Foundations · Pile testing & NDT
Dynamic pile test (PDA): CASE method capacity calculator
From the force and velocity measured at the pile head at the peak (t1) and one wave return later (t1 + 2L/c): total resistance RTL, static resistance RSP with Case damping, driving stress and the design capacity.
Standard: ASTM D4945 · AS 2159-2009 Section 8 · CASE method (Rausche & Goble)
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Pile length below gauges L | 20 | m |
| Pile modulus E | 40 | GPa |
| Pile area at gauges A | 0.2025 | m² |
| Wave speed c | 4000 | m/s |
| Force at t1 (first peak) | 3620 | kN |
| Velocity at t1 | 1.669 | m/s |
| Force at t1 + 2L/c | 420 | kN |
| Velocity at t1 + 2L/c | -0.15 | m/s |
| Case damping Jc (toe soil) | 0.4 | |
| Permanent set per blow | 4 | mm |
| Concrete f′c (driving stress check) | 50 | MPa |
| Design action E* | 1200 | kN |
| Geotechnical reduction φg | 0.65 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Impedance Z = EA/c | 2,025 | kN·s/m |
| Wave return time 2L/c | 10.00 | ms |
| Z·v1 | 3,380 | kN |
| Z·v2 | -303.8 | kN |
| Downward wave at t1 = (F1 + Zv1)/2 | 3,500 | kN |
| Upward wave at t2 = (F2 − Zv2)/2 | 361.9 | kN |
| Peak compressive stress F1/A | 17.88 | MPa |
| Limit: driving stress 0.85f′c | 42.50 | MPa |
| Total resistance RTL = ½[(F1 + Zv1) + (F2 − Zv2)] | 3,862 | kN |
| Static resistance RSP = RTL − Jc(2Fd1 − RTL) | 2,607 | kN |
| Design capacity φg·RSP | 1,694 | kN |
- ✓ φg·RSP ≥ E*
- ✓ Driving stress ≤ 0.85f′c
- ✓ Set ≥ 2 mm/blow (resistance substantially mobilised)
Method, formulas and assumptions
- Impedance Z = EA/c = 40*1000000*0.2025/4000 = 2025 kN·s/m
- Wave return time 2L/c = 2*20/4000*1000 = 10 ms
- Z·v1 = 2025*1.669 = 3379.7 kN
- Z·v2 = 2025*-0.15 = -303.75 kN
- Downward wave at t1 = (F1 + Zv1)/2 = (3620+3379.7)/2 = 3499.9 kN
- Upward wave at t2 = (F2 − Zv2)/2 = (420--303.75)/2 = 361.88 kN
- Peak compressive stress F1/A = 3620/0.2025/1000 = 17.877 MPa
- Limit: driving stress 0.85f′c = 0.85*50 = 42.5 MPa
- Total resistance RTL = ½[(F1 + Zv1) + (F2 − Zv2)] = 3499.9+361.88 = 3861.7 kN
- Static resistance RSP = RTL − Jc(2Fd1 − RTL) = 3861.7-0.4*(2*3499.9-3861.7) = 2606.5 kN
- Design capacity φg·RSP = 0.65*2606.5 = 1694.3 kN
- RSP assumes the toe resistance is mobilised and damping acts at the toe. Confirm capacity by signal matching (CAPWAP) on representative blows, as AS 2159 requires for higher φg.
- φg for dynamic testing depends on the testing proportion and the risk rating (AS 2159 Cl 4.3); enter the value from your assessment.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.