, but, from the observed heights of trenches which have stood without sheathing, it is probable that values of
from 100 to 300 lb. per sq. ft. can be counted on for most trenching. For the present, the only safe way is to be guided by experience, such as has been elicited by Mr. Meem’s paper, “The Bracing of Trenches and Tunnels, With Practical Formulas for Earth Pressures.”
As to the exact distribution of the stresses, theory cannot speak definitely, for the conditions are different from those in the case of the retaining wall, the passive resistance of which opposes the active earth thrust. For the braced trench, the earth, at first, simply resists the active pressure exerted by the braces, when first put in and keyed-up tight, particularly on that upper portion where the active earth thrust is nothing or very small. As the construction proceeds, the braces will receive more and more of the active earth thrust, which necessarily increases with the depth of trench. In fact, the distribution of stress, indicated by the arrows in [Fig. 24], although true in the case of a retaining wall, where the earth has been deposited behind it, is not necessarily or generally true in a sheeted trench, because of the manner of its construction. Thus, in digging a trench, the bracing is put in at intervals, but when a brace is inserted near the bottom of the trench, the digging is continued for several feet without bracing, until a depth is attained at which it is thought best to insert another brace. Before the latter is put in, the unprotected face of the trench, say 6 ft. in depth, can exert no pressure, as it would in the case of the retaining wall. The thrust that would be exerted, for this area, on the supposed wall, does not exist for the unsupported face of the trench, for the full horizontal thrust of the earth for the whole depth has been taken up by the braces above the unsupported area. This state of affairs is characteristic of the work as it proceeds, the lowest brace that is put in at first carries only the stress due to the keying-up, but takes more and more stress as the excavation proceeds. It can thus very well happen that the upper or the middle braces may receive more stress in the end, than the lower braces. In fact, this was asserted to be generally true, for well-drained material, by many engineers in the valuable discussion on Mr. Meem’s paper referred to. Other engineers advised caution in accepting this view, and asserted that in wet or saturated ground the lower braces were most severely stressed. If it were possible to force a board of a size equal to the length and depth of a trench, vertically downward, excavate and brace, all in a millionth of a second, then one can conceive that the distribution of stress shown in [Fig. 24] might be realized; but, for trenches as actually constructed, the distribution of stress in the earth mass is very much altered from this, though it would appear that the total earth pressure would be given, at least approximately, by the construction of [Fig. 25], or by the use of [Equation (7)].
The writer hopes that Mr. Meem may agree to the foregoing explanation, for the subject of trenches was entered into in great detail, in order to explain, if possible, all the facts, as presented by many engineers who held very diverse views about the explanation of them. Mr. Meem’s [Fig. 22] can illustrate the writer’s view: if bracing only extends, say, from
to
, then the braces must exert sufficient horizontal thrust to prevent the descent of the wedge, say
