numerical analysis of k0 to tunnels in rock masses ... · pdf filerock mass characteristics to...

International Research Journal of Applied and Basic Sciences © 2013 Available online at www.irjabs.com ISSN 2251-838X / Vol, 4 (6): 1572-1581 Science Explorer Publications

Numerical analysis of K0 to tunnels in rock masses exhibiting strain-softening behaviour (Case study in

Sardasht dam tunnel, NW Iran)

Vahid Hosseinitoudeshki

Department of Civil Engineering� Zanjan Branch� Islamic Azad University� Zanjan� Iran

Corresponding Author email: [email protected]

ABSTRACT: This paper presents the results of numerical analysis of K0 (�h/�v) to tunnels excavated in rock masses obeying Hoek–Brown failure criterion with strain-softening post-failure behaviour. The numerical analysis was investigated in the Sardasht dam tunnel in north-west of Iran. The tunnel has a horseshoe cross-section through 4350 m in length with 3.9 in radius and will be used to transfer water to the powerhouse dam. Cretaceous slates with inter-beds of sandstone and phyllite crop out in whole of the tunnel route. In numerical analysis, a 2D finite element program with software Phase2 was utilized together with the convergence–confinement method. Considering that the tunnel is located at different depths, six sections of the tunnel have been selected and in each section, the K0 value is determined from the known relations and has been used in numerical analysis. The results of the evaluations show that in rocks exhibiting strain-softening behaviour, with reducing the amount of K0, the values of displacement and plastic zone around the tunnel increase but the style of deformation maintains uniform. Keywords: Numerical analysis; K0; Sardasht dam tunnel; Strain-softening

INTRODUCTION

One of the most important tasks in rock mechanics and engineering geology is to estimate of the value of K0

(�h/�v) and its effects on underground spaces. The K0 is defined as the ratio between the major horizontal stress (�h) and the vertical stress (�v) (Goodman, 1989), being �v the weight of overburden. In this paper, the value of K0 is estimated via the equation of Sengupta (1998, in Singh and Goel, 1999) that is applicable in compressive tectonic setting.

In general, strain-softening is the effect of localization of deformation and is founded in the incremental theory of plasticity (Hill, 1950; Kaliszky, 1989), that was developed in order to model plastic deformation processes, in which a material is characterized by a failure criterion and a plastic potential. The strain-softening behaviour is characterized by a gradual transition from a peak failure criterion to a residual one (Fig. 1) and can be seen in rocks with geological strength index between 25 and 75 (25<GSI<75) (Alejano et al. 2009).

Tunneling in mountainous region with active tectonic requires crossing through increasingly difficult geological

conditions. Iran terrene is one of the most tectonically active regions of the world because the Arabian–Eurasian collision has been occurred. Numerous studies in the Iran have shown ongoing convergence and active tectonic in this area (Jackson et al., 2002; Allen et al., 2003; Allen et al., 2004).

A detailed geological and geotechnical study was carried out in the project area to determine the geomechanical characteristics of the rock masses. Numerical analysis of K0 could be done by determining the displacements and plastic zone around of tunnel and then compare the results of numerical method with critical displacements obtained from the hazard warning levels (equations of Sakurai, 1993). Furthermore, Ground Reaction Curve (GRC) could be drawn and the amount of tunnel wall deformation prior to support installation could be determined using the diagram proposed by Vlachopoulos and Diederichs (2009).

The main motivation for this study is to analysis the different sections of tunnel in order to find effect of in situ stress ratio in stability of Sardasht dam tunnel, so that we can assess efficacy of K0 to tunnels in rock masses exhibiting strain-softening behaviour. This tunnel, with about 4350 m in length and 3.9 m in radius, will be

Intl. Res. J. Appl. Basic. Sci. Vol., 4 (6), 1572-1581, 2013

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excavated in south east of Sardasht in northwest of Iran (Fig. 2) and will be used to transfer water to the powerhouse dam.

Figure 1. Diagram shows that strain-softening behaviour is related to rock masses with 25<GSI<75. (after Alejano et al. 2009)

Figure 2. The location map of the study area.

Geology

The study area is located in in Sanandaj - Sirjan structural zone (Aghanabati, 2004) which has been affected regional convergence in the NE-SW direction. In the regional tectonic, Sanandaj – Sirjan zone is located in the Turkish-Iranian plateau (Allen et al. 2004). It extends from eastern Anatolia to eastern Iran, and typically has elevations of 1.5–2 km.

The whole rock types observed in the project area include cretaceous slates with inter-beds of sandstone and phyllite. Cleavage is the most important structural elements in these rocks that is visible in most outcrops and the general slope is towards the northeast (Figure 3). Sandstone inter-beds are generally fine-grained and in some horizons become siltstone but sandstone is dominant. The only structure that can cut the rout of tunnel is Zirmarg fault that the tunnel will be crossed at approximately 20 to 30 meters.

Hillsides in the region have more or less the same slope and the slope varies from 25 to 40 degree and rocky outcrops are widespread. The topography condition is such that overburden in the length of tunnel varies from 0 to 600 meters (Table 1).


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Figure 3. The general landscape of slate and phyllite that showing cleavage in these rocks.

Table 1. Overburden variations in the length of tunnel.

400 – 600 m 100 – 400 m 0 -100 m Overburden

623 m 2562 m 1195 m Length of tunnel

MATERIAL CHARACTERISTICS OF ROCKS

Rock mass characteristics

To acquire the rock masses characteristics, site investigations were carried out on the outcrops along the tunnel route, the sidewalls and faces of galleries, and the core logs of few borehole drillings. The information obtained of these investigations will be used on the rock mass classification as indices. Classification of the rock masses

Rock mass classification systems have been developed to create some order out of chaos in site investigation procedures (stille and Palmstrom, 2003) and to define an empirical approach to tunnel design which provide guidelines for stability performance, and suggest appropriate support systems.

The RMR and Q ratings have been determined using field data and the mechanical properties of intact rock samples. The Rock Mass Rating (RMR) System (Bieniawski, 1989), classifies rock masses using the following parameters: uniaxial compressive strength (UCS), Rock Quality Designation (RQD), spacing of fractures, condition of fractures, groundwater conditions, and orientation of fractures. The average RMR rating for the rock masses assessed to be from 40 to 50, with an average value of 45 (Table 2). This rating classifies the alternation of slate and sandstone and phyllite as fair rock masses.

Table 2. The RMR and Q values in the rock masses in the tunnel.

Rock mass classification system RMR Q

Rating 40-50 0.77-1.81 45 1.29 Rock Mass Quality fair rock poor

The Q rock mass classification system is also known as the NGI (Norwegian Geotechnical Institute) have

been developed by Barton et al. (1974). It is defined in terms of RQD, the function of joint sets (Jn), discontinuity roughness (Jr), joint alteration (Ja), water pressure (Jw) and stress reduction factor (SRF). The Q values for the rock masses are from 0.77 to 1.81, with an average value of 1.29 (Table 2). According to the Q classification system, the alternation of slate and sandstone and phyllite can be considered as poor rock masses. Mechanical properties of the rock masses

The rock mass properties such as the rock mass strength (�cm), the rock mass deformation modulus (Em) and the rock mass constants (mb, s and a) were calculated by the Rock-Lab program defined by Hoek et al. (2002). This program has been developed to provide a convenient means of solving and plotting the equations presented by Hoek et al. (2002).

In Rock-Lab program, both the rock mass strength and deformation modulus were calculated using equations of Hoek et al., 2002, and the rock mass constants were estimated using equations of Geological Strength Index (GSI) (Hoek et al., 2002) together with the value of the alternation of slate and sandstone and phyllite material


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constant, mi (value in Table 3). Mean RMR values (Table 2) have been used to estimate the GSI index for these rocks (Table 3) that exhibiting strain-softening behaviour. Also, the value of disturbance factor (D) that depends on the amount of disturbance in the rock mass associated with the method of excavation, was considered zero for the rock masses (Table 3), it means these rocks would not be disturbed more than this during blasting.

Table 3. Geomechanical properties of the rock masses. GSI mi D mb s a �cm Em �t (MPa) (MPa) (MPa)

40 7 0.00 0.821 0.0013 0.511 1.465 878.09 -0.019

Finally, the shear strength parameters of the rock mass (C and �) for the rock masses were obtained using

the relationship between the Hoek–Brown and Mohr–Coulomb criteria (Hoek and Brown, 1997) and are presented in Table 4.

Table 4. The amounts of in-situ stresses and shear strength parameters of the rock mass in the six sections of tunnel. No. section of tunnel

Value of overburden (m)

σ V

(MPa)

σ H

(MPa)

Κ0 C (MPa)

� (deg)

1 100 2.75 4.80 1.75 0.26 32.30 2 200 5.50 8.10 1.47 0.39 26.86 3 300 8.25 11.40 1.38 0.50 23.99 4 400 11.00 14.70 1.34 0.59 22.04 5 500 13.75 18.00 1.31 0.67 20.59 6 600 16.50 21.30 1.29 0.75 19.44

In-situ stress in the rock masses

The value of K0 in the six sections of tunnel was calculated regarding to the tunnel depth (the amount of overburden) and the rocks unit weight. Regarding to tectonic situation of area that has been located in the compressional zone, the values for maximum and minimum horizontal stresses are more than the vertical stresses (Singh and Goel, 1999). The equation of Sengupta (1998, in Singh and Goel, 1999) could be used for these

tectonic settings. This equation is defined as: σσ VH 2.15.1 +=, where:

Ζ= .γσ V .

First, the values of vertical stress (σ V ) have been calculated considering the mean density values of 2.75 g/cm3 for the rock masses and the amount of overburdens in each section of tunnel (Table 4). Also, the values of

maximum horizontal stress (σ H ) in each section of tunnel have been obtained from the equation of Sengupta (Table 4). Finally, the value of K0 in the each section of tunnel was calculated regarding to equation of

σσ VH=Κ0 and are shown in table 4. Numerical analysis of K0 to tunnel

Numerical analyses of K0 in the rock masses were accomplished using a two-dimensional hybrid element model, called Phase2 Finite Element Program (Rocscience, 1999). This software is used to simulate the three-dimensional excavation of a tunnel. In three dimensions, the tunnel face provides support. As the tunnel face proceeds away from the area of interest, the support decreases until the stresses can be properly simulated with a two-dimensional plane strain assumption. In this finite element simulation, based on the elasto-plastic analysis, deformations and stresses were computed. These analyses used for evaluations of the tunnel stability in the rock masses. The geomechanical properties for these analyses were extracted from Table 3. The Hoek and Brown failure criterion was used to identify elements undergoing yielding and the plastic zones of the rock masses in the tunnel surrounding.

To simulate the excavation of tunnel in the crushed rock masses, a finite element models was generated with horseshoe section and 3.9 m span (Fig. 4). The outer model boundary was set at a distance of 5 times the tunnel radius and six-nodded triangular elements were used in the finite element mesh.

In the first step, the maximum tunnel wall displacement and the radius of the plastic zone, far from the tunnel face were determined in each section of tunnel. The radius of the plastic zone far from the tunnel face was determined from extent failed zone represented by a number of crosses (Fig. 5b) indicating elements in the finite element analysis have failed.


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Figure 4. Numerical modeling of Sardasht dam tunnel

In the second step, the stability of tunnel in the rock masses was assessed by comparing displacements

obtained from the numerical method with critical displacements resulted of the hazard warning levels. If displacements obtained from the numerical method are smaller than ones of the hazard warning levels, the stability of the tunnel will be concluded. But if these displacements become greater than ones of the hazard warning levels, then some actions must be taken to stabilize the tunnel. The hazard warning levels could be determined from

critical strain (ε c ). The critical strain could successfully be used for assessing displacement measurements in

tunnels, such as crown settlements and convergence. The critical strain (ε c ) is always smaller than strain at failure, and calculate as follows:

Ε

=σ

εc

c

where σ c is uniaxial compressive strength of rock mass (MPa) and Ε is Young‚s modulus (MPa). Sakurai

(1993) obtained the relation of critical strain, compressive strength and Young‚s modulus and presented three hazard warning levels, as follows:

Hazard warning level �: Logε c = - 0.25 Log Ε - 0.85



where Ε is Young‚s modulus per 2cmKg .The hazard warning levels � and � indicate long time and short

time stability of tunnel, respectively. The hazard warning level � is suggested as the base of tunnel design.

Regarding the value of Young‚s modulus ( Ε ) in the rock masses (Table 3), the values of critical strain for each hazard warning levels were calculated. These values for the Sardasht dam tunnel are 0.0261, 0.011 and 0.0047, respectively. The values of allowable displacements on the basis of the hazard warning levels were determined using the values of critical strain and radius of tunnel, as follows:

a

uc

c =ε

where uc is allowable displacement on the basis of the hazard warning levels, and a is radius of tunnel. By

comparing displacement obtained from numerical methods with allowable displacements on the basis of the hazard warning levels (Table 5) it appears that tunnel is stable or instable.


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Table 5. Allowable displacements on the basis of the hazard warning levels �, �, �. Allowable displacement on the basis of the hazard warning level � (cm)

Allowable displacement on the basis of the hazard warning level � (cm)

Allowable displacement on the basis of the hazard warning level � (cm)

10.18 4.33 1.83

The third step is determination of the amount of tunnel wall deformation prior to support installation using the

Vlachopoulos and Diederichs method. The plot in figure 5d was created using the Vlachopoulos and Diederichs equations (Vlachopoulos and Diederichs, 2009). Using this plot, the amount of closure prior to support installation could be estimated with knowing plastic zone radius (Rp), tunnel radius (Rt), displacement far from the tunnel face(Umax), and distance from tunnel face(X). - Section 1

In this section, the overburden is 100 meters and the value of K0 is equal to 1.75. The maximum tunnel wall displacement and the radius of the plastic zone in this section of tunnel are shown in figures 5a and 5b. By comparing displacements obtained from numerical method in the roof, floor and walls of tunnel (6.4, 7.6 and 5.6 cm), with allowable displacements on the basis of the hazard warning levels (Table 5), it appears that the tunnel in short time is stable but in long time becomes instable and a support system should be applied for the rock masses stabilization.

Ground Reaction Curve (GRC) in the roof of tunnel is shown in figures 5c and demonstrates relations between displacement and released hydrostatic stress. Furthermore, determination of the amount of tunnel roof deformation prior to support installation in this section is done using figure 5d. The Closure/max closure in the roof of the tunnel is equal to 0.359, and the closure prior to support installation equals (0.359) × (0.072) m. Thus, the allowable displacement in the roof of the tunnel prior to support installation in this section is 2.58 cm.

Section 2

In this section, the overburden is 200 meters and the value of K0 is equal to 1.47. The maximum tunnel wall displacement and the radius of the plastic zone in this section of tunnel are shown in figures 6a and 6b. By comparing displacement obtained from numerical method in the roof, floor and walls of tunnel (22.5, 24 and 15 cm), with allowable displacements on the basis of the hazard warning levels (Table 5), it appears that the tunnel is instable and a support system should be applied for the rock masses stabilization.


Figure 5. In the section 1 of tunnel (a) Total displacements in around of the tunnel. (b) Extent of plastic zone in around of the tunnel. (c) Ground Reaction Curve in the roof of tunnel. (d) The plot of Vlachopoulos and Diederichs. In the roof of tunnel: The

distance from tunnel face/tunnel radius = (1/3.90) = 0.256. The plastic zone radius/tunnel radius = (9.21/3.90) = 2.362. From the above plot this gives Closure/max closure approximately equal to 0.359.


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Section 3 In this section, the overburden is 300 meters and the value of K0 is equal to 1.38. The maximum tunnel wall

displacement and the radius of the plastic zone in this section of tunnel are shown in figures 7a and 7b. By comparing displacement obtained from numerical method in the roof, floor and walls of tunnel (45, 47.5 and 32.5 cm), with allowable displacements on the basis of the hazard warning levels (Table 5), it appears that the tunnel in this section is completely instable and a support system should be applied for the rock masses stabilization.

Figure 6. In the section 2 of tunnel (a) Total displacements in around of the tunnel. (b) Extent of plastic zone in around of the

tunnel. (c) Ground Reaction Curve in the roof of tunnel. (d) The plot of Vlachopoulos and Diederichs. In the roof of tunnel: The distance from tunnel face/tunnel radius = (1/3.90) = 0.256. The plastic zone radius/tunnel radius = (12.99/3.90) = 3.330. From

the above plot this gives Closure/max closure approximately equal to 0.295.




Section 4

In this section, the overburden is 400 meters and the value of K0 is equal to 1.34. The maximum tunnel wall displacement and the radius of the plastic zone in this section of tunnel are shown in figures 8a and 8b. By comparing displacement obtained from numerical method in the roof, floor and walls of tunnel (76, 80 and 56 cm),


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with allowable displacements on the basis of the hazard warning levels (Table 5), it appears that the tunnel in this section is completely instable and a strong support system should be applied for the rock masses stabilization.





Ground Reaction Curve (GRC) in the roof of tunnel is shown in figures 7c and demonstrates relations between displacement and released hydrostatic stress. Furthermore, determination of the amount of tunnel roof deformation prior to support installation in this section is done using figure 7d. The Closure/max closure in the roof of the tunnel is equal to 0.240, and the closure prior to support installation equals (0.240) × (0.450) m. Thus, the allowable displacement in the roof of the tunnel prior to support installation in this section is 10.80 cm. Section 5

In this section, the overburden is 500 meters and the value of K0 is equal to 1.31. The maximum tunnel wall displacement and the radius of the plastic zone in this section of tunnel are shown in figures 9a and 9b. By comparing displacement obtained from numerical method in the roof, floor and walls of tunnel (114, 120 and 90 cm), with allowable displacements on the basis of the hazard warning levels (Table 5), it appears that the tunnel in this section is completely instable and a strong support system should be applied for the rock masses stabilization.

Ground Reaction Curve (GRC) in the roof of tunnel is shown in figures 9c and demonstrates relations between displacement and released hydrostatic stress. Furthermore, determination of the amount of tunnel roof deformation prior to support installation in this section is done using figure 9d. The Closure/max closure in the roof of the tunnel is equal to 0.180, and the closure prior to support installation equals (0.180) × (1.140) m. Thus, the allowable displacement in the roof of the tunnel prior to support installation in this section is 20.52 cm. Section 6

In this section, the overburden is 600 meters and the value of K0 is equal to 1.29. The maximum tunnel wall displacement and the radius of the plastic zone in this section of tunnel are shown in figures 10a and 10b. By comparing displacement obtained from numerical method in the roof, floor and walls of tunnel (153, 161.5 and 127.5 cm), with allowable displacements on the basis of the hazard warning levels (Table 5), it appears that the tunnel in this section is completely instable and a strong support system should be applied for the rock masses stabilization.


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Figure 10. In the section 6 of tunnel (a) Total displacements in around of the tunnel. (b) Extent of plastic zone in around of the tunnel. (c) Ground Reaction Curve in the roof of tunnel. (d) The plot of Vlachopoulos and Diederichs. In the roof of tunnel: The distance from tunnel face/tunnel radius = (1/3.90) = 0.256. The plastic zone radius/tunnel radius = (28.05/3.90) = 7.192. From


Ground Reaction Curve (GRC) in the roof of tunnel is shown in figures 10c and demonstrates relations

between displacement and released hydrostatic stress. Furthermore, determination of the amount of tunnel roof deformation prior to support installation in this section is done using figure 10d. The Closure/max closure in the roof of the tunnel is equal to 0.159, and the closure prior to support installation equals (0.159) × (1.530) m. Thus, the allowable displacement in the roof of the tunnel prior to support installation in this section is 24.33 cm.


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CONCLUSIONS This study provides an estimation of the K0 that could be used as input data for stability analysis of the

Sardasht dam tunnel. Overall, the rocks with strain-softening behaviour have the effect of localization of deformation and causes instability problems for underground openings. In this case, the following conclusions could be noted: Numerical analysis of K0 in the Sardasht dam tunnel shows that with decreasing the value of K0, the amount of displacement and radius of plastic zone around the tunnel increase. By increasing depth of the tunnel, minor changes in the value of K0 causes signification changes in the amount of displacement around of the tunnel. The displacements obtained from the numerical approach are very greater than critical displacements resulted from Sakurai's hazard warning levels (1.83, 4.33, and 10.18 cm) and indicating strong instability in the rock masses in the tunnel face. The closures prior to support installation in the roof of tunnel which determined from Vlachopoulos and Diederichs increase with decreasing the value of K0. The Ground Reaction Curves (GRC) in different sections of tunnel show uniform deformation style in the roof of tunnel.

ACKNOWLEDGMENTS The authors wish to thank the Taradod Rah Consultant Engineers for access to the data on first constructional

stage of Sardasht dam tunnel

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