Prediction of Saturated Hydraulic Conductivity of Silty Sand Soils Based on Gradation Characteristics Abdellah Cherif Taiba1*

Prediction of Saturated Hydraulic Conductivity of Silty Sand Soils Based on Gradation Characteristics
Abdellah Cherif Taiba1*, Youcef Mahmoudi1, Leila Hazout 2, Mostefa Belkhatir1,3, Wiebke Baille3

1Laboratory of Material Sciences & Environment, University of Chlef (Algeria)
2 Saâd Dahlab University of Blida (Algeria)
3Laboratory of Foundation Engineering, Bochum Ruhr University (Germany)
(*) Corresponding author e-mail: [email protected]

Abstract
Hydraulic conductivity is the most common parameter for predicting the contamination and movement of water between soil particles. This parameter is measured in laboratory and in field using some apparatus. A number of investigators reported that the hydraulic conductivity has been related to the particle size of soils. In this context, a series of saturated hydraulic conductivity tests were carried out on three different sands named “Chlef sand, Fontainebleau sand and Hostun sand” mixed with low plastic silty fines. The sand-silt mixture samples were reconstituted at an initial relative density “Dr=55%” and were tested in the constant head permeability apparatus. The obtained results indicate that the measured saturated hydraulic conductivity decreases with the decrease of the grain size (D10, D50) and the increase of the coefficient of uniformity (Cu) of the materials under study. The introduced grading characteristics ratios (D10R “effective diameter ratio”, D50R “Mean grain size ratio” and CUR “coefficient of uniformity ratio”) appear as pertinent parameters for the prediction of the saturated hydraulic conductivity of the silty sand under consideration.
Keywords: Hydraulic conductivity, silty sand, effective diameter ratio, mean grain size ratio, coefficient of uniformity ratio
Abbreviations
CS= Chlef sand
Cu = Coefficient of uniformity
CUR = Coefficient of uniformity ratio
D10 = Effective diameter
D10R = Effective diameter ratio
D30, D60 = Grain size corresponding to 30% and 60% finer, respectively
D50 = Mean grain size
D50R = Mean grain size ratio
Dr = Initial relative density
HS=Hostun sand
Fc = Fines content
FS=Fontainebleau sand
Ip = Plasticity index
Ks= Saturated hydraulic conductivity
ML = Low plastic silt
R² = Coefficient of determination
SP = Poorly graded sand
USCS = Unified Soil Classification System
1. Introduction
Determination saturated hydraulic conductivity of soil is an important stage for engineering studies dealing with the movement of water between soil grain voids 15. Indeed, the importance of this physical property of soil is related to finding out acceptable solutions for studying instability problems that could be triggered by environmental natural disasters 30. It is of significant importance in relationship to some geotechnical problems, settlement computations, and stability analyses 5. 32 reported that the hydraulic conductivity is measured according to different techniques as laboratory methods, field methods (pumping test of wells, auger whole test and tracer test) and calculation from empirical equations. Therefore, 6 reported that the hydraulic conductivity is a suitable engineering parameter of soil depending on the average pores size of soil matrix and the temperature of the environment. 7 confirmed that the hydraulic conductivity could be predicted using capillary models, statistical models and hydraulic radius theories.
Moreover, mathematical correlations for estimation saturated hydraulic conductivity using particle size distribution have been developed by several investigators in literature 5, 27, 33 and 34. In other hand, 16 proposed an estimation of the coefficient of permeability of an unsaturated soil based on physical properties of soils that include grain size analysis, degree of saturation or water content, and porosity of the soil. 18 demonstrated clearly that the Ks is related to the grain size distribution of granular porous media. 13 and 19 proposed the following relationships between the saturated hydraulic conductivity and the effective diameter as:
Ks=8.91+61.08(D10) (1) and Ks=16.16+121.5 (D10)² (2)
Where Ks is expressed in (m/day) and D10 is the soil particle diameter (mm) that 10% of all particle are finer (smaller) by weight. Moreover, 14 and 20 suggested linear and quadratic equations to estimate the Ks with the mean grain size (D50) which is 50% of particles are finer by weight as follow:
Ks=16.88+10.60*(D50) (3) and Ks=20.90+6.52*(D50)² (4)
1 estimated hydraulic conductivity from soil particle diameters (D10 and D50) of 32 sandy soil samples according to the following relationship:
Ks=1.505+ I0+ 0.025(D50-D10) ² (5)
Where Ks is expressed in (cm/s), I0 is the x-intercept of straight line formed by joining of effective diameter (D10) and mean grain size (D50). Therefore, very limited studies have been reported in published literature to evaluate the correlation between Ks and particle size distribution of sand mixed with fines 3 and 4. 31 indicated that the hydraulic conductivity of sand was higher magnitude in comparison to Ks of sand mixed with low plastic fines. Similar observations also reported by 2 and 29. In addition, 3 and 4 suggested that the hydraulic conductivity could be correlated very well with the fines content up 50%. Indeed, is decreased with the increase of fines content for the range of (Fc=0% to Fc=50%). 21 reported that the hydraulic conductivity decreased slowly with fines content up to Fc=30%, beyond that it continued to decrease significantly with further increase in fines content for different sand-silt mixtures. 35 found that the hydraulic conductivity of calcarous sand affected by different factors such as shape and particle size distribution.
The present study aims to explore the relationship between the saturated hydraulic conductivity (Ks) and grain size distribution in terms of grading characteristics ratios (“D10R= D10sand/D10mixture”, “D50R= D50sand/D50mixture” and “CUR=Cusand/Cumixture”) of three different sands (Chlef sand, Fontainebleau sand and Hostun sand) mixed with low plastic fines. The laboratory sand-silt mixture samples were reconstituted at an initial relative density (Dr=55%) and were tested in the constant head permeability apparatus.
2. Experimental program
2.1 Index properties of the tested materials
The tests were performed on the three different sands: Chlef (Algeria) sand named as “CS”, Fontainebleau (France) sand named as “FS” and Hostun (France) sand named as “HS”. The sands were mixed with low plastic Chlef silty fines contents ranging from 0% to 40% (from Algeria). Liquid limit and plastic limit of the Chlef silt were 33.72% and 26.71 %, respectively. The microscopic views of tested materials are shown in Figure 2. Standard methods were applied to investigate particle size distribution (grain size curve) and consequently determine of the granulometric characteristics (D10, D50 and Cu). Soils were classified according to the Unified Soil Classification System (USCS) as poorly graded sand (SP). The values of the parameters (D10, D50, Cu, “D10R= D10sand/D10mixture”, “D50R= D50sand/D50mixture” and “CUR=Cusand/Cumixture”) and the measured saturated hydraulic conductivity of the tested samples that were used in this study are summarized in Table 1.
2.2 Sample preparation
The Chlef sand-silt mixture, Fontainebleau sand-silt mixture and Hostun sand-silt mixture samples were reconstituted with dry funnel pluviation method that was recommended by several researchers through the published literature 8, 9, 10, 11, 12, 17, 23, 24, 2 5, 26 and 36.. The dry soil is deposited in cylindrical cell of about 78cm² cross sectional area with the help of a funnel by controlling the height; this method consists in filling the mould by tipping in rain of dry sand.
2.3 Hydraulic conductivity measurement
The silty sand samples were wetted by capillarity for some hours. Therefore, the water is then allowed to flow through the soil with maintaining a constant pressure head and saturated hydraulic conductivity was measured when outflow rate becomes constant. In this study, the saturated hydraulic conductivity was measured using a constant- head permeability apparatus at an initial relative density (Dr=55%) and constant temperature (20°C). The volume of the water (q) flowing during a certain time (t) is measured when a steady vertical water flow, under a constant head, is maintained through the soil sample. Then, the K values of the samples tested were calculated using Darcy’s law (K=ql/ah).
Where q: is the discharge, a: is the cross sectional area of sample, h: is the hydraulic load on sample and l: is the length of sample. The experimental program of this study is illustrated in Figure (1).

Figure 1: Flow chart experimental program of the tested materials

Table 1: Summary of grain size characteristics and measured hydraulic conductivity of tested materials
3. Results and discussion
3.1 Estimation of the saturated hydraulic conductivity as function of gradation characteristics (D10, D50 and Cu)
For the purpose of analyzing the effects of the effective diameter (D10) and mean grain size (D50) on the measured saturated hydraulic conductivity (Ks) of sand-silt mixtures (Figure 2) reproduces the test results obtained from the current study. The obtained data indicate that the measured saturated hydraulic conductivity decreases in a linear manner with the decrease of the various grain size parameters for the different sand-silt mixture samples reconstituted with fines content ranging from 0% to 40% at an initial relative density of 55%. Moreover, it is clearly observed from the plot that for the different graded sand–silt mixtures, the smaller effective size (D10) and mean grain size (D50), the smaller measured saturated hydraulic conductivity (Ks). In addition, the test results indicate that the effective diameter (D10) appears as a pertinent parameter to predict the measured saturated hydraulic conductivity with higher coefficient of correlation (R²=0.90) for the tested sand-silt mixture samples (Figure 2a) in comparison to the mean grain size (D50) (Figure 2b). The outcome of this laboratory investigation is in good agreement with the results of 3, 4, 5, 28 and 35.
Figure 2: Measured saturated hydraulic conductivity versus grading characteristics of silty sand
(a)- Effective diameter (D10)
(b)- Mean grain size (D50)

Figure 3 reproduces the relationship between the measured saturated hydraulic conductivity (Ks) and the coefficient of uniformity (Cu) of three different sands mixed with low plastic fines ranging from 0% to 40%. The sand-silt samples were reconstituted in laboratory at an initial relative density (Dr=55%). As can be seen from this plot that the measured saturated hydraulic conductivity (Ks) decreases with the increase of coefficient of uniformity (Cu). Moreover, it is clearly observed that for the different graded sand-silt mixtures, the higher coefficient of uniformity (Cu), the smaller measured saturated hydraulic conductivity (Ks) of silty sand under consideration. The obtained results indicate that the coefficient of uniformity (Cu) display a good power function (R2 =0.94) with the saturated hydraulic conductivity for the samples reconstituted at the initial relative density (Dr = 55%) within the range of fines content of tested materials (0%? Fc ? 40%). The outcome of this experimental research is parallel to the findings of 3, 4, 5, 28 and 35. The following expression is suggested to evaluate the relationship between the measured saturated hydraulic conductivity (Ks) and coefficient of uniformity (Cu) of the materials under study:
Ks= 31.65*(Cu)(-1.17) (6)
Figure 3: Measured saturated hydraulic conductivity versus coefficient of uniformity of silty sand

3.2 Estimation of the saturated hydraulic conductivity based on the granulometric characteristics ratios (D10R, D50R and CUR)
The effects of the effective diameter ratio (D10R = D10sand/D10mixture), the mean grain size ratio (D50R = D50sand/D50mixture) and the coefficient of uniformity ratio (CUR = Cusand/Cumixture) on the measured saturated hydraulic conductivity (Ks) of three different sands (Chlef sand “CS”, Fontainebleau sand “FS” and Hostun sand “HS”) mixed with low plastic fines for the range of Fc=0% to Fc=40% are illustrated in Figure 4. It is clear from Figure 4a and Figure 4b that the measured hydraulic conductivity correlates well (0.60 ? R2 ? 0.90) with the effective diameter ratio (D10R = D10sand/D10mixture) and the mean grain size ratio (D50R = D50sand/D50mixture) according to a power function of tested sand-silt mixture samples reconstituted at the initial relative density (Dr = 55%). The measured saturated hydraulic conductivity decreases with the increase of (D10R, D50R). Moreover, it is observed from Figure 4a and Figure 4b for the different graded sand-silt mixtures, that the higher effective diameter ratio (D10R = D10sand/D10mixture) and mean grain size ratio (D50R = D50sand/D50mixture), the smaller measured saturated hydraulic conductivity of sand-silt mixture samples. The following expressions are suggested to evaluate the relationship between the measured saturated hydraulic conductivity and grading characteristics ratios in terms of (D10R, D50R) of the materials under study:
Ks= 10.73*(D10R)(-1.04) (7)
Ks= 4.45*(D50R)(-4.90) (8)
Figure 4c shows clearly that the measured saturated hydraulic conductivity (Ks) decreases linearly with the decrease of the coefficient of uniformity ratio (CUR = Cusand/Cumixture). The obtained data indicate that the lower coefficient of uniformity ratio (CUR), the lower measured saturated hydraulic conductivity of sand-silt mixture samples. The introduced grading characteristics ratios (D10R, D50R and CUR) appear as suitable parameters that could be used to characterize the sand–silt mixture hydraulic conductivity for the fines content range (Fc=0%, 10%, 20%, 30% and 40%) and the initial relative density (Dr=55%) under consideration. Moreover, the decreasing in the measured saturated hydraulic conductivity is due to the fact of low plastic fines filling the gaps between sand particles decreasing the flow of water in the voids of sand-silt mixtures under study.
Figure 4: Measured saturated hydraulic conductivity versus grading characteristics ratios of silty sand
(a)- Effective diameter ratio (D10R)
(b)- Mean grain size ratio (D50R)
(c)- Coefficient of uniformity ratio (CUR)

4. Conclusion
Data of over 15 sand-silt mixture samples are used in this study to explore new empirical formula for the determination of the saturated hydraulic conductivity through the granulometric characteristics ratios (D10R, D50R and CUR) of silty sand soils. The main findings are summarized as follows:
1. The obtained data indicate that the measured saturated hydraulic conductivity decreases linearly with the decrease of grain size in terms of (effective diameter “D10” and mean grain size “D50”) of sand-silt mixture samples. However, it decreases according a power function with the increase of the uniformity coefficient “Cu” of silty sand soils. Moreover, the results show that the correlations between the measured hydraulic conductivity with the effective diameter “D10” and uniformity coefficient “Cu” are better compared to the measured saturated hydraulic conductivity related with mean grain size “D50”.
2. The obtained results show successful approximation of the hydraulic conductivity (Ks) from the particle size characteristics in terms of (D10R = D10sand/ D10mixture, D50R = D50sand/ D50mixture and CUR= Cusand/ Cumixture) of sand-silt samples.
5. References
1. Alyamani M S, and Z Sen (1993) Determination of hydraulic conductivity from complete grain-size distribution curves. Ground Water 31, (4) 551-555.
2. Bandini P, and S Sathiskumar (2009) Effects of silt content and void ratio on the saturated hydraulic conductivity and compressibility of sand-silt mixtures. Journal of Geotechnical and Geoenvironmental Engineering 135, (12) 1976–80.DOI:10.1061=(asce)gt.1943-5606.0000177.
3. Belkhatir M, T Schanz, and A Arab (2013) Effect of ?nes content and void ratio on the saturated hydraulic conductivity and Undrained shear strength of sand–silt mixtures. Environmental Earth Sciences 70, 2469–79. DOI:10.1007=s12665-013-2289-z.
4. Belkhatir M, A Arab, N Della, and T Schanz (2014) Laboratory study on the hydraulic conductivity and pore pressure of sand-silt mixtures. Marine Georesources ; Geotechnology 32, 106–22. DOI:10.1080=1064119X.2012.71071
5. Boadu F K (2000 )Hydraulic Conductivity of Soils from Grain-Size Distribution: New Models. Journal of Geotechnical and Geoenvironmental Engineering.
6. Cabalar AF, Akbulut N (2016) Effects if the particle shape and size of ssands on the hydraulic conductivity. Acta Geotechnica Slovinica Vol (2) 83-93.
7. Chapuis RP (2004) Predicting the saturated hydraulic conductivity of sand and gravel using effective diameter and void ratio. Can. Geotech. J. 41, 787–795.
8. Cherif Taiba A, Mahmoudi Y, Hazout L, Belkhatir M, and Tom Schanz T (2015) Laboratory research into the influence of grading characteristics ratio on excess pore water pressure of silty sand soils. 7th Symposium on construction in seismic zones (SYCZS’2015), Chlef, Algeria.
9. Cherif Taiba A, Mahmoudi Y, Belkhatir M, Kadri A, Schanz T (2016) Insight into the effect of granulometric characteristics on static liquefation sucseptibility of silty sand soils. Geotech Geol Eng DOI 10.1007/s10706-015-9951-z.
10. Cherif Taiba A, Mahmoudi Y, Belkhatir M, Kadri A, and Tom Schanz T (2017a) Experimental Characterization of the Undrained Instability and Steady State of Silty Sand Soils under Monotonic Loading Conditions. International Journal of Geotechnical Engineering, DOI: 10.1080 /19386362.2017.1302643.
11. Cherif Taiba A (2017b) Laboratory Study on Susceptibility of Liquefaction of Silty Sand Soils: Effect of Size and Shape of Grain. PhD.Thesis, University of Chlef, Algeria.
12. Cherif Taiba A, Mahmoudi Y, Belkhatir M, and Schanz T (2018) Experimental Investigation into the Influence of Roundness and Sphericity on the Undrained Shear Response of Silty Sand Soils. Geotechnical Testing Journal. DOI.10.1520/GTJ20170118.
13. Cirpka OA (2003) Environmental Fluid Mechanics I: Flow in Natural Hydrosystems.
14. Cronican AE, and M M Gribb (2004) Literature review: Equations for predicting hydraulic conductivity based on grain-size data. Supplement to Technical Note entitled: Hydraulic conductivity prediction for sandy soils. Published in Ground Water, 42, (3) 459-464.
15. Erzin Y, Gumaste SD, Gupta AK, Singh DN (2009) Artificial neural network (ANN) models for determining hydraulic conductivity of compacted fine-grained soils. Can. Geotech. J. 46, 955–968.
16. Fattah MY, Ahmed MD, Ali NA (2014) Prediction of Coefficient of Permeability of Unsaturated Soil. Journal of Engineering, College of Engineering, University of Baghdad, Vol. 20, No. 2, pp. 33-48.
17. Fattah MY, Salim NM, Haleel RJ, (2018) Effect of Relative Density on Liquefaction Potential of Sandy Soil from Small Laboratory Machine Foundation Model. International Journal of Science and Research (IJSR), Vol. 7(1), pp. 661-672, DOI: 10.21275/ART20179288.
18. Freeze RA, and Cherry JA (1979) Groundwater. Prentice Hall Inc., Englewood Cliffs, New Jersey.
19. Han H, D Gimenez, L Lilly (2008) Textural averages of saturated soil hydraulic conductivity predicted from water retention data. Geoderma, 146, 121-128.
20. Hazen A (1892) Some physical properties of sands and gravels. Massachusetts State Board of Health, Annual Report, 539-556.
21. Hsiao DH, Phan NTA, Hsieh YT, Kuo HY (2015) Engineering behavior and correlated parameters from obtained results of sand-silt mixtures. Soils dynamics and earthquake engineering 77, 137-151.
22. Layadi K, Semmane F, and Yelles-Chaouche AK (2016) Site-effects investigation in the city of Chlef (formerly El- Asnam), Algeria, using earthquake and ambient vibration data. Bulletin of the Seismological Society of America, 106 (5). doi:10.1785/0120150365.
23. Mahmoudi Y, Cherif Taiba A, Hazout L, Belkhatir M, and Schanz T (2015a) Laboratory Study on Shear Behavior of Overconsolidated Sand: Effect of the Initial Structure. 13th Arab Structural Engineering Conference ,Blida, Algeria.
24. Mahmoudi Y, Cherif Taiba A, Belkhatir M, and Schanz T (2015b) Experimental investigation on shear strength of overconsolidated soils: Effect of fines content. 7th Symposium on construction in seismic zones, Chlef, Algeria.
25. Mahmoudi Y, Cherif Taiba A, Belkhatir M, Schanz T (2016a) Experimental Investigation on Undrained Shear Behavior of Overconsolidated Sand-Silt Mixtures: Effect of Sample Reconstitution. Geotechnical Testing J. DOI: 10.1520/GTJ20140183.
26. Mahmoudi Y, Cherif Taiba A, Belkhatir M, Arab A, and Schanz T (2016b) Laboratory study on undrained shear behaviour of overconsolidated sand–silt mixtures: effect of the fines content and stress state. International Journal of Geotechnical Engineering, DOI: 10.1080/19386362.2016.1252140.
27. Mualem Y (1976) A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources. Res., 12, 593–622.
28. Salarashayeri AF, Siosemarde M (2012) Prediction of Soil Hydraulic Conductivity from Particle-Size Distribution. World Academy of Science, Engineering and Technology 61.
29. Sathees T (2006) Saturated hydraulic conductivity of poorly graded sands with nonplastic silt using a ?exible wall permeameter. MS thesis, New Mexico State Univ., Las Cruces, NM.
30. Sivapullaiah PV, Sridharan A, Stalin VK (1999) Hydraulic conductivity of bentonite–sand mixtures. Can. Geotech. J. 37, 406–413.
31. Thevanayagam S (2000) Liquefaction of silty soils-Considerations for screening and retro?t strategies. In Proceedings 2nd International workshop on mitigation of seismic effects on transportation structures, ed. C. Loh, K. Kawashima, and I. Buckle, 314. Taipei, Taiwan: National Center for Research on Earthquake Engineering.
32. Todd DK., and Mays LW (2005) Groundwater Hydrology. John Wiley & Sons, New York.
33. Van Dam JC, Stricker JN M, and Droogers P (1992) Inverse method for determining soil hydraulic function from one-step outflow experiments. Soil Sci. Soc. Am. J., 56, 1042–1050.
34. Van Genuchten M Th, and Leji F (1989) On estimating the hydraulic properties of unsaturated soils. In Proceedings of the International Workshop on Indirect Method of Estimating Hydraulic Properties of Unsaturated Soils (eds van Genuchten, M. Th. et al.), 11–13 October, US Salinity Laboratory and Department of Soil and Environmental Science, Univ. of California, Riverside, 1–14.
35. Wang Y, Y Ren, and Q Yang (2017) Experimental study on the hydraulic conductivity of calcareous sand in South China Sea. Marine Georesources & Geotechnology. doi:10.1080/1064119X.2017.1279245
36. Yamamuro JA,Wood FM, Lade PV (2008) Effect of depositional method on the microstructure of silty sand. Canadian Geotechnical Journal 45, (11), 1538–1555.
List of Figures

Tested Soils

Chlef sand (CS) Fontainebleau sand (FS) Hostun sand (HS)

Sample preparation
(Dry funnel pluviation with Dr= 55%)

Constant- head permeability apparatus

Cylindrical cell of about 78cm² Room Temperature (T=20°C)

Hydraulic Conductivity measurements using
Darcy’s law (K=ql/ah).

Figure 1 : Flow chart of experimental program of the tested materials.

(a) (b)
Figure 2: Measured saturated hydraulic conductivity versus grading characteristics of silty sand
(a)- Effective diameter (D10)
(b)- Mean grain size (D50)

Figure 3: Measured saturated hydraulic conductivity versus coefficient of uniformity of silty sand

(a) (b)

(c)
Figure 4: Measured saturated hydraulic conductivity versus grading characteristics ratios of silty sand
(a)- Effective diameter ratio (D10R)
(b)- Mean grain size ratio (D50R)
(c)- Coefficient of uniformity ratio (CUR)

List of Tables
Table 1: Summary of grain size characteristics and measured hydraulic conductivity of tested materials

Soils Mean grain size D50 (mm) Effective diameter D10 (mm) Coefficient of uniformity Cu Effective diameter ratio D10R Mean grain size ratio D50R Coefficient of uniformity ratio CUR Hydraulic conductivity values Ks (m/day)
CS_(0) 0.59 0.27 2.63 1 1 1 12.84
FS _(0) 0.56 0.20 3.16 1 1 1 14.65
HS _(0) 0.37 0.26 1.54 1 1 1 18.09
CS-90_Silt-10 0.55 0.08 8.20 3.39 1.09 0.32 2.18
CS-80_Silt-20 0.49 0.02 27.2 11.78 1.22 0.10 0.87
CS-70_Silt-30 0.42 0.01 54.3 26.99 1.42 0.05 0.27
CS-60_Silt-40 0.24 0.003 120.5 81.27 2.53 0.02 0.14
FS-90_Silt-10 0.49 0.08 6.9 2.38 1.13 0.46 3.02
FS-80_Silt-20 0.46 0.03 24 8.69 1.22 0.13 1.09
FS-70_Silt-30 0.45 0.02 28.42 10.31 1.26 0.11 0.49
FS-60_Silt-40 0.45 0.01 45.92 16.76 1.24 0.07 0.16
HS-90_Silt-10 0.35 0.12 3.20 2.15 1.04 0.50 3.64
HS-80_Silt-20 0.25 0.02 13.13 11.26 1.48 0.12 1.37
HS-70_Silt-30 0.22 0.01 28.76 26.45 1.65 0.05 0.87
HS-60_Silt-40 0.21 0.003 84.44 79.04 1.69 0.02 0.17