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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

References

  • ASTM International (2011) ASTM D2487-11. Standard practice for classification of soils for engineering purposes (unified soil classification system). ASTM International, West Conshohocken. https://doi.org/10.1520/D2487-17

  • ASTM International (2011) ASTM D3999-11/D3999M-11e1. Standard test methods for the determination of the modulus and damping properties of soils using the cyclic triaxial apparatus. ASTM International, West Conshohocken. https://doi.org/10.1520/D3999_D3999M

  • Bjerrum L, Landva A (1966) Direct simple-shear test on a Norwegian quick clay. Geotechnique 16(1):1–20. https://doi.org/10.1680/geot.1966.16.1.1

    Article  Google Scholar 

  • Burland J (1990) On the compressibility and shear strength of natural clays. Geotechnique 40(3):329–378. https://doi.org/10.1680/geot.1990.40.3.329

    Article  Google Scholar 

  • Burland J, Rampello S, Georgiannou V, Calabresi G (1996) A laboratory study of the strength of four stiff clays. Geotechnique 46(3):491–514. https://doi.org/10.1680/geot.1996.46.3.491

    Article  Google Scholar 

  • Cavallaro A, Lanzo G, Pagliaroli A, Maugeri M, Lo Presti DC (2003) A comparative study on shear modulus and damping ratio of cohesive soil from laboratory tests. In: Di Benedetto H et al (eds) Proc 3rd Int Symp on Deformation Characteristics of Geomaterials. AA Belkema, Lisse, pp 257–265. https://doi.org/10.1201/NOE9058096043.ch32

  • Darendeli MB (2001) Development of new family of normalized modulus reduction and material damping curves. PhD thesis. University of Texas, Austin

  • D'Elia B, Lanzo G, Pagliaroli A (2003) Small-strain stiffness and damping of soils in a direct simple shear device. In: New Zealand Society for Earthquake Engineering (ed) Pacific Conference on Earthquake Engineering. Christchurch, New Zealand

  • Derriche Z, Cheikh-Lounis G (2004) Caractéristiques géotechniques des marnes Plaisanciennes d’Alger. Bull Eng Geol Environ 63:367–378. https://doi.org/10.1007/s10064-004-0246-5

    Article  Google Scholar 

  • Doroudian M, Vucetic M (1995) A direct simple shear device for measuring small strain behaviour. Geotech Test J 18(1):69–85. https://doi.org/10.1520/GTJ10123J

    Article  Google Scholar 

  • El Mohtar CS, Drnevich VP, Santagata M, Bobet A (2013) Combined resonant column and cyclic Triaxial tests for measuring undrained shear Modulus reduction of sand with plastic fines. Geotech Test J 36(4):484–492. https://doi.org/10.1520/GTJ20120129

    Article  Google Scholar 

  • Guerreiro P, Kontoe S, Taborda P (2012) Comparative study of stiffness reduction and damping curves. In: 15th World Conference on Earthquake Engineering. Lisbon, pp 24–28

  • Hardin BO, Drenvich VP (1972) Shear modulus and damping in soils: design equation and curves. J Soil Mech Found Div 98(7):667–692

  • Isenhower W (1979) Torsional simple shear/resonant column properties of San Francisco Bay mud. MSc thesis. University of Texas at Austin, Austin

  • Isenhower W, Stokoe K (1981) Strain-rate dependent shear modulus of San Francisco Bay mud. In: Int Conf on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, II. Univ. of Missouri, Rolla, St. Louis, pp 597–602

  • Ishibashi I, Zhang X (1993) Unified dynamic shear moduli and damping ratios of sand and clay. Soils Found 33(1):182–191. https://doi.org/10.3208/sandf1972.33.182

    Article  Google Scholar 

  • Iwasaki T, Tatsuoka F, Takagi Y (1978) Shear moduli of sands under cyclic torsional shear loading. Soils Found 18(1):39–56. https://doi.org/10.3208/sandf1972.18.39

    Article  Google Scholar 

  • Kallioglou T, Tika T, Pitilakis K (2008) Shear Modulus and damping ratio of cohesive soils. J Earthq Eng 12(6):879–913. https://doi.org/10.1080/13632460801888525

    Article  Google Scholar 

  • Kishida T (2008) Seismic site effects for the Sacramento-San Joaquin delta. PhD thesis. University of California, Davis

  • Kishida T (2016) Comparison and correction of Modulus reduction models for clays and silts. J Geotech Geoenviron 143(4). https://doi.org/10.1061/(ASCE)GT.1943-5606.0001627

  • Kokusho T, Yoshida Y, Esashi Y (1982) Dynamic properties of soft clay for wide strain range. Soils Found 22(4):1–18. https://doi.org/10.3208/sandf1972.22.4_1

    Article  Google Scholar 

  • Lanzo G, Vucetic M, Doroudian M (1997) Reduction of shear modulus at small strains in simple shear. J Geotech Geoenviron Eng 123(11):1035–1042. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:11(1035)

    Article  Google Scholar 

  • Lanzo G, Pagliaroli A, Tommasi P, Chiocco FL (2009) Simple shear testing of sensitive, very soft offshore clay for wide strain range. Can Geotech J 46(11):1277–1288. https://doi.org/10.1139/T09-059

    Article  Google Scholar 

  • Lo Presti D (1991) Discussion on "Threshold strain in Soils". In: Associazione geotecnica Italiana (ed) X ECSMFE on Deformation of Soils and Displacements of Structures. 4. AA Balkema, Florence, pp 1282–1283

  • Lo Presti D, Jamiolkowski M, Pallara O, Cavallaro A (1997) Shear modulus and damping of soils. Geotechnique 47(3):603–617. https://doi.org/10.1680/geot.1997.47.3.603

    Article  Google Scholar 

  • Mortezaie AR, Vucetic M (2012) Small-strain cyclic testing with standard NGI simple shear device. Geotech Test J 35(6):935–948. https://doi.org/10.1520/GTJ20120007

    Article  Google Scholar 

  • Mortezaie A, Vucetic M (2016) Threshold shear strain for cyclic degradation and cyclic pore water pressure generation in two clays. J Geotech Geoenviron 142(5):04016007

    Article  Google Scholar 

  • Ng C, Bolton M, Dasari G (1995) The small strain stiffness of a carbonate stiff clay. Soils Found 35(4):109–114. https://doi.org/10.3208/sandf.35.4_109

    Article  Google Scholar 

  • Pagliaroli A, Lanzo G, Tommasi P, Di Fiore V (2014) Dynamic characterization of soils and soft rocks of the central archaeological area of Rome. Bull Earthq Eng 12(3):1365–1381. https://doi.org/10.1007/s10518-013-9452-5

    Article  Google Scholar 

  • Royer L, Moussu H, Aymé J, Aymé A, Bouillon M (1961) Carte géologique de l'Algérie détaillée, feuille n°20, Chéragas. Service de la catre géologique de l'Algérie, Alger

    Google Scholar 

  • Santucci de Magistris F, d'Onofrio A, Evangelista L, Foti S, Maraschini M, Monaco P, Amoroso S, Totani G, Lanzo G, Pagliaroli A, Madiai C, Simoni G, Silvestri F (2013) Geotechnical characterization of the Aterno valley for site response analyses. Riv Ital Geotec 47(3):23–43

    Google Scholar 

  • Schmertmann J (1969) Swell sensitivity. Geotechnique 19(4):530–533. https://doi.org/10.1680/geot.1969.19.4.530

    Article  Google Scholar 

  • Seed HB, Wong RT, Idris IM, Tokimatsu K (1986) Moduli and damping factors for dynamic analyses of cohesionless soils. J Geotech Eng 112(11):1016–1032. https://doi.org/10.1061/(ASCE)0733-9410(1986)112:11(1016)

    Article  Google Scholar 

  • Shibuya S, Mitachi T, Fukuda F, Degoshi T (1995) Strain rate effect on shear modulus and damning of normally consolidated clay. Geotech Test J 18(3):365–375. https://doi.org/10.1520/GTJ11005J

    Article  Google Scholar 

  • Silvestri F (1991). Stress-strain behaviour of natural soils by means of cyclic/dynamic torsional shear tests. In: Proc Sym on "Experimental Characterization and Modelling of Soils and Soft Rocks". Hevelius Edizioni, Naples

  • Stokoe II KH, Huang SK, Lee JK, Andrus RD (1995) Effects of various parameters on the stiffness and damping of soils at small to medium strains. In: Shibuya S et al (eds) Pre-faillure deformation of geomaterials. Proc Int Sym, 2. A.A. Balkema, Rotterdam, pp 785–816

  • Stokoe KH, Darendeli MB, Andrus RD, Brown LT (1999) Dynamic soil properties: laboratory, field and correlation studies. In: Pedro Sêco e Pinto (ed) Proc 2nd Int Conf on Earthquake Geotechnology. A.A. Balkema, Rotterdam, pp 811–846

  • Stokoe KH, Darendeli MB, Menq FY, Choi WK (2004) Comparison of linear and nonlinear dynamic properties of gravel, sand silts and clays. In: Proc V ICSDEE & III ICEGE. Berkeley, CA

  • Tabata K, Vucetic M (2010) Threshold shear strain for cyclic degradation of three clays. In: 5th Int Conf on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. San Diego, p 1.15a

  • Tan K, Vucetic M (1989) Behavior of medium and low plasticity clays under cyclic simple shear conditions. In: Cakmak AS, Herrera I (eds) Proc 4th Int Conf on Soil Dynamics and Earthquake Engineering. Mexico, p 131–142

  • Vardanega P, Bolton M (2013) Stiffness of clays and silts: normalizing shear modulus and shear strain. J Geotech Geoenviron Eng 39 (9):1575–1589. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000887

  • Verrucci L, Lanzo G, Tommasi P, Rotonda T (2015) Cyclic and dynamic behaviour of soft pyroclastic rock. Geotechnique 65(5):359–373. https://doi.org/10.1680/geot.SIP.15.P.012

    Article  Google Scholar 

  • Vucetic M (1994) Cyclic threshold shear strains in soils. J Geotech Eng 120(12):2208–2228. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2208)

    Article  Google Scholar 

  • Vucetic M, Dobry R (1988) Cyclic triaxial strain-controlled testing of liquefiable sands. Advanced triaxial testing of soil and tock (STP 977). https://doi.org/10.1520/STP29093S

  • Vucetic M, Dobry R (1991) Effect of soil plasticity on cyclic response. J Geotech Eng 117(1):89–107. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:1(89)

    Article  Google Scholar 

  • Vucetic M, Lanzo G, Doroudian M (1998a) Damping at small strains in cyclic simple shear test. J Geotech Geoenviron 124(7):585–594. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:7(585)

    Article  Google Scholar 

  • Vucetic M, Lanzo G, Doroudian M (1998b) Effect of the shape of cyclic loading on damping ratio at small strains. Soils Found 38(1):111–120. https://doi.org/10.3208/sandf.38.111

    Article  Google Scholar 

  • Zhang X, Andrus RD, Juang H (2005) Normalized shear modulus and material damping ratio relationships. J Geotech Geoenviron 131(4):453–464. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:4(453)

    Article  Google Scholar 

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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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