It is believed that the above rate of 0.002 ft. per sec., equivalent to 1⅜ ins. per minute, or 7 ft. per hour, is not sufficient to move any of the material. The velocity of water percolating through sand is found to vary directly as the head and inversely as the distance.
The value of “c” in the formula is larger for sands of filters favorable for flow, and smaller for compacted materials and dams.
Mr. Morison thought it might be nearer the actual conditions to assume d = 0.50 mm.; c = 500; and l = 5,000 ft.; in which case the seepage would only amount to 2.5 ft. per sec. In this last assumption the “effective size” of sand grains is 2½ times that classed as “permeable material” at the North Dike of the Wachusett Reservoir.
Prof. Philipp Forchheimer, of Gratz, Austria, recommends the use of the formula,
| h | |
| — = | a√ + b√² |
| l |
for the percolation through soils between loam and loamy sand. Sellheim, Masoni, Smreker, Kröber and other authorities on filtration use still other formulas, to which the reader and student is referred for further research.
The writer, having had occasion in his professional practice to study quite carefully the subject of ground waters, and their percolation or flow through different classes of materials and under varying conditions, is of the opinion that rarely does the cross-section of a stream-channel, filled with sand, gravel and debris, present, even approximately, a homogeneous or uniform mass; and that there are, almost without exception, strata of material much coarser and more porous than the general average. In other words, that it is extremely difficult to arrive at a uniformity coefficient. It is unwise to place much reliance upon an estimated flow where this is the case. The formula may be used with confidence where the layers are artificially made, and where there is no uncertainty regarding the uniform character of the material. In most natural channels there are distinct lines of flow, and under considerable hydrostatic head or pressure these lines of flow would surely enlarge. There is a wide difference between permissible and dangerously excessive percolation through an earth embankment. The local features, economical considerations and magnitude of the risks, all bear upon this question and must be considered for each particular case.
It is of interest to compare the estimated cost of the three designs proposed for the Bohio Dam, based upon the same unit prices, as follows:
| French Engineers’ design | $3,500,000 |
| Isthmian Canal Commissioners’ design | 8,000,000 |
| Mr. Morison’s design | 2,500,000 |
No comments will be made upon these figures, further than to remark that the successful building of a stable dam, accomplished by the use of an excessive quantity of materials and at a cost beyond reasonable requirements, is mainly instructive as illustrating “how not to do it.” It is creditable to execute substantial works at a reasonable cost, but it reflects no credit upon any one to construct them regardless of expense.