Rock Mass Rating – an overview

RMR should be determined as an algebraic sum of ratings for all of the parameters given in Tables 6.1 to 6.5 and Table 6.10 after adjustments for orientation of discontinuities given in Tables 6.8 and 6.9.

From: Engineering Rock Mass Classification, 2011

Related terms:

Bhawani Singh, R.K. Goel, in Engineering Rock Mass Classification, 2011

The geomechanics classification or the rock mass rating (RMR) system was initially developed at the South African Council of Scientific and Industrial Research (CSIR) on the basis of experiences in shallow tunnels in sedimentary rocks. This chapter provides an overview on RMR with discussion on estimation, application, and precaution of RMR. To apply the geomechanics classification system, a given site is divided into a number of geological structural units in such a way that each type of rock mass is represented by a separate geological structural unit. The following six parameters are determined for each structural unit: Uniaxial compressive strength (UCS) of intact rock material, rock quality designation (RQD), joint or discontinuity spacing, joint condition, groundwater condition, and joint orientation. RQD is determined from rock cores or volumetric joint count; it is the percentage of rock cores in one meter of drill run. RMR is determined as an algebraic sum of ratings for all of the parameters. On the basis of RMR values for a given engineering structure, the rock mass is sorted into five classes: very good (RMR 100–81), good (80–61), fair (60–41), poor (40–21), and very poor (<20). It must be ensured that double accounting for a parameter is not done in the analysis of rock structures or in estimating the rating of a rock mass.

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Lianyang Zhang, in Engineering Properties of Rocks (Second Edition), 2017

5.2.2 Rock Mass Rating (RMR)

The RMR or the Geomechanics Classification System, proposed by Bieniawski (1973), was initially developed for tunnels. In recent years, it has been applied to the preliminary design of rock slopes and foundations as well as to the estimation of the in-situ deformation modulus and strength of rock masses. The RMR uses six parameters that can be determined in the field (see Table 5.2):

Table 5.2. Geomechanics Classification of Jointed Rock Masses

A. Classification Parameters and Their Rating
Parameter Range of Values
1 Strength of intact rock Point-load strength index (MPa) >10 4–10 2–4 1–2 For this low range, unconfined compressive test is preferred
Unconfined compressive strength (MPa) >250 100–250 50–100 25–50 5–25 1–5 < 1
Rating 15 12 7 4 2 1 0
2 Drill core quality RQD (%) 90–100 75–90 50–75 25–50 < 25
Rating 20 17 13 8 3
3 Spacing of discontinuities (m) > 2 0.6–2 0.2–0.6 0.06–0.2 < 0.06
Rating 20 15 10 8 5
4 Conditions of discontinuities Very rough surfaces, Not continuous, No separation, Unweathered wall rock Slightly rough surfaces, separation < 1 mm, Slightly weathered walls Slightly rough surfaces, separation < 1 mm, Highly weathered walls Slickensided surfaces or Gouge < 5 mm thick or Separation 1–5 mm continuous Soft gouge > 5 mm thick or Separation > 5 mm Continuous
Rating 30 25 20 10 0
5 Ground water Inflow per 10 m tunnel length (l/min) None or < 10 or 10–25 or 25–125 or > 125 or
Ratio of joint water pressure to major principal stress 0 or < 0.1 or 0.1–0.2 or 0.2–0.5 or > 0.5 or
General conditions Completely dry Damp Wet Dripping Flowing
Rating 15 10 7 4 0
B. Rating adjustment for joint orientations
Strike and dip orientations of discontinuities Very favorable Favorable Fair Unfavorable Very Unfavorable
Ratings Tunnels and mines 0 − 2 − 5 − 10 − 12
Foundations 0 − 2 − 7 − 15 − 25
Slopes 0 − 5 − 25 − 50 − 60
C. Rock mass classes and corresponding design parameters and engineering properties
Class No. I II III IV V
RMR 100–81 80–61 60–41 40–21 <20
Description Very Good Good Fair Poor Very poor
Average stand-up time 20 years for 15 m span 1 year for 10 m span 1 week for 5 m span 10 h for 2.5 m span 30 min for 1 m span
Cohesion of rock mass (MPa) > 0.4 0.3–0.4 0.2–0.3 0.1–0.2 < 0.1
Internal friction angle of rock mass (°) > 45 35–45 25–35 15–25 < 15
Deformation modulus (GPa)a > 56 56–18 18–5.6 5.6–1.8 < 1.8

a Deformation modulus values are from Serafim and Pereira (1983).

Based on Bieniawski, Z.T., 1989. Engineering Rock Mass Classifications. John Wiley, Rotterdam.

unconfined compressive strength of the intact rock

RQD

spacing of discontinuities

condition of discontinuities

ground water conditions

orientation of discontinuities

All but the intact rock strength are normally determined in the standard geological investigations and are entered on an input data sheet. Table 5.3 shows the guidelines for assessing the discontinuity condition. The unconfined compressive strength of intact rock is determined in accordance with standard laboratory procedures but can be estimated in situ from the point-load strength index.

Table 5.3. Guidelines for Classifying Discontinuity Condition

Parameter Range of Values
Discontinuity length (persistence/continuity) Rating 6 4 2 1 0
Measurement (m) < 1 1–3 3–10 10–20 > 20
Separation (aperture) Rating 6 5 4 1 0
Measurement (mm) None < 0.1 0.1–1 1–5 > 5
Roughness Rating 6 5 3 1 0
Description Very rough Rough Slight Smooth Slickensided
Infilling (gouge) Rating 6 4 2 2 0
Description and Measurement (mm) None Hard filling
< 5
Hard filling
> 5
Soft filling
< 5
Soft filling
> 5
Degree of weathering Rating 6 5 3 1 0
Description None Slight Moderate High Decomposed

Note: Some conditions are mutually exclusive. For example, if infilling is present, it is irrelevant what the roughness may be, since its effect will be overshadowed by the influence of the gouge. In such cases, use Table 5.2 directly.

Based on Bieniawski, Z.T., 1989. Engineering Rock Mass Classifications. John Wiley, Rotterdam.

Rating adjustments for discontinuity orientation are summarized for underground excavations, foundations and slopes in Part B of Table 5.2. A more detailed explanation of these rating adjustments for dam foundations is given in Table 5.4, after ASCE (1996).

Table 5.4. Ratings for Discontinuity Orientations for Dam Foundations and Tunneling

A. Dam Foundations
Dip
0°–10°
Dip 10°–30° Dip
30°–60°
Dip
60°–90°
Dip direction
Upstream Downstream
Very favorable Unfavorable Fair Favorable Very unfavorable
B. Tunneling
Strike perpendicular to tunnel axis Strike parallel to tunnel axis Irrespective of strike
Drive with dip Drive against dip
Dip
45°–90°
Dip
20°–45°
Dip
45°–90°
Dip
20°–45°
Dip
45°–90°
Dip
20°–45°
Dip
0°–20°
Very favorable Favorable Fair Unfavorable Very unfavorable Fair Fair

Based on ASCE, 1996. Rock Foundations: Technical Engineering and Design Guides as Adapted from the US Army Corps of Engineers. No. 16, ASCE Press, New York, NY.

The six separate ratings are summed to give an overall RMR, with a higher RMR indicating a better quality rock. Based on the observed RMR value, the rock mass is classified into five classes named as very good, good, fair, poor and very poor, as shown in Part C of Table 5.2. Also shown in Part C of Table 5.2 is an interpretation of these five classes in terms of roof stand-up time, cohesion, internal friction angle and deformation modulus for the rock mass.

It is noted that Table 5.2 shows the 1989 version of the RMR system. In many cases, the RMR data may be based on the 1976 version of the RMR system. RMR76 can be converted to RMR89 by adding a value of 5.

Seismic velocity measurements can also be used to estimate RMR values. Based on the data of limestones, mudstones, marls and shales at a dam site in Wadi Mujib, Jordan, El-Naqa (1996) obtained the following empirical correlation between RMR and P-wave velocity:

(5.1)RMR=59.8vpFvp00.26r=0.84

where vpF is the P-wave velocity of the in situ rock mass; vp0 is the P-wave velocity of the corresponding intact rock; and r is the correlation coefficient.

Cha et al. (2006) obtained the following simple linear relation between RMR and shear-wave velocity measured using a refraction microtremor technique, in order to evaluate the rock condition for the design of a proposed railway tunnel at a site consisting of different types of granite (granite and felsite) and volcanic rocks (dacitic tuff, andesitic tuff, and andesite):

(5.2)RMR=36.2vs−10

where vs is the shear-wave velocity of the rock mass in km/s.

Banks (2005) derived an empirical relation between the basic RMR and the slope angles in mature, natural rock outcrops:

(5.3)basicRMR=0.4S+52

where the basic RMR is the RMR without the adjustment to account for the influence that discontinuity orientations may have on the particular application; and S is the slope angle in mature, natural outcrops in degrees.

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Bhawani Singh, R.K. Goel, in Engineering Rock Mass Classification, 2011

Using Rock Mass Rating

Bieniawski’s rock mass rating (RMR; Chapter 6) may also be used to obtain net allowable bearing pressure as per Table 20.2 (Singh, 1991; Mehrotra, 1992). Engineering classifications listed in Table 20.2 were developed based on plate load tests at about 60 sites and calculating the allowable bearing pressure for a 6 m wide raft foundation with settlement of 12 mm. Figure 20.2 shows the observed trend between allowable bearing pressure and RMR (Mehrotra, 1992), which is similar to the curve from plate test data from IIT Roorkee (Singh, 1991). The permissible settlement is reduced as failure strain of a geological material decreases such as in rock mass. The plate load test is the most reliable method for determining the allowable bearing pressure of both rock mass and soil.

Table 20.2. Net Allowable Bearing Pressure (qa) Based on RMR

Class No. I II III IV V
Description of rock Very good Good Fair Poor Very poor
RMR 100–81 80–61 60–41 40–21 20–0
qa (t/m2) 600–440 440–280 280–135 135–45 45–30

The RMR should be obtained below the foundation at depth equal to the width of the foundation, provided RMR does not change with depth. If the upper part of the rock, within a depth of about one-fourth of foundation width, is of lower quality the value of this part should be used or the inferior rock should be replaced with concrete. Since the values here are based on limiting the settlement, they should not be increased if the foundation is embedded into rock.

During earthquake loading, the values of allowable bearing pressure from Table 20.2 may be increased by 50% in view of rheological behavior of rock masses.

Source: Mehrotra, 1992.

Figure 20.2. Allowable bearing pressure on the basis of rock mass rating and natural moisture content (nmc = 0.60–6.50%).

(From Mehrotra, 1992)

Sinha et al. (2003) reported that contamination of rock mass by seepage of caustic soda not only reduces the bearing capacity of foundation by about 33% in comparison to that of uncontaminated rock mass, but it also causes swelling and heaving of the concrete floors. Because of this, the alkaline soda was neutralized by injecting acidic compound and grouting the rock mass with cement grout.

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Pengzhi Pan, … Xin Wang, in Rockburst, 2018

7.3.4 Discussion

Based on our model for rockbursts with DDA, it would be worthwhile to discuss the interrelation between rock mass quality, as scaled by the rock mass rating (RMR) (Bieniawski, 1973) and rockburst hazard, so as to provide a useful rockburst prediction approach for tunneling practitioners.

It is widely agreed that rockbursts do not occur in weak rocks. Rock masses prone to rockbursts are typically stiff, strong, and brittle, with uniaxial compressive strength of 100–400 MPa with Young’s modulus > 20 GPa (Obert & Duvall, 1967). To try and constrain the rock mass quality levels at which rockbursts can be expected, we generate four block system meshes with DDA that represent rock mass qualities between “Good” and “Very Good” according to Bieniawski (1973), as shown in Table 7.3.1 and demonstrated in Fig. 7.3.4A–D. Two joint sets with the opposite inclinations of 60 degrees and an initial hydrostatic stress p of 55 MPa are assumed in all simulations.

Table 7.3.1. DDA Input Parameters for RMR Groups

RMR Young’s modulus (GPa) Poisson’s ratio ν Joint spacing (m) Joint friction (degrees) Monitored blocks
65 30 0.23 1.0 35 567
75 50 0.22 1.5 40 254
85 70 0.21 2.5 45 97
95 90 0.20 5.0 50 27

Modified from Hatzor, Y. H., He, B. G., & Feng, X. T. (submitted). Rockburst hazard in blocky rock masses. Tunnelling and Underground Space Technology.

Fig. 7.3.4. Effect of rock mass quality on rockburst potential: (A) spacing of 5.0 m; (B) spacing of 2.5 m; (C) spacing of 1.5 m; (D) spacing of 1.0 m; (E) energy components distribution in affected zone due to tunneling; (F) kinetic energy of block system in affected zone and initial energy stored in a circular area before it is removed by tunneling, as obtained with DDA; and (G) field monitoring of rockburst events related to rock mass quality during drill and blast excavation at Jinping hydroelectric project.

Modified from Hatzor, Y. H., He, B. G., & Feng, X. T. (submitted). Rockburst hazard in blocky rock masses. Tunnelling and Underground Space Technology; Feng X. T., Chen B. R., Zhang C. Q., Li S. J. & Wu S. Y. (2013). Mechanism, warning and dynamic control of rockburst development processes. Beijing: Science Press (in Chinese).

The initial strain energy density stored in the rock mass prior to excavation is inversely proportional to Young’s modulus and Poisson’s ratio (Eq. 7.3.1); this is reflected well in the results shown in Fig. 7.3.4E. Moreover, both the elastic strain energy and the kinetic energy of the block system decrease considerably with improving RMR, whereas the dissipated energy of shear sliding along preexisting joints is less correlated with RMR.

These findings lead us to an attempt to address the kinetic energy of the block system in the affected zone due to tunnel removal (in an annulus SB between 0.5 to 1.5D from the tunnel center of an area of 628 m2), in terms of the initial elastic strain energy that was stored in the area and was removed by the excavation (a circle SA of an area of 79 m2). As can be appreciated form Fig. 7.3.4F, the initial strain energy in the excavated area, as well as the kinetic energy of the block system in the affected zone, decrease with improved rock mass quality. For an RMR of 65 the ratio between kinetic and stored energies is 1.51, but it drops to 0.24 for an RMR of 95.

Indeed, field observations of rockbursts during the construction of Jinping hydroelectric project indicate that most of the rockbursts took place in rocks with Young’s modulus ranging from 20 to 55 GPa (Liu, Wang, Zhang, Jia, & Duan, 2011; Zhang et al., 2014), corresponding to the RMR values in the range of 65–75 here, lending support to our numerical results. Moreover, ~ 88% of 300 rockburst events documented in the course of excavation of Jinping tunnels (Feng et al., 2013) occurred in rock mass with uniaxial compressive strength of σc = 100–140 MPa (Liu et al., 2016), corresponding to the lower end of the “Good rock” category in terms of Bieniawski (1973), in agreement with our DDA results (see Fig. 7.3.4G). The collection of rockburst events by Feng et al. (2013) also reveals that 12% of rockbursts occurred in the “Very good rock” category, and that no rockbursts were recorded in the “Fair rock” category. These findings confirm our DDA result that rock mass ratings between RMR = 65 and 75 are most prone to rockburst hazard.

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Bhawani Singh, R.K. Goel, in Engineering Rock Mass Classification, 2011

The New Approach

Attempts to correlate Q and RMR in Eqs. (9.3) through (9.7) ignore the fact that the two systems are not truly equivalent. It seems, therefore, that a good correlation can be developed if N and RCR are considered.

RCR and rock mass number N from 63 cases were used to obtain a new interrelation. The 63 cases consisted of 36 from India, 4 from the Kielder experimental tunnel (reported by Hoek & Brown, 1980), and 23 from the Norwegian Geotechnical Institute (NGI) (reported by Bieniawski, 1984). Details about the six parameters for Q and information about joint orientation vis-à-vis tunnel axis with respect to these 23 NGI cases were picked up directly from Barton et al. (1974). Estimates of UCS (qc) of rock material were made from rock descriptions given by Barton et al. (1974) using strength data for comparable rock types from Lama and Vutukuri (1978). Using the obtained ratings for joint orientation and qc and RMR from Bieniawski (1984), it was possible to estimate values of RCR. Thus, the values of N and RCR for the 63 case histories were plotted in Figure 9.2 and the following correlation was obtained:

Figure 9.2. Correlations between N and RCR.

(From Goel et al., 1995b)

(9.8)RCR=8lnN+30,forqc>5MPa

Equation (9.8) has a correlation coefficient of 0.92, and it is not applicable to the borderline of soil and rock mass according to data from Sari and Pasamehmetoglu (2004). The following example explains how Eq. (9.8) could be used to obtain RMR from Q and vice versa.

Example 9.1

The values of the parameters of RMR and Q collected in the field are given in Table 9.2.

Table 9.2. Values of the Parameters of RMR and Q Collected in the Field

RMR system Q-system
Parameters for RMR Rating Parameters for Q Rating
RQD (80%) 17 RQD 80
Joint spacing 10 Jn  9
Joint condition 20 Jr  3
Ja  1
Groundwater 10 Jw  1
RCR = 57 N = 26.66
Crushing strength qc +4 SRF  2.5
Joint orientation (−)12
RMR = 49 Q = 10.6

(a) RMR from Q

N=(RQD JrJw)/(JnJa)=26.66as shown in Table 9.2

Corresponding to N = 26.66, RCR = 56.26 (Eq. 9.8)

RMR = RCR + (ratings for qc and joint orientation as per Eq. 9.2)

RMR = 56.26 + [4 + (−)12]

RMR = 48.26 (It is comparable to RMR = 49 obtained from direct estimation as shown in Table 9.2.)

(b) Q from RMR

RCR = RMR − (ratings for qc and joint orientation as per Eq. 9.2)

RCR = 49 − (4 − 12)

RCR = 57

Corresponding to RCR = 57, N = 29.22 (Eq. 9.8)

Q=(N/SRF)=29.22/2.5

Q = 11.68 (almost equal to the field estimated value, Table 9.2)

The slight difference in directly estimated values of Q and RMR and those obtained by the proposed interrelation are due to the inherent scatter in Eq. (9.8).

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Bhawani Singh, R.K. Goel, in Engineering Rock Mass Classification, 2011

Mohr-coulomb strength parameters

Stability analysis of a rock slope requires assessment of shear strength parameters, that is, cohesion (c) and angle of internal friction (ϕ) of the rock mass. Estimates of these parameters are usually not based on extensive field tests. Mehrotra (1992) carried out extensive block shear tests to study the shear strength parameters of rock masses. The following inferences may be drawn from this study:

1.

The rock mass rating (RMR) system can be used to estimate the shear strength parameters c and ϕ of the weathered and saturated rock masses. It was observed that the cohesion (c) and the angle of internal friction (ϕ) increase when RMR increases (Figure 16.1).

Figure 16.1. Relationship between rock mass rating and shear strength parameters, cohesion (c), and angle of internal friction (ϕ) (nmc: natural moisture content).

(From Mehrotra, 1992) 2.

The effect of saturation on shear strength parameters has been found to be significant. For poor saturated (wet) rock masses, a maximum reduction of 70% has been observed in cohesion (c), whereas the reduction in angle of internal friction (ϕ) is of the order of 35% when compared to those for the dry rock masses.

3.

Figure 16.1 shows that there is a non-linear variation of the angle of internal friction with RMR for dry rock masses. This study also shows that ϕ values of Bieniawski (1989) are somewhat conservative.

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Bhawani Singh, R.K. Goel, in Engineering Rock Mass Classification, 2011

Need for engineering geological map

Nature tends to be heterogeneous, which makes it easy to predict its weakest link. More attention should be focused on the weak zones (joints, shear zones, fault zones, etc.) in the rock mass that may cause wedge failures and/or toppling. Rock failure is localized and three dimensional in heterogeneous rock mass and not planar, as in homogeneous rock mass.

First, a geological map on macro-scale (1:50,000) should be prepared before tunneling or laying foundations. Then an engineering geological map on micro-scale (1:1000) should be prepared soon after excavation. This map should highlight geological details for an excavation and support system. These include Q, RMR, all the shear zones, faults, dip and dip directions of all joint sets (discontinuities), highest ground water table (GWT), and so forth along tunnel alignment. The engineering geological map helps civil engineers immensely. Such detailed maps prepared based on thorough investigation are important for tunnel excavations. If an engineering geological map is not prepared then the use of a tunnel boring machine (TBM) is not advisable, because the TBM may get stuck in the weak zones, as experienced in Himalayan tunneling. An Iraqi proverb eloquently illustrates this idea:

Ask 100 questions, but do not make a single mistake.

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Gao-Feng Zhao, in High Performance Computing and the Discrete Element Model, 2015

2.5.4 Block caving

Block caving is considered to be the most economic choice for large-scale underground mining, which costs only about 10% (~ 5–10 AUDs per ton) of the cost of stopping methods (~ 30–60 AUDs per ton). This approach involves a number of classical rock mechanics problems, for instance deformation of rocks under excavation at great depth, fracturing of rock under dynamic and quasi-dynamic loading, fragmentation of fractured rock under gravitational force and granular flow of rock fragments under gravity. These in turn control many crucial aspects relating to block caving, such as stability and serviceability of undercuts and draw horizons; caveability and production; and ground surface subsidence. The ground surface subsidence can further trigger additional serious geotechnical hazards and may jeopardize mine infrastructure. One example was reported in the Palabora copper mine, where a 300 m landslide was trigged by a block caving operation, affecting the water and power lines, a railway line and water reservoirs. Three approaches are available to analyze rock mechanics problems in block caving: empirical methods, experimental methods and numerical methods. Using the design charts with the design parameters (e.g. mining rock mass rating, height of the caved rock, and minimum and maximum spans of the footprint), the caveability, production and ground surface subsidence of block caving can be approximated in a simple manner. The main shortcoming of the empirical approach is the difficulty of determining the parameters related to rock masses, for example the mining rock mass rating and the density of fractured rock. Furthermore, the empirical method also ignores the stress–strain relationship of the rock masses and the influence of geological structures, and other site-specific issues that can affect the actual caving behavior significantly.

The experimental approach can provide physical insights into the behavior of rock masses mined in block cavings. However, due to the large expense and time in the model construction, only a few tests on block cavings can be found in the literature, for example the 2D caving model tests conducted by McNearny and Abel [MCN 93] from Colorado School of Mines, and the three-dimensional (3D) model tests conducted by Trueman et al. [TRU 08] from the University of Queensland. These physical models provided useful information on the response of rock masses during block caving (e.g. the failure patterns of the caving zone and the deflection of the whole model including the ground surface subsidence). However, given the cost associated with each test and the construction time, physical tests are cost prohibitive for practical purposes. Moreover, some unrealistic assumptions must be made in the model testing, for example the horizontal stresses are not simulated correctly, the blocks are arranged uniformly [MCN 93] and the rock mass is in a discrete/granulated state without undergoing failure or fracturing [TRU 08]. These assumptions lead to model test results that can only be used for research purposes rather than a predictive model to guide the actual operation in block caving.

With the improvement of modern computers and computing power, numerical modeling techniques have become exceptionally useful in scientific research and engineering applications, and provide the most promising solution to study mechanical behavior of rock masses [BRO 08]. However, there are many limitations in current numerical techniques and, in practice, empirical methods, such as Laubscher’s method [LAU 00], are still the most commonly used methods in block caving. For example, the FEM, as the mainstream numerical tool in scientific research and engineering applications, is still limited in modeling fracturing and fragmentation of rock masses due the lack of sophisticated constitutive models for rock mass and the difficulty in parameter selection. The DEM is promising in simulating the complex mechanical interactions of rock masses such as fracturing and fragmentation. Nevertheless, a major shortcoming of the DEM is that proper calibration of the model parameters is required to obtain reasonable results [CAM 13]. In addition, due to the lack of advanced constitutive models for the DEM, it is unlikely that the DEM with a large element size (required for practical problems) can capture the nonlinear deformation of rock masses at the pre- and post-failure stage. The FEM/DEM [MUN 95] is a newly developed method to integrate FEM and DEM while avoiding their disadvantages. However, implementing this method into a computer code requires complex routines. Moreover, there are 12 DOFs for each numerical unit of the 3D FEM/DEM (6 DOFs for DEM) and is computationally costly. In addition, proper calibration is still required for the FEM/DEM to model fracturing and fragmentation; furthermore, a sophisticated constitutive model is still needed for the FEM/DEM to realistically model the nonlinear deformation of rock masses.

In this example, DICE2D is preliminarily used to model the block caving process. The computational model of the block caving model used in DICE2D is shown in Figure 2.23(a). A long-wall mining model is built as shown in Figure 2.23(b) to provide a comparison. The particle model uses the final packed particles in the previous example. In the block caving, a portion of the middle wall is removed to further fracture the ore body. In contrast, in the long-wall mining simulation, the right support wall is moved downward during the calculation. Figures 2.24 and 2.25 show the failure process of the rock masses under these two conditions. It can be found that the failure of the block mining is a granular-like type. The long-wall mining method first makes fractures in the continuum and then breaks it into blocks that will further be broken into small pieces.

Figure 2.23. Simplified model configurations for block caving and long wall mining

Figure 2.24. Block caving simulation using multi-core DICE2D. For a color version of the figure, see www.iste.co.uk/zhao/computing.zip

Figure 2.25. Long-wall mining simulated by multi-core DICE2D. For a color version of the figure, see www.iste.co.uk/zhao/computing.zip

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Lianyang Zhang, in Engineering Properties of Rocks (Second Edition), 2017

4.5.2 Rock Quality Designation (RQD)

RQD was proposed by Deere (1964) as a measure of the quality of borehole core. The RQD is defined as the ratio (in percent) of the total length of sound core pieces that are 0.1 m (4 in.) or longer to the length of the core run. The value 0.1 m is referred to as the threshold value. RQD is perhaps the most commonly used method for characterizing the jointing in borehole cores, although this parameter may also implicitly include other rock mass features such as weathering and core loss.

For RQD determination, the ISRM recommends a core size of at least NX (size 54.7 mm) drilled with double-tube core barrel using a diamond bit. Artificial fractures can be identified by close fitting of cores and unstained surfaces. All the artificial fractures should be ignored while counting the core length for RQD. A slow rate of drilling will also give better RQD. The correct procedure for measuring RQD is shown in Fig. 4.9.

Fig. 4.9. Procedure for measurement and calculation of rock quality designation RQD.

Based on Deere, D.U., 1989. Rock quality designation (RQD) after twenty years. U.S. Army Corps of Engineers Contract Report GL-89-1, Waterways Experiment Station, Viksburg, MS.

Correlations between RQD and linear discontinuity frequency λ have been derived for different discontinuity spacing distribution forms (Priest and Hudson, 1976; Sen and Kazi, 1984; Sen, 1993). For a negative exponential distribution of discontinuity spacings, Priest and Hudson (1976) derived the following relationship between RQD and linear discontinuity frequency λ

(4.21)RQD=100e−λtλt+1

where t is the length threshold. For t = 0.1 m as for the conventional RQD defined earlier, Eq. (4.21) can be expressed as:

(4.22)RQD=100e−0.1λ0.1λ+1

Fig. 4.10 shows the relations obtained by Priest and Hudson (1976) between measured values of RQD and λ, and the values calculated using Eq. (4.22).

Fig. 4.10. Relationship between RQD and discontinuity frequency λ.

From Priest, S.D., Hudson, J., 1976. Discontinuity spacing in rock. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 13, 135–148.

For values of λ in the range 6–16 m− 1, a good approximation to measured RQD values was found to be given by the linear relation:

(4.23)RQD=110.4−3.68λ

Fig. 4.11 plots the relationship between RQD and mean discontinuity spacing proposed by Bieniawski (1989) for determining the combined RQD and spacing ratings in the evaluation of Rock Mass Rating (RMR) (see Chapter 5).

Fig. 4.11. Relationship between RQD and mean discontinuity frequency.

From Bieniawski, Z.T., 1989. Engineering Rock Mass Classifications. John Wiley, Rotterdam.

It is noted that Eq. (4.21) is derived with the assumption that the length of the sampling line L is large so that the term e− λL is negligible. For a short sampling line of length L, Sen and Kazi (1984) derived the following expression for RQD with a length threshold t:

(4.24)RQD=1001−e−λL−λLe−λLe−λtλt+1−e−λLλL+1

Fig. 4.12 shows the variation of RQD with the length of the sampling line L for discontinuity frequency λ = 10 m− 1 and length threshold t = 0.1 m. It can be seen that when L is smaller than about 0.5 m or when λL < 5, RQD increases significantly when L increases. When L is larger than 0.5 or when λL > 5, RQD changes little with L. Therefore, it is important to use sampling lines that are long so that λL > 5 and e− λL is negligible.

Fig. 4.12. Variation of RQD with the length of sample line L.

Based on Sen, Z., Kazi, A., 1984. Discontinuity spacing and RQD estimates from finite length scanlines. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 21, 203–212; Priest, S.D., 1993. Discontinuity Analysis for Rock Engineering. Chapman & Hall.

Seismic velocity measurements have also been used to estimate RQD. By comparing the P-wave velocity of in situ rock mass with laboratory P-wave velocity of intact drill core obtained from the same rock mass, the RQD can be estimated by (Deere et al., 1967):

(4.25)RQD%=vpFvp02×100

where vpF is the P-wave velocity of in situ rock mass; and vp0 is the P-wave velocity of the corresponding intact rock.

Bery and Saad (2012) derived a correlation based on the data of granites in Penang and Sarawak, Malaysia:

(4.26)RQD%=0.97vpFvp02×100r=0.99

where r is the correlation coefficient. It can be seen that Eq. (4.26) is very similar to Eq. (4.25)

Based on the data of limestones, mudstones, marls and shales at a dam site in Wadi Mujib, Jordan, El-Naqa (1996) obtained the following empirical correlation between RQD and P-wave velocities:

(4.27)RQD%=0.77vpFvp01.05×100r=0.89

where vpF, vp0, and r are as defined earlier.

Sjögren et al. (1979) and Palmström (1995) proposed the following hyperbolic correlation between RQD and P-wave velocities:

(4.28)RQD%=vpq−vpFvpq×vpF×kq×100

where vpF is the P-wave velocity of in situ rock mass; vpq is the P-wave velocity of a rock mass with RQD = 0; and kq is a parameter taking into account the actual conditions of the in situ rock mass. Based on regression analysis of the data obtained for heavily fractured calcareous rock masses out-cropping in southern Italy (Fig. 4.13), Budetta et al. (2001) obtained vpq and kq as vq = 1.22 km/s and kq = − 0.69, respectively, ie,

Fig. 4.13. Correlation between RQD and P-wave velocity vpF for heavily fractured calcareous rock in southern Italy.

From Budetta, P., de Riso, R., de Luca, C., 2001. Correlations between jointing and seismic velocities in highly fractured rock masses. Bull. Eng. Geol. Env. 60, 185–192.

(4.29)RQD%=1.22−vpF1.22×vpF×−0.69×100.

Like the discontinuity frequency, RQD varies with the direction of the borehole or sampling line. As an example, Fig. 4.14 shows the variation of estimated RQD by Choi and Park (2004) for a site in the west-southern part of Korea on the lower hemisphere equal-angle stereo projection net. The variation of RQD with direction can be clearly seen. Therefore, it is important to specify the corresponding direction when stating a RQD value.

Fig. 4.14. Variation of estimated RQD with scanline direction.

From Choi, S.Y., Park, H.D., 2004. Variation of rock quality designation (RQD) with scanline orientation and length: a case study in Korea. Int. J. Rock Mech. Min. Sci. 41, 207–221.

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