Investigating Size Effects on Gradient-Related Crack Behavior in Frozen Sand Samples: A Simplified Approach and Application

The stability performance of the frozen curtain formed under standpipe freezing is closely associated with the weak zone penetrated by thermal gradient-related fracture (TGF). The TGF-rich zone further affects the liquid phase flow when the frozen curtain is thawed. However, there is a lack of studies on the TGF-rich zone within the frozen curtain. To address this gap, a simplified and practical 2D bonded particle model-based numerical simulation strategy was developed to identify the possibility of acquiring field characteristics of the TGF-rich zone by conducting numerical tests on samples considering size effects. The results, validated by the experiment, indicated that the influence of size on crack localization zone was comparable to that of the parameter gradient but had a weaker characteristic on crack orientation, which represents the orientation of TGF. In particular, the characterization result of the TGF-rich zone using crack localization zone in the simulation closely matched that using lateral strain localization zone both in simulation and experiment. Regarding the size effects of the TGF-rich zone revealed in the simulation, the estimated field length of the TGF-rich zone accounted for approximately 30% of the zone width characterized by a horizontal thermal gradient, with maximum orthotropic deformation occurring at about 10% of the zone width. These observations validate the existence of TGF within the frozen curtain and contribute to the development of a precise grouting technique to mitigate subsidence within soil deposits subjected to freeze-thaw.