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

by Robert Mallet

CHAPTER IX.

CONDITIONS AS TO FORM AND STRUCTURE IN BUILDINGS, WHICH MODIFY THE EFFECTS OF SHOCK—FIVE PRINCIPAL CONDITIONS.

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It will now be necessary to refer to the special effects produced, by the architectural figure, and other particular conditions of buildings, &c., upon the principal phenomena due to the shock upon them, as just described. The treating of this might give rise to almost endless details; reference will therefore only be made to a few of the salient conditions, and their modifying effects, from which the intelligence of the observer can deduce, all others that may come before him.

What has preceded has been exemplified, by an imaginary roofless rectangular building, on level ground, and without any apertures. We have now to discuss how the actual conditions of buildings as we find them (having those of Italy in view primarily, however) affect and modify the results. We may discuss this under the following heads of effects, produced by the wave of each class, as modified by the following conditions, viz.:—

1st. The form, magnitude, height, and unsymmetrical character of construction.

2nd. The form of the surface or foundation, and the relations of buildings in juxtaposition, as in towns.

3rd. The class of masonry and materials, their flexibility and elasticity, &c.

4th. The reactions on roofs and floors, and of these again, upon the other parts of buildings.

5th. The effects of apertures in walls, as gateways, doors, windows, &c.

After these some observations upon the perturbing effects produced by the physical and geological features of the country, will conclude the first part of this Report.

The final dissolution and fall of every compound structure in masonry, occurs by the successive development, of two stages of dislocation. Were it possible that a building could be overturned by the shock, as a whole, the conditions of its overthrow, would of course depend simply upon its "moment of stability." This, however, owing to the imperfect bond at the joints, and the relations of magnitude, to the strength of the materials, can never occur, except in the case of very lofty towers or minarets, spires, or single columns, &c. In such a case the mass may be overturned, and dissolution then takes place principally by the stroke of its fall to the ground.

In all other cases, however, the great fractures are produced in the first instance, which break up the whole, into a number of distinct, and more or less independent masses. The immediately subsequent movements of each of these, depends upon its own moment of stability, in as far as it is unsupported, or unaffected by the stability, or by the fall of others. The disintegration of the building—viz., whether it shall split up at all—depends, as we have seen, upon—

1st. The direction (as to horizontal obliquity and emergence) and the velocity of the wave, directly, and the density of the materials.

2nd. Upon the tenacity and bond of the materials, inversely, and upon the form and magnitude of the structure.

Both these relations being modified, by the elasticity and flexibility, of the materials.

The directions of the great fractures producing disintegration depend upon—

1st. The direction (as to obliquity and emergence) of the wave; i. e., on the abnormal and emergent angles.

2nd. The form of the structure as a whole, and of its several parts, or details, previous to severance.

Lastly. The fall of each separate mass, if then severed, depends upon its own moment of stability. If any such separated mass fall, it does so in the direction of its least. horizontal dimension: or as for any practical purpose of seismic observation, the moment of inertia due to the oversetting force must lie in this direction (for otherwise the mass falls by twisting), we may limit the consideration to that case.

If $t$ be the thickness of the bed joint of masonry upon which the mass overturns, cut by a vertical plane passing through the centre of gravity of the mass and the line of transit of the wave; $i$, the slope of the joint, if any, to the horizon; $r$, the fraction of $t$, that measures the distance of the point where the line of resistance cuts it, from the mid-length; $r'$, the distance from the bisecting point of $t$, to where it is intersected by the vertical through the centre of gravity of the mass, $\mathrm {W}$ its weight, and $\Sigma$ its moment of stability; then

$\Sigma =\mathrm {W} \times (r\pm r')t\cos i,$

according as the line of resistance and the vertical through the centre of gravity, are at the same or at opposite sides of the bisection of $t$.

The weight of the mass (whatever be its form, assumed approaching regular), may be expressed

$\mathrm {W} =\phi \times lbt\times \delta$

$\phi$ being a factor, determined by the angles that its three dimensions $l$, $b$, and $t$ make with each other, and on its form, and $\delta$ the specific gravity of the masonry. Therefore

$\Sigma =\phi (r\pm r')\cos i\times lbt^{2}\times \delta .$

If $\mathrm {F}$ be the force necessary to fracture the mortar at the joint $t$, acting in the direction of the wave transit,

$\mathrm {F} +\phi (r\pm r')\cos i\times lbt^{2}\times \delta$

is equal the total resistance of the mass to being overturned by the force of the shock, acting at the centre of gravity in the same line, but opposite direction

$\mathrm {V} \times \delta \times lbt\times \delta .$

For similar forms of the fractured and separated masses, therefore, and like direction of emergence and velocity of wave, the resistance to fracture $\mathrm {F}$, depends upon the cohesion per unit of surface and total area of fracture, and the resistance to fall $\Sigma$, upon the density of the masonry, the height, the breadth, and the square of that one of the two horizontal dimensions, which lies in the direction of the shock, and may be called the thickness.

The mass being severed free, from all others, by fracture, it depends upon the value of $(\tau \pm \tau ')$, and upon the emergent angle of the wave, whether it shall fall forward, in the direction of the wave transit, or in the reverse one. And from the nature of the applied force (being that of inertia), $\delta$ disappears.

Such are the general conditions as to equilibrium, upon which the fracture and fall of the separated masses, producing final dissolution of the building or structure, depends, and from which, equations for various architectural forms and conditions may be deduced.

The circumstances of fall of simple rectangular buildings have now been explained. Cruciform buildings, such as churches, are affected much in the same ways, the twelve sides of such a building being, in fact, capable of being viewed or arranged, as separable into those as three simple rectangular ones.

Polygonal buildings are rare, and when the number of sides are few, and the length of each considerable, do not present features materially different.

Cylindrical buildings, or conic frastra, however, which may be viewed as polygons of an infinite number of sides, have some peculiarities.

Whatever be the direction of shock, if horizontal, upon such a building, its effects are the same. The distinction of normal and abnormal wave does not exist as respects them; and unless the angle of emergence of the wave be extreme, or nearly vertical, the lines of fracture are the same in every case, viz, vertically through the axis and transverse to the line of shock. This arises from the fact that the area of fracture, and therefore the total resistance, $\mathrm {F}$, due to it, augment rapidly as the angle of its obliquity with the vertical, through the cylindrical walls increases. So that although the direct tendency of the wave $ab$ is to throw off a cylindric ungula, $edc$ (Fig. 59), by a fracture

perpendicular to its direction in $cf$, yet its direction at either side of the vertical plane of the wave transit, so obliquely through the joints, that the building always parts in the weaker line, by diametrical vertical fissures through $km$. The separated masses have now each a moment of stability, the fraction $t^{2}$, in which is enormous, being equal to the radius of the cylinder or the base of the cone; and hence the fragments of such towers are seldom overturned.

Where the value of $\mathrm {F}$ is small, as in the very bad rubble masonry of the ancient towers, and the angle of emergence considerable, however, we have instances of the mass thrown out assuming the form of a curved ungula, obviously by the fracture commencing vertically, and following down the joints gradatim from $k$ to $p$, and thence to $c$; of this a remarkable example occurs at, Átena.

When the emergence is still more vertical, and the shock powerful, a number of nearly equidistant fissures form round the top of the walls commencing vertically, and masses are thrown out, each carrying down with it an ungular-shaped toe, so that the tower becomes shorn around the summit at a greater or less distance down, by the descent of several separate masses from it, in the form of Fig. 60, and, as better seen in the Photog. No. 61, page 42, at Marsiconuovo. The original fissures are here, no doubt, produced chiefly by the twisting movements, transferred quite round the walls, by transversal vibrations as referred to when treating of the wave of vertical emergence.

This applies but to a limited extent to the semi-cylindrical "apses" which form the chancel ends, of so many of the more ancient churches. These generally split Off at or near the re-entering angles of the quoins, by which they are joined on to the body of the building, if the wave transit approach a line, transverse to that diameter; if otherwise, the walls of the "apse" split vertically in the direction of the opposite diameter.

Towers of extreme altitude and very narrow base, such as slender minars, single columns, lofty campaniles, &c., involve a number of complicated and curious considerations, as respects their resistance to fracture and to overthrow by shocks.

In these the elastic modulus, density, and range of flexibility before fracture of the masonry, the time of vibration of the structure viewed as a compound elastic pendulum—together with the direction of wave transit, and the relation that may subsist between the amplitude of the wave, its maximum velocity, and the pendulum time and range of vibration of the towers—all are elements. It is not requisite for our present purposes, however, here to pursue the investigation.

The effect generally, of want of symmetry in the severed masses, is to reduce them by further dislocation, prior to complete overthrow. For example: a portion of a uniform wall, severed by transverse fissures from the remainder, but having a buttress of its own or of less height somewhere along its length, is again transversely broken close to the buttress, the moment of resistance to fall being different in each. The relation of the buttress to the wall, as a support against transverse forces of a statical sort, is no longer the same, when the overthrow is produced by a force applied with the rapidity of the wave of shock; there may not be time, to transmit its own stability to the remainder of the wall.

Where the buttress is at the same time a tower rising much beyond the height of the remainder of the building, these generally tend to mutual destruction; the primary fissures occur at the junctions or near them; the walls and the tower have different times of vibration, as elastic pendulums of different lengths, and whether by chance isochronous or not, produce mutual damage, by their impulses upon each other. This is peculiarly striking, in the case of many of the meaner class, of Italian rural churches, where the belfry tower is built into one of the quoins of the main rectangular building, the two adjacent side walls are frequently completely destroyed by transverse rocking of the tower; although the latter may have only suffered fissuring at the lower portions, and that which was above the level of the church walls be overthrown.

Sketch Pl. 62		Photo Pl. 80
	⁠
Vincent Brooks, lith. London
Santa Dominica, Montemurro looking south from the Palazzo Fino	⁠	Church at Picerno

High towers and of narrow base, fall as one mass, breaking off diagonally somewhere above the base, whatever be the direction of the wave. When, however, the angle of emergence is very steep, a certain amount of shearing force is introduced, and the angle of severance becomes very sharp likewise, so that a sharp angular "aiguille" of shattered masonry remains standing, often bearing a considerable proportion to the whole original height. A remarkable example of this form of fracture is given in Fig. 62 of the tower of the monastery of Santa Dominica, at Montemurro, sketched from the top of the Palazzo Fino, although in this instance probably due only to accidental causes, and not to steep emergence. Isolated fragments thrown from the summits of such towers, owing to their own velocity of pendulous vibration, do not always, by reference to the observed distance of projection, represent without correction, measures of the true direction or velocity of the wave. They are thrown like a stone from a sling, with a certain velocity and direction due to the shock, plus or minus, another, or perhaps a different direction and velocity, due to the proper motion of the tower; of this the observer requires to be on guard.

Unsymmetrical construction of building, always involves unsymmetrical phenomena of distribution. If compelled to adopt such a building, (in lack of better,) for observation, the first thing to be done to disentangle the phenomena, is to consider the effects, due to the want of symmetry alone. If, for example, we find the opposite walls of a cardinal church, one standing and the other prostrate, the wave transit having been abnormal, and nearly in their lines of length, the first point to be ascertained is, was the prostrate wall symmetrical in form and structure with that remaining. Unless the effects of the roof may have overthrown it, we shall generally find, that the fallen wall was either of much inferior masonry, or smaller thickness, out of plumb originally, or full of windows and doors, the standing wall being solid.