Contributions diverses: Tectonique.

1. TH. DAHLBLOM, The angle of shear (page 773).

2. ERNEST HOWE, Landslides and the sinking of ground above mines (page 775).

3. D. McDONALD, Excavation deformations (page 779). Discussion.

4. E. O. HOVEY, Note on landslides (page 793). Discussion.

5. GEORGE KNOX. Mining subsidence (page 797).

6. M. S. MASO and W. D. SMITH, The relation of seismic disturbances in the Philippines to geologic structure (page 807).

7. W. PAULCKE, Über tektonische Experimente (page 835).

THE ANGLE OF SHEAR.

BY

TH. DAHLBLOM,

Superintendent of Mines, Falun, Sweden.

The force of gravity creates a stress in the steep wall of a mine or in the side of a mountain, in the direction of least resistance. This action may be conceived as a wedging away of the rock from behind, or the force of gravity may be regarded as divided into two components, one in the direction of the least, the other in the direction of the greatest resistance (Fig. 1).

When the stress exceeds the tensile strength of the rock, a part will be wedged off. And, since the stress increases with the steepness of the exposed slope, the ratio between the stress and the tensile strength will result in a varying slope. The angle which this slope makes with the perpendicular is the angle of shear or the angle of pull.

The angle of shear depends not only on the tensile strength, but also on the elasticity of the rock. There is exerted against the plane A B (Fig. 2), both the pressure due to the weight of the rock above (=p) and the pressure due to the wedging force (= s), the resultant of which is u. This raises the compression of the rock in the section A B above the normal. And this abnormal compression causes a little sinking and also a slight horizontal movement of the rock between C and B, in consequence of which joints are opened and the cohesion or tensile strength of the rock is reduced.

If a large part of the rock falls, the sudden removal of the compressing mass will allow a sudden expansion in the abnormally compressed region, and this release manifests itself locally as an earthquake or concussion, which has the effect of reducing the friction. The initial friction, which is much greater than the friction during motion, is thus reduced and the

rock-fall and the angle of shear are correspondingly increased to much greater values than they would have had if the adjustment had been accomplished by creep or wedging off of small masses. Examples of this are afforded by great landslides, as that at Frank, Alberta, in 1903, where the angle of shear amounted to 52° 55° 20'1

Since the weight of the rock causes the stress, and the pressure due to weight increases with depth, the stress and the angle of shear must also increase with the depth. Also, great stress will cause rock-flowage. Hence, at sufficient depth the rock will be nearly plastic and the angle of pull or shear will be nearly 90°, as it is in liquids. Under insignificant pressure, on the contrary, the angle of shear will be negative, resulting in a vaulted room (Glockenbildung), a very common feature in the mining of coal or ore-seams (Fig. 3).

The question is, therefore, very complicated. The angle of shear depends on the pressure, the strength of the rock, the joints or cleavage in it, and on the size of the caved and unstable rock-mass. The angle of shear will be tangent to a curve (A B, Fig. 4).

The sides and bottoms of deep valleys are generally covered by talus, the weight of which balances the horizontal pressure. In mines worked by caying, the debris also offers more or less resistance to the horizontal force; consequently, reports on areas that have been mined should contain information not only as to the depth to which a mine has been worked out, but also as to the approximate depth of the débris in it. Information regarding this question is desirable, especially for mining men, and the experience neumulated in mining and railway and canal construction is the only source of this information. Collected, it means the conservation of life as

well as money

1 The pyar landslide at Frank, Alberta, Sessional Paper No. 25, Ann. Rep. Dept. of the Intori 'mada, 1903,

LANDSLIDES AND THE SINKING OF GROUND

ABOVE MINES.

BY

ERNEST HOWE,

Newport, R. I., U.S.A.

In many regions the settling of ground above extensive mine workings is of common occurrence and leads to serious damage to property on the surface, not only immed ately above the mines, but often at considerable distances away.

The force of gravity, exerted vertically downward, that tends to overcome equilibrium in a partially supported mass of rock or earth may be resolved into two components, one of which is in the direction of least resistance to movement; the angle that this component makes with the vertical has been called the "angle of pull." The surface area subject to disturbance depends upon the various angles of pull of the unstable ground, and a determination of these angles may sometimes be a matter of considerable importance.

1

Although the problem as suggested by DAHLBLOM is largely an engineering one, it may be considered with advantage from a geological point of view. PENCK has considered theoretically the conditions that may lead to landslides, and has shown that they are dependent on certain factors, some of which are purely mechanical while others are largely geological. These factors are the weight of the unstable mass, the cohesion of the rock, the coefficient of friction for the different materials involved, and, finally the angle of inclination from the horizontal of that surface which is one of least cohesion of the rock mass with the parent rock. Of these factors, the cohesion, or strength of the rock, together with the coefficient of friction, are dependent on a number of strictly geological conditions, and it is obvious that they have a direct influence on the value of the angle of pull. It is the purpose of the present paper to call attention to these geological factors; as far as they are concerned, the settling of ground above mines does not differ materially from surface slides, so that a review of the conditions affecting them may be of interest in the present connection.

In a study made some years ago in the mountains of southwest Colorado, the causes that were believed to have been responsible for the numerous landslides were summarized as follows:2

1 PENCK, A., Morphologie der Erdoberfläche, I, 222-231, 1894.

2 HOWE, E., Landslides of the San Juan Mountains, Colorado. Prof. Paper No. 67,

U.S. Geol. Surv., Washington, 1909.

Internal Causes:

1. Physical condition of the rocks. Cohesion, jointing, presence of soft or incompetent layers.

2. Structural conditions. Folding, faulting.

3. Topographic conditions. Oversteep hillsides or cliffs.

External Causes:

1. Earthquakes.

2. Readjustment of stresses within the mountains.

3. Saturation of the ground by water.

4. Frost.

These causes are essentially the same as those recognized by HEIM and others who have studied landslides in mountain regions.

It is unlikely that any one cause has ever been responsible for a landslide. In all cases that have been studied it has been found that two or more of the conditions mentioned have, in all probability, combined to bring about landslide action. It is agreed by all observers that internal conditions favourable to landslides may continue for long periods without any movement on the part of the threatened mass, and that some external element is necessary to give the final shove, as it were, which sets the unstable material in motion. It is improbable that any one, or even all, of the external causes could initiate landslides in a region of stability or where internal conditions favourable for landslides were lacking. The internal causes may be likened to the charge of dynamite in a drill-hole while the external cause is comparable to the lighting of the fuse.

Probably the commonest of the external causes of landslides is saturation of the ground by water. By this process the weight is increased and the coefficient of friction reduced, while, if the element of cohesion enters into the conditions, it also may be affected by the presence of water. In a large majority of landslides of which there are definite records and the pre-existing conditions are known, long continued or unusually heavy rains occurred before slipping took place.

Leaving the question of variation in weight of the unstable mass to the engineers, it will be seen that, other things being equal, the value of the angle of pull is directly dependent on certain physical and structural conditions of the rocks. As suggested under the head of the internal causes of landslides, the structural conditions of folding or faulting, jointing, and the presence of soft or incompetent layers are undoubtedly the most important from a practical point of view, since cohesion may be reduced to zero by any one of these factors. Nevertheless, weak rocks with little tenacity together with a low coefficient of friction, may offer ideal conditions for landslides, even if the other factors are lacking.

Many of the landslides of greatest magnitude in southern Colorado have been attributed to a shale horizon 375 metres thick which has failed to support massive rocks resting upon it. Sedimentary beds or rocks having a strongly developed slaty cleavage dipping in the direction of pull of an over