PERMFILE41761

• Permit No: M1999002
• IBM Index Class Name: Permit File
• Doc Date: 6/18/1999
• Doc Name: OBJECTORS EXHIBITS
• Media Type: D
• Archive: No

Analytical Methods
along bedding planes are also applicable (or slippage along
other discontinuities.
DEVELOPi<1ENT AND PREL]iVIINARY
EVALUATION OF METHODS FOR
PREDICTING SUBSIDENCE
In this section, analytical methods for predicting sub-
sidence which include the capability of accounting for the
inability of rock to withstand tensile stresses and the possi-
bility of slippage along bedding planes are described. Ex-
amples were analyzed to determine the significance of
these phenomzna on the prediction of subsidence.
"No tension" analysis
When numerous cracks and fissurzs are present in a
rock mass, it has bzen assumed that the rock is incapable
of withstanding tensile stresses. A procedure for modell-
ingthis nonlinear behavior has been presented by Zienkie-
wicz, et al. (1968). This method, called "no tension" or
"stress transfer" analysis, consists of five essential sups:
(a) Assign initial stresses to the rock mass, and cal-
culate boundary loads rzquired on the cavity' (ace
to simulate the creation of the opening.
(b) Analyze the problem as an elastic case. Add the
induced changes in stress to the initial stresses
and compute the principal stresses.
(c) Determine elements in which tension exists. As
thz material is assumed incapable of sustaining
tensions, the calculated tensile principal stresses
are eliminated without permitting any point in
[he structure to displace. In order to maintain
equilibrium, external equivalent nodal point
forces are calculated and temporarily applied to
the structure.
(d) The elastic analysis is repeated to remocz the
balancing nods! point forces and the check for
tensiiz stresses is repeated.
(e) If, at thz end of stags (d). [ht tznsih principal
stresses are still in zxistenci, steps (c) and (d)art
repeated until all tensile stresses are reduced to
an acceptable level.
In Step (c), when the linear elastic solution indicates that
the rock is subjected to [ensile stresses greatzr than the
tensile strength, the rock is assumed to be fractured and
incapable oftransferring stresses between two orthogonal
directions. To include this effect, a correction has to be
made on the stress before the stress transfer process is
performed. In the case where both principal tensile
stresses v,' and oy' are to be transferred, the "correctzd"
stresses are given by

• 105

Slippage along bedding planes
Gadding plants are likely to be present in szdimentary
rocks in which thz majority of the solution and coal min-
ing is carried out, Shear strength along bidding planes is
considered to be weaker than that of intact rocks. As the
shear stress overcomes thz shear strength along these
planes dui to chanees in stress induced by thz creation of
underground cavities, slippage may occur along these rock
beds. This type of behavior may causz changes in the
subsidence profile calculated by the elastic analysis of the
underground cavity assuming the rock to bz a continuum.
The two major di.bcultizs of incorporating this aspect of
rock behavior into an analytical modzl for predicting field
trzhavior are (1) thz detzrntination of thz number and
location of thz bedding planes, and (2) chi representation
of thz behavior of [hzse bedding plants, i.e., assigning the
stress-strain behavior and the strength of these weak
planes. The numbzr and location of the weak planes may
be approximately estimated from 3-D velocity logs [akin
in the mined areas. It is, however, difficult to determine
the stress-strain behavior of these bedding plants. As a
first step to study the effects of the presettcz of the weak
beddine planes in the rock mass above the cavity on thz
subsidence profile, it is assumed in this study that [hest
bedding plants werz eery weak in resisting shear stress
along the bedding planes and would yizld upon creation
of an opening.
Illustrative problem
A rock profile with the sizz and I~xation of the cavity
shown in Figure 4 was analyzed [o studs the effects of
no-tension rock characteristics and the presence of bzd-
ding plants on the subsidence profile. Thrze weak bedding
planes were assumed, and their locations art shown in
Figure -i. Thzsz weak plants were assiened to a very low
shear modulus and. therefore, oRzrzd very li[tlz rzsistance
to movzmzn[ along the plant. Thz result of the analysis
indicates that the vertical subsidence at the cznterlini of
the cavity is thrze times as large as the calculated without
[he presence of thz bidding plants. Furthermore, thz
shape of the subsidence profile indicates a greater localiza-
tion of [he subsidence to an aria about the cavity than for
the elastic continuum case. This shapz is in general agree-
ment with that observed in the field. The subsidence pro-
file obtained from the analysis is presented in Figure 5.
The results of the analysis indicate that the presence of
weak bidding plants above the cavity has a major effect
on thz magnitude and distribution of the subsidence. It
may be noted that a "no-tension"' analysis, i.z., assuming
that the rock mass in its natural state is incapable of
sustaining tensile stresses, provides a slight increase in
subsidence.