The raw field N-value recorded during a Standard Penetration Test is not ready for use in geotechnical design calculations. It reflects the energy actually delivered by the specific hammer used on that rig, the length of drill rods in the hole at the time of the test, the diameter of the borehole, the configuration of the split-spoon sampler, and the confining pressure of the surrounding soil — all of which vary between rigs, drillers, countries, and depths. Using uncorrected N-values in empirical correlations is one of the most common errors in SPT interpretation, and it can lead to significant overestimates or underestimates of soil properties.
This article explains each of the five SPT correction factors in full, gives the accepted expressions for each, shows how they combine in the (N1)60 formula, and provides a worked numerical example. Understanding these corrections — and applying them correctly — is essential before using SPT data for soil classification, bearing capacity estimation, or liquefaction assessment.
Why raw N-values cannot be used directly #
The SPT was first standardised in the United States in the 1950s, and for decades N-values from different rigs were compared and used in correlations without systematic energy measurement. Researchers gradually recognised that the actual energy delivered to the drill rods — which drives the sampler into the soil — varied enormously between equipment types and operating practices.
Field measurements conducted in the 1970s and 1980s (Seed et al., 1985; Skempton, 1986) established that the energy efficiency of commonly used hammer systems ranged from below 30% to above 90% of the theoretical free-fall energy. A donut hammer operated by an inexperienced driller on a worn cathead rope might deliver only 35–40% efficiency. A modern automatic hammer with a calibrated trip mechanism delivers 80–95%. In the same soil at the same depth, these two systems would produce N-values that differ by a factor of 2 or more — not because the soil is different, but because the test energy is different.
All empirical SPT correlations in the published literature were calibrated against a specific reference condition — a hammer energy efficiency of 60% of the theoretical free-fall energy. To use any published correlation validly, the raw field N must first be adjusted to what it would have been had it been measured under that reference condition. That is what the five correction factors achieve.
The (N1)60 formula #
The fully corrected SPT N-value, normalised to both 60% hammer energy and 100 kPa effective overburden stress, is:
(N1)60 = N × Ce × Cr × Cb × Cs × CN
where:
| Symbol | Factor name | Corrects for | Typical range |
|---|---|---|---|
| N | Raw field blow count | Uncorrected test value | 0–50+ (refusal >50) |
| Ce | Energy ratio correction | Hammer energy efficiency relative to 60% reference | 0.50–1.60 |
| Cr | Rod length correction | Energy loss in short rod strings | 0.75–1.00 |
| Cb | Borehole diameter correction | Reduced confinement in wide boreholes | 1.00–1.15 |
| Cs | Sampler liner correction | Presence or absence of liner in split-spoon | 1.00–1.20 |
| CN | Overburden stress correction | Normalises to 100 kPa effective vertical stress | 0.50–2.00 |
Each factor is described in detail in the sections below. Applied together, they transform the raw field N into a standardised value that can be legitimately compared between sites, rigs, and depths, and used in the published correlations for relative density, friction angle, liquefaction susceptibility, and other properties.
Ce — Energy ratio correction #
The energy ratio correction Ce is the most important of the five factors and the one with the largest potential impact on the corrected N-value. It accounts for the efficiency of the hammer system — specifically, what fraction of the theoretical free-fall energy (Etheoretical = m × g × h = 63.5 kg × 9.81 m/s² × 0.76 m ≈ 473 J) is actually transmitted to the drill rods and then to the sampler.
Ce = Er / 60
where Er is the energy ratio of the hammer system in percent. A hammer delivering 60% efficiency gives Ce = 1.0 — no correction needed. A hammer delivering 80% gives Ce = 80/60 = 1.33, meaning the corrected N60 will be 33% higher than the raw N (the same soil produced a lower blow count because more energy was delivered per blow).
Energy ratios by hammer type #
| Hammer type | Release mechanism | Typical Er (%) | Ce range |
|---|---|---|---|
| Safety hammer | Cathead & rope (2 turns), pinned drop | 55–70% | 0.92–1.17 |
| Donut hammer | Cathead & rope (2 turns) | 30–60% | 0.50–1.00 |
| Automatic (trip) hammer | Mechanical cam or trip release | 80–100% | 1.33–1.67 |
| Hydraulic hammer | Hydraulic cylinder release | 80–95% | 1.33–1.58 |
The donut hammer has the widest range of energy ratios because its cathead-and-rope release mechanism is highly operator-dependent — rope condition, number of turns, and driller technique all affect the energy delivered. Two drillers using the same donut hammer on the same rig can produce energy ratios that differ by 15–20 percentage points.
Measuring energy ratio directly #
ASTM D4633 defines the procedure for measuring hammer energy delivery directly using strain gauge and accelerometer instrumentation on the drill rods. Direct measurement is the most reliable approach and is strongly recommended for projects where SPT data will be used in liquefaction analysis, where hammer type is uncertain, or where rigs from different countries with different standard practices are being used. Without direct measurement, the tabulated typical values above should be used with the understanding that they introduce uncertainty into the correction.
For a detailed comparison of hammer systems, see SPT hammer types — safety, donut and automatic compared.
Cr — Rod length correction #
When the hammer blow is applied to the top of the drill rods, the energy travels downward as a compressive stress wave. In very short rod strings, the stress wave reaches the sampler quickly but the reflected wave returns before the hammer has finished transmitting energy — effectively truncating the energy delivery. This means that shallow tests (short rod lengths) systematically receive less energy than deep tests using the same hammer, producing higher-than-expected raw N-values at shallow depth.
The rod length correction Cr compensates by reducing the corrected N-value slightly for short rod strings and leaving it unchanged for long ones.
| Rod length below anvil (m) | Cr |
|---|---|
| < 3 m | 0.75 |
| 3–4 m | 0.80 |
| 4–6 m | 0.85 |
| 6–10 m | 0.95 |
| > 10 m | 1.00 |
In practice, SPT tests are rarely performed at rod lengths below 3 m — the first test in a borehole is typically at 1.5 m depth with rod lengths sufficient to reach the surface plus the anvil height. For most routine investigations where the first test is at 1.5–3.0 m, Cr = 0.75–0.80 applies only to those shallowest tests, and Cr = 1.0 applies to all tests at depths greater than roughly 10 m.
The rod length correction is frequently overlooked in practice — particularly for the first one or two tests in a borehole — which leads to artificially low (N1)60 values at shallow depth and can significantly affect bearing capacity estimates for shallow foundations.
Cb — Borehole diameter correction #
The standard borehole diameter for SPT testing is 65–115 mm. When the borehole diameter exceeds this range — typically 150–200 mm — the soil around the sampler is less confined, which allows the sampler to penetrate more easily for the same blow count, producing an artificially low N-value. The borehole diameter correction Cb increases the corrected N to account for this reduced confinement.
| Borehole diameter (mm) | Cb |
|---|---|
| 65–115 mm (standard range) | 1.00 |
| 150 mm | 1.05 |
| 200 mm | 1.15 |
The borehole diameter correction is small in magnitude (maximum 15%) and applies only when non-standard large-diameter boreholes are used. For the great majority of routine investigations using standard hollow stem auger or NW/HW rotary drilling with borehole diameters in the 100–115 mm range, Cb = 1.00 and no correction is applied.
Cs — Sampler liner correction #
The standard split-spoon sampler (ASTM D1586) is designed to be used without an inner liner — the soil sample enters the barrel directly and the inner diameter of 35 mm (1⅜ in) is the effective sample diameter. However, some samplers are manufactured with a provision for a thin brass or steel liner that reduces the inner diameter slightly. The presence or absence of the liner relative to the sampler’s design specification affects the friction between soil and sampler during driving.
| Sampler configuration | Cs |
|---|---|
| Standard sampler without liner (as designed) — most common | 1.00 |
| Sampler designed for liner but used without liner (over-sized barrel) | 1.10–1.30 |
| Sampler with liner present (as designed) | 1.00 |
The sampler liner correction is the least commonly applied of the five factors in practice — most modern SPT programmes use ASTM-compliant samplers without liners, giving Cs = 1.00. The correction becomes relevant when older equipment is used or when the sampler configuration is non-standard. When in doubt, inspect the sampler and confirm whether the barrel has been manufactured with liner provisions before defaulting to Cs = 1.00.
CN — Overburden stress correction #
The overburden stress correction is conceptually different from the other four factors. While Ce, Cr, Cb, and Cs all correct for equipment and procedural factors, CN corrects for a fundamental soil behaviour effect: at greater depth, higher confining pressure from the weight of overlying soil compresses the soil around the sampler, making it harder to penetrate for the same soil density. Identical sand at 2 m and 10 m depth will give very different N-values — not because the sand is different, but because the confining stress is different.
CN normalises the N-value to what it would be at a reference effective vertical stress of 100 kPa (approximately 1 atmosphere), making it possible to compare and use in correlations independently of depth.
Liao & Whitman (1986) — the most widely used expression #
For σ’v0 ≤ 100 kPa (shallow depths, above the reference stress):
CN = (Pa / σ’v0)0.5
For σ’v0 > 100 kPa (deep tests, above the reference stress):
CN = (Pa / σ’v0)0.5 (same expression, now gives CN < 1.0)
where Pa = atmospheric pressure = 100 kPa, and σ’v0 = effective vertical stress at the test depth (kPa). An upper limit of CN ≤ 2.0 is applied to prevent unrealistically large corrections at very shallow depth.
CN values at typical test depths #
| Test depth (m) | Approx. σ’v0 (kPa)* | CN (Liao & Whitman) | Effect on N |
|---|---|---|---|
| 1.5 | ~27 | 1.92 (capped at 2.0) | Nearly doubles N |
| 3.0 | ~54 | 1.36 | +36% to N |
| 5.0 | ~90 | 1.05 | +5% to N |
| 7.0 | ~126 | 0.89 | −11% to N |
| 10.0 | ~180 | 0.75 | −25% to N |
| 15.0 | ~270 | 0.61 | −39% to N |
| 20.0 | ~360 | 0.53 | −47% to N |
* Approximate values assuming γ = 18 kN/m³ and water table at 3 m depth. For accurate results, calculate σ’v0 from the actual unit weight profile and groundwater level for each borehole.
Alternative overburden correction methods #
Several alternative expressions for CN exist in the literature. Dartis SPT and DartiGeo support multiple overburden correction methods, allowing engineers to select the appropriate method for their design standard or regional practice:
| Method | Expression | Common use |
|---|---|---|
| Liao & Whitman (1986) | CN = (Pa / σ’v0)0.5, max 2.0 | Liquefaction assessment (Youd et al., 2001); most widely used internationally |
| Peck et al. (1974) | CN = 0.77 × log(20 / σ’v0) for σ’v0 > 24 kPa | Older North American practice; still encountered in existing reports |
| Seed (1976) | Graphical chart, approximated as Liao & Whitman | Early liquefaction analysis references |
| Skempton (1986) | CN = 2 / (1 + σ’v0/Pa) | British practice; gives lower CN at shallow depth than Liao & Whitman |
| Boulanger & Idriss (2014) | CN = (Pa / σ’v0)α, α = f(Dr) iterative | Modern liquefaction assessment; density-dependent correction |
For most routine geotechnical investigations not involving liquefaction assessment, Liao & Whitman (1986) is the standard choice. For liquefaction analysis, the correction method should match the procedure being followed — Youd et al. (2001) uses Liao & Whitman; Boulanger & Idriss (2014) uses their own iterative expression.
N60 vs (N1)60 — when to use each #
Applying all five correction factors gives (N1)60 — corrected for both equipment factors and overburden stress. However, not every SPT correlation uses (N1)60. Some correlations use N60 (energy-corrected but not overburden-corrected), because the overburden effect is already embedded in the correlation equation itself.
Using the wrong input — applying (N1)60 to a correlation calibrated against N60, or vice versa — introduces a systematic error that worsens at the extremes of depth. Always check the original reference paper to confirm which N-value the correlation was developed from before applying it.
| Use | Correct input | Notes |
|---|---|---|
| Relative density (Dr) — sands | (N1)60 | Skempton (1986), Jamiolkowski et al. (1985) |
| Friction angle (φ’) — sands | (N1)60 | Most modern correlations |
| Liquefaction assessment (CRR) | (N1)60cs | Clean-sand equivalent value; additional fines correction applied on top |
| Undrained shear strength — clays | N or N60 | Many clay correlations use raw N or N60; check reference |
| Bearing capacity (Meyerhof, Terzaghi & Peck) | N60 | SPT-based bearing capacity methods embed overburden effects implicitly |
| Elastic modulus (Es) — sands | N60 | Bowles (1996); Webb (1970) |
| Shear wave velocity (Vs) | N60 or (N1)60 | Varies by correlation — check reference carefully |
Worked example #
The following example shows how to apply all five correction factors to compute (N1)60 for a single SPT test.
Given information #
| Parameter | Value |
|---|---|
| Test depth | 6.0 m below ground surface |
| Raw field N-value | 22 blows |
| Hammer type | Automatic (trip) hammer, measured Er = 82% |
| Rod length below anvil | 6.5 m |
| Borehole diameter | 100 mm |
| Sampler type | Standard split-spoon, no liner |
| Soil unit weight above GWT (0–3 m) | 18 kN/m³ |
| Saturated unit weight below GWT (3–6 m) | 20 kN/m³ |
| Groundwater table depth | 3.0 m below ground surface |
Step 1 — Calculate effective vertical stress (σ’v0) at 6.0 m #
Total vertical stress at 6.0 m:
σv0 = (18 × 3.0) + (20 × 3.0) = 54 + 60 = 114 kPa
Pore water pressure at 6.0 m (GWT at 3.0 m, water depth = 3.0 m):
u = 9.81 × 3.0 = 29.4 kPa
Effective vertical stress:
σ’v0 = 114 − 29.4 = 84.6 kPa
Step 2 — Calculate each correction factor #
| Factor | Expression | Value |
|---|---|---|
| Ce | Er/60 = 82/60 | 1.37 |
| Cr | Rod length = 6.5 m → from table | 0.95 |
| Cb | Borehole diameter = 100 mm (standard range) | 1.00 |
| Cs | Standard sampler, no liner | 1.00 |
| CN | (100 / 84.6)0.5 = (1.182)0.5 | 1.087 |
Step 3 — Calculate N60 and (N1)60 #
N60 (energy, rod, borehole, and sampler corrections only — no overburden):
N60 = 22 × 1.37 × 0.95 × 1.00 × 1.00 = 22 × 1.302 = 28.6 ≈ 29
(N1)60 (all five corrections including overburden):
(N1)60 = 29 × 1.087 = 31.5 ≈ 32
Interpretation #
The raw field N of 22 becomes N60 = 29 after equipment corrections — primarily because the automatic hammer delivers significantly more than 60% efficiency. After overburden normalisation, (N1)60 = 32. The soil at this depth would be classified as dense sand based on (N1)60. Using the uncorrected N = 22 directly in a dense-sand correlation (calibrated against (N1)60) would classify this soil as only medium-dense — a significant underestimate that would affect friction angle, relative density, bearing capacity, and liquefaction assessments.
Water table correction — a note #
Some older textbooks and practice guides include a water table correction to the SPT N-value, applied when saturated fine sands or silts are tested below the water table. This correction (reducing N by 50% of the amount exceeding 15, capped at various limits) was proposed by Terzaghi & Peck (1948) to account for the tendency of saturated fine sands to dilate during shearing in drained conditions, which they believed caused artificially high N-values.
This water table correction is not part of the modern five-factor correction framework and is explicitly excluded from the Youd et al. (2001) liquefaction procedure and from most current geotechnical design standards. It is retained in Dartis SPT as an optional input for users working to older standards or regional codes that still require it, but it should not be applied when using the (N1)60 framework for modern correlations.
The correct treatment of the water table in SPT interpretation is through the effective vertical stress σ’v0 calculation used in the CN overburden correction — the water table is already accounted for through the effective stress, not through a separate N-value reduction.
How DartiGeo and Dartis SPT apply corrections automatically #
Manually applying five correction factors at every SPT test depth across multiple boreholes is time-consuming and error-prone — particularly when the groundwater level, unit weights, and rod lengths change with depth. Both DartiGeo and Dartis SPT automate the entire correction workflow:
- Hammer type and energy ratio are entered once per borehole (or per rig if multiple rigs were used). Ce is calculated automatically at every test depth.
- Rod length is derived automatically from the test depth and the anvil height above ground — no manual entry required for each test. Cr is looked up from the appropriate table at each depth.
- Borehole diameter is entered once per borehole. Cb is applied uniformly to all tests in that borehole.
- Sampler configuration is selected once and Cs applied to all tests.
- Overburden stress is calculated at every test depth from the soil layer profile (unit weights and layer boundaries entered in the borehole log) and the groundwater level. Multiple CN methods are available: Liao & Whitman (1986), Peck et al. (1974), Skempton (1986), and Boulanger & Idriss (2014).
- Both N60 and (N1)60 are computed and displayed at every depth, alongside the raw N profile, for direct comparison.
- Corrected values are displayed as variation-with-depth plots showing N, N60, and (N1)60 together — making it immediately visible how the correction changes the interpretation at different depths.
- All correction factor values — every Ce, Cr, Cb, Cs, CN, and resulting N60 and (N1)60 at each depth — are included in the professional PDF/Word report with the published expressions used for each factor, providing full calculation transparency for peer review and regulatory submission.
Download a free 14-day trial of DartiGeo or Dartis SPT →
Frequently asked questions #
Do I need to apply all five correction factors every time? #
For most routine geotechnical investigations, Ce, Cr, and CN are always applied — they have the largest effect and are always relevant. Cb = 1.00 for standard borehole diameters (65–115 mm), so no correction is needed in the vast majority of cases. Cs = 1.00 for standard samplers without liners, which is again the common case. In practice, you will usually calculate all five and find Cb = Cs = 1.00, which is fine — the important thing is to consciously confirm their values rather than skip the check.
What is the maximum value of CN? #
The overburden correction factor CN is capped at a maximum of 2.0, regardless of the calculated value. Without this cap, CN would approach infinity as effective vertical stress approaches zero — producing physically meaningless corrected N-values at very shallow depths. In practice the cap applies only to tests at very shallow depths (typically above 1.5–2.0 m) where σ’v0 is less than approximately 25 kPa. The cap value of 2.0 is standard across all major liquefaction and geotechnical design procedures.
What happens to the corrections if the water table is above ground level (artesian conditions)? #
If artesian conditions exist — where the piezometric level is above the ground surface — the pore water pressure at any depth is calculated from the artesian head, not from the depth to the water table measured in the borehole. This increases the pore pressure at every depth, reducing the effective vertical stress σ’v0 below what it would be for a normal water table. The CN correction then produces larger corrections (higher (N1)60 relative to N60) throughout the profile. This situation is important to identify during borehole drilling and should be recorded on the borehole log.
Why do some reports show different (N1)60 values for the same raw N? #
Different (N1)60 values from the same raw N arise from differences in: the assumed hammer energy ratio (measured vs typical assumed value); the choice of overburden correction method (Liao & Whitman vs Skempton vs Peck et al.); the unit weights and groundwater level used to compute effective vertical stress; and whether the rod length and borehole diameter corrections have been applied. Reports that do not document every correction factor value and the expressions used cannot be independently verified or compared with other investigations. This is why professional SPT reports should show all factor values at every test depth alongside the corrected N values.
Related articles #
- Standard Penetration Test (SPT) — complete guide
- SPT procedure step by step — ASTM D1586 explained
- SPT hammer types — safety, donut and automatic compared
- SPT correlations — estimating soil properties from N-value
- Estimating bearing capacity from SPT N-values
- Liquefaction potential from SPT — Seed & Idriss method
- Borehole logging — complete guide
- Foundation design — bearing capacity and settlement guide
