Application of Mohr-Coulomb yield criterion in geo-technical engineering
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1 GLOBAL GEOLOGY Vol. 29 No. 4 Dec Mohr-Coulomb Tresca Mises Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb TV TU452 A doi /j. issn Application of Mohr-Coulomb yield criterion in geo-technical engineering LIU Ying 1 2 YU Li-hong 3 1. College of Construction Engineering Jilin University Changchun China 2. Changchun Vanke Co. Ltd Changchun China 3. HydroChina Beijing Engineering Corporation Beijing China Abstract The yield curves and yield stress of Tresca Mises Double shear and Mohr-Coulomb yield criterions were discussed and compared to find the differences among them. The relation among Mohr-Coulomb yield criterion and the others were discussed and comfirmed the safety of Mohr-Coulomb yield criterion in geo-technical engineering and the relationships between fracture plane location and slip curves when the rock and soil fractured. The different yield criterions were analyzed and compared taking Yabiluo hydropower station geo-stresses for example and demonstrated the safety of Mohr-Coulomb yield criterion and the difference between failure surface and slip curves. Key words Mohr-Coulomb yield criterion safety Yabiluo hydropower station geo-stresses slip curves Tresca Mises Drukle-Plager Mohr-Coulomb Mohr
2 Coulomb Mohr-Coulomb S -D Strength Difference Effect τ c τ max Mohr-Coulomb Tresca φ 10 σ Tresca σ Mises σ DJ Mohr-Coulomb 11 π Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Tresca 1 Mohr-Coulomb Mises 1. 1 Mohr-Coulomb σ 1 σ 2 σ 3 3 Tresca 4 Mohr-Coulomb τ max = σ 1 σ 3 /2 = σ s /2 1 3 Mises 4 σ 1 - σ σ 2 - σ σ 3 - σ 1 2 = 6C = 2σ 2 s J 2 = C τ 13 + max τ 12 τ 23 = c c c = σ s τ 13 + max τ 12 τ 23 = σ s 3 Mohr-Coulomb 6-9 τ n = σ n tgφ + c 4 σ 1 - σ 3 = σ 1 + σ 3 sinφ + 2ccosφ 5 f = 1 2 I 1sinφ + cosθ σ 1 槡 3 sinθ sinφ J σ 槡 2 - ccosφ = π /6 θ σ π / Mohr-Coulomb σ m = σ 1 + σ 2 + σ 3 /3 σ 2 = σ m 1 σ m M M τ max = ± σ 1 σ 3 /2 Tresca π /4 α β Mohr-Coulomb τ max = ± σ 1 σ 3 /2 τ = τ max sinφ τ max τ max = c σ s = σ 1 + σ 2 /2 - σ 1 + σ 2 /2 sinφ 7 1 Fig. 1 Mohr-Coulomb Relations between failure surface and slip curves of Mohr-Coulomb yield criterion
3 4 Mohr-Coulomb 635 π /4 + φ /2 φ = 0 φ /2 1 2 Mohr-Coulomb 3. 2 Mohr-Coulomb 37 km π Mohr-Coulomb km 10 km 6 km V 25 ~ ~ ~ 80 m NE62 80 ~ 100 m Mohr-Coulomb 0. 24% Drukle Plager 13 π Mohr- 45% ~ 70% Coulomb 20% ~ 40% 5% ~ 25% Zienkiewicz and Pande ~ π Mohr-Coulomb Mohr- Coulomb 10 ~ 30 m π Mohr-Coulomb 1 ~ Mohr- m Coulomb Mohr-Coulomb Mohr-Coulomb 3 30 km km 1. 6 km 70 ~ m 63 km 616 km m m MW 32 km m 3 1 ZK10
4 Ⅱ Ⅲ NE50 ~ 85 NW SE 60 ~ 85 2 NW275 ~ 300 SW 17 σ H NE 40 ~ 65 σ h σ v 3 1 NE60 ~ 85 NW SE 70 ~ 85 2 NW310 ~ 330 NE SW 70 ~ 85 3 NW275 ~ 295 NE SW 80 ~ ~ ZK m m m m m m m m m m T g VII c = MPa φ = ~ 60 km NE -NEE σ H = 3 p s p r - p 0 8 σ h = p s 9 σ v = γd ~ 120 m Fig. 2 Theory Mohr s circle and its envelope lines 3
5 4 Mohr-Coulomb 637 Table 1 1 ZK10 Results of hydraulic fracturing stress of hole ZK10 /m /MPa /MPa P b P r P s P H P 0 T S H S h S V / / / N65 W N20 W N10 E N32 E P H P 0 P b P r P s T S h S H S v 2 Table 2 Statistics of yield stress results σ s /MPa Tresca Mises Mohr-Coulomb ZK10 c = 0. 6 ~ 0. 8 MPa φ = 35 ~ Tresca Mises c φ ZK10 Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb 3 9 Mohr-Coulomb c φ Fig. 3 Relations between rock mass failure surface and slip curves of No. 9 measures
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