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A discussion on the adjustment parameters of the Slope Mass Rating (SMR) system for rock slopes
A discussion on the adjustment parameters of the Slope Mass Rating (SMR) system for rock slopes Jun Zheng, Yu Zhao, Qing L¨u, Jianhui Deng, Xiaohua Pan, Yunzhen Li PII: DOI: Reference:
S0013-7952(16)30064-3 doi: 10.1016/j.enggeo.2016.03.007 ENGEO 4251
To appear in:
Engineering Geology
Received date: Revised date: Accepted date:
2 November 2015 15 March 2016 19 March 2016
Please cite this article as: Zheng, Jun, Zhao, Yu, L¨ u, Qing, Deng, Jianhui, Pan, Xiaohua, Li, Yunzhen, A discussion on the adjustment parameters of the Slope Mass Rating (SMR) system for rock slopes, Engineering Geology (2016), doi: 10.1016/j.enggeo.2016.03.007
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ACCEPTED MANUSCRIPT Title: A discussion on the adjustment parameters of the Slope Mass Rating (SMR) system for rock slopes Author Names: Jun Zheng a, Yu Zhao a, Qing Lü a, *, Jianhui Deng b, Xiaohua Pan a, Yunzhen Li c Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China
b
State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource &
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a
c
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Hydropower, Sichuan University, Chengdu 610065, China
Sichuan Academy of Environmental Science, Chengdu 610041, China
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*Corresponding Author: Tel.:+86 57188208732 fax: +86 57188208732. E-mail address: [email protected]
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Abstract: Rock mass classification systems are common tools used in the design and construction of rock engineering. Numerous classification systems have been developed for rock slopes, of which the Slope Mass
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Rating (SMR) system is the most popular. Consequently, many rock slope classification systems have been derived from the SMR system. However, these systems are not good at determining the values of the two
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adjustment parameters F1 and F3, implying that the original SMR system may contain theory defects. In this paper, we propose some corrected methods for determining F1 and F3 and perform a series of analyses
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considering the three failure modes of rock slopes: plane, wedge, and toppling failures. The results of the
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discrepancy analysis from F1 illustrate that, with respect to each of the aforementioned three failure modes the calculated original SMR index is larger than, or equal to, the real value, and the designed slope is possibly in danger. The results of the discrepancy caused by the F3 illustrate that for each of the aforementioned three failure modes, the calculated original SMR index is smaller than, or equal to, the real value, and the designed slope might be conservative and not economical. Key words: Slope Mass Rating (SMR); Rock slope stability; Structurally-controlled failures; Adjustment factors; Kinematic analysis 1. Introduction A rock mass is a natural geological material; it is also an assemblage of intact rock blocks and discontinuities (e.g., joints, weak bedding planes, weak zones, weak schistosity planes, and faults). Due to the long-term geological processes, the geometrical and mechanical properties of a rock mass are extremely complex. Moreover, its environment is also complex (e.g., the groundwater conditions and in-situ stress both have great variations). To quantify the complex properties of a rock mass based on past experience (Stille and Palmström, 2003), various taxonomies, usually called as rock mass classification systems, have been developed. Those
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ACCEPTED MANUSCRIPT classification systems are of great significance to improving the design and construction of rock mass engineering (Wu and Wang, 2014). Many classification systems are presented in Table 1. Of them, the Slope Mass Rating (SMR) system (Romana, 1985) is widely used for rock slopes (e.g., Huang and Fan, 1998; Romana et al., 2003; Irigaray et
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al., 2003; Yilmaz et al., 2012; Siddique et al., 2015; among others). The SMR was derived from the Rock Mass Rating (RMR) system (Bieniawski, 1979). The RMR system was originally created for tunneling
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applications (Bieniawski, 1979), but the author (Bieniawski, 1989) proposed slope adjustment factors to take into account whether the discontinuities strike and dip are favorable or not to slope failure (Tomás et al.,
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2007). However, it is not easy in practice to apply the RMR system to slopes, because Bieniawski (1989) only provided five adjustment ratings (0, -5, -25, -50, and -60) with respect to five orientation relationships
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between the discontinuities and slope face (i.e., very favorable, favorable, fair, unfavorable, and very unfavorable), however did not propose a detailed quantitative definition of the five orientation relationships.
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The SMR system eliminated the aforementioned shortcomings of the RMR system and has become the most important classification for rock slopes. Hence, the SMR system has been used as the basis of many other
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systems. Chen (1995) developed the Chinese Slope Mass Rating (CSMR) system by adding the discontinuity condition (e.g., faults or intercalated layers, bedding planes, and joints) and slope height to the SMR system.
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Tomás et al. (2007) modified the SMR system by replacing the discrete classifications of the SMR with continuous functions. Daftaribesheli et al. (2011) addressed the Fuzzy Slope Mass Rating (FSMR) system
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using a fuzzy set theory to quantify the ambiguous results influenced by the uncertainties of the characteristics of the rock masses. Tomás et al. (2012) built upon their 2007 work and developed a graphical approach for the SMR, based on the stereographic representation of the discontinuities and the slope to obtain the adjustment parameters; this system easily calculates the correction parameters of the SMR in cases where all slopes have the same dip with a different strike, as in linear infrastructure and open pit mining. Singh et al. (2013) described a New Slope Mass Rating (NSMR), incorporating a new parameter, the overburden thickness profile, into the SMR system; this parameter is best suited while preparing the stability map of mountain areas, where tectonic activity is high. Though the SMR system has been widely used in practice and has led to the development of numerous classification systems for rock slopes, there are some theoretical defects for determining the parameters F1 and F3 in the computational formula of the SMR index given by Romana (1985). Therefore, the primary aim of this study is to correct the determination methods for F1 and F3. Note that the similar defects exist in the above-mentioned derived classification systems from the SMR system. 2. Review of the SMR system
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ACCEPTED MANUSCRIPT The SMR index, introduced by Romana (1985), is determined by adding four adjustment factors to the basic RMR proposed by Bieniawski (1979). These factors depend on the discontinuity-slope relationship and the method of excavation (Romana, 1985). The SMR can be determined by (Romana, 1985): SMR = RMR b + 𝐹1 𝐹2 𝐹3 + 𝐹4
(1)
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where: (a) RMRb is the basic RMR index resulting from Bieniawski's (1979) rock mass classification without any
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adjustment, it can be obtained by adding five parameters including strength of intact rock material (uniaxial compressive strength or point load strength) (Rδ), rock quality designation (RRQD), spacing of discontinuities
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(RSD), condition of discontinuities (RCD), and condition of Groundwater (RCG) as follows: RMR b = 𝑅𝛿 + 𝑅𝑅𝑄𝐷 + 𝑅𝑆𝐷 + 𝑅𝐶𝐷 + 𝑅𝐶𝐺
(2)
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(b) F1 depends on the parallelism between the dip directions of the discontinuity and the slope face (denoted as αd and αs, respectively) in the cases of a plane or toppling failure (Romana, 1985), and between the trend
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of the intersecting line of the two discontinuities (labeled as αil) and αs in the cases of a wedge failure (Anbalagan et al., 1992);
(c) F2 refers to the dip angle of discontinuity (denoted as βd) in the case of a plane failure (Romana, 1985) (Anbalagan et al., 1992);
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and the plunge of the intersecting line of two discontinuities (labeled as βil) in the case of a wedge failure
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(d) F3 reflects the relationship between βd and the dip angle of the slope (βs) in the cases of a plane or toppling failure (Romana, 1985) and between βil and βs, in the cases of a wedge failure (Anbalagan et al., 1992); and
(e) F4 is an adjustment factor that depends on the excavation method (Romana, 1985). Note that Romana (1985 and 1993) did not consider the wedge failure for rock masses in the original SMR system; Anbalagan et al. (1992) added the wedge failure into the system. A wedge failure is probably the most common and general case dealt with in rock slope stability analyses (Hoek and Bray, 1981; Zheng, 2015). Therefore, in this investigation, a wedge failure was considered. The values for F1, F2, F3, and F4 can be obtained by referring to Tables 2 and 3. According to Romana (1985 and 1993) and Anbalagan et al. (1992), the values of γ, η, and ζ can be obtained as follows: |𝛼d − 𝛼s | plane failure 𝛾 = {|𝛼d − 𝛼s − 180| toppling failure |𝛼il − 𝛼s | wedge failure
(3a, 3b, 3c)
𝛽 𝜂={ d 𝛽il
plane failure wedge failure
(4a, 4b, 4c)
plane failure toppling failure wedge failure
(5a, 5b, 5c)
𝛽d − 𝛽s 𝜁 = {𝛽d + 𝛽s 𝛽il − 𝛽s
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ACCEPTED MANUSCRIPT where: γ, η, and ζ are the parameters necessary for determining the values of F1, F2, and F3, respectively. 3. Review of kinematic analysis 3.1. Plane failure
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According to Hoek and Bray (1981) and Goodman (1989), the conditions of a kinematic plane failure are: (1) 0 ≤ γ < γPlim, where γ is the intersecting angle between the dip directions of the discontinuity and the slope
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face, and the whole range of γ is between 0° and 180°; γPlim is the limit value of γ, and its range is between 0°
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and 90°; the values of γPlim are suggested as 90°, 30°, and 20° or 30° by Goodman (1989), Hoek and Bray (1981), and Rocscience (2014), respectively;
(2) βd > φ, where φ is the friction angle of the discontinuity; and
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(3) βsa > βd, where βsa is the apparent dip angle of the slope in the direction of the dip direction of the discontinuity (Fig.1). It should be noted that βsa is the apparent dip angle of the slope, not the true dip angle
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of the slope (βs). 3.2. Toppling failure
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Hoek and Bray (1981) and Goodman (1989) stated that the kinematic toppling conditions include: (1) 0 ≤ γ < γTlim, where γ is the intersecting angle between the dip directions of the discontinuity and the slope face,
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and the entire range of γ is between 0° and 180°; γTlim is the limit value of γ, and its range is between 0° and
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90°. Note that the value of γTlim is usually suggested as 30° (Goodman, 1989); (2) βd > φ; (3) βsa > 90° －βd + φ (Fig. 2); and (4) the spacing between the discontinuities should be small, to allow for the formation of thin layers of rock. 3.3. Wedge failure
The most common case of a wedge failure is a wedge sliding onlyalong the intersecting line of two discontinuities. In this case, the kinematic wedge sliding can be visualized as sliding on a special plane (a fictitious discontinuity) having the intersecting line as the steepest descent line of the fictitious discontinuity. Thus, the conditions of a kinematic wedge failure can be described as in Hoek and Bray (1981) and Goodman (1989): (1) 0 ≤ γ < γWlim, where γ is the intersecting angle between the trend of the intersecting line of two discontinuities and the slope face, and the entire range of γ is between 0° and 180°; γWlim is the limit value of γ, and its range is between 0° and 90°; the values of γWlim are suggested as 90° (Goodman, 1989); (2) βil > φ; and (3) βsa > βil, where βsa is the apparent dip angle of slope in direction of the trend of the intersecting line. 4. Existing defects for determining parameters F1 and F3 and the corrected approaches 4.1. Plane failure
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ACCEPTED MANUSCRIPT Comparing the determination methods for F1, F2, and F3 with the three conditions of kinematic plane failure, it is not difficult to find that F1, F2, and F3 reflects the three failure conditions, respectively. Eq. (3a) is used to calculate the intersecting angle γ between αd and αs. Since the ranges of both αd and αs are between 0° and 360° (Priest, 1993), the calculated values of γ from Eq. (3a) are incorrect in some cases. For example,
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assume that αd = 10°, αs = 352° as shown in Fig. 3, then γ = 342° according to Eq. (3a), and F1 = 0.15 (Table 2); however, the information in Fig. 3 illustrates that γ should be equal to 18° and F1 should be equal to 0.7, |𝛼d − 𝛼s | 360° − |𝛼d − 𝛼s |
if |𝛼d − 𝛼s | ≤ 180° if |𝛼d − 𝛼s | > 180°
(6)
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𝛾={
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according to Table 2. Therefore, γ with respect to a plane failure should be expressed as:
As described by Romana (1985), in the mode of a plane failure, F3 refers to the probability that
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discontinuities daylight on the slope face. The information in Table 2 and Eq. (5a) shows that when βd - βs < 0, in other words βs > βd, the discontinuity can daylight on the slope face. However, as stated above,
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condition (3) of a kinematic plane failure is βsa > βd.
As illustrated in Fig. 4, Oy represents the direction of north, Ox represents east, ABCD is the slope face, OB points the dip direction of the slope, αs is the dip direction of the slope, βs is the dip angle of the slope;
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EFGH is the discontinuity plane, OC points to the dip direction of the discontinuity, αd is the dip direction of
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the discontinuity, βd is the dip angle of the discontinuity, γ is the intersecting angle of the dip directions of the of discontinuity.
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slope and the discontinuity, and βsa is the apparent dip angle of the slope in the direction of the dip direction Fig. 4 illustrates that EFGH can or not daylight on the slope face; this directly depends on the relationship between βsa and βd, not on the relationship between βs and βd. Therefore, it is not correct to say that the value of F3 is determined according to the value of βd - βs in the SMR system proposed by Romana (1985). In addition, ζ , in the cases of a plane failure, should be expressed as: 𝜁 = 𝛽d − 𝛽sa
(7)
where βsa can be determined by (Zheng et al., 2015): 𝛽sa = atan(tan𝛽s cos𝛾)
(8)
The following example is used to illustrate the possible problems caused by the original determination method for F3, proposed by Romana (1985). Assume that there are two rock slopes (i.e., slopes i and j). The values of some of the parameters are obtained as follows: RMR b𝑖 = RMR b𝑗 = RMR b
(9)
𝐹4𝑖 = 𝐹4𝑗 = 𝐹4
(10)
where: RMRbi and RMRbj are the values of the RMRb of slopes i and j, respectively; F4i and F4j are the values of the F4 of slopes i and j, respectively. The mean orientations of the most unfavorable discontinuity sets
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ACCEPTED MANUSCRIPT existing in the two slopes are given in Table 4. The obtained values of F1, F2, and F3 (according to Table 2) are also presented in Table 4. Substituting Eqs. (9-10) and the values of F1, F2, and F3 in Table 4 into Eq. (1) yields: (11)
SMR𝑗 = RMR b − 9 + 𝐹4
(12)
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SMR 𝑖 = RMR b − 7.5 + 𝐹4
Combining Eqs (11) and (12) results in:
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SMR 𝑖 − SMR𝑗 = 1.5 > 0
(13)
Therefore, the values of the SMR index for slopes i and j show that the stability of slope i is higher than
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that of slope j. The kinematic analysis is also applied to the two slopes. The results illustrate that: (a) βsai =
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81.1° > βdi = 74°, 0 ≤ γi = 38 < γPlim = 90° (Goodman, 1989), and βdi = 74° > φi = 35°, and thus the slope i is unstable; (b) βsaj = 29.6° < βdj = 70°, and thus the slope j is stable. The kinematic analysis shows that the stability of slope i is lower than that of slope j. The dip direction of the discontinuity existing in slope i is
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close to the dip direction of slope i. The dip direction of the discontinuity existing in slope j is close to the strike of slope j. According to the engineering experience, apparently the stability of slope i is lower than that
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of slope j. Using the corrected approaches proposed in the paper, we can know that the value of SMRbi -
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SMRbj is equal to -7.5, and hence, the stability of slope i is lower than that of slope j. The results of the case fully illustrate that the SMR system proposed by Romana (1985) might yield
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incorrect results in some cases, due to the flawed determination approach for F3. Consequently, the corrected approaches proposed in this paper can yield the correct results. 4.2. Toppling failure
Similarly, there are some defects for determining F1 and F3, in regard to the toppling failures in the original SMR system proposed by Romana (1985). Hence, γ and ζ should be expressed as follows: 𝛾={
180° − |𝛼d − 𝛼s | |𝛼d − 𝛼s | − 180°
if |𝛼d − 𝛼s | ≤ 180° if |𝛼d − 𝛼s | > 180°
𝜁 = 𝛽d + 𝛽sa
(14) (15)
4.3. Wedge failure There are some similar problems for determining F1 and F3 in the cases of wedge failures in the original SMR system proposed by Romana (1985). As such, γ and ζ should be given by: 𝛾={
|𝛼il − 𝛼s | 360° − |𝛼il − 𝛼s |
if |𝛼il − 𝛼s | ≤ 180° if |𝛼il − 𝛼s | > 180°
𝜁 = 𝛽il − 𝛽sa where αil and βil can be obtained as follows (Zheng et al, 2015):
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(16) (17)
ACCEPTED MANUSCRIPT 𝑰12 = 𝒏1 × 𝒏2
(18)
where n1 and n2 are the upward unit normal vector of the two discontinuities forming the wedge and I12 is the vector along the intersecting line of the two discontinuities: if 𝑧12 < 0
𝑰′12 = −𝑰12 if 𝑧12 > 0
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{
𝑰′12 = 𝑰12
(19)
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where I′12 is the downward vector along the intersecting line of the two discontinuities; and z12 is the z
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component of I12. By denoting the coordinates of I′12 as x′12, y′12, and z′12, the plunge βil and trend αil
𝛽il = sin−1 (
|𝑧′12 |
2
2
√𝑥′ +𝑦′12 +𝑧′12 12
(
𝑥′12
2
) (20)
)
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𝛼il = 𝑡𝑎𝑛 {
−1
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of I′12 can be expressed as (Kulatilake 1985):
𝑦′12
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where the range of βil is between 0° and 90°; the range of αil is between 0° and 360° and is measured clockwise from the y-axis. The coordinate quadrant of αil is determined by the signs of x′12 and y′12. In summary, the input parameters of the SMR corrected by this paper are presented in Fig. 5.
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5. Discrepancy analysis for SMR indexes between the original SMR system proposed by Romana (1985) and the corrected system
5.1. Analysis of discrepancies caused by F1 Comparing Eqs. (3a) and (6), it is not difficult to find that, with respect to a plane failure, (a) when |αd - αs| ≤ 180°, the value of the SMR index, according to Romana (1985), is correct; and (b) when |αd - αs| ≥ 180°, the value of γ determined according to Romana (1985) is larger than its real value, the obtained value of F1 is possibly smaller; as such, a possibly larger value of the SMR will be calculated. Hence, the designed slope is possibly in danger, according to the calculated SMR index. According to Eqs. (3b) and (14), in the cases of a toppling failure, (a) when 0° ≤ αd - αs ≤ 180° or αd αs > 180°, the value of the SMR index, calculated by Romana (1985), is correct; and (b) when αd - αs < 0°, the value of γ determined by Romana (1985) is larger than its real value, the obtained value of F1 is possibly smaller, and a possibly larger value of the SMR will be calculated. Hence, the designed slope is possibly in danger, according to the calculated SMR index. Similarly, by comparing Eqs. (3c) and (16), in regard to a wedge failure, (a) when |αil - αs| ≤ 180°, the value of the SMR index, according to Romana (1985), is correct; and (b) when |αil - αs| ≥ 180, the value of γ
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ACCEPTED MANUSCRIPT given by Romana (1985) is larger than its real value, the obtained value of F1 is possibly smaller, and a possibly larger value of the SMR will be calculated. Hence, the designed slope is possibly in danger, according to the calculated SMR index. In summary, the discrepancy analysis for F1 shows that, with respect to each of the three failure modes
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(i.e., plane, toppling, and wedge failure), the SMR index calculated by Romana (1985) is larger than, or equal to, the real value. As such, the designed slope is possibly in danger, according to the calculated SMR index.
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5.2. Analysis of discrepancies caused by F3 5.2.1 Plane failure
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The true dip angle of a slope is always larger than, or equal to, its apparent dip angle. Hence, the value of ζ calculated by Eq. (5a) is always smaller than, or equal to, the value calculated by Eq. (7). The obtained value
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of F3 is always smaller than, or equal to, its real value. A smaller value of SMR will possibly be calculated. And hence, the designed slope might be conservative and not economical, according to the calculated SMR
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index.
The range of γ (0° -180°) is divided into 36 equal parts; 37 values (0°, 5°, ..., 175°, 180°) can be obtained for γ. The ranges of βd and βs, both of which are between 0° and 90°, are separately divided into 18 equal
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parts. Each of the obtained 19 values (0°, 5°, ..., 85°, 90°) are then respectively assigned to βd and βs. There
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are 37 × 19 × 19 = 13357 hypothetical cases developed by combining them.
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For each of the 13357 hypothetical cases, the values of the SMR index can be calculated by the two methods discussed previously: (1) the method proposed by Romana (1985) and (2) The method proposed in this paper. The difference in the values of the SMR index between the two methods is the discrepancy caused by F3. The statistical histogram of the discrepancy was given in Fig. 6(a). The results in Fig. 6(a) illustrate that a 79.6% discrepancy is within 3; only 0.4% is larger than 10. The results reveal that, with respect to F3, the original method proposed by Romana (1985) has little influence on the value of the SMR index in most cases of a plane failure. However, in those cases with around a 20 discrepancy, the original method will probably cause a waste in the economy. Therefore, it is recommended that the proposed method in this paper is adopted to determine the value of F3 with respect to a plane failure for an SMR system. 5.2.2. Toppling failure Similarly, the following conclusion can be obtained: in the cases of a toppling failure, the SMR index calculated by Romana (1985) is smaller than, or equal to, the real value. As such, the designed slope might be conservative and not economical, according to the calculated SMR index. The aforementioned 1357 hypothetical cases were also used for a toppling failure. The results are presented in Fig. 6(b). The figure shows that an 85.9% discrepancy is within 1; only 0.21% is larger than 5. It seems that, with respect to F3, Romana’s (1985) method has little influence on the value of the SMR index in 8 / 25
ACCEPTED MANUSCRIPT most of the cases of a toppling failure. However, in those cases with around a 5 discrepancy, the original method might still cause waste in the economy. Therefore, we recommend that the proposed method in this paper is adopted to determine the value of F3 for a toppling failure for an SMR system. 5.2.3. Wedge failure
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In the cases of a wedge failure, the SMR index calculated by Romana (1985) is smaller than, or equal to, the real value. As such, the designed slope might be conservative and not economical, according to the
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calculated SMR index.
The aforementioned 13357 hypothetical cases were used for a wedge failure. It should be noted that, for
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the plane and toppling failure, γ was the intersecting angle between the dip directions of discontinuity and slope, but for the wedge failure, γ was the intersecting angle between the dip direction of the slope and the
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trend of the intersecting line of the two discontinuities. Note that in cases of a wedge failure, βd should be replaced by βil. As stated previously, a wedge failure can be visualized as sliding on a fictitious discontinuity
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having the intersecting line as the steepest descent line of the fictitious discontinuity. Therefore, the same statistical results as a plane failure can be obtained for a wedge failure as illustrated in Fig. 6(a). The same
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conclusion can be made as follows: the proposed method in this paper should be adopted to determine the
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6. Summary and conclusions
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value of F3 in the cases of a wedge failure for the SMR system.
Based on the list in Pantelidis (2009), a summary table of the existing rock mass classification systems was presented. A brief review of the SMR system and kinematic analysis was also stated. The theoretical defects for determining the values of the adjustment parameters F1 and F3 in the computational formula of an SMR index, developed by Romana (1985), were discussed. The corrected determination approaches for F1 and F3 were then developed. In addition, the discrepancy analysis for the original determination method was also performed in the study. The results of the discrepancy analysis from F1 show that, with respect to each of the three failure modes (plane, toppling, and wedge failure), the SMR index calculated by Romana (1985) is larger than, or equal to, the real value. Hence, the designed slope is possibly in danger, according to the calculated SMR index. Therefore, the developed method in this paper to determine the value of F1 should be adopted for an SMR system. The results of the discrepancy caused by F3 illustrate that, for each of the aforementioned three failure modes, the SMR index calculated by Romana (1985) is smaller than, or equal to, the real value. and the designed slope might be conservative and not economical, according to the calculated SMR index. Overall, 13357 hypothetical cases were designed and applied for analyzing the discrepancy caused by F3 with respect to each of the three failure modes. The results show that: (1) in the cases of a plane or wedge failure, 79.6% discrepancy is within 3, and only 0.4% is larger than 10; (2) for a toppling failure, 85.9% discrepancy is 9 / 25
ACCEPTED MANUSCRIPT within 1, and only 0.21% is larger than 5; (3) with respect to F3, the original method proposed by Romana (1985) has little influence on the value of the SMR index in most of cases for all three failure modes; (4) however, the original method might bring waste into an economy for a particular case with a larger discrepancy; and (5) therefore, the proposed method in this paper should be adopted to determine the value of
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F3 for an SMR system. It is worthy to note that similar defects exist in other classification systems (Chen, 1995; Tomás et al.,
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2007 and 2012; Daftaribesheli et al., 2011; Singh et al., 2013) that have been derived from the SMR system; the corrected approach developed in this paper is also applicable to those derived systems. Consequently,
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study while using the SMR system or its derived methods.
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engineers are encouraged to adopt the corrected determination approaches for F1 and F3 proposed by this
Acknowledgments
CSMR F1, F2, F3, F4 F4i, F4j FSMR I12 I′12 n 1, n 2 NSMR RCD RCG RMR RMRb RRQD RSD Rδ SMR x′12, y′12, z′12 z12 αd αil αs βd βil βs βsa
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Notation
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D
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The work was funded by the National Basic Research Program of China (973 Program; No. 2015CB057903), the National Natural Science Foundation Projects (No. 41502268 & No. 41202216), the Fundamental Research Funds for the Central Universities(2016QN4018), and the Research Programs of Transportation Department of Zhejiang Province (No. 2014H21 & No. 2013H46). The authors would also like to thank Professor Resat Ulusay and other two anonymous referees for reviewing the paper and providing valuable suggestions.
Chinese Slope Mass Rating four adjustment parameters of SMR system values of F4 of slopes i and j, respectively Fuzzy Slope Mass Rating vector along the intersection line of two discontinuities downward vector along the intersection line of two discontinuities upward unit normal vector of two discontinuities forming the wedge New Slope Mass Rating condition of discontinuities condition of Groundwater Rock Mass Rating basic RMR index Rock quality designation spacing of discontinuities uniaxial compressive strength or point load strength Slope Mass Rating coordinates of I′12 z component of I12 dip directions of discontinuity trend of the intersection line of two discontinuities dip directions of slope dip angle of discontinuity plunge of the intersection line of two discontinuities dip angle of slope apparent dip angle of slope in the direction of the dip direction of discontinuity for plane or toppling failure; the apparent dip angle of slope in the direction of the trend of the intersection line for wedge failure
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γ, η, ζ γPlim γTlim γWlim φ Oy Ox ABCD OB EFGH OC i, j RMRbi, RMRbj
intersection angle between the dip directions of discontinuity and slope face for plane or toppling failure; intersection angle between the trend of the intersection line of two discontinuities and the dip direction of slope for wedge failure three parameters for determining the values of F1, F2, and F3, respectively limit value of γ for plane failure limit value of γ for toppling failure limit value of γ for wedge failure friction angle of discontinuity north direction east direction slope face pointing the dip direction of slope discontinuity plane pointing the dip direction of discontinuity slope number values of RMRb of slopes i and j, respectively
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γ
References
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Anbalagan R., Sharma S., Raghuvanshi T.K., 1992. Rock mass stability evaluation using modified SMR approach. In: Proceedings of 6th national symposium on rock mechanics, Bangalore, India, 258–68. Barton N.R., Lien R., Lunde J., 1974. Engineering classification of rock masses for the design of tunnel support. Rock Mech. Rock Eng. 6(4): 189–239. Bieniawski Z.T., 1973. Engineering classification of rock masses. Trans. S. Afr. Inst. Civ. Eng. 15, 335–44. Bieniawski Z.T., 1976. Rock mass classification in rock engineering. Proceedings of the symposium on explorer for rock engineering, Johannesburg, 97–106. Bieniawski Z.T., 1979. The geomechanics classification in rock engineering applications. Proceedings of the 4 th international congress on rock mechanics, Montreux, 41–48. Bieniawski Z.T., 1989. Engineering rock mass classifications. NewYork: Wiley. Chen Z., 1995. Recent developments in slope stability analysis. Proceedings of the 8th international congress ISRM, Tokyo, 1041– 8. Daftaribesheli A., Ataei M., Sereshki F., 2011. Assessment of rock slope stability using the Fuzzy Slope Mass Rating (FSMR) system. Appl. Soft. Comput. 11(8), 4465–4473. Deere D.U., 1963. Technical description of rock cores for engineering purposes. Rock Mech. Eng. Geol. 1(1), 17–22. Franklin J.A., Louis A.C., Masure P., 1974. Rock material classification. Proc. 2 nd Int. Cong. Eng. Geol., IAEG, Sao Paulo, 325– 341. Goodman R.E., 1989. Introduction to rock mechanics, 2nd edn. Wiley, NewYork. Hack R., 1996. Slope stability probability classification. Vol. 43 ITC Delft Publication, Enschede, Netherlands. Hack R., Price D., Rengers N., 2003. A new approach to rock slope stability—a probability classification (SSPC). Bull. Eng. Geol. Environ. 62, 167–184. Hoek E., Bray J.W., 1981. Rock Slope Engineering, 3nd edition. Institute of Mining and Metallurgy, London. Hoek E., Kaiser P.K., Bawden W.F., 1995. Support of underground excavations in hard rock. Rotterdam: Balkema. Hoek E., Marinos P., Benissi M., 1998. Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses: the case of the Athens schist formation. Bull. Eng. Geol. Environ. 57,151–60. Huang C., Fan J., 1998. The SMR method and case history of slope rock mass quality classification. Geotech. Eng. Tech. 43(1), 7– 15. (in Chinese) International Society for Rock Mechanics (ISRM), 1981. Basic geotechnical description of rock mass quality. Int. J. Rock Mech. Min. Sci. 18, 85–110. Irigaray C., Fernández T., Chacón J., 2003. Preliminary rock-slope-susceptibility assessment using GIS and the SMR classification. Nat. Hazards 30(3), 309–324. Kulatilake P.H.S.W., 1985. Fitting of Fisher distribution on discontinuity orientation data. J. Geolog. Educ. 33, 266–269. Laubscher D.H., 1977. Geomechanics classification of jointed rock masses—mining applications. Trans. Inst. Min. Metall. 86, A1– 8. Laubscher D.H., 1984. Design aspects and effectiveness of support systems in different mining conditions.Trans. Inst. Min. Metall. 93, A70–82. Laubscher D.M., Page C.H., 1990. The design of rock support in high stress or weak rock environments. Proceedings of the 92 nd Canadian Institute of Mining and Metallurgy, Ottawa. Lauffer H., 1958. Gebirgsklassifizierung für den Stollenbau.Geol Bauwesen 24(1), 46–51.
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Lindsay P., Campbell R.N., Fergusson D. A., Gillard G.R., Moore T.A., 2001. Slope stability probability classification, Waikato coal measures, New Zealand. Int. J. Coal Geol. 45(2), 127–145. Marinos P., Hoek E., 2000. GSI—a geologically friendly tool for rock mass strength estimation. Proceedings of the geological engineering 2000 conference, Melbourne, 1422–46. Marinos P., Hoek E., 2001. Estimating the geotechnical properties of heterogeneous rock masses such as flysch. Bull Eng. Geol. Environ. 60: 85–92. Marinos V., Marinos P., Hoek E., 2005. The geological strength index: applications and limitations. Bull. Eng. Geol. Environ. 64, 55–65. Mazzocola D.F., Hudson J.A., 1996. A comprehensive method of rock mass characterization for indicating natural slope instability. Q. J. Eng. Geol. 29, 37–56. Moon B.P., Selby M.J., 1983. Rock mass strength and scarp forms in Southern Africa. Geografiska Ann—SerA 65A(1–2), 135–45. National Standards Compilation Group of People’s Republic of China (NSCGPRC), 1995. GB 50218-94 Standard for engineering classification of rock masses. Beijing: China Planning Press. (in Chinese) Nicholson D.T., 2002. Identification of deterioration hazard potential for quarried rockslopes. Quarry Manage 29(1), 43–52. Nicholson D.T., 2003. Breakdown mechanisms and morphology for man-made rockslopes in North West England. North West Geogr. 3(1), 12–26. Nicholson D.T., 2004. Hazard assessment for progressive, weathering-related breakdown of excavated rockslopes. Q. J. Eng. Geol. Hydrogeol. 37, 327–46. Nicholson D.T., Hencher S.R., 1997. Assessing the potential for deterioration of engineered rock slopes. Proceedings of the IAEG symposium, Athens, 911–917. Nicholson D.T., Lumsden A.C., Hencher S.R., 2000.Excavation-induced deterioration of rockslopes. Landslides in research, theory and practice, vol.3. London: Thomas Telford, 1105–1110. Olivier H.J., 1979. A new engineering-geological rock durability classification. Eng. Geol. 14(4), 255–279. Aydan, Ö., Ulusay, R., Tokashiki, N., 2014. A new rock mass quality rating system: rock mass quality rating (RMQR) and its application to the estimation of geomechanical characteristics of rock masses. Rock Mech. Rock Eng. 47(4), 1255–1276. Palmström A., 1995. RMi-a rock mass characterization system for rock engineering purposes. PhD Thesis, Oslo University, Norway. Pantelidis, L., 2009. Rock slope stability assessment through rock mass classification systems. Int. J. Rock Mech. Min. Sci. 46(2), 315-325. Priest S.D., 1993. Discontinuity analysis for rock engineering, Chapman & Hall, London. Rabcewicz L., 1964. The New Austrian Tunnelling Method. Water Power. 11, 453–457. Ritter W., 1879. Die Statik der Tunnelgew ölbe. Berlin: Springer. Robertson A.M., 1988. Estimating weak rock strength. Proceedings of the SME annual meeting, Phoenix, 1–5. Rocscience, 2014. Dips V6.0 Tutorial Manual 04: Toppling, Planar Sliding, Wedge Sliding. Toronto: Rocscience Inc. Romana M., 1985. New adjustment ratings for application of Bieniawski classification to slopes. Proceedings of the international symposium on role of rock mechanics, Zacatecas, Mexico, 49–53. Romana M., Serón J.B., Montalar E., 2003. SMR Geomechanics classification: Application, experience and validation. ISRM 2003–Technology roadmap for rock mechanics, South African Institute of Mining and Metallurgy, 981–984. Romana M., 1993. A geomechanical classification for slopes: slope mass rating. Comprehensive Rock Eng. 3, 575-599. Selby M.J., 1980. A rock mass strength classification for geomorphic purposes: with tests from Antarctica and New Zeland. Zeit Geomorph 24(1), 31–51. Selby M.J., 1982. Rock mass strength and the form of some inselbergs in the central Namib desert. Earth Surf. Proc. Landforms 7(5), 489–97. Şen Z., Sadagah B.H., 2003. Modified rock mass classification system by continuous rating. Eng. Geol. 67(3), 269–280. Siddique T., Alam M.M., Mondal M.E.A, Vishal V., 2015. Slope mass rating and kinematic analysis of slopes along the national highway-58 near Jonk, Rishikesh, India. J. Rock Mech. Geotech. Eng. 7(5), 600–606. Singh A., Connolly M., 2003. VRFSR—an empirical method for determining volcanic rock excavation safety on construction sites. J. Div. Civ. Eng. Inst. Eng. (India) 84, 176–91. Singh A., 2004. FRHI—a system to evaluate and mitigate rockfall hazard in stable rock excavations. J. Div. Civ. Eng. Inst. Eng. (India) 85, 62–75. Singh R.P., Dubey C.S., Singh S.K., Shukla D.P., Mishra B.K., Tajbakhsh M., Ningthoujam P.S., Sharma M., Singh, N., 2013. A new slope mass rating in mountainous terrain, Jammu and Kashmir Himalayas: application of geophysical technique in slope stability studies. Landslides, 10(3), 255-265. Stille H., Palmström A., 2003. Classification as a tool in rock engineering. Tunn. Undergr. Sp. Techn. 18(4), 331–345. Terzaghi K., 1946. Rock defects and loads on tunnel supports. Rock tunneling with steel supports. vol. 1. Youngstown, OH: Commercial Shearing and Stamping Company, 17–99. Tomás R., Cuenca A., Cano M., García-Barba J., 2012. A graphical approach for slope mass rating (SMR). Eng. Geol. 124, 67–76. Tomás R., Delgado J., Serón J. B., 2007. Modification of slope mass rating (SMR) by continuous functions. Int. J. Rock Mech. Min. Sci. 44(7), 1062–1069. Ünal E., 1996. Modified rock mass classification: M-RMR system. Milestones in rock engineering, the Bieniawski Jubilee collection. Rotterdam: Balkema, 203–223.
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Wickham G.E., Tiedemann H., Skinner E.H., 1972. Support determination based on geologic predictions. Proceedings of the 1 st North American rapid excavation tunneling conference, NewYork: AIME, 43–64. Wu A., Wang B., 2014. Engineering rock mass classification method based on rock mass quality index BQ for rock slope. Chinese J. Rock Mech. Eng. 33(4), 699–706. (in Chinese) Yaşar E., 1995. The properties and classification of anisotropic rocks. PhD Thesis. University of Nottingham, UK. Yilmaz I., Marschalko M., Yildirim M., Dereli E., Bednarik M., 2012. GIS-based kinematic slope instability and slope mass rating (SMR) maps: application to a railway route in Sivas (Turkey). Bull. Eng. Geol. Envir. 71(2), 351–357. Zheng J., Kulatilake P.H.S.W., Deng J., Wei J., 2015. Development of a probabilistic kinematic wedge sliding analysis procedure and application to a rock slope at a hydropower site in China. Bull. Eng. Geol. Environ. 1-16, DIO: 10.1007/s10064-015-07643.
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Fig. 1. Kinematic analysis for plane failure (after Goodman (1989)).
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Fig. 2. Kinematic analysis for toppling failure (after Goodman (1989)).
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Fig. 3. An example to illustrate that Eq. (3a) is flawed in some cases with respect to plane failure.
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Fig. 4. Diagrammatic sketch to illustrate that the discontinuity can exactly daylight on the slope face.
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Fig. 5. Input parameters of SMR corrected by this paper.
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(b) Toppling failure
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(a) Plane or wedge failure
Fig. 6. Statistical histogram of the discrepancy of values of SMR index calculated by Romana’s (1985) method and modified method proposed by the study.
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ACCEPTED MANUSCRIPT Table 1 Summary of the existing rock mass classification systems, which was revised on the basis of the list given by Pantelidis (2009). Abbreviation
Authors & Data
Application
Comments
–
-
Ritter, 1879
Tunnels
The first attempt for the formalization of an empirical approach to tunnel design.
Rock load
-
Terzaghi, 1946
Tunnels
The earliest reference to the use of rock mass classification for the design of tunnel support.
Stand-up time
-
Lauffer, 1958
Tunnels
Rock Quality Designation
RQD
DeDeer, 1963
General
New Austrian Tunneling Method
NATM
Rabcewicz, 1964
Rock Structure Rating
RSR
Wickham et al., 1972
Rock Mass Rating
RMR
Bieniawski, 1973, 1976, 1979, and 1989
Tunnels and cuttings
A raw rating adjustment for discontinuity orientation for application in slopes was added in the 1979 version of the RMR system.
Rock Tunneling Quality Index
Q
Barton et al., 1974
Tunnels
They are the most commonly used classification systems for tunnels
Size-Strength Classification
-
Franklin et al., 1974
General
The method has not been used widely.
Mining Rock Mass Rating
MRMR
Laubscher, 1977, 1984, and 1990
Mines
Based on RMR (1973).
Engineering-Geological Rock Durability Classification
-
Olivier, 1979
Tunnels
Providing a quantitative appraisal of rock durability.
Rock Mass Strength
RMS
Selby, 1980 and 1982; Moon and Selby. 1983
Cuttings
Based on natural slope data base.
Geotechnical Description
-
ISRM, 1981
General
It is widely used for characterizing the properties of rock masses.
Slope Mass Rating
SMR
Romana 1985; Romana et al., 2003
Cuttings
Based on RMR (1979).The most commonly used classification system for slopes.
Slope Rock Mass Rating
SRMR
Robertson, 1988
Cuttings
Based on RMR; The classification is provided for of weak altered rock mass materials from drill-hole cores.
Index of Rock Mass Basic Quality
BQ
NSCGPRC, 1995
General
It is determined by the hardness degree of rock and the intactness index of rock mass.
Chinese Slope Mass Rating
CSMR
Chen, 1995
Cuttings
Adjustment factors have been applied to the SMR system for the discontinuity condition and slope height.
Geological Strength Index
GSI
Hoek et al., 1995
General
Based on RMR (1976).
Rock Mass index
RMi
Palmström, 1995
General
Characterizing the strength of the rock mass for construction purposes.
Rock Mass Classification Rating
RMCR
Yaşar, 1995
General
Using 12 parameters from laboratory and in situ experiments.
Modified Rock Mass Rating
M-RMR
Ünal, 1996
Mines
For weak, stratified, anisotropic and clay bearing rock masses.
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Name of the system
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Related to the stand-up time of an unsupported tunnel excavation.
Tunnels
Scientitical empirical approach.
Small tunnels
First rating system for rock masses.
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Component factor of many classification systems.
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Mazzaccola and Hudson, 1996
Natural slopes
A rock mass characterization method for the indication of natural slope instabilities.
Slope Stability Probability Classification
SSPC
Hack, 1996; Hack et al., 2003
Cuttings
Probabilistic assessment of in dependently different failure mechanics.
Rock slope Deterioration Assessment
RDA
Nicholson and Hencher, 1997; Nicholson et al., 2000; Nicholson, 2002, 2003, and 2004
Cuttings
For shallow, weathering-related breakdown of excavated rock slopes.
Geological Strength Index
GSI
Hoek et al., 1998; Marinos and Hoek, 2000 and 2001; Marinos et al., 2005
General
For non-structurally controlled failures.
Adapted Slope Stability Probability Classification
-
Lindsay et al., 2001
Cuttings
Volcanic Rock Face Safety Rating
VRFSR
Singh and Connolly, 2003
Cuttings (temporary excavations)
Modified Rock Mass Classification
M-RMR
Şen and Sadagah, 2003
Falling Rock Hazard Index
FRHI
Singh, 2004
Modification of slope mass rating
-
Tomás et al., 2007
Fuzzy Slope Mass Rating
FSMR
New Slope Mass Rating
Rock Mass Quality Rating
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-
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Based on SSPC.
For volcanic rock slopes to determine the excavation safety on construction sites.
Based on RMR (1989)
Cuttings (temporary excavations)
Developed for stable excavations to determine the degree of danger to workers.
Cuttings
Modifying the SMR system by continuous functions.
Daftaribesheli et al., 2011
Cuttings
Based on SMR.
NSMR
Singh et al., 2013
Cuttings
Incorporating a new parameter of overburden thickness profile into the SMR system
RMQR
Aydan et al, 2014
General
It is used to estimate the geomechanical properties of rock masses.
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General
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ACCEPTED MANUSCRIPT Table 2 Adjustment parameters (F1, F2, and F3) for SMR (modified from Romana (1985) by Anbalagan et al. (1992)) Parameters
Very favorable
Favorable
Normal
Unfavorable
Very unfavorable
P/T/W
γ
> 30°
30-20°
20-10°
10-5°
< 5°
P/T/W
F1
0.15
0.40
0.70
0.85
1.00
P/W
η
< 20°
20-30°
30-35°
35-45°
> 45°
P/W
F2
0.15
0.40
0.70
0.85
1.00
T
F2
1.00
1.00
1.00
1.00
1.00
P/W
ζ
> 10°
10-0°
0°
0-(-10)°
< (-10)°
T
ζ
< 110°
110-120°
> 120°
-
-
P/T/W
F3
0
-6
-25
-50
-60
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Type of failure
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Note: P, plane failure; T, toppling failure; W, wedge failure; γ, η, and ζ are the parameters for determining the values of F1,
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ACCEPTED MANUSCRIPT Table 3 Adjustment parameter (F4) for SMR (Romana, 1985) Natural slope
Presplitting
Smooth blasting
Blasting or mechanical
Deficient blasting
F4
+15
+10
+8
0
-8
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Method
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ACCEPTED MANUSCRIPT Table 4 The mean orientations and friction angles of the most un-favorable discontinuity sets existing in the slopes i and j, and
γ (°)
βd (°)
βs (°)
φ(°)
F1
F2
F3
i
38
74
83
35
0.15
1.00
-50
j
86
70
83
35
0.15
1.00
-60
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# of slope
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the obtained values of F1, F2, and F3.
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ACCEPTED MANUSCRIPT Highlights A comprehensive summary of rock mass classification systems is presented.
A review of the development of SMR system is given.
Corrections for adjustment parameters F1 and F3 in the SMR system is proposed.
The corrections are also applicable to those derived SMR system.
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S0013-7952(16)30064-3 doi: 10.1016/j.enggeo.2016.03.007 ENGEO 4251
To appear in:
Engineering Geology
Received date: Revised date: Accepted date:
2 November 2015 15 March 2016 19 March 2016
Please cite this article as: Zheng, Jun, Zhao, Yu, L¨ u, Qing, Deng, Jianhui, Pan, Xiaohua, Li, Yunzhen, A discussion on the adjustment parameters of the Slope Mass Rating (SMR) system for rock slopes, Engineering Geology (2016), doi: 10.1016/j.enggeo.2016.03.007
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ACCEPTED MANUSCRIPT Title: A discussion on the adjustment parameters of the Slope Mass Rating (SMR) system for rock slopes Author Names: Jun Zheng a, Yu Zhao a, Qing Lü a, *, Jianhui Deng b, Xiaohua Pan a, Yunzhen Li c Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China
b
State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource &
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a
c
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Hydropower, Sichuan University, Chengdu 610065, China
Sichuan Academy of Environmental Science, Chengdu 610041, China
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*Corresponding Author: Tel.:+86 57188208732 fax: +86 57188208732. E-mail address: [email protected]
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Abstract: Rock mass classification systems are common tools used in the design and construction of rock engineering. Numerous classification systems have been developed for rock slopes, of which the Slope Mass
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Rating (SMR) system is the most popular. Consequently, many rock slope classification systems have been derived from the SMR system. However, these systems are not good at determining the values of the two
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adjustment parameters F1 and F3, implying that the original SMR system may contain theory defects. In this paper, we propose some corrected methods for determining F1 and F3 and perform a series of analyses
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considering the three failure modes of rock slopes: plane, wedge, and toppling failures. The results of the
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discrepancy analysis from F1 illustrate that, with respect to each of the aforementioned three failure modes the calculated original SMR index is larger than, or equal to, the real value, and the designed slope is possibly in danger. The results of the discrepancy caused by the F3 illustrate that for each of the aforementioned three failure modes, the calculated original SMR index is smaller than, or equal to, the real value, and the designed slope might be conservative and not economical. Key words: Slope Mass Rating (SMR); Rock slope stability; Structurally-controlled failures; Adjustment factors; Kinematic analysis 1. Introduction A rock mass is a natural geological material; it is also an assemblage of intact rock blocks and discontinuities (e.g., joints, weak bedding planes, weak zones, weak schistosity planes, and faults). Due to the long-term geological processes, the geometrical and mechanical properties of a rock mass are extremely complex. Moreover, its environment is also complex (e.g., the groundwater conditions and in-situ stress both have great variations). To quantify the complex properties of a rock mass based on past experience (Stille and Palmström, 2003), various taxonomies, usually called as rock mass classification systems, have been developed. Those
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ACCEPTED MANUSCRIPT classification systems are of great significance to improving the design and construction of rock mass engineering (Wu and Wang, 2014). Many classification systems are presented in Table 1. Of them, the Slope Mass Rating (SMR) system (Romana, 1985) is widely used for rock slopes (e.g., Huang and Fan, 1998; Romana et al., 2003; Irigaray et
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al., 2003; Yilmaz et al., 2012; Siddique et al., 2015; among others). The SMR was derived from the Rock Mass Rating (RMR) system (Bieniawski, 1979). The RMR system was originally created for tunneling
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applications (Bieniawski, 1979), but the author (Bieniawski, 1989) proposed slope adjustment factors to take into account whether the discontinuities strike and dip are favorable or not to slope failure (Tomás et al.,
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2007). However, it is not easy in practice to apply the RMR system to slopes, because Bieniawski (1989) only provided five adjustment ratings (0, -5, -25, -50, and -60) with respect to five orientation relationships
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between the discontinuities and slope face (i.e., very favorable, favorable, fair, unfavorable, and very unfavorable), however did not propose a detailed quantitative definition of the five orientation relationships.
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The SMR system eliminated the aforementioned shortcomings of the RMR system and has become the most important classification for rock slopes. Hence, the SMR system has been used as the basis of many other
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systems. Chen (1995) developed the Chinese Slope Mass Rating (CSMR) system by adding the discontinuity condition (e.g., faults or intercalated layers, bedding planes, and joints) and slope height to the SMR system.
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Tomás et al. (2007) modified the SMR system by replacing the discrete classifications of the SMR with continuous functions. Daftaribesheli et al. (2011) addressed the Fuzzy Slope Mass Rating (FSMR) system
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using a fuzzy set theory to quantify the ambiguous results influenced by the uncertainties of the characteristics of the rock masses. Tomás et al. (2012) built upon their 2007 work and developed a graphical approach for the SMR, based on the stereographic representation of the discontinuities and the slope to obtain the adjustment parameters; this system easily calculates the correction parameters of the SMR in cases where all slopes have the same dip with a different strike, as in linear infrastructure and open pit mining. Singh et al. (2013) described a New Slope Mass Rating (NSMR), incorporating a new parameter, the overburden thickness profile, into the SMR system; this parameter is best suited while preparing the stability map of mountain areas, where tectonic activity is high. Though the SMR system has been widely used in practice and has led to the development of numerous classification systems for rock slopes, there are some theoretical defects for determining the parameters F1 and F3 in the computational formula of the SMR index given by Romana (1985). Therefore, the primary aim of this study is to correct the determination methods for F1 and F3. Note that the similar defects exist in the above-mentioned derived classification systems from the SMR system. 2. Review of the SMR system
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ACCEPTED MANUSCRIPT The SMR index, introduced by Romana (1985), is determined by adding four adjustment factors to the basic RMR proposed by Bieniawski (1979). These factors depend on the discontinuity-slope relationship and the method of excavation (Romana, 1985). The SMR can be determined by (Romana, 1985): SMR = RMR b + 𝐹1 𝐹2 𝐹3 + 𝐹4
(1)
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where: (a) RMRb is the basic RMR index resulting from Bieniawski's (1979) rock mass classification without any
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adjustment, it can be obtained by adding five parameters including strength of intact rock material (uniaxial compressive strength or point load strength) (Rδ), rock quality designation (RRQD), spacing of discontinuities
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(RSD), condition of discontinuities (RCD), and condition of Groundwater (RCG) as follows: RMR b = 𝑅𝛿 + 𝑅𝑅𝑄𝐷 + 𝑅𝑆𝐷 + 𝑅𝐶𝐷 + 𝑅𝐶𝐺
(2)
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(b) F1 depends on the parallelism between the dip directions of the discontinuity and the slope face (denoted as αd and αs, respectively) in the cases of a plane or toppling failure (Romana, 1985), and between the trend
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of the intersecting line of the two discontinuities (labeled as αil) and αs in the cases of a wedge failure (Anbalagan et al., 1992);
(c) F2 refers to the dip angle of discontinuity (denoted as βd) in the case of a plane failure (Romana, 1985) (Anbalagan et al., 1992);
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(d) F3 reflects the relationship between βd and the dip angle of the slope (βs) in the cases of a plane or toppling failure (Romana, 1985) and between βil and βs, in the cases of a wedge failure (Anbalagan et al., 1992); and
(e) F4 is an adjustment factor that depends on the excavation method (Romana, 1985). Note that Romana (1985 and 1993) did not consider the wedge failure for rock masses in the original SMR system; Anbalagan et al. (1992) added the wedge failure into the system. A wedge failure is probably the most common and general case dealt with in rock slope stability analyses (Hoek and Bray, 1981; Zheng, 2015). Therefore, in this investigation, a wedge failure was considered. The values for F1, F2, F3, and F4 can be obtained by referring to Tables 2 and 3. According to Romana (1985 and 1993) and Anbalagan et al. (1992), the values of γ, η, and ζ can be obtained as follows: |𝛼d − 𝛼s | plane failure 𝛾 = {|𝛼d − 𝛼s − 180| toppling failure |𝛼il − 𝛼s | wedge failure
(3a, 3b, 3c)
𝛽 𝜂={ d 𝛽il
plane failure wedge failure
(4a, 4b, 4c)
plane failure toppling failure wedge failure
(5a, 5b, 5c)
𝛽d − 𝛽s 𝜁 = {𝛽d + 𝛽s 𝛽il − 𝛽s
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ACCEPTED MANUSCRIPT where: γ, η, and ζ are the parameters necessary for determining the values of F1, F2, and F3, respectively. 3. Review of kinematic analysis 3.1. Plane failure
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According to Hoek and Bray (1981) and Goodman (1989), the conditions of a kinematic plane failure are: (1) 0 ≤ γ < γPlim, where γ is the intersecting angle between the dip directions of the discontinuity and the slope
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face, and the whole range of γ is between 0° and 180°; γPlim is the limit value of γ, and its range is between 0°
SC
and 90°; the values of γPlim are suggested as 90°, 30°, and 20° or 30° by Goodman (1989), Hoek and Bray (1981), and Rocscience (2014), respectively;
(2) βd > φ, where φ is the friction angle of the discontinuity; and
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(3) βsa > βd, where βsa is the apparent dip angle of the slope in the direction of the dip direction of the discontinuity (Fig.1). It should be noted that βsa is the apparent dip angle of the slope, not the true dip angle
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of the slope (βs). 3.2. Toppling failure
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Hoek and Bray (1981) and Goodman (1989) stated that the kinematic toppling conditions include: (1) 0 ≤ γ < γTlim, where γ is the intersecting angle between the dip directions of the discontinuity and the slope face,
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and the entire range of γ is between 0° and 180°; γTlim is the limit value of γ, and its range is between 0° and
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90°. Note that the value of γTlim is usually suggested as 30° (Goodman, 1989); (2) βd > φ; (3) βsa > 90° －βd + φ (Fig. 2); and (4) the spacing between the discontinuities should be small, to allow for the formation of thin layers of rock. 3.3. Wedge failure
The most common case of a wedge failure is a wedge sliding onlyalong the intersecting line of two discontinuities. In this case, the kinematic wedge sliding can be visualized as sliding on a special plane (a fictitious discontinuity) having the intersecting line as the steepest descent line of the fictitious discontinuity. Thus, the conditions of a kinematic wedge failure can be described as in Hoek and Bray (1981) and Goodman (1989): (1) 0 ≤ γ < γWlim, where γ is the intersecting angle between the trend of the intersecting line of two discontinuities and the slope face, and the entire range of γ is between 0° and 180°; γWlim is the limit value of γ, and its range is between 0° and 90°; the values of γWlim are suggested as 90° (Goodman, 1989); (2) βil > φ; and (3) βsa > βil, where βsa is the apparent dip angle of slope in direction of the trend of the intersecting line. 4. Existing defects for determining parameters F1 and F3 and the corrected approaches 4.1. Plane failure
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ACCEPTED MANUSCRIPT Comparing the determination methods for F1, F2, and F3 with the three conditions of kinematic plane failure, it is not difficult to find that F1, F2, and F3 reflects the three failure conditions, respectively. Eq. (3a) is used to calculate the intersecting angle γ between αd and αs. Since the ranges of both αd and αs are between 0° and 360° (Priest, 1993), the calculated values of γ from Eq. (3a) are incorrect in some cases. For example,
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assume that αd = 10°, αs = 352° as shown in Fig. 3, then γ = 342° according to Eq. (3a), and F1 = 0.15 (Table 2); however, the information in Fig. 3 illustrates that γ should be equal to 18° and F1 should be equal to 0.7, |𝛼d − 𝛼s | 360° − |𝛼d − 𝛼s |
if |𝛼d − 𝛼s | ≤ 180° if |𝛼d − 𝛼s | > 180°
(6)
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𝛾={
RI
according to Table 2. Therefore, γ with respect to a plane failure should be expressed as:
As described by Romana (1985), in the mode of a plane failure, F3 refers to the probability that
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discontinuities daylight on the slope face. The information in Table 2 and Eq. (5a) shows that when βd - βs < 0, in other words βs > βd, the discontinuity can daylight on the slope face. However, as stated above,
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condition (3) of a kinematic plane failure is βsa > βd.
As illustrated in Fig. 4, Oy represents the direction of north, Ox represents east, ABCD is the slope face, OB points the dip direction of the slope, αs is the dip direction of the slope, βs is the dip angle of the slope;
D
EFGH is the discontinuity plane, OC points to the dip direction of the discontinuity, αd is the dip direction of
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the discontinuity, βd is the dip angle of the discontinuity, γ is the intersecting angle of the dip directions of the of discontinuity.
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slope and the discontinuity, and βsa is the apparent dip angle of the slope in the direction of the dip direction Fig. 4 illustrates that EFGH can or not daylight on the slope face; this directly depends on the relationship between βsa and βd, not on the relationship between βs and βd. Therefore, it is not correct to say that the value of F3 is determined according to the value of βd - βs in the SMR system proposed by Romana (1985). In addition, ζ , in the cases of a plane failure, should be expressed as: 𝜁 = 𝛽d − 𝛽sa
(7)
where βsa can be determined by (Zheng et al., 2015): 𝛽sa = atan(tan𝛽s cos𝛾)
(8)
The following example is used to illustrate the possible problems caused by the original determination method for F3, proposed by Romana (1985). Assume that there are two rock slopes (i.e., slopes i and j). The values of some of the parameters are obtained as follows: RMR b𝑖 = RMR b𝑗 = RMR b
(9)
𝐹4𝑖 = 𝐹4𝑗 = 𝐹4
(10)
where: RMRbi and RMRbj are the values of the RMRb of slopes i and j, respectively; F4i and F4j are the values of the F4 of slopes i and j, respectively. The mean orientations of the most unfavorable discontinuity sets
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ACCEPTED MANUSCRIPT existing in the two slopes are given in Table 4. The obtained values of F1, F2, and F3 (according to Table 2) are also presented in Table 4. Substituting Eqs. (9-10) and the values of F1, F2, and F3 in Table 4 into Eq. (1) yields: (11)
SMR𝑗 = RMR b − 9 + 𝐹4
(12)
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SMR 𝑖 = RMR b − 7.5 + 𝐹4
Combining Eqs (11) and (12) results in:
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SMR 𝑖 − SMR𝑗 = 1.5 > 0
(13)
Therefore, the values of the SMR index for slopes i and j show that the stability of slope i is higher than
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that of slope j. The kinematic analysis is also applied to the two slopes. The results illustrate that: (a) βsai =
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81.1° > βdi = 74°, 0 ≤ γi = 38 < γPlim = 90° (Goodman, 1989), and βdi = 74° > φi = 35°, and thus the slope i is unstable; (b) βsaj = 29.6° < βdj = 70°, and thus the slope j is stable. The kinematic analysis shows that the stability of slope i is lower than that of slope j. The dip direction of the discontinuity existing in slope i is
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close to the dip direction of slope i. The dip direction of the discontinuity existing in slope j is close to the strike of slope j. According to the engineering experience, apparently the stability of slope i is lower than that
D
of slope j. Using the corrected approaches proposed in the paper, we can know that the value of SMRbi -
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SMRbj is equal to -7.5, and hence, the stability of slope i is lower than that of slope j. The results of the case fully illustrate that the SMR system proposed by Romana (1985) might yield
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incorrect results in some cases, due to the flawed determination approach for F3. Consequently, the corrected approaches proposed in this paper can yield the correct results. 4.2. Toppling failure
Similarly, there are some defects for determining F1 and F3, in regard to the toppling failures in the original SMR system proposed by Romana (1985). Hence, γ and ζ should be expressed as follows: 𝛾={
180° − |𝛼d − 𝛼s | |𝛼d − 𝛼s | − 180°
if |𝛼d − 𝛼s | ≤ 180° if |𝛼d − 𝛼s | > 180°
𝜁 = 𝛽d + 𝛽sa
(14) (15)
4.3. Wedge failure There are some similar problems for determining F1 and F3 in the cases of wedge failures in the original SMR system proposed by Romana (1985). As such, γ and ζ should be given by: 𝛾={
|𝛼il − 𝛼s | 360° − |𝛼il − 𝛼s |
if |𝛼il − 𝛼s | ≤ 180° if |𝛼il − 𝛼s | > 180°
𝜁 = 𝛽il − 𝛽sa where αil and βil can be obtained as follows (Zheng et al, 2015):
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(16) (17)
ACCEPTED MANUSCRIPT 𝑰12 = 𝒏1 × 𝒏2
(18)
where n1 and n2 are the upward unit normal vector of the two discontinuities forming the wedge and I12 is the vector along the intersecting line of the two discontinuities: if 𝑧12 < 0
𝑰′12 = −𝑰12 if 𝑧12 > 0
PT
{
𝑰′12 = 𝑰12
(19)
RI
where I′12 is the downward vector along the intersecting line of the two discontinuities; and z12 is the z
SC
component of I12. By denoting the coordinates of I′12 as x′12, y′12, and z′12, the plunge βil and trend αil
𝛽il = sin−1 (
|𝑧′12 |
2
2
√𝑥′ +𝑦′12 +𝑧′12 12
(
𝑥′12
2
) (20)
)
MA
𝛼il = 𝑡𝑎𝑛 {
−1
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of I′12 can be expressed as (Kulatilake 1985):
𝑦′12
TE
D
where the range of βil is between 0° and 90°; the range of αil is between 0° and 360° and is measured clockwise from the y-axis. The coordinate quadrant of αil is determined by the signs of x′12 and y′12. In summary, the input parameters of the SMR corrected by this paper are presented in Fig. 5.
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5. Discrepancy analysis for SMR indexes between the original SMR system proposed by Romana (1985) and the corrected system
5.1. Analysis of discrepancies caused by F1 Comparing Eqs. (3a) and (6), it is not difficult to find that, with respect to a plane failure, (a) when |αd - αs| ≤ 180°, the value of the SMR index, according to Romana (1985), is correct; and (b) when |αd - αs| ≥ 180°, the value of γ determined according to Romana (1985) is larger than its real value, the obtained value of F1 is possibly smaller; as such, a possibly larger value of the SMR will be calculated. Hence, the designed slope is possibly in danger, according to the calculated SMR index. According to Eqs. (3b) and (14), in the cases of a toppling failure, (a) when 0° ≤ αd - αs ≤ 180° or αd αs > 180°, the value of the SMR index, calculated by Romana (1985), is correct; and (b) when αd - αs < 0°, the value of γ determined by Romana (1985) is larger than its real value, the obtained value of F1 is possibly smaller, and a possibly larger value of the SMR will be calculated. Hence, the designed slope is possibly in danger, according to the calculated SMR index. Similarly, by comparing Eqs. (3c) and (16), in regard to a wedge failure, (a) when |αil - αs| ≤ 180°, the value of the SMR index, according to Romana (1985), is correct; and (b) when |αil - αs| ≥ 180, the value of γ
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ACCEPTED MANUSCRIPT given by Romana (1985) is larger than its real value, the obtained value of F1 is possibly smaller, and a possibly larger value of the SMR will be calculated. Hence, the designed slope is possibly in danger, according to the calculated SMR index. In summary, the discrepancy analysis for F1 shows that, with respect to each of the three failure modes
PT
(i.e., plane, toppling, and wedge failure), the SMR index calculated by Romana (1985) is larger than, or equal to, the real value. As such, the designed slope is possibly in danger, according to the calculated SMR index.
RI
5.2. Analysis of discrepancies caused by F3 5.2.1 Plane failure
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The true dip angle of a slope is always larger than, or equal to, its apparent dip angle. Hence, the value of ζ calculated by Eq. (5a) is always smaller than, or equal to, the value calculated by Eq. (7). The obtained value
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of F3 is always smaller than, or equal to, its real value. A smaller value of SMR will possibly be calculated. And hence, the designed slope might be conservative and not economical, according to the calculated SMR
MA
index.
The range of γ (0° -180°) is divided into 36 equal parts; 37 values (0°, 5°, ..., 175°, 180°) can be obtained for γ. The ranges of βd and βs, both of which are between 0° and 90°, are separately divided into 18 equal
D
parts. Each of the obtained 19 values (0°, 5°, ..., 85°, 90°) are then respectively assigned to βd and βs. There
TE
are 37 × 19 × 19 = 13357 hypothetical cases developed by combining them.
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For each of the 13357 hypothetical cases, the values of the SMR index can be calculated by the two methods discussed previously: (1) the method proposed by Romana (1985) and (2) The method proposed in this paper. The difference in the values of the SMR index between the two methods is the discrepancy caused by F3. The statistical histogram of the discrepancy was given in Fig. 6(a). The results in Fig. 6(a) illustrate that a 79.6% discrepancy is within 3; only 0.4% is larger than 10. The results reveal that, with respect to F3, the original method proposed by Romana (1985) has little influence on the value of the SMR index in most cases of a plane failure. However, in those cases with around a 20 discrepancy, the original method will probably cause a waste in the economy. Therefore, it is recommended that the proposed method in this paper is adopted to determine the value of F3 with respect to a plane failure for an SMR system. 5.2.2. Toppling failure Similarly, the following conclusion can be obtained: in the cases of a toppling failure, the SMR index calculated by Romana (1985) is smaller than, or equal to, the real value. As such, the designed slope might be conservative and not economical, according to the calculated SMR index. The aforementioned 1357 hypothetical cases were also used for a toppling failure. The results are presented in Fig. 6(b). The figure shows that an 85.9% discrepancy is within 1; only 0.21% is larger than 5. It seems that, with respect to F3, Romana’s (1985) method has little influence on the value of the SMR index in 8 / 25
ACCEPTED MANUSCRIPT most of the cases of a toppling failure. However, in those cases with around a 5 discrepancy, the original method might still cause waste in the economy. Therefore, we recommend that the proposed method in this paper is adopted to determine the value of F3 for a toppling failure for an SMR system. 5.2.3. Wedge failure
PT
In the cases of a wedge failure, the SMR index calculated by Romana (1985) is smaller than, or equal to, the real value. As such, the designed slope might be conservative and not economical, according to the
RI
calculated SMR index.
The aforementioned 13357 hypothetical cases were used for a wedge failure. It should be noted that, for
SC
the plane and toppling failure, γ was the intersecting angle between the dip directions of discontinuity and slope, but for the wedge failure, γ was the intersecting angle between the dip direction of the slope and the
NU
trend of the intersecting line of the two discontinuities. Note that in cases of a wedge failure, βd should be replaced by βil. As stated previously, a wedge failure can be visualized as sliding on a fictitious discontinuity
MA
having the intersecting line as the steepest descent line of the fictitious discontinuity. Therefore, the same statistical results as a plane failure can be obtained for a wedge failure as illustrated in Fig. 6(a). The same
D
conclusion can be made as follows: the proposed method in this paper should be adopted to determine the
AC CE P
6. Summary and conclusions
TE
value of F3 in the cases of a wedge failure for the SMR system.
Based on the list in Pantelidis (2009), a summary table of the existing rock mass classification systems was presented. A brief review of the SMR system and kinematic analysis was also stated. The theoretical defects for determining the values of the adjustment parameters F1 and F3 in the computational formula of an SMR index, developed by Romana (1985), were discussed. The corrected determination approaches for F1 and F3 were then developed. In addition, the discrepancy analysis for the original determination method was also performed in the study. The results of the discrepancy analysis from F1 show that, with respect to each of the three failure modes (plane, toppling, and wedge failure), the SMR index calculated by Romana (1985) is larger than, or equal to, the real value. Hence, the designed slope is possibly in danger, according to the calculated SMR index. Therefore, the developed method in this paper to determine the value of F1 should be adopted for an SMR system. The results of the discrepancy caused by F3 illustrate that, for each of the aforementioned three failure modes, the SMR index calculated by Romana (1985) is smaller than, or equal to, the real value. and the designed slope might be conservative and not economical, according to the calculated SMR index. Overall, 13357 hypothetical cases were designed and applied for analyzing the discrepancy caused by F3 with respect to each of the three failure modes. The results show that: (1) in the cases of a plane or wedge failure, 79.6% discrepancy is within 3, and only 0.4% is larger than 10; (2) for a toppling failure, 85.9% discrepancy is 9 / 25
ACCEPTED MANUSCRIPT within 1, and only 0.21% is larger than 5; (3) with respect to F3, the original method proposed by Romana (1985) has little influence on the value of the SMR index in most of cases for all three failure modes; (4) however, the original method might bring waste into an economy for a particular case with a larger discrepancy; and (5) therefore, the proposed method in this paper should be adopted to determine the value of
PT
F3 for an SMR system. It is worthy to note that similar defects exist in other classification systems (Chen, 1995; Tomás et al.,
RI
2007 and 2012; Daftaribesheli et al., 2011; Singh et al., 2013) that have been derived from the SMR system; the corrected approach developed in this paper is also applicable to those derived systems. Consequently,
NU
study while using the SMR system or its derived methods.
SC
engineers are encouraged to adopt the corrected determination approaches for F1 and F3 proposed by this
Acknowledgments
CSMR F1, F2, F3, F4 F4i, F4j FSMR I12 I′12 n 1, n 2 NSMR RCD RCG RMR RMRb RRQD RSD Rδ SMR x′12, y′12, z′12 z12 αd αil αs βd βil βs βsa
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Notation
TE
D
MA
The work was funded by the National Basic Research Program of China (973 Program; No. 2015CB057903), the National Natural Science Foundation Projects (No. 41502268 & No. 41202216), the Fundamental Research Funds for the Central Universities(2016QN4018), and the Research Programs of Transportation Department of Zhejiang Province (No. 2014H21 & No. 2013H46). The authors would also like to thank Professor Resat Ulusay and other two anonymous referees for reviewing the paper and providing valuable suggestions.
Chinese Slope Mass Rating four adjustment parameters of SMR system values of F4 of slopes i and j, respectively Fuzzy Slope Mass Rating vector along the intersection line of two discontinuities downward vector along the intersection line of two discontinuities upward unit normal vector of two discontinuities forming the wedge New Slope Mass Rating condition of discontinuities condition of Groundwater Rock Mass Rating basic RMR index Rock quality designation spacing of discontinuities uniaxial compressive strength or point load strength Slope Mass Rating coordinates of I′12 z component of I12 dip directions of discontinuity trend of the intersection line of two discontinuities dip directions of slope dip angle of discontinuity plunge of the intersection line of two discontinuities dip angle of slope apparent dip angle of slope in the direction of the dip direction of discontinuity for plane or toppling failure; the apparent dip angle of slope in the direction of the trend of the intersection line for wedge failure
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ACCEPTED MANUSCRIPT
PT
RI
SC
γ, η, ζ γPlim γTlim γWlim φ Oy Ox ABCD OB EFGH OC i, j RMRbi, RMRbj
intersection angle between the dip directions of discontinuity and slope face for plane or toppling failure; intersection angle between the trend of the intersection line of two discontinuities and the dip direction of slope for wedge failure three parameters for determining the values of F1, F2, and F3, respectively limit value of γ for plane failure limit value of γ for toppling failure limit value of γ for wedge failure friction angle of discontinuity north direction east direction slope face pointing the dip direction of slope discontinuity plane pointing the dip direction of discontinuity slope number values of RMRb of slopes i and j, respectively
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γ
References
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Anbalagan R., Sharma S., Raghuvanshi T.K., 1992. Rock mass stability evaluation using modified SMR approach. In: Proceedings of 6th national symposium on rock mechanics, Bangalore, India, 258–68. Barton N.R., Lien R., Lunde J., 1974. Engineering classification of rock masses for the design of tunnel support. Rock Mech. Rock Eng. 6(4): 189–239. Bieniawski Z.T., 1973. Engineering classification of rock masses. Trans. S. Afr. Inst. Civ. Eng. 15, 335–44. Bieniawski Z.T., 1976. Rock mass classification in rock engineering. Proceedings of the symposium on explorer for rock engineering, Johannesburg, 97–106. Bieniawski Z.T., 1979. The geomechanics classification in rock engineering applications. Proceedings of the 4 th international congress on rock mechanics, Montreux, 41–48. Bieniawski Z.T., 1989. Engineering rock mass classifications. NewYork: Wiley. Chen Z., 1995. Recent developments in slope stability analysis. Proceedings of the 8th international congress ISRM, Tokyo, 1041– 8. Daftaribesheli A., Ataei M., Sereshki F., 2011. Assessment of rock slope stability using the Fuzzy Slope Mass Rating (FSMR) system. Appl. Soft. Comput. 11(8), 4465–4473. Deere D.U., 1963. Technical description of rock cores for engineering purposes. Rock Mech. Eng. Geol. 1(1), 17–22. Franklin J.A., Louis A.C., Masure P., 1974. Rock material classification. Proc. 2 nd Int. Cong. Eng. Geol., IAEG, Sao Paulo, 325– 341. Goodman R.E., 1989. Introduction to rock mechanics, 2nd edn. Wiley, NewYork. Hack R., 1996. Slope stability probability classification. Vol. 43 ITC Delft Publication, Enschede, Netherlands. Hack R., Price D., Rengers N., 2003. A new approach to rock slope stability—a probability classification (SSPC). Bull. Eng. Geol. Environ. 62, 167–184. Hoek E., Bray J.W., 1981. Rock Slope Engineering, 3nd edition. Institute of Mining and Metallurgy, London. Hoek E., Kaiser P.K., Bawden W.F., 1995. Support of underground excavations in hard rock. Rotterdam: Balkema. Hoek E., Marinos P., Benissi M., 1998. Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses: the case of the Athens schist formation. Bull. Eng. Geol. Environ. 57,151–60. Huang C., Fan J., 1998. The SMR method and case history of slope rock mass quality classification. Geotech. Eng. Tech. 43(1), 7– 15. (in Chinese) International Society for Rock Mechanics (ISRM), 1981. Basic geotechnical description of rock mass quality. Int. J. Rock Mech. Min. Sci. 18, 85–110. Irigaray C., Fernández T., Chacón J., 2003. Preliminary rock-slope-susceptibility assessment using GIS and the SMR classification. Nat. Hazards 30(3), 309–324. Kulatilake P.H.S.W., 1985. Fitting of Fisher distribution on discontinuity orientation data. J. Geolog. Educ. 33, 266–269. Laubscher D.H., 1977. Geomechanics classification of jointed rock masses—mining applications. Trans. Inst. Min. Metall. 86, A1– 8. Laubscher D.H., 1984. Design aspects and effectiveness of support systems in different mining conditions.Trans. Inst. Min. Metall. 93, A70–82. Laubscher D.M., Page C.H., 1990. The design of rock support in high stress or weak rock environments. Proceedings of the 92 nd Canadian Institute of Mining and Metallurgy, Ottawa. Lauffer H., 1958. Gebirgsklassifizierung für den Stollenbau.Geol Bauwesen 24(1), 46–51.
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D
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Lindsay P., Campbell R.N., Fergusson D. A., Gillard G.R., Moore T.A., 2001. Slope stability probability classification, Waikato coal measures, New Zealand. Int. J. Coal Geol. 45(2), 127–145. Marinos P., Hoek E., 2000. GSI—a geologically friendly tool for rock mass strength estimation. Proceedings of the geological engineering 2000 conference, Melbourne, 1422–46. Marinos P., Hoek E., 2001. Estimating the geotechnical properties of heterogeneous rock masses such as flysch. Bull Eng. Geol. Environ. 60: 85–92. Marinos V., Marinos P., Hoek E., 2005. The geological strength index: applications and limitations. Bull. Eng. Geol. Environ. 64, 55–65. Mazzocola D.F., Hudson J.A., 1996. A comprehensive method of rock mass characterization for indicating natural slope instability. Q. J. Eng. Geol. 29, 37–56. Moon B.P., Selby M.J., 1983. Rock mass strength and scarp forms in Southern Africa. Geografiska Ann—SerA 65A(1–2), 135–45. National Standards Compilation Group of People’s Republic of China (NSCGPRC), 1995. GB 50218-94 Standard for engineering classification of rock masses. Beijing: China Planning Press. (in Chinese) Nicholson D.T., 2002. Identification of deterioration hazard potential for quarried rockslopes. Quarry Manage 29(1), 43–52. Nicholson D.T., 2003. Breakdown mechanisms and morphology for man-made rockslopes in North West England. North West Geogr. 3(1), 12–26. Nicholson D.T., 2004. Hazard assessment for progressive, weathering-related breakdown of excavated rockslopes. Q. J. Eng. Geol. Hydrogeol. 37, 327–46. Nicholson D.T., Hencher S.R., 1997. Assessing the potential for deterioration of engineered rock slopes. Proceedings of the IAEG symposium, Athens, 911–917. Nicholson D.T., Lumsden A.C., Hencher S.R., 2000.Excavation-induced deterioration of rockslopes. Landslides in research, theory and practice, vol.3. London: Thomas Telford, 1105–1110. Olivier H.J., 1979. A new engineering-geological rock durability classification. Eng. Geol. 14(4), 255–279. Aydan, Ö., Ulusay, R., Tokashiki, N., 2014. A new rock mass quality rating system: rock mass quality rating (RMQR) and its application to the estimation of geomechanical characteristics of rock masses. Rock Mech. Rock Eng. 47(4), 1255–1276. Palmström A., 1995. RMi-a rock mass characterization system for rock engineering purposes. PhD Thesis, Oslo University, Norway. Pantelidis, L., 2009. Rock slope stability assessment through rock mass classification systems. Int. J. Rock Mech. Min. Sci. 46(2), 315-325. Priest S.D., 1993. Discontinuity analysis for rock engineering, Chapman & Hall, London. Rabcewicz L., 1964. The New Austrian Tunnelling Method. Water Power. 11, 453–457. Ritter W., 1879. Die Statik der Tunnelgew ölbe. Berlin: Springer. Robertson A.M., 1988. Estimating weak rock strength. Proceedings of the SME annual meeting, Phoenix, 1–5. Rocscience, 2014. Dips V6.0 Tutorial Manual 04: Toppling, Planar Sliding, Wedge Sliding. Toronto: Rocscience Inc. Romana M., 1985. New adjustment ratings for application of Bieniawski classification to slopes. Proceedings of the international symposium on role of rock mechanics, Zacatecas, Mexico, 49–53. Romana M., Serón J.B., Montalar E., 2003. SMR Geomechanics classification: Application, experience and validation. ISRM 2003–Technology roadmap for rock mechanics, South African Institute of Mining and Metallurgy, 981–984. Romana M., 1993. A geomechanical classification for slopes: slope mass rating. Comprehensive Rock Eng. 3, 575-599. Selby M.J., 1980. A rock mass strength classification for geomorphic purposes: with tests from Antarctica and New Zeland. Zeit Geomorph 24(1), 31–51. Selby M.J., 1982. Rock mass strength and the form of some inselbergs in the central Namib desert. Earth Surf. Proc. Landforms 7(5), 489–97. Şen Z., Sadagah B.H., 2003. Modified rock mass classification system by continuous rating. Eng. Geol. 67(3), 269–280. Siddique T., Alam M.M., Mondal M.E.A, Vishal V., 2015. Slope mass rating and kinematic analysis of slopes along the national highway-58 near Jonk, Rishikesh, India. J. Rock Mech. Geotech. Eng. 7(5), 600–606. Singh A., Connolly M., 2003. VRFSR—an empirical method for determining volcanic rock excavation safety on construction sites. J. Div. Civ. Eng. Inst. Eng. (India) 84, 176–91. Singh A., 2004. FRHI—a system to evaluate and mitigate rockfall hazard in stable rock excavations. J. Div. Civ. Eng. Inst. Eng. (India) 85, 62–75. Singh R.P., Dubey C.S., Singh S.K., Shukla D.P., Mishra B.K., Tajbakhsh M., Ningthoujam P.S., Sharma M., Singh, N., 2013. A new slope mass rating in mountainous terrain, Jammu and Kashmir Himalayas: application of geophysical technique in slope stability studies. Landslides, 10(3), 255-265. Stille H., Palmström A., 2003. Classification as a tool in rock engineering. Tunn. Undergr. Sp. Techn. 18(4), 331–345. Terzaghi K., 1946. Rock defects and loads on tunnel supports. Rock tunneling with steel supports. vol. 1. Youngstown, OH: Commercial Shearing and Stamping Company, 17–99. Tomás R., Cuenca A., Cano M., García-Barba J., 2012. A graphical approach for slope mass rating (SMR). Eng. Geol. 124, 67–76. Tomás R., Delgado J., Serón J. B., 2007. Modification of slope mass rating (SMR) by continuous functions. Int. J. Rock Mech. Min. Sci. 44(7), 1062–1069. Ünal E., 1996. Modified rock mass classification: M-RMR system. Milestones in rock engineering, the Bieniawski Jubilee collection. Rotterdam: Balkema, 203–223.
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Wickham G.E., Tiedemann H., Skinner E.H., 1972. Support determination based on geologic predictions. Proceedings of the 1 st North American rapid excavation tunneling conference, NewYork: AIME, 43–64. Wu A., Wang B., 2014. Engineering rock mass classification method based on rock mass quality index BQ for rock slope. Chinese J. Rock Mech. Eng. 33(4), 699–706. (in Chinese) Yaşar E., 1995. The properties and classification of anisotropic rocks. PhD Thesis. University of Nottingham, UK. Yilmaz I., Marschalko M., Yildirim M., Dereli E., Bednarik M., 2012. GIS-based kinematic slope instability and slope mass rating (SMR) maps: application to a railway route in Sivas (Turkey). Bull. Eng. Geol. Envir. 71(2), 351–357. Zheng J., Kulatilake P.H.S.W., Deng J., Wei J., 2015. Development of a probabilistic kinematic wedge sliding analysis procedure and application to a rock slope at a hydropower site in China. Bull. Eng. Geol. Environ. 1-16, DIO: 10.1007/s10064-015-07643.
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Fig. 1. Kinematic analysis for plane failure (after Goodman (1989)).
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Fig. 2. Kinematic analysis for toppling failure (after Goodman (1989)).
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Fig. 3. An example to illustrate that Eq. (3a) is flawed in some cases with respect to plane failure.
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Fig. 4. Diagrammatic sketch to illustrate that the discontinuity can exactly daylight on the slope face.
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Fig. 5. Input parameters of SMR corrected by this paper.
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(b) Toppling failure
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(a) Plane or wedge failure
Fig. 6. Statistical histogram of the discrepancy of values of SMR index calculated by Romana’s (1985) method and modified method proposed by the study.
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ACCEPTED MANUSCRIPT Table 1 Summary of the existing rock mass classification systems, which was revised on the basis of the list given by Pantelidis (2009). Abbreviation
Authors & Data
Application
Comments
–
-
Ritter, 1879
Tunnels
The first attempt for the formalization of an empirical approach to tunnel design.
Rock load
-
Terzaghi, 1946
Tunnels
The earliest reference to the use of rock mass classification for the design of tunnel support.
Stand-up time
-
Lauffer, 1958
Tunnels
Rock Quality Designation
RQD
DeDeer, 1963
General
New Austrian Tunneling Method
NATM
Rabcewicz, 1964
Rock Structure Rating
RSR
Wickham et al., 1972
Rock Mass Rating
RMR
Bieniawski, 1973, 1976, 1979, and 1989
Tunnels and cuttings
A raw rating adjustment for discontinuity orientation for application in slopes was added in the 1979 version of the RMR system.
Rock Tunneling Quality Index
Q
Barton et al., 1974
Tunnels
They are the most commonly used classification systems for tunnels
Size-Strength Classification
-
Franklin et al., 1974
General
The method has not been used widely.
Mining Rock Mass Rating
MRMR
Laubscher, 1977, 1984, and 1990
Mines
Based on RMR (1973).
Engineering-Geological Rock Durability Classification
-
Olivier, 1979
Tunnels
Providing a quantitative appraisal of rock durability.
Rock Mass Strength
RMS
Selby, 1980 and 1982; Moon and Selby. 1983
Cuttings
Based on natural slope data base.
Geotechnical Description
-
ISRM, 1981
General
It is widely used for characterizing the properties of rock masses.
Slope Mass Rating
SMR
Romana 1985; Romana et al., 2003
Cuttings
Based on RMR (1979).The most commonly used classification system for slopes.
Slope Rock Mass Rating
SRMR
Robertson, 1988
Cuttings
Based on RMR; The classification is provided for of weak altered rock mass materials from drill-hole cores.
Index of Rock Mass Basic Quality
BQ
NSCGPRC, 1995
General
It is determined by the hardness degree of rock and the intactness index of rock mass.
Chinese Slope Mass Rating
CSMR
Chen, 1995
Cuttings
Adjustment factors have been applied to the SMR system for the discontinuity condition and slope height.
Geological Strength Index
GSI
Hoek et al., 1995
General
Based on RMR (1976).
Rock Mass index
RMi
Palmström, 1995
General
Characterizing the strength of the rock mass for construction purposes.
Rock Mass Classification Rating
RMCR
Yaşar, 1995
General
Using 12 parameters from laboratory and in situ experiments.
Modified Rock Mass Rating
M-RMR
Ünal, 1996
Mines
For weak, stratified, anisotropic and clay bearing rock masses.
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Name of the system
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Related to the stand-up time of an unsupported tunnel excavation.
Tunnels
Scientitical empirical approach.
Small tunnels
First rating system for rock masses.
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Component factor of many classification systems.
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Mazzaccola and Hudson, 1996
Natural slopes
A rock mass characterization method for the indication of natural slope instabilities.
Slope Stability Probability Classification
SSPC
Hack, 1996; Hack et al., 2003
Cuttings
Probabilistic assessment of in dependently different failure mechanics.
Rock slope Deterioration Assessment
RDA
Nicholson and Hencher, 1997; Nicholson et al., 2000; Nicholson, 2002, 2003, and 2004
Cuttings
For shallow, weathering-related breakdown of excavated rock slopes.
Geological Strength Index
GSI
Hoek et al., 1998; Marinos and Hoek, 2000 and 2001; Marinos et al., 2005
General
For non-structurally controlled failures.
Adapted Slope Stability Probability Classification
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Lindsay et al., 2001
Cuttings
Volcanic Rock Face Safety Rating
VRFSR
Singh and Connolly, 2003
Cuttings (temporary excavations)
Modified Rock Mass Classification
M-RMR
Şen and Sadagah, 2003
Falling Rock Hazard Index
FRHI
Singh, 2004
Modification of slope mass rating
-
Tomás et al., 2007
Fuzzy Slope Mass Rating
FSMR
New Slope Mass Rating
Rock Mass Quality Rating
RI
PT
-
NU
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Based on SSPC.
For volcanic rock slopes to determine the excavation safety on construction sites.
Based on RMR (1989)
Cuttings (temporary excavations)
Developed for stable excavations to determine the degree of danger to workers.
Cuttings
Modifying the SMR system by continuous functions.
Daftaribesheli et al., 2011
Cuttings
Based on SMR.
NSMR
Singh et al., 2013
Cuttings
Incorporating a new parameter of overburden thickness profile into the SMR system
RMQR
Aydan et al, 2014
General
It is used to estimate the geomechanical properties of rock masses.
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ACCEPTED MANUSCRIPT Table 2 Adjustment parameters (F1, F2, and F3) for SMR (modified from Romana (1985) by Anbalagan et al. (1992)) Parameters
Very favorable
Favorable
Normal
Unfavorable
Very unfavorable
P/T/W
γ
> 30°
30-20°
20-10°
10-5°
< 5°
P/T/W
F1
0.15
0.40
0.70
0.85
1.00
P/W
η
< 20°
20-30°
30-35°
35-45°
> 45°
P/W
F2
0.15
0.40
0.70
0.85
1.00
T
F2
1.00
1.00
1.00
1.00
1.00
P/W
ζ
> 10°
10-0°
0°
0-(-10)°
< (-10)°
T
ζ
< 110°
110-120°
> 120°
-
-
P/T/W
F3
0
-6
-25
-50
-60
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Type of failure
MA
Note: P, plane failure; T, toppling failure; W, wedge failure; γ, η, and ζ are the parameters for determining the values of F1,
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F2, and F3, respectively.
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ACCEPTED MANUSCRIPT Table 3 Adjustment parameter (F4) for SMR (Romana, 1985) Natural slope
Presplitting
Smooth blasting
Blasting or mechanical
Deficient blasting
F4
+15
+10
+8
0
-8
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Method
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ACCEPTED MANUSCRIPT Table 4 The mean orientations and friction angles of the most un-favorable discontinuity sets existing in the slopes i and j, and
γ (°)
βd (°)
βs (°)
φ(°)
F1
F2
F3
i
38
74
83
35
0.15
1.00
-50
j
86
70
83
35
0.15
1.00
-60
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# of slope
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the obtained values of F1, F2, and F3.
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ACCEPTED MANUSCRIPT Highlights A comprehensive summary of rock mass classification systems is presented.
A review of the development of SMR system is given.
Corrections for adjustment parameters F1 and F3 in the SMR system is proposed.
The corrections are also applicable to those derived SMR system.
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