An example of estimating rock mass deformation around an underground opening using numerical modeling

An example of estimating rock mass deformation around an underground opening using numerical modeling

ARTICLE IN PRESS International Journal of Rock Mechanics & Mining Sciences 47 (2010) 272–278 Contents lists available at ScienceDirect International...

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ARTICLE IN PRESS International Journal of Rock Mechanics & Mining Sciences 47 (2010) 272–278

Contents lists available at ScienceDirect

International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms

An example of estimating rock mass deformation around an underground opening using numerical modeling C.O. Aksoy , O. Kantarci, V. Ozacar Dokuz Eylul University, Department of Mining Engineering, Izmir, Turkey

a r t i c l e in f o

a b s t r a c t

Article history: Received 12 March 2009 Received in revised form 11 November 2009 Accepted 1 December 2009 Available online 4 January 2010

In rock engineering, rock strength is regarded as an important rock mass parameter and it is widely estimated using the uniaxial compressive strength (UCS) test. A UCS test in laboratory requires sampling and preparation of core samples, which necessitates time consuming and expensive studies. Furthermore, preparation of cores is almost impossible for a weak rock material taken from foliated, laminated or thinly bedded rock masses of low Rock Quality Designation (RQD) values (0–20%). In this case, determination of UCS by laboratory test may be impossible in compliance with ISRM or ASTM standards. To overcome this difficulty, indirect tests, such as Point Load Index (PLI), Schmidt Hammer (SH) Rebound Number tests are often employed to predict the UCS. However, indirect tests are likely to yield UCS values with large standard deviations depending on the geological origin of the rock mass. The Block Punch Index (BPI) has recently been developed to overcome the drawbacks of UCS and indirect tests and to minimize the errors arisen from the structural deficiencies and large standard deviations. In this study, determination of rock mass behavior in laminated–foliated Bornova Melange (yellowish-brown flysch and grayish-black flysch) and well-jointed Yamanlar Volcanics–Altindag Formation, where the second phase of the Izmir Metro tunnels was excavated is aimed. The BPI ratings were directly used in RMR calculations and indirectly used to estimate the UCS values of rock materials. Then, the obtained results were input into numerical models along with the rock mass strength (UCSRM) and deformation modulus of rock mass (ERM). The results obtained from the numerical models agreed with that obtained results from inner tunnel convergence and ground settlement measurements. & 2009 Elsevier Ltd. All rights reserved.

Keywords: Block punch index Rock mass classification RMR Metro tunneling Weak rock masses Ground settlement Tunnel convergence

1. Introduction Rock engineers have implemented various researches in order to determine the behavior and characteristics of rock masses. Hence, a number of rock mass classification systems have been developed. Each system has its own merits and demerits [1]. Producing reliable results particularly for weak or very weak rocks requires knowledge and experience [2]. A list of some rock mass classification systems that have been developed since 1946 is given in Table 1 [3]. Today, RMR [4], Q [5], GSI [6–9] and RMi [10] are the most widely utilized systems. The strength of rock material, which is commonly quantfied by the uniaxial compressive strength (UCS), is an essential input parameter for determining the strength of rock masses at a large scale. Sometimes preparation of high quality cores is almost impossible from rock material—especially from weak rock masses having low RQD values (0–20%) and foliated, laminated or thinly bedded rock masses, and from block-in-matrix type rocks [11,12].

 Corresponding author. Tel.: + 90 232 412 75 22; fax: + 90 232 453 08 68.

E-mail address: [email protected] (C.O. Aksoy). 1365-1609/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2009.12.001

Indirect methods, such as point load index (PLI) and Schmidt Hardness Index (SH), are often employed when it is impractical to prepare test samples according to the standards suggested by ISRM [13] or ASTM [14]. Moreover, because of the large range of conversion coefficients (from 10 to 50) between UCS and PLI [4,15–26], and large error range in the estimation of UCS from SH due to the compact energy used [27], the Block Punch Index (BPI) test with a slightly narrow range of conversion factor (between 2.9 and 7.6) has gained some acceptance in the estimation of UCS, especially for weak-very weak rocks. The mean conversion factor between the BPI and UCS is obtained as 5.1 [30]. Detailed information about BPI test procedure and the use of BPI for predicting UCS of rock material can be found in [2,13,17,18, 27–34]. Although the conversation factor to estimate UCS of rock material from BPIc varies between 2.9 and 7.6 depending on the type of rock material, the average value is suggested as 5.1 [30]. Depending on the unique conversion factor, the internal friction angle of rock materials obtained is almost same for any kind of rock material. Sonmez and Tunusluoglu [27] overcome the limitation of the use of a unique conversion factor by using the mi coefficient of the Hoek–Brown criterion as an indicator of rock

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Table 1 Some classification systems [3]. Classification system

Form and typea

Main applications

Source

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

Design of steel support in tunnels

Terzaghi, 1946

Tunnelling design

Laufer, 1958

Descriptive and behaviouristic form Tunneling concept Descriptive form General type

Excavation and design in incompetent (overstressed) ground Input in rock mechanics

¨ Rabcewicz, Muller and Pacher, 1958–1964 Patching and Coates, 1968

Descriptive form General type

Based on particles and blocks for communication

Deer et al., 1969

Numerical form General type

Size-strength classification

Numerical form Functional type

Rock structure rating classification (RSR) Rock mass rating classification (RMR) Q-classification system Typological classification Unified rock classification system Basic geotechnical classification (BGD) Geological strength index (GSI) Rock mass index system (RMi)

Numerical form Functional type

Based on core logging; used in other classification Deer et al., 1967 systems Based on rock strength and block diameter, used Franklin, 1975 mainly in mining Design of (steel) support in tunnels Wickham et al., 1972

Numerical form Functional type

Design of tunnels, mines, and foundations

Bieniawski, 1973

Numerical form Functional type Descriptive form General type Descriptive form General type Descriptive form General type

Design of support in underground excavation Use in communication Use in communication General applications

Barton et al., 1974 Maluta and Holzer, 1978 Williamson, 1980 ISRM, 1981

Numerical form Functional type Numerical form Functional type

Design of support in underground excavation General characterization, design of support, TMB progress

Hoek, 1994 ¨ Palmstrom, 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).

Fig. 2. Geological map of tunnel direction.

Table 2 Geomechanical properties of rocks [11,31,32].

Fig. 1. Suggested BPI ratings [28].

type (Eq. (1)). The value of the conversion factor between BPIc and UCS varies from 2 to 9 depending on the value of mi: UCS ¼ 0:80ð2:226Þm0:3824 BPIC i

ð1Þ

The type of rock materials encountered in the route of tunnel are Andesite (mi = 2575), Agglomera (mi =17 74) and Mudstone– Siltstone (mi =7 72). The conversion factor (A) is obtained between 3.8 and 6.2 depending on the types of rocks, by Eq. (1). Type 1 route tunnels of 64 m2 cross-section have been investigated as part of the second stage of the Izmir Metro Project. Detailed information regarding the geological units in the tunnel route is given in the Section 2. Determination of rock mass behavior and the identification of the measures to be taken were

Parameter

Qa

Kb1

Kb2

Kb3

Kb4

BPIc (MPa) UCS (MPa) Cohesion, c (MPa) Water content, w (%) Internal friction angle, j (1) Poisson ratio, n Natural unit weigth, g (kg/m3)

– – 0.13 18 12 0.35 2000

5.15 – 0.18 16 16 0.3 2630

7.36 – 0.32 15 19 0.27 2680

12.57 64.22 4.20 4 63 0.26 2780

9.80 49.18 2.40 6 51 0.24 2720

Qa: Alluvion. Kb1: Particled, severely altered Bornova Melange (yellowish brown). Kb2: Poorly altered Bornova Melange (grayish black). Kb3: Sligthly-intermediately weathered andesite (Yamanlar Volcanites). Kb4: Sequencing of agglomerate–sandstone–mudstone–siltstone (Altindag Forma˘ tion).

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Table 3 Geological ınformation of tunnel and results of the BPI [17,18,31]. Geological unit

Rock type

BPI (MPa)

Lithological unit remarks

Yamanlar volcanites Altindag formation

Andesite

12.57 (7 6.50)

Agglomerate

11.80 (7 7.32)

Yamanlar Volcanites Sligthly intermediately weathered andesite, sometimes massive, not disturbed, UCS: 35–92 MPa, RQD: 40–70% Altindag Formation Sequencing of agglomerate–sandstone–mudstone–siltstone, not disturbed, sometimes heavily weathered, UCS: 27– 65 MPa, RQD: 40–80%

Bornova melange

Sandstone Mudstone Siltstone

7.89 (7 3.43) 2.55 (7 0.75) 9.69 (7 5.34)

Yellowish Brown Flysch

5.15 (7 3.18)

Greyish Black Flysch

7.36 (7 3.48)

Bornova Melange Top of the tunnel face: Bornova Melange, Particled, severely altered, foliated, laminated, with clay filling, very weak with underground water, yellowish brown flysch UCS: Not available; RQD: 0–10 Bench and invert of tunnel face: Bornova Melange, poorly altered, foliated, laminated, schistozied, very weak with underground water, grayish black flysch, UCS: Not available; ROD: 0–15

performed based on the RMR System [4]. However, the BPI, suggested in [30], was employed in place of UCS, PLI and SH for the Bornova Melange, which is a laminated, foliated and weak-tovery-weak rock mass. Considering the abovementioned facts, the BPI rating was directly used in RMR calculations for the ratings of UCS used in RMR. Suggested BPI Ratings are given in Fig. 1 [30]. Since it is quite difficult to determine the rock mass parameters in the laboratory, the researchers developed some equations based on empirical studies. Since this study employs RMR, in the determination of rock mass parameters equations including RMR were used. Rock mass parameters obtained from RMR-based empirical equations values were directly input in the numerical modeling. The effect of ground water in the tunnels was also integrated into the model. Numerical models were calibrated by measurements for both sections with or without ground water.

2. Geological conditions of tunnel route The tunnel construction route of the second stage of the Izmir Metro Project, which will be integrated with the first one, follows the line in the southwest of Izmir Gulf between Ucyol and Fahrettin Altay. Excavations in the tunnel have been underway through eight service shafts. Dominating rock units in the route of tunnel are low-to-medium altered andesites known as Yamanlar Volcanics; agglomerate–sandstone–siltstone–mudstone sequence known as Altındag formation; yellowish-brown flysch and grayish-black flysch known as Bornova Melange (Fig. 2). Geomechanical properties of lithological units for these rock types are obtained from the drilling studies near the section of the tunnel, in-situ studies and the results of the tests conducted on the samples taken from the field (Table 2) [16,35,36].

3. Determination of rock mass behavior In rock engineering, knowledge of the behavior of rock mass is essential in the design of structures in rock [1,4]. Rock mass classification systems are often employed to assess the characterization and behavior of rock masses for preliminary design purposes. RMR is known as the most popular classification system and it has found wide application in various types of engineering projects. However, it has certain restrictions for weak or very weak rock masses [1,2,32,37–41]. Due to the weak and heavily jointed property of rock masses studied in this study, the most

substantial restrictions of RMR method have been the determination of strength of rock material. Although the strength of rock material is considered as a scaling parameter in many empirical equations used for predicting of rock mass strength, it is one of the basic RMR parameters. As mentioned before, some index tests such as PLI and SH were proposed to overcome the difficulties encountered during sample preparation from weak and laminated rock masses. Alternatively, the assessment of UCS, PLI and SH on the rock material of rock masses including laminations and schistosity are almost impossible. The use of the BPI test employed on small disk specimen is the most practical way for determination of UCS for this type of rock [13,28]. In order to minimize the aforementioned restrictions and difficulties encountered during the calculation of rock material strength required for the RMR values in this study, the BPI rating, suggested by Ulusay and Sulukcu [30], was used in estimation of the UCS. The BPI values were determined according to the standards suggested by ISRM [13]. The results of the study are displayed in Table 3. The BPI tests were carried out especially for weak-very weak, laminated–foliated Bornova Melange (yellowish-brown flysch and grayish-black flysch), well-jointed Yamanlar Volcanics and Altindag Formations. Therefore, a total of 2317 BPI tests (Fig. 3) were performed on the samples taken from tunnel excavation faces along the tunnel route. The rock mass parameters such as deformation modulus (ERM) and uniaxial compressive strength (UCSRM) are the fundamental input parameter in the numerical analyses. As is well known, a representative large specimen, including joint patterns, is required to obtain UCSRM and ERM directly from laboratory methods. In addition, this type of test equipment is very expensive and rarely found in conventional laboratories. Therefore, empirical equations are generally used for predicting UCSRM and ERM during design stages. Some of the well-known empirical equations developed to determine the Emass and smass of rock mass are given in Tables 4 and 5. As seen in Tables 4 and 5, some of the equations were used RMR as input. To reduce the number of models to be analyzed numerically, only Kalamaris and Bieniawski’s equation [42] was used. In fact, the other equations, which consider RMR as input, can be used for comparison. However, to reduce the number of numerical models this stage of the study, UCSRM was determined by Kalamaris and Bieniawski’s equation [42]:

scmass ¼ sci exp½ðRMR100Þ=24

ð2Þ

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Table 4 Empirical based equation for determining elasticity modulus of rock masses. Researchers Bieniawski [47] Serafim and Pereira [39] Grimstad and Barton [48] Hoek and Brown [49] Read et. al. [43]

Equation

Note

Emass (GPa) = 2RMR  100 Emass (GPa) = 10ðRMR10Þ=40

RMR 450 RMR o 50

Emass ðGPaÞ ¼ 25logQ

For Q 41

Emass ðGPaÞ ¼

qffiffiffiffiffiffi sCY

10010

Emass ðGPaÞ ¼ 0:1ðRMR=10Þ3

Palmstrom [3]

Emass ðGPaÞ ¼ 5:6ðRMRÞ0:375

Barton [5]

Emass ðGPaÞ ¼ 10QC h i1;1811 Emass ¼ 0:135 Ei ð1 þ RQD=100Þ WD

Kayabasi et. al. [50] Gokceoglu et. ˘ al. [51] Sonmez et. al. [52] Sonmez et. al. [53] Hoek and Diederichs [54]

for sci o 100 MPa

ðGSI10=40Þ

for RMR 40.1 sci Qc ¼ Q 100

1=3

Emass ¼ 0:001

h

ðEi =sci Þð1 þ RQD=100Þ WD

i1;5528

Emass ¼ Ei ðsa Þ0:4 Emass ¼ Ei 10½ððRMR100Þð100RMRÞ=4000EXPðRMR=100ÞÞ h i 1ðD=2Þ Emass ¼ E 0:02 þ 1 þ eð60 þ 15DGSIÞ=11

If there is no deformation measurement on intact rock material:Ei ¼ MR  sci MR, rate of modulus and D = 0, no blasting damage

Table 5 Empirical based equations for determining strength of rock masses. Researchers Hoek and Brown [55] Yudhbir et. al. [56] Ramamurthy [57] Kalamaris and Bieniawski [42] Bhasin and Grimstad [58] Sheorey [59] Trueman [60] Aydan and Dalgic [61] Palmstrom [3] Barton [5] Hoek et. al. [6]

Equation (units MPa)

Note

sCMASS ¼ sci exp½ðRMR100Þ=18

sci is UCS of intact rock (MPa)

sCMASS ¼ sci exp½7:65ðRMR100Þ=100 sCMASS ¼ sci exp½ðRMR100Þ=18:75 sCMASS ¼ sci exp½RMR100Þ=24 sCMASS ¼

g density of rock mass (t/m3)

 sci  1=3 100 7gQ

sCMASS ¼ sci exp½ðRMR100Þ=20 sCMASS ¼ 0:5expð0:06RMRÞ sCMASS ¼

RMR RMR þ bð100RMRÞ

sci

b =6

sCMASS ¼ RMR ¼ sci Jp  sci 1=3 sCMASS ¼ 5g Q 100 sCMASS ¼ sci sa

Emass is the elasticity modulus of rock mass (in GPa). The obtained results are given in Table 6 [18,31].

4. Geotechnical studies on the tunnel route Fig. 3. BPI test for the Bornova Melange.

Similarly, the deformation modulus of rock masses was calculated by considering the following [43]:

sci ¼ 5:1BPI

ð3Þ

Emass ¼ 0:1ðRMR=10Þ3

ð4Þ

where scmass is the strength of rock mass (in MPa), sci is the UCS of the rock material (in MPa), BPI is block punch index (in MPa) and

In addition to the geological investigations along the tunnel route, a total of forty-five boreholes (1526.32 m) [44,45] and fifteen boreholes (283.5 m) were drilled during the project planning and construction, respectively [35,46]. Geological cross-sections were taken following each advancement at the tunnel excavation face. Moreover, measurements of pressiometer, piozemeter, inclinometer, rod extensometer, tunnel convergence and ground settlements were taken periodically. In this research, it is focused on the in-situ convergence measurements and ground settlement measurements. In-situ tunnel convergence measurements and ground settlement measurements have been

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Table 6 RMR Ratings for rock masses of tunnel route [18,31]. Geological unit

Rock type

40 38 30 25 36

5.24 3.77 2.17 0.57 3.43

0.015a 6.40 5.49 2.70 1.56 4.67

Yellowish brown flysch 16 Greyish black flysch 23

0.79 1.34

0.41 0.80

Filling/Alluvion Yamanlar Volcanites Andesite Altindag Formation Agglomerate Sandstone Mudstone Siltstone Bornova Melange

a

RMR smass (MPa) Emass (GPa)

Obtained from pressiometer test.

Fig. 5. General models of numerical modeling support systems.

In the numerical modeling, the finite elements based PLAXIS 3D V.2.00 was used. Excavation and support stages were integrated as step-by-step into the models. In Fig. 5, a general view is shown for the models which were integrated with tunnel support systems for three rock masses. Deformation results obtained from numerical models and in-situ measurements are illustrated in Fig. 6. Fig. 4. The sample of in-situ tunnel convergence and ground settlement measurements.

taken every 5 m in tunnel and 20 m on the street, respectively. The convergence measurements have been taken with the optical tool and type extensometer and the ground settlement measurements have been taken with the conventional measurement tools. The sample of the measurements is given in Fig. 4 [16,18,31].

5. Numerical modeling study Rock mass parameters obtained from empirical equations given above were used in the numerical model. Tunnel convergence and ground settlement values were recorded in order to compare with the values obtained from numerical models. Also, the existence of groundwater in tunnel route and its effect on the rock mass in which tunnel behavior was excavated were also integrated into the numerical model. Numerical models were calibrated with the measurements in the locations with and without groundwater.

6. Results and discussions The predicted and measured values of ground settlements and vertical convergences are close for Yamanlar Volcanites and Altindag formation (Fig. 5). Although the ground settlement measurements are different from model values for the third model which modeled for Bornova Melange, the in-situ convergence measurements values are also close. It should be remembered that UCSRM and ERM are determined from one empirical equation, therefore some differences between predicted and measured values may be obtained. However, the differences should be within the acceptable limits.

7. Conclusions In this study, the ground settlements and convergence measurements were compared with the values obtained by numerical calculations. For this purpose the strength and deformation modulus of rock masses were determined from the

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Fig. 6. Results of numerical modeling and field measurement.

empirical equations of [42] and [43]. In fact, some other wellknown empirical equations, which consider RMR as input, can be considered for comparison. However, to reduce the number of cases, only these two empirical equations were used. In addition, due to the difficulties in the preparation of samples for the UCS test, the BPI test was used as an alternative for prediction of strength of rock material, which is an important property in the prediction of rock mass behavior. Finally, it can be said that similar ground settlements and vertical convergence values were obtained from both numerical analyses and in-situ measurements.

Acknowledgements This study was conducted under the scientific project numbered 108M151 of TUBITAK (The Scientific and Technological Research Council of Turkey) and 2005384 of Dokuz Eylul University of Scientific Research Bureau, and the protocol made with Bozoglu ˘ Construction Inc. The author would like to thank the Nevin GENC from Metropolitan Municipality of Izmir, Metin ERIS and Levent Nuray from STFA (consulting firm), Mustafa Attaroglu and Yalc- ın Yılmaz from Bozoglu Group Construction Inc. for their collaboration. References [1] Aksoy CO. Review of rock mass rating classification: historical developments, applications and restrictions. J Min Sci 2008;44(1):51–63. [2] Ulusay R, Sonmez H. Engineering properties of rock masses. Ankara: Chamber of Geological Engineering of Turkey; 2002. (in Turkish). ¨ A. On classification systems. In: Proceedings of the Geo Eng 2000, [3] Palmstrom Melbourne, 2000. [4] Bieniawski ZT. Engineering rock mass classifications. New York: Wiley; 1989. [5] Barton N. Some new Q-value correlations to assist in site characterisation and tunnel design. Int J Rock Mech Min Sci 2002;39:185–216. [6] Hoek E, Marinos P, Benissi M. Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses: the case of Athens schist formation. Bull Eng Geol Environ 2002;57:151–60. [7] Sonmez H, Ulusay R. Modifications to the Geological Strength Index (GSI) and their applicability to stability of slopes. Int J Rock Mech Min Sci 1999;36: 743–60. [8] Sonmez H, Ulusay R. A discussion on the Hoek–Brown failure criterion and suggested modifications to the criterion verified by slope stability case studies. Yerbilimleri 2002;26:77–99. [9] Cai M, Kaiser PK, Uno H, Tasaka Y, Minami M. Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci 2004;41:3–19.

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