Rock Mass Rating Worked Examples: 3 Fully Solved Problems
The best way to learn the Rock Mass Rating (RMR) classification system is to work through complete examples that mirror real-world geotechnical scenarios. This page presents three fully solved RMR problems covering different rock types, engineering applications, and rock quality classes. Each example walks through the entire process from site description and field data to parameter-by-parameter rating assignment, total RMR calculation, rock class determination, and engineering interpretation with support recommendations.
These examples use the Bieniawski 1989 rating tables throughout. Use them as templates for your own calculations, and verify your results with our free online RMR calculator. For a refresher on the rating tables and classification system, refer to our RMR parameters guide and classification table page.
Example 1: Granite Tunnel — Good Rock
Site Description
A 10 m wide horseshoe-shaped railway tunnel is being driven through a Precambrian granite batholith at a depth of 120 m below ground surface. The granite is medium to coarse grained, slightly weathered to fresh, and contains three dominant joint sets. The tunnel axis trends N30E, and the site investigation has produced the following data from borehole core logging and laboratory testing of core specimens.
Field Data
| Parameter | Field Data |
|---|---|
| Rock type | Medium-grained biotite granite, slightly weathered |
| UCS (lab testing, 5 specimens) | Average 145 MPa (range 120–175 MPa) |
| RQD (average of 8 core runs) | 82% |
| Discontinuity spacing (closest set) | Average 0.8 m (Joint Set 1, subvertical) |
| Persistence | 1–3 m (most joints terminate against other joints) |
| Aperture | < 0.1 mm (tight joints with minor surface staining) |
| Roughness | Rough (undulating surfaces with visible asperities) |
| Infilling | None (clean joint surfaces) |
| Weathering of joint walls | Slightly weathered (minor discolouration, rock still hard) |
| Groundwater | Damp (moisture visible on some joints, no free water flow) |
| Dominant joint orientation | Joint Set 1: strike N60W, dip 75° NE (perpendicular to tunnel axis, dipping with drive) |
Parameter-by-Parameter Rating
Parameter 1 — UCS: The average UCS of 145 MPa falls in the 100–250 MPa range. This is a strong rock typical of slightly weathered granite. Rating = 12.
Parameter 2 — RQD: The average RQD of 82% falls in the 75–90% range, classified as "Good" quality. The granite is moderately jointed but intact core recovery is strong, with most core pieces well over 100 mm in length. Rating = 17.
Parameter 3 — Spacing: The closest discontinuity set has an average spacing of 0.8 m, falling in the 0.6–2 m range ("Wide"). This spacing produces block dimensions suitable for self-supporting behaviour in moderate-span excavations. Rating = 15.
Parameter 4 — Condition of Discontinuities:
- 4a. Persistence: 1–3 m. Most joints terminate at intersections with other sets, limiting their continuity. Sub-rating = 4.
- 4b. Aperture: < 0.1 mm. Joints are essentially closed with only minor surface staining indicating past water movement. Sub-rating = 5.
- 4c. Roughness: Rough. Undulating surfaces with clearly visible asperities that would provide strong shear resistance. Sub-rating = 5.
- 4d. Infilling: None. Joint surfaces are clean with no gouge, clay, or mineral filling. Sub-rating = 6.
- 4e. Weathering: Slightly weathered. Minor discolouration (iron staining) on joint surfaces, but the rock adjacent to the joints remains hard and structurally intact. Sub-rating = 5.
Total Condition Rating = 4 + 5 + 5 + 6 + 5 = 25.
Parameter 5 — Groundwater: Damp conditions with moisture visible on some joint surfaces but no free water or dripping. This corresponds to the "Damp" category. Rating = 10.
Basic RMR Calculation
Basic RMR = 12 + 17 + 15 + 25 + 10 = 79
Orientation Adjustment
Joint Set 1 strikes N60W with a dip of 75 degrees NE. The tunnel axis trends N30E. The strike is roughly perpendicular to the tunnel axis, and the joints dip steeply (45–90 degrees) in the direction of drive. According to Bieniawski's tunnel orientation guidelines, this is a "Very Favourable" configuration because the tunnel drives into the face of the dipping joints, which tend to be self-supporting in the crown. Orientation Adjustment = 0.
Adjusted RMR and Rock Class
Adjusted RMR = 79 + 0 = 79 → Class II (Good Rock)
Engineering Interpretation
With an adjusted RMR of 79, this granite rock mass falls near the top of Class II (Good Rock). The stand-up time is approximately 1 year for a 10 m span, providing ample time for support installation during normal construction operations. The estimated rock mass cohesion is 300–400 kPa with a friction angle of 35–45 degrees. The deformation modulus estimated from Bieniawski's correlation (Em = 2 RMR − 100) is approximately 58 GPa, indicating stiff rock mass conditions with minimal expected convergence.
Support Recommendation
For a 10 m span tunnel in Class II rock, Bieniawski 1989 recommends locally placed rock bolts (3 m long, spaced 2.5 m) in the crown where structural analysis identifies potential wedges. A 50 mm layer of shotcrete may be applied to the crown as a safety measure. No systematic pattern bolting is required. The full-face excavation method can be used with round advances of 2.5–4 m.
Example 2: Shale Highway Slope — Fair Rock
Site Description
A 25 m high highway cut slope is being designed through a sequence of Carboniferous shale and siltstone at a proposed road alignment in a mountainous region. The rock is moderately weathered with well-developed bedding planes dipping at 35 degrees towards the proposed slope face. The design requires evaluating the rock mass quality using RMR with slope-specific orientation adjustments to determine safe slope angles and stabilisation requirements.
Field Data
| Parameter | Field Data |
|---|---|
| Rock type | Dark grey carbonaceous shale with thin siltstone interbeds |
| UCS (point load testing, Is50 = 1.8 MPa, factor 22) | Estimated 40 MPa |
| RQD (from 3 boreholes, average) | 55% |
| Discontinuity spacing (bedding planes) | Average 150 mm |
| Persistence | 10–20 m (bedding planes are laterally extensive) |
| Aperture | 0.1–1 mm (slightly open bedding partings) |
| Roughness | Slightly rough (planar bedding surfaces with minor undulations) |
| Infilling | Soft filling < 5 mm (thin clay films on bedding surfaces) |
| Weathering of joint walls | Moderately weathered (brown discolouration penetrating 2–5 mm from surface) |
| Groundwater | Wet (free water seeping from bedding planes after rain events) |
| Dominant discontinuity orientation | Bedding: strike parallel to slope face, dip 35° towards slope face (daylighting on face) |
Parameter-by-Parameter Rating
Parameter 1 — UCS: The estimated UCS from point load testing is 40 MPa (Is50 = 1.8 MPa multiplied by factor 22). This falls in the 25–50 MPa range, which is typical for moderately weathered shale. Rating = 4.
Parameter 2 — RQD: The average RQD of 55% falls in the 50–75% range, classified as "Fair." This reflects the closely bedded nature of the shale, with frequent bedding partings reducing the length of intact core pieces. Rating = 13.
Parameter 3 — Spacing: The average bedding plane spacing of 150 mm falls in the 60–200 mm range ("Close"). This closely spaced bedding creates thin slabs that are prone to buckling and toppling on the slope face. Rating = 8.
Parameter 4 — Condition of Discontinuities:
- 4a. Persistence: 10–20 m. Bedding planes in shale are laterally extensive, extending across the full width of the slope exposure. Sub-rating = 1.
- 4b. Aperture: 0.1–1 mm. Bedding partings are slightly open, probably due to stress relief and weathering near the surface. Sub-rating = 4.
- 4c. Roughness: Slightly rough. Bedding surfaces are essentially planar at the large scale with only minor millimetre-scale roughness. Sub-rating = 3.
- 4d. Infilling: Soft filling < 5 mm. Thin clay films (less than 2 mm thick) coat most bedding surfaces, reducing the effective friction angle along these planes. Sub-rating = 2.
- 4e. Weathering: Moderately weathered. Brown discolouration extends 2–5 mm into the rock from the bedding surfaces, and the rock adjacent to joints is noticeably weaker than the interior. Sub-rating = 3.
Total Condition Rating = 1 + 4 + 3 + 2 + 3 = 13.
Parameter 5 — Groundwater: Free water seeps from bedding planes, particularly after rainfall events. The conditions are described as "Wet" during the rainy season, which is the design condition. Rating = 7.
Basic RMR Calculation
Basic RMR = 4 + 13 + 8 + 13 + 7 = 45
Orientation Adjustment (Slopes)
The bedding planes strike parallel to the proposed slope face and dip at 35 degrees towards the slope face. This means the bedding planes daylight on the slope face, creating a direct kinematic condition for plane sliding failure. According to the Bieniawski 1989 slope orientation guidelines, bedding planes dipping out of the slope face at angles between 20 and 45 degrees with strike subparallel to the slope constitute an "Unfavourable" orientation. Orientation Adjustment = -50.
Adjusted RMR and Rock Class
Adjusted RMR = 45 + (-50) = -5
The adjusted RMR is negative, which is mathematically possible when severe slope orientation adjustments are applied. For classification purposes, any adjusted RMR below 21 is assigned to Class V (Very Poor Rock). Rock Class: V (Very Poor Rock).
Engineering Interpretation
Although the basic RMR of 45 indicates fair rock mass quality in general terms, the critically unfavourable orientation of the bedding planes relative to the slope face reduces the effective rock mass quality to Class V for this specific slope application. This result strongly indicates that a conventional steep cut slope is not feasible without significant intervention. The daylighting bedding planes with clay infilling create a high risk of large-scale planar sliding failure. The estimated rock mass cohesion for Class V is less than 100 kPa, and the friction angle is less than 15 degrees, which are insufficient to maintain stability on the 35-degree bedding surface, particularly under wet conditions when pore pressures further reduce the effective shear resistance.
Support Recommendation
The slope design must address the kinematic sliding mechanism directly. Options include: flattening the overall slope angle to below the bedding dip angle (less than 35 degrees) with adequate factor of safety; installing fully grouted passive rock anchors or tensioned cable anchors through the bedding planes to provide restraining forces; constructing horizontal drainage boreholes to depressurise the bedding planes and reduce pore water pressures; building a buttress fill at the toe of the slope to increase the resisting forces; or a combination of these measures. A detailed limit equilibrium analysis incorporating the measured bedding plane shear strength and groundwater pressures is essential for final design.
Example 3: Limestone Dam Foundation — Poor Rock
Site Description
A concrete gravity dam with a maximum height of 45 m is proposed on a Devonian limestone foundation. Site investigation boreholes and an exploration adit have revealed that the limestone is karstic in places with solution-widened joints, clay-filled cavities, and variable weathering. The foundation assessment requires RMR classification to estimate the rock mass deformation modulus and determine whether the foundation can support the dam loads without excessive settlement or sliding.
Field Data
| Parameter | Field Data |
|---|---|
| Rock type | Grey crystalline limestone, moderately to highly weathered |
| UCS (lab testing, 6 specimens) | Average 35 MPa (range 18–55 MPa, high variability) |
| RQD (average of 12 core runs) | 38% |
| Discontinuity spacing (most closely spaced set) | Average 250 mm (subvertical joint set through bedding) |
| Persistence | 3–10 m (joints extend through multiple beds) |
| Aperture | 1–5 mm (solution widened joints with irregular openings) |
| Roughness | Slightly rough (solution-smoothed surfaces with minor pitting) |
| Infilling | Soft filling > 5 mm (red-brown clay fills solution cavities and wider joints) |
| Weathering of joint walls | Highly weathered (significant dissolution, pitted and etched surfaces) |
| Groundwater | Dripping (active water seepage from multiple joints in adit, estimated 50 L/min per 10 m) |
| Dominant joint orientation | Subvertical joints striking N-S, dam axis E-W; bedding near horizontal; joints dip steeply beneath the dam footprint |
Parameter-by-Parameter Rating
Parameter 1 — UCS: The average UCS of 35 MPa falls in the 25–50 MPa range. The high variability (18–55 MPa) reflects the heterogeneous weathering typical of karstic limestone, where some zones are relatively fresh while others are significantly weakened by dissolution. Rating = 4.
Parameter 2 — RQD: The average RQD of 38% falls in the 25–50% range, classified as "Poor." The low RQD reflects both the frequency of natural fractures and the presence of dissolved zones along bedding planes where the core has broken into short pieces. Rating = 8.
Parameter 3 — Spacing: The most closely spaced discontinuity set has an average spacing of 250 mm, falling in the 200–600 mm range ("Moderate"). While the bedding planes are more widely spaced (0.5–1 m), the subvertical joint set with 250 mm average spacing controls the minimum block dimension. Rating = 10.
Parameter 4 — Condition of Discontinuities:
- 4a. Persistence: 3–10 m. The subvertical joints extend through multiple limestone beds and are traceable for several metres in the exploration adit. Sub-rating = 2.
- 4b. Aperture: 1–5 mm. Solution widening has opened many joints to between 1 and 5 mm, with some localised wider openings at joint intersections. Sub-rating = 1.
- 4c. Roughness: Slightly rough. The limestone joint surfaces have been smoothed by solution but retain minor pitting and millimetre-scale roughness that provides some frictional resistance. Sub-rating = 3.
- 4d. Infilling: Soft filling > 5 mm. Red-brown residual clay from limestone dissolution fills many of the wider joints and solution cavities. In places the clay thickness exceeds 10–20 mm, completely separating the rock walls. Sub-rating = 0.
- 4e. Weathering: Highly weathered. The limestone adjacent to joints shows significant dissolution with pitted, etched, and weakened surfaces. Solution channels and enlarged vugs are visible along many joint surfaces. Sub-rating = 1.
Total Condition Rating = 2 + 1 + 3 + 0 + 1 = 7.
Parameter 5 — Groundwater: Active water seepage from multiple joints in the exploration adit with an estimated inflow of 50 L/min per 10 m section. This falls in the 25–125 L/min range ("Dripping"). The karstic limestone has significant secondary permeability through the solution-widened joint network. Rating = 4.
Basic RMR Calculation
Basic RMR = 4 + 8 + 10 + 7 + 4 = 33
Orientation Adjustment (Foundations)
The dominant subvertical joints strike N-S while the dam axis is oriented E-W, meaning the joints are perpendicular to the dam axis. The bedding planes are near horizontal. For a gravity dam, the critical sliding mechanism involves horizontal thrust at the base of the dam. Subvertical joints perpendicular to the dam axis do not create an unfavourable sliding geometry; however, the near-horizontal bedding planes with clay infilling could act as a sliding surface under the dam's horizontal water thrust. This orientation is assessed as "Fair" for foundation applications. Orientation Adjustment = -7.
Adjusted RMR and Rock Class
Adjusted RMR = 33 + (-7) = 26 → Class IV (Poor Rock)
Engineering Interpretation
The adjusted RMR of 26 places this karstic limestone foundation in Class IV (Poor Rock). The estimated rock mass cohesion is 100–200 kPa with a friction angle of 15–25 degrees. Using the Serafim and Pereira deformation modulus correlation for RMR values below 50, Em = 10^((RMR-10)/40) = 10^((26-10)/40) = 10^0.4 = approximately 2.5 GPa. This relatively low deformation modulus indicates that the foundation will undergo significant deformation under the dam loading, and settlement analysis is essential. The karstic features with clay-filled solution cavities are a major concern for both bearing capacity and seepage beneath the dam.
Support Recommendation
The poor foundation conditions require comprehensive treatment before dam construction can proceed. Recommended measures include: consolidation grouting with cement-based grout to fill solution cavities and improve the rock mass modulus and strength; a multi-row grout curtain extending to competent rock beneath the dam to reduce seepage and uplift pressures; dental concrete treatment to clean out and backfill surface dissolution features, clay-filled pockets, and any accessible solution cavities within the foundation footprint; a drainage gallery within the dam body with drilled drain holes into the foundation to control uplift pressures; and instrumented monitoring including piezometers, extensometers, and settlement gauges throughout construction and the initial impoundment period. A comprehensive grouting programme may improve the effective RMR by 5–10 points by reducing groundwater pressures and improving joint conditions.
Summary Comparison Table
The following table provides a side-by-side comparison of all three worked examples, highlighting how the same RMR framework produces different outcomes based on rock type, geological conditions, and engineering application.
| Parameter | Example 1: Granite Tunnel | Example 2: Shale Slope | Example 3: Limestone Foundation |
|---|---|---|---|
| Rock Type | Biotite granite | Carbonaceous shale | Karstic limestone |
| Application | Railway tunnel | Highway cut slope | Gravity dam foundation |
| P1: UCS Rating | 12 | 4 | 4 |
| P2: RQD Rating | 17 | 13 | 8 |
| P3: Spacing Rating | 15 | 8 | 10 |
| P4: Condition Rating | 25 | 13 | 7 |
| P5: Groundwater Rating | 10 | 7 | 4 |
| Basic RMR | 79 | 45 | 33 |
| Orientation Adjustment | 0 (very favourable) | -50 (unfavourable) | -7 (fair) |
| Adjusted RMR | 79 | -5 | 26 |
| Rock Class | II — Good | V — Very Poor | IV — Poor |
| Cohesion (kPa) | 300–400 | < 100 | 100–200 |
| Friction Angle (°) | 35–45 | < 15 | 15–25 |
| Em (GPa) | ~58 | N/A (slope) | ~2.5 |
Key Lessons from These Examples
- Orientation adjustment can dominate the result: Example 2 demonstrates how a rock mass with a fair basic RMR (45) can be classified as Very Poor (Class V) for slope applications when the discontinuity orientation is critically unfavourable. The slope adjustment of -50 reduced the rating by more than the entire basic score. Always apply the correct application-specific adjustment table.
- Discontinuity condition is the most influential basic parameter: Compare the condition ratings across the three examples: 25 for the granite (tight, rough, clean joints), 13 for the shale (persistent bedding with clay films), and 7 for the limestone (solution-widened, clay-filled joints). The 18-point difference in condition rating between granite and limestone accounts for the largest portion of their 46-point difference in basic RMR.
- Rock type alone does not determine RMR: Limestone can range from Class I (massive, reefal limestone with no karst) to Class V (heavily karstified with clay-filled solution features). Similarly, granite can range from Class I (fresh, massive) to Class IV (deeply weathered saprolitic granite). The specific geological conditions at the site, not the rock name, determine the classification.
- Multiple parameters often correlate: In the shale example, several adverse conditions occur together: low UCS, low RQD, close spacing, poor discontinuity conditions, and wet groundwater. This correlation is geologically logical because closely bedded, weathered shale naturally exhibits these conditions simultaneously. Recognise that one adverse geological feature often produces low ratings across multiple parameters.
- Engineering interpretation requires more than the RMR number: The adjusted RMR and rock class provide a starting point, but engineering recommendations must consider the specific failure mechanisms relevant to each application. For the tunnel, the concern is wedge stability. For the slope, it is planar sliding along bedding. For the foundation, it is bearing capacity, settlement, and seepage. The same rock class can require very different engineering responses depending on the application.
- Deformation modulus estimation depends on the RMR range: For RMR values above 50, use Em = 2 RMR - 100 (Bieniawski). For RMR values below 50, use Em = 10^((RMR-10)/40) (Serafim and Pereira). Using the wrong correlation will produce significant errors in deformation modulus estimation and consequently in settlement predictions.
Frequently Asked Questions
For tunnels, the orientation adjustment depends on the geometric relationship between the dominant discontinuity set's strike and dip and the tunnel axis direction. Bieniawski 1989 provides qualitative guidelines: driving perpendicular to the joint strike with joints dipping 45–90 degrees in the direction of drive is "Very Favourable" (adjustment 0). Driving perpendicular to strike with dip 20–45 degrees in the direction of drive is "Favourable" (adjustment -2). Driving parallel to strike regardless of dip angle is generally "Fair" to "Very Unfavourable" (adjustment -5 to -12). A dip of 0–20 degrees regardless of strike is "Fair" (adjustment -5). For complex geometries with multiple joint sets, assess each set separately and use the most unfavourable adjustment, or perform a detailed kinematic wedge analysis to determine the critical orientation.
The slope orientation adjustments in the Bieniawski 1989 system are dramatically more severe than tunnel adjustments because slope stability is inherently more sensitive to discontinuity orientation. For slopes, unfavourable joint orientations can directly create kinematic conditions for plane sliding, wedge failure, or toppling, with the full gravitational weight of the rock mass above the failure surface driving the instability. Tunnels benefit from the confinement provided by the surrounding rock mass, which resists block displacement even when joints are unfavourably oriented. The maximum slope adjustment is -60 compared to only -12 for tunnels, reflecting this fundamental difference in structural mechanics. This is why even a "fair" basic RMR can produce a Class V result when the slope orientation is critically adverse.
Yes, these examples demonstrate the correct procedure and format for RMR calculations and can serve as templates. Follow the same structure for each assessment: document the site conditions and all available field data, assign ratings for each of the six parameters with explicit justification referencing the Bieniawski 1989 rating tables, sum the first five ratings to obtain the basic RMR, apply the appropriate orientation adjustment for your specific application type (tunnel, slope, or foundation), determine the rock class, and provide engineering interpretation and recommendations based on the class. Always substitute your own measured field data rather than using assumed or estimated values. You can cross-check your manual calculation results using our free online RMR calculator, which applies the same Bieniawski 1989 rating tables and produces a downloadable PDF summary.