Packing Densification Response–Constrained Fractal Characterization and Compaction Performance Evaluation of Widely Graded Granular Materials.
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| Title: | Packing Densification Response–Constrained Fractal Characterization and Compaction Performance Evaluation of Widely Graded Granular Materials. |
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| Authors: | Ren, Guo-Feng1 (AUTHOR), Wang, Xin-Qing2,3 (AUTHOR), Wang, Yi1,3 (AUTHOR), Hu, Qiu-Yue1,4 (AUTHOR), Pei, Xiang-Jun1,3,4 (AUTHOR), Zhang, Xiao-Chao2,3 (AUTHOR) |
| Source: | Materials (1996-1944). Jun2026, Vol. 19 Issue 12, p2675. 18p. |
| Subjects: | Particle size distribution, Granular materials, Fractal analysis, Soil density |
| Abstract: | Highlights: A response-constrained PSD truncation framework is proposed for non-ideal PSDs. The unit-mass densification contribution coefficient identifies effective size ranges. A preliminary lower fitting limit is supported by geometry and response data. Truncated indices improve maximum dry density characterization for non-ideal PSDs. Not all particle-size fractions in widely graded granular materials contribute equally to compaction densification. For non-ideal particle-size distributions (PSDs) with local deviations or fine-end disturbances, the full-range fractal index may be influenced by particle-size fractions that contribute weakly to densification and, therefore, may not consistently represent the maximum dry density response. To address this problem, this study proposes a response-constrained truncation framework to identify a more effective PSD fitting range for fractal characterization. First, 20 concave and S-shaped PSDs from previous experiments were re-analyzed to compare full-range and truncated indices. Then, 21 progressively truncated specimens derived from three standard fractal PSDs were tested by relative density experiments. A unit-mass densification contribution coefficient, ηj, was defined from adjacent maximum dry density differences and particle-fraction mass contents. The ηj-d responses exhibited unimodal patterns, and the transition diameter dc shifted with PSD coarseness. For the two material sources, replacing the full-range index with the truncated index increased the R2 values between the fractal index and maximum dry density from 0.195 to 0.886 and from 0.191 to 0.856, respectively. A continuous percentile search showed that the optimal characteristic scale was concentrated near q ≈ 30, with a robust common optimum of q = 30.53. Sensitivity analysis for β = 0.85–0.95 indicated that 0.225d30 falls within the transition region from highly effective filling to reduced densification efficiency. Accordingly, dL = 0.225d30 is proposed as a preliminary engineering estimate of the lower fitting limit for non-ideal PSDs. The framework is intended for widely graded materials whose full-range fractal parameters are inconsistent with compaction response. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Highlights: A response-constrained PSD truncation framework is proposed for non-ideal PSDs. The unit-mass densification contribution coefficient identifies effective size ranges. A preliminary lower fitting limit is supported by geometry and response data. Truncated indices improve maximum dry density characterization for non-ideal PSDs. Not all particle-size fractions in widely graded granular materials contribute equally to compaction densification. For non-ideal particle-size distributions (PSDs) with local deviations or fine-end disturbances, the full-range fractal index may be influenced by particle-size fractions that contribute weakly to densification and, therefore, may not consistently represent the maximum dry density response. To address this problem, this study proposes a response-constrained truncation framework to identify a more effective PSD fitting range for fractal characterization. First, 20 concave and S-shaped PSDs from previous experiments were re-analyzed to compare full-range and truncated indices. Then, 21 progressively truncated specimens derived from three standard fractal PSDs were tested by relative density experiments. A unit-mass densification contribution coefficient, ηj, was defined from adjacent maximum dry density differences and particle-fraction mass contents. The ηj-d responses exhibited unimodal patterns, and the transition diameter dc shifted with PSD coarseness. For the two material sources, replacing the full-range index with the truncated index increased the R2 values between the fractal index and maximum dry density from 0.195 to 0.886 and from 0.191 to 0.856, respectively. A continuous percentile search showed that the optimal characteristic scale was concentrated near q ≈ 30, with a robust common optimum of q = 30.53. Sensitivity analysis for β = 0.85–0.95 indicated that 0.225d30 falls within the transition region from highly effective filling to reduced densification efficiency. Accordingly, dL = 0.225d30 is proposed as a preliminary engineering estimate of the lower fitting limit for non-ideal PSDs. The framework is intended for widely graded materials whose full-range fractal parameters are inconsistent with compaction response. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 19961944 |
| DOI: | 10.3390/ma19122675 |
