J. Cent. South Univ. (2013) 20: 3667−3675 DOI: 10.1007/s11771-013-1894-z

Hydraulic and mechanical properties of wax-coated sands Jesmani Mehrab1, 2, Bardet Jean-Pierre2, Jabbari Nima2, Kamalzare Mehrad3 1. Department of Civil Engineering, Imam Khomeini International University, Qazvin 34149, Iran; 2. Sonny Astani Department of Civil and Environmental Engineering, Viterbi School of Engineering, Los Angeles 91007, USA; 3. Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, New York 12180, USA © Central South University Press and Springer-Verlag Berlin Heidelberg 2013 Abstract: Wax-coated sands are a new category of synthetic soils, which are gradually becoming a reliable construction material. Because of their valuable drainage ability and mechanical properties, wax coated sandy soils are specifically applicable to pavement construction of horseracing tracks and sport fields. Although the mechanical and hydraulic properties of these synthetic soils are well-proven, there is still a lack of studies on how the soil samples behave differently when mixing with different wax fractions. Adding the wax affects permeability and compressibility of pure sand. Intensity of influences is a function of weight percentage of wax that has been added, and other physical and environmental factors. The effects of wax content on hydraulic properties (permeability), and mechanical properties (stress−strain behavior, compressibility) of sandy soils based on a series of experimental efforts were investigated. Obtained experimental results infer that increasing the amount of wax up to 6% causes an about 50% increase in permeability, mainly because of the significant effect of wax in lowering the friction along with covering and filling the angular parts of particles’ surfaces and forming rounded particles. In addition, wax-coated sands show a 20% to 60% decrease in confined compression modulus compared to non wax-coated sands. Key words: wax-coated sand; confined compression coefficient; permeability; compressibility; stress−strain behavior

1 Introduction Mechanical and hydraulic properties of natural sandy soils are highly sensitive to moisture. For example, they sometimes liquefy; an extreme case in which the shear strength is almost completely lost; on the other hand, sand sometimes loses its infiltration capability due to rapid loading, which makes it harder to drain water. In order to overcome these difficulties in practical applications, such as building construction, horseracing fields and sport surfaces, one advantageous approach is to use additives including waxes, polymers, synthetic fibers, and rubber chips in an effort to improve soil properties [1]. One important goal in generating synthetic soils is to imitate useful properties of a natural soil and, at the same time, mitigate some deficiencies in mechanical behaviors which are part of the nature of soils. Synthetic surfaces, specifically, are being constructed in a way to have the best performance in adverse temperatures, obtain an appropriate drainage capability and hold

minimum mechanical properties while behaving like a natural soil to the greatest extent possible [1]. The process of coating soil with a basically hydrophobic wax has benefits, such as promoting and stabilizing mechanical and hydraulic properties. It is worth noting that, compared to chemical ground improvement techniques, coating is a method that works differently. In the physical process of coating, there are two major steps, melting and the formation of a thin film around grains of sandy soils. Whereas, a chemical improvement method such as lime addition consists of mixing the soil with additives, and allowing it to build chemical bonds between the grain and the additive [2−3]. BARDET [4] investigated the application of wax coating for sandy soils with a non-negligible silt/clay fraction. Advantages like altering the mechanical behavior, preventing dust formation in dry conditions, and decreasing deterioration of material properties at high water content were studied. It was found that the hydraulic properties of wax-coated sands are different from those of pure sands. When utilized in horseracing tracks, for instance, along with some changes in the

Received date: 2012−09−17; Accepted date: 2013−02−08 Corresponding author: Kamalzare Mehrad, Professor, Tel: +1−518−4967778; E-mail: [email protected]

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permeability coefficient, drainage capability will improve in the soil. An important reason for these findings is the exploitation of the soil hydrophobicity of artificial sands. Amongst other factors discussing soil permeability, hydrophobicity is well-known to agricultural scientists, but as yet rarely considered by geotechnical engineers [5]. Mixing a sandy soil with wax results in the formation of a hydrophobic compound which takes a longer period of time for water droplets to penetrate the surface [1]. HALLETT [6] studied the percolation of water droplets to a soil with a high degree of water repellency. It was found that water droplets remain on the surface of soil and do not percolate. Instead of percolation, remaining droplets evaporated freely and more frequently. The value of contact angle (θ) between the liquid and solid surfaces can best give sense on determining the degree of hydrophobicity or hydrophilicity of a soil. Although in studying soil physical properties, it is very common to assume θ=0, in a case of an extremely hydrophobic soil, the contact angle shows values greater than 90°. TILLMAN et al [7] found that soils demonstrate different tendencies to absorb water, leading to bearing various degrees of water repellency and taking contact angle values between 0° to 90°. Figure 1 categorizes soils in terms of water repellency.

Fig. 1 Contact angle and forms of water repellency in soil [6]: (a) Contact angle ≥ 90°, no infiltration; (b) 0° < Contact angle < 90°, resistant to water; (c) Contact angle≈0°, no resistance to water

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Figure 1(a) illustrates the condition in which the contact angle is greater than 90°, infiltration barely occurs, and a water droplet maintains its spherical shape to a great extent. Here, soil shows an extremely hydrophobic behavior. In another instance, when the contact angle is within the range of 0°−90° (Fig. 1(b)), water expands over the surface and loses its original shape. Although it seems that soil absorbs water easily, infiltration is still impeded by soil, resulting in a slow rate of penetration. Governing behavior, for these types of soils, is hydrophobic. The third form of water repellency is when soil makes a 0° contact angle with water leading to a very low degree of resistivity toward water (Fig. 1(c)) [6]. Hydrophobicity, also, causes the liquid to slip over the solid surface. This slippage effect arises from the decrease in viscosity in a layer which is thin and also adjacent to the particle wall [8]. When exposed to heavy and continuous rainfalls, water repellent soils infiltrate the flow with a higher rate via forming flow paths which are called fingers. Once these fingers are formed, water and contaminants transportation takes place more readily [9]. Addition of wax can be helpful in facilitating this transport phenomenon through the fingers, simply by making the media greasy and providing the water droplet with the ability of slipping through the lubricated soil much more easily. Wax also changes the geometrical shape of the sand particles from a rough surface into a rounded edge which is also effective in promoting the flow current through the fingers. Using additives to promote the mechanical behavior of sand is a widely accepted method used by practitioners. Root-zone mixture, for example, is a combination of sandy soil, water, and peat which is used in constructing professional golf courses. The mechanical behavior of these mixtures significantly depends on the moisture content, peat content, and the shape and size distribution of the particles. As an example, peat addition to the sand along with increasing the moisture of the mixture, results in larger compression when compared with the pure sand. The reason is because of the presence of water which lowers the friction and makes it easier for the grains to move when undergoing loads. Peat also contributes to increasing the compressibility of the mixture. The bulk modulus of root-zone sand mixtures is the other parameter which tends to gain larger values when exerting more pressure on the samples. The addition of moisture and peat solidifies the samples. Furthermore, increase in mean pressure is effective on the shear modulus values of the samples so that in higher pressures

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larger values of shear modulus can be obtained. In this case, a ductile behavior is a likely result of being in a moist condition [10]. In the case of wax-coated sands, wax as an additive affects mechanical properties of natural sandy soils. When the stiffness is concerned, sand is relatively solid when compared to wax, hence wax as a soft substance significantly changes sand stiffness and bestows more compressibility to the sand grains. This work investigates the effect of addition of various percentages of wax on permeability and compressibility properties of the mixtures. Using soil samples with different wax percentages and carrying out a series of grain size distribution, permeability, and compressibility tests, this research aims to suggest meaningful relations between increase in weight percent of wax and the values of permeability coefficient and compressibility modulus. A former study by the authors suggests that compression has a few effects on shear strength parameters of wax-coated sand and when comparing to natural sandy soils, wax-coated sand is less affected by changes in water content [2].

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is of high importance. Viscosity, for instance, is a physical property that plays a vital role in manufacturing wax-coated sands. Determining the viscosity parameter of a wax is helpful in practice when wax-coated sand is going to be produced on site. Moreover, viscosity affects stress−strain behavior of the wax-coated sand. Since storage and loss moduli of the wax samples are directly related to the viscosity, a study has been done at different temperatures in order to have a better understanding of the behavior of different wax samples of the SASOL Company. Different waxes have different melting temperatures and can be used in various weather conditions. Eventually, wax with the label S9908 with a moderate viscosity value was chosen for this work (Fig. 3).

2 Preparing samples The improved soil that has undergone a series of tests in this research is a blend of poorly graded sand and weight percent of wax. The coefficient of uniformity (Cu) and coefficient of curvature (Cc) for the pure sand are respectively equal to 3.00 and 1.02, and therefore, it is categorized as SP (poorly graded sand) according to USCS system. Figure 2 shows the grain size distribution of the pure sand.

Fig. 3 Storage and loss moduli versus temperature for S9908 wax sample

After choosing the wax, soil samples were prepared by melting the wax and thoroughly mixing it with the pre-heated sand to obtain a homogeneous mixture. The fractions used are 1%, 2%, 4%, and 6% (mass fraction) of each sample. A microscopic picture of a sand particle surrounded with wax is presented in Fig. 4. After preparing mixed samples and before performing the tests, samples have been compacted and remolded using an energy compaction value close to that of practical application, particularly horseracing tracks.

Fig. 2 Grain size distribution of poorly graded (SP) pure sand

Wax is a petroleum product with an extensive use in horseracing surfaces. Since different waxes have different physical and chemical properties, which in all instances affect the behavior of the final mixture, choosing an appropriate wax for this type of application

Fig. 4 Microscopic picture of sand grain with wax on surface

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3 Laboratory test results and discussion After preparing soil samples with different values of wax, the samples have been tested for grain size distribution, permeability with the falling head, and compressibility. 3.1 Grain size distribution For all the samples, sieve analysis was carried out to find out the effect of wax on the size distribution. The test was readily done for samples with 0, 1%, 2%, and 4% wax and the s-shape curves were plotted as assumed, in a manner, the sample with 1% wax did not show a significant difference in the curve compared to that of pure sand. It can be inferred that 1% wax cannot significantly change the grading. From 2% to 4% of wax, as the wax content increases, the grain size increases and the finer percent for a specific size decreases. However, the increase in particle size is because of the cohesion between the particles which is provided by wax (Fig. 5).

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responsible for this case. Since wax, by itself, is a hydrophobic agent, it lowers the inter-particle friction of the saturated media and due to lubrication effects of wax, particles become rounded which lets water droplets spend lower energy levels to go through the soil. Figure 6 also indicates that the permeability coefficient increases by increasing the wax content. As it was previously mentioned, there are two main reasons to be offered: Material effects in which the presence of wax makes the medium greasy, and renders adverse effects of friction in wasting water droplet energy while seeping through the soil. Moreover, since wax is a hydrophobic chemical when it undergoes shearing loads, it shows a finite slip on the surface (resulting from the general hydrodynamic boundary condition). The degree of interaction between surface water and the surface roughness determines the slip length [9], and geometrical effects in which the originally rough surface particle becomes rounded after coating with wax. In this case, angles are first filled with wax and then become smoother as wax surrounds the particle, finally resulting in forming a rounded-edge particle. Equation below shows the mathematical relation between permeability coefficient and the wax percentage. k=−0.000 1 w2+0.001 4 w+0.009 3

(1)

where k is permeability coefficient, cm/s; w is the absolute percentage of wax.

Fig. 5 Grain size distribution of samples coated with various wax percentages

Although sieve analysis resulted in reasonable grain size distribution curves for the samples with 1%, 2%, and 4% wax, it was not doable for the sample with 6% of wax, accurately based on the real particle size. Two main reasons can explain this fact: Waxy materials clog the sieve opening, and cohesion between particles (due to wax effects) causes them to stick to each other and form bigger bundles that may apparently increase the diameter of the sand particles leading to misleading results. 3.2 Permeability Figure 6 shows the variation of permeability coefficient as a function of wax percentage. As the amount of applied wax increases, the degree of repellency of the soil increases and helps the water slip through the soil easier. Chemistry of the wax is

Fig. 6 Coefficient of hydraulic conductivity versus wax percentage

3.3 Compressibility 3.3.1 Stress−strain behavior Stress−strain curves for soils with different wax contents are illustrated in Fig. 7. Figure 7 shows a regular pattern in which by increasing the wax content, the soil media becomes softer leading to a less stiff behavior when undergoing load. So, for the same stress of 1 600 kPa, for example, larger values of strain are

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achieved as the wax percentage increases. Based on this fact, we expect to see a decrease in confined compression modulus (M) by increasing the wax content. Another important point is that since the confined compression test has been carried out (zero horizontal strain), the stiffness of the soil samples (the slope of the curves) gains higher values by exerting more load on samples.

constant value. At low-range stresses, there is a rapid increase in Msec with increase in stress, whereas at higher-range stresses there is not a significant change in Msec. When the wax content is concerned, there is an indirect proportionality between wax percentage and Msec, so that the greater the wax contents, the lower the Msec. Moreover, Msec is linearly proportional to the strain. Increasing wax content has a significant effect on the soil strain, as an example, when compared different samples with the same Msec, the sample with 6% wax shows the largest strain, followed by the samples with 4%, 2%, and 1% wax.

Fig. 7 Stress−strain curves for different wax percentages

Mathematical equations for stress−strain curves for different wax percentages are as follows: σ=649 522ε2+2 371.6ε, w=1%

(2)

σ=544 726ε2−8 252.6ε, w=2%

(3)

σ=283 235ε2−2 630.6ε, w=4%

(4)

σ=190 567ε2−1 526ε, w=6%

(5)

Fig. 8 Variation of secant confined compression modulus versus stress

where σ is stress, kPa; ε is strain. Also, a unique equation can be calculated in order to relate stress, strain, and wax content (Eq. (6)). σ=(873 734e−0.252w)ε2+(784.83w2−4 597w−2 197.9)ε (6) 3.2.2 Confined compression modulus Compressibility moduli of the samples have been achieved via two methods: calculating the slope of the line which connects the origin and any particular point on the curve (Secant confined compression modulus, Msec) and calculating the slope at any specific point on the curve (Tangential confined compression modulus, Mtan). In this work, Msec has been obtained through experimental procedure. Having Msec calculated, Mtan values can be found using an equation relating Msec and Mtan. 3.3.3 Secant confined compression modulus (Msec) Variations of Msec as a function of stress and strain are shown in Figs. 8 and 9, respectively. Based on the graphs and for all the samples, by increasing the load Msec increases up to a certain point and then obtains a

Fig. 9 Variation of secant confined compression modulus versus strain

Curve fittings of the Msec as a function of stress and strain are presented in Eqs. (7) to (11) and Eqs. (12) to (16), respectively. Msec=2×10−5σ3−5.18×10−2σ2+64.44σ, w=0 −5 3

−2 2

(7)

Msec=1×10 σ −3.48×10 σ +47.79σ, w=1%

(8)

Msec=7×10−6σ3−2.46×10−2σ2+36.78σ, w=2%

(9)

Msec=5×10−6σ3−1.64×10−2σ2+26.09σ, w=4%

(10)

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−2 2

Msec=7×10 σ −2.29×10 σ +29.07σ, w=6%

(11)

5

(12)

5

(13)

5

Msec=3.50×10 ε, w=2%

(14)

Msec=1.9×105ε, w=4%

(15)

Msec=1.71×105ε, w=6%

(16)

Msec=8.05×10 ε, w=0 Msec=5.24×10 ε, w=1%

Two more mathematical equations are presented as Eqs. (17) and (18), one expressing Msec as a function of wax content and stress, and the other for relating Msec to wax content and strain. Msec=(10−6w2−9×10−6w+2×10−5)σ3+(−2.2×10−3w2+ 1.79×10−2w−5.18×10−2)σ2+(1.970 6w2−17.667w+ 64.435)σ (17) Msec=(8×105e−0.301w)ε

(18)

3.3.3 Normalized secant confined compression modulus (MN-sec) In order to have a better sense of the effects of wax on lowering the stiffness of wax-coated sand, a normalized secant confined compression modulus (MN-sec) has been defined as the fraction of Msec of each sample to Msec of the pure sand (w=0%). Figures 10 and 11 demonstrate the variation of MN-sec of each sample with stress and strain, respectively. As it is demonstrated in the graphs, by increasing the wax content, MN-sec gains smaller values. In general, the sample with 1% wax has the largest MN-sec values, ranging from 0.79 to 0.83, whereas soil with 6% wax has the smallest values ranging from 0.46 to 0.47. Also, it can be inferred from Fig. 11 that when the wax percentage increases, the curve shifts to the right, resulting from the effect of wax on making the sand softer and causing it to reach larger strain values. Also, according to Fig. 10, it can be concluded that MN-sec is

Fig. 11 Variation of secant confined compression modulus versus strain

small at low pressures, but by increasing the pressure, it gains higher values. The reason is the effect of pressure on the wax coating particles, so that while wax layers stay unchanged at low pressures, as the load increases wax layers begin to seprate. Exerting more pressure results in compression of the sand particles, causing soil to behave like pure sand. Accordingly, the secant compression modulus of the mixed soil nears to that of the pure sand. In other words, MN-sec obtains values near one. Equations (19) to (22) list the mathematical equations relating MN-sec to stress, while Eqs. (23) to (26) show the formulas between MN-sec and strain. MN-sec=0.033 4lnσ+0.583 8, w=1%

(19)

MN-sec=0.046 6lnσ+0.352 7, w=2%

(20)

MN-sec=0.047 1lnσ+0.174 9, w=4%

(21)

w=6%, MN-sec=0.003 9lnσ+0.434 3

(22)

MN-sec=0.105 9lnε+1.146 4, w=1%

(23)

MN-sec=0.167 5lnε+1.166 2, w=2%

(24)

MN-sec=0.167 4lnε+0.943 4, w=4%

(25)

MN-sec=0.008 1lnε+0.482 1, w=6%

(26)

Equations (27) and (28) present the two-variable equations that show the relationship of MN-sec with stress and wax percentage and the relationship of MN-sec with strain and wax percentage.

Fig. 10 Variation of secant confined compression modulus versus stress

MN-sec=(−0.005 1w2+0.030 1w+0.007 9)lnσ+(0.052 6w2− 0.398 9w+0.933 6) (27) 2 MN-sec=(−0.020 1w +0.121w+0.005 3)lnε+(−0.033 8w2+ 0.101 9w+1.085) (28)

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3.3.4 Tangential confined compression modulus (Mtan) Mtan can be calculated from Msec for any specific point using Eq. (29): Mtan=Msec+ε(ΔMsec/Δε)

(29)

Therefore, the experimental results of Mtan are not presented here.

4 Theoretical approach

t1  a  bd

where a=0 and b 

4.1 Thickness of wax coating and calibration Using a geometrical approach and considering Fig. 12, the relation between wax percentage, sand particle diameter, and wax thickness can be calculated via following equation: w′=Wwax/Wsand=γw·Vw /(γs·Vs)

(30)

where Wwax and Wsand are masses of wax and sand, respectively; γw and γs are specific masses of wax and sand, respectively; and Vw and Vs are volumes of wax and sand, respectively. Also, the followings are some ideal assumptions needed to be paid attention to when applying Eq. (30): spherical sand particles and even distribution of wax resulting in a constant thickness over the particle surface. Calculations are as follows: 3

w 

Wwax Wsand

   3 w  s  1  1    w    18 1.5  3 0.04  1  1  0.02 mm   9 2  

t2 2

As it was previously pointed out, Eq. (31) is valid under ideal geometrical assumptions. In this work, however, some other factors are playing roles such as pressure, air bulbs in wax layers (around sand particles) after wax solidification, inconsistency in wax coating thickness, direct contact among sand particles, and angularity and roughness of particles which interfere with theoretical assumptions. Therefore, differences between theoretical and experimental results seem to be unavoidable. As a result, a calibration must be applied to obtain a high degree of consistency between theoretical and experimental results along with including the effect of load on the wax thickness. Calibration calculations based on the properties of the tested materials have been presented as follows: Ms=18 000 kN/m2, Mw=5 000 kN/m2, γs=18 kN/m3, and γw=9 kN/m3. Considering Fig. 12, equivalent confined compression modulus can be computed via Eq. (33):

Me 

3

4  t2  4 t  π  t   π 2   w  Vw  w 3  2 1  3  2      3  s  Vs s 4  t2  π  3 2

 s 1  3 w  1  1. A graphical  w 2  

representation of this equation is displayed in Fig. 13. Example 1 Assuming w′=4%, γs=18 kN/m3, γw=9 kN/m3, and d50=1.5 mm, wax thickness would be t1 

This section aims to derive formulations on thickness of wax coating and equivalent confined compression of the mixture based on pure theoretical studies calibrated with experimental data. It should be noticed that presented equations have their own assumptions (based on the used material properties and some geometrical simplifications) and approximations (due to curve fitting analysis). This proposed method, however, can be applied for other similar studies to find new equations.

(32)

t w  M w  ts  M s 2t1M w  t 2 M s  t w  ts 2t1  t 2

By rearranging the equation:  t1   t2

 Ms  Me    Lab 2M e  M w 

3 3 4  t 2  t   π   t1    2     2    w 3  2 . 3 s 4  t2  π  3 2

Doing the math will finally result in Eq. (31): t1 

t2 2

   3 w  s  1  1   w  

(31)

Therefore, wax thickness is linearly related to sand particle diameter using the following equation:

Fig. 12 Geometry of sand and wax

(33)

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of constant stiffness springs, derived based on the presumptions of the linear behavior of materials with a constant compression module, and located in a semi-infinite medium with horizontal stratification. By substituting the equivalent value for 2t1:    t 2  3 w s  1  1 M w  t 2 M s   w  M e,Th      t 2  3 w s  1  1  t 2   w   Fig. 13 Wax thickness vs sand diameter

And finally:

where Ms is the laboratory value of modulus of soil when w=0; Me is the laboratory value of modulus of soil when w≠0; and Mw is the wax modulus. Obviously, on the right hand side of this equation pressure and wax percentage are two main effective factors on Ms and Me and with the aid of curve-fitting calculations. Finally, thickness ratio, pressure, and wax percentage are related to each other through Eq. (34):  t1   t2

   [1.06 w3  9.187 w 2  20.076w   Lab 24.607] 0.18 ln w0.658 3

 1    Th 2

 2w  1  1 3

 t1     t 2  Lab  {[1.06 w3  9.187 w 2  20.076 w   t1     t 2  Th 1 24.607] 0.18 ln w0.658 3 } /{ [3 2w  1  1]}  2 0.450 1w 0.18 ln w0.658 3 6147.6e  (36)

 t1   t2

 t    1  Lab  t 2

Example 2 Assuming w=4%, γs=18 kN/m3, γw=9 kN/m3, Mw= 10 000 kN/m2, and Ms=18 000 kN/m3, equivalent confined compression modulus is obtained as follows:

M e,Th

  (6 147.6e 0.450 1w   0.18 ln w0.658 3 ) (37)  Th

4.2 Equivalent confined compression modulus and calibration Equivalent confined compression modulus can be computed via Eq. (33). This equation expresses a model

   M w  3 w s  1  1  M s   w      3 w s  1

w

  18 10 000 3 0.04  1  1  18 000   9    17 700 kN/m 2 18 3 0.04 1 9

(35)

Dividing Eq. (34) by Eq. (35), Eq. (36) can be achieved in which the coefficient of pressure is only a function of wax ratio which is defined as an exponential function:

(36)

w

(34)

Using Eq. (31) and assuming γs=18 kN/m3 and γw= 9 kN/m3 thickness will be calculated theoretically as follows:  t1   t2

M e,Th

   M w  3 w s  1  1  M s   w     3 w s  1

The experimental result in this work does not comply with the assumptions used in Eq. (33). For instance, compression modulus is changing with load and is not constant, the medium is finite with constraints on sides (radial strain equals to zero), and there is no tangible stratification of wax and sand. Hence, it has been predicted to find dissimilarity between theoretical and experimental results which necessitates obtaining calibration factors to make the theory and experiment more consistent. Assuming Mw=5 000 kN/m2, Ms=18 000 kN/m2, γs=18 kN/m3 and γw=9 kN/m3:

M e,Th 

5 000(3 2w  1  1)  18 000 3 2w  1

(39)

Then, the following steps have been taken to obtain M e,Lab in different values of wax the final equation of M e,Th ratio:

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1) Finding Me,Th form Eq. (39). 2) Using Eqs. (8) through (11) for Me,Lab. 3) Dividing Me,Lab by Me,Th. 4) Neglecting small coefficients of σ2 and σ3. 5) Defining the coefficient of σ as a function of w. M e, Lab M e, Th

 (10  4 w 2  0.000 9w  0.003 5) 

M e, Lab  M e, Th (10 4 w 2  0.000 9w  0.003 5) 

(40)

5 Conclusions 1) Compared to natural sand, there is a higher permeability coefficient for wax-coated sandy soils with a direct relation between wax content and the value of permeability coefficient. Adding up to 6% of wax can increase the permeability by more than 50% due to the following two major reasons: lower friction in the sandy media by offering a slippery surface for the water droplets when going through the soil, and newly formed rounded geometrical shape for sand particles resulting from filling the gaps of basically sharpen-edge particles with greasy material and making it smoother. These result in lowering energy loss of water during passing the soil pores. 2) Wax addition can also change the stress−strain behavior of the pure sand, in a way that samples obtained less stiffness compared to the pure sand. The reason is the presence of wax as a very soft material versus the sand grain with a relatively solid texture. The amount of wax, obviously, has a significant effect on the degree of stiffness of the samples. The sample with the highest amount of wax (6%) exhibited the smallest normalized secant compression modulus ranging from 0.46 to 0.47, while when using less wax, the values fall within the ranges 0.46 to 0.52 for 4% wax, 0.64 to 0.70 for 2% wax, and 0.79 to 0.83 for 1% wax. Also, as a general trend for all samples, by increasing the load the normalized secant compression modulus obtains larger values, because of the effect of loading on compressing particles and making the soil sample behave like pure sand. Increasing the wax up to 5% will significantly increase the coefficient of hydraulic conductivity; but the effect of higher percentage of wax on the coefficient of hydraulic conductivity can be ignored. On the other hand, the secant modulus decreases by increasing the percentage of wax, and the soil becomes softer. Soils with smaller wax percentages have higher secant modulus and are obviously harder. Therefore, 5% wax can be considered as the optimum wax content, so then the coefficient of

hydraulic conductivity and the secant modulus would have reasonable and suitable amounts. 3) A specific approach has also been presented, which finds the relationships between theoretical and experimental values of thickness of wax and confined compression modulus. Using equations with simplified assumptions raises the importance of calibration factors as a function of different pressures and wax ratios. The suggested method can be used for other studies to find similar calibrating equations. It should also be mentioned that although only one kind of sand has been used in this research, the presented method and lab procedure can be used for other sands too.

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