Slope mass rating

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:[6][7]

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

Adjustment factors for SMR. P: planar failure; T: toppling failure; W: wedge failure. Modified from [8] and [9]

where:

• RMR_b is the RMR index resulting from Bieniawski's Rock Mass Classification without any correction.
• F₁ depends on the parallelism between discontinuity, α_j (or the intersection line, α_i, in the case of wedge failure) and slope dip direction.
• F₂ depends on the discontinuity dip (β_j) in the case of planar failure and the plunge, β_i 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 (β_s) and discontinuity (β_j) dips (toppling or planar failure cases) or the immersion line dip (β_i) (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.[10]

Tomás et al.[11] 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.[12] 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.[13] 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

• β_s < β_j;
• A value higher than 30º and β_j < 20º

b) For wedge failure

• β_s < β_i;
• A value higher than 30º and β_i; < 20 °C) For toppling failure
• β_j < 30º
• A value higher than 30º
• β_j+β_s ≤ 120º

Where β_s is the angle of the slope, β_j is the discontinuity dip, β_i 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.[14][15]

SMR index can be calculated through the open source software SMRTool,[16] 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.[17]

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).[18][19][20]