Rock mass characterization

A laboratory specimen of rock is a small cylinder cut from between the fractures. The rock that engineers actually deal with in a slope, a tunnel or a foundation is a rock mass: intact blocks of rock separated by joints, bedding planes, faults, foliation and other discontinuities. The rock mass is almost always weaker, more deformable and more permeable than the intact rock, often by a large factor, because its behaviour is controlled by the discontinuities. Rock mass characterization is the systematic description of those discontinuities and the rock between them, leading to classification systems that engineers use for preliminary design of slopes, tunnels and foundations.

Types of discontinuities

Discontinuity is the general term for any break in the rock with low or no tensile strength. The main types are:

• Joints: fractures with no visible movement parallel to their surfaces. They form from cooling, unloading as overlying rock erodes, folding and regional stresses, and they usually occur in sets of roughly parallel fractures. Two or three sets plus random joints are common, cutting the rock into blocks.
• Bedding planes: surfaces between sedimentary layers, often persistent over large areas and sometimes coated or filled with clay.
• Foliation and cleavage: planes of weakness in metamorphic rocks formed by aligned minerals.
• Faults: fractures along which the rock on either side has moved. Faults may contain crushed rock (breccia) and finely ground clay-like gouge, and the rock next to them is often heavily fractured. Fault zones are weak, may carry or block groundwater, and are a common source of problems in tunnels and cuts.
• Shear zones and sheared clay seams: zones of distributed movement, including bedding-plane shears in shale sequences, whose strength may have fallen to a low residual value.

Describing discontinuities

Each discontinuity set is described by a standard list of properties, because each property affects the strength, deformability or permeability of the rock mass.

• Orientation: the dip and dip direction of the discontinuity plane, measured with a compass-clinometer. Orientation relative to the slope face or tunnel axis is often the single most important factor in stability.
• Spacing: the perpendicular distance between adjacent discontinuities of one set. Closely spaced joints give small blocks and a weaker, more permeable mass.
• Persistence: how far a discontinuity extends. A highly persistent joint can form a complete sliding surface; a short one must break intact rock to fail.
• Roughness and waviness: rough, undulating surfaces must ride up over asperities to slide, which increases shear strength; smooth, planar surfaces offer little resistance beyond the basic friction of the rock.
• Aperture and infilling: the width of the opening and the material in it. Open joints transmit water; joints filled with soft clay can be very weak, especially if the filling is thicker than the roughness amplitude so that rock walls never touch.
• Wall strength and weathering: weathered joint walls are weaker than fresh rock.
• Seepage: whether the discontinuity is dry, damp, wet, dripping or flowing. Water pressure in joints reduces the normal stress and therefore the frictional resistance.

Rock quality designation (RQD)

Rock quality designation, introduced by Deere in the 1960s, is a simple index of fracturing measured on drill core. RQD is the sum of the lengths of intact core pieces that are at least 100 mm long, divided by the total length of the core run, expressed as a percentage. Only pieces of sound rock are counted, and breaks caused by drilling or handling should be ignored, so the logger must judge whether each break is natural. RQD should be measured on core of about 50 mm diameter or larger, and logged immediately after drilling, before the core deteriorates.

RQD is quick and universal, which is why it appears on almost every rock core log. It also has limitations. It ignores joint orientation, condition and infilling; it depends on the direction of the borehole relative to the joint sets, so a vertical hole parallel to vertical joints can give a misleadingly high value; and the 100 mm threshold means that a rock with joints at 90 mm spacing and one at 110 mm spacing can give very different RQD values for nearly the same rock mass. RQD is best used as one input to a fuller classification, not as a stand-alone design parameter.

Estimating RQD without core

Where only exposures are available, such as in a cut face or tunnel wall, RQD can be estimated from the number of joints per cubic metre, called the volumetric joint count \(J_v\). A widely used approximation is \(\text{RQD} \approx 115 - 3.3 J_v\), limited to between 0 and 100 per cent. Another approach uses the average joint spacing along a scanline: with joints spaced randomly at an average frequency \(\lambda\) per metre, the expected RQD is \(100 e^{-0.1\lambda}(0.1\lambda + 1)\). These relations give quick estimates for preliminary assessment, but they are approximate.

# RQD from core pieces and from joint counts
import math

run_length = 1500  # mm
pieces = [220, 45, 130, 60, 310, 90, 35, 180, 115, 70, 150]
long_pieces = [p for p in pieces if p >= 100]
rqd = 100 * sum(long_pieces) / run_length
classes = [(25, "very poor"), (50, "poor"), (75, "fair"), (90, "good"), (101, "excellent")]
quality = next(name for limit, name in classes if rqd < limit)
print(f"RQD from core: {rqd:.1f}% ({quality})")

# From a volumetric joint count in a cut face
for jv in (5, 10, 20, 30):
    est = max(0, min(100, 115 - 3.3 * jv))
    print(f"Jv = {jv:2d} joints/m3 -> RQD ~ {est:.0f}%")

# From scanline joint frequency (Priest and Hudson form)
for lam in (2, 5, 10, 20):
    est = 100 * math.exp(-0.1 * lam) * (0.1 * lam + 1)
    print(f"{lam:2d} joints per m along scanline -> RQD ~ {est:.0f}%")

RQD from core: 73.7% (fair)
Jv =  5 joints/m3 -> RQD ~ 98%
Jv = 10 joints/m3 -> RQD ~ 82%
Jv = 20 joints/m3 -> RQD ~ 49%
Jv = 30 joints/m3 -> RQD ~ 16%
 2 joints per m along scanline -> RQD ~ 98%
 5 joints per m along scanline -> RQD ~ 91%
10 joints per m along scanline -> RQD ~ 74%
20 joints per m along scanline -> RQD ~ 41%

The Rock Mass Rating (RMR) system

Bieniawski's Rock Mass Rating, developed in the 1970s and revised in 1989, combines several properties into a single number from 0 to 100. Each of five parameters receives a rating, the ratings are summed, and an adjustment is made for discontinuity orientation relative to the structure. The parameters and the approximate range of their ratings in the 1989 version are:

The RMR value has been correlated with many design quantities: the stand-up time of an unsupported tunnel span, tunnel support recommendations, approximate rock mass cohesion and friction angle, and the rock mass deformation modulus. One widely quoted relation for the deformation modulus in gigapascals is \(E_m = 10^{(RMR - 10)/40}\), which gives about 10 GPa for RMR 50 and about 32 GPa for RMR 70. Correlations like this are approximate and are most useful in feasibility studies and for comparing sites.

Other systems are also widely used. The Q system of Barton and colleagues, developed in Norway, combines RQD, the number of joint sets, joint roughness and alteration, water and stress conditions into a single value on a logarithmic scale, and is common in tunnelling. The Geological Strength Index (GSI), associated with Hoek, is estimated from charts of rock structure and surface condition and feeds directly into the Hoek–Brown strength criterion used in numerical analysis. Experienced practitioners often calculate more than one index and check that they tell a consistent story.

The example shows why orientation matters so much in rock slopes. The same rock mass that would stand steeply if the joints dipped into the slope may need a flatter angle, bolting or a catchment ditch if the joints dip out of it.

Kinematic analysis of rock slopes

Before calculating a factor of safety, an engineer checks whether failure is kinematically possible: whether the geometry of the discontinuities and the slope face lets blocks move. Three classic mechanisms are checked. Plane failure needs a discontinuity that strikes roughly parallel to the face, dips out of it less steeply than the face so it daylights, and dips more steeply than its friction angle. Wedge failure occurs when two discontinuities intersect along a line that plunges out of the face more steeply than the friction angle. Toppling occurs when steep discontinuities dip into the slope and divide the rock into slabs or columns that rotate outward. These checks are done graphically on stereonets, which plot the orientations of planes as points or great circles, or with software.

Provincial highway rock cuts in British Columbia are designed and maintained with these principles, and the province manages rockfall hazard along its mountain highways through rock scaling, bolting, mesh, catchment ditches and fences. Rockfall is one of the most frequent geohazards affecting the highway network.