Abstract
During the microstructural analysis of weakly cemented sandstone, the granule components and ductile structural parts of the sandstone are typically generalized. Considering the contact between granules in the microstructure of weakly cemented sandstone, three basic units can be determined: regular tetrahedra, regular hexahedra, and regular octahedra. Renormalization group models with granule- and pore-centered weakly cemented sandstone were established, and, according to the renormalization group transformation rule, the critical stress threshold of damage was calculated. The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold. The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model. The granule-centered calculation provides the lower limit (18.12%), and the pore-centered model provides the upper limit (36.36%). Within this range, the weakly cemented sandstone is in a phase-like critical state. That is, the state of granule aggregation transforms from continuous to discrete. In the relative stress range of 18.12%– 36.36%, the weakly cemented sandstone exhibits an increased proportion of high-frequency signals (by 83.3%) and a decreased proportion of low-frequency signals (by 23.6%). The renormalization calculation results for weakly cemented sandstone explain the high–low frequency conversion of acoustic emission signals during loading. The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.
Highlights
The Ordos and Yulin areas of western China exhibit typical lithologies for the region, with the strata mainly composed of weakly cemented Jurassic sandstone
The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold
The critical stress threshold for weakly cemented sandstone damage is studied, and the results effectively explain the conversion between high- and low-frequency signals of acoustic emissions during the weakly cemented sandstone loading process
Summary
The Ordos and Yulin areas of western China exhibit typical lithologies for the region, with the strata mainly composed of weakly cemented Jurassic sandstone. Weakly cemented sandstone has the property of self-similarity, which is the most important physical feature considered in the renormalization group method (Ji 2004). The relations among the physical properties of weakly cemented sandstone at different scales are a key topic of study. Wilson (1971a, b) used the renormalization group method to study continuous phase transitions, and found that the self-similarity exhibited by the system at different scales near the critical point could be described by the renormalization group method (Goldenfeld 1992). This discovery provides a more reasonable and effective theoretical expression for continuous phase transition, as well as a more direct physical basis for the renormalization group method. The critical stress threshold for weakly cemented sandstone damage is studied, and the results effectively explain the conversion between high- and low-frequency signals of acoustic emissions during the weakly cemented sandstone loading process
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