SoilParametersEstimation

Soil Analysis strongly depends on the determination of soil mechanical parameters from in-situ and laboratory test.

In-situ Tests

The StandardPenetrationTest (SPT), the ConePressureTip test (CPT) and grain size distribution can be used to estimate mechanical parametr used in mathematical soil models

Relative Density vs Number of Blows Count (Absolute/Relative)

Correlation has been introduced between Number of Blows Count in SPT and the Relative Density, overburden pressure in Meyerhof 1957 (units must be KPa)

$$ N=( a + b \cdot \frac{\sigma_{v}^{'}}{98} )\cdot D_{R}^{2} $$ where:

• the Relative Density \(D_{R}\)
• verburden pressure \(\sigma_{v}^{'}\),

Setting the constants \(a=17\), \(b=24\) lead to approximate relationship

$$ N=( 0.173 + 0.244 \cdot \sigma_{v}^{'} )\cdot D_{R}^{2} $$

Generally speaking the blow count is function of the overburden pressure and of the relative density, so the use of the normalized \(N_{1}\) (blow count at the depth with \(\sigma_{v}^{'}\) allowing to compare values obtained at different depths) leads to the definition of the following coefficient as a function of the grain size distribution

$$ \frac{N_{1}}{D_{R}^{2}}=C_{D} $$

Ref. 3 propose the following expression for \(C_{D}\):

$$C_{D}=\frac{9}{(e_{max}-e_{min})^{2}}$$

Relative Density vs Cone Tip Pressure

The cone tip pressure expressed by:

$$q_{c}$$

can be correlated to the relative density and to the lateral effective pressure

Jamiolkowsky

$$ D_{R}=\frac{1}{3.10} \cdot \log{ \frac{q_c/p_a}{17.7 \cdot(\sigma_v/p_a)^{0.5} } } $$

Lancelotta

The following parameters are relevant to normal consolidated quartzly sand

$$ D_{R}=-98 + 66 \cdot \log{ \frac{q_c}{ (\sigma_v)^{0.5} } } $$

Liquefaction Potential

Liquafaction Potential are more extensivly treated HERE

Permeability

For Hydraulic Conductivity a stand alone topic ha been created click here to browse the topic

Undrained Cohesion and "qc" Correlation

Undrained cohesion and tip load in CPT can be correlated using various theory as reported in ( 2 Cap 7.9 )

Shear Modulus

The Shear Modulus can be used to characterize the soil stiffness. It can be correlated to the above mentioned in situ tests: SPT or CPT, or to the soil parameter and history stress level

SPT Correlation

From reference 8 , SPT value normalized to standard energy and 100 kPa overburden pressure
which in the following is set as \(p_a\)

$$ \frac{G_{max}}{p_a}=438\cdot \sqrt[3]{N_{1}} \cdot \sqrt{ \frac{ \sigma_{v}^{'} }{ p_a } } $$

From reference 9

$$ \frac{G_{max}}{p_a}=156 \cdot ( N_{60} )^{0.68} $$

where \(N_{60}\) is normalized only for the energy content.

CPT Correlation

For sand 11

$$ \frac{G_{max}}{p_a}=290 \cdot \sqrt[4]{ \frac{ q_c }{ p_a } } \cdot \left( \frac{ \sigma_{v}^{'} }{ p_a } \right)^{0.375} $$

and for clay 10

$$ \frac{G_{max}}{p_a} = 100 \cdot \left( \frac{ q_c }{ p_a } \right)^{0.695} e^{-1.13} $$

where \(e\) is the void ratio

Sandy Soil Parameter

The general formulae for sandy soil can be expressed as:

$$ G_{max} = C_A \cdot F(e) \cdot (\sigma_{a}^{'})^{n_a}\cdot(\sigma_{b}^{'})^{n_b}\cdot(\sigma_{c}^{'})^{n_c} \cdot p_{a}^{(1-n_a-n_b-n_c)} $$

The tabulated values of the parameters present in the above formula can be found in 2 (pag 346). The value is expressed as a function of the anisotropic initial stress state (the stress is expressed for each cartesian plane) that can be too complex to determine. a simpler relation is expressed as follows:

$$ G_{max} = C_A \cdot F(e) \cdot (\sigma_{m}^{'})^{n}\cdot p_{a}^{(1-n)} $$

In the above relationship th eshear modulus is expressed as a function of the mean tension:

$$ \sigma_{m}^{'} = \frac{1}{3} (\sigma_1+\sigma_2+\sigma_3) $$

In presence of clay, due to influence of the cohesion the previous value has to be multiplied by:

$$ (OCR)^{K} \\ K = 0.0025 \cdot PI^{0.66} $$

where PI is the Plasticity Index

Reference

[1] Meyerhof, G.G. 1957. Discussion on Research on determining the density of sands by penetration testing. Proc. 4th Int. Conf. on Soil Mech. and Found. Engrg., Vol. 1: 110.

[2] Renato Lancelotta, Geotecnica Zanichelli 1987

[3] M. CUBRINOVSKI, K. ISHIHARA, "Correlation between penetration resistance and relative density of sandy soils"

[4] ROBERT E. K., JAMES K. M., Arias Intensity Assessment of Liquefaction Test Sites on the East Side of San Francisco Bay Affected by the Loma Prieta, California, Earthquake of 17 October 1989”, http://walrus.wr.usgs.gov/geotech/arias/

[5] M.S. Nataraja, H. S. Gill, . Ocean Waves-Induced Liquefaction Analysis. Journal of Geotechnical Engineering, April 1983 Vol. 109 No4.

[6] R. B. Seed, K. O. Cetin, et alii, RECENT ADVANCES IN SOIL LIQUEFACTION ENGINEERING:A UNIFIED AND CONSISTENT FRAMEWORK, 26th Annual ASCE Los Angeles Geotechnical Spring Seminar, Keynote Presentation, H.M.S. Queen Mary, Long Beach, California, April 30, 2003.

[7] Justine Odong, Evaluation of Empirical Formulae for Determination of Hydraulic Conductivity based on Grain-Size Analysis, Journal of American Science, 3(3), 2007,

[8] Ohta, Y. and N. Goto, 1976, “Estimation of S-Wave Velocity in terms of Characteristic Indices of Soil”, Butsuri-Tanki, Vol. 29, No. 4, pp. 34-41.

[9] Imai, T. and K. Tonouchi, 1982, “Correlation of N-value with S-Wave Velocity and Shear Modulus”, Proceedings, 2nd European Symposium on Penetration Testing, Amsterdam, pp. 57-72.

[10] Mayne, P. W. and G. J. Rix, 1993, “Gmax-qc relationship for Clays”, Geotechnical Testing Journal, ASTM, Vol. 16, No. 1, pp. 54-60.

[11] Rix, G. J. and K. H. Stokoe, 1991, “Correlation of Initial Tangent Modulus and Cone Penetration Resistance”, Calibration Chamber Testing, International Symposium on Calibration Chamber Testing, A. B. Huang, ed., Elsevier Publishing, New York, pp. 351-362.

-- RobertoBernetti - 16 Feb 2010