SPT and CPT Correlation Problems on the PE Geotechnical Exam
SPT N-value corrections (energy, overburden, rod-length) and CPT-to-SPT correlations (Robertson) for the PE Geotechnical exam — three worked NCEES-style problems plus the SPT correction-factor reference table.
The Standard Penetration Test (SPT) and Cone Penetration Test (CPT) are the two field tests every geotechnical engineer relies on, and the PE Civil Geotechnical exam tests whether you can apply the corrections correctly. Raw SPT N-values are nearly meaningless without the energy correction; a 70%-energy hammer reading delivers a different blow count than a 60%-energy hammer for the exact same soil. Similarly, a CPT cone tip resistance of 80 tsf in a clean sand correlates to one SPT N-value, but the same 80 tsf in a silty soil correlates to a different one because the friction ratio matters. The correction chain itself is straightforward; the trap is in the inputs.
The good news: the core SPT corrections (energy and overburden) live in the NCEES PE Civil Reference Handbook §3.8.1, and the full CPT toolkit — Robertson Soil Behavior Type, the Ic index, and the friction-ratio classification — is in FHWA NHI-16-072 (Geotechnical Site Characterization, GEC No. 5), which is one of the searchable design-standard PDFs supplied on exam day. A few factors (the borehole, rod-length, and sampler corrections from Skempton 1986) are textbook values you should know rather than handbook look-ups. The skill the exam tests is recognizing which corrections apply to a given measurement, picking the right values, and chaining them in the right order — not formula recall.
This post walks through the three in-situ-testing problem types NCEES tests, with three fully solved worked examples (raw-N to (N₁)₆₀ correction chain, CPT qc-to-SPT N₆₀ correlation by Robertson's method, and soil-type identification from CPT friction ratio using the Soil Behavior Type Index Iₓ).
Why in-situ testing matters on the PE Geotechnical exam
Per the April 2024 NCEES PE Civil Geotechnical specification, Topic 1 (Site Characterization) carries 8–12 questions out of 80. Sub-topic 1E (in-situ testing — SPT, CPT, pressuremeter, pore-pressure dissipation, dilatometer, dynamic cone penetration, plate load, and field vane shear) is a core piece of that block. Beyond the direct Topic-1 questions, SPT and CPT show up as upstream inputs to almost every Topic-9 / Topic-10 foundation problem (you back out φ or su from N or qc) and to every liquefaction analysis (Topic 4: cyclic resistance ratio comes from (N₁)₆₀ or qc1Ncs). Mastering corrections puts a substantial fraction of a passing score on the table before you ever get to design.
Core concepts you must master
SPT N-value corrections
The "raw" N-value reported in a boring log is uncorrected. Before using it in any correlation, you have to normalize for the equipment that actually delivered the blows and for the depth of measurement. The handbook gives the energy correction (§3.8.1.1) and the overburden adjustment (§3.8.1.2); the borehole, rod-length, and sampler factors come from Skempton (1986) and Kulhawy & Mayne (1990). Combined form:
(N1)60 = N60 · CN
The corrections:
- CE energy correction: CE = energy ratio (ER) / 60%. Donut hammer ER ≈ 45–60%; safety hammer ER ≈ 70–85%; automatic hammer ER ≈ 80–100%.
- CB borehole diameter: 1.0 for 65–115 mm; 1.05 for 150 mm; 1.15 for 200 mm.
- CR rod-length: 0.75 for < 3 m; 0.80 for 3–4 m; 0.85 for 4–6 m; 0.95 for 6–10 m; 1.0 for > 10 m.
- CS sampler: 1.0 for standard sampler with liner; 1.2 for sampler without liner.
- CN overburden correction: Peck–Hanson–Thornburn form (handbook §3.8.1.2): CN = 0.77·log₁₀(20 / Po), with Po = vertical effective stress in tsf and CN capped at 2.0.
(N1)60 vs. (N1)60cs
For liquefaction analysis on silty or fines-bearing sands, an additional fines-content correction converts (N1)60 to its "clean-sand equivalent" (N1)60cs. The Idriss–Boulanger 2008 form: (N1)60cs = (N1)60 + Δ(N1)60, where Δ depends on fines content (FC). For FC < 5%, Δ = 0; for FC > 35%, Δ ≈ 5.5. FHWA NHI-16-072 (§5.6, liquefaction) presents the SPT-based triggering procedure that uses this clean-sand equivalent.
CPT cone resistance and friction ratio
The CPT pushes a 10-cm² cone at 2 cm/s and continuously records:
- qc: cone tip resistance (force on the cone tip / cone area)
- fs: sleeve friction (force on the friction sleeve / sleeve area)
- u2: pore pressure behind the cone tip (CPTu only)
Two derived parameters do most of the interpretation:
Corrected tip resistance: qt = qc + u2·(1 − a)
where a ≈ 0.7–0.8 is the cone area ratio. For clean sands, qt ≈ qc. Low Rf (< 1%) with high qc indicates clean sand; high Rf (> 3%) with lower qc indicates clay.
Robertson Soil Behavior Type (SBT)
Robertson (1990, 2009) classifies soil from CPT data using two normalized parameters:
F = fs / (qt − σv0) × 100% (normalized friction)
The Soil Behavior Type Index Ic combines Q and F:
Robertson's SBT classification by Ic (the Ic-RW boundaries from Robertson & Wride 1998, reproduced in FHWA NHI-16-072 Table 4-16): Ic < 1.31 = gravelly sand; 1.31–2.05 = sand (clean to silty); 2.05–2.60 = sand mixtures (silty sand to sandy silt); 2.60–2.95 = silt mixtures (clayey silt to silty clay); 2.95–3.60 = clay; > 3.60 = organic soils.
CPT-to-SPT correlation (Robertson 2012)
For converting CPT data to equivalent SPT N-values:
For clean sand (Ic ≈ 1.8): the ratio is about 5; qt/Pa = 90 implies N60 ≈ 18. For silty clay (Ic ≈ 2.9): the ratio drops to about 3; the same qt implies a smaller N60. Older heuristics (qc/N ≈ 4–5 for sand, 1–2 for clay) approximate the same idea.
The 3 types of in-situ testing problems on the PE exam
Type 1: SPT N-value correction (raw N → N60 → (N1)60)
Given a raw N from a boring log, the test conditions (hammer type / energy ratio, borehole diameter, rod length, sampler type), and the depth + soil profile (to compute σ′v0). Apply the energy / borehole / rod / sampler corrections in series to get N60, then apply the overburden correction to get (N1)60. Worked below.
Type 2: CPT qc-to-SPT N160 correlation (Robertson method)
Given CPT qc, fs, depth, and water-table information. Compute the friction ratio Rf, identify soil type from Rf (or compute Ic for precision), apply Robertson's correlation to estimate N60, then apply CN for (N1)60. Worked below.
Type 3: Soil-type identification from CPT
Given CPT qc, fs, and depth. Compute Q and F (normalized parameters), compute Ic, classify into Robertson's SBT zone. Worked below.
Worked example: SPT energy correction
Worked example 1 — SPT correction chain. A boring log reports raw N = 18 blows/ft at 25 ft depth in saturated sandy soil (γsat = 120 pcf, water table at ground surface). The test used a safety hammer with measured energy ratio ER = 70%, a 100-mm borehole, 25-ft drill rods (= 7.6 m), and a standard sampler with liner. Compute (N1)60.
Step 1 — Equipment correction factors.
CB = 1.00 (100-mm borehole, in the 65–115 mm range)
CR = 0.95 (rod length 7.6 m, in the 6–10 m range)
CS = 1.00 (standard sampler with liner)
Step 2 — Energy-corrected N.
= 18 · 1.17 · 1.00 · 0.95 · 1.00 = 20.0
Step 3 — Vertical effective stress at the test depth. Water table at surface, saturated soil:
σ′v0 = γ′ · z = 57.6 · 25 = 1,440 psf = 0.72 tsf
Step 4 — Overburden correction (Peck–Hanson–Thornburn).
= 0.77 · log₁₀(27.78) = 0.77 · 1.4437 = 1.11
Step 5 — Combine.
Answer: (N1)60 ≈ 22. Sensitivity check: if the same boring had used a donut hammer (ER = 50%), CE would drop to 0.83 and (N1)60 would fall to about 16 — a 27% reduction for the exact same soil. Energy correction is the single most consequential step; never skip it.
Worked example: CPT qc-to-SPT N60 by Robertson's method
Worked example 2 — CPT-to-SPT correlation. A CPT sounding at 20 ft depth (saturated sand, water table at surface, γsat = 120 pcf) reports qt = 90 tsf and fs = 1.1 tsf. Estimate the equivalent (N1)60 using Robertson's correlation. Take Ic = 1.8 (typical for medium-dense clean sand).
Step 1 — Friction ratio sanity check.
Step 2 — Robertson correlation.
= 8.5 · (1 − 1.8/4.6) = 8.5 · (1 − 0.391) = 8.5 · 0.609 = 5.18
With Pa ≈ 1 tsf (1 atm), qt/Pa = 90:
Step 3 — Apply overburden correction for (N1)60.
CN = 0.77 · log₁₀(20 / 0.576) = 0.77 · log₁₀(34.72) = 0.77 · 1.541 = 1.19
(N1)60 = N60 · CN = 17.4 · 1.19 = 20.7 ≈ 21
Answer: (N1)60 ≈ 21 from CPT. For comparison, the SPT-derived value in WE1 (different depth, different sounding) was 22 — CPT and SPT generally agree within ±20% for clean sands when both are properly corrected, which is one reason both tests are commonly run on the same site. Watch the Ic value: if you'd assumed Ic = 2.5 (silty sand) instead of 1.8, the ratio drops to 8.5·(1 − 0.543) = 3.88, and N60 would jump to 90/3.88 = 23.2 — a 30% increase.
Worked example: soil-type identification from CPT
Worked example 3 — Robertson SBT. A CPT sounding at 15 ft depth in saturated soil (γsat = 120 pcf, water table at surface) reports qt = 25 tsf and fs = 1.5 tsf. Identify the soil type using Robertson's Soil Behavior Type Index Ic.
Step 1 — In-situ stresses. Water table at surface, so total and effective stress differ:
σ′v0 = (120 − 62.4) · 15 = 864 psf = 0.432 tsf
Step 2 — Normalized parameters. Q normalizes by effective vertical stress; F uses net tip resistance:
log₁₀Q = log₁₀(55.8) = 1.747
F = fs / (qt − σv0) × 100% = 1.5 / 24.1 × 100% = 6.22%
log₁₀F = log₁₀(6.22) = 0.794
Step 3 — Compute Ic.
= √[(1.723)2 + (2.014)2]
= √[2.97 + 4.06] = √7.03 = 2.65
Step 4 — Classify by Robertson SBT zone. Ic = 2.65 falls in the 2.60–2.95 zone:
Answer: silt mixture / silty clay (Robertson SBT zone 4). Sanity check via the simpler Rf route: Rf = 1.5/25 × 100% = 6.0%, which sits squarely in the cohesive-soil band. The two methods agree. Why the rigor of Ic matters: Rf alone tells you "high friction → cohesive," but Ic tells you precisely which cohesive soil (silt mixture vs. clay vs. organic), which is what feeds the downstream su or φ′ correlation. Note that Ic = 2.65 sits close to the zone 4/5 boundary — near a boundary, double-check the inputs before committing to a classification.
Common errors that cost points
Forgetting CN at shallow depths
At shallow depths (Po < 1 tsf, roughly the upper 10–15 ft) the overburden correction CN exceeds 1.0 by a meaningful amount. Skipping it entirely (treating N60 = (N1)60) underestimates the corrected blow count by 20–50% near the ground surface, which feeds straight into liquefaction triggering analysis with potentially serious consequences.
Mixing N-corrected with N-uncorrected in a downstream correlation
Foundation-design correlations expect specific corrected forms: bearing capacity from SPT typically uses (N1)60; pile capacity in sand uses N60 directly with one of the SPT-based pile methods; liquefaction triggering uses (N1)60cs. Plugging raw N or the wrong corrected form into the wrong correlation yields wrong answers in different magnitudes. Read the formula's documentation for which N is required.
Misreading the Robertson SBT chart
The Robertson 1990 chart plots normalized friction F on the x-axis and normalized cone resistance Q on the y-axis (log scale). The boundaries between SBT zones are curved, not straight, and the chart can be misread at the boundaries (especially zone 3 vs. 4 vs. 5, where silty clay, clay, and organic soils sit close together). Use the closed-form Ic calculation for unambiguous classification near zone boundaries.
Using qc instead of qt in clay
In clay soils, the pore pressure correction (qt = qc + u2·(1−a)) can be 5–15% of qc. For sands it's negligible. The exam might give you qc and u2 separately and expect you to compute qt — or it might give qt directly. Read carefully which the question provides.
How to study in-situ testing for the PE Geotechnical exam
Phase 1 — Correction-factor fluency (Week 1)
Read handbook §3.8 (in-situ testing) and FHWA NHI-16-072 sections on SPT and CPT end-to-end. Practice writing the SPT correction chain (raw N → N60 → (N1)60) from a blank page until you can identify which corrections apply in under 30 seconds. The same for the Robertson CPT correlation.
Phase 2 — Worked-problem drills (Weeks 2–3)
Work twelve problems across the three types: four full SPT correction chains (vary hammer type, depth, water table); four CPT-to-SPT correlations (vary Ic); four soil-type IDs from CPT. Time yourself: three to five minutes per problem on the exam. PEwise's in-situ testing cluster (Modules 19–24, 77 lessons) covers SPT energy and overburden corrections, CPT analysis with the Robertson SBT chart, and the CPT-to-SPT correlations NCEES tests.
Phase 3 — Integration with foundations and liquefaction (Week 4)
Solve five integration problems where you start from raw SPT or CPT data, apply corrections, and use the corrected N or qc to compute foundation bearing capacity, pile axial capacity, or liquefaction triggering. That chain (raw measurement → correction → correlation → design) is the realistic Topic-1+9+10 pattern on the exam, and it's where in-situ testing actually pays off in points.
Quick reference: SPT correction factors
| Factor | Condition | Value |
|---|---|---|
| CE (energy) | Donut hammer (ER ≈ 45–60%) | 0.75–1.00 |
| Safety hammer (ER ≈ 70–85%) | 1.17–1.42 | |
| Automatic hammer (ER ≈ 80–100%) | 1.33–1.67 | |
| CB (borehole) | 65–115 mm | 1.00 |
| 150 mm | 1.05 | |
| 200 mm | 1.15 | |
| CR (rod length) | < 3 m (< 10 ft) | 0.75 |
| 3–4 m (10–13 ft) | 0.80 | |
| 4–6 m (13–20 ft) | 0.85 | |
| 6–10 m (20–33 ft) | 0.95 | |
| > 10 m (> 33 ft) | 1.00 | |
| CS (sampler) | Standard sampler with liner | 1.00 |
| Sampler without liner | 1.20 | |
| CN (overburden) | Peck–Hanson–Thornburn (Po in tsf) | 0.77·log10(20/Po) |
Sources: energy correction (CE) and overburden correction (CN) — NCEES PE Civil Reference Handbook §3.8.1.1–3.8.1.2 and FHWA NHI-06-088 Eqs. 3-2 and 3-3; borehole, rod-length, and sampler factors (CB, CR, CS) — Skempton 1986 and Kulhawy & Mayne 1990.
Robertson SBT zones (by Ic)
| Ic range | SBT zone | Description |
|---|---|---|
| < 1.31 | 7 | Gravelly sand to dense sand |
| 1.31–2.05 | 6 | Sand (clean to silty) |
| 2.05–2.60 | 5 | Sandy silt to silty sand |
| 2.60–2.95 | 4 | Silt mixtures (clayey silt to silty clay) |
| 2.95–3.60 | 3 | Clay |
| > 3.60 | 2 | Organic soils |
Sources: Robertson 1990 / 2009 / 2012; FHWA NHI-16-072.
Watch the Correction Chain Animated
PEwise's PE Geotechnical course walks through SPT energy correction, overburden correction, and Robertson's CPT chart with each factor entering the calculation in real time on screen — once you can SEE which factor adjusts which raw input, the chain becomes automatic.
Connecting this to your overall PE Geotechnical exam strategy
In-situ testing sits upstream of nearly every Topic 9 / Topic 10 (foundations) and Topic 4 (earthquake / liquefaction) calculation. A confident command of SPT and CPT corrections doesn't just earn the direct Topic-1E points — it makes the downstream design problems faster because you arrive with the right corrected inputs ready. For the liquefaction triggering analysis that uses (N1)60cs directly, see our liquefaction analysis on the PE Geotechnical exam post. For the broader Topic 1 / Topic 2 fundamentals plus the full 24-module curriculum, our geotechnical PE exam study guide walks the syllabus end-to-end.
Final thoughts
SPT and CPT problems reward engineers who treat the correction chain as a recipe: identify the equipment used, look up each correction factor in the right table, multiply in series, then apply the overburden correction last. Once the chain is automatic, the calculation finishes in three minutes. The candidates who pass run that chain reflexively. The candidates who don't second-guess each correction factor and burn time on the wrong setup. Drill the correction chain until it's automatic.
Master In-Situ Testing with PEwise
PEwise's in-situ testing cluster (Modules 19–24, 77 lessons) covers SPT energy and overburden corrections, CPT analysis with the Robertson SBT chart, and the CPT-to-SPT correlations NCEES tests — with worked NCEES-style problems and reference citations. Course author Mahdi Bahrampouri, Ph.D., Geotechnical Earthquake Engineer, built the curriculum directly against FHWA NHI-16-072 (Geotechnical Site Characterization), Robertson 1990 / 2009 / 2012, and the NCEES PE Civil Reference Handbook §3.8.
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