Civil Engineering ETDs

Publication Date

Fall 12-16-2016


The discrete element method (DEM) is employed to study complex behaviors of particulate media. Input parameters may greatly affect the response of DEM models and should therefore be selected carefully. Scaling techniques are employed to enlarge prohibitively small time-steps. To study these techniques, dimensionless input parameters were defined. Responses of models in the dimensionless scale were invariant with choice of density, elastic modulus, and characteristic length if the dimensionless parameters were kept constant. Hence, density scaling is equivalent to use of a higher strain-rate, and stiffness scaling results in a higher strain-rate and an elevated stress state in the dimensionless scale.

In quasi-static simulations, the equilibrium state should be monitored by the proposed moment index. The conventional mass-damping model causes different damping ratios for particles. A new damping model was introduced to address this issue. Comparisons showed superiority of the presented model. The optimum damping ratio was defined as the damping ratio using which the imbalance is minimized in terms of the moment index. For the conventional and proposed damping models the optimum damping ratio were determined approximately equal to 0.3% and 0.5%, respectively.

In quasi-static simulations, very small strain-rates are applied that should not exceed a specific value beyond which the quasi-static conditions cannot be preserved. The quasi-static strain-rate was defined based on the moment index equal to 0.1%. An approximate quasi-static strain-rate can be determined from a few simulations at high strain-rates. Predictive equations were developed based on initial void ratio, confining pressure, and particle-size distribution of samples. The equations showed adequate accuracy in estimating quasi-static strain-rate, better than that of the inertial number, and suited for the peak state.

Three relationships were developed. The imbalance, in terms of the moment index, depends on the product of strain-rate and damping ratio. Peak friction coefficient shows a linear relationship with the moment index. Using this relationship, the quasi-static peak friction coefficient can be estimated by conducting a few simulations at higher strain-rates (saving of computation effort). The relationship between peak friction coefficient and product of damping ratio and dimensionless strain-rate was derived, which can, also, be utilized to estimate the quasi-static peak friction coefficient.


Dimensionless, DEM, Damping, Size-dependent, quasi-static, strain-rate

Document Type




Degree Name

Civil Engineering

Level of Degree


Department Name

Civil Engineering

First Committee Member (Chair)

Tang-Tat Ng

Second Committee Member

Walter Gerstle

Third Committee Member

Arup Kanti Maji

Fourth Committee Member

Yu-Lin Shen