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Original Paper
Application of Rock Mass Characterization for Determining the
Mechanical Properties of Rock Mass: a Comparative Study Mahmoud
Hashemi1 , Sh. Moghaddas2 and R. Ajalloeian3
Received: 25 July 2008 Accepted: 23 March 2009 Published online:
16 April 2009
Abstract The results of geotechnical explorations, engineering
geological investigation (including laboratory and in situ tests)
and field observations have been used, along with borehole logging
charts, to obtain the rock mass geotechnical data. Based on the
data, the rock mass along the Sabzkuh water conveyance tunnel route
was classified by rock mass rating (RMR), Q-system (Q), rock mass
index (RMi) and geological strength index (GSI) (3 methods). A new
series of correlations were established between the systems based
on the data collected from the study area. These relationships were
then compared with those reported in the literature, and two new
relations were recommended. The classifications were utilized to
calculate mechanical properties (rock mass strength and deformation
modulus) of the rock mass along the tunnel according to available
empirical relations, and to distinguish the upper-bound and
lower-bound relations.
Keywords Rock mass classification - RMR - Q - RMi - GSI -
Mechanical properties - Geotechnical explorations - Tunnel
1 Introduction
1.1 Background
Rock Mechanics and Rock Engineering Springer-Verlag
200910.1007/s00603-009-0048-y
(1) Department of Civil Engineering, Faculty of Engineering, The
University of Isfahan, 81744-73441 Isfahan, Iran
(2) Engineering Geology, Sabir Engineering Co., Tehran, Iran(3)
Department of Geology, Faculty of Science, The University of
Isfahan, Isfahan, Iran
Mahmoud Hashemi Email: [email protected]
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Rock mass classifications play an important role in estimating
the strength and deformability of rock masses and in assessing the
stability of rock slopes. They also serve as an index to rock
rippability, dredgeability, excavibility, cuttability, and
cavibility (Bieniawski 1989).
During the past 50 years, there have been numerous efforts
around the world to create a suitable engineering rock mass
classification system so that the preliminary evaluation of
feasibility, development and stability/service of engineering
structures/projects, would be possible and fairly reliable.
Terzaghis (1946) rock-load classification scheme could be
considered to be the first empirical classification system for rock
mass. Subsequently, various researchers proposed different rock
mass classification systems, including Laufer (1958), Deere et al.
(1967), Wickham et al. (1972), Bieniawski (1973), Barton et al.
(1974), Hoek (1994), Hoek et al. (1995) and Palmstrm (1995). Many
researchers have also tried to correlate the various classification
systems [mostly between rock mass rating (RMR) and Q-system (Q)].
Some relations have been proposed by Bieniawski (1976), Rutledge
and Preston (1978), Moreno (1980), Cameron-Clarke and Budavari
(1981), Abad et al. (1984), Kaiser and Gale (1985), Al-Harthi
(1993), Barton (1995), Turul (1998) and Kumar et al. (2004).
The construction of underground structures, such as powerhouses,
gas and petroleum storage systems, nuclear waste storage spaces,
and water conveyance tunnels are of high importance. The very first
step for the design and stability analysis of such structures is to
use numerical and analytical modeling methods. The methods use the
mechanical properties (deformation modulus and strength) of the
rock mass as input parameters.
Typically, a series of field tests, such as plate loading,
jacking, flat jacking, or block shear testing, are conducted to
obtain the parameters. The tests are expensive and time-consuming,
especially when they are done in underground openings.
Therefore, the empirical (indirect) methods for estimating the
parameters are the easiest, quickest and simplest alternatives.
During years of developments in rock engineering, various
empirical methods have been proposed, where these use the
classification systems as a base. To judge the relations, one needs
time to verify the relations by applying them at various sites with
different types of rocks and conditions for rock mass so that the
advantages and disadvantages will be apparent and the relations can
be improved. Although none of the relations is absolutely the best,
we may find the best one under certain conditions by comparing
them.
The estimation of uniaxial compressive strength of rock mass
using classification systems is important for correct evaluation of
underground structure stability.
For this purpose, various relations have been suggested,
including those by Yudbir et al. (1983), Kalamaras and Bieniawski
(1993), Singh (1993), Goel (1994), Bhasin and Grimstaad (1996),
Singh et al. (1997), Sheory (1997), Aydan and Dalgi (1998), Hoek et
al. (2002), Barton (2002), and Ramamurthy (2004).
A literature review of existing relations is presented by
Edelbro et al. (2007). They demonstrated that the results of the
application of the relations vary significantly, even when one
system is used by different, qualified engineers. A comparison
between the estimated rock mass with in situ measured rock mass
strength indicates the reliability of the various systems.
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To determine the engineering properties of rock mass for use in
numerical analyses, the evaluation of deformation modulus using the
classification systems is essential. Bieniawski (1978) estimated
the modulus using the RMR value. Subsequently, various empirical
relations estimating the modulus based on the classification
systems have been proposed, including those by Serafim and Pereira
(1983), Nicholson and Bieniawski (1990), Verman (1993), Verman et
al. (1997), Mitri et al. (1994), Singh (1997), Hoek and Brown
(1997), Palmstrm and Singh (2001), Barton (2002), Hoek et al.
(2002), Kayabai et al. (2003), Gokeoglu et al. (2003), Ramamurthy
(2004), Sonmez et al. (2004), and Zhang and Einstein (2004).
It is important to note that the evaluation of all input data
for the various above relations is subjective; i.e., different
input values are estimates by different people based on the same
field conditions. Therefore, different values are derived, even
with the same relation.
1.2 The Study Area The Sabzkuh water conveyance project
(including the Sabzkuh diversion dam, open channel and tunnel and
Choghakhor dam rehabilitation) is designed to transfer 90 million
m3 of water annually from the Sabzkuh drainage basin to the
Choghakhor dam reservoir. The project is located about 109 km south
of Shahr-e-Kord city and 90 km south west of Borujen city,
Chaharmahal-Bakhtyari province. The study area is situated on the
north side of Zagros mountain between 5050 to 5058 eastern
longitude and 3145 to 3158 northern latitude. The surface run-off
along the Sabzkuh River may be kept by a diversion dam, which is a
4.5 km long open channel that runs to a main. The main is 8.574 km
long, and the water is finally carried to the Choghakhor dam
reservoir (Fig. 1). The tunnel cross section has a horseshoe shape
with a diameter changing from 4.2 to 3.2 m.
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Fig. 1 Location map of the study area
2 Engineering Geological Assessment The lithology of the tunnel
route mainly consists of limestone, marly and dolomitic limestones,
dolostone, shale and variable sizes of alluvium. The lowest and the
uppermost lithologies belong to Camberian and Quaternary,
respectively. The Sabzkuh syncline is the main geologic structure
at the project area. The axis of the syncline is extended in the
NWSE direction in which the Sabzkuh River flows. The Sabzkuh tunnel
passes the north limb of the syncline and is extended in the SWNE
direction. From the viewpoint of structural geology,
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the stratification is regular along the tunnel route from the
inlet section to the F11 fault. Moving from the F11 fault towards
the outlet, the stratigraphy of the area is disturbed due to the
active structural geology, intensive erosion and complex lithology
of the area. The morphology of the area mainly consists of high
mountains and deep valleys with steep walls. At the project area,
there are karstic features and traces, including sinkholes,
solution dolines, lapies, poljes and shallow caves, which are
locally observed in limestone. A total of six boreholes have been
drilled, with overall length of 1,646 m, using wireline and rotary
core boring methods along the tunnel route. The longest borehole is
522.1 m long. Currently, approximately ten additional boreholes are
being drilled, where these are concentrated in the weak zones and
critical areas. Since the overburden is high (around 1,200 m in the
middle of tunnel route), the borehole drilling has become very
difficult and time- and money-consuming. Therefore, geophysical
exploration is preferred for these sections of the tunnel route. In
addition, the pilot (probe) horizontal boreholes are planned ahead
of main tunnel excavation (Fig. 2).
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Fig. 2 The geological map and geotechnical longitudinal
cross-section of the tunnel route
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For geotechnical evaluation and rock mass classification, the
field observation, geophysical exploration, borehole logging, the
field tests and laboratory experiments have been used and studied
thoroughly. The studies show that the rocks in the area are
slightly to moderately weathered.
Regarding the joint conditions, the wall surfaces of the joints
are mostly rough. The infillings mainly consist of calcite, ferrous
oxide and finely ground (clay to silt size) lithic particles.
The joint pattern along most parts of the tunnel consists of
three sets (two joint sets and bedding). In some areas, four joint
series are observed (three joint sets and one bedding). The results
of laboratory tests that were mainly carried out on the borehole
and some field samples show that the uniaxial compressive strength
of rocks varies from 10 to 125 MPa (Table 1).
Table 1 Summery of laboratory test results of boreholes and
field samples
Segment no.
Tunnel section
Lithology
Value of laboratory tests
From To
Uniaxial comprehensive strength (MPa)
Modulus of elasticity (GPa)
Max. Min. Ave. Max. Min. Ave. 1 0 + 000 0 + 043 Limestone 118 68
85 33 27 31
2 0 + 043 0 + 325 Marlstone and marl 28 12 15 21 15 15
3 0 + 325 0 + 461 Limestone 105 63 85 32 28 30
4 0 + 461 0 + 679
Marly limestone and calcareous shale
74 42 55 25 21 23
5 0 + 679 1 + 247 Limestone 95 52 60 32 26 29
6 1 + 247 12 + 150 Limestone and marly limeston
75 25 38 28 23 24
7 2 + 150 2 + 770 Limestone 110 53 65 30 27 31
8 2 + 770 3 + 088 Dolostone and dolomitic limestone
118 50 67 33 29 32
9 3 + 088 3 + 868 Dolostone and dolomitic limestone
112 50 62 33 28 31
10 3 + 868 4 + 015 Dolostone and marly limestone
98 48 58 29 23 26
Limestone,
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The RQD is mostly evaluated from the borehole cores, and in some
cases, it is determined using the Palmstrm (1982) method:
where J V is the volumetric joint count and is calculated
as:
where s i is the average spacing of ith joint set.
Joint wall aperture is generally higher than 1 mm. In some
stations, there are very high joint apertures (more than 50 mm),
which are mostly seen on the ground surface. Figure 3 shows one of
the cases in which a joint set is observed in a calcareous
formation (DaryanFahlian
11 4 + 015 4 + 705 dolostone and dolomitic limestone
108 52 64 31 26 29
12 4 + 705 4 + 715 Marly limestone 45 27 35 22 15 16
13 4 + 715 5 + 120 Dolostone 125 56 70 32 26 30 14 5 + 120 5 +
745 Dolostone 106 53 66 33 27 30
15 5 + 745 5 + 871 Marly limestone 44 25 32 23 15 17
16 5 + 871 6 + 193 Limestone, dolostone and dolomitic
limestone
92 55 62 30 26 28
17 6 + 193 6 + 352 Marly limestone 42 25 32 23 15 17
18 6 + 352 6 + 442 Dolostone 100 48 63 30 28 28
19 6 + 442 6 + 576 Limestone, dolostone and dolomitic
limestone
90 42 60 32 27 30
20 6 + 576 6 + 823 Marly limestone 42 22 30 22 12 14
21 6 + 823 7 + 980 Limestone, dolostone and dolomitic
limestone
90 42 58 28 25 27
22 7 + 980 8 + 059 Brecciated limestone 20 10 15 10 8 8
23 8 + 059 8 + 231 Micaceous shale 41 23 29 23 16 18
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Formation). The joint set wall spacing has been widened due to a
secondary dissolution process, so that the joint aperture is
increased to 1540 cm. The joint has a dip/dip direction of 84/110
and is approximately parallel to the tunnel axis. The joint set
wall condition is also rough.
Fig. 3 One of the cases in which a joint set is observed in a
calcareous formation (DaryanFahlian Formation)
The geological features of the tunnel route are partially shown
in Figs. 4, 5 and 6.
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Fig. 4 A shear zone is presented near the outlet between the
CHT1 and CHT2 boreholes that are a result of an active fault
(F16)
Fig. 5 The joint sets in the Khanekat formation in a level
higher than CHT3 borehole and in contact with Neyriz formation. The
joint wall condition is rough and dissoluble
Fig. 6 A dissolution and karstic cavity with dimensions of more
than a meter in the SarvakIlam formation near the ST202
borehole
A shear zone is also presented in Fig. 4, located near the
outlet between the CHT1 and CHT2 boreholes; it is a result of an
active fault (F16). The zone is extended to 100 m in width and may
affect the rock mass at the tunnel level. The zone consists of
lithic pieces with diameters
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ranging from 1 to 100 cm that are connected by a matrix from the
original formation. The lithic pieces belong to the Khanekat
formation, which consists mostly of limestone, dolostone and
dolomitized limestone.
The joint sets in the Khanekat formation at a higher level than
the CHT3 borehole and in contact with the Neyriz formation are
shown in Fig. 5. The joint wall condition is rough and
dissoluble.
A dissolution and karstic cavity with dimensions more than a
meter in the Sarvak-Ilam formation near the ST202 borehole is also
presented in Fig. 6. The cavity was made by the karstic dissolution
process, probably due to the presence of three joint sets. The
joint sets aperture measures more than 1 mm. The joint walls are
mostly rough and rarely undulating (Moghaddas 2004; Hashemi et al.
2004a, b; Ajalloeian et al. 2004).
3 Rock Mass Classification 3.1 Introduction Over the past five
decades, various rock mass classification systems have been
proposed by different researchers. All the systems tend to utilize
the rock mass characteristics using either quantitative or
qualitative methods in rock engineering. The characteristics are
undoubtedly the essential requirements for empirical design and
numerical modeling. However, none of the systems could utilize all
of the characteristics. This may be due to lack of homogenity and
isotropy in the material.
The characteristics of a particular rock mass could vary from
one site to another site, perhaps due to differences in engineering
judgments and site conditions. This has led to the creation of
various classification systems instead of a single system.
The most well-known classification systems are briefly explained
in the following sections.
3.1.1 The RMR System
Bieniawski (1973) proposed a geomechanical classification system
(RMR). The system has been revised many times, and the latest
version was proposed in 1989. The system calculates an index by
summing the ratings for six main factors: the uniaxial compressive
strength of the rock material, the RQD value, spacing, condition
and orientation of discontinuities, and ground water
conditions.
The system defines the rock mass as one of five classes based on
structural geology and strength characterization.
3.1.2 The Q-System
Barton et al. (1974) from NGI presented a tunneling quality
index, called the Q-system. The system is widely applied to various
underground openings. Multiple revisions have been
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proposed for the system (Grimstaad and Barton 1993; Barton
2002), which classifies the rock mass as one of nine classes. The
index of the system ranges from 0.001 to 1000 on a logarithmic
scale and is calculated as:
3.1.3 The RMi System
Palmstrm (1995) proposed the rock mass index (RMi)
classification system. The RMi is a volumetric parameter indicating
the approximate uniaxial compressive strength of a rock mass by
combining c and a jointing parameter (JP). JP represents the block
volume (V b) plus the joint condition (jC). The joint condition can
be estimated by joint roughness (jR), joint alteration (jA) and
joint size (jL).
The RMi system is similar to the Q-system. For instance, jA and
jR in the RMi are approximately similar to J r and J a in the
Q-system, respectively.
The system evaluates the rock mass as one of seven classes. In
addition, it has been recently revised (Palmstrm 2000; Palmstrm and
Singh 2001).
3.1.4 The GSI System
Hoek et al. proposed the geological strength index (GSI) to
obtain reliable input data, especially those related to rock mass
properties required as inputs into numerical analysis (Hoek 1994;
Hoek et al. 1995; Hoek and Brown 1997). In the last decade, the
index was further developed and modified, particularly in poor and
heterogeneous rock masses for designing projects such as tunnels,
slopes and foundations in rocks (Hoek et al. 1998, 2005; Sonmez and
Ulusay 1999, 2002; Marinos and Hoek 2000, 2001; Cai et al.
2004).
The GSI has been evaluated using three different methods that
are described in the following sections.
3.1.4.1 Evaluation of GSI Based on Field Observations
The GSI was first developed based on field observation: the
experienced engineering geologist evaluates the rock mass
conditions from outcrops (overview and structural geology). Then,
the results are compared with the corresponding evaluation table
(Hoek and Brown 1997). Finally, the table yields the GSI.
(1)
RQD rock quality designation J
n the joint set number
J r roughness number of least favorable joint
J a alteration number of least favorable joint
J w the joint water reduction factor SRF stress reduction
factor.
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3.1.4.2 Evaluation of GSI Based on Other Rock Mass
Classification Systems
According to this method, the GSI is determined through other
rock mass classification systems, such as RMR (1976 and 1989) and Q
(Hoek et al. 1995). The method is mostly convenient for the sites
in which the stratification outcrops and rock formations are not
present, but GSI estimation is required.
Based on RMR76 (Bieniawski 1976), the GSI is equal to the sum of
the ratings for four parameters: UCS, RQD, spacing and condition of
discontinuities, but the rating for the groundwater condition and
joint orientation are set to ten and zero, respectively (Hoek et
al. 1995):
For RMR76 < 18, a new parameter, Q is introduced:
For RMR89 (Bieniawski 1989), the formulation is similar to that
of RMR76. The only difference is that the groundwater condition
rating is set to 15:
Again, for RMR89 < 23, Q has been used.
It should be mentioned that the minimum rating for RMR76 and
RMR89 are 18 and 23, respectively, according to the above
conditions.
3.1.4.3 Evaluation of GSI Based on Block Volume and Joint
Surface Condition Factor
Cai et al. (2004) recently proposed a new approach based on the
block size and condition, block volume (V b) and joint condition
factor (J C). The approach was intended to increase the performance
of GSI and to make it more quantitative. Block size is determined
from the joint spacing, joint orientation, number of joint sets and
joint persistence. Compared to the variation in joint spacing, the
effect of the intersection angle between join sets is relatively
small. Thus, for practical purpose, the block volume for three or
more joint sets can be approximated as
where S i is the spacing of each joint.
(2)
(3)
(4)
(5)
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The joint surface condition (J C), which is defined by the
roughness, weathering, and infilling, is similar to the factor used
by Palmstrm (1995) to quantify the joint surface conditional and is
defined as:
where J W, J S and J A are the large-scale waviness, small-scale
smoothness and joint alteration factor, respectively.
The background of the chart provided by Cai et al. is the same
as the chart produced by Hoek and Brown (1997), but the HoekBrown
chart has been precisely quantified by Cai et al. using V b and J
C.
3.1.5 The RCR and N
Goel et al. (1996) studied the various relationships between Q
and RMR and found them to be diverse and divergent. They noted that
the UCS of intact rock ( c) indirectly presents the Q formulation.
In addition, the SRF is not present in the RMR calculation.
Therefore, they assumed that the UCS and joint orientation, and SRF
may be dropped from the RMR and Q formulations, respectively.
This led to the creation of two new concepts: rock condition
rating (RCR) and rock mass number (N). Based on the correlation
between RCR and N values for the 63 case studies from India, and
other countries, they proposed the following relationships with a
satisfactory correlation coefficient of 0.92:
where RCR = RMR (rating for c and joint orientation) and N = Q
(assuming SRF = 1).
3.2 Correlation Between the Rock Mass Classification Systems As
the various engineering rock mass classification systems were being
developed, a question arose: if two classification systems are
applied to two different sites, how can the rock masses in the two
sites be compared. The answer is to establish a correlation between
the systems in order to calculate one from another. Since some
parameters may be used in one system but not in the other, such
correlations may be used as an approximate tool and not as an
alternative for routine calculation of another system.
Various researchers have tried to correlate the systems. If the
systems are simultaneously applied in various sites, the relations
will become more convergent. Some of the relations are listed in
Table 2.
Table 2 Comparision of various correlations among the rock mass
classifications
(6)
(7)
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3.3 Results and Discussion
3.3.1 Classification Systems
Each classification system contains various parameters with
different ratings. One may find a parameter common between the
systems while the rating (dividing the boundaries and assigned
values) is different among the systems. Roughness, spacing,
alteration, and infilling are some of the parameters. Another
difference is that the systems utilize the parameters in different
ways and ranges. For example, RQD has a maximum value of 15 in the
RMR system, whereas it is directly involved in Q evaluation and
varies from 10 to 100. On the other hand, the RQD is a way to
calculate block volume (J
v) in RMi system. Some parameters are
present in one system, but absent in another system. Some
examples of such parameters are the groundwater condition in the
RMi system, the strike and dip of joints and uniaxial compressive
strength ( c) in the Q system, and the rock mass stress reduction
factor (SRF) in RMR and RMi systems. In addition, the RQD depends
on the drilling method, and the effect of the groundwater condition
depends on the drainage conditions.
Researcher(s) Correlation (relation no.) Estimated parameter
Bieniawski (1976) RMR from Q
Rutledge and Preston (1978) RMR from Q
Moreno (1980) RMR from Q Cameron-Clarke and Budavari (1981)
RMR from Q
Abad et al. (1984) RMR from Q
Kaiser and Gale (1985) RMR from Q
Al-Harthi (1993) RMR from Q
Barton (1995) RMR from Q
Turul (1998) RMR from Q
Kumar et al. (2004)
RMR from Q RMR from RMi
RMi from Q
RCR from N
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Considering the range of the ratings, the Q and RMi systems are
more sensitive than the RMR. In RMR, a range is established,
whereas in the other two methods (Q and RMi, and especially Q), the
parameters are individually and directly involved in formulas.
Therefore, the main disadvantage for the present systems is the
different ranges for a particular parameter in various systems due
to their different logic and structure.
As another example, the rating sensitivity of the joint spacing
in RMR is less than in RMi and GSI (third method, Cai et al. 2004)
because the parameter is very important in determining the block
volume, and therefore the final rating in RMi and GSI. Thus, the
joint spacing rating for RMi and GSI is more sensitive than
RMR.
Finally, none of the systems as considered to be complete. This
is also the reason that no consistent relations can be found
between the various systems.
The engineering rock mass classification has been done for 23
segments passing rock formations using four systems: RMR89, Q, RMi
and GSI (2 methods) (Fig. 7).
Fig. 7 The engineering rock mass classification for 23 segments
passing rock formations using 4 systems: RMR89, Q, RMi and GSI (3
methods)
The GSI was determined for almost all the segments using the
first method. There were two lithological units (marly limestone of
Khanekat Formation and dolostone of Dalan Formation) whose outcrops
were not available near the tunnel. Their GSI were evaluated based
on the available outcrops away from the tunnel route applying the
geological conditions of the tunnel route. The third GSI method
(3.1.4.3) was also used for all the segments to compare it with the
other two methods of GSI. Figure 7 shows that there was no apparent
difference between first and third methods of GSI. Marinos et al.
(2005) implied that the determination of GSI from third method is
not applicable for tectonically disturbed structures, such as
segment 22. They also recommended that where direct assessment of
depth conditions is not possible, such as segment 10 (Fig. 3), the
GSI in depth can be evaluated by proper adjustment of the depth
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condition in their recommended GSI chart.
However, the first GSI method is mainly based on the real GSI
characteristic (quick field evaluation of rock mass strength). Both
(first and third) methods are similar in the sense that they
evaluate the rock mass strength according to the exposed-in-surface
(outcrop) conditions, where the rock mass is determined by the
number of joint sets, alteration, wall roughness, degree of
fracturing (blocky structure) in rock mass. Therefore, GSI does not
consider the underground (depth) conditions, such as groundwater,
dip and strike of discontinuities (with respect to excavation
direction) and in situ stress characteristics.
It is also evident that the third method is similar to the RMi
system in the sense that it involves the block volume measurement
and joint condition factor. Perhaps, the only difference between
the GSI and RMi systems is that GSI does not consider the UCS ( c)
of intact rock.
For the rock masses along the tunnel route, the GSI varies in
the ranges of 2260 and 2556, for the first (Hoek et al. 1995) and
third (Cai et al. 2004) methods, respectively.
Moreover, based on the surface field evaluation, and considering
the shear zones due to faults activities, the rock mass along the
tunnel lies in the Disintegrated-Blocky class, as per the GSI
system.
The other systems such as RMR89, Q and RMi evaluate the rock
mass as very poor and fair, exceptionally poor and poor, and low
and high quality, respectively.
Overall, based on the qualitative description of rock mass, the
Q is the most conservative method (considering the weakest
description for rock mass), whereas the RMi gives the radical
(strongest) description for rock mass.
Along segment 1: as compared to other segments, RMR and Q
present high values and evaluate the rock mass similarly to the RMi
description, probably due to low overburden, reasonable strength of
intact rock (leading to SRF 1) and dry conditions for groundwater
in this segment. In addition, the rock mass is mostly blocky,
leading to higher values of RMi and GSI (Fig. 7).
Along segments 8 and 9: the RMi yields higher values than Q
because of the thick bedding, high values of J
v or the block volume formed by discontinuities, high RQD and
the uniaxial
compressive strength of intact rock, whereas these parameters
are not involved in the Q calculations, except RQD and ci
(indirectly). The high SRF due to high overburden and groundwater
condition are the other reasons for the low Q values. In this
segment of the tunnel, the RMR and GSI values are also high due to
the above reasons.
Along segment 21: due to a relatively low overburden, and
therefore, low SRF, the Q value is increased even more than that
for RMi. In addition, the RMR and GSI values are relatively low and
high, respectively, due to groundwater conditions and other
effective factors.
Along segment 22: there is a likely intersection of a shear zone
and the tunnel in depth. Therefore, the rock mass classification
calculations are very difficult for almost all the systems. Due to
the high crushing effect, the block volume value is very low,
leading to minimum values for RMi and GSI. The Q values are also
low, due to an important factor
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(SRF). The RMR evaluation is also low due to various factors,
such as very low strength and groundwater conditions.
These were the most effective parameters, whereas the other
parameters could be effective as well.
In segments 12, 15, 17 and 20: the values of all the systems are
low and almost similar. This may be due to the intersection of the
tunnel with a deep low-strength layer that belongs to the base of
the Khanekat formation, which consists of marlstone, marly
limestone, and siltstone.
3.3.2 Proposed Correlations Between the Systems
In the earlier studies, a series of correlations have been
established, and various relations were proposed which are mostly
between the Q and RMR (Table 2).
Correlated data from the Sabzkuh tunnel, along with the other
correlations available in literature (10 cases), are presented in
Fig. 8.
Fig. 8 Correlated data from the Sabzkuh tunnel, along with the
other correlations available in the literature (10 cases)
It is shown that the closest relation to the Sabzkuh tunnel data
is the one proposed by Rutledge and Preston (1978).
The recommended relation for the Sabzkuh tunnel data is
(22)
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Figure 9 shows the correlation between RMi and RMR values for
the Sabzkuh tunnel route
Fig. 9 Correlation between RMi and RMR values for the current
case and comparing with relation by Kumar et al. (2004)
It is observed that there is no similarity between the above
relation and the available literature (Kumar et al. 2004).
Figure 10 presents the correlation between Q and RMi for the
Sabzkuh tunnel data
(23)
(24)
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Fig. 10 Correlation between Q and RMi in this case and available
literature (Kumar et al. 2004)
A comparison of the above relation with available literature
(relation 20, Table 2, Kumar et al. 2004) shows that the relations
match well, especially for low values of Q (Q < 0.35). However,
relation (20) by Kumar et al. 2004 did not show good agreement with
the Sabzkuh data for high values of Q (Q > 0.35).
Figure 11 presents correlation between N and RCR for the Sabzkuh
tunnel data as:
Fig. 11 Correlation between N and RCR in this case and available
literature (Goel et al. 1996 and Kumar et al. 2004)
Comparison of the recommended relation and available literature
(Goel et al. 1996; Kumar et
(25)
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al. 2004) shows that the proposed relation in the current study
lays between the two relations in available literature.
Figure 12 shows the correlation between RMR and GSI (Hoek et al.
1995) in the current study as:
Fig. 12 Correlation between RMR and GSI (Hoek et al. 1995) in
the current study
This relation is calculated based on the first method of GSI
(Hoek et al. 1995) and RMR89.
Figure 13 shows the correlation between the first method of GSI
(Hoek et al. 1995) and the third method of GSI (Cai et al. 2004) in
the current study with a strong correlation coefficient:
Fig. 13 Correlation between first method of GSI (Hoek et al.
1995) and third method of GSI (Cai et al. 2004) in the current
study
(26)
(27)
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It is evident that there is little difference between the two
methods.
4 Determination of Mechanical Properties for Rock Masses
4.1 Uniaxial Compressive Strength of Rock Mass
4.1.1 Background
Various parameters have been used as input for different
empirical relations to get the UCS of rock mass. The parameters are
mostly related to classification systems and the rock mass
constants. However, the uniaxial compressive strength of intact
rock is used in the majority of the relations. Some of the
relations are presented in Table 3.
Table 3 Various relations for estimation of rock mass
strength
Researchers Equation (in terms of MPa) (relation no.) Limitation
Yudbir et al. (1983)
Kalamaras and Bieniawski (1993)
Singh (1993) (kN/m3)
Goel (1994) N = Q (with SRF = 1) B = tunnel width (m)
Bhasin and Grimstaad (1996)
Sheory, 1997
Aydan and Dalgi 1998
Hoek et al. (2002)
s = exp[(GSI 100)/(9 3D)] a = 1/2 + (1/6)(eGSI/15 e20/3) Q c = Q
0 ci/100
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The following points are interesting regarding the relations
presented in Table 3. First, Yudbir et al. modified the original
intact rock criterion (Bieniawski 1973) for rock mass. In addition,
Singh et al. (1997) evaluated the relation given by Bhasin and
Grimstaad (1996). They concluded that the relation is convenient
for good classes of rock mass (Q > 10, ci > 100 MPa). They
also evaluated the relation given by Singh (1993) and concluded
that the relation can be properly used for weak classes of rock
mass (Q < 10, ci > 2 MPa). Ramamurthy (2004) found the
following relation for rock mass:
where Jf is the joint factor and is set to 0 and 500 for intact
rock and rock mass, respectively, in site conditions. In addition,
Ramamurthy (2001) found the following relation as:
Substituting (38) into (39), the relation is obtained as given
by Ramamurthy (2004), which is very similar to the relation
proposed by Kalamaras and Bieniawski (1993) (Table 3).
In addition, the RQD0 is the oriented RQD in the loading or
measurement direction (in the TBM model, it is in the tunneling
direction).
4.1.2 Results and Discussion
The rock mass strength estimated using the above relations shows
a wide range (Fig. 14).
Barton (2002) Q 0 = Q (with RQD0)
Ramamurthy (2004)
(38)
(39)
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Fig. 14 The rock mass strength estimated using relations
available in literature
The relations proposed by Goel (1994) and Singh (1993) estimate
high values (upper bound) for cm, whereas the relation proposed by
Barton (2002) and Yudbir et al. (1983) yields low values (lower
bound).
Some relations, such as those proposed by Aydan and Dalgi (1998)
and Kalamaras and Bieniawski (1993), give average (medium) values.
It seems that the relation given by Hoek et al. (2002) that is
widely used in geotechnical softwares is somewhat conservative. As
explained earlier, the relations given by Kalamaras and Bieniawski
(1993) and Ramamurthy (2004) give similar results.
The cm parameter decreases as the stability and strength
condition of the rock mass becomes weaker, due to the direct effect
of ci and the values given by the classification systems.
Interestingly, none of the relations directly consider the
tunnel dimension (diameter) as a parameter, except the relation
given by Goel (1994).
For the upper bound relations, the variation of cm is much
higher, whereas the input parameter of the relations (such as
intact rock strength) varies in a small range (for example for
segments 1 and 2 with strong and weak rock masses, respectively)
(Fig. 14).
The other case studies by Edelbro et al. (2007) revealed that
the N, Yudhbir-RMR76, RMi, Q-,
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and HoekBrown-GSI methods appeared to yield reasonable agreement
with the measured strengths. These methods are thus considered the
best candidates for realistic strength estimation, provided that
care is taken when choosing values for each of the included
parameters in each method. This study has also clearly shown the
limits of the presently available strength estimation methods for
rock masses, and further work is required to develop more precise,
practical, and easy-to-use methods for determining the rock mass
strength (Edelbro et al. 2007).
4.2 Deformation Modulus of Rock Mass
4.2.1 Background
The deformation modulus of a rock mass is apparently different
from that of intact rock. To obtain the modulus of a rock mass,
there are direct (in situ) methods, which require extensive and
costly field operations, similar to those needed to obtain cm.
Therefore, indirect empirical relations were proposed to
calculate the E m
based on a particular classification system for rock mass. Some
of the relations are listed in Table 4.
Table 4 Various relations for estimation of rock mass
deformation modulus
Researchers Equation (relation no.) Limitation Bieniawski
(1978)
RMR > 50
Serafim and Pereira (1983)
RMR 50
Nicholson and Bieniawski (1990)
Verman (1993), Verman et al. (1997)
H > 50 m
Mitri et al. (1994)
Singh (1997) Q < 10
Palmstrm and Singh (2001)
1 > RMi > 0.1 1 < RMi < 30 ci < 100 MPa
Barton (2002) Q c = Q (ci/100)
Hoek et al. ci 100 Mpa
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a = 0.160.35, (0.16 for hard rocks and 0.35 for weak rock)
b D is the disturbance factor or the effect of blast damaged
stress relaxation (D = 01)
cWD is the weathering degree (14) E i and E m are in GPa, ci in
MPa and H is overburden in meter
In addition, values of deformation modulus of intact rock
(belonging to various lithologies) from laboratory tests are given
in Table 1.
Regarding the relation proposed by Verman (1993) and Verman et
al. (1997), it is assumed that the deformation modulus of the rock
mass increases with RMR and tunnel depth. This depth dependency of
the deformation modulus is likely to be more pronounced in weaker
rock masses and is almost absent in strong, brittle rock masses,
due to the effect of the confining pressure (Verman et al.
1997).
The relation given by Ramamurthy (2004) was also derived by
substituting relation (38) in the following (Ramamurthy 2001):
4.2.2 Results and Discussion
The above relations were used to estimate the E m along the
tunnel route (Fig. 15). It seems that the convergence of the
results calculated by the E m relations is greater than the results
given by the cm relations.
(2002) ci > 100 Mpa
Kayabai et al. (2003)
Gokeoglu et al. (2003)
Ramamurthy (2004)
Sonmez et al. (2004)
Zhang and Einstein (2004)
Hoek and Diederichs (2006)
(40)
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Fig. 15 Estimated Em by various relations available in
literature along the tunnel route
It can be concluded from Fig. 15 that the relation provided by
Ramamurthy (2004) gives the lowest value of E m. Therefore, it is
the most conservative relation when compared to the other
relations. The relation by Singh (1997) gives the second lowest
values. The other two relations, provided by Mitri et al. (1994)
and Gokeoglu et al. (2003) yield the highest values of E m.
It seems that the relation by Hoek and Diederichs (2006) is more
sensitive than that of Hoek et al. (2002) to the variation of D
values. By increasing the D parameter from 0 to 1, the relation by
Hoek and Diederichs (2006) shows more reduction than the relation
by Hoek et al. (2002). In addition, the modulus values generated by
the Hoek and Diederichs (2006) relation are close to that given by
the relation proposed by Singh (1997) in weak lithologies.
The other relations provided by Bieniawski (1978), Serafim and
Pereira (1983), and Hoek et al. (2002) generate medium values for E
m. The relations proposed by Palmstrm and Singh (2001) present
medium E m values, but these are not applicable for RMi > 30 and
RMi < 0.1, which is the case for segment 22.
The relation provided by Kayabai et al. (2003) seems to be
illogical and, when compared to
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the other relations, it is basically a different relation.
Of course, the relation provided by Kayabai et al. (2003) has
been modified by Gokeoglu et al. (2003). The latter also yields
results totally different from the other relations, probably due to
a decrease in ci values.
The two relations given by Verman (1993), Verman et al. (1997),
and Singh (1997) consider the overburden as a parameter, which is a
crucial factor, especially at high overburden values. These two
relations overall give reasonable values of E
m.
As the overburden increases, the E m values also become higher
according to both relations.
It should be recalled that determination of the deformation
modulus in loading and unloading cases shall be differentiated.
5 Conclusions The rock mass along the Sabzkuh tunnel has been
divided into 23 segments and classified using RMR, Q, RMi and GSI
(2 methods). The GSI varies in the ranges of 2260
(Disintegrated-Blocky) and 2556, for the first and third methods,
respectively. Please note that the quantification of GSI (Cai et
al. 2004) is not applied in tectonically disturbed rock masses in
which the structural fabric has been destroyed, such as segment 22.
In such rock masses, the application of the original qualitative
approach (Hoek et al. 1995) based on careful visual observations is
recommended (Marinos et al. 2005).
The other systems, such as RMR and Q and RMi, evaluate the rock
mass as very poor and fair, exceptionally poor and poor and low and
high quality, respectively. Overall, the Q and RMi yield the most
conservative and radical descriptions of rock mass,
respectively.
Based on Sabzkuh tunnel data, the following relations are
proposed (Table 5). The relations in the lower two rows of Table 5
are introduced for the first time in the available literature. Note
the RMR value was obtained by summing the rating of all influence
factors (six parameters). However, these relations may not be taken
to be unique because they are related to a certain rock mass type.
Moreover, the effects of anisotropy, dissolution and karstification
are not considered in these relations.
Table 5 The recommended relations based on the Sabzkuh tunnel
data
Equation (relation no.) r Fig. no. RMR = 5.37 ln Q + 40.48 (22)
0.73 8 RMR = 7.5 ln RMi + 36.8 (23) 0.69 9 RMi = 1.082Q 0.4945 (24)
0.73 10 RCR = 6 ln N + 33.84 (25) 0.59 11 GSI (Hoek et al. 1995 ) =
0.692 RMR89 + 22.32 (26) 0.86 12
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The closest QRMR correlation to the Sabzkuh tunnel data is the
Rutledge and Preston (1978).
The relations proposed by Goel (1994) and Singh (1993) estimate
high values (upper bound) for cm, whereas the relations proposed by
Barton (2002) and Yudbir et al. (1983) yield low values (lower
bound); this shows a wide range for cm. For the upper bound
relations, the variation of cm is very sensitive to variation in
the input parameter.
The Ramamurthy (2004) relation gives the lowest (lower bound)
value of E m, whereas the Mitri et al. (1994) and Gokeoglu et al.
(2003) relations yield the highest (upper bound) values of E m.
The tunnel overburden is involved directly in E m calculations
only by Verman (1993), Verman et al. (1997) and Singh (1997)
relations. As the overburden increases, the E m values also become
higher according to both the relations.
The relation by Hoek and Diederichs (2006) is more sensitive
than Hoek et al. (2002) to the variation of D values. Moreover, the
modulus values by the Hoek and Diederichs (2006) relation are
similar to those generated by the Singh (1997) relation in weak
lithologies.
Acknowledgments Thanks are expressed to the Mahab-Ghods
Consulting Engineers Company, especially R. Banihashemi and A.
Ahangaran for providing a site visit. We also thank professor Hoek,
professor Palmstrm and professor Gokeoglu for providing useful
points while writing this paper.
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