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A one-dimensional viscoelastic and viscoplastic constitutive approach to modeling the delayed behavior of clay and organic soils

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Abstract

Accurate modeling of the time-dependent behavior of geomaterials is of great importance in a number of engineering structures interacting with soft, highly compressible clay layers or with organic clays and peats. In this work, a uniaxial constitutive model, based on Perzyna’s overstress theory and directly extendible to multiaxial stress conditions, is formulated and validated. The proposed constitutive approach essentially has three innovative aspects. The first concerns the implementation of two viscoplastic mechanisms within Perzyna’s theory in order to distinguish between short-term (quasi-instantaneous) and long-term plastic responses. Similarly, elastic response is simulated by combining an instantaneous and a long-term viscous deformation mechanism. The second innovative aspect concerns the use of a bespoke logarithmic law for viscous effects, which has never been used before to simulate delayed soil behavior (as far as the authors are aware). The third concerns the model’s extensive validation by simulating a number of different laboratory test results, including conventional and unconventional oedometer tests with small and large load increments/decrements and wide and narrow loading/unloading cycles, constant rates of stress and strain tests, and oedometer tests performed in a Rowe consolidation cell with measurement of pore pressure dissipation.

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Acknowledgements

The authors gratefully acknowledge Financial Support from European Union FP7, Project under Contract Number PIAPP-GA-2013-609758-HOTBRICKS.

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Author notes

  1. Aldo Madaschi

    Present address: School of Architecture, Civil and Environmental Engineering, ENAC, Laboratory of Soil Mechanics, LMS, École Polytechnique Fédérale de Lausanne, EPFL, GC Station 18, 1015, Lausanne, Switzerland

Authors and Affiliations

  1. Department of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, 38123, Italy

    Aldo Madaschi & Alessandro Gajo

Authors
  1. Aldo Madaschi
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  2. Alessandro Gajo
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Correspondence to Alessandro Gajo.

Appendix

Appendix

The polynomial coefficients a, b, and c of the viscosity function given in Eq. (7) depend on two parameters, \(\beta\) and \(\gamma\), which define the position of the transition point (between the logarithmic and polynomial branches) and the tangent of the viscosity function at the origin of the axis (see Fig. 4).

The coefficients were simply obtained by imposing the smooth continuity of the function at the transition point:

$$\begin{aligned} a&= \frac{\gamma \ \log \beta }{\beta \,{\dot{\epsilon}_\text{ref}}} \end{aligned}$$
(13a)
$$\begin{aligned} b&= \frac{3 \log \beta - 2 \ \gamma \ \log \beta -1}{\left(\beta \;{\dot{\epsilon}_\text{ref}}\right)^2} \end{aligned}$$
(13b)
$$\begin{aligned} c&= \frac{\gamma \ \log \beta + 1 - 2 \log \beta}{\left(\beta \;{\dot{\epsilon}_\text{ref}}\right)^3} \end{aligned}$$
(13c)

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Madaschi, A., Gajo, A. A one-dimensional viscoelastic and viscoplastic constitutive approach to modeling the delayed behavior of clay and organic soils. Acta Geotech. 12, 827–847 (2017). https://doi.org/10.1007/s11440-016-0518-9

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