Method, limits and references
How the pile drivability tool works, what it leaves out, and where its methods come from. Version 0.2.3.
Disclaimer
The tool is offered as is, without warranty. It does not replace a site investigation, a qualified engineer's judgement, a commercial wave equation program, or dynamic and static load testing on the actual piles. Nothing typed into the tool is saved. To keep the tool available for everyone, it limits how often one address can run an analysis and keeps a short log of refused requests. Each address can run one analysis a minute and 10 a day.
Method
Wave equation analysis (tab 02)
The pile is modelled after Smith (1960) as a chain of lumped masses joined by springs. Each segment carries a soil element on its side, and the toe has its own element. Each soil element is elastic up to a displacement called the quake, then perfectly plastic at its share of the static resistance, plus a viscous (Smith) damping term that adds resistance in proportion to velocity. The hammer is a rigid ram that strikes a cushion spring at an impact speed of √(2 · efficiency · g · stroke). The cushion carries compression only: it can push the ram and the pile apart but never pull them together, and the ram may leave the cushion on rebound. The equations are stepped forward in time with an explicit scheme whose time step is kept below the travel time of a stress wave across one segment and below the natural period of the stiffest spring and mass pair, the cushion included.
One run gives the permanent set per blow, the peak compression and tension along the pile and the energy delivered. The bearing graph repeats the run at several multiples of the soil resistance to relate resistance to blow count. The driveability profile against depth is derived from that bearing graph (resistance accumulated with depth, then interpolated); it is not a separate wave equation run at each depth, and it does not model soil setup, relaxation or fatigue of the soil during driving.
Driving stress check
Peak compression is compared with the AASHTO driving stress limit reproduced in FHWA-HI-97-013 (Section 11.3): 0.9 × minimum yield strength for steel piles. With no steel grade selected the check reports "not evaluated" rather than passing.
Signal matching (tab 04)
The signal matching tab follows the idea of Rausche, Goble and Likins (1985): adjust the soil model until the computed pile top force matches the measured one, given the measured velocity. Here it is an automated least squares search over a small set of parameters. What it does: fits total resistance, its split along the shaft and toe, quakes and damping to a force and velocity record, and reports the match quality. What it does not do: it is not the commercial CAPWAP program, it has not been calibrated against static load tests, it cannot tell whether a record is of good quality, and a good match does not prove a unique answer. The included records are synthetic, generated by this engine.
Main assumptions
- One-dimensional, linear elastic pile with uniform properties along its length.
- Soil modelled by Smith quake and damping; no radiation damping, no soil plug dynamics, no residual stress between blows.
- Hammer reduced to a ram, an efficiency, a cushion stiffness and a cushion coefficient of restitution (1.0 by default, so the cushion stores and returns energy without loss); no separate helmet mass and no diesel combustion model.
- Default quake and damping values are textbook starting points (FHWA GEC-12 Vol II §12.6.7), not site measurements.
Known limits
- Cushion stiffness is an assumed value in most runs and changes the peak stresses. Very stiff cushions (above about 3,000,000 kN/m) give sharper peaks and more tension; use a value typical of the real hammer cushion and helmet. The energy closure figure shown with each run should stay small; a few percent or more means the run needs more segments or time steps.
- Each request is limited in size and run time on this host, and each address to one analysis a minute and 10 in any 24 hours.
- Vibratory driveability is an early estimate with its own on-screen notes.
Worked example: open-ended steel pipe pile in a made-up layered soil
Example only, not a real site
A 610 mm steel pipe pile, 21 m long, driven 20 m into an invented profile of soft clay over medium dense and dense sand, using a published catalogue hydraulic impact hammer. Every soil number is a round, made-up value chosen to show how the tool works.
| Pile | An open-ended steel pipe, 610 mm outside diameter with a 12.7 mm wall (steel area 0.0238 m²), 21 m long. 1 m stays above ground, 20 m goes into the soil. Steel stiffness 210 GPa, density 7850 kg/m³, grade S355 (minimum yield 355 MPa). |
|---|---|
| Model detail | The pile is cut into 100 short segments joined by springs. More segments give a finer answer and take longer to run. |
| Hammer | Hydraulic impact hammer from the published catalogue data (ram mass and stroke read from the manufacturer's datasheet record). The tool turns the drop into impact speed using an assumed 80% efficiency, a typical starting value for this hammer type, not a measured one. |
| Cushion | A stiffness of 500,000 kN/m stands in for the hammer cushion and helmet. It is an assumed round value; real cushions vary and change the stresses. |
| Soil layers | Positions are measured down the pile from its head. 1 to 6 m: soft clay, about 10 kPa skin friction, 96 kN in total. 6 to 15 m: medium dense sand, about 25 kPa, 431 kN. 15 to 21 m: dense sand, about 45 kPa, 517 kN. These are invented values for a demonstration. |
| Toe | 450 kN of end bearing on the steel ring at the toe (the pile is assumed to drive unplugged). |
| Quake and damping | Quake is how far the soil moves before it yields: 2.5 mm everywhere here. Damping adds resistance that grows with pile speed: 0.65 s/m in the clay, 0.16 s/m in the sands and 0.50 s/m at the toe. These are textbook-style starting values (Smith 1960; FHWA GEC-12 Vol II §12.6.7, converted from s/ft), not site measurements. |
| Total resistance | About 1494 kN of soil resistance at the end of driving (skin plus toe). The bearing graph repeats the run at other resistance levels to show how blow count changes. |
| Hammer record | Junttan HHK 7A (Junttan Oy): ram 7000 kg, stroke 1.2 m, rated energy 82 kJ. Source: Junttan HHK 7A (/9) datasheet. |
How to read the result
- Blow count: blows needed for 250 mm of penetration at this resistance. Below about 10 to 20 blows per 250 mm is easy driving; values approaching about 100 blows per 250 mm (refusal) mean the hammer may not get the pile down.
- Driving stress: the highest compression in the pile during a blow. It must stay below the limit, here 0.9 × 355 = 319.5 MPa.
- Tension: matters most for concrete piles; shown for completeness.
Typical outputs on the reference build. Since v0.2.1 the cushion carries compression only, so the rebound tension spike older builds reported is gone. Small differences between builds are normal.
| Blow count | 10.8 blows per 250 mm (set 23.1 mm per blow) |
|---|---|
| Peak compression | 134.7 MPa, 42% of the 319.5 MPa limit |
| Peak tension | 1.4 MPa |
| Energy into the pile | 64.5 kJ of 82 kJ rated |
| Energy closure | 0.65% |
Open the tool and press "Run the worked example".
References
- Smith, E.A.L. (1960). Pile-driving analysis by the wave equation. Journal of the Soil Mechanics and Foundations Division, ASCE, 86(SM4), 35 to 61. doi:10.1061/JSFEAQ.0000281
- Hannigan, P.J., Rausche, F., Likins, G.E., Robinson, B.R. and Becker, M.L. (2016). Design and Construction of Driven Pile Foundations, Geotechnical Engineering Circular No. 12, Vol. I (FHWA-NHI-16-009) and Vol. II (FHWA-NHI-16-010). Federal Highway Administration, Washington DC. fhwa.dot.gov GEC 12
- Hannigan, P.J., Goble, G.G., Thendean, G., Likins, G.E. and Rausche, F. (1998). Design and Construction of Driven Pile Foundations, Vol. I (FHWA-HI-97-013). Federal Highway Administration, Washington DC. rosap.ntl.bts.gov/view/dot/58200
- Rausche, F., Goble, G.G. and Likins, G.E. (1985). Dynamic determination of pile capacity. Journal of Geotechnical Engineering, ASCE, 111(3), 367 to 383.
- ASTM D4945, Standard Test Method for High-Strain Dynamic Testing of Deep Foundations. ASTM International, West Conshohocken PA (cited, not reproduced).
- DNV-RP-C203, Fatigue design of offshore steel structures. DNV. dnv.com
- Hammer data: each catalogue entry links to the manufacturer's own published datasheet.
Version and changes
Tool version 0.2.3.
- 0.2.3 (2026-10-31): fair-use limits so the shared server stays responsive: one analysis a minute and 10 a day per address (rolling 24 hours, repeats included), with a countdown when a limit is reached and a "Runs left today" line by the Run buttons.
- 0.2.2 (2026-10-31): new look to match the GeoMan ANZ site: drawing frame and title block, site fonts and colours, inputs set out as schedules, results as a calculation summary with OK and CHECK stamps, plots restyled. No change to the engine or its numbers.
- 0.2.1 (2026-10-31): cushion energy fix. The cushion force is now taken at one time level, the cushion pushes but never pulls, and the time step respects the cushion. The hammer can no longer deliver more energy than the ram had. Worked example: set 23.1 mm (was 22.5), peak tension 1.4 MPa (was about 35).
- 0.2.0 (2026-10-31): configurable URL prefix for hosting under /tools/pile-drivability/app/, request size and run limits, error messages without internal details, this method and limits page, the disclaimer banner, and a one-click fictional worked example. Driving stress limits now cited to FHWA-HI-97-013.
- 0.1.0 (2026-09-28): first internal release: wave equation, bearing graph, PDA signal processing, automated signal matching, fatigue, vibratory estimate and hammer catalogue.