1 Introduction

Tectonic activities in the Nepal Himalaya have resulted in major discontinuities in the form of shear zones and faults. Three major thrusts, Main Central Thrust (MCT), Mountain Boundary Thrust (MBT), and Main Frontal Thrust (MFT), and several minor shear zones and faults dominate the lithology in this region (Upreti 1999). Faults in the Nepal Himalaya are identified in two basic categories: (1) ductile faults and (2) brittle faults. Faults that develop in ductile rock mass in deeper parts of the crust may or may not change the mechanical properties of the affected rock mass, and there is no significant difference between block and matrix of the faults. On the other hand, brittle faults that occur relatively close to the surface of the earth are characterized by sheared and loose rock matrix composed of strong to very weak rock blocks. Such brittle faulted rock mass have either cohesionless fault breccias and fault gouge, or cohesive cataclasite (Sunuwar (2005); Wise et al. (1984)). Tunneling in such faulted rock mass is very challenging, and needs proper understanding of the geological condition.

Groundwater inflow into tunnel aggravates instability. The basic act of external water pressure in rock mass is a reduction of effective stress, and thereby a reduction in the rock mass strength. Severity of instability increases when tunnels pass through weak and faulted rock mass below groundwater level. Tunneling under such condition often leads to ‘flowing ground’, where the faulted rock mass mixes with the groundwater and flows towards the tunnel opening. If proper support measures are not applied, large deformation will occur, which may even lead to complete closure of the tunnel.

The Modi Khola Hydroelectric Project in Nepal faced similar tunneling problems. Though frequent alteration of rock mass in the Himalayas is generally expected, an unexpected fault appeared in the mid part of the pressure tunnel. Tunnel excavation under fully saturated conditions, through highly sheared, disintegrated schist mixed with gravelly quartzite rock mass, was very difficult and challenging. This paper presents challenges associated with excavation, consequences of difficult ground conditions with groundwater, and remedial works applied to tackle severe squeezing. The paper also back-calculates rock mass strength, analyses the effect of groundwater in squeezing, and assesses interaction between faulted rock mass, rock stresses and applied rock support.

2 The Modi Project

Modi Khola Hydroelectric Project lies about 45 km west of Pokhara in Nepal. Major underground structures in the project are a 1,503-m–long inverted-D shaped headrace tunnel with an approximately 15 m2 cross sectional area, a 51-m–deep circular vertical shaft that is 4.7 m in diameter, a 423-m–long pressure tunnel with a varying cross sectional area of 22–27 m2, and a 40 m deep underground surge shaft with a diameter of 10.2 m (Figs. 1, 2).

Fig. 1
figure 1

Geological plan and lay out of the Modi project (redrawn based on Himal Hydro 2001)

Full size image
Fig. 2
figure 2

Geological profile along the tunnel system of Modi Project (redrawn based on Himal Hydro 2001)

Full size image

2.1 Geology of the Project Area

Modi Project lies in the Lesser Himalayan Midland Zone of Nepal, which mainly consists of rocks like quartzite, phyllite, schist, metasandstones, and phyllitic slates. The underground components of the project pass through greenish to white, fine grained and fractured but strong quartzite. On some occasions, thin bands of gray to green highly sheared mica schist, chloritic schist and fractured quartzite were found along the headrace and the pressure tunnels (Paudel et al. 1998). The project area is bounded by several thrusts, and the nearest one is Lumle Thrust, which lies at about 2 km northeast. In addition to other small faults across the headrace tunnel, the fault zone in the pressure tunnel near the Adit-2 junction (Figs. 2, 3) was the most critical with regard to tunnel stability.

Fig. 3
figure 3

Layout of the pressure tunnel

Full size image

2.2 Description of Fault Zone

The pressure tunnel in the upstream of the fault passes through medium to highly jointed, occasionally clay-filled, hard, medium grained green quartzite (Figs. 1, 2). The rock mass in this tunnel reach was of very poor to fair quality according to the rock mass quality index Q (Barton et al. 1974), which ranged from 0.23 to 6.4. Downstream from the Adit-2 junction, the pressure tunnel passes through altered, disintegrated and weathered green quartzite with occasional intercalation of phyllitic schist. The rock mass at this tunnel reach was of very poor to fair quality, with Q-value ranging from 0.18 to 4.1 (Himal Hydro 2001). The 77-m–long Adit-2 tunnel that connects to the pressure tunnel mostly passes through massive and strong green quartzite. However, the middle part of the pressure tunnel (41–126 m upstream from Adit-2 junction) passes through a faulted rock mass (Figs. 1, 2, 3). This fault was not detected before tunnel excavation, due to overlaying conglomerate above the tunnel alignment and overburden soil on the valley side slopes. This fault consists mainly of extremely to exceptionally poor rock mass, which is composed of completely decomposed fault gouge and fault breccia. The fault has an orientation of 308°/32° trending 38°–218°. It makes an angle of 26° with the tunnel alignment, which has a trend of 12°–192° (Figs. 3, 4). Since the orientation of both the fault and the tunnel are near parallel, the effect of the fault zone appeared to a relatively longer stretch of the pressure tunnel upstream of the Adit-2 junction (Figs. 2, 3).

Fig. 4
figure 4

Rosette of the tunnel and the fault

Full size image

The fault typically consists of protoliths, damaged zones and fault core. The core of the fault extends to about 85 m. Quartzite in the upstream and phyllitic quartzite in the downstream are damaged due to faulting activity. A layer of phyllitic schist prevails immediately downstream of the fault core. Measurement of dip and strike of the fault protoliths and damaged zones shows that the fault is dipping away from the river, towards the North–West. The projection of the fault also shows that the fault should have been exposed to the ground surface, running almost parallel to the Modi River (Fig. 3). It shows that the exposure of the fault close to surface is away from the river at the downstream part, but close to the right bank of the river at the upstream, which indicates that the fault meets the riverbed somewhere upstream. The exposure of the faults on the surface, however, is covered by conglomerate above the pressure tunnel and by alluvial deposits at the right bank of the Modi River.

2.3 Tunneling Problems in the Fault

In contrast to the exposed fresh, strong and massive green quartzite at the Adit-2 portal and the nearby area, very weak rock mass was encountered within the relatively short distance of 76 m from the Adit-2 portal. The borehole logs showed existence of a scoop-like shape (Fig. 2) of bed rock, over which a thick layer of conglomerate deposited after a change of Modi River course to the present location. The rock mass at the initial part of the Adit-2 junction with pressure tunnel consists of poor quality, with a typical Q-value range of 0.08–0.21. The rock mass is mainly composed of highly altered and fractured green quartzite with thick layer of sheared phyllitic schist. The left wall of the junction close to Adit-2 is dominated with green quartzite, whereas the crown and right wall are mostly dominated by highly sheared phyllitic schist. According to the Q-system (Grimstad and Barton 1993), the junction of 7 m span would require at least 9–12 cm thick shotcrete with 3-m–long bolts. Despite this requirement, only 75 mm thick steel fiber shotcrete and 3 m long cement grouted bolts were applied. Since the pressure tunnel would be steel penstock lined as a final support, it was envisaged that less rock support would be possible, which at the later stage turned out not to be a smart decision. The weak rock mass conditions, the temporary rock support that was applied less than required, and groundwater inflow led to a collapse in the crown of the pressure tunnel at the junction. The tunnel was later stabilized by additional application of 100-mm–thick steel fiber reinforced shotcrete and more 3–4 m long rock bolts. Steel ribs were introduced in the pressure tunnel after the overbreak was crossed. However, another overbreak was met about 27 m upstream from the junction; where completely decomposed, clay-rich and water-saturated phyllitic schist appeared. The tunnel was supported with 75 to 100-mm–thick steel fiber reinforced shotcrete in combination with steel ribs at 1 m spacing (Fig. 5). Despite careful excavation, the tunnel collapsed, which resulted in flow of the fault gouge and fault breccia mixed with water (Fig. 6). Later, it was realized that the stiffness of the slide material could be increased by introducing a proper drainage system.

Fig. 5
figure 5

Excavation and stabilization of the tunnel

Full size image
Fig. 6
figure 6

Flowing mass from the tunnel crown (Himal Hydro 2001)

Full size image

The advantage of drill and blast tunneling under such conditions was that the tunnel could be excavated in multiple stages. Hence, heading and benching methods were implemented. Pre-grouting was performed in the crown covering tunnel periphery above the spring line. A grouting length of 8 m was adopted, with provision of the drain pipes. The sequence of tunneling operation adopted was: (1) face sealing, (2) installation of perforated iron pipes, (3) grouting, (4) heading excavation, (5) installation of steel ribs of ISHB 150 × 150 × 6 mm, and (6) application of 100-mm–thick steel fiber reinforced shotcrete along the tunnel periphery and onto the face. Rock mass behind the walls was grouted before the bench was excavated. Benching was done only after 3–4 cycles of the heading. Advancement of the tunnel heading was about 0.3–0.5 m per cycle, depending upon the prevailing rock mass condition (Fig. 5). The rock mass condition improved after excavation of 126 m upstream from the Adit-2 junction, and normal drill and blast method was resumed thereafter (Himal Hydro 2001).

Grouting in the arch was performed in three stages: first, at a shallow angle of 15° before removal of the slid rock mass; second, at depth of 8 m at ~45°; and third, at the face before heading excavation commenced. The thickness of the grouted rock mass was not measured; however, based on the depth of injection, it is assumed that effective thickness of the grouted zone is approximately 4 m behind the tunnel periphery (Fig. 5).

As the tunnel excavation proceeded across the fault and reached 83 m upstream from the Adit-2 junction, severe squeezing was observed at several locations behind the tunnel face (Fig. 7). Squeezing initiated with failure of joints in steel ribs; in particular, along the spring line of the tunnel; and continued throughout the fault zone. Severity of squeezing reached its maximum mainly to the hill side wall-bottom; however, the extent of squeezing to the river side wall was relatively less. The degree of squeezing measured at different locations is given in Table 1.

Fig. 7
figure 7

Squeezing and remedial works (Himal Hydro 2001)

Full size image
Table 1 Measured deformations in the pressure tunnel (Himal Hydro 2001)
Full size table

The pressure tunnel was supposed to be partly concrete lined and partly steel penstock lined after completion of excavation as final support. The diameter of steel penstock pipe along the pressure tunnel was designed to be 3.5 m. Due to severe squeezing and shifting of the center line of the tunnel, the available tunnel opening was not sufficient to accommodate the designed penstock steel pipe. The pressure tunnel lost considerable dimension due to squeezing, and the minimal workable space behind the steel pipe became insufficient. Thus, re-excavation of the squeezed tunnel wall was carried out, and the tunnel invert was lowered. Damaged steel ribs were removed in pieces, walls and crowns were excavated with due care, additional shotcrete was applied, and new steel ribs were installed. Horizontal H-beam struts were also provided at the lowered tunnel invert. Rock support that was applied in the fault zone is summarized in Table 2.

Table 2 Applied support in the fault zone (Himal Hydro 2001)
Full size table

In the beginning part, i.e. before the fault zone, less rock support was needed, whereas the fault zone required extensive grouting and more stiff supports, consisting of steel ribs and thick steel fiber reinforced shotcrete.

3 Groundwater Inflow

The pressure tunnel is aligned below the permanent ground water table (Fig. 8). Since the rock mass possesses various layers with differing permeability properties, the seeping water will therefore form a drainage profile having zero pore pressure at the excavated tunnel opening, and a maximum somewhere between the permanent ground water level and the tunnel opening. Analysis of the groundwater flow and generation of pore pressure profile was carried out by numerical modeling, which is discussed in Sect. 5.

Fig. 8
figure 8

Section A-A in Fig. 3 of the pressure tunnel at 65 m upstream of Adit-2

Full size image

Permeability of the rock mass determines the extent of groundwater inflow into the tunnel. A fault with clay present in the core exhibits relatively lower permeability compared to the damaged zones and protoliths dominated by fracture systems. A reliable estimate of permeability of fault breccia and fault gouge is a difficult and challenging task. The permeability and porosity of quartzite, phyllite and clay mixed fractured rocks are approximately estimated based on Nilsen and Palmstrøm (2000), and are presented in Table 3.

Table 3 Approximated permeability and porosity of material/rock mass
Full size table

4 Rock Mass Property Evaluation

The lithology around the pressure tunnel is mainly comprised of five different rock masses of exceptionally weak to very good quality. The presence of tectonic and topographic stresses, ground water inflow into the tunnel and application of rock support add complexity when analyzing the stability of the tunnel. Although most analytical and semi-analytical methods handle such cases with assumptions and simplifications, it is important to understand the behavior of rock mass and its interaction with external stress and applied support. It is very necessary that reliable rock mass parameters are estimated so that rock mass behavior with respect to tunnel excavation, support application and pore pressure is analyzed properly. A good way to establish rock mechanical properties is to do back-calculations of the cases using analytical approaches and numerical modeling.

In a plane strain condition, tunnel deformation is basically dependent on three parameters: (1) rock mass strength, (2) rock stress condition, and (3) support pressure. According to Hoek and Marinos (2000), the ratio of uniaxial compressive strength of rock mass to in-situ stress in an isostatic stress condition can be used to roughly estimate potential tunnel squeezing problems. In vice versa, having known deformation and applied rock support, it is also possible to approximately back-calculate rock mass strength considering an isostatic stress condition using Eqs. (1) and (2), as suggested by Hoek and Marinos (2000).

$$ \frac{{{{\updelta}}_{\text{i}} }}{{d_{0} }} = \left( {\left. {0.002 - 0.0025 \times \frac{{p_{\text{i}} }}{{p_{0} }}} \right)} \right. \times \frac{{{{\upsigma}}_{\text{cm}} }}{{p_{0} }}^{{\left( {2.4\frac{{p_{\text{i}} }}{{p_{0} }} - 2} \right)}} $$
(1)
$$ \frac{{{{\updelta}}_{\text{i}} }}{{d_{0} }} = 0.002 \times \frac{{{{\upsigma}}_{\text{cm}} }}{{p_{0} }}^{ - 2} $$
(2)

where δ i is tunnel side wall deformation in meters, d 0 is original tunnel diameter in meters, p i is internal support pressure in MPa, p 0 is in-situ stress in MPa, and σ cm is rock mass strength in MPa. Eq. (1) is used to compute tunnel strain when support pressure is applied, and Eq. (2) is used when there is no or negligible support pressure.

The overburden in the pressure tunnel at this fault zone is ~80 m, with little variation along the tunnel alignment (Figs. 2, 8). However, as shown in Table 1, the deformation values vary significantly at different locations. As applied injection-grouting was not evenly distributed in the tunnel periphery, it might be a reason for the different degrees of squeezing, which varied at different tunnel chainages.

Following the equations suggested by Carranza-Torres and Fairhurst (2000), applied rock supports consisting of steel ribs ISHB 150 × 150 × 6 at 50 cm spacing and 100-mm–thick steel fiber reinforced shotcrete in a closed circular tunnel will have a support capacity of ~1.28 MPa. As the pressure tunnel was Inverted-D in shape and also did not have steel strut and support in the invert, the applied support would therefore not be able to offer support pressure similar to that of a closed ring shape. According to Barton et al. (1974), the support pressure required by such exceptionally poor rock mass as found in the fault may vary from 1 to 3 MPa. Since applied rock support did not withstand the external pressure and considerable squeezing occurred, the effective support pressure offered must in principle be much less than the value of 1.28 MPa. Panthi (2006) indicated that the measured mean support pressure with a rock support consisting of shotcrete and steel ribs without invert strut was 0.71 MPa at the headrace tunnel of Kaligandaki “A” Hydroelectric Project located in the same river valley, downstream. Comparing the size of the tunnels of Kaligandaki and Modi and the extent of squeezing, it was determined that the effective support pressure offered by the rock support at this weakness zone is ~0.64 MPa or even less.

To estimate the rock mass strength (σ cm), it is first assumed that the rock mass is homogeneous and in isostatic stress condition. Similarly, the in-situ stress around the tunnel periphery may be considered to be equal to gravity stress, which is 2.08 MPa. With this assumption, Eqs. (1) and (2) are used to back-calculate rock mass strength (σ cm) for an equivalent circular tunnel radius of 2.51 m. This back-calculation gave rock mass strength (σ cm) with varying results at different tunnel deformation values presented in Table 1. The rock mass strength values ranged from 0.05 to 0.10 MPa (Table 4).

Table 4 Back-calculation of strength of the faulted rock mass
Full size table

As Table 4 indicates, the rock mass close to the start of the fault has a higher strength that gradually reduces to the mid of the fault, which is very logical considering the real case. The mean value of rock mass strength in the fault zone seems to be around 0.07 MPa, which gives a corresponding intact rock strength (σ ci) of ~1 MPa, according to Hoek et al. (2002).

Deformation in a tunnel is inevitable if rock mass is very weak. However, it can be controlled by two important considerations: (1) adequate support measure and (2) time of application. In a three-dimensional state, the deformation in the tunnel is also influenced by distance from the tunnel face. Though supports are applied immediately after the opening of the face, deformation behind the face still continues to develop. A similar phenomenon was observed in the Modi pressure tunnel. High squeezing was observed when the face of the heading was 38–18 m ahead of the squeezed sections, which was ~3–7 times the tunnel diameter.

Despite many analytical approaches available to address the three-dimensional behavior of tunnel deformation (Anagnostou and Kovari 2003; Barbosa 2009; Carranza-Torres and Zhao 2009; Shin et al. 2010) in a complexity of non-circular tunnel section with multi-staged excavation in water-bearing heterogeneous rock mass with anisotropic stress environment, such as the case presented above; a three dimensional numerical analysis with face effect and approximated rock mass strength using Hoek and Marinos' (2000) approach may prove to be a useful tool to back-calculate the actual in-situ stress state and assess the effect of groundwater on overall tunnel stability.

5 Numerical Modeling

The stage-wise tunnel excavation procedure that was adopted in this fault zone includes pre-consolidation grouting, excavation in stages of heading, benching, and supporting. The presence of water inflow added complexity in the excavation, and later, high squeezing occurred. According to Hoek (1999) (in Barla 2000), the use of numerical modeling is highly recommended to analyze the stability of the tunnel under such conditions. Therefore, a finite difference numerical code, FLAC3D, is used to analyze this case, in which the rock mass is assumed a continuum media.

5.1 Model Setup

Because of asymmetric topography near the surface, a complete model with free surface was prepared. The model covers a 76-m–long stretch with a 159-m width across the tunnel and 70–170 m deep valley topography, as shown in Fig. 9. It represents the rock mass from 25 to 101 m upstream of the Adit-2 junction. An Inverted-D shaped tunnel with radius of 2.35 m and bench depth of 2.35 m is modeled, with separate groups of tunnel heading and benching similar to that used during construction of Modi pressure tunnel in the fault zone. Boundary conditions of all sides of the model are fixed along the normal direction, except for the top surface boundary, which is kept free.

Fig. 9
figure 9

FLAC3D Model

Full size image

The model includes six different types of rock masses, as listed in Table 5 and shown in Fig. 8. The mechanical and physical properties of the faulted rock mass and grouted rock mass around the tunnel have been estimated with reference to the computations made in Sect. 4. In addition, properties of the rock mass adjacent to the fault have been estimated according to the geological log records made during excavation and laboratory tests of rock samples. From 41 m upstream of Adit-2 junction onwards, the property of 4-m–thick rock mass around the tunnel arch and walls has been changed to grouted rock mass. Computation of the rock mass parameters in Table 5 has been done following equations suggested by Hoek et al. (2002). Only dry density of the rock mass has been assigned, since FLAC3D takes fluid influence into account (Itasca Inc. 2004). Considering the behavior of the very weak rock mass of the fault, the rock mass in the model is assumed as elastic perfectly plastic material satisfying Mohr–Coulomb criterion. It is also assumed that the very weak and faulted rock mass will not dilate, as recommended by Hoek and Brown (1997). On the other hand, appropriate dilatancy angles are assumed for other rock masses adjacent to the fault.

Table 5 Estimated rock mass properties
Full size table

The model comprises both vertical and horizontal stresses. In addition to the horizontal component of vertical stress due to gravity effect, tectonic stress plays an important role in the total component of horizontal stress. The magnitude of such tectonic horizontal stress varies considerably depending upon geographical location, geological environment and distance from the main tectonic fault system (Panthi 2012). The lithology and river morphology in the project area shows that the pressure tunnel has uniform rock cover of 25 m and a deposit of conglomerate on top of it (Fig. 8). The topography above the quartzite rock layer is a hill with slope at both sides (Fig. 1). Thus, it is logical to assume that the conglomerate and alluvial deposit represent non-tectonic layers, and hence, the tectonic stresses can be considered effective only in the rock layers below these deposits. Horizontal stress due to gravity is, however, also considered for the overlying conglomerate strata.

The magnitude of in-situ stresses documented by Nepal (1999) and back-calculated by Panthi (2012) shows substantial variation of horizontal stress according to lithology, geographical location and overburden. In a faulted rock mass such as in this case, it is extremely difficult to successfully measure the in-situ rock stress state; in particular, the tectonic contribution of the horizontal stress. In the absence of field-measured rock stress around the project vicinity, back analysis using numerical modeling is the best and only reliable approach in this endeavor. In the Modi project, considerable magnitude of tectonic stress is expected to have contributed to the large deformation in the tunnel wall.

To establish an approximate horizontal tectonic stress component, three different magnitudes of tectonic stresses, 2 MPa, 3 MPa, and 4 MPa, are used in the analysis. In addition to the tectonic component of the in-situ stresses, gravity also contributes to the magnitude of horizontal stress. This, according to Panthi (2012), can be expressed as follows:

$$ {{\upsigma}}_{\text{h}} = \frac{{{\upnu}}}{{1 - {{\upnu}}}}{{\upsigma}}_{\text{v}} + {{\upsigma}}_{\text{tec}} $$
(3)

where σ h is horizontal stress, ν is poisson’s ratio, σ v is vertical stress and σ tec is the horizontal component of tectonic stress. As suggested by Panthi (2012), tectonic stress in the central Himalayan chain is mainly oriented in an almost North–South direction, and hence a similar orientation of the tectonic stress is also expected in the project area. As the tunnel trends 12°–192°, it imposes a smaller resolved component of the tectonic stress, as in the plane (i.e. across the tunnel alignment) and out of the plane (i.e. along the longitudinal tunnel alignment). The detail calculations of the results based on this principle are shown in Table 6.

Table 6 Estimated in-situ stresses in the tunnel
Full size table

5.2 Groundwater

Due to the topography and location of the tunnel below the river, it is logical to assume that the river water level is always maintained at a minimum of 14 m above tunnel crown; and groundwater level at the hill side is at a higher elevation so that it flows through the rock and drains into the river. This assumption is also in conformity with the observation of water inflow during tunnel excavation.

In order to analyze the effect of groundwater in the stability of the tunnel, two principle states of groundwater have been adopted. The first state is a base case where water level above the tunnel center is assumed to be at 21.6 m, maintaining a constant water level in the river at 885 masl (Fig. 8). This is based on the assumption that the groundwater level is maintained at the interface of conglomerate and quartzite rock mass. To illustrate the net effect of groundwater on the stability of the tunnel, a second case of no water (dry) condition has also been analyzed. In both cases, the tunnel is drained, which is similar to the actual excavation process, where perforated drain pipes were installed around the tunnel wall and arch.

Pore pressure in the model is set according to the depth of water above the tunnel center, whereas boundaries for pore pressure are kept fixed at both vertical ends so that there can be flow through it. Since the FLAC3D model demands rock mass permeability values, three distinguished layers of rock mass with different porosity and permeability (Table 3) have been used. As there is less variation of these parameters for phyllitic schist and phyllitic quartzite from that of phyllite, estimated values are kept the same as for the phyllite. On the other hand, if dominated with gouge material, the fault core will have low permeability. Quartzite is assumed to have the smallest permeability value, whereas conglomerate is mostly above groundwater table, and thus does not have any influence on the stability in relation to ground water. Since the tunnel and the grouted rock mass are drained, it is assumed that these parameters will remain unchanged. However, it is important to note that the change in permeability values will not make significant variations in the overall deformation values. This is due to the fact that only the pore pressures will be calculated by the model.

5.3 Sequence of Excavation and Rock Support

Tunnel excavation and support application are modeled similar to the actual site condition. Initial 16 m (25–41 m upstream from Adit-2 junction) is excavated full face and rock support is applied immediately after excavation. From 16 m onwards, grouting in the arch and tunnel face is done before excavation. Tunnel excavation is hereafter divided into heading and benching, and there is no lag of time for tunnel support application since it immediately follows the excavation. Side wall grouting and bench excavation are done once heading is ahead by three to four rounds of excavation. Stages of excavation and rock support are as according to Table 2. Shotcrete is modeled as an elastic shell element, whereas steel-ribs are modeled as beam elements. The estimated properties of the rock support are given in Table 7.

Table 7 Estimated properties of shotcrete and steel rib
Full size table

The model is set to an initial no displacement state and displacement at any grid point is made cumulative. Thus, any displacement observed on the tunnel wall is displacement of the rock mass prior to support application and displacement of the support itself.

5.4 Simulation Results

Numerical simulations are computed at four sections of the tunnel, namely, 50, 60, 65, and 70 m upstream from the Adit-2 junction, to verify the actual tunnel displacements. For this purpose, rock mass and rock support properties (Tables 5, 7) with different horizontal tectonic stress components (Table 6) are adopted. Displacements in the tunnel crown, spring level and bottom of the wall are computed at several locations of the tunnel model. At first, only mechanical model is run without water for the three cases of tectonic stresses. Model with tectonic stress that yields displacement close to the actual displacement is then run as uncoupled Mohr–Coulomb mechanical isotropic fluid model. This hydro-mechanical model determines the phreatic line of groundwater table upon each advance of the tunnel. A net effect of ground water in the tunnel is assessed by comparing the mechanical and hydro-mechanical models.

5.4.1 Effect of Tectonic Stress

Tectonic stress has considerable effect on the horizontal displacement of the tunnel walls. The higher the tectonic stress component, the higher the horizontal displacement in the walls will be. Such deformation is high in the wall-bottom compared to that at the spring level and in the crown, due to additional lateral pressure caused by the tectonic horizontal stress. Since the rock mass in the invert was not strengthened by grouting or any other support, inward movement of the rock mass from invert is obvious. The deformed side walls then cause the crown to move downward. It is also noted that the deformation in the tunnel crown is smaller at higher magnitudes of tectonic stress, which corresponds to the actual conditions in the tunnel in this fault. This is mainly because of higher longitudinal confinement of the rock mass, due to higher tectonic stress along the longitudinal axis of the tunnel. Simulated results of incremental tectonic stress (from 2 to 3 MPa and 2 to 4 MPa, with corresponding displacements in the tunnel crown, spring level and wall-bottom) at the selected three locations are presented in Fig. 10.

Fig. 10
figure 10

Simulated radial tunnel strain (deformation) increment with incremental tectonic stresses in dry conditions, at the crown (a), spring line (b), and wall-bottom (c)

Full size image

In Fig. 10, continuous lines show radial strain increment when tectonic stress is increased from 2 to 3 MPa, whereas dotted lines show the same when tectonic stress is increased from 2 to 4 MPa. Simulation indicates that the tunnel will deform continuously even after the tunnel face has reached well ahead by more than 30 m. The crown experiences decrement of displacement by more than 2 % upon an increment of 1 MPa tectonic stress. On the other hand, the spring line and wall-bottom experience an increment by more than 2 and 5 %, respectively.

Figure 10 also illustrates that total tunnel strain (deformation) increment at the wall-bottom from 2 to 4 MPa tectonic stress is between 30 and 35 %, and the corresponding average deformation in the wall-bottom is 0.67 m, which is close (slightly less) to the tunnel deformation that was actually measured (Table 1). Since the rock masses in the tunnel were much saturated, it is obvious that the deformation would be larger than that of the simulated result under dry conditions.

The pressure tunnel has a uniform rock cover of 25 m, if overlaying conglomerate is excluded. Moreover, at this location, the parent rock mass is below the Modi River bed (Fig. 8), which is the deepest point of the lithology. Therefore, the topographic influence of in-situ rock stress should be at a minimum level. Likewise, Panthi (2012) suggests that the horizontal tectonic stress magnitude may exceed 7 MPa in the Himalayas under conditions where massive and isotropic rock masses with no significant topographic effect prevail. The fault zone along this pressure tunnel is squeezed within massive quartzite from both sides, and should therefore be influenced by Himalayan tectonic push. However, since this fault zone is also a distressed zone and the pressure tunnel is only 25 m below the surface bed rock, the magnitude of horizontal tectonic stress should be less than that argued by Panthi (2012). This gives fairly good grounds to assume that the magnitude of tectonic horizontal stress in the faulted rock mass is in the range of 4 ± 0.5 MPa. With this finding, it will be interesting to look at the simulation results under fully saturated groundwater conditions; these are discussed in the following section.

5.4.2 Effect of Groundwater

In a drained tunnel, pore pressure will vary according to rock mass hydraulic property and static head. A steady state of the water table is gradually lowered to the tunnel upon excavation. After complete excavation of the pressure tunnel up to 81 m upstream from the Adit-2 junction, the pore pressure distribution around the tunnel will be as shown in Fig. 11. With inflow of water into the tunnel, pore pressure will be null around it, including the bench.

Fig. 11
figure 11

Pore pressure distribution in the excavated tunnel: cross section (left), longitudinal section (right)

Full size image

The simulated results show that the tunnel will have high inward movement, despite adopting a heading and benching method of excavation. The deformation mostly follows the orientation of the faulted rock mass, sandwiched between quartzite at the top and phyllitic schist at the bottom (Fig. 12). At the beginning stretch of the tunnel (up to 41 m upstream), shotcrete at the hill side wall has high deformation, whereas it has less at the river side wall (Fig. 13). This is quite justifiable, since at this beginning section of the tunnel, there exists fairly competent phyllitic schist rock mass at the river side compared to faulted rock mass at the hill side (Fig. 3). The tunnel stretch in the middle of the fault zone, which ranges from 50 m upstream to 70 m upstream from the Adit-2 junction, experiences a total of 61–87 cm inward movement (deformation) at the hill side wall after the application of tunnel rock support (Table 1). Similar, deformation in the shotcrete at the tunnel reaches from 41 to 47 m upstream from the Adit-2 junction, where steel ribs were placed at closer spacing of 30 cm, experiences less deformation. Similar deformation is also observed in the simulated results with steel ribs (Fig. 14). The achieved simulation results at 50, 60, 65 and 70 m upstream from the Adit-2 junction are 0.61, 0.77, 0.87, and 0.71 m, respectively, which are comparable to those actually observed in the tunnel (Table 1).

Fig. 12
figure 12

Displacement around the tunnel at 65 meters upstream from Adit-2 junction

Full size image
Fig. 13
figure 13

Displacement in the shotcrete in fully saturated condition

Full size image
Fig. 14
figure 14

Displacement in steel ribs in fully saturated condition

Full size image

6 Discussion

In faulted poor rock mass, deformation ahead of a tunnel face is significant, and it continues to increase as the tunnel excavation advances. In an isotropic stress condition with homogenous rock mass, instantaneous tunnel closure in a circular tunnel reaches its maximum value when the tunnel face is advanced by approximately four times the tunnel diameter (Carranza-Torres and Fairhurst 2000). Though these assumptions differ slightly in this case due to non-circular tunnel, the displacements in the crown, spring level and wall-bottom of the pressure tunnel exhibit trends similar to longitudinal profiles at different tunnel locations (Fig. 15).

Fig. 15
figure 15

Longitudinal displacement profile of the tunnel at 50, 60, 65 and 70 m upstream from Adit-2 junction

Full size image

Figure 15 illustrates longitudinal deformation of the tunnel contour with respect to advancement of the tunnel face, for with and without groundwater considerations. Since the groundwater table in the fluid model has relatively shallow head over the tunnel, there is no such significant difference between deformations. However, the amounts of deformation vary considerably at different locations. As vertical stress is not the major principal stress, the crown of the tunnel has least displacement, which is quite logical. Since there is no invert strut applied, it is very obvious that the bottom of the wall has the maximum displacement. Similar to the explanation given by Vlachopoulos and Diederichs (2009), the longitudinal displacement profiles progress fairly flatter because of the small steps of excavation and the splitting of the section into heading and benching. It is to be noted here that the deformations behind the face are cumulative and inclusive of the pre-support displacement, as shown in these figures.

Figure 15 also demonstrates a uniform additional deformation in the tunnel due to presence of groundwater in the rock mass. Relative increment of tunnel deformation from dry to saturated ground conditions (water in consideration) generally ranges from 4 to 14 % in the crown, 10 to 30 % in the spring line, and 5 to 20 % in the wall-bottom (Fig. 16).

Fig. 16
figure 16

Effect of groundwater in tunnel deformation

Full size image

The faulted rock mass is already sheared and at the plastic state prior to excavation of the tunnel. There will be further deterioration in the rock mass strength as excavation advances (Fig. 17). Plastic deformation is pronounced in the hill side wall, which is also evidenced by high displacement, as shown in Figs. 12, 13, and 14. High deformation in side wall-bottom and significant heaving up of the invert are mainly due to low support pressure in the side walls, and in particular, at the bottom.

Fig. 17
figure 17

Plastic deformation at (left to right) 50, 60, 65, and 70 m upstream of the Adit-2 junction

Full size image

This demonstrates the need of rock mass strength improvement in the invert of the tunnel. Often, instability is believed to occur towards the gravity direction, but in very weak and faulted rock mass, failure can also initiate from the invert, and consequently a large deformation may occur in the side walls as well. In contrast, failure in the crown of the tunnel was mainly due to poor strength of the grouted rock mass. Even in higher strength grouted rock mass, displacement in the crown often occurs because of subsidence of the grouted rock mass in the wall once invert heaving occurs in the tunnel floor. Moreover, had invert steel struts been provided in addition to the applied rock support, there would have been significant reduction of the tunnel deformation in the side walls, as shown in Fig. 18. In this circumstance, the bottom of the walls at the middle part of the fault might have <0.05 m deformation, whereas the invert might have experienced deformation of about 0.24 m.

Fig. 18
figure 18

Deformation in shotcrete and steel rib with invert strut

Full size image

Similarly, there will be inward horizontal displacement at the bottom of the heading excavation, as there are no horizontal struts installed. Such displacement is high in the mid portion of the fault zone, with a maximum of 0.20 m. The tunnel reach with closer spacing of steel ribs (41–47 m upstream from the Adit-2 junction) will have lesser deformation around the tunnel periphery, whereas deformation in the un-grouted beginning part of the tunnel (25–41 m upstream from the of Adit-2 junction) with phyllitic schist rock mass will continue to have deformation, but at a lower magnitude.

7 Conclusions

Tunnels in faulted rock mass are subjected to instabilities. In addition, groundwater has a negative impact on the stability of the tunnel. Often, ‘flowing’ conditions prevail when substantial inflow of water is mixed with heavily crushed rock material, as with the fault gouge and fault breccias of the Modi pressure tunnel. Such risk of collapse and flow of rock mass was successfully reduced at this pressure tunnel by draining and pre-consolidation grouting around the tunnel periphery. However, it was not possible to completely hinder the deformation in rock mass and considerable side wall movement that took place at this fault zone.

Low water head over the tunnel crown did not have a considerable effect on overall tunnel deformation. Splitting the tunnel sections into heading and benching was advantageous in reducing total deformation. In addition, the heading excavation helped to reduce the magnitude of deformation of the tunnel. Upon excavation of the tunnel bench, the rate of deformation in the walls increased substantially.

Back-calculation carried out for the estimation of rock mass strength using numerical modeling helped to approximately back-calculate the tectonic component of horizontal stress. The simulation indicated that the tectonic component of horizontal stress in the faulted rock mass is around 4 MPa.

It is demonstrated that the deformation in the faulted zone sandwiched between fairly competent rock mass of the Modi pressure tunnel was high in the hill side wall-bottom. Similarly, the over-break in the faulted rock mass was limited by the overlying strata of massive quartzite. It is also worth noting that the pre-excavation deformation in the faulted rock mass increased as the tunnel reached to the middle of the fault zone. Due to the presence of phyllitic schist at the right wall, the tunnel experienced less deformation at the river side wall than at the hill side. Deformation in walls could be significantly reduced if grouting was done in the invert, and steel struts were provided at the tunnel invert. This, however, would not completely prevent squeezing of the spring line in the heading part.

The above analysis is based on simulation with final stage (complete) deformation. Numerical simulation with multiple records of convergence would have given even better conformity with the actual deformation behavior in the faulted rock mass. In addition, it is unlikely that the rock mass was completely homogeneous and that the grouting effect on the rock mass was as uniform as is assumed here. These are the main reasons for some degree of variation in computed and actually measured deformations. In addition, many parameters were estimated as input for the analysis. Simulation code itself is an uncertainty of the analysis. However, the results achieved are of quite good quality, and some of the findings may be of great value for tunnels that are excavated through similar ground conditions.