Numerical Evaluation of the Amplification Characteristic of Randomly Heterogeneous Alluvial Deposits

  • Reza Jamshidi ChenariEmail author
  • Shirin Aminzadeh Bostani Taleshani
Original Paper


The estimation of the local site effects, which is inherently stochastic, on the amplitude and the frequency content of seismic wave through alluvial deposits, is an important and substantial step in the seismic risk mitigation. To this end, the random field theory along with the Monte Carlo simulations was employed to evaluate ground response of a half-space viscoelastic medium under stochastic variation of the shear wave velocity (SWV) adopted from five different sites. The results of the stochastic analyses are then compared to the deterministic computations assuming hyperbolic variation of SWV. This study will emphasize the importance of the stochastic variation of the shear wave velocity profile. An eminent input from the current study is that the sole consideration of the deterministic component in site response analyses is not well representative of the real seismic behavior of the alluvial deposits.


Heterogeneity Site response Alluvial deposits Monte Carlo simulations Random field theory 

List of symbols


Correlation matrix

Am and Bm

Recursion site response coefficients for layered deposits


Coefficient of variation of shear wave velocity


Ratio of surface to base shear wave velocities

f1 and f2

“Level-off” parameters


First-mode natural frequency of the soil deposit

F1, F2, F3

FDM constants


Transfer function


Soil shear modulus


Soil complex shear modulus


Soil layer’s thickness


Complex number (i2 = 1)


Complex wave number


Lower triangular matrix


Vertical correlation distance


Layer number


Number of realizations


Probability variable


Elastic shear stress tensor


Depth-dependent stress amplitude


Time domain


Deterministic “trend” component of a geotechnical property

u (z, t)

Horizontal displacement at depth z and time t


Depth-dependent displacement amplitude


Surface shear wave velocity


Base shear wave velocity


Shear wave velocity


Deterministic component of shear wave velocity profile


Equivalent shear wave velocity


Stochastic component of shear wave velocity profile


Average shear wave velocity of the upper 30 m of a soil profile


Stochastic “off-trend” component of a geotechnical property


Depth below the ground surface


Complex impedance ratio


Viscous damping


In situ geotechnical property


Vertical scale of fluctuation


Mean shear wave velocity


Soil mass density


Standard deviation


Lag distance


Angular frequency

ε (z, p)

Gaussian random vector field



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Copyright information

© Indian Geotechnical Society 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of GuilanRashtIran

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