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Relationship Between Shear Wave Wavelength and Pseudo-Dynamic Seismic Safety Factor in Expanded Landfill

  • Research Article - Civil Engineering
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Abstract

Using the pseudo-dynamic limit equilibrium method, the average safety factor for the expanded landfill against the over-berm failure was calculated to replace the true safety factor under the earthquake condition. The effect of the shear wave wavelength on the average safety factor was then studied by considering various parameters. After the analysis of different working conditions, the most unfavorable shear wave wavelength was obtained. Results indicate that the geometric parameters of the landfill strongly affect the most unfavorable shear wave wavelength except for the angle of back slope of berm measured from horizontal. The results, however, show that the property parameters about the landfill slightly influence the most unfavorable shear wave wavelength which generally occurs around 77.5 m. Furthermore, in the seismic design of the expanded landfill against the over-berm failure, the effect of height of berm on the most unfavorable shear wave wavelength should be carefully considered, but the effect of the angle of back slope of berm measured from horizontal, apparent cohesion between liner components beneath block wedge, or interface friction angle of liner components beneath block wedge can be ignored.

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Abbreviations

a hw(z, t):

Acceleration in horizontal direction at t and z below top surface of landfill (m/s2)

a vw(z, t):

Acceleration in vertical direction at t and z below top surface of landfill (m/s2)

B T :

Top width of waste mass (m)

C A :

Apparent cohesive force between liner components beneath active wedge (kN/m)

C B :

Apparent cohesive force between liner components beneath block wedge (kN/m)

C P :

Apparent cohesive force between liner components beneath passive wedge (kN/m)

C AP :

Apparent cohesive force at interface between active and passive wedges (kN/m)

C PB :

Apparent cohesive force at the interface between passive and block wedges (kN/m)

c :

Apparent cohesion of waste mass (kN/m2)

c A :

Apparent cohesion between liner components beneath active wedge (kN/m2)

c B :

Apparent cohesion between liner components beneath block wedge (kN/m2)

c P :

Apparent cohesion between liner components beneath passive wedge (kN/m2)

dz :

Thickness of slice (m)

E HAP :

Normal force from active wedge acting on passive wedge (kN/m)

E HBP :

Normal force from block wedge acting on passive wedge (kN/m)

E HPA :

Normal force from passive wedge acting on active wedge (kN/m)

E HPB :

Normal force from passive wedge acting on block wedge (kN/m)

E VAP :

Frictional force acting on side of passive wedge next active wedge (kN/m)

E VBP :

Frictional force acting on side of passive wedge next block wedge (kN/m)

E VPA :

Frictional force acting on side of active wedge next passive wedge (kN/m)

E VPB :

Frictional force acting on side of block wedge next passive wedge (kN/m)

F A :

Frictional force acting on bottom of active wedge (kN/m)

F B :

Frictional force acting on bottom of block wedge (kN/m)

F P :

Frictional force acting on bottom of passive wedge (kN/m)

f a :

Amplification factor of waste mass (dimensionless)

FS:

Safety factor for the entire waste mass (dimensionless)

FSV :

Safety factor at the interface between two wedges (dimensionless)

FSmin :

Minimum safety factor (dimensionless)

FSmax :

Maximum safety factor (dimensionless)

FSave :

Average safety factor (dimensionless)

G :

Shear modulus of waste mass (kPa)

g :

Acceleration due to gravity (m/s2)

H :

Height of waste mass at back slope (m)

H B :

Height of berm (m)

H L :

Height from top wedge to bottom of berm (m)

H T :

Height of waste mass above back slope (m)

k h :

Horizontal seismic coefficient (dimensionless)

k v :

Vertical seismic coefficient (dimensionless)

m w(z):

Mass of a thin element of waste mass at z (kg/m)

N A :

Normal force acting on bottom of active wedge (kN/m)

N B :

Normal force acting on bottom of block wedge (kN/m)

N P :

Normal force acting on bottom of passive wedge (kN/m)

Q hw(t):

Horizontal seismic force acting on waste mass for different wedge at t (kN/m)

Q vw(t):

Vertical seismic force acting on waste mass for different wedge at t (kN/m)

Q hA(t):

Horizontal seismic force acting on active wedge (kN/m)

Q vA(t):

Vertical seismic force acting on active wedge (kN/m)

Q hB(t):

Horizontal seismic force acting on block wedge (kN/m)

Q vB(t):

Vertical seismic force acting on block wedge (kN/m)

Q hP(t):

Horizontal seismic force acting on passive wedge (kN/m)

Q vP(t):

Vertical seismic force acting on passive wedge (kN/m)

T :

Period of lateral shaking (s)

t :

Duration (s)

V s :

Shear wave velocity (m/s)

V p :

Primary wave velocity (m/s)

v :

Poisson’s ratio of waste mass (dimensionless)

W A :

Weight of active wedge (kN/m)

W P :

Weight of passive wedge (kN/m)

W B :

Weight of block wedge (kN/m)

z :

Depth below top surface of landfill (m)

α :

Angle of back slope of berm measured from horizontal (°)

β :

Angle of back slope of waste mass measured from horizontal (°)

γ :

Unit weight of waste mass (kN/m 3)

δ A :

Interface friction angle of liner components beneath active wedge (°)

δ B :

Interface friction angle of liner components beneath Block wedge (°)

δ P :

Interface friction angle of liner components beneath passive wedge (°)

η :

Angle of front slope of waste mass measured from horizontal (°)

θ :

Angle of landfill cell subgrade measured from horizontal (°)

λ :

Shear wave wavelength (m)

λ m :

Most unfavorable shear wave wavelength (m)

\({\xi}\) :

Angle of landfill cover slope measured from horizontal (°)

\({\rho}\) :

Density of waste mass (kg/m3)

\({\phi}\) :

Internal friction angle of waste mass (°)

\({\omega}\) :

Angular frequency of base shaking (1/s)

References

  1. Koerner, R.; Soong, T.: Stability assessment of ten large landfill failures. Adv. Transp. Geoenviron. Syst. Geosynth. 1–38 (2000) doi:10.1061/40515(291)1

  2. Qian X.D., Koerner R.M.: Stability analysis when using an engineered berm to increase landfill space. J. Geotech. Geoenviron. Eng. 135(8), 1082–1091 (2009). doi:10.1061/(ASCE)GT.1943-5606.0000065

    Article  Google Scholar 

  3. Qian X.D., Koerner R.M., Gray D.H.: Translational failure analysis of landfills. J. Geotech. Geoenviron. Eng. 129(6), 506–519 (2003). doi:10.1016/(ASCE)1090-0241(2003)129:6(506)

    Article  Google Scholar 

  4. Qian X.D., Koerner R.M.: Effect of apparent cohesion on translational failure analyses of landfills. J. Geotech. Geoenviron. Eng. 130(1), 71–80 (2004). doi:10.1061/(ASCE)1090-0241(2004)130:1(71)

    Article  Google Scholar 

  5. Qian X.D.: Limit equilibrium analysis of translational failure of landfills under different leachate buildup conditions. Water Sci. Eng. 1(1), 44–62 (2008). doi:10.3882/j.issn.1674-2370.2008.01.006

    Article  Google Scholar 

  6. Qian X.D., Koerner R.M.: Modification to translational failure analysis of landfills incorporating seismicity. J. Geotech. Geoenviron. Eng. 136(5), 718–727 (2010). doi:10.1061/(ASCE)GT.1943-5606.0000281

    Article  Google Scholar 

  7. Savoikar P., Choudhury D.: Effect of cohesion and fill amplification on seismic stability of municipal solid waste landfills using limit equilibrium method. Waste Manage. Res. 28(12), 1096–1113 (2010). doi:10.1177/0734242X09348531

    Article  Google Scholar 

  8. Savoikar P., Choudhury D.: Translational seismic failure analysis of MSW landfills using pseudodynamic approach. Int. J. Geomech. 12(2), 136–146 (2012). doi:10.1061/(ASCE)GM.1943-5622.0000127

    Article  Google Scholar 

  9. Chen Y.M., Gao D., Zhu B., Chen R.: Seismic stability and permanent displacement of landfill along liners. Sci. China Technol. Sci. 51(4), 407–423 (2008). doi:10.1007/s11431-008-0031-y

    Article  Google Scholar 

  10. Feng S.J., Chen Y.M., Gao L.Y., Gao G.Y.: Translational failure analysis of landfill with retaining wall along the underlying liner system. Environ. Earth Sci. 60(1), 21–34 (2010). doi:10.1007/s12665-009-0166-6

    Article  Google Scholar 

  11. Feng S.J., Gao L.Y.: Seismic analysis for translational failure of landfills with retaining walls. Waste Manage. 30(11), 2065–2073 (2010). doi:10.1016/j.wasman.2010.05.008

    Article  Google Scholar 

  12. Sun S.L., Ruan X.: Seismic stability for landfills with a triangular berm using pseudo-static limit equilibrium method. Environ. Earth Sci. 68(5), 1465–1473 (2013). doi:10.1007/s12665-012-1843-4

    Article  Google Scholar 

  13. Choudhury D., Savoikar P.: Seismic stability analysis of expanded MSW landfills using pseudo-static limit equilibrium method. Waste Manage. Res. 29(2), 135–145 (2011). doi:10.1177/0734242X10375333

    Article  Google Scholar 

  14. Ruan X., Sun S.L., Liu W.L.: Effect of the amplification factor on seismic stability of expanded municipal solid waste landfills using the pseudo-dynamic method. J. Zhejiang Univ. Sci. A 14(10), 731–738 (2013). doi:10.1631/jzus.A1300041

    Article  Google Scholar 

  15. Steedman R., Zeng X.: The influence of phase on the calculation of pseudo-static earth pressure on a retaining wall. Geotechnique. 40(1), 103–112 (1990). doi:10.1680/geot.1990.40.1.103

    Article  Google Scholar 

  16. Zeng X., Steedman R.: On the behavior of quay walls in earthquakes. Geotechnique. 43(3), 417–431 (1993). doi:10.1680/geot.1993.43.3.417

    Article  Google Scholar 

  17. Choudhury D., Nimbalkar S.S: Seismic passive resistance by pseudo-dynamic method. Geotechnique. 55(9), 699–702 (2005). doi:10.1680/geot.2005.55.9.699

    Article  Google Scholar 

  18. Ruan X., Cheng Q.Q., Sun S.L.: Active seismic pressure against retaining wall backfilled with cohesive soils. Soil Mech. Found. Eng. 50(3), 116–122 (2013). doi:10.1007/s11204-013-9221-0

    Article  Google Scholar 

  19. Ruan X., Yu R.L., Sun S.L.: Analysis of seismic active earth pressure on retaining walls based on pseudo-dynamic method. J. Highw. Transp. Res. Dev. (English Edn). 7(2), 34–39 (2013). doi:10.1061/JHTRCQ.0000311

    Article  Google Scholar 

  20. Ruan X., Sun S.L.: Seismic stability of reinforced soil walls under bearing capacity failure by pseudo-dynamic method. J. Cent. South Univ. 20(9), 2593–2598 (2013). doi:10.1007/s11771-013-1773-7

    Article  Google Scholar 

  21. Das B.M., Ramana G.: Principles of Soil Dynamics. Cengage Learning, Connecticut (2010)

    Google Scholar 

  22. Matasovic N., Kavazanjian E.: Cyclic characterization of OII landfill solid waste. J. Geotech. Geoenviron. Eng. 124(3), 197–210 (1998). doi:10.1061/(ASCE)1090-0241(1998)124:3(197)

    Article  Google Scholar 

  23. Wiegel R.L.: Earthquake Engineering. Prentice Hall, Inc., New Jersey (1970)

    Google Scholar 

  24. Kavazanjian, E.: Hanshin earthquake-reply. Geotech Bulletin Board, NSF Earthquake Hazard Mitigation Programme, Helsinki (1995)

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Authors and Affiliations

  1. School of Transportation Engineering, Hefei University of Technology, Hefei, 230009, China

    Xiaobo Ruan

  2. School of Civil Engineering and Architecture, Nanchang University, Nanchang, 330031, China

    Hai Lin

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  1. Xiaobo Ruan
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  2. Hai Lin
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Correspondence to Xiaobo Ruan.

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Ruan, X., Lin, H. Relationship Between Shear Wave Wavelength and Pseudo-Dynamic Seismic Safety Factor in Expanded Landfill. Arab J Sci Eng 40, 2271–2288 (2015). https://doi.org/10.1007/s13369-015-1721-y

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  • DOI: https://doi.org/10.1007/s13369-015-1721-y

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