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

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.

• Terzaghi, K. (1943). Theoretical Soil Mechanics. Wiley.
• 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.
• Coduto, D. P. (2001). Foundation Design: Principles and Practices, 2nd ed. Prentice Hall.
• 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.
• Terzaghi, K. & Peck, R. B. (1967). Soil Mechanics in Engineering Practice, 2nd ed. Wiley.
• Stroud, M. A. (1974). The standard penetration test in insensitive clays and soft rocks. Proc. ESOPT I, 2, 367–375.
• Skempton, A. W. (1953). The colloidal activity of clays. Proc. 3rd ICSMFE, 1, 57–61.
• Skempton, A. W. (1986). Standard penetration test procedures. Géotechnique, 36(3), 425–447.
• Casagrande, A. (1948). Classification and identification of soils. Trans. ASCE, 113, 901–930.
• 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.
• Boussinesq, J. (1885). Application des potentiels…; Newmark, N. M. (1935). Simplified computation of vertical pressures in elastic foundations.
• Bishop, A. W. (1955). The use of the slip circle in the stability analysis of slopes. Géotechnique, 5(1), 7–17.
• Fellenius, W. (1936). Calculation of the stability of earth dams. Trans. 2nd Congress on Large Dams.
• Jaky, J. (1944). The coefficient of earth pressure at rest. J. Soc. Hungarian Architects & Engineers.
• Seed, H. B. & Idriss, I. M. (1971). Simplified procedure for evaluating soil liquefaction potential. JSMFD, ASCE, 97(SM9), 1249–1273.
• Youd, T. L. et al. (2001). Liquefaction resistance of soils: NCEER/NSF workshop summary. JGGE, ASCE, 127(10), 817–833.
• Hardin, B. O. & Black, W. L. (1968). Vibration modulus of normally consolidated clay. JSMFD, ASCE, 94(SM2), 353–369.
• Marchetti, S. (1980). In situ tests by flat dilatometer. JGED, ASCE, 106(GT3), 299–321.
• Ménard, L. (1957). Mesures in situ des propriétés physiques des sols. Annales des Ponts et Chaussées.
• 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.