The character of the subsidence

The character of the subsidence, its extent, and the time when it will develop over an underground opening seems to depend upon many factors, the most important of which are the size and shape of the opening and its depth below the surface; the number and attitude of incompetent beds, bedding planes, faults, and joints; the method of mining and the rate at which mining operations advance; and the com-position, physical character, and shearing strength of the material.

In general, the character and extent of subsidence will vary with the size of the underground opening, diminishing progressively from large open stopes through small or filled stopes to undisturbed formation. When the opening lies relatively close to the surface, the overlying rock may collapse soon after the removal of the ore, although the strength of the rock and the size of the opening are modifying factors. If the opening is located a greater distance below the surface, an appreciable period of time may elapse between the mining of the ore and the first evidence of surface subsidence. During this period the rock slabs off and caves from the roof of the stope, developing an arch which gradually migrates upward toward the surface. Two tons of broken rock in the stopes occupy about the same space or volume as three tons of rock in place. Thus, if the opening is rather small, the increase in vol¬ume of the broken rock may be sufficient to fill the developing arch and partially or wholly support the surface. If the supports of the arch are competent and the keystone is maintained, nothing further may happen. However, if the opening is large, the arch may migrate up¬ward and finally break through to the surface with attendant surface subsidence. The volume of the surface subsidence is usually less than the volume of the broken material. However, in cases where the block subsides as a unit, the volumes may be nearly equal.

The character of the material in which the opening is developed is important. Moulton classifies materials into three general groups:

The first class includes the materials from moist sands to the firmest rock, all of which act as solids. In surface excavations all homogeneous materials within this group stand with a vertical face to a given depth; below that depth they fail in shear with a characteristic shape of bank after failure.

The second class comprises any granular material, such as dry sand or gravel, that occurs as separate grains and lacks cohesion. The angle of repose controls the manner in which materials within this group stand in surface excavations.

The third class includes semi-liquid materials; quicksand, wet clays, and, in general, all saturated ground that develops pressures of a hydrostatic nature. At critical depths these materials become plastic and flow in such a manner as to develop pressures proportional to the depth.

Many mines, both open-pit and underground, are developed in materials which act as solids. According to Moulton, if the depth of the opening is sufficiently great that the resistance of the material to shearing stresses is overcome by gravity, and if the material is homogeneous and free from planes of weakness, the bounding, surface-subsidence cracks may be determined by drawing a line of one-half to one slope (63°26') from the lowest point on the side bf the excavation to the surface. The actual plane of rupture extends vertically downward from the surface to one-half the depth of the excavation below the surface and then curves inward as a segment of a sphere to the bottom of the opening. Haines points out that failure will occur in that form which allows the greatest possible weight to be opposed by the smallest possible resistance, in other words a sphere. This accounts for the one-half to one slope and the curved or hemispherical form of the lower half of the fracture. The fact that the upper portion of the fracture is generally vertical probably results from the condition that the tangent from the sphere to the surface of the earth is shorter than the are in the upper quadrant.

Crane points out that in many cases the earth is not homogeneous and that planes of weakness such as incompetent beds, bedding planes, schistosity, joints, and faults control to a large extent the manner of subsidence and the area affected by subsidence. The number, spacing, and attitude of the planes of weakness vary from one locality to another and even from one rock formation to another at the same locality, so that it is not surprising that no two cases of subsidence are exactly alike. Other factors, such as folding and the presence of dikes and sills of igneous rock, affect the situation only inasmuch as they contribute planes of weakness.