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Geologic Info for Rock Slope Engineering . 1. Geologic mapping of formations and units needed to generate surface-geology maps and cross-sections

Rock Engineering Basics

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**1. **Rock Engineering Basics Rock: compact, indurated natural material (composed of one or more minerals) that requires drilling, blasting, wedging, or other “brute force” to excavate.
Rock Substance: solid rock material which does not contain obvious structural features (discontinuities) and which usually can be sampled and tested in the lab; known as “intact rock”.
Rock Mass: a complex system of natural rock material comprised of blocks of intact rock and structural features (discontinuities) that allow for interactions among the blocks; too large and complex to sample and test in the lab

**3. **Geologic Info for Rock Slope Engineering 1. Geologic mapping of formations and units needed to
generate surface-geology maps and cross-sections
2. Site topography and proposed cut-slope geometries (best to display cross-sections 1:1 with no vertical exaggeration)

**5. **Geologic Info for Rock Slope Engineering 1. Geologic mapping of formations and units needed to
generate surface-geology maps and cross-sections
2. Site topography and proposed cut-slope geometries (best to display cross-sections 1:1 with no vertical exaggeration)
3. Relevant rock-strength data for the rock substance
4. Engineering properties of rock discontinuities, including
orientation, geometry, shear strength
5. Groundwater regime (water table, piez. head distributions)

**8. **Electronic Dip Meter and Vibrating Wire PiezometerElectronic Dip Meter and Vibrating Wire Piezometer

**9. **Uniaxial Compressive Strength
A cylinder of rock taken from drill-core is cut square on the ends, then the ends are ground smooth, and the specimen loaded to failure in a testing machine. The length-to-diameter ratio (L/d) typically ranges between 2 and 3.
UCS = Pf / A (stress units of psi, psf, MPa, tsm)
where: Pf = ultimate failure load (at rupture);
A = cross-sectional area of the cylindrical specimen
= pd2/4

**10. **Reporting of UCS Standardized Results
Empirical corrections of the tested value of UCS to “standardized” L:d values are given below:
For L:d of 2:1
UCS2:1 = UCS / [0.88 + 0.24(d/L)]
For L:d of 1:1
UCS1:1 = UCS / [0.778 + 0.222(d/L)]

**11. **Point Load Index The point load test is conducted on a piece of drill core (with ragged ends) with L/d > 1.5 whereby the core piece is loaded perpendicular to the core axis between cone-shaped platens until failure occurs and the core is “split”. The core diameter and instrument gage pressure at failure are recorded. The Point Load Index then is given by:
PtL = Pg(Ar) / d2
where: d= core diameter, Pg = instrument gage pressure at specimen failure, and Ar = cross-sectional area of instrument loading ram.

**14. **Using PtL to Estimate UCS
UCS ? PtL(14 + 0.175d)
for d measured in units of mm
For typical core diameters (47 – 61 mm), use the
approximation:
UCS ? 23(PtL)

**15. **Estimating UCS Using a Schmidt Hammer
A Schmidt Type-L rebound hammer can be used to approximate the UCS. A reasonable estimate of the rock unit weight also is needed.
Rebound measurements often are quite variable, so the field investigation should include at least 10 measurements at a given sampling site (for averaging purposes).

**16. **Brazilian Disk Tension Testing
A small disk of rock core with known diameter (d) and thickness (h) is loaded along its diameter to induce an apparent tensile stress field and cause the disk to rupture. The tensile strength then is given by:
T = 2(Pf) / (pdh)
where Pf = failure load at which the disk ruptured
A general rule-of-thumb: (10 x T) ? UCS

**17. **Mapping & Display of Discontinuity Data Field mapping methods to obtain information on discontinuity orientations, spacing, length, roughness, etc.:
Scanline mapping – detailed mapping of individual discontin-uities that intersect a designated mapping line or linear “window”

**20. **Mapping & Display of Discontinuity Data Field mapping methods to obtain information on discontinuity orientations, spacing, length, roughness, etc.:
Scanline mapping – detailed mapping of individual discontin-uities that intersect a designated mapping line or linear “window”
Fracture-Set mapping (Cell mapping) – mapping of fracture-set properties observed within user-defined cells on the rock exposure

**21. **Mapping & Display of Discontinuity Data Field mapping methods to obtain information on discontinuity orientations, spacing, length, roughness, etc.:
Scanline mapping – detailed mapping of individual discontin-uities that intersect a designated mapping line or linear “window”
Fracture-Set mapping (Cell mapping) – mapping of fracture-set properties observed within user-defined cells on the rock exposure
Oriented core logging – mapping of oriented drill core to obtain orientations, fracture spacings, roughness

**27. **Display of Discontinuity Orientations The orientations of planar discontinuities are best displayed and evaluated by plotting their poles (normals) on lower-hemisphere stereographic projections (known as “stereonet plots”). A cluster of such poles then represents a fracture set having “planes” in similar orientations.

**28. **Display of Discontinuity Orientations
Poles near the center of the stereonet are for shallow-dipping (fairly flat) fractures, and poles near the outer edge of the stereonet are for steeply dipping fractures.
Thus, a cluster of fracture poles in the upper-right portion of the lower-hemisphere stereonet plot indicates a fracture set with planes dipping toward the southwest.

**29. **Shear Strength Modeling for Discontinuities
1. Linear Mohr-Coulomb failure envelope with y-intercept (known as cohesion) and slope (known as the coefficient of friction, tanf):
t = c + sn’ tanf
where: t = shear strength along the discontinuity;
sn’ = effective normal stress acting on the discontinuity;
c = cohesion (generally equal to zero or a very small
value for clean rock fractures);
f = friction angle.

**30. **Shear Strength Modeling for Discontinuities
2. General nonlinear, power-curve model:
t = c + a(sn’ )b
where: t = shear strength along the discontinuity;
sn’ = effective normal stress acting on the discontinuity;
a, b, c = power-curve parameters.
Note that when b = 1.0, this model reduces to a linear model with the parameter a = tanf. Therefore, this general model also covers the special case of the linear model.

**31. **Shear Strength Modeling for Discontinuities
3. JRC model of shear strength (nonlinear model):
t = sn’ · tan[(JRC)log10(JCS/sn’) + fb]
where: t = shear strength along the discontinuity;
sn’ = effective normal stress acting on the discontinuity;
JRC = joint roughness coefficient (typ. values: 2 to 6);
JCS = joint-wall compressive strength (UCS of intact rock);
fb = base friction angle (i.e., for saw-cut, smooth surfaces).

**32. **Shear Strength Modeling for Discontinuities
4. Back-analysis of a rock-slope failure with well-defined geometry and groundwater conditions:
We set the FOS equal to 1.0, and back-calculate the corresponding combinations of f and waviness that seem appropriate (linear shear-strength model with zero cohesion). We can follow the same approach with the JRC model of shear strength (select appropriate values of fb, JCS, and JRC that give FOS = 1.0).

**33. **Shear Strength Analysis of Laboratory Direct-Shear Data
During the laboratory direct-shear test of a natural
rock joint, data are collected to record the shear load
as a function of the applied normal load and the shear
displacement. The graph of shear load vs. shear
displacement for each applied normal load provides
the basis for describing the shear strength of the
specimen.

**35. ** Laboratory Direct-Shear Data
The contact area in shear when the specimen attains either the
peak shear load or the residual shear load is needed to
calculate the corresponding normal stress and shear stress
(strength) for any particular graph trace (trial).
For circular or rectangular specimens, this contact area can be
calculated directly, once the pertinent shear displacement is
identified. For irregularly shaped specimens, a reference table
must be constructed that displays the contact area as a
function of shear displacement.

**36. ** Laboratory Direct-Shear Data
A least-squares regression program (such as Taussm
or the Mathcad sheet entitled “TauRegr”) then
provides the linear and power models for shear
strength, as shown in the typical plots of shear
strength on the overheads

**37. ** Overall Shear Strength for Highly Fractured
Rock Masses
Exponential RQD Method
Required input:
Average RQD (Rock Quality Designation) of the
rock mass (%)
Estimated c (psi) and f for intact rock
Estimated c (psi) and f for natural fractures
Intermediate factors (weights):
A = .475exp(.007 x RQD) B = .188exp(.013 x RQD)
Then:
cm = cr (B2) + cf (1-B2) in psi
fm = fr (A2) + ff (1-A2) in deg.

**38. **
2. Hoek-Brown Rock Mass Strength Model
Required input:
mi - Hoek-Brown constant (a material constant
ranging from about 4 to 33)
GSI - Geological Strength Index (see handout)
Ci - uniaxial compressive strength of intact rock
D - estimated rock-mass disturbance factor (0 for
insitu rock or for carefully designed blasting
programs; 1 for poor blasting practices with
considerable overbreak)
See Mathcad calculation sheet for examples.