A comparative study of the determination of rock mass deformation modulus by using different empirical approaches

Engineering Geology 131–132 (2012) 19–28

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A comparative study of the determination of rock mass deformation modulus by using different empirical approaches C. Okay Aksoy a,⁎, Melih Geniş b, Gülsev Uyar Aldaş c, Vehbi Özacar a, Samet C. Özer d, Özgür Yılmaz b a

Dokuz Eylul University, Department of Mining Engineering, Izmir, Turkey Zonguldak Karaelmas University, Department of Mining Engineering, Zonguldak, Turkey Ankara University, Department of Geophysical Engineering, Ankara, Turkey d Istanbul Technical University, Department of Mining Engineering, Istanbul, Turkey b c

a r t i c l e

i n f o

Article history: Received 20 October 2011 Received in revised form 4 January 2012 Accepted 20 January 2012 Available online 31 January 2012 Keywords: Rock mass Deformation modulus Numerical modelling Tunneling

a b s t r a c t The increase in rock engineering projects over the last decade, has made an increase in the importance of the determination of the rock mass parameters. Although properties of rock material are usually determined at laboratory, it can also be determined by special in situ tests. These in situ tests are both expensive and time consuming. Therefore, empirical equations are developed to estimate rock mass properties by several researchers. In numerical modelling, rock mass properties are important. Furthermore controlling the results of models, making back analysis and taking the feedback are very important. Comparison of different empirical equations of deformation modulus of rock mass suggested by different researchers by using field displacement measurements and numerical modelling results is aimed in this study. © 2012 Elsevier B.V. All rights reserved.

1. Introduction In a rock engineering project, final design processes are very time consuming, expensive and need great experience. Feng and Hudson (2010) explained what should have been done to find how much information is needed at which of a project. Feng and Hudson (2004) discussed the ways ahead for rock engineering design methodologies and presented two updated flow charts (Hudson and Feng, 2007; Feng and Hudson, 2010). Information, design geometry, uncertainties about application in design exist in the literature (Mazzoccola et al., 1997; Andersson et al. 2004; Feng and An, 2004; Feng and Hudson, 2004; Hudson and Feng, 2007; Feng and Hudson, 2010). In the beginning of the design process, definition and characterization of rock mass had to be done. For this purpose, some researchers have developed rock mass classification systems (Table 1). These systems are frequently used at the preliminary design phase. The rock mass properties (e.g. deformation modulus) needed at the design process are determined by empirical equations based on those systems. The static modulus of deformation is among the parameters that best represent the mechanical behaviour of a rock and of a rock mass, in particular when it comes to underground excavations. All in situ deformation tests are expensive and difficult to conduct. They are mostly conducted in special test adits or drifts excavated

⁎ Corresponding author: Tel.: + 90 232 412 75 22; fax: + 90 232 453 08 68. E-mail address: [email protected] (C.O. Aksoy). 0013-7952/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2012.01.009

by conventional drill and blast, having a span of 2 m and a height of 2.5 m using various forms of test methods. It is generally known that in situ tests of the deformation modulus of rock mass are subject to measurement errors, both from equipment, test site preparation and blasting damage in the test adit (Palmstrom and Singh, 2001). Also these measurements involve limited volumes of the rock mass. Therefore, good site characterizations of the rock mass and use of an appropriate indirect method may in many cases give better results than expensive in situ measurements (Palmstrom and Singh, 2001). Some empirical equations for determining rock mass deformation modulus are given in Table 2. Applications and comparison of those empirical equations with each other are performed recently (Hashemi et al., 2010; Justo et al., 2010). Numerical modelling studies, based on empirical equations, should be confirmed by in situ field measurements. In this research, numerical modelling studies of tunnels having different rock mass properties are investigated. Rock mass deformation modulus, as one of the important input parameters at numerical models, was determined by empirical equations and then displacement occurring around opening was compared with field measurements. 2. Geological and geotechnical properties In this study, hydroelectric power plants at Ordu, Tokat, Amasya, Bartın and Izmir metro tunnels are used as the cases. Supports and rock masses of tunnels in Tokat, Amasya, Bartın and Ordu are different but their cross-sections are almost the same (23 m 2). Also metro tunnels in Izmir have different rock masses and 64 m 2 cross-

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Table 1 Some rock classification and characterization systems (revised from Palmström, 1995, Edelbro et al., 2006, Palmström and Stille, 2007). Name

Form and typea

Main applications and remarks

Author and first version

Terzaghi rock load classification system Lauffer's stand-up time classification New Australian tunneling method (NATM) Rock classification for rock mechanical purposes Unified classification of soils and rocks Rock Quality Designation (RQD)

Descriptive and behaviouristic form Functional type Descriptive form General type Descriptive and behaviouristic form tunneling concept Descriptive form General type Descriptive form General type Numerical form General type Numerical form Functional type Numerical form Functional type Numerical form Functional type Numerical form Functional type Numerical form Functional type Descriptive form General type Descriptive form General type Descriptive form General type Numerical form Functional type Numerical form Functional type Numerical form Functional type

Tunnels with steel support (unsuitable for modern tunnelling)

Terzaghi (1946)

For input in tunnelling design (conservative)

Lauffer (1958)

For excavation and design in incompetent ground (utilized in squeezing ground condition) For input in rock mechanics

Rabcewicz (1964, 1965)

Size-strength classification Rock Structure Rating (RSR) Rock Mass Rating (RMR) Q Classification System Mining RMR (MRMR) Typological classification Unified rock classification system Basic geotechnical classification (BGD) Slope Mass Rating (SMR) Geological Strength Index (GSI) Rock Mass Index (RMi)

Based on particles and blocks for communication Based on core logging; used in other classification systems

Patching and Coates (1968) Deere et al. (1969) in Deere and Deere (1988) Deere et al. (1967)

Based on rock strength and block diameter, used mainly in mining Franklin (1975) For design of (steel) support in tunnels (not useful with steel fibre Wickham et al. (1972) schotcrete) For design of tunnels, mines, and foundations Bieniawski (1973) For design of support in underground excavation (tunnel, large caverns) Rock support in mining

Barton et al. (1974)

For use in communication

Laubscher (1975) in Laubscher (1977) Matula and Holzer (1978)

For use in communication

Wiliamson (1980)

For general applications

ISRM (1981)

Forecast stability problems and support techniques for slopes

Romana (1985)

Indicates the strength of rock masses, input to engineering applications Rock engineering, general characterization, design of support

Hoek (1994) Palmström (1995)

a

Glossary:

— — — — —

Descriptive form: input to the system is mainly based on descriptions; Numerical form: input parameters are given numerical ratings according to their character; Behaviouristic form: input is based on rock mass behaviour in a tunnel; General type: system is worked out to serve as a general characterization; Functional type: system is structured for a special application (for example, for rock support).

sections (Aksoy, 2008). Geological properties of study fields and tunnel supports are given in Table 3. The distributions of rock mass characterizations in GSI chart are also given in Fig. 1. The most important parameters that affect rock engineering design are rock mass properties. Preliminary designs request the determination of these parameters. Rock mass classification systems are easy and very useful methods to determine rock mass properties. Uniaxial compressive strength and deformation modules of intact rock are obtained from the laboratory tests in accordance with the methods suggested by ISRM, ASTM or other international standards. However, uniaxial compressive strength of rock material is determined indirectly by BPI because preparing a standard sample for uniaxial compressive strength was not possible at the Izmir metro tunnel in Bornova. Geomechanical properties of rock units are given in Table 4. At the study areas, different rock mass classification systems such as RMR, Q, GSI and RMi were used and the results were given in Table 5. Rock mass deformation modules used at numerical analyses are calculated by using empirical equations proposed by Nicholson and Bieniawski (1990), Palmstrom (1996), Palmstrom and Singh (2001), Barton (2002), Sonmez et al. (2004), Hoek and Diederichs (2006) (Table 6). The empirical equation proposed by Barton (2002) used Qc value instead of Q value. The basic reason for selecting these equations is that these empiric equations are updated and published recently.

3. Numerical modelling study Excavation-support stages in the field are integrated exactly in modelling studies. The methodology used at a numerical modelling is the same as the methodology used at this type of works. In a numerical modelling study, firstly excavation stage is completed and then support is carried out. Those processes are defined into models in various stages, depending on the construction of tunnel. All the parameters in modelling process (meshing, boundary condition etc.) are chosen the same for all cases. The cross-section of 22.6 m2 and 64 m 2 tunnels is given in Fig. 2. Plaxis 3D Tunnel, a three-dimensional finite element program developed for the analysis of tunnels and underground constructions (Plaxis 3D, 2004) is used. In the analyses, the behaviour of rock mass is described by the use of the linear elastic-perfectly plastic model with the Mohr–Coulomb yield criterion and a non-associative flow rule. Vertical in situ stress (σv, 0) applied to the model boundaries was assumed to be equal to overburden stress. The initial horizontal stress (σh, 0) is related to the initial vertical stress by the coefficient of lateral earth pressure (k), (σh, 0 = k*σv, 0). As boundary condition, model size is defined three times longer than the tunnel's size to prevent tunnels from the boundary condition. Structural elements (such as shotcrete, bolt) were implemented to the model as geogrid and plate elements according to the field excavation stage.

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Table 2 Some equations for determining deformation modulus of rock mass. Researchers

Equation

Notes

Bieniawski (1978) Sefarim and Pereira (1983)

Emass = 2 RMR − 100 (GPa) Emass = 10(RMR − 10)/40 (GPa) h
i Ei RMR Emass ¼ 100 0:0028 RMR2 þ 0:9 exp 22:82 h n
oi Emass ¼ Ei 0:5 1− cos π RMR 100

For RMR > 50 For RMR b 50

Emass = 5.6 RMi0.375 (GPa) Emass = 7 RMi0.4 (GPa) qffiffiffiffiffiffiffiffi GSI−10 σ ci Emass ¼ 100 10 40 ðGPaÞ
 RMR 3 Emass ¼ 0:1 10 ðGPaÞ

For 1 > RMi > 0.1, moderately jointed rock mass For 1 b RMi b 30, moderately jointed rock mass

Nicholson and Bieniawski (1990) Mitri et al. (1994) Palmström (1996) Palmstrom and Singh (2001) Hoek and Brown (1997) Read et al. (1999)

For σcib 100 MPa

1

Kayabasi et al. (2003)

Emass ¼ 10 Q c 3 Q c ¼ Q σ ci =100  1:1811 E ð1þRQ D=100Þ Emass ¼ 0:135 i WD 

1:5528

Gokceoglu et al. (2003)

Emass ¼ 0:001

Sonmez et al. (2004)

Emass = Ei(sa)0.4

s = exp[(RMR − 100)/9]

Barton (2002)

ðEi =σ ci Þ ð1þRQ D=100Þ WD

a = 0.5 + 1/6[exp(− GSI/15) − exp(− 20/3))] exp(− RMR/100))] [((RMR − 100)(100 − RMR)/4000

Emass = Ei10 1−D=2 Emass ¼ Ei 0:02 þ ð 60þ15 D−GSI Þ=11 1þe

Sonmez et al. (2006) Hoek and Diederichs (2006)

s = exp[(RMR − 100)/9] If there is no deformation measurement on intact rock material: Ei = MR ⋅ σci

RQD: rock quality designation. RMR: rock mass rating. RMi: rock mass index. Q: rock mass quality rating. GSI: geological strength index. σci: UCS of intact rock. E i: deformation modulus of intact rock. Emass: deformation modulus of rock mass. MR: modulus ratio. WD: weathering degree. D: disturbance factor. s, a: Hoek–Brown rock mass constants.

Table 3 Geological remarks of tunnel locations and support type. Location Tunnel Rock units code

Excavation type

Support type

Geological remarks

Ordu

TO-1 TO-2 TO-3

Basalt Basalt Basalt

Blasting Blasting Blasting

Shotcrete, d = 5 cm Bolt, l = 2 m and 2 × 2 Shotcrete, d = 5 cm Bolt, l = 2 m and 2 × 2 Shotcrete, d = 5 cm Bolt, l = 2 m and 2 × 2

Amasya

TA1-1 TA1-2

Clayey limestone Sandstone

TT1-1

Claystone

Impact hammer and blasting Impact hammer and blasting Impact hammer

TT1-2

Sandy limestone Claystone

Blasting

Impact hammer

TB1-1

Claystone– mudstone Claystone– mudstone Limestone

TB1-2

Sandstone

Blasting

TI1-A

Andesite

Impact hammer

TI1-S

Sandstone

Impact hammer

TI1-F

Flysch

Impact hammer

Shotcrete, d = 10 cm Bolt, l = 2.5 m and 2 × 2, Steel support = 0.8–1.25 m Shotcrete, d = 10 cm Bolt, l = 2.5 m and 2 × 2, Steel support = 0.8–1.25 m Shotcrete, d = 10–15 cm Bolt, l = 2–3 m and 2 × 2, Steel support = 0.8–1.00 m Shotcrete, d = 10–15 cm Bolt, l = 2–3 m and 2 × 2, Steel support = 0.8–1.10 m Shotcrete, d = 10–15 cm Bolt, l = 2–3 m and 2 × 2, Steel Support = 0.8–1.20 m Shotcrete, d = 10–15 cm Bolt, l = 2–3 m and 2 × 2, Steel support = 0.8–1.20 m Shotcrete, d = 10–15 cm Bolt, l = 2–3 m and 2 × 2, Steel support = 0.8–1.20 m Shotcrete, d = 5–10 cm Bolt, l = 2 m and 2.5 × 2.5 m Shotcrete, d = 5–10 cm Bolt, l = 2 m and 2.5 × 2.5 m Shotcrete, d = 20–30 cm Bolt, l = 4–6 m and 1.5 × 1.5, Steel support = 1–1.5 m Shotcrete, d = 20–30 cm Bolt, l = 4–6 m and 1 × 1, Steel support = 1–1.25 m Shotcrete, d = 30 cm Bolt, l = 6 m and 1 × 1, Steel support = 0.8–1 m

Blocky, very few widely spaced discontinuities, slightly weathered, RQD: 75 Blocky, very few widely spaced discontinuities, slightly weathered, RQD: 80 Blocky, very few widely spaced discontinuities with ground water, slightly weathered, RQD: 55 Very blocky, moderately weathered with clay band, RQD: 55

Tokat

TT2-1 TT3-1 TT3-2 Bartın

Izmir

Impact hammer

Impact hammer Blasting

Very blocky, slightly weathered with clay band, RQD: 65 Blocky-disturbed, faulted and many discontinuities, highly weathered, RQD: 30 Disintegrated, slightly weathered, RQD: 35 Blocky-disturbed, faulted and many discontinuities with underground water, highly weathered, RQD: 25 Blocky-disturbed, faulted and many discontinuities, moderately weathered, RQD: 30–35 Blocky-disturbed, faulted and many discontinuities with clay band, , highly weathered, RQD: 35 Blocky, slightly weathered, RQD: 70–75 Blocky, highly weathered, RQD: 30–35 Very blocky, sligthly weathered andesite, RQD: 50–55 Very blocky, moderately weathered, sometimes highly weathered siltstone and claystone, RQD: 35–45 Particle, severely altered, foliated, laminated, with clay filling, very weak with underground water, yellowish brown flysch, RQD: 0–15

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Fig. 1. The distributions of rock mass on GSI chart (modifed from Hoek and Marinos, 2000).

4. Monitoring of field measurement Measurement stations were set up at certain points in the tunnels to determine the convergence occurrence while and after the tunnel excavations and time-dependent changes. Places of measurement stations are given in Fig. 3 as Station Points A, B and C. The vertical displacement values, where the convergences end, were used in the comparison with the results of numerical modelling studies.

5. Results and discussions 12 hydroelectric plant tunnels and 3 metro tunnels were examined in the scope of this research. The descriptions of the rock mass

in tunnels were made with the most-used rock mass classifications (RMR, Q, GSI and RMI). Deformation module of the rock masses was estimated by the help of different empirical equations based on those classifications. The main purpose of this study is to compare the numerical modelling results and convergence measurements at tunnels having different rock mass properties. Results obtained from these comparisons were used for questioning the rock mass deformation modulus performances obtained through empirical equations. Although the classification systems used to characterize the rock masses containing discontinuities is inadequate in some cases, today, they are one of the most-used methods. Significant problems may happen especially in the representation of very weak, extremely weak and very blocky systems with some classification systems.

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Table 4 Geomechanical properties of rock material and rock mass. Location Rock unit

Water content (%)

Unit weight (kN/m3)

Uniaxial compressive strength Deformation modulus (σci) (MPa) (Ei) (GPa)

Cohesion (Cmass) Internal friction angle of (MPa) rock mass (o)

Poisson ratio

Ordu

2.35 2.35 2.35 8.65

26.2 26.2 26.2 23.4

195 201 246 28.5

18.25 18.90 19.45 7.15

2.58 3.0 5.22 0.21

65.89 66.14 66.70 37.93

0.23 0.23 0.23 0.32

7.15 5.70 2.1

23.8 23.5 24.2

32.5 32.1 99.45

8.65 3.15 5.55

0.4 0.08 0.22

51.93 22.80 41.84

0.28 0.34 0.25

5.25 9.10

23.5 23.9

44.0 51.0

5.05 6.45

0.08 0.13

23.72 28.77

0.34 0.30

11.20

23.7

49.4

4.85

0.11

26.86

0.30

2.15 3.65 4.0 6.0 16.0

26.5 21.7 27.8 27.2 26.3

119.2 145.2 64.1 42.1 26.3

9.36 3.32 12.14 7.85 0.90

1.15 0.25 0.50 0.26 0.081

56.49 47.48 66.80 60.71 41.72

0.23 0.28 0.26 0.24 0.30

Amasya

Tokat

Bartın Izmir

Basalt Basalt Basalt Clayey limestone Sandstone Claystone Sandy limestone Claystone Claystone– mudstone Claystone– mudstone Limestone Sandstone Andesite Sandstone Flysch

Table 5 Rock mass classifications of studied tunnels. Location

Rock unit

RMR

Q

GSI

RMi

Ordu

Basalt Basalt Basalt Clayey limestone Sandstone Claystone Sandy limestone Claystone Claystone–mudstone Claystone–mudstone Limestone Sandstone Andesite Sandstone Flysch

68 70 74 50 59 25 30 23 30 27 60 29 50 40 17

7.38 8.91 11.39 6.84 16.31 0.37 0.21 0.22 0.41 0.30 4.95 0.04 3.04 1.43 0.01

73 75 79 52 64 30 35 28 35 32 65 32 55 45 22

12.41 17.97 37.7 0.41 2.34 0.004 0.01 0.003 0.01 0.006 2.82 0.00906 0.44 0.069 0.001

Amasya Tokat

Bartın Izmir

Some troubles also come up with laboratory tests to determine the deformation modules. For example Elasticity Module/UCS ratios can be variable. This situation is partially a result of test conditions and this may slightly affect the results of the study. Even though there are limitations and inadequacies, these methods have been used constantly by rock engineers. In order to evaluate the method's performance, comparing the field measurements and numerical modelling results was considered as a suitable way. Rock deformation modules obtained through empirical equations suggested by different researchers were used as input data to the numerical models of 15 tunnels mentioned above. Keeping all the initial parameters and boundary conditions constant, except rock deformation modulus, results were examined. Vertical deformation values obtained from both measurement points at tunnels and from numerical models were evaluated for examination of results (Table 7). In Table 7, numerical modelling results obtained from rock mass deformation modulus suggested by different researchers and in situ measurements are given as graphics. RMi based graphics for some

Table 6 The deformation modulus of rock mass used for numerical modelling. Location Rock unit

Nicholson and Bieniawski (1990)

Amasya

Tokat

Bartın Izmir

Basalt Basalt Basalt Clayey limestone Sandstone Claystone Sandy limestone Claystone Claystone– mudstone Claystone– mudstone Limestone Sandstone Andesite Sandstone Flysch

Barton (2002)

Sonmez et al. (2004)

Hoek and Diederichs (2006)
Emass ¼ Ei 0:02  1−D=2 þ 1 þ eð60þ15 D−GSIÞ=11

3 Emass = 5.6 RMi0.375 (1 > RMi > 0.1) E mass ¼ 10 Q c Emass = 7 RMi 0.4(1 b RMi b 30)

Emass = Ei(sa)0.4

5.60 6.25 7.46 1.08

19.17 22.23 29.90 4.01

24.33 26.16 30.38 12.49

8.25 9.06 10.49 2.46

6.09 6.82 8.02 1.20

1.88 0.14 0.33

9.84 N/A N/A

17.44 4.93 5.94

3.89 0.66 1.31

2.91 0.26 0.63

0.20 0.38

N/A N/A

4.59 5.94

0.99 1.52

0.36 0.73

0.24

N/A

5.31

1.07

0.45

2.11 0.18 1.83 0.76 0.02

10.60 N/A 4.12 N/A N/A

18.07 5.31 12.49 8.43 1.44

3.34 0.45 4.47 2.31 0.14

3.30 0.16 4.96 1.76 0.05

Emass

Ordu



3 2 RMR Ei 6 7 2 ¼ 4 0:0028 RMR þ 0:9e 22:82 5 100

Palmström (1996) Palmstrom and Singh (2001)

1

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Fig. 2. Simple view of models mesh (a, hydroelectric power plant tunnels; b, metro tunnels).

tunnels do not exist in this table. Because, Palmström (1996) and Palmstrom and Singh (2001), do not suggest any equations for the case in which RMi values are higher than 30 and smaller than 0.1. When rock parameters in Table 4 and rock mass deformation modules in Table 6 are examined, it is seen that RMi and Q based rock mass deformation modules are considerably high. The results from the studies show that, in case of hard rock mass condition and big size of block, numerical modelling results obtained through deformation modules suggested by Palmstrom and Singh

(2001)'s equations, are close to in situ measurements. The most important reason of this is considered as block size. Because the most important parameter of RMi is the block size and representing the rock mass is much easier when the block size increases. This case proves the above mentioned fact that there is trouble in representation of rock mass having discontinuity and weak, very weak and blocky conditions. The accuracy of the result can be observed in Table 6 that gives numerical modelling results. Investigating the rock mass deformation

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modulus suggested by Barton (2002) in Table 6, it is seen that their values are higher than others. Palmstrom and Broch (2006) explained this situation with the criticism to Q system; “requirement of wide blocks to characterize joints correctly”. Higher rock mass deformation values can be comprehended from vertical convergence measurements obtained both from in situ measurements and numerical modelling (Table 7). The main parameter for rock mass deformation modules, obtained from the empirical equation suggested by Sonmez et al. (2004) and Hoek and Diederichs (2006), is the GSI values. Both studies give very close results about the rock mass deformation modules. It stands out that rock mass deformation modules determined by Sonmez et al. (2004) are lower in hard rocks and higher in weak rocks. Examining the in situ measurements and numerical modelling results, it is observed that studies using rock mass deformation modules suggested by Sonmez et al. (2004), are closer to real measured values. In light of this information, it can be said that, rock deformation modulus suggested by Palmstrom and Singh (2001) are very close to field measurement results at high embrittle rocks. Similarly, rock mass deformation modulus suggested by Sonmez et al. (2004) at other rock mass gives closer results to field measurements of the studied areas. 6. Conclusions

Fig. 3. Simple view of measurement stations (a; for hydroelectric power plant project, b; for metro project).

Rock mass deformation modulus is a very important parameter in rock engineering studies. One of the methods to determine this parameter is performing in situ tests and the other one is using empirical equations suggested by different researchers. This important parameter used in numerical modelling serves to represent rock mass. Hudson and Feng (2007) give the flow chart of “how the numerical modelling studies should be made”. It is also important to keep in mind that most empirical methods in rock engineering give

Table 7 Comparison of results of numerical modelling with field measurements. Location

Code

Ordu

TO1

Photo

Analyses results

TO2

TO3

(continued on next page)

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Table 7 (continued) Location

Code

Amasya

TA1-1

TA1-2

Tokat

TT1-1

TT1-2

TT2-1

TT3-1

TT3-2

Photo

Analyses results

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Table 7 (continued) Location

Code

Bartın

TB1-1

Photo

Analyses results

TB1-2

Izmir

Tİ1-A

TI1-S

TI1-F

NB: Nicholson and Bieniawski (1990) PS: Palmström (1996), Palmstrom and Singh (2001), B: Barton (2002). S: Sonmez et al. (2004) HD: Hoek and Diederichs (2006).

averaged values and that there may be significant variation (Palmstrom and Stille, 2007). Working at 12 hydroelectric plant tunnels and at 3 metro tunnels, having different rock mass conditions, rock mass deformation modulus calculated from different empirical equations were evaluated. In this assessment, results of numerical modelling that the calculated rock mass deformation modules used and in situ vertical convergence measurement results were compared and results are listed below: i) Rock mass deformation modules obtained from Barton (2002) empirical equation are higher than other empirical equations. In numerical model results, less deformation is determined with respect to measured deformation values from field. ii) Rock mass deformation modules calculated through suggested empirical equation by Palmstrom and Singh (2001) gives more realistic results in tunnels which have hard (almost brittle level) and big block sized rock mass. For medium and weak rock masses (especially very blocky rock mass), however, results diverge from measured deformation values. Thus, it is

considered that using RMi based rock mass deformation modules are more convenient for hard and big block sized masses. iii) Rock deformation modules obtained from empirical equations suggested by Sonmez et al. (2004) and Hoek and Diederichs (2006) are very close to each other. However, it is detected that, rock mass deformation values obtained from the equation suggested by Sonmez et al. (2004) are lower in hard and big block-sized rock masses and higher in weak and little block sized rock masses than that suggested by Hoek and Diederichs (2006). iv) Performance of the equation suggested by Sonmez et al. (2004) for determining the rock mass deformation modulus in numerical modelling is more realistic.

Acknowledgements This study is realized by utilizing number 106M589 project which is supported by TUBITAK. Authors thank N. Genç, H. Aydın and E.

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