How Long to Reach Water: Excavated Volume, Hoisting Work, and Digging Time by Depth and Soil

Hand digging a well is often planned with a single rate: so many metres per day, continued downward until water is reached. This paper tests that planning habit with a transparent work model for a circular shaft of stated diameter, and finds that it does not survive the arithmetic. The shaft is divided into two kinds of work that behave differently with depth. Loosening a cubic metre of ground costs the same effort at any depth, while lifting the resulting spoil out of the shaft costs more time the deeper the digging face lies, because each bucket must be raised through a greater distance at a limited human power. Summing the two gives a total time that grows faster than depth: it contains a term proportional to depth and a second term proportional to the square of depth. For the nominal shaft the excavated volume to a depth of 20 m is 22.62 m³, corresponding to spoil masses of 38.45 t in loose sand and gravel, 40.72 t in medium clay, 42.98 t in stiff clay, and 47.50 t in weathered rock and hardpan, moved in 1,301, 1,414, 1,470, and 1,583 bucket lifts respectively. Modelled time to reach 20 m with a two-person team is 3.91 crew-days in loose sand and gravel, 5.70 crew-days in medium clay, 8.81 crew-days in stiff clay, and 19.57 crew-days in weathered rock and hardpan. The second 10 m of depth costs more than the first in every soil class: by 25.2% in loose sand and gravel, 17.7% in medium clay, 11.7% in stiff clay, and 5.7% in weathered rock and hardpan. Hoisting accounts for half of the instantaneous working time at a depth of 19.23 m in loose sand and gravel, 35.72 m in medium clay, 64.58 m in stiff clay, and 156.18 m in weathered rock and hardpan. The practical message is twofold. In soft ground the depth penalty arrives within the range of ordinary well depths and must be priced into any schedule. In hard ground loosening dominates for far longer, so progress is governed mainly by how slowly the face itself can be broken.