# Slope mass rating

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Slope mass rating (SMR) is a rock mass classification scheme developed by Manuel Romana [1][2][3] to describe the strength of an individual rock outcrop or slope. The system is founded upon the more widely used RMR scheme,[4] which is modified with quantitative guidelines to the rate the influence of adverse joint orientations (e.g. joints dipping steeply out of the slope).

## Definition

Rock mass classification schemes are designed to account for a number of factors influencing the strength and deformability of a rock mass (e.g. joint orientations, fracture density, intact strength), and may be used to quantify the competence of an outcrop or particular geologic material. Scores typically range from 0 to 100, with 100 being the most competent rock mass. The term rock mass incorporates the influence of both intact material and discontinuities on the overall strength and behavior of a discontinuous rock medium. While it is relatively straightforward to test the mechanical properties of either intact rock or joints individually, describing their interaction is difficult and several empirical rating schemes (such as RMR and SMR) are available for this purpose.

### SMR index calculation

SMR uses the same first five scoring categories as RMR:

1. Uniaxial compressive strength of intact rock,
2. Rock Quality Designation (or RQD),
3. Joint spacing,
4. Joint condition (the sum of five sub-scores), and
5. Groundwater conditions.

The final sixth category is a rating adjustment or penalization for adverse joint orientations, which is particularly important for evaluating the competence of a rock slope. SMR provides quantitative guidelines to evaluate this rating penalization in the form of four sub-categories, three that describe the relative rock slope and joint set geometries and a fourth which accounts for the method of slope excavation. SMR addresses both planar sliding and toppling failure modes, no additional consideration was made originally for sliding on multiple joint planes. However, Anbalagan et al.[5] adapted the original classification for wedge failure mode.

The final SMR rating is obtained by means of next expression:

${\displaystyle SMR=RMR_{b}+F_{1}\times F_{2}\times F_{3}+F_{4}}$

Adjustment factors for SMR. P: planar failure; T: toppling failure; W: wedge failure. Modified from [6] and [7]

where:

• RMRb is the RMR index resulting from Bieniawski's Rock Mass Classification without any correction.
• F1 depends on the parallelism between discontinuity, αj (or the intersection line, αi, in the case of wedge failure) and slope dip direction.
• F2 depends on the discontinuity dip (βj) in the case of planar failure and the plunge, βi of the intersection line in wedge failure. As regards toppling failure, this parameter takes the value 1.0. This parameter is related to the probability of discontinuity shear strength.
• F3 depends on the relationship between slope (βs) and discontinuity (βj) dips (toppling or planar failure cases) or the immersion line dip (βi) (wedge failure case). This parameter retains the Bieniawski adjustment factors that vary from 0 to −60 points and express the probability of discontinuity outcropping on the slope face for planar and wedge failure.
• F4 is a correction factor that depends on the excavation method used.

Although SMR is worldwide used, sometimes some misinterpretations and imprecisions are made when applied. Most of the observed inaccuracies are related to the calculation of the ancillary angular relationships between dips and dip directions of the discontinuities and the slope required to determine F1, F2 and F3 factors. A comprehensive definition of these angular relationships can be found in [8].

### SMR index modifications

Tomás et al.[9] proposed alternative continuous functions for the computation of F1, F2 and F3 correction parameters. These functions show maximum absolute differences with discrete functions lower than 7 points and significantly reduce subjective interpretations. Moreover, the proposed functions for SMR correction factors calculus reduce doubts about what score to assign to values near the border of the discrete classification.

The proposed F1 continuous function that best fits discrete values is:

${\displaystyle F_{1}={\frac {16}{25}}-{\frac {3}{500}}\arctan \left({\frac {1}{10}}\left(|A|-17\right)\right)}$

where parameter A is the angle formed between the discontinuity and the slope strikes for planar and toppling failures modes and the angle formed between the intersection of the two discontinuities (the plunge direction) and the dip direction of the slope for wedge failure. Arctangent function is expressed in degrees.

${\displaystyle F_{2}={\begin{cases}{\frac {9}{16}}-{\frac {1}{195}}\arctan \left({\frac {17}{100}}B-5\right),&{\text{for planar and wedge failure}}\\1,&{\text{for toppling failure}}\end{cases}}}$

where parameter B is the discontinuity dip in degrees for planar failure and the plunge of the intersection for wedge failure. Note that the arctangent function is also expressed in degrees.

${\displaystyle F_{3}={\begin{cases}-30+{\frac {1}{3}}\arctan C,&{\text{for planar and wedge failure}}\\-13-{\frac {1}{7}}\arctan \left(C-120\right),&{\text{for toppling failure}}\end{cases}}}$

where C depends on the relationship between slope and discontinuity dips (toppling or planar failure cases) or the slope dip and the immersion line dip for wedge failure case. Arctangent functions are expressed in degrees.

Alternatively, Tomás et al.[10] also proposed a graphical method based on the stereographic representation of the discontinuities and the slope to obtain correction parameters of the SMR (F1, F2 and F3). This method allows the SMR correction factors to be easily obtained for a simple slope or for several practical applications as linear infrastructures slopes, open pit mining or trench excavations.

A four-dimensional visual analysis of SMR geomechanical classification, performed by Tomás et al. [11] by means of the Worlds within Worlds methodology to explore, analyze and visualize the relationship among the main controlling parameters of this geomechanical classification, revealed that several cases exist where the slope-discontinuity geometrical relationship scarcely affects slope stability (i.e. F1×F2×F3≃0), and as a consequence SMR can be computed by correcting basic RMR only with the F4 factor using next equation with a maximum error lower than nine points:

${\displaystyle SMR=RMR_{b}+F_{4}}$

These cases in which the influence of the geometry of the slope and the discontinuities is negligible (i.e. F1×F2×F3≃0) are:

a) For planar failure

• βs < βj;
• A value higher than 30º and βj < 20º

b) For wedge failure

• βs < βi;
• A value higher than 30º and βi; < 20 °C) For toppling failure
• βj < 30º
• A value higher than 30º
• βjs ≤ 120º

Where βs is the angle of the slope, βj is the discontinuity dip, βi is the plunge of the intersection line between two discontinuities and A is the parallelism between the discontinuity (or intersection line for wedges) and slope dip directions.

Other approaches have been proposed to adapt SMR to different situations as high slopes, flysch formations or even heterogeneous materials.[12][13]

### Application of the SMR index

SMR index can be calculated through the open source software SMRTool,[14] which permits to compute SMR from the geomechanical data of the rock mass and the orientation of the slope and the discontinuities. This software was used to calculate the SMR index using 3D point clouds.[15]

SMRTool is an open source software which aids to calculate the SMR adjustment factors. It depicts the relation between the slope and the discontinuity in order to understand the values of those factors.

Some authors have proposed different methodologies to map the failure susceptibility in rock slopes by computing the SMR index using a Geographical Information System (GIS).[16][17][18]

## References

1. ^ Romana M. (1985). New adjustment ratings for application of Bieniawski classification to slopes. Proc. Int. Symp. on the Role of Rock Mechanics: 49-53.
2. ^ Romana M. (1995). The geomechanical classification SMR for slope correction. Proc. Int. Congress on Rock Mechanics 3: 1085-1092.
3. ^ STMR. "STMR Servicio Tecnico de Mecanica de Rocas". www.stmr.es (in Spanish). Retrieved 2016-03-31.
4. ^ Bieniawski, Z.T. (1989). Engineering Rock Mass Classifications: A Complete Manual for Engineers and Geologists in Mining, Civil, and Petroleum Engineering. John Wiley & Sons. ISBN 978-0-471-60172-2.
5. ^ Anbalagan R, Sharma S, Raghuvanshi TK. Rock mass stability evaluation using modified SMR approach. In: Proceedings of 6th nat symp rock mech, Bangalore, India, 1992. p. 258–68.
6. ^ Romana M. El papel de las clasificaciones geomecánicas en el estudio de la estabilidad de taludes. In: del IV Simposio Nacional sobre taludes y laderas inestables, vol. 3; 1997:955–1011.
7. ^ Anbalagan R, Sharma S, Raghuvanshi TK. Rock mass stability evaluation using modified SMR approach. In: Proceedings of 6th nat symp rock mech, Bangalore, India, 1992. p. 258–68
8. ^ Pastor, José Luis; Riquelme, Adrián J.; Tomás, Roberto; Cano, Miguel (2019-12-01). "Clarification of the slope mass rating parameters assisted by SMRTool, an open-source software". Bulletin of Engineering Geology and the Environment. 78 (8): 6131–6142. doi:10.1007/s10064-019-01528-9. hdl:10045/99191. ISSN 1435-9537.
9. ^ Tomás, R.; Delgado, J.; Serón, J. B. (2007-10-01). "Modification of slope mass rating (SMR) by continuous functions". International Journal of Rock Mechanics and Mining Sciences. 44 (7): 1062–1069. doi:10.1016/j.ijrmms.2007.02.004.
10. ^ Tomás, R.; Cuenca, A.; Cano, M.; García-Barba, J. (2012-01-04). "A graphical approach for slope mass rating (SMR)". Engineering Geology. 124: 67–76. doi:10.1016/j.enggeo.2011.10.004.
11. ^ Tomás, R.; Valdes-Abellan, J.; Tenza-Abril, A. J.; Cano, M. (2012-07-01). "New insight into the slope mass rating geomechanical classification through four-dimensional visualization". International Journal of Rock Mechanics and Mining Sciences. 53: 64–69. doi:10.1016/j.ijrmms.2012.04.002.
12. ^ Romana, M., Serón, J.B., Montalar, E., SMR Geomechanics classification: Application, experience and validation ISRM 2003–Technology roadmap for rock mechanics, South African Institute of Mining and Metallurgy, 2003.
13. ^ Romana, M., Tomás, R., Serón, J.B. (2015). Slope Mass Rating (SMR) geomechanics classification: thirty years review. ISRM Congress 2015 Proceedings - International Symposium on Rock Mechanics, Quebec, Canada, May 10 to 13 2015. ISBN 978-1-926872-25-4, 10 pp
14. ^ Adrián, Riquelme Guill; Roberto, Tomás Jover; Antonio, Abellán Fernández. "SMRTool (MATLAB)". rua.ua.es. Retrieved 2016-04-08.
15. ^ Riquelme, Adrián J.; Tomás, Roberto; Abellán, Antonio (2016-04-01). "Characterization of rock slopes through slope mass rating using 3D point clouds". International Journal of Rock Mechanics and Mining Sciences. 84: 165–176. doi:10.1016/j.ijrmms.2015.12.008. hdl:10045/52313.
16. ^ Irigaray, C., Fernández, T. & Chacón, J. Preliminary Rock-Slope-Susceptibility Assessment Using GIS and the SMR Classification. Natural Hazards, 30, 309-324, doi: 10.1023/B:NHAZ.0000007178.44617.c6.
17. ^ Tomás, R., Cano, M., Cañaveras, J.C:, Cuenca, A., Delgado, J., Estévez, A., Pina, J.A., Nuevas funciones continuas para el cálculo del Slope Mass Rating (SMR): aplicación mediante un sistema de información geográfica a los taludes rocosos de una cantera. Revista de la Sociedad Geológica de España, 19, 87-97, 2006
18. ^ 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). Bulletin of Engineering Geology and the Environment, 71, 351-357, doi: 10.1007/s10064-011-0384-5.