Optimum Penetration of Friction Piles

How deep and how hard should a friction pile be driven to achieve the minimum unit cost of bearing capacity? The tradeoffs are modeled in terms of optimum depth of penetration limited by: (1) Available order length; and (2) allowable blow count on the last foot of penetration. Usually, it will prove cost effective to drive the longest pile available as deep and as hard as possible no matter how much time is required, as long as the pile is not damaged. There exists a narrow range of conditions where this approach is contraindicated. A suitable formula for finding the optimum depth of penetration within the range is derived. The increase in blow count with increased penetration is developed as gradient $r*\text{.}$ As a dimensionless factor, this parameter is a relative measure of the resistance of soil to penetration. Among other uses it is a measure of work. This factor can also be expressed in blows per foot (meter) per foot (meter). In this context, it is used with the formula for finding the optimum depth of penetration.