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Critical State Soil Mechanics Phần 8

Tham khảo tài liệu 'critical state soil mechanics phần 8', khoa học tự nhiên, công nghệ môi trường phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 151 so that ơ 2ơ I 3 sin p I p 7 I 7 K 3 3 - 3 sin p J I 2sinp I - q r r-r I I K I 1-sinp J -q1 _ 6sinp I - I z-------. r r r l . I p 3 sinp peak 8.8 The second possibility involves failure in compression withKl ơ max ơ r ơ . . and 11 sin p V r I li ơr 1 - sin p J which gives 6sin p 3 - sin p r I r r 8.9 Fig. 8.10 Mohr-Rankine Limiting-stress Ratios Thus there are two lines which are drawn dotted on the q p plane Fig. 8.10 and which indicate states when compression and extension tests respectively reach their peak Mohr-Rankine stress ratio. V2 fz a b Fig. 8.11 Mohr-Rankine Criterion in Principal Stress Space 152 If we also want the principal stress space representation we simply convert scales by factors of 1 and-73 and obtain the dotted lines in Fig. 8.11 a . A section of principal stress space on the plane CE normal to the space diagonal is shown in Figs. 8.11 b and 8.12. The peak stresses in Fig. 8.12 now lie on an irregular hexagonal cone of an almost triangular section in the plane perpendicular to the space diagonal. Principal points on the Mohr-Rankine peak stress locus are C and E which refer to peak stress ratios in compression and extension.5 ơi Fig. 8.12 Mohr-Rankine Limiting Surface for k O The yield surface of Fig. 5.1 is a surface of rotation about the space diagonal which for states rather drier than critical lies outside the irregular cone of Fig. 8.12. Thus the Mohr - Rankine criterion predicts that for these states a limiting stress ratio occurs before the yield surface is reached. We now compare this prediction with some data of states of failure. 8.4 Data of States of Failure We have already discussed the data of experiments which Henkel interpreted to give broad support to Rendulic s generalized effective stress principle. In Figs. 7.22 and 7.23 we see that state paths end with failure states which lie on two lines rather similarly placed in their asymmetry about the space diagonal as the prediction of the Mohr -Rankine criterion. In detail .