Great Neapolitan Earthquake of 1857/Part I. Ch. VIII
CHAPTER VIII.
SHOCKS OF VERTICAL OR NEARLY VERTICAL EMERGENCE—EFFECTS ON RECTANGULAR BUILDINGS.
We now arrive at the fifth and last class of waves, viz., those of vertical or very nearly vertical emergence, upon which it is necessary to make some remarks.
As a strictly normal or abnormal wave, i. e. with perfectly horizontal transit (unless by reflection) is impossible from a focus beneath the surface, so an absolutely vertical emergence is in strictness limited, to the single point of the earth's surface vertically above the focus, or to the seismic vertical itself. Inasmuch however, as in reality the disturbance producing impulse is not confined to a mathematical point, but (whatever be its nature) extends over a greater or less, and in all cases a very considerable area, and lies also at such a considerable depth, that lines extending from it to the surface make but small angles with each other; so a tolerably large area is found in the midst of every earthquake-shaken region within which the angle of emergence is so steep that it may be viewed, as respects the effects of the wave, as practically vertical.
In the preceding remarks upon the four first orders of wave-paths, we have viewed the wave itself as of one sheet and the movement of any particles in the wave to be forward and backward in a right line or in an elliptic or some other closed curve, in a vertical plane, neglecting the transversal movement (which is small) for the present. This, although perhaps not physically true, was sufficient for our purpose.
Were we at liberty to consider the vibration of the wave with vertical emergence performed in like manner, the movement of any point of matter upon the surface due to it would be limited to two motions—one directly up and down, due to the amplitude, and the other forward and backward horizontally, due to its altitude and to the senses. The movement would thus be similar to that of a normal or subnormal wave. The universal testimony, however, of those who have experienced these vertically-arriving shocks is of a twisting and wriggling motion in different planes, violent in its changes of direction, and attended by a movement up and down of much greater range, to which the word "sussultatore" is often applied.
It seems highly probable that the path of a wave particle moving normally or nearly so, may be elliptic, as in Fig. 52 a, in a vertical plane, and with a smaller transversal vibration performed in a horizontal plane as in Fig. 52 b. The actual relation of altitude and amplitude, so far as observation yet is afforded, seem more as in Fig. 53 c, or even in a far higher ratio to each other, and the transversal vibration still smaller, as in Fig. 53 d, so that in normal or slightly emergent waves the transversal movement is little noticed, (as, indeed, is true pro tanto of the movement in altitude); hence, as stated, we may neglect for present purposes, the transverse movement altogether as respects such waves.
In the case of vertical emergence, however, the path of a moving particle being in one vertical plane elliptic, and the major axis being the line of transit, will have the form of Fig. 54 e, in a vertical plane atright angles to the former, and in an horizontal plane at the earth's surface the path will be as in Fig. 55 h. In ascending through heterogeneous formations even the more complex forms of Fig. 56 g and f, or Fig. 57 k and l, may be those of the path of the wave particle, the vertical being the movement of largest range, in every instance. In either of those cases the sensible effect upon the earth's surface must be the same as if bodies, besides being lifted up and down, were alternately whirled round in small circles in the directions of the bent arrows 1 and 2 in Fig. 58 m. In vibrating elastic masses having special and pendulous vibrations of their own, when set in motion by the wave, the axis may rapidly, though with a much slower relative movement, rotate in the direction of the external arrows or in the reverse one. The formidable torsional and wrenching strains which are known to arise from vertical shocks, are most probably thus produced.
It must be remarked, however, that these torsional strains—"Vorticosi" of the Italians and Mexicans—must not be supposed capable of producing those twistings of objects upon their bases, such as vases, chimneys, obelisks, &c., of which we shall record many examples, but which are due to other circumstances first explained by myself several years since.[1]
A continuous jarring movement, consisting of a rapidly arriving series of waves, moving in a horizontal plane, as in Fig. 57 l, often occurs, and in lofty buildings, such as churches or towers, when the time of torsion vibration of the building itself (once set in motion), happens to be isochronous with that of the wave vibration, twisting strains of enormous violence result.
The effect upon the walls, then, of the vertical wave is chiefly to produce fractures which are transverse to the lines of twisting distortion. As the twist is alternately in opposite directions, these fractures cross each other, the opposite contained angles being double, those of the lines of maximum torsion strain with the vertical. These motions being accompanied by rapid up-and-down ones of much greater range, each distinct story of the building acquires a separate momentum of its own, in virtue of the weight and attachment to the walls, of the floors and objects upon them. All the fractures tend therefore to separate and close again, as the wave makes its transit; and the several masses, moving horizontally at the same time, with a rotation alternate and increasing as it ascends the building, the replacements do not often coincide with the displacements, and in a few seconds the stability of the walls may be so far destroyed, that the whole falls to the ground in ruin the most complete. Fissures running horizontally or nearly so from the quoins are not unfrequently observable where the emergence is very steep or nearly vertical, examples of which may be observed at both sides of the N.W. wall of the church of Pertosa (Photog. No. 25, page 42).
With vertical or nearly vertical emergence also, gravity acting with inertia, in the first semiphase of the wave, upon the masses of masonry situated directly above doorways, windows, and other such apertures, their tendency to come down is great; and hence, not only are vertical fissures formed over such openings, but they are open widest at bottom, one of which will be remarked breaking across the stone lintel over the west door of Pertosa church (Photog. No. 25), but diagonal fissures crossing the piers between windows, where there are doors or other opes beneath, in a lower story, of which examples occur in the Palazzo Palmieri at Polla and will be observed in the Photogs. 178 and 180, Part II.
It is upon the heavy Italian roofs and floors, however, already described, that the most instant and formidable effects are produced by vertical emergence. Upon these the vertical velocity produces a moment of inertia acting directly downwards, and therefore favoured by gravity. Arched roofs, groining, and that form of arched ceiling constructed of hollow pottery, then spread the walls, as they come down, and falling upon the floors below, bring them down in succession. The details of movement will, however, be best given further on.
Upon the whole, the phenomena of vertical emergence, afford little ground for exact observation, with a view to trace the elements of the shock, and their limited occurrence is not to be regretted, on this ground. When once seen they present general features by which they can almost always be recognized with tolerable certainty, but not such as will enable us to ascertain directly, the line which produced downwards, should intersect the centre of impulse beneath the central field. That must be sought for otherwise, by observations at a greater distance from the seismic vertical, where the wave movements have become more uniform, and less complicated. When ascertained by the method of intersections of wave-paths, aided, if occasion serve, by determinations of velocity of transit, applied to the values of the angle e, its correctness may be tested and controlled, within certain limits, by the coincidence or not, of the focus thus obtained, with the observed area of vertical phenomena, somewhere within which the seismic vertical is situated.
- ↑ 'Trans. Roy. Irish Acad.; vol. xxi. p. 1, 1846.