SoilLab

Scientific record

Methods and references

Formulae, assumptions, authors, standards and copy-ready citations for every calculation implemented in SoilLab Research.

Method 1

Standard penetration test

Energy and overburden correction, density, friction angle, undrained strength, foundation screening and liquefaction.

Source: Skempton (1986); Liao & Whitman (1986); Peck, Hanson & Thornburn (1974); Stroud (1974)

N₆₀ = N · (Eₘ / 0.60) · Cᵦ · Cₛ · Cᵣ
(N₁)₆₀ = Cₙ · N₆₀, Cₙ = √(100 / σ′ᵥ) ≤ 1.7
φ′ = 27.1 + 0.30N₆₀ − 0.00054N₆₀²; sᵤ ≈ 5N₆₀ kPa
  • Atmospheric reference pressure is 100 kPa.
  • Empirical correlations require local calibration.

Method 2

Cone penetration test

Friction ratio, soil behaviour type, undrained strength and direct bearing-capacity estimates.

Source: Robertson (1990, 2009, 2010); Meyerhof (1956, 1974); Schmertmann (1978); Bustamante & Gianeselli (1982)

Rᶠ = fₛ / q𝚌 × 100%
I𝚌 = √[(3.47 − log₁₀(q𝚌/pₐ))² + (log₁₀Rᶠ + 1.22)²]
sᵤ = (qₜ − σᵥ₀) / Nₖₜ
  • SBT is a behaviour type, not a laboratory USCS classification.
  • Default Nₖₜ requires site calibration.

Method 3

VST, DMT, PMT, PLT and DCP

Strength, stiffness, bearing response and empirical CBR from field measurements.

Source: ASTM D2573; Marchetti (1980); Ménard (1957); ASTM D1194; ASTM D6951; Kleyn (1975); Harrison (1989)

VST: sᵤ = T / [πD²(H/2 + D/6)]
DMT: Eᴅ = 34.7(p₁ − p₀)
DCP: CBR = 10^(2.48 − 1.057 log₁₀DCPI)
  • Instrument geometry and units must match the selected standard.
  • DCP–CBR is an empirical screening correlation.

Method 4

Atterberg limits

Liquid limit by cone or cup, plastic limit, plasticity index and Casagrande chart.

Source: BS 1377-2; ASTM D4318; Casagrande (1948)

PI = LL − PL
A-line: PI = 0.73(LL − 20)
U-line: PI = 0.9(LL − 8)
  • Liquid-limit regression is evaluated at 20 mm penetration or 25 blows.

Method 5

Particle-size distribution

Dry sieve grading, characteristic diameters and gradation coefficients.

Source: BS 1377-2; ASTM D6913; Stokes’ law

Cᵤ = D₆₀ / D₁₀
C𝚌 = D₃₀² / (D₁₀D₆₀)
  • Characteristic diameters use logarithmic interpolation.
  • Hydrometer corrections depend on the recorded apparatus and temperature.

Method 6

Compaction, CBR, permeability and strength

Compaction, penetration resistance, hydraulic conductivity, shear box, consolidation and triaxial testing.

Source: BS 1377; ASTM D698/D1557, D1883, D2434, D3080, D2435, D2850/D4767

ρd = ρ / (1 + w)
Constant head: k = QL / (Aht)
Mohr–Coulomb: τ = c′ + σ′ tan φ′
  • Reported precision does not replace apparatus calibration.
  • Drainage and stress interpretation follow the selected test mode.

Method 7

Phase and index relations

Water content, void ratio, porosity, saturation, unit weights, relative density, activity and sensitivity.

Source: Lambe & Whitman (1969); Terzaghi & Peck (1967); Skempton (1953)

w = (Mₜ − Mᴅ) / Mᴅ
n = e / (1 + e); S = wGₛ / e
Dᵣ = (eₘₐₓ − e) / (eₘₐₓ − eₘᵢₙ)
  • Water unit weight is 9.81 kN/m³.
  • Density-state bands follow Terzaghi & Peck.

Method 8

Borehole logging

Strata description, sampling record, water strike and SPT profile presented as a scaled borehole log.

Source: BS EN ISO 22475-1; BS 5930; ASTM D1586; ASTM D2488

N = d₁ + d₂ + d₃ (three 150 mm drives after seating)
σᵥ = Σγᵢhᵢ; σ′ᵥ = σᵥ − u
Layer thickness = z_bottom − z_top
  • Ground level is the log datum; depths are measured below ground level.
  • Unit weights above and below the water table are user-supplied.

Method 9

Shallow foundation bearing capacity

Ultimate and allowable bearing pressure of pads, strips and rafts with shape, depth, inclination and eccentricity corrections, plus elastic settlement.

Source: Terzaghi (1943); Meyerhof (1963); Hansen (1970); Vesić (1973); Bowles (1996)

q_ult = c·N𝚌·s𝚌·d𝚌·i𝚌 + q·N𝑞·s𝑞·d𝑞·i𝑞 + 0.5·γ′·B′·Nᵧ·sᵧ·dᵧ·iᵧ
B′ = B − 2e_B; L′ = L − 2e_L
s_e = q·B(1 − ν²)I_w / E_s
  • Homogeneous soil beneath the footing to a depth of about 2B.
  • Drained parameters for sand, undrained for clay; groundwater reduces the γ term.

Method 10

Pile (deep) foundation capacity

Shaft friction and end bearing for driven and bored piles from static parameters or SPT N₆₀, with group efficiency.

Source: Tomlinson (1994); Meyerhof (1976); Burland (1973); Converse–Labarre group efficiency

Q_u = Q_s + Q_p = Σ f_s·A_s + q_p·A_p
Sand: f_s = K_s·σ′ᵥ·tan δ; Clay: f_s = α·c_u
η = 1 − (θ/90)[(n−1)m + (m−1)n] / (nm)
  • Effective stress on the shaft is capped beyond the critical depth (≈15D) in sand.
  • Negative skin friction is applied only when selected.

Method 11

USCS and AASHTO classification

USCS symbols and descriptions, AASHTO group and group index.

Source: ASTM D2487; AASHTO M145; ASTM D3282; Casagrande (1948)

GI = 0.2a + 0.005ac + 0.01bd
USCS coarse/fine boundary: 50% passing 0.075 mm
Dual-symbol fines range: 5–12%
  • Measured PSD and Atterberg values should be used for reportable classifications.
  • Organic and peat identification requires visual and laboratory evidence.

Bibliography

Selected references

Casagrande, A. (1948). Classification and identification of soils. Transactions of the ASCE, 113, 901–930.

BibTeX
@article{casagrande1948, author={Casagrande, Arthur}, title={Classification and Identification of Soils}, journal={Transactions of the ASCE}, volume={113}, pages={901--930}, year={1948}}

Robertson, P. K. (1990). Soil classification using the cone penetration test. Canadian Geotechnical Journal, 27(1), 151–158.

BibTeX
@article{robertson1990, author={Robertson, P. K.}, title={Soil Classification Using the Cone Penetration Test}, journal={Canadian Geotechnical Journal}, volume={27}, number={1}, pages={151--158}, year={1990}}

Skempton, A. W. (1986). Standard penetration test procedures. Géotechnique, 36(3), 425–447.

BibTeX
@article{skempton1986, author={Skempton, A. W.}, title={Standard Penetration Test Procedures}, journal={Géotechnique}, volume={36}, number={3}, pages={425--447}, year={1986}}

Skempton, A. W. (1953). The colloidal activity of clays. Proceedings of the 3rd ICSMFE, 1, 57–61.

BibTeX
@inproceedings{skempton1953, author={Skempton, A. W.}, title={The Colloidal Activity of Clays}, booktitle={Proceedings of the 3rd ICSMFE}, volume={1}, pages={57--61}, year={1953}}

Marchetti, S. (1980). In situ tests by flat dilatometer. Journal of the Geotechnical Engineering Division, 106(GT3), 299–321.

BibTeX
@article{marchetti1980, author={Marchetti, Silvano}, title={In Situ Tests by Flat Dilatometer}, journal={Journal of the Geotechnical Engineering Division}, volume={106}, number={GT3}, pages={299--321}, year={1980}}

Vesić, A. S. (1973). Analysis of ultimate loads of shallow foundations. Journal of the Soil Mechanics and Foundations Division, 99(SM1), 45–73.

BibTeX
@article{vesic1973, author={Vesi\'c, A. S.}, title={Analysis of Ultimate Loads of Shallow Foundations}, journal={Journal of the Soil Mechanics and Foundations Division}, volume={99}, number={SM1}, pages={45--73}, year={1973}}

Meyerhof, G. G. (1963). Some recent research on the bearing capacity of foundations. Canadian Geotechnical Journal, 1(1), 16–26.

BibTeX
@article{meyerhof1963, author={Meyerhof, G. G.}, title={Some Recent Research on the Bearing Capacity of Foundations}, journal={Canadian Geotechnical Journal}, volume={1}, number={1}, pages={16--26}, year={1963}}

Meyerhof, G. G. (1976). Bearing capacity and settlement of pile foundations. Journal of the Geotechnical Engineering Division, 102(GT3), 197–228.

BibTeX
@article{meyerhof1976, author={Meyerhof, G. G.}, title={Bearing Capacity and Settlement of Pile Foundations}, journal={Journal of the Geotechnical Engineering Division}, volume={102}, number={GT3}, pages={197--228}, year={1976}}

Tomlinson, M. J. (1994). Pile Design and Construction Practice (4th ed.). London: E & FN Spon.

BibTeX
@book{tomlinson1994, author={Tomlinson, M. J.}, title={Pile Design and Construction Practice}, edition={4}, publisher={E \& FN Spon}, address={London}, year={1994}}

Youd, T. L. et al. (2001). Liquefaction resistance of soils. Journal of Geotechnical and Geoenvironmental Engineering, 127(10), 817–833.

BibTeX
@article{youd2001, author={Youd, T. L. and others}, title={Liquefaction Resistance of Soils}, journal={Journal of Geotechnical and Geoenvironmental Engineering}, volume={127}, number={10}, pages={817--833}, year={2001}}

SoilLab Research is an engineering and teaching aid. Correlations must be calibrated against site-specific testing and reviewed by a competent geotechnical professional.