The term cohesion will be employed for the force uniting the particles of the earth, whether that force be adhesion or true cohesion. Friction resists the separation of surfaces only when motion is attempted parallel to the surface of contact, while cohesion resists motion in any direction. Cohesion is proportional to the area of contact, depends upon the nature of the materials, and is independent of the normal pressure.
The coefficient of cohesion, i.e., a measure of the cohesion of earth, may be obtained as follows: Dig a number of trenches of different depths with vertical sides, and lengths several times their widths. Examine the trenches from time to time, and after several days it will be observed that all over a certain depth will have caved along a line something like CD, Fig. 109. Measure the distance EC, being careful to choose a trench in which C is at least some little distance above the bottom of the trench. If h = EC, w = the weight of a cubic unit of the earth, = the angle of repose, and C = the coefficient of cohesion, then * If w = 100 lb. per cu. ft., and = then C = 14.4 h, which shows that in ordinary soil cohesion is equal to 14.4 lb. per sq. ft. per linear foot of vertical rupturing depth. This value of the co efficient of cohesion is for earth under comparatively light com pression; but experiment and experience show that compression increases the cohesion, and therefore the value of C deduced as above is too small for any practical retaining wall.
Equation 10 was deduced on the assump tion that the surface of rupture is a plane, but it is near enough correct to show that under ordinary conditions cohesion is great enough to affect materially the formulas for the lateral thrust of earth. All formu las for earth pressure assume that the material to be supported is clean, dry sand—a material that is seldom, or never, found in practice,—and as all other soils possess considerable cohe sion, all formulas for earth pressure must be regarded as approxi mate owing to the disregard of cohesion.
There is a great difference of opinion among recognized authorities as to the reliability of the theories of earth pressure. Some contend that the results are of little or no practical value, while others claim that the theories are as trustworthy as the theoretical analysis relating to any other branch of construction. It is proposed to consider the preceding theoretical formulas in the light of experience and ex periments.
All theories of earth pressure are based upon three assumptions, each of which has been seriously questioned. The first of these
assumptions is that the surface of rupture is a plane; the second that the point of application of the resultant pressure is at of the height of the wall from the bottom; and the third relates to the angle between the back of the wall and the resultant pressure. For con venience, each of these assumptions will be considered separately, although they are not entirely independent.
This assumption is most nearly correct in the case of dry, clean sand, and most in error with a tough, tenacious clay. In practice, sand is seldom either dry or clean; and usually the material behind the wall is not even approximately pure sand. Therefore, in most cases this assumption is considerably in error. It is common ex perience that banks of earth will frequently stand, at least for some time, at an angle considerably greater than the frictional angle of repose, which is proof that under ordinary conditions the cohesion of the earth is sufficient to modify materially the theoretical results for the lateral pressure.
Further, universal experience shows that when a bank of earth breaks away, as when a trench caves in (whether or not it is sheeted), or when a retaining wall fails, the surface of rupture is not a plane, but is nearly vertical near the top, and has a decided curvature at the bottom, i.e., has a form somewhat like the curve CD in Fig. 107, page 490.* In a rough way the line of fracture on the surface AD, Fig. 107, is usually at a distance back from the vertical face equal to about half the height of the face. The surface of rupture is sub stantially the same whether the earth is in its natural undisturbed position or is an artificial fill, unless the latter is freshly made and composed of nearly dry material. Of course, any bank of earth will in time take a slope at approximately the so-called angle of repose; but even then the surface of repose is not strictly a plane, since at its upper edge the surface is convex upward and at its lower edge is concave upward. However, this natural slope is not due to any cleavage plane in the material, but to the action of rain and wind, and perhaps also of frost.