CPT Calculator — qc, fs, u2 to Geotechnical Parameter Correlations
The Cone Penetration Test (CPT) and its variant with pore pressure measurement (CPTu) provide a continuous record of three variables: tip resistance (qc), sleeve friction (fs), and pore pressure (u2). This calculator transforms these three numbers into the design parameters you need for foundation design: friction angle φ in sands, relative density Dr, undrained shear strength Su in clays, OCR, and soil type. It uses the consolidated correlations of Robertson 1990, Kulhawy & Mayne 1990, and Mayne 2007, a mandatory reference in soil mechanics studies for bridge, wind turbine, and high-rise building projects.
What is it and when is it applied?
The CPT drives a 60° cylindrical cone (diameter 35.7 mm, area 10 cm²) at a constant rate of 20 mm/s and records qc and fs every 1-2 cm. The CPTu adds a pressure transducer behind the tip. The advantage over the SPT is the continuity of the record and repeatability. It is applied in loose to medium sands, soft to medium clays, and silts; it loses precision in gravels (the cone refuses) and in rocks. It is mandatory in projects with Vs30 < 180 m/s for seismic classification DS 61/2011, and highly recommended in port, anchored wall, and high-rise building projects with deep foundations.
Applied Formulas
Friction ratio (soil type): Rf = (fs / qc) · 100 [%]
Pore pressure parameter: Bq = (u2 − u0) / (qt − σv0), with qt = qc + u2·(1 − a), a ≈ 0.8
Friction angle in sands (Kulhawy & Mayne 1990):
φ' = 17.6° + 11.0° · log₁₀(qt1N), where qt1N = (qt / pa) · (pa / σ'v0)^0.5, pa = 101.3 kPa
Relative density (Baldi et al. 1986):
Dr = (1/2.91) · ln[qc / (157 · (σ'v0 / pa)^0.55)] · 100 [%]
Undrained shear strength in clays:
Su = (qt − σv0) / Nkt, with Nkt = 12-18 (typically 14 in normal clays)
Overconsolidation ratio OCR (Mayne 1991):
OCR = k · (qt − σv0) / σ'v0, k ≈ 0.33 for soft clays
Soil type (Robertson 1990): chart Ic = √((3.47 − log Q)² + (log F + 1.22)²), with Q = qt1 and index F = fs / (qt − σv0) · 100
Calculation example
| Parameter | Value |
|---|---|
| Analysis depth z | 6.0 m |
| Water table | 1.5 m below surface |
| γ above water table | 17 kN/m³ |
| γsat below water table | 19.5 kN/m³ |
| qc measured at z=6 m | 8.5 MPa |
| fs measured | 85 kPa |
| u2 measured | 60 kPa |
| u0 hydrostatic | (6 − 1.5) · 9.8 = 44.1 kPa |
Vertical stresses at z = 6 m: σv0 = 17 · 1.5 + 19.5 · 4.5 = 25.5 + 87.75 = 113.3 kPa. σ'v0 = σv0 − u0 = 113.3 − 44.1 = 69.2 kPa. We correct qc → qt: qt = qc + u2·(1 − 0.8) = 8,500 + 60·0.2 = 8,512 kPa ≈ 8.51 MPa. Rf = (fs/qc)·100 = (85/8,500)·100 = 1.0 %. Bq = (60 − 44.1)/(8,512 − 113.3) = 15.9/8,398.7 = 0.002 → almost zero, indicative of sand. qt1N = (8,512/101.3) · (101.3/69.2)^0.5 = 84.0 · 1.209 = 101.6. Friction angle: φ' = 17.6 + 11·log₁₀(101.6) = 17.6 + 11·2.007 = 17.6 + 22.1 = 39.7°. Relative density: Dr = (1/2.91)·ln[8,500/(157·(69.2/101.3)^0.55)]·100 = 0.344·ln[8,500/(157·0.823)]·100 = 0.344·ln(65.8)·100 = 0.344·4.19·100 = 143.9 % → Dr is limited to 100 % = very dense. With Rf = 1 % and high Q, Robertson places the sample in zone 6 (clean sands to silty sands).
Result: φ' ≈ 40° · Dr ≈ 100 % (very dense) · Robertson type zone 6 (sand) · Bq ≈ 0 (drained).
Interpretation of results
The CPT describes a very dense sand, relatively well-graded, with no generation of excess pore pressure upon penetration (Bq ≈ 0). A φ' of 40° is typical of mechanically compacted sands or ancient alluvial sediments. For shallow foundations you can use this φ' in Terzaghi/Vesic with a reduction factor of 1-2° for cone scale effects versus the actual footing diameter. Be cautious extrapolating Dr > 85 %: the Baldi method saturates and it is recommended to report "Dr > 85 % / very dense" without an exact number.
Reference standards
- ASTM D5778 — Standard test method for electronic friction cone and piezocone penetration testing
- ISO 22476-1 — Geotechnical investigation — Field testing part 1: electrical cone and piezocone
- Robertson, P.K. (1990). Soil classification using the cone penetration test
- Kulhawy, F.H. & Mayne, P.W. (1990). Manual on estimating soil properties for foundation design, EPRI EL-6800
- Baldi, G. et al. (1986). Interpretation of CPT and CPTu — Part 2
Frequently asked questions
CPT or SPT, which is better?
CPT is more accurate, repeatable, and provides a continuous record. SPT is cheaper and detects gravels. In clean sands and soft clays CPT wins; in alluvial gravels and sanitary landfills SPT remains because the cone refuses. The ideal is to combine both in relevant projects: SPT every 1.5 m for correlation and continuous CPT for the detailed profile.
What is the Nkt factor and how do I choose it?
Nkt relates (qt − σv0) to Su in clays. Typical values: 10-12 for very soft clays, 14-16 for normal clays, 16-20 for stiff clays. If you have a UU triaxial test or laboratory data, calibrate Nkt on site and use it throughout the profile. Without calibration, use 14 and report the ±20 % uncertainty.
How is liquefaction detected with CPT?
Robertson & Wride 2009 provides the standard method: calculate the normalized and fines-corrected qc1Ncs, then compare with the CRR curve of the design earthquake. If CSR > CRR there is liquefaction. According to the national code, the maximum probable earthquake with Ao according to seismic zone is used. See the dedicated liquefaction calculator.
Is CPT useful for direct bearing capacity?
Yes. Direct methods (Schmertmann 1978, Eslami & Fellenius 1997) calculate qult of a footing without going through φ: qult = kq · average qc in the influence zone (B below the base). For driven piles: the LCPC-Bustamante & Gianeselli 1982 method is the European standard and provides qs (shaft friction) and qp (tip) directly from qc.