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Investigation on shear modulus and damping ratio of Algiers marls under cyclic and dynamic loading conditions

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Abstract

A sound knowledge of the dynamic properties of soils is needed to solve several geotechnical engineering problems associated with earthquakes. Here we describe a laboratory investigation performed to measure the dynamic properties of the Plaisancian deposit of marls in the Algiers region using cyclic triaxial tests, cyclic double specimen direct simple shear tests, cyclic torsional shear tests and dynamic resonant column tests. The key parameters governing the nonlinear soil behavior under cyclic/dynamic loading and their relative importance in terms of affecting the dynamic properties of soils, wich are communaly represented by the normalized equivalent shear modulus reduction and damping ratio curves, are illustrated and discussed. We also address the differences in the deduced parameters obtained with different tests, procedures and interpretation criteria. The comparison between test results and empirical or semi-empirical relations for normalized equivalent shear modulus and damping ratio curves highlights a number of limitations and shortcomings of predictive models currently widely used.

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Abbreviations

\( {C}_c^{\ast } \) :

Intrinsic compression index

C s :

Swelling index

\( {C}_s^{\ast } \) :

Intrinsic swelling index

C u :

Undrained shear strength

G 0 :

Maximum shear modulus

G eq, 1 :

Equivalent shear modulus at the first cycle

G eq, N :

Equivalent shear modulus at the Nth cycle

G eq :

Equivalent shear modulus

G eq/G 0 :

Normalized equivalent shear modulus

I 0 :

Mass polar moment of inertia of the torsional driving system

I C :

Consistency index

I V :

Void index

K 0 :

Coefficient of earth pressure at rest

V S :

Shear wave velocity

W D :

Energy dissipated in one cycle (area enclosed by the loop)

W S :

Elastic peak strain energy stored during the cycle (area enclosed by the triangle)

\( {e}_{100}^{\ast } \) :

Void ratio at a vertical effective stress (\( {\sigma}_v^{\prime } \)) of 100 kPa for the reconstituted material

f 0 :

Frequency of the first torsional mode of vibration

f 1 and f 2 :

frequencies at which the amplitude is \( \sqrt{2}/2 \) times the amplitude at the resonance frequency f0

p ′ :

Isotropic mean effective confining stress

w L :

Liquid limit

γ c :

Cyclic shear strain amplitude

γ pp :

Double-amplitude shear strain

γ s :

Soil solids density

γ td :

Threshold shear strain for cyclic degradation

γ tl :

Linear threshold shear strain

γ tp :

Threshold shear strain for cyclic pore water pressure buildup

γ tv :

Volumetric threshold shear strain

δ G :

Degradation index

ε c :

Cyclic axial strain amplitude

θ max :

Amplitude of vibration

\( {\sigma}_h^{\prime } \) :

Horizontal effective stress

\( {\sigma}_m^{\prime } \) :

Anisotropic mean effective confining stress

\( {\sigma}_v^{\prime } \) :

Vertical effective stress

τ pp :

Double-amplitude shear stress

ω 0 :

Resonant circular frequency

CH:

Flat clay

CTX:

Cyclic triaxial

DSDSS:

Double specimen direct simple shear

MH:

Elastic silt

RC:

Resonant column

TS:

Torsional shear

Δu :

Excess porewater pressure

Δu/p ′ :

Normalized excess pore water pressure

B :

Skempton coefficients

CC:

Calcium carbonate

CF:

Clay fraction

D :

Damping ratio

E :

Young’s modulus

FC:

Fine content

H :

Specimen height

I :

Mass polar moment of inertia of the specimen

ICL:

Intrinsic compression line

K :

Coefficient of permeability

N :

Number of loading cycles

OCR:

Over-consolidation ratio

PI :

Plasticity index

R :

Radius of the specimen

SCL:

Sedimentation compression line

e :

Void ratio

f :

Loading frequency

u :

Pore water pressure

w :

Water continent

γ :

Unit weight

θ :

Single-amplitude torsional angle

ν :

Poisson’s ratio

ρ :

Mass density of the cylindrical specimen

τ :

Shear-stress amplitude

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Acknowledgments

This work was supported by the National Earthquake Engineering Research Center of Algiers. Special thanks to Jean-François Serratrice (Cerema, France) for helpful advice concerning the CTX test procedure. We gratefully acknowledge Alexis Averlan (SolMesure, France) for helpful advice in CTX apparatus setup and Tahar Aissaoui (Soil Tech Engineering, Algeria) for the availability of soil samples and geotechnical reports. The help of Silvano Silvani (La Sapienza University of Rome, Italy) in DSDSS and other geotechnical tests is greatly appreciated. The support of Prof. Luigi Callisto and Alessandro Pagliaroli is also gratefully acknowledged.

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Authors and Affiliations

  1. Département Microzonage Sismique, Centre National de Recherche Appliquée en Génie Parasismique (CGS), Rue Kaddour Rahim, BP 252 Hussein Dey, 16040, Algiers, Algeria

    Samir Bedr & Nourredine Mezouar

  2. Laboratoire Ingénierie de Transport et Environnement (TPiTE), École Nationale Supérieure des Travaux Publics (ENSTP), Rue Sidi Garidi, BP 32 Vieux Kouba, 16051, Algiers, Algeria

    Samir Bedr

  3. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Via A. Gramsci 53, 00197, Rome, Italy

    Luca Verrucci & Giuseppe Lanzo

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  1. Samir Bedr
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  2. Nourredine Mezouar
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  3. Luca Verrucci
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  4. Giuseppe Lanzo
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Correspondence to Samir Bedr.

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Bedr, S., Mezouar, N., Verrucci, L. et al. Investigation on shear modulus and damping ratio of Algiers marls under cyclic and dynamic loading conditions. Bull Eng Geol Environ 78, 2473–2493 (2019). https://doi.org/10.1007/s10064-018-1310-x

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