Rock Engineering Basics by pyz17071

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									              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
    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)
    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)
         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
   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)]
                   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.
      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)
  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).
         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
   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”
   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
   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
      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.
                                                   N



                              ++ +   +                        + +
                              ++ ++                           +         +
                                 +  +                           +


                                               + +
                 W                                                                E
                           + ++                 +
                          + +
                           + +

                                           +                      + +
                                               +                  ++



                                                   S

                     Example of low er-hemis. stereonet plot of fracture poles.
      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.
     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.
  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.
  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).
  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).
                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.
        Residuals
                             N4
Shear
Load
                                  Normal
                                  Loads
                             N3



                          N2
                        N1

           Shear Displacement
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.
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
Overall Shear Strength for Highly Fractured
   Rock Masses
1.   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.
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.

								
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