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The corresponding stress-strain response shows rapid softening as p approached zero, with the hysteretic loops taking on an inverted s-shape. The stress path—that is, q/(2 pc ) versus p / pc —moved progressively toward the origin during cyclic loading until it stabilized with repeating loops emanating from the origin. The interconnections among the various plots in Figure 16 can be illustrated by considering the positions of the points A and B. , the specimen is under an isotropic state of stress).
This ξ R changes the CRR by amounts that depend on the initial D R , because of the curvature of the CRR versus ξ R relationship (which applies to all values of D R and consolidation stresses). org Liquification-172002 book July 14, 2008 11:3 Figure 24. CRR versus ξ R for reconstituted specimens of Fraser Delta sand (Boulanger 2003a, with permission from ASCE). reduction in the CRR, as expressed through the K σ factor, depends on the initial D R . The K σ relationships derived from the CRR versus ξ R relationship (Figures 24 and 25) match the relationships derived directly from the experimental results (Figures 20 and 22), as expected.
Org Liquification-172002 book July 14, 2008 11:3 Figure 29. Effect of the relative state parameter index ξ R on the static shear stress ratio correction factor K α (Boulanger 2003a). 49), with the ξ R values simply tracking the progression from D R = 35%–68%, since all tests were at the same confining stress. The dependence of K α on the effective confining stress is also depicted in Figure 29 by the results of the cyclic triaxial tests on tailings sand by Vaid and Chern (1985) (Figure 28b). For determining K α from these triaxial tests, the cyclic resistances were normalized by the mean effective consolidation stresses (Boulanger 2003a).