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© ASCE 06016003-4 J. Geotech. Geoenviron. Eng.

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Conclusions

Many geotechnical problems involve either very low, very high, or a wide range of effective stress. In this study, previously suggested compression models and other functions are modified to satisfy asymptotic conditions at low and high stress levels. These models are used to fit the response of normally consolidated remolded soils, structured natural soils, and overconsolidated soils. The fol- lowing salient observations can be made: • At least four parameters are required to fit soil compression data

gathered in a wide stress range. Physical insight, databases, and the high correlation between compressibility and the void ratio at low stress help to constrain the parameter space to determine a self-consistent set of fitting parameters;

• Models in terms of σ 0β (arctangent, hyperbolic, power, and exponential) show more flexibility to capture the compression response of structured natural soils with pronounced brittle transitions at the yield stress;

• The use of a single continuous function to capture soil com- pressibility data avoids numerical discontinuities, facilitates computing the tangent constrained modulus for numerical methods, and eludes ad hoc procedures to identify the yield stress; and

• The computed tangent constrained modulus should not be mistaken for the instantaneous small-strain modulus measured during the test. The tangent stiffness is a mathematical con- cept that reveals the instantaneous rate of fabric change during a large strain test. By contrast, a small-strain perturbation test gives a constant fabric stiffness that is determined by contact deformation.

Acknowledgments

This research was conducted by the authors while at the Georgia Institute of Technology. Support for this research was provided by the Department of Energy Savannah River Operations Office and the Goizueta Foundation. Additional support was provided by the Convergence R&D program of MSIP/NST (Convergence Research-14-2-ETRI) and the KAUST endowment.

Supplemental Data

Tables S1 and S2 are available online in the ASCE Library (www. ascelibrary.org).

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Fig. 2. Correlation between low-stress void ratio and compressibility: (a) classical Terzaghi model as the correlation between void ratio e1 kPa and Cc for remolded and natural sedimentary clays; (b) hyperbolic function fitted with β ¼ 1; in both cases, the solid line shows the cen- tral trend defined by the equation shown in each frame; dotted lines show the þ= − 1 standard deviation from the central trend

© ASCE 06016003-5 J. Geotech. Geoenviron. Eng.

J. Geotech. Geoenviron. Eng., 06016003