Influence factors on the nonlocal parameter and scale factor in strain gradient nonlocal Biot theory

In our previous work, the strain gradient nonlocal Biot poromechanics model was proposed, in which two key size parameters, i.e., the nonlocal parameter and scale factor, were introduced. However, an extensive discussion and the value range on these two parameters were absent. In this work, we present the method for determining these parameters and the influences of grain size, Porosity, and grain size distribution on these size parameters are also discussed for the first time. The results show that: I) the nonlocal parameter increases while the scale factor decreases with increasing grain size. There exists a critical grain size, below which the scale factor has a more prominent effect on the wave dispersion. A unified exponential equation of li /dm = A + B exp(-dm /C) (i = 0,1) can be employed to describe the relationship between these two dimensionless parameters and the mean grain size. II) Porosity significantly influences the wave velocity but has a negligible influence on the nonlocal parameter and scale factor. III) For media with a mix of grain sizes, the nonlocal parameter increases, but the scale factor decreases when the proportion of the fine grain content decreases. IV) The values of the nonlocal parameter and scale factor are on the order of millimeters. This work determined the value range and influence factors of these two critical parameters introduced in strain gradient nonlocal Biot theory, which is of great significance for popularizing and applying this theory to engineering practices.