Questions 8.1 -8.1 0:
rock masses
48.1 For a simple sedimentary rock mass in which the only effective
fractures are the bedding planes, the elastic modulus of the rock mass
can be found from the addition of the displacements due to both the
intact rock and the fractures, noting that the rock mass can comprise
more than one stratum, each containing bedding plane fractures with
different frequencies.
Unfractured strata. Consider firstly the case of n strata of intact rock,
each with a thickness ti and modulus of elasticity Ei. Derive an ex-
pression for the composite elastic modulus, E,, of the rock mass in a
direction normal to the strata by considering the total displacement (and
hence strain) of the total thickness of the rock mass due to the applied
stress. Write the expression in terms of Ei and ti, and assume that the
interfaces between adjacent units have no mechanical effect.
Strata with bedding planefractures. Now consider the case where each
stratum of rock contains a set of bedding plane fractures parallel to
the stratum boundaries. The fracture frequency of the set within each
stratum is unique - stratum i possesses a frequency hi; similarly, the
modulus of deformation (i.e. applied stress/displacement) within each
stratum is unique and for unit i is Edi. Extend the expression for E, to
include ti, Ei, hi and Edi.
48.2 For the unfractured and fractured stratified rock mass geometries
described in Q8.1, develop expressions for the composite shear modulus
of a rock mass, G,, using a shear stress t and the parameters ti, Gi, hi,
and Gdi.48.3 When the application of stress is not perpendicular to the fractures,
as in Q8.l and Q8.2, it is necessary to transform the stress components
in order to establish rock mass deformation moduli using the fracture
stiffnesses or compliances. This results in equations for the rock mass
modulus, E,, of the type (Wei and Hudson, 1986)