get_xi_rho#

PySeismoSoil.helper_site_response.get_xi_rho(Vs: ndarray, formula_type: Literal[1, 2, 3] = 3) → tuple[float | numpy.ndarray, float | numpy.ndarray][source]#

Generate damping (xi) and density (rho) from the given 2-column Vs profile.

Parameters:

  • Vs (np.ndarray) – 1D Vs profile information (i.e., Vs only, no thickness information).

  • formula_type (Literal[1, 2, 3]) –

    Type of formula to determine damping from Vs.

    1 - Use this rule:

    • Vs < 250 m/s, xi = 5%;

    • 250 <= Vs < 750 m/s, xi = 2%;

    • Vs >= 750 m/s, xi = 1%;

    2 - Use the formula proposed in Taborda & Bielak (2013):

    Qs = 10.5-16Vs+153Vs^2-103Vs^3+34.7Vs^4-5.29Vs^5+0.31Vs^6

    (unit of Vs: km/s)

    3 - Use the rule by Archuleta and Liu (2004) USGS report:

    • Qs = 0.06Vs (Vs <= 1000 m/s)

    • Qs = 0.14Vs (1000 < Vs <= 2000 m/s)

    • Qs = 0.16Vs (Vs > 2000 m/s)

    Note: xi = 1 / (2 * Qs) (https://earthquake.usgs.gov/cfusion/external_grants/reports/04HQGR0059.pdf)

Returns:

  • xi (float | np.ndarray) – Damping ratio, having the same shape as the input Vs. (unit: 1)

  • rho (float | np.ndarray) –

    Soil mass density, calculated with this rule:

    • Vs < 200 m/s, rho = 1600

    • 200 <= Vs < 800 m/s, rho = 1800

    • Vs >= 800 m/s, rho = 2000

    (Unit of rho: kg/m3)