of hydraulic conductivity of the fracture which parallel to the stress is zero (Fig. 7b). 2.6. Aperture closure in fractured rocks Relation between aperture closure and stress is governed by factors of fracture, and there is much difficulty in making an accurate forecast, or at least in experiments. The deformation of frac-
Fig. 7. Variation in hydraulic conductivity with two direction of medium fractures with included angles: (a) h = 30° and (b) h = 90°.
ture apertures in fractured rocks is considerably more complex than when considering a single fracture. Strain, displacement, and rotation of rock blocks also affect the aperture closure at the same time, and an in situ experiment is both difficult and costly. In this paper, the aperture variation in fractured rocks is estimated by using a code, the UDEC. UDEC (Universal Distinct Element Code) (Itasca, 2004) is a discontinuous code that simulates either the quasi-static or dynamic response to loading of rock media containing multiple, intersecting joint structures. Because it is not limited to a particular type of problem or initial conditions, UDEC may be applied to any case where an understanding of the two-dimensional response of such structures is needed. It also provides rigid
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or deformable blocks, multiple material models, full dynamic capability, and high resolution graphics to expedite the modeling process. Solution parameters may be specified by the user to maximize the user’s control over the duration, extent, and efficiency of the model run. Instead of the linear stress–strain relation in porous-elastic models, it fits to the hyperbolic relation from the simulated results to approximate the real deformation. Because of these advantages, this code is chosen to forecast the closure of fractures in rock mass, as shown in Fig. 8. The rock mass includes fractures and blocks. By considering that the stresses derive from the weight of the rock itself and that the top, and the stresses on the boundary is given from the density of rock and depth. In addition, top and side of the model is a free boundary in horizontal and vertical direction, respectively. Then the variation in stress and aperture closure were obtained from the readout.
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After fitting to the hyperbolic curve (Eq. (3)) and Eq. (4), the representative loading and unloading curves of each set of fractures are acquired. 2.7. Stress after excavating When excavating in virgin rocks, the equilibrium of stresses in the rock mass is disrupted and the stresses are redistributed. By applying the theory of elasticity to the behavior of a rock mass, relations between the induced and virgin stresses can be determined for various conditions of excavation geometry and internal support pressure. However, elastic analyses can only be completely satisfactory if the material behaves in an elastic manner over most of the stress region. After tunneling, the variation of the radial and shear stresses on the walls of the opening is zero since it is a free surface, and the tangential stress varies by increasing other than falling quickly. When the tangential stress around the opening is greater than about one-half of the confined compressive strength, cracks will begin to form. There are usually some rock breakages due to construction and a zone of relaxation around the skin of the opening, but the new cracks are conspicuous in forming slabs parallel to the periphery. Bray (1967) assumed that the construction of the tunnel creates intolerable stress conditions that result in a failure of the rocks according to the Mohr–Coulomd theory and permit the analysis of the extent of failures, the plastic zone. The plastic behavior of the region near the tunnel has the effect of extending the influence of the tunnel considerably farther in the surrounding rocks. The fractured rock is considered as being constructed of rigid blocks in this study and fractures due to the deformation combined with the both in plastic model are unable to obtain (Shen and Barton, 1997). The redistribution stresses after excavation are also obtained from the same model by UDEC. The tunnel is added in the center of the rock mass and the stresses are recorded and combined with the stress–closure curve in the former section. Thus, the stress-dependent aperture and hydraulic conductivity could be obtained. 3. Results and discussion 3.1. Sensitivity analysis The parameters of fractures and the tunnel are the major factors which affect the disturbed stresses. These factors determine the hydraulic conductivity around the tunnel. In order to obtain the effect of these factors in this study, the results of cases with different parameters are taken to comprehend the divergence. Fractured rock models with a size of 100 m 100 m are built based on the mechanical parameters of Szeleng sandstone along the Syueshan tunnel (Table 1) and the radius of the tunnel is 2.4 m, the same as the pilot tunnel.
Fig. 8. Boundary statements of: (a) displacement and (b) initial stresses in concept model of the UDEC.
3.1.1. Orientation Fig. 9 shows three different orientations of fracture sets, with h = 0°, h = 45° and h = 90°. Because there is only one set fracture in our cases, the direction of hydraulic conductivity is the same as the orientation of the fracture. After excavating, there is a minimum hydraulic conductivity change in the fracture orientation on the wall and the direction of the maximum is vertical to the minimum. Since the radial stress decreases due to excavation, the normal stress in the direction vertical to the fractures is also decreased, so that the conductivity is raised. On the other hand, the increase in tangential stress varies in increasing but the aperture closed in the direction of fracture. The minimum hydraulic conductivity variation is in this direction on the wall.
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Fig. 9. Variation in hydraulic conductivity in three directions of fracture sets, h = 0°, h = 45° and h = 90°.
Fig. 10. Variation in hydraulic conductivity when h = 0° with different space, s = 5 m, s = 10 m and s = 20 m.
Fig. 11. Variation in hydraulic conductivity when h = 0° with different initial aperture, ei = 500 lm, ei = 200 lm and ei = 100 lm.
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3.1.2. Space The analysis in different spaces of fractures reveals that the stress change is the major divergence in distinct fracture space, and this factor makes the difference. The space, on the whole, makes the variance of stress decrease when it increases so that the hydraulic conductivity change is smaller, as shown in Fig. 10. Nevertheless, the difference of variation between these three cases is not obvious. 3.1.3. Initial aperture Initial aperture is an important factor in the normal stress–closure relation. The fracture with a bigger initial aperture is compressed more easily. Therefore, when loading is applied, more variance of hydraulic conductivity can be found. The initial aperture controls the magnitude and maximum closure and affects the hydraulic conductivity to a great extent (Fig. 11). 3.1.4. Radius of tunnel The radius of the tunnel decides the range of the excavation disturbance zone. When the tunnel is bigger, this zone would grow and the range of hydraulic conductivity changes is bigger. Fig. 12 shows that the variance in hydraulic conductivity in a tunnel exca-
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vation with the radius of either 5.4 m or 2.4 m, which is equal to the main tunnel and pilot tunnel of the Syueshan tunnel, respectively. 3.2. Case study Fig. 13 shows the variance in hydraulic conductivity in the major hydraulic direction (h = 71.5°), the average direction of two sets of fracture. In case 1, the largest increase in hydraulic conductivity in contrast to the initial state was on the opening wall of tunnel, and the range was from 0% to 5%, with the range of variance about three times that of the tunnel radius. In addition, the minimum variation occurred in the major directions of fractures on the opening wall (point A in Fig. 13a) because the increase in the tangential stresses limits the fractures opening in this direction. On the other hand, the hydraulic conductivity in the major direction, Kh=71.5°, increased in the area vertical to the major direction (point B in Fig. 13a) as result of the decrease in radial stress. In case 2, the increase in hydraulic conductivity around the opening wall is from 8% to 17% and the range of variance is about five times that of the tunnel radius. The minimum variance is located in the major hydraulic direction (point A0 ) and the
Fig. 12. Variation in hydraulic conductivity in the x-direction with different tunnel radius, R = 2.4 m and R = 5.4 m.
Fig. 13. Variation of hydraulic conductivity in h = 71.5° with the depth of: (a) 330 m, (b) 185 m.
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maximum is in the direction vertical to the point A (point B0 ). It is obvious that the variation and range of disturbed hydraulic conductivity of case 1 at the depth of 330 m are greater than those of case 2 at the depth of 185 m. This reason is because the initial stresses are bigger and the change of stress is larger in case 1. As a result, the effect of excavation is an increase in hydraulic conductivity in the tangential direction and a decrease in the radial direction. The major reason is that the redistributed stresses cause the fracture aperture to change. The most surprising result is that excavating dose not seems to increase the seepage of fracture outcrops. But the tangential stress increase and force the fractures to close. In the other hand, the radial stress decreases and this leads to the increase in tangential hydraulic conductivity, the change would not increase the leakage of groundwater directly, but a channel surrounding the tunnel is formed if there is a fractured zone or fault across the tunnel. Thus, regional groundwater could escape from this rapidly and cause huge seepage and collapse.
4. Conclusion Changes in the fracture aperture and hydraulic conductivity fields, due to the redistribution of stresses, can be predicted by the methodology developed in this study. The strength of this research is to introduce the hyperbolic relation between normal stress and aperture closure. Using UDEC to obtain this relation in fractured rocks enables better understanding of the connection between stresses changes and variation in hydraulic conductivity in a broad spectrum of rock masses. By simulating the initial aperture, orientation, space, radius of the tunnel and initial stress, we are able to derive the variation in hydraulic conductivity and the distribution cause by these factors. Because of stresses change in the radial and tangential directions, the permeability of rock mass is increased in the tangential direction and decreased in the radial direction. The methodology is applied to the Syueshan tunnel, Taiwan and the case study shows the feasibility of the method in engineering applications. A notable finding is that the excavating would not increase the seepage of fractures directly because the increased tangential stresses cause the closure of fractures. At the same time, the reduction in radial stress causes the tangential permeability to rise and then makes a tube channel around the tunnel. Even though this channel does not influence the seepage in the model, it may become an indirect factor when this axial ‘‘tube” is connected to any permeable structure cross the tunnel. In addition, the channel could link other aquifers and then magnify the range of influence, increasing the seepage and thus causing serious damage.
Acknowledgments This study was supported in part by National Science Council, Taiwan (NSC 95-2221-E-006-291) and data supported from Sinotech, Taiwan. The support is gratefully acknowledged. References Bai, M., Elsworth, D., 1993. Transient poroelastic response of equivalent porous media over a mining panel. Eng. Geol. 35, 49–64. Bandis, S.C., Lumsden, A.C., Barton, N.R., 1983. Fundamentals of rock joint deformation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 20 (6), 249–268. Bray, J.W., 1967. A study of jointed and fractured rock, II. Theory of limiting equilibrium. Rock Mech. Eng. Geol. 5, 197–216. Cai, M., Kaiser, P.K., 2005. Assessment of excavation damaged zone using a micromechanics model. Tunn. Undergr. Space Technol. 20 (4), 301–310. Castillo, E., 1972. Mathematical model for two-dimensional percolation through fissured rock. In: Proceedings of International Symposium on Percolation through Fissured Rock, Stuttgart, Germany, T1-D1-7. Cheng, W.-L., Chang, W.-C., 1998. Case study of TBM construction in the highly broken and water gush zone. Geotech. Technol. 66, 5–24. Goodman, R.E., 1976. Methods of Geological Engineering in Discontinuous Rock. West Publishing Co.. 58-90. Goodman, R.E., Shi, G., 1985. Block Theory and Its Application to Rock Engineering. Prentice-Hall. Itasca, 2004. UDEC Manuals, Itasca Consulting Group Inc., Minneapolis. Ivars, D.M., 2006. Water inflow into excavations in fractured rock – a threedimensional hydro-mechanical numerical study. Int. J. Rock Mech. Min. Sci. 43, 705–725. Jing, L., Ma, Y., Fang, Z., 2001. Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. Int. J. Rock Mech. Min. Sci. 38, 343–355. Li, C.C., 2006. Disturbance of mining operations to a deep underground workshop. Tunn. Undergr. Space Technol. 21 (1), 1–8. Liu, J., Elsworth, D., Brady, B.H., 1999. Linking stress-dependent effective porosity and hydraulic conductivity fields to RMR. Int. J. Rock Mech. Min. Sci. 36, 581– 596. Liu, T.K., Chen, C.H., Yang, T.F., Lee, M., 2005. Tritium concentrations and radiocarbon ages of gushing groundwater from Hsuehshan Tunnel, northern Taiwan. TAO 16 (4), 909–917. Pusch, R., 1989. Alteration of the hydraulic conductivity of rock by tunnel excavation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 26 (1), 79–83. Shen, B., Barton, N., 1997. The disturbed zone around tunnels in jointed rock masses. Int. J. Rock Mech. Min. Sci. 34, 117–125. Taiwan Area National Expressway Engineering Bureau, 1990. Nankang-Ilan Expressway Route Selection Study Geological Investigation for the Pinglin Tunnel, Final Report. Taiwan Area National Expressway Engineering Bureau, 1991. Geological Investigation Final Report for Pinlin-Taochen Section at basic design stage of National Taipei-Ilan Expressway. Taiwan Area National Expressway Engineering Bureau, 1997. Brief Report of Geological Investigation for the Pinglin Tunnel pilot tunnel construction project of National Taipei-Ilan Expressway. Taiwan Area National Expressway Engineering Bureau, 1999. Second Year Work Result Report on Water gush Problem Assessment and Investigation Services for Pinglin Tunnel, National Taipei-Ilan Expressway Project. Tseng, D.J., Tsai, B.R., Chang, L.C., 2001. A case study on ground treatment for a rock tunnel with high groundwater ingression in Taiwan. Tunn. Undergr. Space Technol. 16 (3), 175–183. Witherspoon, P.A., Wang, Y.S.Y., Gale, J.E., 1980. Validity of cubic law for fluid flow in a deformed fracture. W.R.R 16, 1016–1024.
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Review
An approach to assessing the hydraulic conductivity disturbance in fractured rocks around the Syueshan tunnel, Taiwan Hung-I Lin, Cheng-Haw Lee * Department of Resources Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 14 February 2008 Received in revised form 22 June 2008 Accepted 24 June 2008 Available online 15 August 2008 Keywords: Fractured rock Seepage UDEC Syueshan tunnel Hydraulic conductivity
a b s t r a c t The Syueshan tunnel, a long and recently completed tunnel in Taiwan, suffered many collapses due to huge groundwater surges during excavation. Thus, variations in hydrological conditions in fractured rocks after excavation have become a topic of interest in the field. A proposed model has been developed to predict the disturbance of hydraulic conductivity caused by excavating around the Syueshan tunnel in fractured rocks. The closure of fractures is assumed to be the sole factor that causes hydraulic conductivity changes, and a hyperbolic relation between normal stress and closure is introduced instead of using a linear relation in this estimation. The magnitude and range of disturbed hydraulic conductivity are straightforwardly evaluated by coupling the models of the redistributed stress, stress-dependent closure and the cubic law. A computer program, UDEC (Universal Distinct Element Code), is used to estimate the relation between normal stress, closure, and the disturbed stress after excavation. Linking the model of redistribution stresses and closure, the variation of apertures in the excavation’s disturbance zone can be obtained and the change of hydraulic conductivity estimated by the cubic law. Results show that the effect of the fracture parameters on the permeability changes and the redistributed stresses is the principal cause of hydraulic conductivity changes. Furthermore, large increases in tangential stresses result in the closure of fractures, so that excavation is not the immediate cause of groundwater surges. In addition, reductions in radial and increases in tangential hydraulic conductivity form a permeable excavation disturbance zone around the tunnel. This axial channel would become a diversion of regional groundwater, causing the huge seepage at the intersection of the fractured zone. Ó 2008 Elsevier Ltd. All rights reserved.
Contents 1. 2.
3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integrated model development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Stress-dependent closure of aperture in fractured rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Redistributed stresses after excavating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Disturbed hydraulic conductivity around tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Deformation of a single fracture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Stress-dependent hydraulic conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Aperture closure in fractured rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Stress after excavating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. Initial aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4. Radius of tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
* Corresponding author. Tel.: +886 62757575; fax: +886 62380421. E-mail address: [email protected] (C.-H. Lee). 0886-7798/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2008.06.003
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1. Introduction The Syueshan tunnel, the fourth longest in the world, is located in the northeast of Taiwan (Fig. 1) and finally opened to the public on June 16, 2006 after a 15-year construction. The tunnel is 12.9km long and penetrates through the Syueshan Mountain Range, encountering many complicated geological conditions along the tunnel alignment, where there are several folds and faults. There were 42 collapses in the pilot tunnel and 48 collapses in the main tunnel during construction, and the major causes were the seepage of groundwater. There were many times when the TBM, tunnel boring machine, was badly buried in major collapses after huge groundwater surges (TANEEB, 1999). Even at the time of writing, six months after opening, there are groundwater leakages in many sections of the tunnel. There are not only caused by the fractured zones or faults, but also by the disturbance zone caused by the excavation process. The Syueshan tunnel passes through several stratums, including Fangchiao, Makang, Tatungshan, Tsuku, Kankou, and Szenleng
223
Sandstone, and major geological structures, including the Yingtzulai Syn-cline fold, Taotiaotzu Syncline fold, Shihtsao fault, Shihpai fault, Paling fault, Shanghsin fault, and the Chingyin fault, from west to east as shown in Fig. 2, and there are five major faults during the last 3 km in the east end of the tunnel. Moreover, this area is located on the Szenleng sandstone, which is part of Eocene formation series. The color of this sandstone is mainly gray to white, occasionally dark gray, and is formed of quartzite particles which range in size from fine to medium grains. The Szeleng Sandstone mainly consists of slightly metamorphosed quartzitic sandstone and argillite, occasionally interbedded with carbonaceous shale. Quartzitic sandstone appears in relatively thick layers, whereas the thickness of the interbedding layer, argillite or carbonaceous shale, varies from a few millimeters to a few meters (Cheng and Chang, 1998; Tseng et al., 2001; Liu et al., 2005). Szenleng sandstone is sturdy because its major component is quartz, and thus it is hard, brittle, and abrasive. Thus, Szenleng sandstone causes a lot of wear to TBM drilling bits and disc cutters. In addition, this area is located in the north-eastern part of the
Fig. 1. Location of Syueshan tunnel.
Fig. 2. Geological profile of the Shueshan tunnel (after Tseng et al., 2001).
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Table 1 Parameters of rock mass and fractures (TANEEB, 1990, 1991, 1997, 1999) Parameters of rock mass Bulk modulus Rock density Shear modulus Cohesion Friction angle Tensile strength Normal stiffness Shear stiffness
1.36 108 Pa 2600 kg/m3 0.89 108 Pa 1.085 107 Pa 30° 3.319 106 Pa 19.68 MPa/m 5.68 MPa/m
Parameters of fractures on cross-section Orientation Space Initial aperture
59°, 84° 10 m 0.2 mm
Shui-Shan mountains, which is strongly influenced by the Okinawa Trough expansion. In turn, many previously unrecorded strike slip faults were observed along this tunnel, and the five major normal faults cross this tunnel conduce to many fractured zones. It means that the rock mass at the east portal section of the Shueshan tunnel is highly fractured, especially in the fault zones. During the excavation of the pilot tunnel, the TBM was buried 13 times because of collapses and groundwater leakage. The most series damage occurred in the 10th collapses, when it took 221 days to dig out the TBM. In order to find out the reason of this groundwater gush problem, there were many geological investigations and field experiments in the Szenleng sandstone. Therefore, the 10th TBM burial is chosen to be one case. On the other hand, to compare with a different tunnel depth, the 7th TBM burial is chosen as the second case. These two cases are both located in Szeleng sandstone and the difference between them is the depth and the initial stress; the depth of case 1 is 185 m and that of case 2 is 330 m. The mechanical parameters of rock mass and fractures were obtained from both the route selection study report (TANEEB, 1990, 1991) and in the report on the water gush problem (TANEEB, 1997, 1999), and are shown in Table 1. Based on the parameters, a proposed model has been provided to consider the influence of effective stress redistribution induced by excavation and the related variance of hydraulic conductivity after cylindrical opening in a fractured rock mass. 2. Integrated model development The integrated model is developed to estimate the stressdependent closure of fractures and changes in hydraulic conductivity around the tunnel due to excavation. The disturbance of these openings is mainly because the destruction of the rock structure leads to variation in the stresses, and these changes lead to the deformation and displacement of rock mass. In addition to the mechanical problems, these alterations in fractures also result in new hydraulic properties. The condition of loading and unloading is the major factor in fracture aperture closure in rock mass, and these fractures are the main passages of groundwater. There are three major steps necessary in order to estimate the stress-dependent closure and hydraulic conductivity due to excavation. The flow chart is described in following and shown in Fig. 3. 2.1. Stress-dependent closure of aperture in fractured rocks The relationship between closure and stress was often assumed to be linear in both the continuum (Pusch, 1989; Bai and Elsworth, 1993; Liu et al., 1999; Cai and Kaiser, 2005) and discrete approaches (Goodman and Shi, 1985; Jing et al., 2001). However, Goodman (1976) contains the results of some simple tests to propose a hyperbolic relation between normal stress and normal
Fig. 3. Flow chart for determining the stress-dependent hydraulic conductivity in fractured rocks.
closure. When loading is applied on fractures, a few contacts on the fractures wall would deform at first, and fissure occurs or breaks, then more contacts increase the stiffness. The hyperbolic relation is different from the linear one, but the actual relation is difficult to determine in fractured rocks and it is hardly worth obtaining the deformation of each fracture. In this paper, the representative hyperbolic normal stress–closure curve of the specific fractured rock model is acquired by the program, UDEC (Universal Distinct Element Code). 2.2. Redistributed stresses after excavating Assuming that the change in fracture apertures in the rock mass follows hyperbolic curve, and the hydraulic conductivity variation is solely dependent on the aperture, the disturbance caused by excavating can be estimated by considering the redistributed stresses (Ivars, 2006; Li, 2006). In contrast to the linear relationship, the hyperbolic one is a more practical and serviceable approach. In order to estimate the variation of aperture closure, the UDEC computer program is also applied to evaluate the redistribution stresses after excavation. By linking the variation of stress and relation between normal stress and closure, the spatial closure is obtained. 2.3. Disturbed hydraulic conductivity around tunnel Based on the former result, we assume that the matrix is impermeable and the anisotropic hydraulic conductivity of fractured rocks is dependent on the orientation and closure of fractures. The disturbed hydraulic conductivity around the tunnel is estimated by the aperture of fractures and the cubic law (Witherspoon et al., 1980), which is an idealized flow along an open fracture in terms of the flow between a pair of smooth parallel plates. 2.4. Deformation of a single fracture The hydraulic conductivity of a single fracture is governed by several factors, such as aperture, roughness and filler, and it is difficult to measure. To be simplified, an equivalent hydraulic aper-
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225
ture b, assumed to be in parallel fracture and with the properties of the fluid, is used to describe the capability of fluid conductivity in real fractures (Witherspoon et al., 1980).
Kf ¼
qw gb2 12l
ð1Þ
where Kf is the hydraulic conductivity of the fracture, qw is the density of water, g is the gravitational acceleration, and l is the kinematic viscosity. Meanwhile, a discontinuity subjected to increases in normal stress and shear stress exhibits local normal displacements and shear displacements, which may be expected to depend on the geometry, strength, deformability, and other mechanical properties of the rock matrix and fractures. Goodman (1976) contains the results of some simple tests which find that fracture closure increases with stress but approximates to a limit to propose the following hyperbolic relation between normal stress rn and normal displacement Dv
rn ¼ rni þ Rrni
t Dv Dv < Dvmax Dvmax Dv
ð2Þ
where rni is the initial seating pressure such that Dr = rn rni, Dvmax is the maximum normal displacement produced by rn increased from the specified seating pressure, and parameters R and t are determined experimentally. However, sometimes even though the parameters R and t are fitted by Dr and Dv, the maximum closure, Dvmax, is difficult to obtain in experiments. Bandis et al. (1983) investigated the suitability of Eq. (2) for modeling a compression test on the unweathered fractures to identify certain limitations in the hyperbolic relation. They proposed an alternative expression that gives the normal stress rn for a specific small initial seating stress rni as follows
rn rni ¼
Dv a bDv
ð3Þ
where a and b are constant parameters. As shown in Fig. 4, in contrast to the loading curve, the unloading stress–opening curves are also hyperbolic, but the hysteresis effect means that the opening would not reach the initiation, and the first, second and third cycles are each of similar shapes. In tunnel excavation, the fractures open and apertures increase when unloading. However, in a multiple regression analysis, Bandis et al. (1983) found the maximum closure Dvmax could be estimated from the compressive strength rd of the rock as follows
Dvmax R
rd
S
ei
ð4Þ
where ei is the initial aperture and in mm, rd is in MPa, and the empirical parameters R and S are as tabulated above. Because the unloading curve is difficultly obtainable, we assumed that the ratio of unloading and loading closure is constant and the maximum closure reduces as a result of hysteresis effect. This ratio is assumed as the maximum closure ratio of the 2nd and 1st circles. That is written as
0:65 rd 0:03 eu 4:46 ei rd ¼ 0:68 ¼ 0:52 el ei rd 8:57 e
ð5Þ
Fig. 4. Static diagram of normal stresses rn versus discontinuity closure Dv for unweathered discontinuities in a range of rock types for three loading cycles; experimental data points omitted (after Bandis et al., 1983).
2.5. Stress-dependent hydraulic conductivity In fractured rocks, the hydraulic conductivity of the matrix is much lower than for the fractures. The fluid flow in the matrix can be neglected and a rock mass be assumed to possess n families of plane, parallel and constant width fractures with different orientations and densities. Following Castillo (1972), the flux, Q, across the segment can be defined as
Q¼
n X bi ABðV i NÞ si i¼1
ð6Þ
where bi and si are fracture aperture and spacing, respectively; A is the segment length; B is the thickness (perpendicular to the section); Vi is the fluid velocity vector in the fractures; and N is the normal vector. If the medium is continuous, VN, the velocity in the direction of N, could be written as
V¼
Q AB
ð7Þ
Combining Eqs. (6) and (7) gives rise to
Q¼
n X bi V i cos ai si i¼1
ð8Þ
where ai is the angle between the direction of N and the strike of the fractures. Applying Darcy’s law, we obtain
V ¼ K N rh V i ¼ K i rh cos ai
ð9Þ ð10Þ
i
where eu is unloading closure increment after the maximum closure, el is the closure when loading. The unit of both the aperture is mm. To integrate Eq. (3) with Eq. (5), the loading and unloading curves could be obtained by a set of normal stress and closure data.
where h is the total head and Ki is the hydraulic conductivity in the i direction. Substituting Eqs. (9) and (10) into Eq. (8) yields (Liu et al., 1999)
KN ¼
n X bi K i cos2 ai si i¼1
ð11Þ
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Fig. 6. Normal stress versus fracture closure on loading and unloading (data from Table 1).
Fig. 5. The model assumes an applied loading of rN and two fractures with initial aperture of b1 = b2 = 0.2 mm.
Table 2 Empirical parameters in Eq. (4) (Bandis et al., 1983) Parameter
Cycle 1
Cycle 2
Cycle 3
R S
8.57 0.68
4.46 0.65
6.41 0.72
When loading or unloading is applied in fractured rocks, aperture change is the major factor which induces the variation in hydraulic conductivity. The aperture variation is dependent upon the loading or unloading caused by excavation. An example is tested with two fractures, as shown in Fig. 5, by assuming that the relation between normal stress rn and closure follows Eq. (3) with constant a = 15 and b = 10. The hysteresis ratio is according to Eq. (5) and the parameters in Table 2, where the initial aperture is 0.2 mm and the uniaxial compressive strength of the intact rock is 150 MPa. The result of the relation between normal stress and aperture is shown in Fig. 6. The closure of each fracture could be determined in two samples with h = 30° and h = 90° when loading. And integrate the cubic law to the closure, the stress dependent hydraulic conductivity is shown in Fig. 7a and b. Both he figures show the apparent equivalent continuous hydraulic conductivity of rocks with two fractures in different angles, and the aperture and hydraulic conductivity of each fracture decreased when loading applied. In this two figures, aperture closure while stress is applied makes the hydraulic conductivity decrease and the other factor is the orientation of fractures. Because the closure is dependent on the normal stress, closure and variance of hydraulic conductivity of the fracture which parallel to the stress is zero (Fig. 7b). 2.6. Aperture closure in fractured rocks Relation between aperture closure and stress is governed by factors of fracture, and there is much difficulty in making an accurate forecast, or at least in experiments. The deformation of frac-
Fig. 7. Variation in hydraulic conductivity with two direction of medium fractures with included angles: (a) h = 30° and (b) h = 90°.
ture apertures in fractured rocks is considerably more complex than when considering a single fracture. Strain, displacement, and rotation of rock blocks also affect the aperture closure at the same time, and an in situ experiment is both difficult and costly. In this paper, the aperture variation in fractured rocks is estimated by using a code, the UDEC. UDEC (Universal Distinct Element Code) (Itasca, 2004) is a discontinuous code that simulates either the quasi-static or dynamic response to loading of rock media containing multiple, intersecting joint structures. Because it is not limited to a particular type of problem or initial conditions, UDEC may be applied to any case where an understanding of the two-dimensional response of such structures is needed. It also provides rigid
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or deformable blocks, multiple material models, full dynamic capability, and high resolution graphics to expedite the modeling process. Solution parameters may be specified by the user to maximize the user’s control over the duration, extent, and efficiency of the model run. Instead of the linear stress–strain relation in porous-elastic models, it fits to the hyperbolic relation from the simulated results to approximate the real deformation. Because of these advantages, this code is chosen to forecast the closure of fractures in rock mass, as shown in Fig. 8. The rock mass includes fractures and blocks. By considering that the stresses derive from the weight of the rock itself and that the top, and the stresses on the boundary is given from the density of rock and depth. In addition, top and side of the model is a free boundary in horizontal and vertical direction, respectively. Then the variation in stress and aperture closure were obtained from the readout.
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After fitting to the hyperbolic curve (Eq. (3)) and Eq. (4), the representative loading and unloading curves of each set of fractures are acquired. 2.7. Stress after excavating When excavating in virgin rocks, the equilibrium of stresses in the rock mass is disrupted and the stresses are redistributed. By applying the theory of elasticity to the behavior of a rock mass, relations between the induced and virgin stresses can be determined for various conditions of excavation geometry and internal support pressure. However, elastic analyses can only be completely satisfactory if the material behaves in an elastic manner over most of the stress region. After tunneling, the variation of the radial and shear stresses on the walls of the opening is zero since it is a free surface, and the tangential stress varies by increasing other than falling quickly. When the tangential stress around the opening is greater than about one-half of the confined compressive strength, cracks will begin to form. There are usually some rock breakages due to construction and a zone of relaxation around the skin of the opening, but the new cracks are conspicuous in forming slabs parallel to the periphery. Bray (1967) assumed that the construction of the tunnel creates intolerable stress conditions that result in a failure of the rocks according to the Mohr–Coulomd theory and permit the analysis of the extent of failures, the plastic zone. The plastic behavior of the region near the tunnel has the effect of extending the influence of the tunnel considerably farther in the surrounding rocks. The fractured rock is considered as being constructed of rigid blocks in this study and fractures due to the deformation combined with the both in plastic model are unable to obtain (Shen and Barton, 1997). The redistribution stresses after excavation are also obtained from the same model by UDEC. The tunnel is added in the center of the rock mass and the stresses are recorded and combined with the stress–closure curve in the former section. Thus, the stress-dependent aperture and hydraulic conductivity could be obtained. 3. Results and discussion 3.1. Sensitivity analysis The parameters of fractures and the tunnel are the major factors which affect the disturbed stresses. These factors determine the hydraulic conductivity around the tunnel. In order to obtain the effect of these factors in this study, the results of cases with different parameters are taken to comprehend the divergence. Fractured rock models with a size of 100 m 100 m are built based on the mechanical parameters of Szeleng sandstone along the Syueshan tunnel (Table 1) and the radius of the tunnel is 2.4 m, the same as the pilot tunnel.
Fig. 8. Boundary statements of: (a) displacement and (b) initial stresses in concept model of the UDEC.
3.1.1. Orientation Fig. 9 shows three different orientations of fracture sets, with h = 0°, h = 45° and h = 90°. Because there is only one set fracture in our cases, the direction of hydraulic conductivity is the same as the orientation of the fracture. After excavating, there is a minimum hydraulic conductivity change in the fracture orientation on the wall and the direction of the maximum is vertical to the minimum. Since the radial stress decreases due to excavation, the normal stress in the direction vertical to the fractures is also decreased, so that the conductivity is raised. On the other hand, the increase in tangential stress varies in increasing but the aperture closed in the direction of fracture. The minimum hydraulic conductivity variation is in this direction on the wall.
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Fig. 9. Variation in hydraulic conductivity in three directions of fracture sets, h = 0°, h = 45° and h = 90°.
Fig. 10. Variation in hydraulic conductivity when h = 0° with different space, s = 5 m, s = 10 m and s = 20 m.
Fig. 11. Variation in hydraulic conductivity when h = 0° with different initial aperture, ei = 500 lm, ei = 200 lm and ei = 100 lm.
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3.1.2. Space The analysis in different spaces of fractures reveals that the stress change is the major divergence in distinct fracture space, and this factor makes the difference. The space, on the whole, makes the variance of stress decrease when it increases so that the hydraulic conductivity change is smaller, as shown in Fig. 10. Nevertheless, the difference of variation between these three cases is not obvious. 3.1.3. Initial aperture Initial aperture is an important factor in the normal stress–closure relation. The fracture with a bigger initial aperture is compressed more easily. Therefore, when loading is applied, more variance of hydraulic conductivity can be found. The initial aperture controls the magnitude and maximum closure and affects the hydraulic conductivity to a great extent (Fig. 11). 3.1.4. Radius of tunnel The radius of the tunnel decides the range of the excavation disturbance zone. When the tunnel is bigger, this zone would grow and the range of hydraulic conductivity changes is bigger. Fig. 12 shows that the variance in hydraulic conductivity in a tunnel exca-
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vation with the radius of either 5.4 m or 2.4 m, which is equal to the main tunnel and pilot tunnel of the Syueshan tunnel, respectively. 3.2. Case study Fig. 13 shows the variance in hydraulic conductivity in the major hydraulic direction (h = 71.5°), the average direction of two sets of fracture. In case 1, the largest increase in hydraulic conductivity in contrast to the initial state was on the opening wall of tunnel, and the range was from 0% to 5%, with the range of variance about three times that of the tunnel radius. In addition, the minimum variation occurred in the major directions of fractures on the opening wall (point A in Fig. 13a) because the increase in the tangential stresses limits the fractures opening in this direction. On the other hand, the hydraulic conductivity in the major direction, Kh=71.5°, increased in the area vertical to the major direction (point B in Fig. 13a) as result of the decrease in radial stress. In case 2, the increase in hydraulic conductivity around the opening wall is from 8% to 17% and the range of variance is about five times that of the tunnel radius. The minimum variance is located in the major hydraulic direction (point A0 ) and the
Fig. 12. Variation in hydraulic conductivity in the x-direction with different tunnel radius, R = 2.4 m and R = 5.4 m.
Fig. 13. Variation of hydraulic conductivity in h = 71.5° with the depth of: (a) 330 m, (b) 185 m.
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maximum is in the direction vertical to the point A (point B0 ). It is obvious that the variation and range of disturbed hydraulic conductivity of case 1 at the depth of 330 m are greater than those of case 2 at the depth of 185 m. This reason is because the initial stresses are bigger and the change of stress is larger in case 1. As a result, the effect of excavation is an increase in hydraulic conductivity in the tangential direction and a decrease in the radial direction. The major reason is that the redistributed stresses cause the fracture aperture to change. The most surprising result is that excavating dose not seems to increase the seepage of fracture outcrops. But the tangential stress increase and force the fractures to close. In the other hand, the radial stress decreases and this leads to the increase in tangential hydraulic conductivity, the change would not increase the leakage of groundwater directly, but a channel surrounding the tunnel is formed if there is a fractured zone or fault across the tunnel. Thus, regional groundwater could escape from this rapidly and cause huge seepage and collapse.
4. Conclusion Changes in the fracture aperture and hydraulic conductivity fields, due to the redistribution of stresses, can be predicted by the methodology developed in this study. The strength of this research is to introduce the hyperbolic relation between normal stress and aperture closure. Using UDEC to obtain this relation in fractured rocks enables better understanding of the connection between stresses changes and variation in hydraulic conductivity in a broad spectrum of rock masses. By simulating the initial aperture, orientation, space, radius of the tunnel and initial stress, we are able to derive the variation in hydraulic conductivity and the distribution cause by these factors. Because of stresses change in the radial and tangential directions, the permeability of rock mass is increased in the tangential direction and decreased in the radial direction. The methodology is applied to the Syueshan tunnel, Taiwan and the case study shows the feasibility of the method in engineering applications. A notable finding is that the excavating would not increase the seepage of fractures directly because the increased tangential stresses cause the closure of fractures. At the same time, the reduction in radial stress causes the tangential permeability to rise and then makes a tube channel around the tunnel. Even though this channel does not influence the seepage in the model, it may become an indirect factor when this axial ‘‘tube” is connected to any permeable structure cross the tunnel. In addition, the channel could link other aquifers and then magnify the range of influence, increasing the seepage and thus causing serious damage.
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