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.

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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