, derived from this equation, gives an extreme upper limit, which is doubtless never attained, as there is nearly always some support from the earth which has not broken out below the level of
.
Where the sheeting and bracing are of sufficient size, are tightly keyed up, and extend to the bottom of the trench, or where the bank is supported by a retaining wall, the earth near the bottom cannot break out, and the equation is not valid.
However, if, from any cause, such as insufficient sheeting, the break has taken place over even a part of
, the mass,
, above will tend to tip over at the top, giving the greatest pressure on the top braces. This appears to explain the phenomena observed by Mr. Meem and others in connection with some trenches.
With regard to tunnel linings, as is well known, the vertical pressure on the top is generally small, the great mass of earth vertically over the tunnel being largely held up by the friction of the earth (caused by the earth thrust) on its vertical sides, exactly as in the case of tall bins, where most of the weight of the grain is held up by the sides of the bin, the theory being very similar in the two cases. In consolidated earth, cohesion assists very materially in this action.