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Reliability-based seismic design of reinforced soil walls for vertical expansion of MSW Landfills

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Abstract

The past few decades have been marked by a rapid acceleration in Municipal Solid Waste (MSW) generation because of industrialization, urbanization, and economic growth combined with a high population growth rate. Thus, the most economically effective alternative to developing new landfills is the construction of reinforced soil walls (RSW) in existing MSW landfills to allow for their vertical expansion. This paper presents a structure for the system reliability-based seismic design optimization (SRBSDO) approach for landfills by incorporating the variability associated with design parameters under seismic conditions. The formulation considers a three-part wedge mechanism based on the pseudo-static limit equilibrium method. The influence of the horizontal seismic acceleration coefficient (kh) on the stability against external and internal modes of failure is studied. A target reliability index of not less than 3.0 is adopted to obtain the optimum dimensions of RSW required to achieve stability against three modes of failure (bearing capacity, sliding, and eccentricity). The dimensions of RSW are presented with respect to vertically expanded heights in the form of design charts. The results of the internal stability analysis of an RSW are provided to obtain the optimum number of geosynthetic reinforcement layers required for the stability of RSW under seismic loading. It is reported that kh has a substantial influence on the reliability of RSW, and higher values of mean and coefficient of variations of kh may cause instability. It is observed that the total length of the reinforcement (B2) should not be less than 0.67 and 0.91 times the height of the RSW (H2) for kh = 0.1 and 0.2, respectively. The minimum required number of reinforcement layers to maintain overall stability are 13 for kh = 0.10 with minimum B2/H2 of 0.66 and 19 for kh = 0.20 with minimum B2/H2 of 0.83.

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Data availability

All data generated or analysed during this study are included in this published article [and its supplementary information files].

Code availability

All steps for the implementation of code is provided in this published article.

Abbreviations

B :

Width of waste mass at the top of the back slope

B 2 :

Width of RSW or length of geosynthetic reinforcement

L 1 :

Horizontal distance between the toe of the back slope and the toe of RSW

B t :

Top width of waste mass

H 1 :

Height of back slope

H 2 :

Height of RSW

H t :

Height of expanded waste mass above back slope

x :

Random variable in limit state space

T:

Transformation function

β :

Reliability index

u :

Angle of front slope of berm

α :

Angle of back slope of berm

ψ :

Angle of back slope of landfill measured from horizontal

η :

Angle of front slope of landfill measured from horizontal

θ :

Angle of subgrade from horizontal

ξ :

Angle of landfill cover slope

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

Unit weight of RSW

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

Unit weight of MSW

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

Unit weight of foundation soil

c sw _ N :

Normalized apparent cohesion of MSW

c sw :

Apparent cohesion of MSW

C SW :

Apparent cohesive force of solid waste

c 1_ N :

Normalized apparent cohesion between liner components beneath wedge1

c 1 :

Apparent cohesion between liner components beneath wedge1

C 1 :

Apparent cohesive force between liner components beneath wedge1

c 2_ N :

Normalized apparent cohesion between liner components beneath wedge2

c 2 :

Apparent cohesion between liner components beneath wedge2

C 2 :

Apparent cohesive force between liner components beneath wedge2

c b _ N :

Normalized apparent cohesion between liner components beneath RSW

c b :

Apparent cohesion between liner components beneath RSW

C B :

Apparent cohesive force between liner components beneath RSW

c 2 b :

Apparent cohesion between solid waste and RSW

C 2 B :

Apparent cohesive force between RSW and wedge2

c s :

Apparent cohesion foundation soil

W B :

Weight of RSW or weight of reinforced soil wall

W 1 :

Weight of wedge1

W 2 :

Weight of wedge2

E V 21 :

Frictional force acting on the side of wedge1

E V 12 :

Frictional force acting on the side of wedge2

E H 12 :

Normal force from wedge1 acting on wedge2

E H 21 :

Normal force from wedge2 acting on wedge1

E V 2 B :

Frictional force acting on the side of RSW next to wedge2

E VB 2 :

Frictional force acting on side of wedge2 next to RSW

E H 2 B :

Normal force from wedge2 acting on RSW

E HB 2 :

Normal force from RSW acting on wedge2

E H 2 Bst :

Normal force from wedge2 acting on RSW in static condition

E V2Bst :

Frictional force acting on the side of RSW next to wedge2 in static condition

∆E H :

Additional horizontal component of seismic force

∆E V :

Additional vertical component of seismic force

k h :

Horizontal seismic acceleration coefficient

k v :

Vertical seismic acceleration coefficient

F B :

Frictional force acting on the bottom of RSW

F 2 :

Frictional force acting on the bottom of wedge2

F 1 :

Frictional force acting on the bottom of wedge1

FS :

Factor of safety

FS 1 :

Factor of safety for wedge1 of an MSW landfill

FS 2 :

Factor of safety for wedge2 of an MSW landfill

FS B :

Factor of safety for RSW

FS V :

Factor of safety at the interface between wedge1 and wedge2, the factor of safety at the interface between RSW and wedge2

FS sli :

Factor of safety of RSW against sliding failure

FS e :

Factor of safety of RSW considering eccentricity criterion

FS b :

Factor of safety of RSW against bearing capacity failure

\({\beta }_{sli}\) :

Reliability index against sliding failure

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

Reliability index against eccentricity failure

\({\beta }_{b}\) :

Reliability index against bearing failure

\({\beta }_{lb}\) :

Lower bound of system reliability index

\({\phi }_{sw}\) :

Internal friction angle of solid waste

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

Friction angle of foundation soil

\({\phi }_{b}\) :

Friction angle of RSW

\({\delta }_{b}\) :

Minimum interface friction angle of liner components beneath RSW

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

Minimum interface friction angle of liner components beneath wedge1

\({\delta }_{2}\) :

Minimum interface friction angle of liner components beneath wedge2, \({\delta }_{1}\)=\({\delta }_{2}\)=\({\delta }_{12}\)

\({\delta }_{2b}\) :

Minimum interface friction angle between wedge2 of MSW landfill and RSW

N 1 :

Normal force acting on the bottom of wedge1

N B :

Normal force acting on the bottom of RSW

N 2 :

Normal force acting on the bottom of wedge2

e :

Eccentricity of the resulting force on the RSW

∑V :

Resultant of vertical forces

M R :

Resisting moment

M O :

Overturning moment

q u :

Ultimate bearing capacity of a foundation of RSW

\({\sigma }_{v}\) :

Vertical stress at the base of RSW

K :

Optimum reinforcement force coefficient

T r :

Reinforcement force

T r max :

Maximum tensile strength of the reinforcement

T D :

Long-term design strength of the reinforcement

T D_N :

Normalized design strength of the reinforcement

T imax :

Maximum load in the soil reinforcement

q :

Surcharge

\({W}_{B{B}_{1}A}\) :

Weight of the log spiral portion BB1A

R B :

Resultant force acting along the radial line of log-spiral

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

Subtended angle of the log-spiral wedge SB1A

\({\theta }_{2}\) :

Angle of the initial radius of log-spiral wedge SB1 with horizontal

\({\theta }{\prime}\) :

Angle of the radial line of the elemental strip with the final radius of the log-spiral wedge, SA

L e :

Embedded reinforcement length

\({\sigma }_{vi}\) :

Effective vertical stress acting on the embedded reinforcement length (Le)

\({\delta }_{br}\) :

Minimum interface friction angle between geosynthetic and reinforced soil

z :

Depth of the reinforcement layer from the top of the RSW height

n :

Number of geosynthetic reinforcement layers

P ri :

Resisting force

FS t :

Factor of safety against tension failure

FS po :

Safety factor against pullout failure

\({\beta }_{t}\) :

Reliability index against tension failure

\({\beta }_{po}\) :

Reliability index against pullout failure

References

  • Babu GLS, Reddy KR, Srivastava A (2014) Influence of spatially variable geotechnical properties of MSW on stability of landfill slopes. J Hazard Toxic Radioact Waste 8(1):27–37

    Article  Google Scholar 

  • Barrows AG (1975) Surface effects and related geology of the San Fernando earthquake in the foothill region between Little Tujunga and Wilson Canyons. In: Oakeshott G (ed) San Fernando earthquake of 9 February 1971. California Division of Mines and Geology, pp 97–117

    Google Scholar 

  • Basha BM, Babu GLS (2010) Optimum design for external seismic stability of geosynthetic reinforced soil walls: Reliability based approach. J Geotech Geoenviron Eng 136(6):797–812

    Article  Google Scholar 

  • Basha BM, Babu GLS (2012) Target reliability-based optimisation for internal seismic stability of reinforced soil structures. Geotechnique 62(1):55–68

    Article  Google Scholar 

  • Basha BM, Babu GLS (2014) Reliability-based load and factor design approach for external seismic stability of reinforced soil walls. Soil Dyn Earthq Eng 60:8–21

    Article  Google Scholar 

  • Basha BM, Basudhar PK (2010) Pseudo static seismic stability analysis of reinforced soil structures. Geotech Geol Eng 28(6):745–762

    Article  Google Scholar 

  • Bathurst RJ, Cai Z (1995) Pseudo-static seismic analysis of geosynthetic reinforced segmental retaining walls. Geosynth Int 2(5):787–830

    Article  Google Scholar 

  • Buranek D, Prasad S (1991) Sanitary landfill performance during the Loma Prieta earthquake. In: Proceedings of the 2nd International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis Missouri, pp 1655–1660. https://scholarsmine.mst.edu/icrageesd/02icrageesd/session13/12

  • Chalermyanont T, Benson C (2005) Reliability-based design for external stability of mechanically stabilized earth walls. Int J Geomech 5(3):196–205

    Article  Google Scholar 

  • Choudhury D, Savoikar P (2010) Seismic translational failure analysis of MSW landfills using pseudo-static approach. GeoFlorida 2010: Advances in analysis, modeling & design. ASCE, Reston, VA, pp 2830–2839. https://doi.org/10.1061/41095(365)288

    Chapter  Google Scholar 

  • Choudhury D, Savoikar P (2011) Seismic stability analysis of expanded MSW landfills using pseudo-static limit equilibrium method. Waste Manag Res 29(2):135–145

    Article  Google Scholar 

  • Datta S, Babu GLS (2016) Prediction of the slope stability of municipal solid waste landfills using the reliability analysis. Proceedings of the Geo-Chicago. Chicago, IL, USA, pp 668–677. https://doi.org/10.1061/9780784480144.066

  • Duncan MJ (2000) Factors of safety and reliability in geotechnical engineering. J Geotech Geoenviron Eng 126:307–316

    Article  Google Scholar 

  • Feng SJ, Gao LY (2010) Seismic analysis for translational failure of landfills with retaining walls. Waste Manag 30:2065–2073

    Article  Google Scholar 

  • Federal Highway Administration (FHWA) (2001) Mechanically stabilized earth walls and reinforced soil slopes design and construction guidelines. FHWA-NHI-00-043, DOT, Washington, DC

    Google Scholar 

  • Ismeik M, Guler E (1998) Effect of wall facing on the seismic stability of geosynthetic-reinforced retaining walls. Geosynth Int 5(1–2):41–53

    Article  Google Scholar 

  • Jahanfar A, Dubey B, Gharabaghi B, Movahed SB (2016) Landfill failure mobility analysis: A probabilistic approach. Int J Environ, Chem, Ecol, Geol Geophys Eng 10(5):500–508

    Google Scholar 

  • Jahanfar A, Gharabaghi B, McBean EA, Dubey BK (2017) Municipal solid waste slope stability modelling: A probabilistic approach. J Geotech Geoenviron Eng 143(8). https://doi.org/10.1061/(ASCE)GT.1943-5606.0001704

  • Johnson ME, Lundy J, Lew M, Ray ME (1991) Investigation of sanitary landfill slope performance during strong ground motion from the Loma Prieta earthquake of October 17, 1989. Proc. 2nd International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. St. Louis, Missouri, pp 1701–1708. https://scholarsmine.mst.edu/icrageesd/02icrageesd/session13/7

  • Koseki J, Barthurst RJ, Güler E, Kuwano J, Maugeri M (2006) Seismic stability of reinforced soil walls. Proceedings of the 8th International Conference on Geosynthetics, Yokohama, Japan, 18–22 September 2006. Millpress Science Publishers, Rotterdam, The Netherlands, pp 51–78

    Google Scholar 

  • Ling HI, Leshchinsky D (1998) Effects of vertical acceleration on seismic design of geosynthetics reinforced soil structures. Geotechnique 48(3):347–373

    Article  Google Scholar 

  • Ling HI, Leshchinsky D, Perry EB (1997) Seismic design and performance of geosynthetic reinforced soil structures. Geotechnique 47(5):933–952

    Article  Google Scholar 

  • Ma P, Lan J, Ke H (2019) Field monitoring of a geogrid reinforced MSE slope. In: Zhan L, Chen Y, Bouazza A (eds) Proceedings of the 8th International Congress on Environmental Geotechnics, ICEG 2018, Environmental Science and Engineering, vol 2. Springer, Singapore, pp 72–731

    Google Scholar 

  • Mahapatra S, Basha BM, Manna B (2022) Leachate Pressure Effect on System Reliability Based Design of Reinforced Soil Walls for Vertical Expansion of MSW Landfills. Int J Geomech, ASCE,. https://doi.org/10.1061/IJGNAI/GMENG-7755

    Article  Google Scholar 

  • Mahapatra S, Basha BM, Manna B (2020) System reliability framework for design of MSE walls for vertical expansion of MSW landfills. J Hazard Toxic Radioact Waste 25(1). https://doi.org/10.1061/(ASCE)HZ.2153-5515.0000559

  • Matasovc N, Kavazanjian E Jr, Augello AJ, Bray JD, Seed RB (1995) Solid waste landfill damage caused by 17 January 1994 Northridge earthquake in Woods. In: Mary C, Seiple WR (eds) The Northridge, California, Earthquake of 17 January 1994. California Department of Conservation, Division of Mines and Geology Special Publication, pp 221–229

  • Mehdizadeh MJ, Shariatmadari N, Karimpour-Fard M (2020) Probabilistic slope stability analysis in Kahrizak landfill: effect of spatial variation of MSW’s geotechnical properties. Bull Eng Geol Environ (2020). https://doi.org/10.1007/s10064-019-01688-8

  • Na UJ, Chaudhuri SR, Shinozuka M (2008) Probabilistic assessment for seismic performance of port structures. Soil Dyn Earthq Eng 28:147–158

    Article  Google Scholar 

  • Nouri H, Fakher A, Jones CJFP (2008) Evaluating the effects of the magnitude and amplification of pseudo-static acceleration on reinforced soil slopes and walls using the limit equilibrium horizontal slices method. Geotext Geomembr 26(3):263–278

    Article  Google Scholar 

  • Orr WR, Finch MO (1990) Solid waste landfill performance during Loma Prieta earthquake. Geotech Waste Fills-Theory and Pract, ASTM STP 1070:22–30

    Article  Google Scholar 

  • Peng M, Sun R, Chen J-F, Rajesh S, Zhang L-M, Yu S-B (2020) System reliability analysis of geosynthetic reinforced soil slope considering local reinforcement failure. Comput Geotech 123:103563

    Article  Google Scholar 

  • Petrovic I, Hip I, Fredlund MD (2015) Application of continuous normal–lognormal bivariate density functions in a sensitivity analysis of MSW landfill. Waste Manag 55. https://doi.org/10.1016/j.wasman.2015.11.021

  • Phoon K, Kulhawy F (1999) Evaluation of geotechnical property variability. Can Geotech J 36:625–639

    Article  Google Scholar 

  • Raghuram ASS, Raviteja KVNS, Basha BM, Moghal AAB (2020) Reliability Based Design Charts for Spatially Variable MSW Landfill Slopes. Geo-Congress 2020, pp. 696-706. American Society of Civil Engineers GSP 316, Reston, VA, pp 696–706. https://doi.org/10.1061/9780784482797.068

    Chapter  Google Scholar 

  • Sayed S, Dodagoudar GR, Rajagopal K (2008) Reliability analysis of reinforced soil walls under static and seismic forces. Geosynth Int 15(4):246–257

    Article  Google Scholar 

  • Sia AHI, Dixon N (2007) Distribution and variability of interface shear strength and derived parameters. Geotext Geomembr 25:139–154

    Article  Google Scholar 

  • Siegel RA, Robertson RJ, Anderson DG (1990) Slope Stability Investigations at a Landfill in Southern California. In: Arvid Landva G, Knowles D (eds) Geotechnics of Waste Fills-Theory and Practice. American Society for Testing and Materials, Philadelphia, pp 259–284

    Chapter  Google Scholar 

  • US Army Corps of Engineers (1997) Engineering and design, introduction to probability and reliability methods for use in geotechnical engineering. Engr. Tech. Letter No. 1110-2-547. Department of the Army, Washington, D.C.

    Google Scholar 

Download references

Funding

Financial support for this project was provided by the Government of India, Ministry of Education, which is gratefully acknowledged.

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Author notes

  1. Shilpi Mahapatra

    Present address: Geotechnical Engineer, AFRY India Pvt. Ltd., Office No 2-5, Ground Floor, Tower-1, Stellar IT Park, Noida, 20130, India

Authors and Affiliations

  1. Former Research Scholar, Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Shilpi Mahapatra

  2. Department of Civil Engineering, Indian Institute of Technology Hyderabad, 502285, Hyderabad, Andhra Pradesh, India

    B Munwar Basha

  3. Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Bappaditya Manna

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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Shilpi Mahapatra, B Munwar Basha, Bappaditya Manna. The first draft of the manuscript was written by Shilpi Mahapatra, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to B Munwar Basha.

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Responsible Editor: Zeynal Abiddin Erguler

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Mahapatra, S., Basha, B. & Manna, B. Reliability-based seismic design of reinforced soil walls for vertical expansion of MSW Landfills. Arab J Geosci 16, 492 (2023). https://doi.org/10.1007/s12517-023-11593-w

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