{"id":534,"date":"2025-03-12T04:28:43","date_gmt":"2025-03-12T04:28:43","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/6-17-pile-driving-formulas\/"},"modified":"2026-03-16T14:11:36","modified_gmt":"2026-03-16T14:11:36","slug":"6-17-pile-driving-formulas","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/6-17-pile-driving-formulas\/","title":{"raw":"6.17 Pile driving formulas","rendered":"6.17 Pile driving formulas"},"content":{"raw":"An alternative method for determining the collapse load of driven piles in situ<\/em> is to correlate it with the energy required to drive the pile into the soil. Several equations have been proposed for this and are implemented in pile driving equipment software to verify whether a pile has reached the required ultimate geotechnical strength Qf<\/sub><\/em> when driven at the pre-determined depth (or determine the penetration depth where the required Qf<\/sub><\/em> is reached).\n\nOne of the earliest equations is the Engineering News (EN) Record formula<\/em>, which was derived in 1888 by AM Wellington, editor of the Engineering News Record, to measure the capacity of light-weight timber piles on the basis of work-energy theory (Lawton et al. 1986):\n\n(6.85)<\/strong> [latex]{Q_{f,test}} = \\dfrac{{{n_1}{W_R}h}}{{{s_p} + {C_1}}}[\/latex]\n\nwhere WR<\/sub><\/em> is the weight of the hammer; h<\/em> is the height of fall; sp<\/sub><\/em> is the pile penetration depth per blow, taken as the average value obtained from the last few driving blows; C1<\/sub><\/em> is a constant, equal to C1 <\/sub><\/em>= 25 mm for drop hammers and C1 <\/sub><\/em>=2 .5 mm for steam hammers; n1<\/sub><\/em> is a constant depending on the hammer efficiency, provided in Table 6.11.\n\n\n\n\n\n\n
Table 6.11. <\/strong>Typical values for the n1<\/sub><\/em> factor (Budhu 2011).<\/caption>\n
Hammer type<\/th>\nn1<\/sub><\/em><\/th>\n<\/tr>\n
Drop hammer<\/td>\n0.75-1.0<\/td>\n<\/tr>\n
Single-acting hammer<\/td>\n0.75-0.85<\/td>\n<\/tr>\n
Double-acting hammer<\/td>\n0.85<\/td>\n<\/tr>\n
Diesel hammer<\/td>\n0.85-1.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nThe EN formula has been modified several times over the years, to account for developments in driving technology. A more recent version of Eq. 6.85 is (Michigan State Highway Department 1965):\n\n(6.86)<\/strong> [latex]{Q_{f,test}} = \\left( {\\dfrac{{{E_{EN}}{W_R}h}}{{{s_p} + C}}} \\right) \\times \\left( {\\dfrac{{{W_R} + n_{EN}^2{W_p}}}{{{W_R} + {W_p}}}} \\right)[\/latex]\n\nwhere EEN<\/sub><\/em> is the efficiency of the hammer, from Table 6.12; C = <\/em>2.54 mm (s<\/em> and h<\/em> in mm too); Wp<\/sub><\/em> is the weight of the pile; nEN<\/sub><\/em> is the coefficient of restitution between the hammer and the pile tip, provided in Table 6.13.\n\n\n\n\n\n
Table 6.12. <\/strong>Typical values for the EEN<\/sub><\/em> factor (Michigan State Highway Department 1965).<\/caption>\n
Hammer type<\/th>\nEEN<\/sub><\/th>\n<\/tr>\n
Single and double-acting hammer<\/td>\n0.70-0.85<\/td>\n<\/tr>\n
Diesel hammer<\/td>\n0.80-0.90<\/td>\n<\/tr>\n
Drop hammer<\/td>\n0.70-0.90<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
Table 6.13. <\/strong>Typical values for the nEN<\/sub><\/em> factor (Michigan State Highway Department 1965).<\/caption>\n
<\/td>\nnEN<\/sub><\/th>\n<\/tr>\n
Cast-iron hammer and concrete piles (without cap)<\/td>\n0.40-0.50<\/td>\n<\/tr>\n
Wood cushion on steel piles<\/td>\n0.30-0.40<\/td>\n<\/tr>\n
Wooden piles<\/td>\n0.25-0.30<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n ","rendered":"

An alternative method for determining the collapse load of driven piles in situ<\/em> is to correlate it with the energy required to drive the pile into the soil. Several equations have been proposed for this and are implemented in pile driving equipment software to verify whether a pile has reached the required ultimate geotechnical strength Qf<\/sub><\/em> when driven at the pre-determined depth (or determine the penetration depth where the required Qf<\/sub><\/em> is reached).<\/p>\n

One of the earliest equations is the Engineering News (EN) Record formula<\/em>, which was derived in 1888 by AM Wellington, editor of the Engineering News Record, to measure the capacity of light-weight timber piles on the basis of work-energy theory (Lawton et al. 1986):<\/p>\n

(6.85)<\/strong> [latex]{Q_{f,test}} = \\dfrac{{{n_1}{W_R}h}}{{{s_p} + {C_1}}}[\/latex]<\/p>\n

where WR<\/sub><\/em> is the weight of the hammer; h<\/em> is the height of fall; sp<\/sub><\/em> is the pile penetration depth per blow, taken as the average value obtained from the last few driving blows; C1<\/sub><\/em> is a constant, equal to C1 <\/sub><\/em>= 25 mm for drop hammers and C1 <\/sub><\/em>=2 .5 mm for steam hammers; n1<\/sub><\/em> is a constant depending on the hammer efficiency, provided in Table 6.11.<\/p>\n\n\n\n\n\n\n\n
Table 6.11. <\/strong>Typical values for the n1<\/sub><\/em> factor (Budhu 2011).<\/caption>\n
Hammer type<\/th>\nn1<\/sub><\/em><\/th>\n<\/tr>\n
Drop hammer<\/td>\n0.75-1.0<\/td>\n<\/tr>\n
Single-acting hammer<\/td>\n0.75-0.85<\/td>\n<\/tr>\n
Double-acting hammer<\/td>\n0.85<\/td>\n<\/tr>\n
Diesel hammer<\/td>\n0.85-1.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The EN formula has been modified several times over the years, to account for developments in driving technology. A more recent version of Eq. 6.85 is (Michigan State Highway Department 1965):<\/p>\n

(6.86)<\/strong> [latex]{Q_{f,test}} = \\left( {\\dfrac{{{E_{EN}}{W_R}h}}{{{s_p} + C}}} \\right) \\times \\left( {\\dfrac{{{W_R} + n_{EN}^2{W_p}}}{{{W_R} + {W_p}}}} \\right)[\/latex]<\/p>\n

where EEN<\/sub><\/em> is the efficiency of the hammer, from Table 6.12; C = <\/em>2.54 mm (s<\/em> and h<\/em> in mm too); Wp<\/sub><\/em> is the weight of the pile; nEN<\/sub><\/em> is the coefficient of restitution between the hammer and the pile tip, provided in Table 6.13.<\/p>\n\n\n\n\n\n\n
Table 6.12. <\/strong>Typical values for the EEN<\/sub><\/em> factor (Michigan State Highway Department 1965).<\/caption>\n
Hammer type<\/th>\nEEN<\/sub><\/th>\n<\/tr>\n
Single and double-acting hammer<\/td>\n0.70-0.85<\/td>\n<\/tr>\n
Diesel hammer<\/td>\n0.80-0.90<\/td>\n<\/tr>\n
Drop hammer<\/td>\n0.70-0.90<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
Table 6.13. <\/strong>Typical values for the nEN<\/sub><\/em> factor (Michigan State Highway Department 1965).<\/caption>\n
<\/td>\nnEN<\/sub><\/th>\n<\/tr>\n
Cast-iron hammer and concrete piles (without cap)<\/td>\n0.40-0.50<\/td>\n<\/tr>\n
Wood cushion on steel piles<\/td>\n0.30-0.40<\/td>\n<\/tr>\n
Wooden piles<\/td>\n0.25-0.30<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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