A Size Effect Model Combining Both Surface Effects and the Fracture Process Zone (FPZ) for Rocks under Uniaxial Compression

Developing a size effect model that can encompass the surface effect and the fracture process zone (FPZ) is still challenging. Here, a combined size effect model (CSE model) is formulated by integrating the surface effect size model and the size effect model of fracture mechanics (SEFM model) associated with the FPZ for rocks under compression. Parametric studies indicate that an increased volume fraction of the interior zone as the sample size increases is responsible for the anomalous size effect (ASE). The normal size effect (NSE) is a result of the decrease in the surface layer's volume fraction and the interior zone's nominal strength as the sample size increases. Moreover, the mixed type ASE-NSE is caused by the competition among the reduced surface volume fraction, the weakened interior zone strength, and the increased interior zone volume fraction as the sample size increases. A validation study demonstrates that the CSE model accurately predicts the ASE, the NSE, and the mixed type ASE-NSE. It was observed that the determination coefficient R2 of the CSE model is greater than that of the SEFM model for the NSE, equivalent to that of the size effect model of surface effects for the ASE and close to that of the improved USEL (IUSEL) for the mixed type ASE-NSE.