Methods & References

The general bearing-capacity equation used (Meyerhof / Hansen / Vesic family):

where q = γ·D_f is the effective overburden at the founding depth, B' is the effective footing width, and N_c, N_q, N_γ are the bearing-capacity factors.

Bearing-capacity factors

For N_γ the method selected determines the form:

• Terzaghi (1943): classical formulation with Kumbhojkar's N_γ approximation.
• Meyerhof (1963): N_γ = (N_q − 1) · tan(1.4 φ').
• Hansen (1970): N_γ = 1.5·(N_q − 1)·tan φ'.
• Vesic (1973): N_γ = 2·(N_q + 1)·tan φ'.

Net ultimate and allowable bearing pressures are reported as q_net,ult = q_ult − γ·D_f and q_net,allow = q_net,ult / FoS (default FoS = 3.0).

Shape factors (Meyerhof / Hansen / Vesic), with r = B'/L':

Depth factors (Hansen), with k = D_f/B' if D_f/B' ≤ 1, else k = atan(D_f/B'):

Inclination factors (Meyerhof) for a load inclined α° from vertical:

For a footing loaded with eccentricities e_B, e_L:

All capacity terms use the effective dimensions B' and L'.

Three classical cases based on water-table depth d_w relative to D_f and B:

• Case I (d_w ≤ D_f): q = γ·d_w + γ'·(D_f − d_w); use γ' in the N_γ term.
• Case II (D_f < d_w < D_f + B): blend γ for the N_γ term linearly between γ' and γ.
• Case III (d_w ≥ D_f + B): no correction.

Elastic (immediate) settlement of a flexible rectangular footing (Bowles, Das):

with influence factor I_w ≈ 0.88 (square), 1.12 (L/B = 2), 1.7 (strip-like). Poisson's ratio ν defaults to 0.3.

Consolidation settlement in clay (Terzaghi, 1925):

Stress increase Δσ is computed by the 2:1 Boussinesq approximation under the footing centre.

Total ultimate axial capacity:

Shaft resistance in sand (effective-stress / β-method)

K_s ≈ 1.0 (bored) – 1.4 (driven); δ = (0.7–0.8)·φ'. An optional critical-depth cap L_c = 15·D limits the effective stress used in shaft computations (Vesic, Meyerhof).

Shaft resistance in clay (α-method, Tomlinson 1957)

Default α = 0.55 (Tomlinson). A β-method alternative is available.

End bearing

n × m piles at centre-to-centre spacing s; D = pile diameter.

Energy-corrected blow count and overburden-corrected (N₁)₆₀:

Friction ratio and the SBT index I_c (Robertson, 1990; 2009; 2010):

Soil Behaviour Type zones are assigned from I_c thresholds (gravelly sand < 1.31 < sand < 2.05 < sand mixture < 2.60 < silt mixture < 2.95 < clay < 3.60 < organic).

Robertson (1990) SBT chart

Points are plotted on log–log axes of normalised penetration resistance Q_t = (q_t − σ_v0)/σ′_v0against normalised friction ratio F_r = f_s/(q_t − σ_v0) × 100 %, over the nine standard behaviour-type zones. The SBT correlation strip on the CPT log can be toggled on or off, and all plots share the global vertical/horizontal scale controls used for export.

Instrument type & rig capacity

Each sounding records its instrument (mechanical/Begemann, electric, piezocone CPTu, or dynamic DCP/DPSH) and the push-rig tonnage (2.5, 5, 10, 20 t). The maximum sustainable tip resistance for the rig is

with a default cone area A_c = 10 cm². Readings at or above q_c,max are flagged as rig refusal rather than soil strength, and dynamic soundings are treated as q_d-equivalent values.

Tabulated ultimate and allowable bearing pressure versus founding depth is produced by three methods:

• Meyerhof (1956, 1974): direct q_ult correlation with the averaged cone resistance beneath the footing.
• Schmertmann (1978): q_c-based capacity with separate treatment of cohesive and cohesionless response.
• LCPC / Bustamante & Gianeselli (1982): equivalent cone resistance q_ce times a soil-class bearing factor k_c.

Undrained shear strength for cohesive layers is derived from the cone with

Corrections (Skempton, 1986). Field blow counts are corrected for hammer energy, borehole diameter, sampler type and rod length, then normalised for overburden:

C_r = 0.75 (<3 m), 0.80 (3–4 m), 0.85 (4–6 m), 0.95 (6–10 m), 1.00 (>10 m); C_b = 1.00/1.05/1.15 for 65–115/150/200 mm holes; C_s = 1.20 for a liner-less sampler.

Strength, density and stiffness

Consistency and density states follow Terzaghi & Peck (1967).

Shallow foundations

Capacity is checked twice and the lower value governs. Ultimate capacity uses the Meyerhof factors with φ′ (granular) or s_u (cohesive); the settlement-governed pressure follows Meyerhof (1965) for 25 mm settlement, scaled linearly to the tolerable settlement:

Pile capacity (Meyerhof, 1976)

Liquefaction triggering (Youd et al., 2001 — NCEER/NSF)

Screening is applied only to saturated, granular horizons above 20 m; (N₁)_60cs ≥ 30 is treated as non-liquefiable.

γ_w = 9.81 kN/m³; air-void ratio A = n(1 − S). Relative density (ASTM D4253/D4254):

Density states follow Terzaghi & Peck (1967): very loose < 15 % < loose < 35 % < medium dense < 65 % < dense < 85 % < very dense.

Activity bands: inactive < 0.75 < normal ≤ 1.25 < active. Sensitivity after Skempton & Northey (1952) up to quick clay (S_t > 16). Consistency is read from LI.

The Casagrande (1948) plasticity chart is plotted with:

Coarse/fine split at 50 % passing the 0.075 mm sieve. Coarse soils are gravel when the gravel fraction exceeds the sand fraction. Gradation:

Well graded requires C_u ≥ 4 (gravel) or ≥ 6 (sand) with 1 ≤ C_c ≤ 3. Fines content < 5 % gives a single symbol, 5–12 % a dual symbol, > 12 % a fines-governed symbol taken from the Casagrande chart (CL, CH, ML, MH, CL-ML, OL, OH, PT).

AASHTO M145 / ASTM D3282 groups A-1 to A-7 are assigned from the fines content, No.10 and No.40 passing, LL and PI, with the group index

where a = F − 35 (0–40), b = F − 15 (0–40), c = LL − 40 (0–20), d = PI − 10 (0–20); GI is reported as 0 for A-1 and A-3, and converted to a subgrade rating from excellent to very poor.

Every logged stratum is classified automatically from the data that falls inside its depth interval — the logged USCS symbol, all SPT tests within the layer, and all CPT points within the layer. Vertical stresses use the layer mid-depth:

Derived parameters, applied according to whether the logged symbol is cohesive or granular:

Density and consistency states follow Terzaghi & Peck (1967). The layer-averaged CPT I_c gives an independent behaviour type; where the CPT indicates fine-grained behaviour (I_c > 2.6) but the log records a coarse soil (or vice-versa) the row is flagged for review. Sending a stratum to the USCS/AASHTO tab seeds an indicative gradation implied by the logged symbol — it must be replaced with measured particle-size data before it is reported.

Effective stress profile (Terzaghi, 1925)

Stress distribution

The 2:1 approximation is retained as a screening option.

Settlement & consolidation rate

Lateral earth pressure & retaining walls

Slope stability

Soil dynamics & liquefaction

CSR and CRR are plotted against depth so the liquefiable horizons are visible directly on the profile.

• Particle size: sieving plus hydrometer (Stokes' law) merged into a single PSD curve; D₁₀, D₃₀, D₆₀, C_u, C_c read by log-interpolation.
• Atterberg limits: cone penetrometer / Casagrande cup (BS 1377-2, ASTM D4318) with flow-curve regression at 25 blows.
• Specific gravity: G_s = (M₂−M₁)/[(M₄−M₁) − (M₃−M₂)] (pycnometer).
• Compaction: ρ_d = ρ/(1+w); OMC and MDD from the parabolic fit, plotted against the zero-air-voids curve ρ_d,zav = G_sρ_w/(1+wG_s).
• CBR: penetration stress at 2.5 mm and 5.0 mm divided by 6.9 MPa and 10.3 MPa standard values, with curve-correction for concavity.
• Permeability: constant head k = QL/(Aht); falling head k = 2.303·(aL/At)·log₁₀(h₁/h₂).
• Shear box & triaxial: Mohr–Coulomb τ = c′ + σ′ tan φ′ by least-squares on the failure envelope; UU, CU (with pore pressure, Skempton A/B) and CD paths supported.
• Consolidation (oedometer): e–log σ′ curve, C_c, C_r, m_v, and c_v by Casagrande log-time and Taylor √time constructions.

• γ_w = 9.81 kN/m³; atmospheric pressure p_a = 100 kPa throughout.
• Where a unit weight is not measured, the entered default (18 kN/m³) is used for overburden — results scale directly with it.
• SPT energy ratio defaults to 0.60 (no correction); borehole diameter, sampler and rod-length factors are applied only when entered.
• Layer-averaged SPT and CPT values are arithmetic means of the tests falling within the logged depth interval; single-test layers carry no statistical confidence.
• Correlations (φ′, s_u, D_r, SBT) are empirical screening tools calibrated for the soils of their original publications and must be checked against laboratory testing.
• Gradation seeded from a logged USCS symbol is indicative only and is not a substitute for a measured PSD.
• Dynamic soundings (DCP/DPSH) are reported as q_d-equivalents; readings at rig capacity denote refusal, not soil strength.
• AI-drafted report narrative quotes only numbers present in the project data and flags unsupported statements for engineer review.

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• Meyerhof, G. G. (1963). Some recent research on the bearing capacity of foundations. Canadian Geotech. J., 1(1), 16–26.
• Meyerhof, G. G. (1976). Bearing capacity and settlement of pile foundations. JGED, ASCE, 102(GT3), 197–228.
• Hansen, J. B. (1970). A revised and extended formula for bearing capacity. Danish Geotechnical Institute Bulletin No. 28.
• Vesic, A. S. (1973). Analysis of ultimate loads of shallow foundations. JSMFD, ASCE, 99(SM1), 45–73.
• Tomlinson, M. J. (1957). The adhesion of piles driven in clay soils. Proc. 4th ICSMFE, 2, 66–71.
• Skempton, A. W. (1951). The bearing capacity of clays. Building Research Congress, London.
• Bowles, J. E. (1996). Foundation Analysis and Design, 5th ed. McGraw-Hill.
• Das, B. M. (2016). Principles of Foundation Engineering, 8th ed. Cengage.
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• Robertson, P. K. (1990). Soil classification using the CPT. Canadian Geotech. J., 27(1), 151–158.
• Robertson, P. K. (2009). Interpretation of cone penetration tests — a unified approach. Canadian Geotech. J., 46, 1337–1355.
• Liao, S. S. C. & Whitman, R. V. (1986). Overburden correction factors for SPT in sand. JGE, ASCE, 112(3), 373–377.
• Converse, F. & Labarre, E. (1963). Group efficiency of piles. (As cited in Bowles, 1996.)
• Robertson, P. K. (2010). Soil behaviour type from the CPT: an update. 2nd Int. Symp. on Cone Penetration Testing.
• Peck, R. B., Hanson, W. E. & Thornburn, T. H. (1974). Foundation Engineering, 2nd ed. Wiley.
• Skempton, A. W. (1986). Standard penetration test procedures. Géotechnique, 36(3), 425–447.
• Liao, S. S. C. & Whitman, R. V. (1986). Overburden correction factors for SPT in sand. JGE, ASCE, 112(3), 373–377.
• Stroud, M. A. (1974). The standard penetration test in insensitive clays and soft rocks. Proc. ESOPT I, 367–375.
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• Youd, T. L. et al. (2001). Liquefaction resistance of soils: NCEER/NSF workshops summary report. JGGE, ASCE, 127(10), 817–833.
• Terzaghi, K. & Peck, R. B. (1967). Soil Mechanics in Engineering Practice, 2nd ed. Wiley.
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• Skempton, A. W. (1953). The colloidal activity of clays. Proc. 3rd ICSMFE, 1, 57–61.
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• Schmertmann, J. H. (1978). Guidelines for Cone Penetration Test: Performance and Design. FHWA-TS-78-209.
• Bustamante, M. & Gianeselli, L. (1982). Pile bearing capacity prediction by means of static penetrometer CPT. Proc. ESOPT II, 493–500.
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• Hardin, B. O. & Black, W. L. (1968). Vibration modulus of normally consolidated clay. JSMFD, ASCE, 94(SM2), 353–369.
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• ASTM D2487, D3282, D4318, D4253/D4254, D1586, D5778, D2573, D1194 — standard test methods and classification practices.
• AASHTO M145. Classification of Soils and Soil–Aggregate Mixtures for Highway Construction Purposes.
• AGS (2017). Electronic Transfer of Geotechnical and Geoenvironmental Data, Edition 4.2.
• British Standards Institution. BS 1377: Methods of test for soils for civil engineering purposes.

SoilLab is an engineering aid; results must be reviewed and signed off by a competent geotechnical engineer. Calibrate parameters against site-specific testing.