The practical conclusion of this whole assumption is that the material in the area, F E C B B{1}_, forms with the equivalent opposite area an arch reacting against the face, C B B{1}_ and that, as heretofore noted, the lower half (or its equivalent, B D{1} G B_) of the weight of this is assumed to be carried by the structure, the upper half being self-sustaining, as shown by the line, B{III} D_{IV}_ (or, for absolute safety, the curved line), and therefore, if rods could be run from sheeting inside the tunnel area to a point outside the line, F B{1}_, as indicated by the lines, 5, 6, 7, 8, 11, 12, 13, etc., that the internal bracing of this tunnel could be omitted, or that the tunnel itself would be relieved of all loading, whereas these rods would be carrying some large portion at least of the weight within the area circumscribed by the curve, D{II} I T G_, and further, that a tunnel structure of the approximate dimensions shown would carry its maximum load with the surface of the ground between D{IV}_ and F, beyond which point the pressure would remain the same for all depths.

In calculating pressures on circular arches, the arched area should first be graphically resolved into a rectangular equivalent, as in the right half of Fig. 4, proceeding subsequently as noted.

The following instances are given as partial evidence that in ordinary ground, not submerged, the pressures do not exceed in any instance those found by the above methods, and it is very probable that similar instances or experiences have been met by every engineer engaged in soft-ground tunneling: 

In building the Bay Ridge tunnel sewer, in 62d and 64th Streets, Brooklyn, the arch timber bracing shown in Fig. 1, Plate XXVI, was used for more than 4,000 ft., or for two-thirds of the whole 5,800 ft. called for in the contract.  The external width of opening, measured at the wall-plate, averaged about 19 ft. for the 141/2-ft. circular sewer and 191/2 ft. for the 15-ft. sewer.  The arch timber segments in the cross-section were 10 by 12-in.  North Carolina pine of good grade, with 2 in. off the butt for a bearing to take up the thrust.  They were set 5 ft. apart on centers, and rested on 6 by 12-in. wall-plates of the same material as noted above.  The ultimate strength of this material, across the grain, when dry and in good condition, as given by the United States Forestry Department tests is about 1,000 lb. in compression.  Some tests[C] made in 1907 by Mr. E.F.  Sherman for the Charles River Dam in Boston, Mass., show that in yellow pine, which had been water-soaked for two years, checks began to open at from 388 to 581 lb. per sq. in., and that yields of 1/4 in. were noted at from 600 to 1,000 lb.  As the tunnel wall-plates described in this paper were subject to occasional saturation, and always to a moist atmosphere, they could never have been considered as equal to dry material.