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Analysis of the stiffness and damping characteristics of compacted sand-in-fines granular composites: a multiscale investigation

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Abstract

Compacted clay-aggregate composites are extensively utilized or found in various geotechnical engineering projects such as the core of earth embankment dams, the pile foundation of offshore structures, or the impervious blankets in waste disposal landfills. In this study, data from resonant column tests at small shear strains are exploited to examine the dynamic shear modulus and energy dissipation characteristics of compacted clay-sand mixtures and develop empirical expressions for their small-strain dynamic properties. The models incorporate the influences of confining pressure (p'), void ratio (e), aggregate content (AC) and clay plasticity index (PI). Moreover, the application of the equivalent plasticity index (PI*) in the estimation of small-strain dynamic properties is rigorously examined. The level of accuracy of the developed models is inspected with simple comparisons against the experimental data. The proposed empirical correlations can be utilized in geotechnical earthquake engineering problems for the seismic stability analysis of geo-structures containing compacted clay-sand mixtures. These empirical models also comprise a basis to discuss the mechanical behavior of composite granular systems at multi-scales. In this regard, the involved micromechanisms, particularly the contact response of sand-clay systems, are discussed integrating the macroscopic results from the present work with micromechanical-based data previously published in the literature. This analysis highlighted the important role of the formed coating of microparticles on the constitutive behavior of sand grains at their contacts, which in turn, provided some additional insights to explain the macroscopic behavior of clay-sand mixtures as obtained from the element-size experiments.

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Abbreviations

\(a\) :

Acceleration

AC :

Aggregate content

\({A}_{D}\) :

A model parameter in the \({D}_{min}\) equation

\({A}_{G}\) :

A model parameter in the \({G}_{max}\) equation

\({c}_{c}\) :

Clay content

\({C}_{u}\) :

Coefficient of uniformity

\(d\) :

Diameter of the soil sample

\({d}_{50}\) :

Mean particle size

\({D}_{min}\) :

Minimum damping ratio

\(e\) :

Void ratio

\({e}_{c}\) :

Void ratio of clay portion

\(f\) :

Frequency

\(f_{1} ,\,f_{2}\) :

The frequencies corresponding to the vibration amplitude of 0.707 Zmax

\({f}_{r}\) :

Resonant frequency

\(f(e)\) :

Void ratio function

\({G}_{max}\) :

Maximum shear modulus

\(I\) :

Mass polar moment of inertia of the soil sample

\({I}_{0}\) :

Mass polar moment of inertia of the drive mechanism

\(l\) :

Distance between the accelerometer and the axis of rotation

\(L\) :

Length of the soil sample

\(m\) :

Mass of the soil sample

MDD :

Maximum dry density

\(n\) :

Number of cycles

\({n}_{D}\) :

A model parameter in the \({D}_{min}\) equation

\({n}_{G}\) :

A model parameter in the \({G}_{max}\) equation

OMC :

Optimum moisture content

\(p^{\prime }\) :

Isotropic confining pressure

\({p}_{atm}\) :

Atmosphere pressure

\(Pc_{a} ,Pc_{b}\) :

Clay contents obtained from the gradation curves of the composite specimens having particles less than 2 and 0.425 mm, respectively.

PI :

Plasticity index

\({PI}^{*}\) :

Equivalent plasticity index

\(R\) :

Radius of the soil sample/Reduction factor in the \({PI}^{*}\) equation

RC :

Relative compaction

\(V\) :

Peak output voltage

\({V}_{s}\) :

Shear wave velocity

\({x}_{G}\) :

A model parameter in the \({G}_{max}\) equation

\({Y}_{measured}\) :

Measured displacement of the accelerometer

\(Z\) :

Amplitude of vibration

\({Z}_{max}\) :

Maximum amplitude of vibration

\(\beta\) :

A coefficient for shear wave velocity determination

\(\gamma\) :

Shear strain

\({\gamma }_{1}\) :

Shear strain amplitude in the first cycle

\({\gamma }_{1+n}\) :

Shear strain amplitude in the (\(1+n\))th cycle

\(\delta\) :

Logarithmic decrement

\(\theta\) :

Rotation angle of the top of the soil sample

\(\rho\) :

Density of the soil sample

\(\omega\) :

Angular frequency of vibration

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Acknowledgements

The work described in this paper was supported by a grant from the International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran; Project No. (6715-P97-5), on the dynamic deformation properties of clay-sand mixtures.

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Authors and Affiliations

  1. Department of Civil Engineering, College of Engineering, California State Polytechnic University, Pomona, CA, USA

    Ali Shafiee

  2. Faculty of Civil Engineering, Jundi Shapur University of Technology, Dezful, Iran

    Akbar Hassanipour

  3. Department of Civil Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran

    Meghdad Payan, Shahla Bahmani Tajani & Reza Jamshidi Chenari

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Shafiee, A., Hassanipour, A., Payan, M. et al. Analysis of the stiffness and damping characteristics of compacted sand-in-fines granular composites: a multiscale investigation. Granular Matter 24, 87 (2022). https://doi.org/10.1007/s10035-022-01247-1

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