Dynamic soil property correlations

groundhog.soildynamics.soilproperties.dampingratio_sandgravel_seed(cyclic_shear_strain, **kwargs)[source]

Damping ratios for sand are compiled from a dataset comprising several sands and gravels. Average values and upper and lower bounds are provided. The comparison of the trends proposed for sand with the datapoints measured on gravel suggests that the trend is applicable for gravels too.

Parameters

cyclic_shear_strain – Cyclic shear strain (\(\gamma_{cyc}\)) [\(pct\)] - Suggested range: 0.0001 <= cyclic_shear_strain <= 1.0

Returns

Dictionary with the following keys:

  • ’D LE [pct]’: Low estimate damping ratio (\(D_{LE}\)) [\(pct\)]

  • ’D BE [pct]’: Average or best estimate damping ratio (\(D_{BE}\)) [\(pct\)]

  • ’D HE [pct]’: High estimate damping ratio (\(D_{HE}\)) [\(pct\)]

../_images/dampingratio_sandgravel_seed_1.png

Proposed trends and measurement data on gravels

Reference - Seed, H. B., Wong, R. T., Idriss, I. M., & Tokimatsu, K. (1986). Moduli and damping factors for dynamic analyses of cohesionless soils. Journal of geotechnical engineering, 112(11), 1016-1032.

groundhog.soildynamics.soilproperties.gmax_shearwavevelocity(Vs, gamma, g=9.81, **kwargs)[source]

Calculates the small-strain shear modulus (shear strain < 1e-4%) from the shear wave velocity and the bulk unit weight if the soil based on elastic theory.

Often, the result of an in-situ or laboratory test will provide the shear wave velocity, which is then converted to the small-strain shear modulus using this function.

Parameters
  • Vs – Shear wave velocity (\(V_s\)) [\(m/s\)] - Suggested range: 0.0 <= Vs <= 600.0

  • gamma – Bulk unit weight (\(\gamma\)) [\(kN/m3\)] - Suggested range: 12.0 <= gamma <= 22.0

  • g – Acceleration due to gravity (\(g\)) [\(m/s2\)] - Suggested range: 9.7 <= g <= 10.2 (optional, default= 9.81)

\[ \begin{align}\begin{aligned}G_{max} = \rho \cdot V_s^2\\\rho = \gamma / g\end{aligned}\end{align} \]
Returns

Dictionary with the following keys:

  • ’rho [kg/m3]’: Density of the material (\(\rho\)) [\(kg/m3\)]

  • ’Gmax [kPa]’: Small-strain shear modulus (\(G_{max}\)) [\(kPa\)]

Reference - Robertson, P.K. and Cabal, K.L. (2015). Guide to Cone Penetration Testing for Geotechnical Engineering. 6th edition. Gregg Drilling & Testing, Inc.

groundhog.soildynamics.soilproperties.modulusreduction_plasticity_ishibashi(strain, PI, sigma_m_eff, multiplier_1=0.000102, exponent_1=0.492, multiplier_2=0.000556, exponent_2=0.4, multiplier_3=-0.0145, exponent_3=1.3, **kwargs)[source]

Calculates the modulus reduction curve (G/Gmax) as a function of shear strain. The curve depends on the plasticity of the material (plasticity index) and the mean effective stress at the depth of interest.

The curve for cohesionless soils can be established by using a plasticity index of 0. At low plasticity, the effect of confining pressure on the modulus reduction curve is more pronounced.

Also calculates the damping ratio of plastic and non-plastic soils based on a fit to empirical data.

Parameters
  • strain – Strain amplitude (\(\gamma\)) [\(pct\)] - Suggested range: 0.0 <= strain <= 10.0

  • PI – Plasticity index (\(PI\)) [\(pct\)] - Suggested range: 0.0 <= PI <= 200.0

  • sigma_m_eff – Mean effective pressure (\(\sigma_m^{\prime}\)) [\(kPa\)] - Suggested range: 0.0 <= sigma_m_eff <= 400.0

  • multiplier_1 – Multiplier in equation for K (:math:``) [\(-\)] (optional, default= 0.000102)

  • exponent_1 – Exponent in equation for K (:math:``) [\(-\)] (optional, default= 0.492)

  • multiplier_2 – First multiplier in equation for m (:math:``) [\(-\)] (optional, default= 0.000556)

  • exponent_2 – First exponent in equation for m (:math:``) [\(-\)] (optional, default= 0.4)

  • multiplier_3 – Second multiplier in equation for m (:math:``) [\(-\)] (optional, default= -0.0145)

  • exponent_3 – Second exponent in equation for m (:math:``) [\(-\)] (optional, default= 1.3)

\[ \begin{align}\begin{aligned}\frac{G}{G_{max}} = K \left( \gamma, \text{PI} \right) \left( \sigma_m^{\prime} \right)^{m \left( \gamma, \text{PI} \right) - m_0}\\K \left( \gamma, \text{PI} \right) = 0.5 \left[ 1 + \tanh \left[ \ln \left( \frac{0.000102 + n ( \text{PI} )}{\gamma} \right)^{0.492} \right] \right]\\m \left( \gamma, \text{PI} \right) - m_0 = 0.272 \left[ 1 - \tanh \left[ \ln \left( \frac{0.000556}{\gamma} \right)^{0.4} \right] \right] \exp \left( -0.0145 \text{PI}^{1.3} \right)\\\begin{split}n ( \text{PI} ) = \begin{cases} 0.0 & \quad \text{for PI } = 0 \\ 3.37 \times 10^{-6} \text{PI}^{1.404} & \quad \text{for } 0 < \text{PI} \leq 15 \\ 7.0 \times 10^{-7} \text{PI}^{1.976} & \quad \text{for } 15 < \text{PI} \leq 70 \\ 2.7 \times 10^{-5} \text{PI}^{1.115} & \quad \text{for } \text{PI} > 70 \end{cases}\end{split}\\\xi = 0.333 \frac{1 + \exp(-0.0145 PI^{1.3})}{2} \left[ 0.586 \left( \frac{G}{G_{max}} \right)^2 - 1.547 \frac{G}{G_{max}} + 1 \right]\end{aligned}\end{align} \]
Returns

Dictionary with the following keys:

  • ’G/Gmax [-]’: Modulus reduction ratio (\(G / G_{max}\)) [\(-\)]

  • ’K [-]’: Factor K in the equation (\(K ( \gamma, \text{PI} )\)) [\(-\)]

  • ’m [-]’: Exponent m in the equation (\(m \left( \gamma, \text{PI} \right) - m_0\)) [\(-\)]

  • ’n [-]’: Factor n in equations (\(n ( \text{PI} )\)) [\(-\)]

  • ’dampingratio [pct]’: Damping ratio (\(\xi\)) [\(pct\)]

Reference - Ishibashi, I., & Zhang, X. (1993). Unified dynamic shear moduli and damping ratios of sand and clay. Soils and foundations, 33(1), 182-191.