Great Neapolitan Earthquake of 1857/Part I. Ch. VI

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Part I. Ch. V

Great Neapolitan Earthquake of 1857 (1862)
by Robert Mallet

Part I. Ch. VI

Part I. Ch. VII

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1780125Great Neapolitan Earthquake of 1857 — Part I. Ch. VI1862Robert Mallet

CHAPTER VI.

FRACTURES CONTINUED—RECTANGULAR BUILDINGS—ABNORMAL SHOCK.

We have next to refer to the abnormal wave, or that passing horizontally, or nearly so, and diagonally through a rectangular building.

In this case the fissures occur at or near the internal angles of the quoins, and are vertical or nearly so, and in so far are the same as those produced by a normal wave. In a rectangular or square building they are also (the main fissures), the same in number (four) generally, but differently disposed. If the abnormal angle (that which measures the horizontal obliquity of the path of the wave, with two of the parallel walls,) is very small, as in Fig. 37, it occasionally

happens that only four main fissures are seen, the alternate ones $g'$ and $f'$ being rather wider than the two others, when the direction of the wave is from $a$ to $b$ , and the sum of $f'+f$ , being greater than that of $g'+g$ , on principles already explained. And sometimes these are accompanied by a much smaller main fissure at $n$ , and either none corresponding in the end $e$ , or one at $n'$ still smaller. In such a case if the abnormal angle be less than 10° it scarcely admits of decisive observation.

When the abnormal angle, however, is greater, as in Fig. 38, four main fissures are formed, which, except in the case where that angle is = 45°, are alternately wide and narrow. Let the direction of the wave transit be $a$ to $b$ , making an angle (in an horizontal plane) less with the wall $os$ than with the wall $on'$ . Then at the end $n$ at which the wave first arrives, the fissure $n$ will be narrow, and $w$ will be wide, and at the opposite end, $n'$ will be narrow and $w'$ wide, and the sum of $w+n$ will be greater than that of $w'+n'$ , all being measured horizontally across the jaws of the fissures at the same level, suppose at the top of the walls.

The cause of this is pretty obvious. Referring to Fig. 35, if the direction of the wave be $a$ to $b$ , the force of

dislocation of the end wall $eh$ , and the side $hw$ , acts in the direction $bc$ , through the centre of gravity of the end wall, and oblique to its plane; it is therefore resolvable into two, one perpendicular to the plane of the wall, $cf$ , the other parallel to its plane, $ch$ , and both through the centre of gravity or of inertia.

The component $ch$ produces the fissure $n$ . The resistance of the base of the wall, $eh$ , in the directions $de$ and $gh$ , uniformly along its length, may be resolved into a parallel force at $fc$ in the centre of the length and at the level of the base, which is below the the level of the component force, $cf$ , through the centre of gravity, there is therefore a dynamic couple, tending to turn the wall to the left round $eh$ , and this produces the fissure $w$ .

The fissure $n$ may take place anywhere along the wall $eh$ , but usually occurs towards $e$ , at a distance from $h$ , that is to the distance of $w$ from $h$ , approximately as the component $fc$ , is to that $ch$ , so that a line drawn across from $n$ to $w$ , either at the inside or outside faces of the walls, will cross the path of the wave at right angles more or less exactly. The position of $n$ , however, is subject to many disturbing circumstances, and it never occurs (as the proportion of the figures might seem to infer) so far from $h$ towards $e$ , that the masonry of the wall $eh$ , cannot yield sufficiently to the shearing strain in the direction of its length, to admit of the opening of the fissure.

Now from the observation of the widths of these respective fissures, we are in a position to find the angular direction in which the path of the wave has traversed the building. For referring to Fig. 36, let $w$ be the wider and $n$ the narrower fissure, whose widths of ope are proportionate to the components $a$ and $b$ ; the path of the wave, being $a$ to $b$ , $\theta$ and $\theta '$ the angles (together = 90°) made by these components with it, and which we require to find, then—

$\sin \theta :\sin \theta '::\alpha :\beta ,$

a

and

b

being equal or proportionate to the widths of

n

and

w

, therefore—

$a:b::1:\tan \theta ',$

or

$b=a,\tan \theta '$

hence

$\tan \theta '={\frac {b}{a}};$

from which either the angle $\theta '$ or its sine can be had from the tables.

As the path of the wave divides the angle made by the two walls (whether the building be square or not) in the ratio of

$\sin \theta :\cos \theta ,{\mbox{ or of }}\sin \theta :\sin \theta ',$

its direction may be easily got geometrically, by an observer not accustomed to trigonometry.

It sometimes happens that eight main fissures may be observed, alternately wide and narrow, in a rectangular building exposed to an abnormal wave. This only happens when the building approaches a square in plan, the abnormal angle being not far from 45°, and the walls very uniform in structure and mass, and built of small material, such as brick.

There are then two fissures, one wider than the other, near each quoin, as in Fig. 39; four are primary and due to the direct action of the wave, the other four seem to arise from the shearing strains in the plane of the respective walls. The case is unusual, but when met with is best rejected for seismometry, as likely to lead to error.

The walls are sometimes, though rarely, found as in Fig. 42, the middle portions of $c$ and $d$ first reached by the wave, being overthrown inwards, and those $a$ and $b$ leaning outwards. This mostly happens from quoins of stability disproportionate to the rest of the building, and unfits it for seismometry.

When the force of shock of an abnormal wave is sufficient to cause prostration of the walls, they almost always fall outwards, and the debris is found as in Fig. 40, $a$ to $b$ being the direction of the wave.

When the building is rectangular, and the abnormal wave in the direction $a$ to $b$ , Fig. 41, arrives first at one of the long side walls, making an angle of 45° less, with the end walls, the latter are generally fissured vertically at $nn$ , but the long side walls are also bowed, or possibly prostrated; the greatest amount of curvature being at $c$ and $c'$ , and the fissures taking the hollow curved forms, seen in the elevation of the wall $gf$ , the central fissures, being secondary or sub-fissures, dependent upon the bowing.

This form of building is difficult to obtain the abnormal angle from, with correctness, and those more nearly square should be sought for.

The remarks that have been made apply to cardinal and ordinal buildings alike, the former, when presented, being by far the best, however, for observation. We are therefore enabled from what precedes, in the case of a cardinal building and abnormal wave, to infer—

1st. The path of the wave.

2nd. The direction of transit motion.

Measures of velocity, can scarcely ever be obtained from an abnormal wave, as the overthrown masses are quoin pieces, which fall attached at right angles, and usually defy attempts to ascertain the moments of inertia and dimensions of base.

If the fissures be clean and well defined, and the walls not too much perforated by openings, or otherwise rendered irregular, good results can be had; it is then, not important that the walls making angles with each other, from which the widths of the directing fissures are taken, should be of equal thickness, because the force acting on each is proportional to its mass, and the section of fracture for equal height is so likewise; but they must be of similar material and masonry. All such conditions, however, will be better understood after we have treated of the perturbation of phenomena produced by architectural and other features, &c.