Relationship between soil structure and water ...

Engineering Geology 205 (2016) 73–80

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Relationship between soil structure and water retention properties in a residual compacted soil Ivan Fernando Otalvaro a, Manoel Porfírio Cordão Neto b,⁎, Pierre Delage c, Bernardo Caicedo d a

Universidad Javeriana, Cali, Colombia Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, Campus Darcy Ribeiro — Asa Norte SG-12, 70910900 Brasília, DF, Brazil Ecole des ponts ParisTech (Navier/CERMES), Paris, 6–8 Av. B. Pascal, F 77455 Marne la Vallee cdx 2, France d Universidad de Los Andes, Bogotá D. C., Colombia: Cra. 1 Este No. 19 A-40, Bogotá, Colombia b c

a r t i c l e

i n f o

Article history: Received 6 April 2015 Received in revised form 12 January 2016 Accepted 29 February 2016 Available online 2 March 2016 Keywords: Mercury intrusion porosimetry Water retention curve Pore size density

a b s t r a c t Soil structure, especially the soil pore size distribution, is a fundamental property that describes the hydromechanical behavior of soils. The volume change behavior, shear strength, water retention capacity and hydraulic conductivity of soil are controlled by the pore size distribution. However, research on soil structure has been limited due to the associated expenses and specialized instruments, such as environmental scanning electron microscopes and mercury intrusion porosimeters (MIPs). In this study, the relationship between the soil water retention curve (WRC) along a drying path and the pore size distribution obtained through an MIP method was reviewed. The WRC for a compacted tropical soil was converted into a soil air injection curve and then used to estimate the pore size density (PSD) function. Relative to the data collected from MIP methods, the results showed an acceptable prediction of the PSD function based on a soil air injection curve. Finally, a series of adjustments to the air injection curve were performed to improve the accuracy of the PSD prediction based on the water retention curve. © 2016 Published by Elsevier B.V.

1. Introduction Compacted soils are used as construction materials in numerous geotechnical works around the world. Most studies about soil compaction are based on Proctor's studies. This method tries to reproduce field compaction in the laboratory by applying controlled mechanical energy to remove the air within the soil without analyzing the soil microstructure. In the last 20 years, abundant research devoted to explaining compaction curves have used the unsaturated theory of soil behavior, supported with a growing interest in the study of soil structure at multi-scale levels from the micrometric scale to the nanometric scale. These studies have incorporated structural effects into the macroscopic behavior predictions of compacted soils (Alonso et al., 1999; Airò-Farulla et al., 2010; Pham and Fredlund, 2011; Alonso et al., 2011). However, most previous studies have examined compacted clays derived from sedimentary processes, and little research exists on the behavior of the compacted residual soils that are currently used in geotechnical works in many parts of the world, especially in the subtropical

⁎ Corresponding author at: Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, Campus Darcy Ribeiro — Asa Norte SG12, Asa Norte, 70910900 Brasília, DF, Brazil. E-mail addresses: [email protected] (I.F. Otalvaro), mporfi[email protected] (M.P.C. Neto), [email protected] (P. Delage), [email protected] (B. Caicedo).

http://dx.doi.org/10.1016/j.enggeo.2016.02.016 0013-7952/© 2016 Published by Elsevier B.V.

and tropical climates of South America and Africa. In addition to their natural complexity, compacted residual soils exhibit local-specific features. For instance, soils in Ouro Preto, Brazil, are characterized by clay aggregations with two dominant pore sizes (Futai and Almeida, 2005), natural soils in Campinas, Brazil, exhibit two dominant pore size volumes separated by three orders of magnitude (Miguel and Bonder, 2012), and soils from Brasilia exhibit high collapsibility in either natural or compacted states (Otálvaro et al., 2015). To better understand the properties of compacted residual soils, it is necessary to characterize their composition and structural arrangement by studying their structure (i.e., the combination of structural arrangement, or fabric, and bonding; Mitchell and Soga, 2005). Different techniques have been employed for this purpose: scanning electronic microscopy (SEM) and mercury intrusion porosimetry (MIP; Diamond, 1970; Collins and McGrown, 1974; Delage and Lefebvre, 1984; Mitchell and Soga, 2005; Romero and Simms, 2008). In this paper, the structural behavior of compacted residual soils was analyzed based on the combined use of MIP and the determination of the water retention curve (WRC) along a drying path. In addition, the relationship between WRC and MIP was investigated to obtain the pore size density based on the WRC. The main advantage of this methodology is the relative simplicity of obtaining water retention curves. The results of the proposed methodology are encouraging and were validated based on a comparison to the results obtained from mercury intrusion porosimetry.

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I.F. Otalvaro et al. / Engineering Geology 205 (2016) 73–80

The methodology and the results obtained can be useful in determining parameters for other hydraulic, thermal and mechanical models. For instance, the distribution of void ratios (small pores and large pores) can be used as input data for constitutive models and conservation equations that are based on the double structure concept of soils. 2. Materials and methods The effect of compaction in lateritic residual soil was investigated in samples obtained from a roadway excavation in Brasilia, Brazil. Brasilia is located in the central highlands of Brazil on an erosion surface from the Tertiary period composed of metasedimentary rocks from the Canastra, Paranoá, Araxá and Bambuí groups (Freitas-Silva and Campos, 1998). Quartz, kaolinite, gibbsite, goethite and hematite minerals were identified by X-ray diffraction. The presence of kaolinite was also inferred from the Atterberg limits and the low value of the cation exchange capacity (CEC); Table 1 summarizes the index properties. The soil is classified as ML according to the Unified Soil Classification System (USCS). Fig. 1 shows the grain-size distribution curves obtained through sieving and laser diffraction; the laser method was preferred because it has a larger range of detectable particle sizes and better accuracy in the micron and submicron ranges (Di Stefano et al., 2010). Conversely, tests were performed with and without dispersant to highlight the effect of aggregations. In fact, silt and clay aggregations were observed on the non-dispersed curve with sand grain-sized aggregations, a typical feature of Brazilian lateritic soils (Futai, 2002; Miguel and Vilar, 2009; Miguel and Bonder, 2012). These silt and clay aggregations are present in the soil even after the compaction and help to explain the hydro-mechanical behavior of these materials. These soils are characterized by a double porous structure corresponding to inter-aggregate pores and intra-aggregate pores (Delage et al., 1996; Fiès and Bruand, 1998; Zhang and Chen, 2005; Koliji et al., 2010; Casini et al., 2012).

Fig. 1. Grain-size distribution.

and the normal and modified Proctor optima. Fig. 2b indicates the negative pore water pressure (i.e., suction) of the tested points, which were obtained using filter paper. 2.2. Water retention curve Previous studies indicated that the WRC of the same Brasilia soil studied here has a bimodal nature (Guimarães, 2002; Delgado, 2002; Silva, 2007). To cover a wide range of suction values from 1 kPa up to 30,000 kPa, a combination of two techniques was used. A suction plate, based on that presented by Feuerharmel et al. (2006), was used for suction ranges equal to or smaller than 16 kPa. In this system, a

2.1. Compacted samples For compaction tests, residual lateritic specimens were made from air-dried material based on the ASTM D698–00a and ASTM D1557–00 procedures. The samples were prepared by manual disaggregation to 17% moisture content (i.e., 3% lower than the natural moisture content of 20%) to push the material through the No. 4 sieve with no difficulty. The identification of the WRC was carried out under seven compaction conditions at various moisture contents and compaction energies, as shown in Fig. 2. In the figure, PM and PN refer to the modified Proctor and the standard Proctor energies, respectively. PIn indicates the intermediate energy between the modified Proctor and the standard Proctor (approximately 1655 kN m/m3). The points were obtained using a modified ASTM D698–00a procedure with a 44.5 kN weight hammer. Point NP24 (i.e., a moisture content of 24%) represents a lower energy of 240 kN-m/m3 that was obtained by reducing the number of blows from 25 to 10 on each layer. The points at which the investigation was conducted are indicated in Fig. 2 and include both the dry and wet sides of the compaction curves Table 1 Index properties. Natural moisture content (%) Liquid limit (%) Plasticity index (%) Specific gravity (Gs) pH distilled water pH KCl solution CEC (mE/100 ml) Ss (m2/g) — BETa USCS classification

23 40 12 2.76 6.0 5.6 8.0 39.4 ML

a Brauner, Emmett and Teller (BET); specific surface is derived from an isotherm for nitrogen (N2) adsorption.

Fig. 2. a) Proctor compaction test and analysis points; b) initial suctions (ASTM Standard D698–00a, 2000).


negative pore water pressure was directly applied to the sample. The maximum possible suction was 80 kPa due to cavitation (Feuerharmel et al., 2006). A filter paper technique was used for suction greater than 10 kPa. The filter paper technique used Whatman No. 42 filter paper as described by Marinho and Oliveira (2006). A three-layered stack of filter paper disks was placed between the soil sample and an acrylic disc. After 15 days, the soil sample and the inner filter paper were carefully weighed with a high-precision balance (±0.1 mg). Weighing was conducted as quickly as possible to minimize water loss. Finally, the suction was calculated from the filter paper water content using the relationship described by Chandler et al. (1992).

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1999; Aung et al., 2001; Simms and Yanful, 2001; Zhang and Li, 2010; Mascarenha et al., 2011). Fig. 3 presents an analogy between the processes of air injection and mercury intrusion. By substituting for the non-wetting liquid in Eq. (1), the capillary pressure can be obtained: ua uw ¼

4σ w cosðθw Þ ; D

ð2Þ

where ua -uw is the matric suction, σw is the surface pressure at the air/ water interface (0.0728 N/m), and θw is the contact angle between the porous medium and the water (assumed to be 0°). If the diameters in Eqs. (1) and (2) are the same, the two pressures are related by the following:

2.3. Mercury intrusion porosimetry

p≈5:102ðua uw Þ:

Mercury intrusion porosimetry (MIP) and nitrogen (N2) adsorption were used to determine the pore size distribution. To preserve the microstructure during dehydration, 8 mm diameter and 10 mm height samples were trimmed with a scalpel prior to liquid nitrogen freezing (−195 °C) and lyophilization. An AutoPore IV 9500 instrument (Micromeritics Instrument Corporation) for mercury intrusion was used. Mercury intrusion was performed in a 5 cm3 penetrometer with mercury pressures between 3.5 kPa and 228 MPa. In addition, two nitrogen adsorption tests were conducted using an ASAP instrument (Micromeritics Instrument Corporation) following an adsorption–desorption isotherm (− 195.312 °C) with absolute pressures between 51.02 and 80.01 mm Hg (6.8 and 10.67 kPa, respectively). In mercury intrusion porosimetry, a non-wetting fluid (mercury) is forced through a porous medium. Assuming cylindrical pores, the penetration curve is converted to a pore size distribution curve using the Young–Laplace equation (Diamond, 1970):

This equation allows for the conversion of the matric suction into mercury intrusion pressure. In addition, the cumulative air injection curve can be obtained from the WRC through the complement between the water volume and the total volume:

p¼

4σ nw cosðθnw Þ ; D

ð1Þ

where p is the non-wetting liquid absolute pressure, σnw is the nonwetting liquid surface tension (0.484 N/m for mercury), θnw is the contact angle between the porous material and the non-wetting liquid (angle varies for clays between 139 and 147° according to Diamond, 1970), and D is the pore diameter. Romero and Simms (2008) may be consulted for further technical detail. In this study, θnw was assumed to be 140°.

ð3Þ

ea ¼ e ew ≈enw ;

ð4Þ

where ea. is the air ratio (between the air and solids volumes), e is the void ratio, ew is the water ratio (between the water and solids volumes), and enw is the non-wetting ratio (between the non-wetting fluid injected and solids volumes). This study adopted the use of the ea. and ew indices to convert the WRC into the soil air injection curve (SAIC) through Eqs. (3) and (4), as practiced by Prapaharan et al. (1985) and, subsequently, into mercury intrusion. Before converting the WRC into the SAIC, the experimental data were modeled using the Durner (1994) equation. This equation is the extension of the Van Genuchten (1980) equation for multimodal functions. The general WRC expression has the following form: ∞

ew ¼ ∑ Ni¼1 ei ∫ s f ðsÞds;

ð5Þ

where ew is the water ratio (Vw/Vs), i is the modal number, ei is the modal void ratio, s is suction, and f(s) is a simple suction-water content function. Using Van Genuchten's (1980) proposal in Eq. (5), the following can be obtained: ei ew ¼ ∑ Ni¼1 11=ni ; 1 þ ðai ∙sÞni

ð6Þ

2.4. Relationship between MIP and WRC

where a and n are adjustment parameters. For a double structure Eq. (6) becomes:

Mercury intrusion in a porous medium is a process similar to air injection in a saturated soil as described along the drying curve of a water retention curve (Prapaharan et al., 1985; Delage et al., 1995; Romero,

ew ¼

eL

nL 11=nL

1 þ ðaL sÞ

þ

es 1 þ ðas sÞns

11=ns :

Fig. 3. Air injected in drying WRC and mercury intrusion in the cylindrical pore (modified from Aung et al., 2001).

ð7Þ

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The total water retention curve for the soil is equal to the sum of the water retention functions for the large-pore series, L, and the small-pore series, s. By applying the superposition principle to Eq. (6), when the suction is zero, the expression transforms into the following: ew ðs→0Þ ¼ eL þ es ≈e;

ð8Þ

where eL and es are the void ratios of the large and small modes, respectively. The contribution of the L and s modes should be equivalent to the total storage capacity of water, which will be equal to the global void ratio. This decomposition was used by other authors when formulating constitutive equations (Zhang and Chen, 2005; Koliji et al., 2010; Alonso et al., 2010; Romero et al., 2011). 3. Results In this section, the WRC and the PSD determined by MIP and N2 are presented and discussed. Additionally, the PSD obtained from the WRC transformation is presented and compared with that obtained by the MIP technique. 3.1. Water retention characteristics The relationship between the water ratio, ew, and the matric suction obtained through the suction plate and filter paper techniques has two dominant modes (Fig. 4). The fitted WRC parameters from the experimental data are shown in Table 2. Through the two techniques, it was possible to measure a suction range between 1.0 kPa and 35 MPa, which is equivalent to the injection of air into pores with sizes between 300 and 0.0083 μm, according to Eq. (2). The dominant modes presented by the water retention curves varied according to

the compaction conditions, even with a three orders of magnitude separation between the modes. When the first mode, which corresponded to the large pores, was dry, it was necessary to increase the suction by two or three orders of magnitude to move the water stored in the small pores. On the points that correspond with the standard Proctor energy (PN), the effect of the moisture compaction on the WRC can be observed (Fig. 4b). The air entry value in the large pore mode increased with the moisture compaction (Table 2). As a result, the shape of the WRC changes, i.e., the large pore region is gradually reduced (Fig. 4) and the small pore region is kept constant. This result was also observed in the reductions of the parameter fittings, aL and nL, which define the inflection point and the slope in the large pore mode, respectively. The nL slope parameter is equivalent to the uniformity coefficient, Cu, on the particle-size curve. When nL is high, the curve is uniform, whereas low values of nL have graded curves. Thus, when nL decreases, the large pore mode transforms from uniformity to well graded. The second mode, which corresponded to small pores, did not show any significant changes in the compaction energy or moisture. This situation is reflected in the es and as parameters shown in Table 2. The effect of the compaction energy at constant moisture compaction values is shown in Fig. 4a. As the energy was increased, there was a reduction of the large pore mode, whereas the small pore mode remained constant. This pattern confirmed the porosimetry data reported by Sridharan et al. (1971) and interpreted by Delage (2009). The reduction in volume due to the effect of energy compaction increased the air entry value. The characteristics of the micro-pore range of WRC were independent from the initial moisture content and the energy. This lack of dependence on environmental factors (moisture content and energy) indicated that the micro-pore region is an inherent property of the material. Moreover, the similarities of the water retention curve at high suctions may be due to mineralogical composition, as was observed by other authors, e.g., Romero et al. (1999). According to Prapaharan et al. (1985), the adsorption effect on soil mineralogy is evident within this WRC range. To validate the results obtained through the other techniques, i.e., the filter paper and suction plate methods, the water retention curve for point NP24 during its drying path is shown in Fig. 5. In general, the results obtained from the techniques agreed with each other. Fig. 5 shows a larger data dispersion for suctions less than 20 kPa for the filter paper method. This variability may be due to the sensitivity of the filter paper to water loss when the package was opened and to the initial determination of the water mass when the filter paper gravimetric water content was greater than 80%.

3.2. Mercury intrusion porosimetry The pore size distribution curves exhibited a bimodal shape similar to the water retention curve (see Fig. 6). As observed in the WRC, the distance between the micro- and macro-dominant diameter is approximately three orders of magnitude. All samples had the same dominant diameter in the micro-pore range of approximately 0.02 μm. Table 2 WRC parameter fitting. Point

Large-pore parameters e

Fig. 4. Soil water retention properties: a) equal moisture compaction content; b) proctor standard dry and wet sides.

NP24 PN20 PN24 PN28 PIn20 PM20 PM24

L

0.307 0.266 0.227 0.244 0.150 0.028 0.158

Small-pore parameters s

aL (1/kPa)

nL

e

0.165 0.150 0.120 0.100 0.100 0.014 0.106

2.514 1.792 1.749 1.288 1.753 2.133 1.270

0.596 0.540 0.570 0.530 0.540 0.550 0.576

as (1/kPa)

ns

0.00007 0.00006 0.00007 0.00007 0.00006 0.00006 0.00006

2.744 3.789 2.990 3.291 3.867 3.761 5.819

χ2/DoF

R2

0.0010 0.0016 0.0030 0.0005 0.0011 0.0006 0.0004

0.99 0.96 0.94 0.99 0.98 0.98 0.99


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the small pores, with pore sizes between 0.017 and 0.1 μm; and iii) a transition zone between the small and large pores characterized by small changes in the mercury volume, with pore sizes between 0.1 and 0.10 μm. The presence of the third zone may be due to the three orders of magnitude difference between the large and small dominant pore sizes. Soil samples with these extrusion curve characteristics have not yet been reported in the literature to the authors' knowledge. Additionally, the separation between the large and small dominant pores seems to be a property particular to only highly weathered lateritic soils in Brazil (Futai and Almeida, 2005; Miguel and Bonder, 2012).

3.3. Prediction of pore distribution density from the WRC

Fig. 5. Comparison of techniques for measuring suction.

This value accounted for the convergence of the water retention curves with suctions greater than 1000 kPa (see Fig. 4). The macroporosity and the dominant pore diameter of a soil sample were found to be proportional to the dry unit weight of the material after compaction (see Fig. 6). As the compaction energy was increased while maintaining a constant moisture content, the dominant pore diameter decreased from 20.52 to 1.24 μm in samples NP24 and PN24, respectively. The mercury extrusion path was practically the same for all tested samples (see Fig. 6). The path was divided into three stages: i) an initial stage in which the pressure was reduced without significant changes to the volume of mercury, with pore sizes between 0.0065 and 0.017 μm; ii) a greater extrusion zone, marked by the extrusion of mercury from

Fig. 6. Intrusion mercury results: a) cumulative curve; b) differential curve.

The PSD function was determined after the WRC was converted into an air injection curve (SAIC). Fig. 7 presents the results of the PSD function obtained through the MIP and SAIC methods. The prediction of the pore size density function was fairly accurate with respect to the dominant pore diameter and diameter distribution. However, a comparison of the pore diameters, as predicted by the PSD function and as measured, indicated a difference of 0.006 μm for small pores and a 1.2 to 8.5 μm range difference for larger pores. For samples compacted at the Proctor standard optimum moisture content, PN24, the PSD function predicted a greater difference with respect to the MIP method. Despite the differences between the MIP and SAIC prediction curves, the method presented in this paper identified the dominant pore diameters, as presented in Table 3. Fig. 8 presents the estimated pore size density functions from SAIC for natural tropical soils using the proposed method.

Fig. 7. Comparison of pore size density functions from MIP and SAIC: a) equal moisture compaction content; b) proctor standard dry and wet sides.

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Table 3 Dominant pore size from MIP, SAIC and nitrogen adsorption. Point

NP24 PN20 PN24 PN28 a

MIP (□m)

N2a (□m)

SAIC (□m)

Large

Small

Small

Large

Small

20.5 13.3 1.2 4.5

0.020 0.020 0.020 0.020

0.027 0.023 – –

29.1 14.5 14.5 5.8

0.015 0.014 0.015 0.015

Derived from nitrogen adsorption (N2).

The lateritic soil studied by Futai and Almeida (2005) for a depth of 1 m has the following property indices: wL = 57%, PI = 29% Gs = 2.63, b74 μm = 57% and e = 1.45. The WRC was determined along the drying path with a suction range between 1 kPa and 16 MPa, which is equivalent to a diameter range between 290 and 0.0185 μm. Hence, the PSD was accurately predicted up to that value, as indicated by the dashed black line (Fig. 8a). The PSD in the large pore region obtained by the SAIC method accurately predicted the shape and dominant pore diameter. However, in the small pore region, the measurements of the WRC were not within the variation range of the predicted pore sizes; further, extrapolation did not produce acceptable results. Miguel and Bonder (2012) studied 4.5 m deep soil samples with following index properties: wL = 50%, PI = 15%, Gs = 3.08, b74 μm = 75% and e = 1.72. The water retention curve was determined in the drying path with a suction range between 1 kPa and 41 MPa, which is equivalent to diameters between 290 and 0.0007 μm, respectively, i.e., a range compatible with the scan performed for the MIP method. The SAICobtained PSD was able to reliably predict the distribution curve shape and the dominant pore diameters of the large and small pores. The

Fig. 8. Pore size density function from natural residual soils.

relatively good data fit for the small pores may be due to the use of an oven-drying step in the preparation of samples for the MIP. It is important to note the differences between the two techniques. Whereas the MIP method does not alter the soil structure during freeze-drying, the structure is altered during the WRC method due to the drying or wetting path of the soil. Thus, the MIP measures only the soil fabric (structural arrangement). The SAIC also reflects the changes in soil fabric and is influenced by the composition of the overall soil structure due to the interaction of water with the soil solid phase (i.e., through capillary action in the macro-pores and physico-chemical interactions in the micro-pores). Fig. 9a presents the volumetric change in the PN20 sample as a result of moisture content exchange during the WRC determination. When these data were used to correct the SAIC curves, the results of the PSD were improved over the macro-pore range but not the micro-pore range (Fig. 9b). 4. Discussion The studied material showed a bimodal pore distribution using both the mercury intrusion method and the water retention curve along the drying path. The WRC drying path for suctions greater than 1000 kPa was the same regardless of the initial compaction conditions. The shape of the pore size density function and the dominant pore diameter obtained by the MIP method were the same as those for sizes less than 0.1 μm, regardless of the initial compaction conditions. Therefore, the compaction conditions did not generate changes in the micro-pore characteristics for the WRC and the MIP. For the studied material, the

Fig. 9. a) Void ratio changes with suction; b) pore size density function obtained from MIP and SAIC with and without volume correction.


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where k is the shape factor (i.e., 5 for spherical particles, 2 for dispersed clays and 4 for flocculates), Ss is the specific surface value and ρs is the solid particle density. Substituting in the micro-pore void ratio (es) and assuming a shape factor (k) of 4, the values obtained by Eq. (7) agree with the MIP-predicted values, as shown in Fig. 10. This result confirmed the influence of composition on the micro-pore-dominant diameter. The volume change-corrected SAIC-predicted PSD in the micro-pore region did not significantly improve the results because the water retention characteristics depend on the water adsorption properties. Thus, an approach that combines WRC parameters and Eq. (7) may produce better results, as the specific surface area is related to the size and shape of particles (Santamarina et al., 2002). Using Eq. (7), the SAIC was adjusted with volume or adsorption corrections (see Fig. 11). The specific surface area of the solid phase of the soil was determined through different techniques, e.g., the adsorption of molecules from an aqueous solution of methylene blue. 5. Conclusions Fig. 10. Dominant small pore size.

dominant small pore size and the void ratios of the small pores were characteristic of the material and did not depend on the formation process or the composition. According to Martins et al. (2004), the pedologic evolution of the Federal District of Brazil included geological periods with climatic conditions alternating between dry-cold and hot-humid, favoring physical and chemical weathering, respectively. In periods of hot-humid conditions, saprolite deepened and the loss of silica and the accumulation of oxides, iron hydroxides and aluminum increased. The duration of these oscillations gradually decreased during the Quaternary Period and gave way to the two current annual seasons. As a consequence of the evolutionary process, the material presented a low cationexchange capacity (CEC) of 8 mE/100 ml with kaolin as the dominant clay mineral. The composition of the soil affected the particle aggregation properties within the soil structure, as reflected in the variable micro-porosity. To quantify the effect of the formation process, the dominant pore size can be analytically determined. According to Santamarina and Jang (2011), the dominant pore size diameter can be obtained as follows: DMean ¼

k∙e ; Ss∙ρs

ð9Þ

The density and pore size functions of the compacted soil specimens were obtained using mercury intrusion porosimetry (MIP) and the drying section of the water retention curve (WRC), i.e., the soil air injection curve (SAIC). To determine the water retention curves, these two techniques were used over a suction range of five orders of magnitude. The bimodal shape of the water retention curve was a function of the initial structure generated during compaction. The increased energy or compaction moisture content did not alter the small pore mode, whereas the large pore mode was reduced. The reduction in the large pore mode was accompanied by an increase in the amount of injected air. By means of the water retention curve and mercury intrusion porosimetry, the number of WRC modes was shown to represent the number and sizes of the dominant pores. Moreover, the difference between the dominant pore sizes maintained the same order of magnitude. The approximation of the pore size distribution density function through the conversion of the soil air injection curve was used to characterize the structure of the soil. Although this approach was acceptable, better results were obtained with the corrective factors presented in this paper. Additionally, the use of the water ratio, ew, as a storage variable allowed for the visual differentiation of the contributions of each mode. Acknowledgments The authors would like to thank the “Conselho Nacional de Desenvolvimento Cientifico e Tec-nológico” CNPq of Brazil and the Department of Civil and Environmental Engineering at the Los Andes University. The authors wish to acknowledge the support of the European Commission via the Marie Curie IRSES project GREAT (PIRSES-GA-2013-612665).The first author sincerely thank Dr. José Camapum de Carvalho for providing the opportunity to discuss tropical soil features. References

Fig. 11. Pore size density function obtained from SAIC with adsorption and volume corrections.

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