A Discrete Element-Based Monte Carlo Study for the calibration of Cyclic Soil Degradation Models for Saturated Sands

Saturated sands under fast cyclic loading can experience excess pore pressure build-up that progressively, deteriorates the geotechnical characteristics of the soil sample, such as strength and stiffness. In extreme cases, the soil can manifest the liquefaction phenomenon. Past laboratory cyclic loading triaxial tests have shown that the main factors affecting this phenomenon are: (i) particle size distribution, (ii) the initial void ratio, (iii) the confining pressure and (iv) the magnitude of cycle stress or strain. Moreover, in real soil, these factors can be considered uncertain due to the inherent soil variability as well as the random nature of the dynamic load. Therefore, in order to investigate thoroughly the impact of each factor on soil degradation, a large number of experimental tests would be required. On the other hand, the Discrete Element Method (DEM) offers an interesting and fast numerical approach to simulate cyclic undrained triaxial testing. Therefore, thanks to the potentiality of this method, a multitude of numerical analyses can be conducted in a shorter time frame.
This paper presents a probability-based cyclic degradation model which can be used to predict the hardening/degradation of the maximum shear stress and equivalent stiffness of saturated sands. Monte Carlo Simulation is carried out on soil samples modelled through the DEM. A lognormal distribution is assumed for each of the uncertain factors of the soil model to account for the inherent variability and measurement scatter. Statistical regression analysis is used to calibrate the parameters of traditional soil damage models considering the randomness of the soil parameters. A sensitivity analysis is also performed to assess the relative importance of each independent factor.
Lastly, statistical moments will be determined through a pertinent Monte Carlo study. Analytical expression of the probability density function will be derived using the C-type Gram-Charlier series expansion. Convergency study will be finally conducted through of the Kullback–Leibler cross-entropy measure.