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Semi empirical hydromechanical model for quantifying effectiveness of loaded granular filters

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Abstract

This paper presents results from a series of filtration tests to investigate geometrical and hydromechanical factors controlling the erosion of base particles and their subsequent capture into sand-gravel filters subjected to uniaxial static loading. The analysis revealed that the effectiveness of a filter, apart from its geometry (i.e. particles and constriction sizes), is also controlled by unique combinations of associated hydromechanical factors such as applied hydraulic gradients and the resulting effective stresses. Furthermore, it is observed that the base soil experiences a significant and continuous reduction in effective stress during internal flow (seepage), and the migration of base particles into the filter initiates after localised fluidisation in the base soil (i.e. at very low effective stress levels). Based on limit equilibrium considerations, a novel theoretical approach, different from all other existing methods, is proposed to estimate the critical hydraulic gradient for base soil erosion into granular filter and hence the retention capacity of filters. The current methodology is subsequently validated using experimental data from the published literature and promising results were obtained.

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Abbreviations

∆y i, δ z :

base particle penetration depth and elemental pore channel (mm)

∅′ :

drained angle of internal friction

γ w and μ w :

viscosity (Pa.s) and unit weight of water (kN/m3)

σ′vm, σ′vt, σ′vb :

mean, top and bottom vertical effective stresses respectively (kPa)

Ɲ m :

dimensionless mechanical number

d b, D cm :

base particle and mean constriction size of the filter media (mm)

F d, F h, F b, F w, F f :

drag, hydrodynamics, buoyancy, gravity and friction forces (kN)

F bm, F bmh, F bmr :

various factor of safety against base particle migration

G s and γ s :

specific gravity and specific unit weight of soil (kN/m3)

h f and h f, p :

filter thickness, predicted filter thickness (mm)

h h :

upstream hydraulic head in dams (m)

i cr, 0 :

theoretical critical hydraulic gradient for soil piping (Terzaghi 1922)

i c0, i and i c0, t :

hydraulic gradient for base particle erosion under no-load condition for unit step erosion and total erosion, respectively

i cp :

hydraulic gradient for base particle erosion into loaded filters

i a and i max :

average and maximum applied hydraulic gradients, respectively

i cr :

observed critical hydraulic gradient for particle migration into filter

i ct :

theoretical hydraulic gradient for particle migration into loaded filter

k fc :

contact friction factor

n f :

filter porosity

p w :

applied water pressure (kPa)

q s :

effective overburden surcharge pressure (kPa)

Q f, V f :

volumetric flow rate (lit/min), macroscopic fluid velocity (cm/s)

References

  • Ahlinhan MF, Achmus M (2010) Experimental investgation of critical hydraulic gradients for unstable soils. Scour and Erosion:599–608

  • Alobaidi I, Hoare DJ (1996) The development of pore water pressure at the subgrade-subbase interface of a highway pavement and its effect on pumping of fines. Geotext Geomembr 14(2):111–135

    Article  Google Scholar 

  • American Society for Testing and Materials (ASTM) (2006a) Standard test methods for maximum index density and unit weight of soils using a vibratory table. In: ASTM D4253-06. West, Conshohocken, Pa

    Google Scholar 

  • American Society for Testing and Materials (ASTM) (2006b) Standard test methods for minimum index density and unit weight of soils and calculation of relative density. In: ASTM D4254-00. West, Conshohocken, Pa

    Google Scholar 

  • Aziz M (2020) Using grain size to predict engineering properties of natural sands in Pakistan. Geomechanics and Engineering 22(2):165–171

    Google Scholar 

  • Aziz M, Towhata I, Yamada S, Qureshi MU, Kawano K (2010) Water-induced granular decomposition and its effects on geotechnical properties of crushed soft rocks. Natural Hazards & Earth Sciences 10(6)

  • Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge

    Google Scholar 

  • Bertram GE (1940) An experimental investigation of protective filters, Soil mechanics Series No. 7. Cambridge, MA: Graduate School of Engineering, Harvard University.

  • Cedergren HR (1977) Seepage, drainage and flow nets. Wiley, New York

    Google Scholar 

  • Chang D, Zhang L (2013) Critical hydraulic gradients of internal eErosion under complex stress states. J Geotech Geoenviron Eng 139(9):1454–1467

    Article  Google Scholar 

  • Fannin R, Moffat R (2006) Observations on internal stability of cohesionless soils. Geotechnique 56(7):497–500

    Article  Google Scholar 

  • Fourie AB, Copeland AM, Barrett AJ (1994) Optimization of the as-placed properties of hydraulic backfill. J South African Instt Min and Met 94(8):199–210

    Google Scholar 

  • ICOLD (International Commission on Large Dams) (1994) Embankment dams-filters and drains. Bulletin, No. 95, Nice: ICOLD

  • Indraratna B, Radampola S (2002) Analysis of critical hydraulic gradient for particle movement in filtration. J Geotech Geoenviron Eng 128(4):347–350

    Article  Google Scholar 

  • Indraratna B, Israr J, Rujikiatkamjorn C (2015) Geometrical method for evaluating the internal instability of granular filters based on constriction size distribution. J Geotech Geoenviron Eng 141(10):04015045-1-14. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001343)

    Article  Google Scholar 

  • Irfan M, Uchimura T (2016) Modified triaxial apparatus for determination of elastic wave velocities during infiltration tests on unsaturated soils. KSCE J Civ Eng:197–207

  • Israr J, Indraratna B (2017) Internal stability of granular filters under static and cyclic loading. J Geotech Geoenviron Eng ASCE 143(6):04017012. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001661)

    Article  Google Scholar 

  • Israr J, Indraratna B (2018) Mechanical response and pore pressure generation in granular filters subjected to uniaxial cyclic loading. Can Geotech J 55:1756–1768. https://doi.org/10.1139/cgj-2017-0393

    Article  Google Scholar 

  • Israr J, Indraratna B, Rujikiatkamjorn C (2016) Laboratory investigation of the seepage induced response of granular soils under static and cyclic loading. Geotech Test J 39(5):795–812

    Article  Google Scholar 

  • Kenney TC, Lau D (1985) Internal stability of granular filters. Can Geotech J 22:215–225

    Article  Google Scholar 

  • Langroudi MF, Soroush A, Tabatabaie SP, Shafipour R (2013) Stress transmission in internally unstable gap-graded soils using discrete element modelling. Powder Technol 247(1):161–171

    Article  Google Scholar 

  • Li M, Fannin RJ 2016 Critical hydraulic gradients for internally unstable cohesionless soils. 69th Annual Canadian Geotechnical Conference, Vancouver, October

  • Locke M, Indraratna B, Adikari G (2001) Time-dependent particle transport through granular filters. J Geotech Geoenviron Eng 127(6):521–529

    Article  Google Scholar 

  • Moffat R, Fannin RJ, Garner SJ (2011) Spatial and temporal progression of internal erosion in cohesionless soil. Can Geotech J 48(3):399–412

    Article  Google Scholar 

  • Plagenhoef S, Evans FG, Abdelnour T (1983) Anatomical data for analyzing human motion. Res Q Exerc Sport 54:169–178

    Article  Google Scholar 

  • Qi Y, Indraratna B, Coop MR (2019) Predicted behavior of saturated granular waste blended with rubber crumbs. International Journal of Geomechanics 19(8):04019079

    Article  Google Scholar 

  • Raut AK, Indraratna B (2008) Further advancement in filtration criteria through constriction-based techniques. J Geotech Geoenviron Eng 134(6):883–887

    Article  Google Scholar 

  • Rice JD, Duncan JM (2010) Deformation and cracking of seepage barriers in dams due to changes in the pore pressure regime. J Geotech Geoenviron Eng 136(1):16–25

    Article  Google Scholar 

  • Richards KS, Reddy KR (2007) Critical appraisal of piping phenomena in earth dams. Bulletin Eng Geology Eng 66(4):381–402

    Article  Google Scholar 

  • Sansalone J, Kuang X, Rainieri V (2008) Permeable pavement as a hydraulic and filtration interface for urban drainage. J Irrig Drain Eng 134(5):666–674

    Article  Google Scholar 

  • Selig ET, Waters JM (1994) Track geotechnology and substructure management. Thomas Telford, London

    Book  Google Scholar 

  • Skempton AW, Brogan JM (1994) Experiments on piping in sandy gravels. Geotechnique 44(3):449–460

    Article  Google Scholar 

  • Smith JL, Bhatia SK (2010) Minimizing soil erosion with geosynthetic rolled erosion control products. Geo-Strata – Geo Inst 14(4):50–53

    Google Scholar 

  • Srivastava A, Sivakumar Babu GL (2011) Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling. Can Geotech J 48(6):956–969

    Article  Google Scholar 

  • Tanaka T, Toyokumi E (1991) Seepage failure experiments on multi layered sand columns. Soil and Foundations 31(4):13–36

    Article  Google Scholar 

  • Terzaghi K (1922) Failure of dam foundations by piping and means for preventing it (in German). Die Wasserkraft. Zeitschrift fur die gesamte Wasserwirtschaft 17(24):445–449

    Google Scholar 

  • To HD, Scheuermann A (2015) Separation of grain size distribution for application of self-filtration criteria in suffusion assessment. Proc. 7th Int. Conf. Scour and Erosion (Taylor & Francis),121-127, London

  • Tomlinson SS, Vaid YP (2000) Seepage forces and confining pressure effects on piping erosion. Can Geotech J 37(1):1–13

    Article  Google Scholar 

  • Trani LDO, Indraratna B (2010) Assessment of subballast filtration under cyclic loading. J Geotech Geoenviron Eng 136(11):1519–1528

    Article  Google Scholar 

  • Vaughan P, Soares H (1982) Design of filters for clay cores of dams. J Geotech Eng Div 108(1):17–31

    Article  Google Scholar 

  • Xiao M, Shwiyhat N (2012) Experimental investigation of the effects of suffusion on physical and geomechanic characteristics of sandy soils. Geotech Test J 35(6):890–900

    Article  Google Scholar 

  • Xiao M, Reddi LN, Steinberg S (2006) Effect of vibrations on pore fluid distribution in porous media. Transp Porous Media 62(2):187–204

    Article  Google Scholar 

  • Zou Y, Chen Q, Chen X, Cui P (2013) Discrete numerical modelling of particle transport in granular filters. Comput Geotech 32(5):340–357

    Google Scholar 

Download references

Acknowledgements

Supports received by the corresponding author in the form of Helan Mountain Research Scholar Program of Ningxia University China, and FDP & IPTA scholarships from University of Engineering and Technology Lahore Pakistan and University of Wollongong Australia, respectively, are acknowledged. Private discussions and consultations of the authors with the Distinguished Professor Buddhima Indraratna, previously at University of Wollongong Australia, are heartily appreciated.

Funding

This study received financial supports from Helan Research Scholar Program of Ningxia University China, Key R&D Program of Ningxia Hui Autonomous Region China (No. 2018BFH03010) and National Natural Science Foundation of China (No. 51768059).

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Authors and Affiliations

  1. School of Civil and Hydraulics Engineering, Ningxia University, Yinchuan, China

    Gang Zhang

  2. Institute of Solid Mechanics, School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan, China

    Jahanzaib Israr

  3. Department of Civil Engineering, University of Engineering and Technology Lahore, Lahore, Punjab, 54890, Pakistan

    Jahanzaib Israr

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  1. Gang Zhang
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Correspondence to Jahanzaib Israr.

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Responsible Editor: Zeynal Abiddin Erguler

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Zhang, G., Israr, J. Semi empirical hydromechanical model for quantifying effectiveness of loaded granular filters. Arab J Geosci 14, 1488 (2021). https://doi.org/10.1007/s12517-021-07875-w

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