Bearing Power

5. There is no way of determining how much energy is consumed in overcoming the inertia of the pile and of the soil at the point of the pile. During the first stage of the blow this inertia has a retarding effect, but during the last stage it tends to increase the penetration; but we can know nothing about either the relative or the absolute amounts of these two effects.

The uncertainties in some of the above cases could be reduced somewhat by deducing a formula for a particular case, as for example a fixed height of fall; but such limitations would greatly detract from the value of such a formula, and at best some of the sources of error mentioned could not thus be eliminated. Therefore, most, if not all, engineers are agreed that a rational pile-driving formula is impracticable.

Not only are the usual theoretical formulas for the bearing power of a pile uncertain, but they are inapplicable to concrete piles or to piles sunk with a water jet. Such formulas are inapplicable to concrete piles owing to the uncertainty as to the energy consumed by the cushion driving-head; and obviously a formula involving the weight of a hammer can not be applied to piles sunk with the water jet, since no hammer is used.

In former editions of this volume the author made an attempt to deduce a rational pile-driving formula. For the most elaborate and a very able attempt to establish a rational formula for bearing power of piles, see an article by E. P. Goodrich, in Transactions of American Society of Civil Engineers, Vol. xLvitt, pages 150-219.

Incidentally the writer of that paper reviews the principal rational formulas for bearing power of piles.

Empirical Formulas.

Numerous empirical formulas have been proposed for the bearing power of piles, several of which claim to be "deduced from experiments"; but in former editions of this volume the author showed that nearly all of them were so defective as to be useless, either because they were of the wrong form, or because the constants were incorrectly determined, or because the limits of the experiments from which they were deduced made them inapplicable to pile driving.

Of all the empirical formulas proposed practically only one—the Engineering News formula—is used by American engineers.

776.

Engineering News Formula. This formula was proposed in 1888 by A. M. Wellington, editor of Engineering News, and is occasionally referred to as Wellington's formula. For a pile driven with a drop hammer, the formula is in which P is the safe load in pounds, W the weight of the hammer in pounds, h the fall of the hammer in feet, and s the penetration or sinking in inches, under the last blow, assumed to be sensible and at an approximately uniform rate. The sinking, s, must be measured only when there is no visible rebound of the hammer and only when the last blow is struck upon practically sound wood. This formula is supposed to give a factor of safety of six; and is also claimed to be safe, for ordinary weights of hammer and the usual height of fall.

The form to use for a pile driven with a single-acting steam hammer is The form to use for a pile driven with a double-acting steam hammer is in which a is the effective area of the piston in square inches, and p the mean effective steam pressure in pounds per square inch.

The above formulas are based upon the relation Ps = 12 W h. This equation would be strictly true if none of the energy of the descending weight were lost; but as there is always considerable loss, the proposer of the formula assumed that the use of a factor of safety of 6 would be sufficient to cover the effect of such loss. If the denominator of either of the above formulas contained s alone, then the formula would give an infinite bearing power when s = 0; and hence to eliminate this absurdity, the denominator of the formula for a drop-hammer pile-driver was made 8 + 1 and that for the steam hammer s + 0.1.

The reliability of the formula can be judged somewhat by an inspection of Table 65, page 394. The record of the first eight experiments is taken from an article in Transactions of American Society of Civil Engineers, Vol. xxvll, pages 146-60; and the last four from Engineering Record, Vol. XLIII, page 450. The first ref erence contains partial details of four tests not included in Table 65, and also gives the particulars of the power required to pull each of five other piles.