One of the most valuable characteristics of the Standard Penetration Test is that the corrected N-value can be correlated with a wide range of soil engineering properties through empirical relationships developed from large databases of field measurements and laboratory tests. These correlations allow engineers to estimate friction angle, relative density, elastic modulus, shear wave velocity, undrained shear strength, and other parameters directly from SPT data — without the cost and time of dedicated laboratory testing for every borehole.
This article covers the principal SPT correlations used in geotechnical engineering practice: what each correlation estimates, which corrected N-value it requires as input, the published equations and their original references, the soil types each correlation applies to, and the inherent limitations of empirical correlation that every engineer should understand before using these relationships in design.
Before applying any correlation, raw field N-values must be corrected to N60 or (N1)60 using the five correction factors (Ce, Cr, Cb, Cs, CN). Using uncorrected N in these correlations produces unreliable results. If you have not yet read the correction factors guide, start there: SPT N-value correction factors — Ce, Cr, Cb, Cs, CN explained.
How SPT correlations work — and their limitations #
SPT correlations are empirical relationships, not fundamental physical laws. They were derived by researchers who collected large datasets pairing SPT N-values measured in the field with independently measured soil properties from laboratory tests on samples taken from the same locations. Statistical regression through these paired datasets produced equations that predict the soil property from the N-value.
This empirical origin has three important consequences for engineering practice:
- Every correlation carries inherent uncertainty. Even in the dataset used to develop the correlation, significant scatter exists around the best-fit line. Predicting a single property value from N alone will always carry uncertainty — which is why running multiple correlations and comparing results is better practice than relying on a single method.
- Correlations are soil-specific. A correlation developed from data on clean quartz sands may be completely inapplicable to calcareous sands, angular crushed rock fill, or lateritic soils. The soil type at the site must match the soil type the correlation was calibrated against. This is why soil-type filtering — described in the next section — is critical.
- Local calibration improves reliability. Where laboratory test data from the same site or a geologically similar local site is available, it can be used to validate which of the published correlations best represents local conditions. A calibrated correlation is always more reliable than a generic one.
With these limitations clearly understood, SPT correlations remain one of the most practically useful tools in geotechnical engineering — fast, economical, and applicable to every borehole where SPT data exists.
Soil type filtering — which correlations apply to which soil #
Each SPT correlation was developed for a specific soil type or types. Applying a sand correlation to a clay, or vice versa, produces meaningless or dangerously misleading results. The three categories used in correlation filtering are:
| Category | Soil types included | USCS symbols |
|---|---|---|
| Coarse-grained | Gravels and sands with less than 50% fines (passing No. 200 sieve) | GW, GP, GM, GC, SW, SP, SM, SC |
| Fine-grained | Silts and clays with more than 50% fines | ML, CL, MH, CH, OL, OH, Pt |
| Both (coarse and fine) | Correlations valid across a broad range of soil types | All symbols |
The soil type at each SPT test depth is determined from the visual description and USCS classification of the split-spoon sample recovered during the test, and from laboratory grain size and Atterberg limits testing where available. Dartis SPT and DartiGeo automatically filter the available correlation library to show only those correlations valid for the soil type recorded at each depth, eliminating the risk of applying an inappropriate equation.
Coarse-grained soil correlations #
Relative density (Dr) #
Applicable soil types: Coarse-grained (sands and gravels) | Input N-value: (N1)60
Relative density Dr expresses the in-situ void ratio of a granular soil as a fraction of the range between its loosest (emax) and densest (emin) possible states:
Dr = (emax − e) / (emax − emin) × 100%
It is a fundamental descriptor of sand state — controlling friction angle, stiffness, liquefaction susceptibility, and compressibility. Because measuring emax and emin requires laboratory testing on the actual soil, SPT-based Dr correlations are widely used for rapid preliminary estimation.
| Method | Equation | Notes |
|---|---|---|
| Skempton (1986) | Dr² = (N1)60 / 60 | Most widely cited; calibrated on clean to slightly silty sands. Simple and fast. |
| Meyerhof (1957) | Dr = √[(N1)60 / (a + b·σ’v0/Pa)] | Stress-dependent form; a and b are empirical constants. Less used today. |
| Kulhawy & Mayne (1990) | Dr² = (N1)60 / (CP · CA · COCR · 60) | Includes corrections for grain compressibility (CP), aging (CA), and overconsolidation (COCR). More accurate for aged or overconsolidated sands. |
| Jamiolkowski et al. (1985) | Dr = −98 + 66 · log[(N1)60] | Developed from calibration chamber tests; gives Dr in percent. |
Dr interpretation table #
| Dr (%) | Density description | Approx. (N1)60 (Skempton) |
|---|---|---|
| 0–15 | Very loose | 0–2 |
| 15–35 | Loose | 2–7 |
| 35–65 | Medium dense | 7–25 |
| 65–85 | Dense | 25–43 |
| 85–100 | Very dense | 43–60 |
Friction angle (φ’) #
Applicable soil types: Coarse-grained (sands and gravels) | Input N-value: (N1)60
The effective friction angle φ’ is the primary strength parameter for granular soils and a direct input to all bearing capacity calculations, slope stability analysis, and lateral earth pressure design. Laboratory direct shear or triaxial testing is the most reliable source, but SPT-based correlations are widely used for preliminary design and for sites where laboratory testing was not included in the investigation programme.
| Method | Equation | Notes |
|---|---|---|
| Peck, Hanson & Thornburn (1974) | φ’ = 28.5 + 15 · Dr (Dr from Meyerhof correlation) | Indirect via Dr; gives approximate range for preliminary design. |
| Wolff (1989) | φ’ = 27.1 + 0.3(N1)60 − 0.00054[(N1)60]² | Direct polynomial fit; one of the most commonly used direct correlations. Gives φ’ in degrees. |
| Hatanaka & Uchida (1996) | φ’ = √[20·(N1)60] + 20 | Simple, robust; calibrated against triaxial tests on undisturbed frozen sand samples — considered among the most reliable direct SPT-φ’ correlations. |
| De Mello (1971) | Graphical; φ’ = f(N, σ’v0) | Stress-dependent; accounts for confining pressure directly rather than via N correction. Still used in some South American practice. |
| Schmertmann (1975) | φ’ = arctan[(N/12.2 + σ’v0/(70·Pa))0.34] | Uses raw N with overburden explicitly; widely used in North American practice. |
Practical guidance: Run multiple friction angle correlations and compare the range of results. For clean medium sands, the methods typically agree within 2–4°. For silty sands, coarse gravels, or angular materials, scatter between methods is larger and local calibration against laboratory triaxial data is advisable before committing to a design φ’ value.
Elastic modulus (Es) — sands and gravels #
Applicable soil types: Coarse-grained | Input N-value: N60
The elastic (Young’s) modulus Es governs the immediate (elastic) settlement of foundations on granular soils and is an input to elastic stress distribution calculations. Direct measurement (pressuremeter, plate load test) is more reliable, but SPT-based estimates are widely used for preliminary settlement calculations and smaller projects.
| Method | Equation | Soil type |
|---|---|---|
| Bowles (1996) | Es = α · N60 | α = 500 kPa (silty sand/silt); 700 kPa (clean sand, fine–medium); 800 kPa (clean sand, medium–coarse); 1000 kPa (sand and gravel) |
| Webb (1970) | Es = 500(N60 + 15) kPa | Clean to slightly silty sands; widely used in practice for its simplicity |
| D’Appolonia et al. (1970) | Es = 793 + 322·N60 kPa (normally consolidated) | Sand; distinguishes NC and OC conditions |
| Schmertmann (1970) | Es = 2·qc (from CPT, not SPT) or 2.5·qc for axisymmetric | CPT-based; cited for comparison when converting CPT to equivalent SPT |
Settlement calculations are highly sensitive to Es, and SPT-based Es estimates carry significant uncertainty — coefficients of variation of 30–50% are common. For critical structures on sand where settlement governs design, CPT-based modulus estimation (using the Schmertmann method with CPT qc profiles) is considerably more reliable and is the preferred approach when CPT data is available. See the CPT guide for the Schmertmann settlement method.
Shear wave velocity (Vs) — sands and gravels #
Applicable soil types: Coarse-grained | Input N-value: N60
Shear wave velocity Vs is used to characterise dynamic soil properties for earthquake response analysis, ground amplification studies, and the calculation of maximum (small-strain) shear modulus Gmax. Direct measurement by MASW, SASW, or downhole/crosshole geophysics is preferred for seismic design, but SPT-based Vs correlations provide useful preliminary estimates.
| Method | Equation | Notes |
|---|---|---|
| Imai & Tonouchi (1982) | Vs = 97 · N600.314 (m/s) | Developed from Japanese data across sand, gravel, and clay; widely used internationally |
| Seed et al. (1983) | Vs = 61.4 · N600.5 (m/s) | Calibrated for sands; commonly used in North American liquefaction practice |
| Ohta & Goto (1978) | Vs = 69 · N600.17 · z0.2 · Fb · Fa (m/s) | Includes depth z and geological age/soil type factors; most comprehensive form |
| Kayabali (1996) | Vs = 56.4 + 3.55·N60 (m/s) | Linear form; simple; calibrated on Turkish sand and gravel data |
Shear modulus (Gmax) — sands and gravels #
Applicable soil types: Coarse-grained | Input N-value: N60 or Vs
The maximum (small-strain) shear modulus Gmax is derived from Vs and the soil mass density ρ using:
Gmax = ρ · Vs²
where ρ = γtotal / g (kg/m³). Gmax is the input for dynamic response and wave propagation analysis. Once Vs is estimated from an SPT correlation, Gmax follows immediately from the equation above without requiring a separate SPT-Gmax correlation.
Some references (e.g. Imai & Tonouchi, 1982; Ohta & Goto, 1978) provide direct Gmax–N expressions as alternatives to the two-step Vs–then–Gmax approach. Both routes give equivalent results for a given set of correlation equations and unit weights.
Fine-grained soil correlations #
Undrained shear strength (su) #
Applicable soil types: Fine-grained (silts and clays) | Input N-value: N or N60
Undrained shear strength su is the primary strength parameter for saturated fine-grained soils under rapid (undrained) loading — the condition that governs bearing capacity at the end of construction before consolidation occurs. SPT-based su correlations are widely used for rapid site characterisation and preliminary bearing capacity assessment in clay, but they are significantly less reliable than vane shear testing or laboratory triaxial/UCS testing.
The fundamental reason for this reduced reliability is that the SPT driving process disturbs fine-grained soils, and the dynamic penetration resistance in clay reflects a complex combination of shear strength, sensitivity, and drainage that does not map cleanly to the undrained shear strength measured in a controlled laboratory test.
| Method | Equation | Notes |
|---|---|---|
| Terzaghi & Peck (1948) | su = 6.25 · N (kPa) | Uses raw uncorrected N; the most widely cited simple correlation. Conservative for stiff, overconsolidated clays. |
| Stroud (1974) | su = f1 · N60 | f1 varies with plasticity index: f1 ≈ 4.5 kPa for PI > 30; f1 ≈ 5.5 kPa for PI 15–30; f1 ≈ 6.0–7.0 kPa for PI < 15. Accounts for PI dependence of the N-su relationship. |
| Sowers (1979) | su = (10 to 15) · N (kPa) for stiff clays; (6.25 to 10) · N for soft clays | Provides a range reflecting the influence of clay consistency; useful for bounding estimates. |
| Hara et al. (1971) | su = 29 · N600.72 (kPa) | Power-law form; non-linear relationship captures better behaviour at both low and high N values. |
| Décourt (1990) | su = (N60 / 8) · (1 + 0.25·σ’v0/Pa) (kPa) | Stress-dependent; includes overburden correction; calibrated on Brazilian data but used widely in South America and internationally. |
Important warning: Do not use SPT-based su correlations for soft clays (N < 4) where the SPT blow count may reflect sensitivity or disturbance effects rather than in-situ strength. For soft clays, field vane shear testing or undisturbed Shelby tube sampling with laboratory UCS or triaxial testing are the appropriate methods. SPT results in soft clays should be treated as qualitative indicators only.
Unconfined compressive strength (qu) #
Applicable soil types: Fine-grained (primarily clays) | Input N-value: N
The unconfined compressive strength qu is related to undrained shear strength by qu = 2·su for a saturated soil tested in undrained conditions with zero confining pressure. SPT-based qu correlations are therefore direct extensions of the su correlations and carry the same limitations.
| Method | Equation | Notes |
|---|---|---|
| Terzaghi & Peck (1948) — derived | qu = 12.5 · N (kPa) | Derived directly from su = 6.25N by qu = 2·su; most common approximate form |
| Sowers (1979) | qu = 15 to 30 · N (kPa) | Range accounts for variability in clay type and consistency |
The consistency classification of clays from raw N-value — alongside approximate su and qu ranges — is widely used in practice as a rapid field assessment tool:
| SPT N (raw field) | Clay consistency | Approx. su (kPa) | Approx. qu (kPa) |
|---|---|---|---|
| < 2 | Very soft | < 12 | < 25 |
| 2–4 | Soft | 12–25 | 25–50 |
| 4–8 | Firm | 25–50 | 50–100 |
| 8–15 | Stiff | 50–100 | 100–200 |
| 15–30 | Very stiff | 100–200 | 200–400 |
| > 30 | Hard | > 200 | > 400 |
Pressuremeter modulus (Ep) #
Applicable soil types: Fine-grained (clays and silts) | Input N-value: N60
The pressuremeter modulus Ep (also called the Ménard modulus EM) is measured directly by a pressuremeter test in a borehole. Where pressuremeter testing has not been performed, SPT-based estimates allow Ménard’s design methods (which are based on Ep) to be applied without additional testing.
| Method | Equation | Notes |
|---|---|---|
| Ménard & Rousseau (1962) — correlation for clay | Ep ≈ 50 · qu (kPa) — indirect via qu | Used when only N and qu correlation are available; approximate |
| Various regional correlations | Ep = α · N60 where α = 400–600 kPa for soft-firm clay | Regional multipliers vary significantly; local calibration strongly recommended before applying in design |
Ep from SPT is a rough approximation. For projects where Ménard pressuremeter design methods are specified, direct pressuremeter testing is always preferable.
Elastic modulus (Es) — clays and silts #
Applicable soil types: Fine-grained | Input N-value: N60
Elastic modulus for clays governs immediate (undrained elastic) settlement and is used in elastic stress-deformation analyses. It is more commonly derived from laboratory testing (triaxial tests at appropriate stress levels) or from correlations with su, but SPT-based estimates are used when laboratory data is unavailable.
| Method | Equation | Notes |
|---|---|---|
| General correlation (various) | Es = (200 to 500) · N60 kPa | Wide range reflects variability in clay type and overconsolidation state; use with caution |
| From su (indirect) | Eu = αu · su, αu = 100–500 | More reliable than direct N correlation; αu depends on OCR and plasticity index |
For primary consolidation settlement prediction in clay — which is usually the governing settlement mechanism — the one-dimensional consolidation test (oedometer) provides Cc, Cr, and cv, which are far more reliable inputs than Es from SPT. See the laboratory testing guide for the consolidation test and its parameters.
Shear modulus (Gmax) — clays and silts #
Applicable soil types: Fine-grained | Input N-value: N60
As with sands, Gmax for clays is most reliably derived from measured Vs (downhole or MASW testing). SPT-based Vs correlations for fine-grained soils can then be used to estimate Gmax:
| Method | Equation | Notes |
|---|---|---|
| Imai & Tonouchi (1982) | Vs = 80.6 · N600.333 (m/s) for clay | Separate regression for clay vs sand from the same study; then Gmax = ρ·Vs² |
| Ohta & Goto (1978) | Vs = 69 · N600.17 · z0.2 · Fb · Fa | Soil type factor Fb = 1.000 for clay (vs 1.086 for sand); applicable to both coarse and fine soils |
Consistency and density from raw N — field guide #
The following classification table uses raw uncorrected field N-values for rapid qualitative assessment during logging. It should not be used as a substitute for corrected N-value correlations in quantitative design, but it is a standard tool for field engineers describing soil consistency and density on the borehole log at the time of testing.
| SPT N (raw field) | Sand — relative density | Clay — consistency |
|---|---|---|
| 0–4 | Very loose | Very soft |
| 4–10 | Loose | Soft to firm |
| 10–30 | Medium dense | Stiff |
| 30–50 | Dense | Very stiff |
| > 50 (refusal) | Very dense | Hard |
These boundaries vary slightly between textbooks and national standards. The values above follow Terzaghi & Peck (1967) and are the most widely cited internationally.
How DartiGeo and Dartis SPT run 200+ correlations automatically #
Manually selecting, applying, and documenting the appropriate correlations for every soil layer in every borehole is time-intensive and carries a high risk of applying an inappropriate equation to the wrong soil type. Dartis SPT and DartiGeo automate the full correlations workflow:
- Automatic soil-type filtering: Based on the USCS soil type recorded for each depth interval, the software automatically filters the full library to show only correlations valid for that soil type — coarse-grained only, fine-grained only, or both. Engineers cannot inadvertently apply a sand friction angle correlation to a clay layer.
- 200+ correlations from published references: The complete library covers all parameter categories described in this article — Dr, φ’, Es, Vs, Gmax, su, qu, Ep — with multiple methods available for each parameter, allowing comparison between approaches.
- Equations shown alongside results: For each correlation applied, the published equation is displayed alongside the computed result — not just the number, but the formula and reference. This allows engineers to review and validate each result and supports transparent reporting to clients and regulators.
- Variation-with-depth plots: Correlation results can be plotted as continuous depth profiles — for example, showing how estimated friction angle varies with depth through the full borehole — giving a visual picture of soil property changes with depth that a table of numbers cannot convey as effectively.
- Corrected N-values fed automatically: N60 and (N1)60 values computed by the correction module (described in SPT N-value correction factors) feed directly into the correlations module. There is no re-entry of corrected values — the two modules work from the same dataset.
- Professional reports: Correlation results for selected methods, with their equations, are exported to a formatted PDF or Word report at the click of a button. Reports can include depth plots, summary tables, and the bearing capacity estimation output.
Download a free 14-day trial of DartiGeo or Dartis SPT →
Frequently asked questions #
Which SPT correlation for friction angle is most reliable? #
No single correlation is universally most reliable — each was calibrated on a different database of soils and laboratory tests. For practical use, Hatanaka & Uchida (1996) is widely regarded as one of the most reliable direct correlations because it was calibrated against triaxial tests on high-quality undisturbed frozen sand samples. Wolff (1989) is the most commonly used in North American practice. The best approach is to run multiple correlations, compare the resulting φ’ values, and apply engineering judgement informed by local experience. Where the results span more than 4–5°, laboratory direct shear or triaxial testing should be considered for the critical design layers.
Can I use SPT correlations for clays in bearing capacity design? #
SPT-based su estimates for clay can be used for preliminary bearing capacity checks and for qualitative classification of site conditions, but they should not be relied upon as the sole basis for final bearing capacity design in clays — particularly for soft clays (N < 4) or for structures where the consequences of a bearing failure would be significant. Final design in clay should use su from laboratory UCS testing (ASTM D2166), undrained triaxial testing (ASTM D4767), or in-situ field vane shear testing, on undisturbed samples from the critical bearing layer.
Why does running multiple correlations give different answers for the same N-value? #
Different correlations were derived from different datasets — different soil types, different geographic regions, different testing protocols, and different statistical fitting methods. Each captures a different slice of the real relationship between N and the target property. The spread between methods is a direct reflection of the genuine uncertainty in that relationship for a given soil type and context. When correlations agree closely, confidence in the estimate is higher. When they diverge significantly, it is a signal that local calibration against laboratory data, or a more direct in-situ measurement, would be valuable before committing to a design value.
What is the difference between Es from SPT and the modulus from an oedometer test? #
The elastic modulus Es estimated from SPT correlations is a Young’s modulus for elastic (drained) deformation — it governs immediate settlement of foundations on granular soils under load. The oedometer test measures the constrained modulus M (= 1/mv) and the compression index Cc, which govern one-dimensional primary consolidation settlement in clay — a time-dependent process. They are fundamentally different parameters for different settlement mechanisms. For sands, Es is the relevant parameter. For clays, consolidation parameters from the oedometer test govern the larger and slower consolidation settlement. See the foundation design guide for how both types of settlement are calculated.
Do SPT correlations account for soil fabric and geological age? #
Standard SPT correlations (Skempton, Wolff, Terzaghi & Peck) do not explicitly account for soil fabric, cementation, ageing, or overconsolidation. The Kulhawy & Mayne (1990) relative density correlation is an exception — it includes an ageing factor CA and an overconsolidation factor COCR that increase Dr estimates for old, overconsolidated sands that are stiffer than their void ratio alone would suggest. For cemented sands or residual soils where the SPT resistance reflects bonding rather than density, standard correlations will overestimate Dr and φ’. Local experience and calibration are essential in such geologies.
Related articles #
- Standard Penetration Test (SPT) — complete guide
- SPT N-value correction factors — Ce, Cr, Cb, Cs, CN explained
- Estimating bearing capacity from SPT N-values
- Relative density from SPT — Dr correlations for sand
- Liquefaction potential from SPT — Seed & Idriss method
- SPT vs CPT — comparison and when to use each
- Cone Penetration Test (CPT) — complete guide
- Geotechnical laboratory testing — complete guide
- Foundation design — bearing capacity and settlement guide
