Jašarević & Kovačević — n index¶

Developed by Jašarević and Kovačević (1996) on the carbonate formations of Croatia, this method has a clear derivation from the RMR system. The procedure is simple: at least three numerical coefficients are assigned relating to the geomechanical properties of the rock mass, and at least as many relating to engineering-geological properties. To each property you assign a value \(n_i\) ranging from 1 to 5.

Coefficient assignment table¶

On the left you find the geomechanical properties, on the right the engineering-geological ones; the last column reports the coefficient \(n_i\).

\(S_u\) (MPa)	\(I_{s\perp}\) (MPa)	\(I_{s\parallel}\) (MPa)	\(V_p\) (km/s)	\(V_p/V_0\)	\(\alpha\)	Water	RQD (%)	\(J_v\)	\(S\) (cm)	Joints (JRC)	\(n_i\)
> 130	> 5.7	> 0.8	> 6.5	> 0.8	70–90	A	> 65	1–2	> 50	16–20	1
100–130	5.3–5.7	0.7–0.8	4.7–6.5	0.6–0.8	0–20	U	45–65	2–5	20–50	12–16	2
70–100	4.7–5.3	0.6–0.7	3.0–4.7	0.4–0.6	20–35	B	35–45	5–10	10–20	8–12	3
40–70	4.3–4.7	0.5–0.6	1.2–3.0	0.2–0.4	35–50	S	25–35	10–15	6–10	4–8	4
< 40	< 4.3	< 0.5	< 1.2	< 0.2	50–70	F	< 25	> 15	< 6	< 4 or infilled	5

where:

\(S_u\) = uniaxial compressive strength of the intact rock (see Uniaxial compressive strength \(S_u\));
\(I_{s\perp}\) = point load index measured perpendicular to the main discontinuity;
\(I_{s\parallel}\) = point load index measured parallel to the main discontinuity;
\(V_p\) = seismic velocity of the longitudinal waves;
\(V_0\) = reference seismic velocity (intact rock);
\(\alpha\) = dip of the most unfavourable discontinuity;
Water = A: none — U: damp — B: wet — S: dripping — F: flowing;
RQD = degree of fracturing of the rock mass (see RQD);
\(J_v\) = number of joints per m³;
\(S\) = discontinuity spacing.

Non-unique values

If the values do not fall within a single row, take the intermediate numerical coefficient: for example, for \(J_v\) between 5 and 15, \(n_i = 3{,}5\) is assumed.

Computing the n index¶

The n index is the average of the assigned coefficients:

\[ n = \frac{1}{N_T}\sum_{i=1}^{N_T} n_i \]

where \(N_T\) is the number of properties considered (minimum 6) in the assignment of the coefficients.

Correlation with RMR¶

The authors suggest the following correlation between the n index and the corrected RMR:

\[ RMR_c = 110 - 20\,n \]

From the value of \(RMR_c\) you derive the class and quality of the rock mass, by analogy with Bieniawski's scale:

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

Characteristic rock mass parameters¶

From \(RMR_c\) you derive the strength and deformability parameters of the rock mass.

Cohesion (Sen):

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

Friction angle (Sen):

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

\[ \varphi\ [°] = 1{,}5\,RMR_c\quad \text{for } RMR_c < 20 \]

Deformation modulus (Jašarević & Kovačević):

\[ E\ [\text{MPa}] = \exp(4{,}407 + 0{,}081 \cdot RMR_c) \]

The authors consider this expression for \(E\) to be more correct than that of Serafim and Pereira (1983):

\[ E\ [\text{GPa}] = 10^{\frac{RMR_b - 10}{40}} \]

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