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

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9.4 DETERMINATION OF TROUGH SUBSIDENCE 295 material properties. A set of properties that gives a subsidence profile reprixlucinb lield data rwisunably well can usually be found after sevcrd trials for most models of material behavior. 9.4 DETERMINATION OF TROUGH SUBSIDENCE A trough subsidence profile for the flat seam is symmetrical with the vertical line passing through the center of the opening. This implies that the center point drops vertically downward. For other points on the original surface, both vertical and horizontal movements occur because the surface stretches as it subsides. Downward vertical movement is called subsidence; lateral or horizontal movement is called horizontal displacement or simply displacement. For example,the point immediately next to the center point drops downward, at the same time moving horizontally toward the center point (Fig. 9.4.1). The distance between these two points is therefore reduced and compression occurs. Subsi- dence further from the center point dtws not reduce the distance between neighboring points as much and consequently the amount of compression between them is less. At the point directly above the edge of the opening, the distance between neighboring points remains the same after subsiding and no strain is associated with the subsidence. Beyond this point, the distance between neighboring points increases after subsiding and results in tension.The point where no strain occurs is the point of inflection. For a critical opening this point is directly above the edge of the opening and coincides with the point of half-maximum subsidence. Since the move- ment of most of the subsiding ground has both vertical and horizontal components, the determination and/or prediction of trough subsidence includes the calculation of subsidence and displacement profiles. 9.4.1 Subsidence Profile Graphical Method In most cases, the point of maximum subsidence, which is directly above the center of the opening, and the point where subsidence diminishes to zero are generally known. A subsidence profile can be drawn rather accurately if the point of half-maximum subsidence can be located, be- cause it is the point of inflection where the curve changes from convex to concave. For the critical width of opening, this point is directly above each edge; it is inside the edges for supercritical widths and outside for subcritical widths.