Contribution of fractal dimension theory into the uniaxial compressive strength prediction of a volcanic welded bimrock

Abstract

This study was carried out on Sille agglomerate which is a typical volcanic welded bimrock. Two precious historical monuments, Koimesis Tes Panagias Church and Sekili hill settlement carved in Sille agglomerate, have maintained their stability without any support for centuries although suffering from weathering and various stability problems. However, due to its heterogeneity and sampling difficulties, the overall strength of Sille agglomerate has not been investigated yet. This paper presents the relationships between fragmentation fractal dimension (DF), fractal dimension of rough block surfaces (DR), number of blocks (BN), and volumetric block proportion (VBP) and the overall uniaxial compressive strength (UCS) of the Sille agglomerate. By using these properties as inputs, three statistically significant empirical models were developed for estimating the UCS of the Sille agglomerate. The results revealed that the DF and DR may be good predictors to estimate the UCS of welded volcanic bimrocks, and defining the properties of blocks by means of fractal theory provides significant contribution to the estimation of the UCS. It is observed that the failure planes in the core samples predominantly pass through the boundaries between matrix and blocks, and such behavior may indicate that the weakest component of the Sille agglomerate is boundaries. Accordingly, the UCS decreases due to the high DR values which create more or further weakest zones in the bimrocks. Finally, it is concluded that the negative correlation between the UCS and the VBP was attributed to increase of the DR due to the increase of the VBP.