Modified RMR (Sen)

Sen and Sadagah (2003) modify the determination of the RMR proposed by Bieniawski without modifying its classification. Instead of reading the scores \(A1\), \(A2\), \(A3\) from the stepped tables, they propose computing the RMR with a simplified continuous equation starting from the parameters of RQD, rock strength \(S_u\) (MPa) and spacing \(s\) (m) only, expressing the hydraulic conditions as a function of the flow rate \(G\).

Bieniawski's coefficients for the discontinuity condition (A4) and for the orientation (A6) are kept unchanged. The result is a continuous RMR, less subjective than reading by ranges.

Input parameters

The parameters enter the equation directly, without going through the stepped scores.

• \(S_u\) — uniaxial compressive strength (MPa), from the Point Load Test (\(S_u = K\,I_s\)), the Schmidt hammer (\(S_u = 0{,}775\,R + 21{,}3\)) or the ISRM estimate: see compressive strength.
• RQD — Rock Quality Designation, from borehole cores or, when these are unavailable, from the mean number of joints: see RQD.
• \(s\) — mean discontinuity spacing (m).
• \(G\) — flow rate expressing the hydraulic conditions.

The coefficients \(A4\), \(A5\) and \(A6\) remain those of Bieniawski. The relevant tables are already reported on the Bieniawski page:

• A4 — discontinuity conditions (sub-parameters \(v_1\)–\(v_5\));
• A5 — hydraulic conditions;
• A6 — discontinuity orientation.

Computing the corrected RMR

The corrected RMR is obtained directly from the continuous equation:

\[ RMR_c = 0{,}2\,RQD + 15\log(s) + 0{,}075\,S_u - 2{,}9\log(G) + 34 + (A_5 + A_6) \]

where \(s\) is the spacing (m), \(S_u\) the strength in MPa and \(G\) the flow rate expressing the hydraulic conditions.

If a borehole from which to derive RQD is missing, the mean number of joints \(n\) is introduced and the equation becomes:

\[ RMR_c = 20\,(1 + 0{,}1n)\,e^{-0{,}1n} - 15\log(n) + 0{,}075\,S_u - 2{,}9\log(G) + 34 + (A_5 + A_6) \]

Rock mass classes

From the value of \(RMR_c\), 5 classes are identified, the same as Bieniawski's:

\(RMR_c\)	100–81	80–61	60–41	40–21	≤ 20
Class	I	II	III	IV	V
Description	Very good	Good	Fair	Poor	Very poor

Characteristic parameters

From \(RMR_c\) the cohesion and friction angle of the rock mass are derived (Sen et al.):

\[ c\ [\text{kPa}] = 3{,}625 \cdot RMR_c \]

\[ \varphi\ [°] = 25\,(1 + 0{,}01\,RMR_c)\ \text{ for } RMR_c > 20; \qquad \varphi = 1{,}5\,RMR_c\ \text{ for } RMR_c < 20 \]

For the relationships between the different classifications and the bibliographic references, see the bibliography.

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