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9A DBT6RMINATION OP TROUGH SUBSIUh:NCE 393 material properties. A set of properties that gives a subsidence profile • n:prrMlucing IicIJ data ruison::hly well can nzu:dly be found alter scverd trials for most malels of material behavior. 9.4 DETEttMINATION OR 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 ss 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 downwanl, 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 occuro. Subsi- dence further 0•urn the center point d:ks nut reduce the diswnee between neighboring points es much and consequently the amount of wmpression lrctwcen them is less. At the point dirccUy above the edge of the opening, the distance between neighboring points remains the same alter subsiding and no strain is associated with the subsidence. Beyond this point, the disurrtce 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 Proflk Gropkkd Mef/rod In most canes, the point of mwrimum subsidence, which is directly above the txntu of the opening, and the point where subsidence diminishes to zero arc 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 criliwl width of opening, this point is dircetly above each edge; it is inside the edges (or superwitical widths and outside for subcrilical widths.