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

by Robert Mallet

CHAPTER V.

FRACTURES CONTINUED—RECTANGULAR BUILDINGS—SUBNORMAL SHOCK.

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We proceed next to consider the effects of a Subnormal wave, or one whose transit is emergent at an angle to the horizon, and in a vertical plane, parallel to two of the walls of a rectangular building.

If the angle of emergence—viz. that contained between the line of transit of the wave and the horizon be small, not exceeding 10° or thereabouts—the effects, when producing fissures or overthrow, can seldom be distinguished alone from those of a normal wave. Fissures are produced near the quoins, at the tops of the walls, and if overthrow takes place the end walls and detached portions of the sides, are thrown outwards as already described. In accordance with the general law, the fractures tend to place themselves at right angles to the direction of wave transit. Thus referring to Fig. 31, where the angle of emergence (of the wave whose direction of transit is $a$ to $b$) is $hia$, the end wall $c$ is thrown back by inertia, and that at $e$ projected forward, with a difference of velocity = $v$, as before. As the joints of the masonry or brickwork, which the fractures follow, upon the whole run vertically and horizontally, and as the fracturing force is transmitted diagonally in the direction $ad$ through the side walls, fracture occurs in jagged lines in directions perpendicular to $ad$, the wave-path. The fissures at the end $c$, therefore, commencing at top, very near the internal angles of the quoins, run down in the direction $pk$, making an angle with the plumb line of the wall $c$ (before disturbance) $cpk=hia$ = the angle of emergence.

The portions of the side walls detached with the ends grow wider as they approach the base. They therefore make the end wall $c$ too rigid, to turn round upon or near its base, as in the former case (Fig. 21), to admit of the fissure $pk$ opening; hence a cross fracture occurs somewhere below one-third the height of the wall $c$, as at $n$, which frees the mass and admits of its movement. This cross fracture may take any direction downwards from $n$ towards $t$, dependent upon the nature of the masonry, &c., and the mass $c$ chiefly turns over, to the extent of opening of the fissure, round the joint at $t$, or may partly slip upon the fractured joints in the direction $da$ and partly turn. When the building is large, and the angle of emergence large also, as in Fig. 32, this cross fracture is usually a curved line, more or less hollow downwards, passing out at the quoins at a bed joint as at $t$, and in such a direction that a chord to the hollow curve from $n$ to $t$ approaches to right angles with $pi$.

The end $e$ (Fig. 31) is projected forward towards $d$ by inertia in the second semi-vibration of the wave. Its fissure is more or less exactly parallel with $pk$ for the greater portion of its length, but it seldom runs to the base of the wall $s$, turning out towards $d$ by a horizontal joint, somewhat above that level, and at a higher point, as the angle of emergence is greater, as may be observed in Fig. 32.

The reason of this is pretty obvious. The inclined direction of the fissure causes it to reach the internal angle of the quoin before it comes down to the base of the end wall $e$, which therefore breaks at that level along an horizontal line, and all below that, not being detached and loaded with the mass above, is unmoved. Cross fractures may or may not, follow from this fissure towards $c$, dependent on the breadth of side wall, occurring between the fissures at the ends $c$ and $e$, and upon the angle of emergence, class of masonry, and other conditions.

In Fig. 32 the effects are shown of the wave when emergent at a still greater angle. The train of phenomena is quite similar to that just described, but with this addition, that where the angle of fracture, $tpi=hia$ = that of emergence, is great, and hence the angle $ipm$ great also, the overhang of the upper part of the side wall, coupled with the momentum in the direction $ip$, due to the small motion of the wave in altitude, produce a fracture somewhere at $m$, or more than one, the direction of which downwards is much modified by the joints, &c. &c., of the masonry, and is generally nearer to the vertical than exactly at right angles to $pi$.

When the emergent wave produces a sufficient shock for complete overthrow of the end walls $c$ and $e$, they fall as in Fig. 33, leaving the fractures of the side modified, by the grind of the descending masses. It is rarely, however, that a shock of an emergent wave, sufficient to throw back one end, and forward the other, occurs without the side walls being also thrown, in or out, or both, either by transversal wave motion or by secondary actions of the falling end walls upon them.

It-was stated above that the direction of diagonal pressure through the wall was in that of the wave transit: this is perhaps not strictly true, for referring to Fig. 34, if $a$ to $b$ be the path and direction of wave transit, and the velocities of the wave itself be equal in altitude to $st$ and in amplitude to $lm$, then the resultant pressure due to its movement in the forward half of the first semi-vibration is in $a'b'$, which, combined with the motion of transit $ab$, will give a resultant pressure somewhere between $b'$ and $b$. As, however, the amplitude $lm$, of the earth wave, appears to be always very great with reference to $st$, there is no practical error (and much convenience for calculation), in considering the line of pressure as coincident with that of wave transit.

If the subnormal wave be orthogonal to that just described, and still affecting a rectangular building, so that its transit passes through the longer sides, these are bowed (if of sufficient length, &c.) outwards, at the side first reached by the wave, and inwards at the opposite one, differing in nothing from the effects of a normal wave upon the same building except that these are all less marked, for the same velocity and amplitude, the effective velocity producing movement in the masses detached, being to that of a normal wave of equal velocity, as $v$: ${\frac {v}{\sec e}}$, $e$ being the subnormal angle, or angle of emergence.

Two other conditions require notice, however, as also affecting the dislocations produced by subnormal waves.

If such a wave, with a given value for the angle $e$, be resolved into a vertical and horizontal component, it is the latter that is chiefly effective in producing dislocation when $e$ is small, the former when it is very great: and the effects of both are modified more or less by the form of the individual blocks of stone of which the wall consists. If these are very long in their beds, they offer a most powerful resistance to fracture or dislocation by a steeply emergent wave; and when thus long bedded, close jointed and squared ashlars, prevent any indication of value being had.

In the choice of buildings, therefore, for arriving at the value of $e$ from subnormal fissures, those must be selected that are of large size, with walls of brick, or of rubble masonry of inferior quality, or at least of small, short-bedded stones in proportion to the size of the walls; and fortunately (for seismic researches) there is no want of such in the south of Italy.

Where, also, the value of $e$ is great, two other circumstances come into play to modify the widths of the fissures, and even affect their direction, more or less.

Referring again to Fig. 32, the effect of the vertical component of the subnormal wave, in its first semiphase, tends to drive the fractured mass at the end $c$ down upon its foundation, and to throw that at $e$ into the air.

Gravity, therefore at the former end, acts with the wave, in the first semiphase, but against it, at the latter end of the building, and vice versa. But the rhomboidal mass of wall between the fissures at the ends $c$ and $e$ is also acted on by gravity with the wave, and the result is frequently to force down great wedges, such as $pnm$, which close the fissure $p$ in such a way as to prevent a certain indication, for these wedges being detached all round, remain where they descended to last. This is, however, a result of less importance, because there never can be a mistake, as to the direction along the wave-path of steeply emergent subnormal shocks, in which the seismic vertical is to be found; it must lie to the side at which the wave-path dips below the horizon.

The overthrowing power, and, to a certain extent, the fracturing power of a subnormal wave differs in the first and second semiphase (without reference to the difference due to difference of velocity), being proportionate to the perpendiculars to the wave-path, let fall from the centres of oscillation to the fulcra round which the fractured masses turn.

This is greatest at the side $e$, towards which the wave travels, and the tendency of this is to equalize the widths of the fissures. Other consequences will be apparent to the mechanical reader on considering the conditions.

From observation of the effects of a subnormal wave, therefore, we may be enabled to arrive at conclusions as to—

1st. The path of the wave—Subnormal.

2nd. The direction of transit—the fissures being occasionally most open at the end first reached by the wave, and the transit always from the end that dips below the horizon.

3rd. The angle of emergence of the wave with the horizon being equal to the angle made by the main fissures (or those transverse to the wave-path) with the vertical.

4th. The velocity of the wave motion may, under favourable circumstances, be inferred from that impressed upon detached and fallen masses.

Abundant examples will occur, in the second part of this Report, of these subnormal waves, and of their effects.