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

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1780137Great Neapolitan Earthquake of 1857 — Part I. Ch. XVII1862Robert Mallet

CHAPTER XVII.

VALUES OF THE COEFFICIENT .




Before concluding this section, it remains to assign the values of the coefficient for practical use.

It consists of two factors: the tenacity or resistance to rupture, by a force suddenly applied; and the specific gravity of the mass fractured off, by direct pull from an unit of section.

When a direct force, producing fracture by extension, is gradually applied to any prism, whose length and section are both unity, the work necessary to produce the rupture is

being the static load gradually applied, and the amount of extension of the body on the unit of length at the limit of rupture. But if be applied at once (suddenly), then , the accumulated work, is twice that necessary for fracture, or the force, whose tension suddenly applied, as by an earthquake shock, shall rupture the prism.

This force we suppose applied by the weight of a prism of the material fractured, whose base is the unit of section fractured; or being the specific gravity

When the question relates to the fracture of a homogeneous body—such as a column shaft, of one block of stone for example then the force to be taken, is that which applies to the material, and its sp. gr. But when the fracture occurs in walls of whatever sort, it takes place by the giving way, by loss of adhesion (generally), or sometimes of its own cohesion, of the mortar or other cement, as being the weakest part of the heterogeneous mass: in which case, is to be taken for the rupturing force of either the adhesion or cohesion (as the case may be) of the mortar or cement, and the specific gravity due to the whole mass of masonry.

Fracture seldom or never occurs through the solid stone, in masonry, but always at the mortar joints, and generally by their loss of adhesion, to the stone at the faces of the joint. It rarely occurs through the brick, in brickwork, and only when the cohesion of the brick itself, is less than that of the cement.

To enable these equations to be applied generally, in earthquake countries, I have arranged the two following tables, I. and II., which embrace almost all the reliable information we as yet have, applicable to the matter, and from which, the value of may be deduced, for a great variety of cases.

Many of the numbers, for want of better experimental data, can only be viewed as approximative.

The most important numbers by far, are those relating to the adhesion and cohesion, of the varieties of common mortar; and, fortunately, these have been ascertained by Boistard, Gauthey, Treussart, and Colonel Totten, with considerable accuracy.

The use of the coefficient , in Eq. XXI. et seq., considers the value of (Eq. ) evanescent, so that the prism at the moment of fracture has not risen through an appreciable angle, at the surface of fracture, and from the extremely small extensibility of mortar, stones, &c., this is sufficiently true to nature.

Table I.

Factors for the coefficient .

Material 1. Weight in pounds per cub. foot
Sp. gr.
2. Pounds per square inch
Resistance to Pressure.
3. Pounds per square inch
Resistance to Tension.
3. Authority for 1 and 2.
Limestone, Caserta, Naples 170 8173 908 Rondelet
Upper Limestone, Geneva 169 4917 546 Gauthey
Jurassic Limestone, Givry 148 4232 496 ..
Cretaceous Limestone (Compeigne) 154 3007 334 Rondelet
Lava, Hard Vesuvian 166 8735 972 ..
Lava, Soft Vesuvian 107 2209 246 ..
Lava, Piperno (Pozzuoli) 162 8140 905 ..
Travertino, Old Roman 147 2297 255 ..
Travertino, Pæstum 141 3102 345 ..
Peperino, Roman 123 3135 347 ..
Tufa, Old Roman 78 797 89 ..
Tufa, Naples 82 718 80 ..
Hard brick 98 1851 206 ..
Soft ill-burnt brick 91 1200 133 ..
Mortar, lime, and sand, unground 102 423 47 ..
Ditto, ditto, ground 119 577 64 ..
Mortar, Pozzolano, of Rome and Naples, unground 92 503 56 ..
Ditto, ditto, ground 105 732 81 ..
Mortar, Old Roman (Campagna) 97 1047 105 ..
Mortar, Old French (Bastile) 94 753 84 ..
Plaster of Paris (mean) .. 500 55 Laisne

It appears, from the few experiments that have been made, that the resistance of stones, &c., to tension, varies from th to th the resistance of the same material to compression. The third column is here calculated on the mean of such data. It cannot be viewed as more than an approximation, except in the cases of mortars, which are from actual experiment, as given by Gauthey ('Sur la Construction des Ponts'), and by Rondelet ('L'Art de Bâtir').

Table II.

Of the specific gravities, cohesion, and mutual adhesion, of various building materials. Factors for the coefficient .

Material 1. Weight in pounds per cub. foot
Specific gravity
2. Resistance to Tension
lbs. per square inch.
3. Adherent Resistance
lbs. per square inch.
3. Authority.
Granite 164 1200? .. T.
Granite to Portland cement .. .. 97 W.
Granite to Parker's cement .. .. 22 W.
Silurian slate 170 2300? .. T.
Oolite (Portland) 132 270 .. W.
Oolite to Portland cement .. .. 146 W.
Oolite to Parker's cement .. .. 42 W.
Sandstone, coal measure 147 234 to 250 .. T.
Millstone grit and Portland cement .. .. 76 W.
Sandstone (Whitby) and Portland cement .. .. 57 W.
Kentish rag and Parker's cement .. .. 29 W.
Brick, best English 135 200 to 230 .. ..
Brick, inferior 97 40 to 80 .. B.
English brick in Portland cement 107 .. .. W.
Portland cement 127 400 .. W.
Parker's cement 120 300 .. W.
Mortar (sand 3, lime 1) 100 to 119 11 to 20 9.88 B.G.
Green and fresh .. 2 .. T. T.
Mortar, ground lime and tiles 100 to 120 40 to 80 5.26 B. G.
Hydraulic mortar T. T.
Jurassic limestone to mortar .. .. 3.80 R.
Brick and tile to mortar .. .. 8.27 R.
Authorities.—T., Tredgold. W., White, 'Trans. Inst. C. E.' B., Barlow. B.G., Boistard and Ganthey, 'Const. des Ponts.' T. T., Treussart and Totten. R., Rondelet.

In the preceding table, the cements had, in all cases, six months to indurate, and the mortars (except in the second case) from six months' to seventeen months' induration.

Examples of very old and good, lime and sand mortar, may be found occasionally in good brickwork—such as that of the Roman amphitheatre at Pozzuoli, for example; or in rubble masonry, where the bond of the stone with lime mortar is peculiarly strong, as with the oolitic building stones, and limestones generally, and with a few sandstones and porous traps, in which the adhesion, of the indurated mortar, becomes fully equal to its cohesion, and both rise above 50 lbs. to the square inch, for forces suddenly applied.

In determining the mean specific gravity, of brickwork and rubble masonry, the proportion of mortar, to the brick or stone in a given volume, may be taken at from th to th, according to the goodness of the work.

Table III.

Deduced values, under different conditions, for the coefficient .

No. Conditions of Fracture. Value of
1 Apennine limestone, broken through the stone 225
2 Cretaceous limestone, ditto ditto 154
3 Apennine limestone rubble masonry, of best quality, broken through the joints 52
4 Apennine limestone rubble masonry, of inferior quality, broken through the joints 30
5 Apennine limestone, rubble masonry of best quality, mortar not indurated 3.9
6 Argillaceous rubble masonry of the Murgia (Apennine marl rocks), best quality, with indurated mortar 55
7 Best Italian or Roman brickwork in mortar 63
8 Inferior brickwork in mortar 30
9 Brickwork, the mortar not yet indurated 2.5
10 Rubble masonry of tufa and mortar, good, with mortar indurated 87
11 Rubble masonry of Travertino, or Peperino, and mortar indurated 51

These values of , are all, for the mortar when yielding in cohesion. When observed to yield in adhesion, the coefficient in each case becomes 0.1, for brickwork and 0.083, for limestone. The values given, are also all for ancient and fully indurated (except 5 and 9) mortar; where the latter is under twenty-five years laid, the value of should be taken (quam prox.) at 3/5 in the table.

Proceeding now to