An inspection of neighbouring quarries and the waste tips, sand or gravel pits, hills and cliffs, cuttings and embankments for roads, river banks, &c., will afford an indication of any local peculiarities caused by the climate or otherwise; and a comparison of the natural slopes assumed when the soil has to withstand vibration, and when not so disturbed, will enable a judgment to be formed of its deleterious effect upon the earth; but above all, an examination of the cuttings and embankments passing through or upon the same geological formation. Reliable evidence can be so obtained upon which the slope of permanent repose can be determined according to the dictates of science and experience, but the probable consequences of instability will demand a due regard to provision against contingent deteriorating influences which may almost destroy cohesion and render it necessary to rely solely upon frictional resistance, the remaining resisting power against movement of the earth, except in solid rock, which may stand with an overhanging or vertical face, whereas mud and quicksand may not be in a state of rest even when horizontal.
The following table of slopes for different earths has been carefully compiled to indicate the probable permanent slope, but it should not be separately considered from the other chapters in this book, as circumstances modify even a considerable range of inclinations; for instance, earths that will be stable at a certain slope in temperate climates will require a much flatter slope in tropical or very cold countries. Those named are more especially for artificially deposited or embanked earths subject to vibration, and, therefore, in cuttings the slope might be steeper, although not so in aluminous soils or those in which the particles become decomposed upon exposure. In Chapter II., under the head of each kind of earth, the approximate slopes of repose are more exactly named, as they would occupy too much space in a table. When not mentioned in Chapter II. the slope is given.
General Note.—The slopes must be flatter according to the amount of water in the same soil or to which it may be subject, the depth of a cutting and height of an embankment, and the presence of all other disturbing influences. Vide Chapter V. for the safe maximum depth of cuttings or height of embankments.
| Table Showing the General Range of Slopes. | ||
|---|---|---|
| Description of Earth. | Inclination. | |
| Peat moss, marsh earth, consolidated mud, silt, hard peat turf, when loaded | Horizontal to 4 to 1 | |
| Alluvial soil | 2 to 1 TO 3 to 1 | |
| Ditto. | When wet | about 4 to 1 |
| Soft wet pasty clay in superficial beds | 3 to 1 TO 4 to 1 | |
| Diluvial firm clay of river beds | 2 to 1 TO 3 to 1 | |
| Alluvial soil. Loam and loamy earth. (Clay and 40 to 70 per cent. of sand) | 1½ to 1 TO 2 to 1 | |
| Ditto. Clay loams. (Clay and about 30 per cent. of sand) | ||
| Ditto. | When wet and crumbling | 3 to 1 TO 4 to 1 |
| Damp clay soil | 3 to 1 | |
| Upheaved and intermixed beds of different sound clays | 2 to 1 TO 3 to 1 | |
| Solid clay mixed with very fine sand | 2 to 1 | |
| Sound yellow clay containing only the normal quantity of water, the surfaces covered after deposition | 2 to 1 TO 3 to 1 | |
| Brown laminated clay, quickly affected by weather:— | ||
| Surface covered | 6 to 1 | |
| Surface exposed | 12 to 1 | |
| Solid blue and firm clays, marl and indurated marl, and boulders imbedded in sand and gravel | 1½ to 1 TO 2 to 1 | |
| Soft chalk, impure and argillaceous | 1½ to 1 TO 2 to 1 | |
| Ditto. | In cuttings | ½ to 1 TO 1 to 1 |
| Hard white chalk, having greater density than the preceding. | 1 to 1 TO 1¼ to 1 | |
| Ditto. | In cuttings | Nearly vertical TO ½ to 1 |
| Ashes | 1 to 1 | |
| Very fine dry sand | 1½ to 1 TO 2 to 1 | |
| Firm sand, surface not completely protected | 1¼ to 1 TO 1½ to 1 | |
| Firm sand in embankments, surface protected by fascine mattresses, as in Holland; and exposed to moderate sea | 2 to 1 (least) TO 3 to 1 | |
| Ditto, on land side. | 1½ to 1 (least) | |
| Firm shale, surfaces covered | ½ to 1 TO 1 to 1 | |
| Note.—When the shale is greasy and becomes unguentous upon being exposed to the weather, it must be considered as a clay. | ||
| Clean gravel and dry shingle | 1¼ to 1 (dry) TO 1½ to 1 (wet) | |
| Ordinary clean coarse sea beach, 3 to 1 at top, graduating according to the depth, size, range, set of the tide, and exposure, to 5 to 1 TO 8 to 1 at moderate depths, and at the base to 20 to 1 TO 30 to 1, the curve of the slope being parabolic if the waves alone disturb it. The angle of repose will be less as the size of the particles become smaller, and between high water and a few feet below low-water mark will seldom be less, if not sheltered, than 4 to 1 to 6 to 1; but coarse firm sand that has become consolidated will often stand at a steeper inclination than a mass of rolling stones, however hard they may be. | ||
| Compact gravel | 1 to 1 | |
| Ordinary road metalling, moderate height | 1 to 1 (clean), TO 1¼ to 1 (stacked, as excavated from road.) | |
| Large concrete blocks. Sheltered position and carefully deposited. Harbour side | ½ to 1 | |
| Large concrete blocks. Exposed site and carefully deposited | 1 to 1 | |
| Rubble mound. Sheltered position | 1¼ to 1 TO 1½ to 1 (harbour side.) | |
| Rubble mound. Exposed to sea | 2½ to 1 (sea slope.) | |
Note.—If an exposed coast, the rubble may require from 4 to 1 to 7 to 1 slope, depending upon its size, the currents, depth, and “fetch” of the sea, and solidity of the mass.
The usual slopes adopted for cuttings and embankments may be said to range from 1 to 1 for firm earth, having particles not seriously affected by water or weather, to 4 to 1, and the most frequent, 1 to 1 TO 1½ to 1 in cuttings and 1½ to 1 in embankments.
With respect to the chief organ of stability in earths other than rock, namely, the frictional resistance; friction during motion is generally considered to be less than the force necessary to overcome it when at rest, and undoubtedly this is the case when the surfaces are similar, and are smooth and hard and not easily impressed, as iron, granite, concrete, and metals generally; but when they are comparatively soft and incapable of resisting indentation at any pressure that they may have to bear, the difference between the coefficient of friction during motion and that at the commencement of motion or of repose will not be so marked, for other resistances may come into action not due solely to surface friction of the mass. A surface may become indented or roughened thus offering opposition to motion not existing at the commencement of movement, and particularly so in any earth of a mixed character possessing hard particles, such as boulders, or sand in clay. On the other hand, in the case of hard rock, solid clay, or other homogeneous earth, the difference between friction during motion and that of friction at rest may be reliably determined.
In soils of a granular or gritty nature small particles become detached during motion, and by pressure occupy or become wedged into any cavities upon the surfaces, and therefore offer resistance which is not alone due to friction of a mass upon a like mass. From this cause friction during motion may seemingly even become greater than during rest, but with material consisting of rounded particles that will not wedge, the friction upon a sliding surface may be lessened by reason of the grains revolving.
In deducing a slope of repose for earth, the lowest value of frictional resistance, whether during motion or at rest, should be taken, and always as if the surfaces were wet. The coefficients of friction, F, during motion usually range between 0·25 to 1·10, and the slope of repose, S to 1, is consequently found by the expression—
S = 1
F,