Abstract
The residual friction angle (\(\varnothing_r'\)) is an important indicator used to evaluate the stability of soil slopes, and most of its correlation studies are based on one or more parameters such as the plasticity index, clay fraction, and normal stress. Existing methods for residual friction angle prediction involving plastic limit measurements have the drawbacks of complicated procedures and excessive errors. In this paper, the flow index is used instead of the plasticity index, the plasticity index of fine-grained soil based on the flow index (FI) is proposed, and the correlation of the residual friction angle is studied. The results indicate that (1) both the flow index and plasticity index can reflect the plasticity capacity of fine-grained soil, but the flow index is simple to obtain and more accurate. (2) Flow index, flow clay factor, flow plasticity angle, and the vertical distance of A-Line (\(\Delta\) FI) can characterize the residual shear properties of fine-grained soils, which generally show that the residual friction angle gradually decreases with increasing plasticity. (3) To address the problem of scattered or excessive data in the existing calculation models, an improved model for calculating the residual friction angle is proposed based on the clay fraction and flow index, and its fitting results are significantly better than those of the existing calculation models. (4) The correlation between residual friction angle and flow index is suitable for predicting the accuracy of residual shear test results, but has limitations when used to predict the residual friction angle.
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This research was supported by the National Natural Science Foundation of China General Program (No. 42177153).
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Appendix
Appendix
The relevant data involved in this study
wL | PI | FI | CF | CFI | ∆FI | αFI | \({\varphi }_{r}\mathrm{^{\prime}}\) | References |
|---|---|---|---|---|---|---|---|---|
75.0 | 38.0 | 50.7 | 30.2 | 0.7 | − 7.3 | 45.0 | 15.0 | (Tiwari and Marui 2005) |
82.0 | 39.1 | 52.1 | 32.2 | 0.6 | − 14.3 | 42.1 | 16.0 | |
78.0 | 38.0 | 50.7 | 30.1 | 0.6 | − 10.9 | 43.3 | 16.0 | |
66.7 | 21.9 | 29.2 | 17.5 | 0.4 | − 18.9 | 34.5 | 22.0 | |
71.0 | 35.0 | 46.7 | 30.2 | 0.7 | − 6.5 | 45.0 | 14.0 | |
72.3 | 37.1 | 49.5 | 31.1 | 0.7 | − 5.3 | 45.8 | 14.0 | |
76.0 | 36.0 | 48.0 | 30.8 | 0.6 | − 11.2 | 42.9 | 16.0 | |
68.1 | 34.6 | 46.1 | 28.8 | 0.7 | − 3.6 | 46.5 | 12.0 | |
84.0 | 52.9 | 70.5 | 45.2 | 0.8 | 1.7 | 49.7 | 11.0 | |
69.2 | 31.0 | 41.3 | 26.3 | 0.6 | − 9.7 | 42.6 | 12.0 | |
81.4 | 43.9 | 58.5 | 37.5 | 0.7 | − 7.2 | 45.7 | 11.0 | |
78.2 | 25.8 | 34.4 | 20.5 | 0.4 | − 27.4 | 32.5 | 12.0 | |
75.5 | 25.6 | 34.1 | 21.5 | 0.5 | − 24.4 | 33.7 | 12.0 | |
77.2 | 49.5 | 66.0 | 38.2 | 0.9 | 5.4 | 51.3 | 10.0 | |
66.0 | 31.0 | 41.3 | 27.7 | 0.6 | − 5.9 | 44.7 | 12.5 | |
55.0 | 18.0 | 24.0 | 19.5 | 0.4 | − 10.4 | 38.0 | 18.8 | |
86.3 | 47.1 | 62.8 | 28.2 | 0.7 | − 8.9 | 45.4 | 10.0 | |
89.0 | 41.9 | 55.9 | 37.5 | 0.6 | − 19.1 | 40.8 | 10.0 | |
73.0 | 35.3 | 47.1 | 22.1 | 0.6 | − 8.5 | 44.0 | 10.1 | |
64.0 | 34.1 | 45.5 | 19.2 | 0.7 | 0.6 | 48.9 | 12.7 | |
68.0 | 38.2 | 50.9 | 28.2 | 0.7 | 1.3 | 49.4 | 9.8 | |
69.0 | 40.0 | 53.3 | 27.2 | 0.8 | 2.5 | 50.0 | 9.8 | |
51.0 | 19.0 | 25.3 | 21.8 | 0.5 | − 4.5 | 43.5 | 10.7 | |
71.5 | 36.4 | 48.5 | 21.2 | 0.7 | − 5.3 | 45.8 | 19.0 | |
55.8 | 32.6 | 43.5 | 20.5 | 0.8 | 8.1 | 54.0 | 18.0 | |
70.0 | 38.0 | 50.7 | 24.0 | 0.7 | − 1.3 | 47.9 | 8.9 | |
65.0 | 34.0 | 45.3 | 22.0 | 0.7 | − 0.7 | 48.1 | 10.7 | |
61.0 | 15.0 | 20.0 | 20.0 | 0.3 | − 21.4 | 28.6 | 16.2 | |
53.0 | 26.0 | 34.7 | 14.0 | 0.7 | 2.6 | 50.3 | 19.3 | |
91.3 | 50.5 | 67.3 | 32.8 | 0.7 | − 10.5 | 45.1 | 10.0 | |
94.6 | 62.4 | 83.2 | 33.2 | 0.9 | 1.3 | 49.8 | 10.0 | |
69.0 | 38.0 | 50.7 | 27.5 | 0.7 | − 0.1 | 48.6 | 9.8 | |
62.0 | 29.0 | 38.7 | 19.9 | 0.6 | − 3.9 | 45.7 | 12.8 | |
59.0 | 19.0 | 25.3 | 20.0 | 0.4 | − 13.7 | 36.1 | 17.6 | |
96.2 | 48.0 | 64.0 | 32.2 | 0.7 | − 19.9 | 41.7 | 12.0 | |
94.7 | 59.2 | 78.9 | 33.5 | 0.8 | − 3.1 | 48.3 | 12.0 | |
63.0 | 32.0 | 42.7 | 24.8 | 0.7 | − 1.1 | 47.8 | 17.1 | |
71.0 | 38.0 | 50.7 | 26.2 | 0.7 | − 2.5 | 47.3 | 11.2 | |
64.0 | 21.0 | 28.0 | 23.0 | 0.4 | − 16.9 | 35.2 | 11.1 | |
79.8 | 36.3 | 48.4 | 40.2 | 0.6 | − 15.4 | 41.1 | 10.0 | |
100.0 | 68.3 | 91.1 | 42.8 | 0.9 | 2.5 | 50.3 | 10.0 | |
120.0 | 65.5 | 87.3 | 42.0 | 0.7 | − 26.5 | 42.4 | 10.9 | |
108.0 | 66.2 | 88.3 | 41.2 | 0.8 | − 10.3 | 46.5 | 14.7 | |
58.0 | 29.2 | 38.9 | 21.3 | 0.7 | 1.0 | 49.1 | 19.2 | |
57.0 | 17.0 | 22.7 | 10.0 | 0.4 | − 14.1 | 34.7 | 12.7 | |
57.0 | 23.0 | 30.7 | 2.8 | 0.5 | − 6.1 | 43.1 | 10.4 | |
61.0 | 24.0 | 32.0 | 18.0 | 0.5 | − 9.4 | 41.1 | 18.1 | |
55.0 | 27.0 | 36.0 | 6.5 | 0.7 | 1.6 | 49.5 | 17.6 | |
82.0 | 51.0 | 68.0 | 31.0 | 0.8 | 1.6 | 49.7 | 15.2 | |
84.0 | 31.0 | 41.3 | 22.0 | 0.5 | − 27.5 | 34.7 | 14.0 | |
54.0 | 19.0 | 25.3 | 10.0 | 0.5 | − 7.9 | 40.4 | 12.9 | |
56.0 | 28.0 | 37.3 | 5.4 | 0.7 | 1.8 | 49.6 | 25.7 | |
49.0 | 9.0 | 12.0 | 5.0 | 0.2 | − 15.5 | 25.9 | 26.7 | |
41.0 | 6.0 | 8.0 | 2.9 | 0.2 | − 10.5 | 25.6 | 28.9 | |
83.0 | 54.0 | 72.0 | 51.0 | 0.9 | 4.4 | 50.8 | 11.0 | |
41.2 | 29.9 | 39.9 | 10.0 | 1.0 | 21.1 | 67.0 | 28.7 | |
46.8 | 30.3 | 40.4 | 10.0 | 0.9 | 15.4 | 60.9 | 23.1 | |
67.7 | 27.5 | 36.7 | 17.0 | 0.5 | − 12.6 | 40.2 | 14.4 | |
72.3 | 29.9 | 39.9 | 17.0 | 0.6 | − 14.9 | 39.7 | 17.2 | |
55.6 | 38.6 | 51.5 | 12.0 | 0.9 | 16.4 | 58.7 | 8.3 | |
56.8 | 34.3 | 45.7 | 16.0 | 0.8 | 9.2 | 54.6 | 7.8 | |
36.0 | 10.0 | 13.3 | 10.0 | 0.4 | 0.4 | 48.7 | 29.0 | |
35.0 | 8.0 | 10.7 | 6.0 | 0.3 | − 1.2 | 44.8 | 29.0 | |
26.0 | 8.0 | 10.7 | 5.0 | 0.4 | 8.7 | 80.8 | 31.0 | |
77.2 | 20.7 | 27.6 | 16.2 | 0.4 | − 33.0 | 27.5 | 25.6 | |
57.0 | 17.3 | 23.1 | 15.2 | 0.4 | − 13.7 | 35.2 | 25.8 | |
57.3 | 12.7 | 16.9 | 11.2 | 0.3 | − 20.1 | 27.1 | 23.4 | |
36.0 | 5.0 | 6.7 | 9.0 | 0.2 | − 6.3 | 29.6 | 23.3 | |
45.0 | 19.0 | 25.3 | 13.0 | 0.6 | 2.3 | 50.7 | 25.5 | |
47.0 | 9.0 | 12.0 | 6.5 | 0.3 | − 13.3 | 27.8 | 28.0 | |
36.4 | 9.6 | 12.8 | 0.4 | 0.4 | − 0.6 | 46.5 | 28.4 | |
31.1 | 11.1 | 14.8 | 1.0 | 0.5 | 7.2 | 65.2 | 24.9 | |
54.0 | 23.5 | 31.3 | 2.4 | 0.6 | − 1.9 | 46.5 | 24.4 | |
48.6 | 16.6 | 22.1 | 4.3 | 0.5 | − 4.9 | 42.3 | 30.1 | |
42.7 | 16.1 | 21.5 | 4.2 | 0.5 | 1.1 | 49.4 | 29.0 | |
32.0 | 4.5 | 6.0 | 1.8 | 0.2 | − 2.5 | 37.8 | 23.6 | |
35.0 | 6.0 | 8.0 | 2.3 | 0.2 | − 3.8 | 36.7 | 21.1 | |
36.0 | 5.5 | 7.3 | 3.9 | 0.2 | − 5.6 | 32.0 | 21.4 | |
65.8 | 42.6 | 56.8 | 6.7 | 0.9 | 9.8 | 53.8 | 21.3 | |
44.6 | 20.7 | 27.6 | 10.9 | 0.6 | 5.1 | 53.6 | 23.2 | |
37.9 | 15.4 | 20.5 | 7.0 | 0.5 | 5.5 | 56.4 | 23.7 | |
47.8 | 21.9 | 29.2 | 8.9 | 0.6 | 3.0 | 51.1 | 17.8 | |
60.0 | 41.0 | 54.7 | 49.0 | 0.9 | 14.5 | 56.8 | 10.0 | (Meisina 2010) |
68.0 | 47.0 | 62.7 | 58.0 | 0.9 | 13.0 | 55.1 | 9.0 | |
33.0 | 18.0 | 24.0 | 34.0 | 0.7 | 14.4 | 70.0 | 17.0 | |
55.0 | 32.0 | 42.7 | 33.0 | 0.8 | 8.3 | 54.2 | 14.5 | |
104.0 | 81.0 | 108.0 | 75.0 | 1.0 | 14.4 | 53.6 | 4.7 | |
54.0 | 30.0 | 40.0 | 41.0 | 0.7 | 6.7 | 53.4 | 16.0 | |
54.0 | 31.0 | 41.3 | 33.0 | 0.8 | 8.1 | 54.3 | 14.0 | |
72.0 | 52.0 | 69.3 | 50.0 | 1.0 | 14.9 | 55.5 | 8.0 | |
57.0 | 38.0 | 50.7 | 45.0 | 0.9 | 13.9 | 57.1 | 6.0 | |
52.0 | 22.0 | 29.3 | 24.0 | 0.6 | − 1.6 | 46.6 | 21.0 | |
63.0 | 40.0 | 53.3 | 53.0 | 0.8 | 9.6 | 54.0 | 11.0 | |
47.0 | 27.0 | 36.0 | 38.0 | 0.8 | 10.7 | 57.7 | 15.0 | |
90.0 | 70.0 | 93.3 | 61.0 | 1.0 | 17.1 | 54.8 | 5.5 | |
31.0 | 11.0 | 14.7 | 34.0 | 0.5 | 7.2 | 65.4 | 17.0 | |
45.0 | 24.0 | 32.0 | 31.0 | 0.7 | 9.0 | 57.1 | 16.0 | |
94.0 | 68.0 | 90.7 | 52.0 | 1.0 | 9.5 | 52.4 | 4.0 | |
68.0 | 46.0 | 61.3 | 48.0 | 0.9 | 11.7 | 54.5 | 8.2 | |
70.0 | 49.0 | 65.3 | 53.0 | 0.9 | 13.3 | 55.0 | 7.6 | |
59.0 | 27.0 | 36.0 | 29.0 | 0.6 | − 3.1 | 46.0 | 9.1 | |
56.0 | 32.0 | 42.7 | 47.0 | 0.8 | 7.1 | 53.4 | 11.3 | |
69.0 | 46.0 | 61.3 | 49.0 | 0.9 | 10.5 | 53.9 | 7.1 | |
64.0 | 43.0 | 57.3 | 45.0 | 0.9 | 12.4 | 55.3 | 6.4 | |
66.0 | 45.0 | 60.0 | 39.0 | 0.9 | 12.7 | 55.2 | 8.5 | |
60.0 | 31.0 | 41.3 | 37.0 | 0.7 | 1.1 | 49.2 | 8.9 |
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Yang, Z., Xu, Z., Qin, X. et al. Evaluation of correlation between plasticity indicator and residual friction angle of fine-grained soils based on the flow index. Bull Eng Geol Environ 83, 52 (2024). https://doi.org/10.1007/s10064-023-03526-4
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DOI: https://doi.org/10.1007/s10064-023-03526-4