1981-11-13_PERMIT FILE - C1981013 ‎(40)‎

• Permit No: C1981013
• IBM Index Class Name: PERMIT FILE
• Doc Date: 11/13/1981
• Doc Name: Subsidence Control Plan
• Section_Exhibit Name: Volume 3 Exhibit 21
• Media Type: D
• Archive: No

304 SURFACE SUBSIDENCE
-O.Gh-0.4-0.4 -0.2 O 0.2 0.4 0.6 0.1111%
1 x
28T�
smax ON
h 1
1
1
i
a d.l '
Fig. 9.4.6 Subsidence profile function(20).
where B is the critical radius or one-half the critical width, S... is the
maximum possible subsidence over the center of the opening, x is the
horizontal distance from the point of half-maximum subsidence, and d is
the distance between the point of half-maximum subsidence and the edge
of opening. Several profile functions have been developed for various coal
fields in the world (20). One of them, based on model and theoretical
investigations, is
S = ISM..J I - tanh(2x/B)1 (9.4.2)
The unknown parameter B can be back-calculated from the measured
subsidence,S,by solving for B in Eq.9.4.2,differentiating with respect to
x, and setting x - 0,
B a S-01 (9.4.3)
S. `
where S'mp„ is the maximum slope observed in the field. It must be noted
that in Eq. 9.4.2,d is assumed to be zero; that is, the point of inflection is
directly above the edge of the opening.
For the supercriticul case, Eq. 9.4.2 still holds,except that S... occurs
over an area in the center of the subsidence trough, rather than at a point.
However,for the subcritical width, the equation becomes more involved.
One method employs the superposition of two critical width profiles. In
Fig. 9.4.7 the excavation A,A, has a subcritical width w. Its induced
surface subsidence profile can be determined by first assuming a critical
width opening with edge at A, and extending beyond A,,, the profile
function of which S, is defined by Eq. 9.4.2. Similarly, a critical width
opening with edge at A, and extending beyond A, is an inverse of the
previous one, the profile function of which is Ss as defined also by Eq.
9.4.2. The resulting subcritical profile is
R
S„ [tanh 2(x B+ ►v) - tanh x (9.4.4)