# Water retention curve of clayey sands determined from pore structure by using various methods

Quoc-Hung Vu, Jean-Michel Pereira, Anh Minh Tang

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Quoc-Hung Vu, Jean-Michel Pereira, Anh Minh Tang. Water retention curve of clayey sands determined from pore structure by using various methods. UNSAT 2023, 8th International Conference on Unsaturated Soils, May 2023, Milos, Greece. pp.09006, 10.1051/e3sconf/202338209006. hal-04385764

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# Water retention curve of clayey sands determined from pore structure by using various methods

Quoc-Hung Vu, Jean-Michel Pereira, and Anh Minh Tang

Navier, Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, France

**Abstract.** Besides standard approaches, the soil water retention curve (SWRC) can be estimated either from pore size distribution obtained by mercury intrusion porosimetry or from the soil freezing characteristic curve. These methods are based on simplified laws such as Young-Laplace for capillary suction or Clausius-Clapeyron for cryo-suction. These laws might not be valid for clayey sands where the presence of clay particles would induce other water retention mechanisms. This study aims to assess the clay content's effect on the validity of these two methods in determining the SWRC of clayey sands. Clay sands were prepared at different clay contents by mixing pure sand with kaolin clay prior to compaction at the Proctor maximum dry density. Five clay contents (dry mass of clay divided by dry mass of soil) were considered (0, 5, 10, 15, and 20%). The reference SWRC was obtained by standard suction measurements. The results show that SWRCs estimated from mercury intrusion porosimetry and soil freezing characteristic curve are generally in agreement with the reference SWRC. However, the results obtained by the soil freezing characteristic curve are limited in terms of suction range (500 to 5 MPa) which is not appropriate for clayey sands, while those from mercury intrusion porosimetry show significant discrepancy because of the structure heterogeneity obtained by Proctor compaction.

## 1 Introduction

The soil water retention curve (SWRC) describes the relationship between water content and suction. This curve plays an important role in modelling the coupled hydro-mechanical behaviour of unsaturated soils [1–3]. SWRC is conventionally determined from suction measurement [4, 5] or control [6, 7] following drying and/or wetting processes.

Soil suction (s) generally includes two components (matric and osmotic) and matric suction is generally the most dominant component in sandy soils in the case without salt presence. By using the Young-Laplace equation [8, 9], matric suction in porous media can be estimated from pore radius. For this reason, SWRC can also be estimated from the pore size distribution (PSD), which is usually determined by mercury intrusion porosimetry (MIP) [10, 11], by using Laplace's equation [12, 13]. However, SWRC obtained from MIP and SWRC obtained by conventional methods generally do not agree for fine-grained soils [14] probably due to pore trapping effect or water and dissolved salts effect on clay fabric compared to the process of mercury intrusion[15].

Besides, soil matric suction can be determined from freezing temperature by using Clausius-Clapeyron equation [16]. However, the consistency between SWRC obtained from soil freezing characteristic curve and that obtained by conventional methods remains questionable because of the complexity of the mechanisms associated with freezing-thawing compared to drying-wetting, such as supercooling, different contact angles [17], accuracy of water content measurement [18] and assumptions behind Clausius-Clapeyron equation [19, 20].

Among factors such as dry density, grain nature, grain size distribution, etc., fines content influences significantly SWRC [21, 22]. Several studies investigated SWRC of sandy soils with different clay contents [23–26] and found that the SWRC of soil with higher clay content has a lower steepness, a higher air entry suction and a higher residual suction. In addition to the

aforementioned effects, increasing clay content from 30% to 100% by dry weight may enlarge the hysteresis of SWRC [27]. For soils with low clay content (0% to 8%), SWRC shows a clear bimodal shape, which is strongly dependent on fines content [28].

This study aims at assessing the effect of clay content on the validity of using mercury intrusion porosimetry and soil freezing characteristic curve in determining SWRC of clayey sands. Clayey sands were prepared at different clay contents by mixing pure sand with kaolin clay prior to the compaction at the Proctor maximum dry density. Five clay contents (dry mass of clay divided by dry mass of soil) were considered (0, 5, 10, 15, and 20%). The reference SWRC was obtained by standard suction measurements. SWRC obtained by the three methods were compared. The results were finally analysed to identify the main mechanisms explaining the effect of fines content on the soil water retention curve.

## 2 Material and experimental methods

<table><caption>Table 1. Physical properties of Fontainebleau sand.</caption><thead><tr><td>Property</td><td>Value</td></tr></thead><tbody><tr><td>Median grain size, D<sub>50</sub>(mm)</td><td>0.21</td></tr><tr><td>Uniformity coefficient, C<sub>U</sub></td><td>1.52</td></tr><tr><td>Minimum void ratio, e<sub>min</sub></td><td>0.54</td></tr><tr><td>Maximum void ratio, e<sub>max</sub></td><td>0.94</td></tr><tr><td>Particle density, ρ<sub>s</sub> (Mg/m<sup>3</sup>)</td><td>2.65</td></tr><tr><td>Minimum dry density, ρ<sub>d,min</sub> (Mg/m<sup>3</sup>)</td><td>1.37</td></tr><tr><td>Maximum dry density, ρ<sub>d,max</sub> (Mg/m<sup>3</sup>)</td><td>1.72</td></tr></tbody></table>
Fontainebleau sand and Speswhite Kaolin clay (whose physical properties are shown in Table 1 and Table 2, respectively) were mixed at various clay contents in dry mass (see Table 3 and Fig. 1). Each mixture was wetted at optimal water content [29] and packed in a plastic bag for at least 24 h for moisture distribution homogenization prior to compaction in a rigid metallic cylindrical mould (150 mm in height and 150 mm in diameter).

<table><caption>**Table 2.** Physical properties of Speswhite Kaolin clay.</caption><thead><tr><td>Property</td><td>Value</td></tr></thead><tbody><tr><td>Liquid limit, LL (%)</td><td>55</td></tr><tr><td>Plastic limit, PL (%)</td><td>30</td></tr><tr><td>Plasticity index, PI</td><td>25</td></tr><tr><td>Specific surface area (m²/g)</td><td>0.94</td></tr><tr><td>Particle density, ρ<sub>s</sub> (Mg/m³)</td><td>2.65</td></tr><tr><td>Particle diameter &lt; 0.002 mm (%)</td><td>79</td></tr><tr><td>Particle diameter &gt; 0.01 mm (%)</td><td>0.5</td></tr><tr><td>Maximum dry density, ρ<sub>d,max</sub> (Mg/m³)</td><td>1.45</td></tr></tbody></table>

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Grain size distribution curves of tested soils.</figcaption></figure>

<table><caption>**Table 3.** Physical properties of samples.</caption><thead><tr><td>Soil</td><td>Clay content (%)</td><td>Water content w (%)</td><td>Dry density ρ<sub>d</sub> (Mg/m³)</td><td>Porosity n (-)</td></tr></thead><tbody><tr><td>S0</td><td>0</td><td>0.21</td><td>1.70</td><td>0.36</td></tr><tr><td>S5</td><td>5</td><td>0.19</td><td>1.77</td><td>0.33</td></tr><tr><td>S10</td><td>10</td><td>0.14</td><td>1.93</td><td>0.27</td></tr><tr><td>S15</td><td>15</td><td>0.13</td><td>1.99</td><td>0.25</td></tr><tr><td>S20</td><td>20</td><td>0.13</td><td>1.96</td><td>0.26</td></tr></tbody></table>

To determine the reference SWRC following the suction measurement method [30], after soil compaction in a mould, three sensors were carefully inserted inside the sample (Fig. 2 and Fig. 3): (i) a tensiometer T8 (1 kPa in accuracy) to measure matric suction (s) [4]; (ii) a time domain reflectometry probe ThetaProbe ML2x (1% in accuracy) to measure volumetric water content (θ<sub>w</sub>); (iii) and a KD2-Pro probe to measure the soil thermal conductivity (whose data were not analysed in this study). Afterwards, the sample was saturated by injecting water from its bottom (during 0.5 to 2 days depending on fines content)

until a layer of water of 10 mm was visible on the top of the specimen. To dry the specimen, two holes created on the top cover were opened to allow evaporation from the top surface (Fig. 3). After a certain duration, the two holes were covered by two lids to prevent moisture exchange with the atmosphere. The equilibrium was reached after several hours prior to the next step; this procedure is similar to that used by Nguyen et al. [31]. Once suction excesses the capacity of the tensiometer (100 kPa), one small piece of soil was extracted from the sample to determine SWRC within a drying-wetting path by using a chilled-mirror dew-point hygrometer (WP4C) following the procedure used by Wang et al. [32].

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Schematic view of the experimental device used for suction measurement. (1) Soil; (2) Metallic cylindrical cell; (3) Insulating cover; (4) Tensiometer; (5) Thermal conductivity probe; (6) Soil water content sensor; (7) Data logging system.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** View from the top of the experimental device used for suction measurement.</figcaption></figure>

For MIP tests, small samples (less than 1 g) were extracted from the compacted specimen using a cutter and freeze-dried by the procedure proposed by Delage and Pellerin [33] prior to conducting mercury intrusion.

For thawing tests, after soil compaction, sensors were installed as shown in Fig. 4. Beside tensiometer and KD2-Pro probe, whose data were not analysed in this study, a ThetaProbe and a temperature sensor (PT100, accuracy ±0.03 °C) were used. Afterwards, soil specimen was saturated prior to being installed in the temperature-controlled bath. To perform the test, soil temperature (T) was first decreased down to -2 °C or -3 °C to
freeze soil water. It was afterwards increased in steps of 0.2 °C until 0 °C to thaw the frozen soil.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Schematic view of the experimental setup used for freezing-thawing tests. (1) Temperature-controlled bath; (2) Soil specimen; (3) Temperature controlling system; (4) Temperature-controlled liquid (30% ethylene glycol + 70% water); (5) Metallic cylindrical cell; (6) Insulating cover; (7) Temperature sensor; (8) Tensiometer; (9) Soil water sensor; (10) Thermal conductivity probe; (11) Data logger system.</figcaption></figure>

## 3 Results

Similar pattern can be observed on SWRC obtained by conventional method (Fig. 5), data for pure sand (S0) was taken from the study of Doussan and Ruy (2009). From saturated state (degree of saturation $S_r$ = 100%), suction increase induced a first decrease of $S_r$ at $s \sim 5$ kPa. Afterward, $S_r$ decreased with a lower rate. When suction exceeded 1000 kPa, $S_r$ decreased again with a higher rate. For suction higher than 5000 kPa, $S_r$ decreased with a smaller rate. At a given suction, $S_r$ was higher for a higher clay content. In addition, for the same soil at the same suction, $S_r$ was slightly smaller during the wetting path than during the drying path. The hysteresis effect of SWRC can be mostly attributed to pore blocking and capillarity. The fact of adding fines in sandy soil changed the arrangement of pores. The latter made clearer hysteresis effect of SWRC in soils with higher fines content. The wetting path was stopped at suction of around 500 kPa because WP4C is less accurate at suction lower than this value. This bimodal shape has been observed by Zhang et al. [28] on well-graded gravel mixed with 0 – 8% of Kaolin clay and explained by the dual porosity (micropores between clay particles and macropores between grains).

<figure><img src="image_6.png" /><figcaption>Fig. 5. SWRC obtained by the conventional method.</figcaption></figure>

Actually, results of MIP tests, Fig. 6, show clearly two families of pores: macropores (entrance pore diameter $d$ = 20 – 100 µm) and micropores ($d$ = 0.1 – 1 µm). The volume of macropores was higher at a lower clay content. Note that tests with S10, S15, and S20 were replicated showing a certain discrepancy. In addition, MIP test could not be performed on pure sand (S0). The bimodal SWRC (Fig. 5) can thus be clearly explained by the double porosity observed with MIP test (Fig. 6). The results of this study evidence the effect of fines content on water retention in the high suction range (> 500 kPa) which corresponds to micropores. The discrepancy between MIP results (Fig. 6) can be explained by the material preparation method. Small samples (less than 1 g) were extracted from large specimens mixed and compacted using the Normal Proctor method. In addition, the mixing order (sand-clay-water) and the water content at compaction in the present study could lead to heterogeneous microstructure after Yin et al. [35].

All the results of the thawing path obtained during the freezing/thawing tests (Fig. 7) show an increase of $\theta_w$ when $T$ increased, indicating the progressing thawing process. Thawing occurred significantly at temperature close to 0 °C for all soils. At a given temperature, soil with higher clay content had higher $\theta_w$.

Results of MIP and thawing tests were then used to estimate SWRC. For MIP test, Laplace equation that links the capillary pressure to the interfacial properties of the fluids-solid system with entrance pore entrance diameter $d$ was applied to obtain the relationship between matric suction and mercury intrusion pressure $u_{Hg}$ [14]:

$$s = 0.196 u_{Hg} \qquad (1)$$

Water content was calculated from the change of intruded mercury void ratio $e_M$ by assuming that water content is null at the highest suction (40 MPa).

Clausius-Clapeyron equation was used to estimate suction during thawing:

$$s = L_f \rho_w \frac{T-T_f}{T_f} \qquad (2)$$

where $\rho_w$ = 1000 kg/m³ is the density of water, $L_f$ = 334 kJ/kg is the latent heat of fusion of water, $T_f$ = 273.15 K is the freezing point of water.
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Results of MIP tests: (a) Intruded mercury void ratio and (b) Pore size density function as a function of the entrance pore diameter.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Results obtained on the thawing path of freezing/thawing tests: volumetric unfrozen water content as a function of the temperature.</figcaption></figure>

Fig. 8 shows SWRCs derived from the three methods for each soil. Generally, the results of MIP should be compared with the drying path while the results of the thawing test should be compared with the wetting path. For clean sand S0, data on the wetting path were not available. Anyway, results obtained by thawing are in good agreement with the drying path (which should be similar to the wetting path for this material in the range

of suction available with the thawing method, i.e. 500 kPa – 3 MPa). For S5, results from MIP is in good agreement with the drying path for the whole range of suction while results from the thawing test are in good agreement with the wetting path (both are limited to suctions higher than 500 kPa). For S10 and S20, observations similar to S5 can be made even if the agreement between MIP and drying path is less obvious, which is consistent with the conclusions by [14]. For S15, a notable discrepancy between the MIP results of can be observed. The difference between SWRCs obtained by the various methods remains smaller than this discrepancy.

For all soils, results of MIP tests show generally a smaller water content (compared to the other methods) at suction higher than 1000 kPa. This difference is more notable at higher clay content. This phenomenon can be explained by the role played by water adsorption on clay particles on the water retention properties of the soil, which cannot be predicted by MIP data and its interpretation based on capillary suction effects.

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** SWRCs determined using the three methods for soils: (a) S0; (b) S5; (c) S10; (d) S15; (e) S20.</figcaption></figure>

## 4 Conclusions

SWRCs of clayey sands (having clay content varying from 0 to 20%) were obtained by three methods. The results show that SWRCs estimated from mercury intrusion porosimetry and soil freezing characteristic curve are generally in agreement with the reference SWRC.

MIP tests can provide SWRC covering a wide range of suction (1 kPa to 40 MPa) which is appropriate for clayey sands. However, it underestimates water content at suction higher than 1000 kPa for sands with high clay content because it neglects the presence of adsorbed water on clay particles. In addition, results obtained by MIP test on sands with high clay content show

significant discrepancy because of soil structure heterogeneity obtained by Proctor compaction.

Soil water characteristic curve can be used to estimate SWRC. However, this method is limited to a small suction range (500 kPa to 3 MPa in this study), which is not appropriate for clayey sands where a wider range is necessary to cover both macropores related to the arrangement of sand particles and micropores related to clay particles.

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