Controlled diesel-mixed soils for roadway embankments: laboratory and ultrasonic characterization

Soils contaminated with hydrocarbons is a repetitive site condition that may occur at locations adjacent to underground fuel tanks and other facilities. The main purpose of this study is to characterize and assess possibilities of reusing contaminated soil in useful applications such as roadway embankments. Accordingly, controlled amounts of diesel were mixed with clays and sands using percentages ranging from 0 to 13.5%. Unconfined compression, direct shear, California bearing ratio, and other tests were conducted on the diesel-mixed soil, along with the ultrasonic test. The ultrasonic test provided measures for the pulse wave velocity and received frequency, which was correlated with other soil parameters such as elastic modulus, resilient modulus, and California bearing ratio. From the main outcomes, it was found that small amounts of diesel can help improved soil shear strength. For instance, adding 5% diesel increased the soil cohesion by 63% and the unconfined compressive strength from 0.14 to 0.21 N/mm2. In sands, the California bearing ratio increased by almost double by adding 5% diesel, which is essential for roadway embankments especially in remote locations. Damping coefficient of soil was determined at different levels of diesel using the ultrasonic wave decay envelops. The ultrasonic waves were analyzed using fast Fourier transform to determine useful correlations between the wave frequency and the diesel content starting from 0 to 13.5%, and it was realized that an uncomplicated ultrasonic test can be acceptably used to assess static and dynamic properties of clean as well as contaminated soils.


Introduction
Hydrocarbon substances such as gasoline, diesel, motor, and crude oils can affect soil layers when leakage occur from industrial facilities, underground fuel tanks, or well drilling sites (Kermani andEbadi 2012 andAmro et al. 2013). Such substances transit to distant locations in presence of groundwater (Estabragh et al. 2014). This means that there are actual cases where soil is already mixed with hydrocarbon without abundant information about the implications on the soil strength and behavior. This usually leads to avoiding any new development or construction on this soil due to the uncertainty of its behavior, even reusing this soil for backfilling and/or compaction purposes. Rajabi and Sharifipour (2019) specified that excessive leakage of hydrocarbons may lead to alterations of soil behavior and properties. However, it was found that mixing controlled amounts of hydrocarbon substances with soil enhanced its static and dynamic properties towards utilization in applications such as roadway embankments (Al-Sanad et al. 1995;Akinwumi et al. 2014;Abousnina et al. 2015;Akpabio et al. 2017;and AbdelSalam and Hasan 2020). Shin and Das (2001) characterized the mechanical properties of heavily contaminated soils and indicated that dense oils reduce the soil bearing capacity. Ratnaweera and Meegoda (2006) mixed chemicals such as glycerol, propanol, and acetone with high-plastic clays, clayey silts, and silty sands. Their results showed that the modulus of elasticity 1 3 313 Page 2 of 12 decreased by increasing the hydrocarbon viscosity. Khamehchiyan et al. (2007) mixed crude oil with low-plastic clays, poorly graded sands, and silty sands with mixing percentages ranging from 4 to 16%, and it was indicated that crude oil reduced the soil shear strength properties. Wilkinson and Alfach (2020) investigated the effect of crude oil contamination on soil surrounding deep foundations and found that oil contamination reduces frictions and increases stress in piles. However, other researchers such as Al-Aghbari et al. (2011) measured changes in the shear strength of silty sands mixed with gasoline and recorded a slight enhancement in the cohesion and a reduction in permeability. Akinwumi et al. (2014) studied the effect of hydrocarbons on lateritic clayey sandy gravels. They found that oil decreased the soil optimum moisture content by mixing oil amounts limited to 4%, while adding more oil gradually increased the California bearing ratio (CBR). It was observed in their study that soil parameters are more sensitive to diesel compared with hydrocarbons such as oil and gasoline. Safehian et al. (2018) mixed illite clay with diesel to improve the overall soil compressibility. Hernández-Mendoza et al. (2021) studied the effect of diesel on clay and detected enhancements on its mechanical behavior. Table 1 presents a summary of results from the literature.
Accordingly, not all hydrocarbons have an unfavorable effect on the soil shear strength, as some advances can be achieved by adding controlled amounts of light hydrocarbon substances such as diesel to soil. This was also evident in earlier studies by Al-Sanad et al. (1995) and Meegoda et al. (1998). Likewise, Khamehchiyan et al. (2007) indicated that small amounts of diesel (within the range of 5% by weight) can be easily and practically mixed with sand to increase the overall bearing capacity needed for geotechnical applications that involve soil compaction. This means that the case of existing soils that are already contaminated with hydrocarbons does not necessarily mean avoiding any construction or development on it, or even reusing these soils in other engineering purposes, especially when dealing with remote locations that need soil embankment, etc. Accordingly, there is a significant cost-benefit of utilizing these contaminated soils compared with the cost of totally avoiding it and compared with the other costs and environmental impact of extracting and transporting clean soils to such remote locations. Recently, AbdelSalam and Hasan (2020) studied the effect of mixing diesel with sand and found that diesel increased the soil compressibility and enhanced the CBR. They also used the ultrasonic test device to develop a correlation between using different percentages of diesel in sand and its effect on the CBR, as they linked the CBR results with the ultrasonic pulse wave velocity.
The ultrasonic test device was initially developed to detect defects in homogenous materials such as steel and concrete (Jones 1953). The device mainly detects the transmitted and received waves inside these materials to give an insight over how kinetic waves are transmitted through a certain mass, which is vital to determine the material dynamic properties. Later, the use of the ultrasonic device expanded to include more materials. For instance, Vasil'eva et al. (1969) performed one of the few attempts to study the usage of the ultrasonic device on soils, as they measured changes in the pulse wave velocity with variations in soil density. Others such as Chen et al. (2016) established a correlation between the ultrasonic pulse wave velocity and strength of frozen silty clays. They measured the change in velocity in correlation to temperature and water content. Wang et al. (2018) studied stress-related compaction effects under loading using the ultrasonic device and concluded that the test is reliable, of low cost, and considered practical to assess soil properties and cracking characteristics. Wang et al. (2020) developed an empirical formula with an acceptable accuracy between the ultrasonic pulse wave and the unconfined compressive strength of unsaturated soils. Although relatively more research has been conducted on the use of ultrasonic pulse wave for rock specimens (Heidari et al. 2021), there are very limited resources of developing the ultrasonic test for more soil types, nor mixtures of soil and hydrocarbon substance. The fact that this device can be used to determine the soil dynamic properties, AbdelSalam and Hasan (2020) indicated that the ultrasonic wave velocity can give an acceptable indication about soil modulus of elasticity, dynamic shear modulus, and damping coefficient instead of using other sophisticated laboratory tests. However, the use of ultrasonic for soil is still scarce. In this study, the mechanical properties of clays and sands were characterized using various mixing percentages with diesel. An intensive experimental program was designed to measure the soil shear strength and compressibility of clean as well as soils mixed with diesel using various percentages ranging from 0 to 13.5%. Results were obtained in the form of handy design charts and equations to be useful for geotechnical practitioners concerned with roadway embankments, compacted soil, and ground improvement. Results were then linked with outcomes from a series of ultrasonic tests conducted on the same soil samples, where correlations were developed between the pulse wave velocity and other mechanical properties such as soil cohesion, friction angle, resilient modulus, and CBR. Finally, the ultrasonic waves were thoroughly analyzed to construct a relation between the wave form and the damping coefficient for clean as well as diesel-mixed clays and sands.

Soil sampling
The cohesive soil used in this study was extracted from boreholes located in the Nile delta region, Port-Said governorate, Egypt. Samples were extracted from a depth equal to 6 m, knowing that volumes of soil within that area were vulnerable to leakage from the underground diesel tanks required for fueling the railway trains. Clean cohesive soil samples were collected and classified following the unified soil classification system as clay with high plasticity (CH), with bulk density (ρ) of 1.875 g/cm 3 . Five samples were used; the first was clean clay, while other samples were mixed with diesel using percentages equal to 2.5%, 5%, 10%, and 13.5%. Adding more diesel led to an extensively greasy mix that was hard and impractical to remold. For the cohesionless soil used in this study, it was clean coarse sand, collected from the 6-of-Octrober region, Giza governorate, Egypt, to represent the typical soils used for compacted fills after AbdelSalam and Hasan (2020). Samples were classified as poorly graded sand (SP) with maximum dry density (ρ dmax ) of 1.92 g/cm 3 , optimum moisture content (OMC) of 6.5%, and void ratio (e) of 0.26. Figure 1 presents the particle distribution curve for the used sand. Diesel mixing percentages with sand were also 0%, 2.5%, 5%, 10%, and 13.5% of the dry sample weight. The maximum percentage of diesel was determined during mixing, whereas adding the OMC in addition to 13.5% diesel led to full saturation of voids and the sand sample started bleeding fluid during compaction. Accordingly, the maximum amount of diesel used for both soil types was 13.5%.

Soil characterization
The experimental testing program initially aimed at characterization of shear strength properties of cohesive and cohesionless soils mixed with various percentages of diesel. Quantified properties included Atterberg limits and plasticity index (PI), internal friction angle (ϕ), cohesion (c), unconfined compressive strength (q u ), CBR, and resilient modulus (M R ). To achieve that, a series of tests such as unconfined compression (UC), direct shear test (DST), CBR, and ultrasonic were conducted. The main objective was to focus on soil properties that are required in the design and construction processes of roadway embankments, with the intension to enhance soil characteristics and compactness using a reduced compaction effort. The idea of mixing soil with limited amounts diesel arose after facing actual cases in Egypt where soil was already mixed with such hydrocarbon without any information about the possibility of construction on these soils nor the use of these soils for backfill and compaction purposes.
The mixing procedures of diesel with soil that was adopted for the UC, DST, CBR, and ultrasonic tests are summarized as follows: (a) the total weight of clay or sand samples was determined during mixing (e.g., 750 g); (b) in the case of clay, the plastic limit (PL) was determined and kept constant, then the corresponding weight of water was calculated (e.g., for PL = 29, the corresponding weight of water = 217 g); (c) the amount of diesel in each test was calculated relative to the sample total weight multiplied by a density conversion factor between the densities of water  (2020) to diesel (density factor = 1.36); (d) accordingly, the weight of diesel required for each mix was calculated (e.g., 5% diesel = 5% × 750 × 1.36 = 51 g); and (e) the water amount required to fill the remaining weight relative to the PL was added (e.g., 217 − 51 = 166 g of water). In the case of sand, the same procedures were followed but based on using a constant OMC of 6.5% for clean sand instead of PL. These procedures were followed to acquire accurate mixing percentages, keep the amounts of water and diesel in samples within practical levels, and avoid placing samples in the oven as much as possible.

Atterberg limits
Atterberg limits were measured for clay samples with different diesel percentages following the ASTM 4318 (ASTM, 2017). Only for the PL and liquid limit (LL) tests, the dieselsoil mixing procedures were changed to be able to measure the actual values of Atterberg limits. This was done by adding the required percentage of diesel by total weight of solids (i.e., 5% diesel for a 750-g dry sample = 37.5 g), then adding the necessary amount of water until reaching the PL and the LL. The water content was determined by placing the samples in the oven for 72 h using a relatively low temperature of 50 °C, keeping in mind that the average flashpoint of diesel is about 60 °C. Accordingly, the LL was measured as 55, 61, 67, 80, and 98 for clean clay, and clay mixed with 2.5%, 5%, 10%, and 13.5% diesel, respectively. As shown in Fig. 2, the PL was 29, 32, 36, 43, and 50 for clean clay and diesel-mixed clay with 2.5%, 5%, 10%, and 13.5%, respectively. Increasing the percentage of diesel required almost double the amount of water required to reach the LL and PL of clay, which was the main reason for not exceeding 13.5% diesel in the samples. PI was presented in the figure, where a linear correlation between the percentage of diesel and the PI was noticed.

Direct shear test
The direct shear tests for clay (DST-C) and sand (DST-S) were conducted using diesel percentages of 0%, 2.5%, 5%, 10%, and 13.5%. The dimensions of the shear box used were 100 × 100 × 20 mm, and tests were conducted following the ASTM D3080 D3080M-11 (2011) to determine the soil shear failure envelop and accordingly c and ϕ. Samples were prepared after the previously described diesel-mixing procedures and using the actual unit weight of soil. For clay, samples were remolded inside the shear box in layers where the contact surface between each layer was inclined by about 45° to avoid interference with the shear failure plane. Three normal stresses (σ n ) were used during testing equal to 39.2, 78.5, and 157 kPa to mimic the actual overburden pressures for the collected soil samples. Before starting the shear test, samples were initially compressed in the shear box for 2 min to ensure uniform distribution of the normal stress during testing. Then, a constant horizontal displacement rate of 1 mm/min was applied to a maximum displacement of 10 mm or until failure. Figure 3 shows the shear stress of during direct shear versus horizontal displacement for various samples with diesel percentages ranging from 0 to 13.5%. Figure 3 a-c represent the DST-C results at different normal stresses for the clay samples. As can be seen from the figures, changing the percentage of diesel in each sample significantly increased the shear stress. Figure 3 d-f represent the DST-S results at different normal stresses for the sand samples, and softer effects on the shear stress were observed. This means that diesel has a direct effect on the shear strength properties of clay, whereas the shear failure envelopes for clay and sand samples should be plotted to determine the actual change in the shear strength parameters. Figure 4 a represents the shear failure envelopes acquired from the DST-C for clay samples, and it was found that a significant increase in c and ϕ was noticed by increasing the amount of diesel. The cohesion of clay increased from 38 to 62 kPa by adding 5% diesel, then above this percentage the typical properties of clay fundamentally changed to include an internal friction ϕ of about 30°. According to Khodary et al. (2018) this could be due to the flocculation of the clay particles in the presence of larger amounts of diesel as presented in Fig. 5, leading to an increase in the interlocking forces between particles and accordingly a significant shift in the shear strength behavior. In fact, it was noticed during preparing the clay samples that using more than 10% diesel replaced larger amounts of water, which led to the formation of clay pebbles with clearly different visual characteristics. Figure 4 b shows the shear failure envelop acquired from the DST-S for sand samples. Change in c was almost negligible, but a slight increase of about 5% was noticed in ϕ by increasing the diesel percentage from 10 to 13.5%.

Unconfined compression
The UC was conducted to measure the compressive strength of the clay samples under axial loading. Test procedures followed the ASTM D(2166) D(2166)M-16 2016 after remolding samples inside a plastic tube with diameter 40 mm and length 80 mm. Same diesel-mixing procedures were followed. During remolding, samples were compacted using a 500-g steel flat head rod until reaching the actual unit weight of 18.75 kN/m 3 . The remolded clay samples were removed from the plastic tube and placed inside a 50-kN axial compression machine. A fixed displacement rate of 1.5 mm/min was applied during testing. Tested cylinders are shown in Fig. 6 a and b, which illustrates the apparent changes in clay surface texture after failure. From the figures, it can be noticed that increasing the percentage of diesel to reach 10% and above led to a considerable change in the clay texture, which became rougher with random crumbles and cracks. Results of the UC test for the five clay samples are presented in Fig. 6     compressive strength has increased from 0.14 to 0.21 N/mm 2 by increasing diesel percentage from 0 to 10%. By adding 13.5% diesel, the behavior of clay changed, a peak stress value of about 0.31 N/mm 2 was noticed at 5% strain followed by stress yield. This agrees with the DST-C outcomes, as mixing amounts of diesel ≥ 10% with clay had a significant effect on the material characteristics and led to a noticeable enhancement in its shear strength.
A relationship between the soil resilient modulus (M R ) and diesel percentage in clay was derived from the UC test results. For that purpose, Eq. (1) after Hossain and Kim (2015) was adopted as it was initially developed for small strain ranges to correlate the M R of soil with the unconfined compressive strength (q u ) that can be measured from the UC test. This equation is also quite similar to the one developed by Lee et al. (1997) who provided a correlation between M R and S u1% (where S u1% is the stress corresponding to 1% strain from the UC test outcomes).
From the UC results, the relation between M R and diesel percentage in clay (D c %) was determined and is presented in Fig. 7. As can be seen from the figure, M R for clean clay was about 61.8 MPa, where that value increased to 70.5 and 86.5 MPa by increasing the diesel percentage to 5 and 13.5%, respectively. The figure also includes a simplified quadratic function between M R and D c %.

California bearing ratio
CBR test on sand was conducted using diesel percentages equal to 0%, 2.5%, 5%, 10%, and 13.5%. The test was performed following the dry method as per the ASTM D(1883)-16 2016, and results were correlated with the DST-S outcomes to provide design parameters and charts for roadway engineers. Figure 8 presents the CBR results for the sand samples with various diesel percentages (D s %). It can be seen from the figure that the change in CBR followed a trend that is similar to the soil compaction curve. A noticeable enhancement in the CBR was recorded when the (1) M R = 141.85 q u + 41935.6[kPa]  percentage of diesel was equal to an optimum value of about 10%. Therefore, limited and controlled amounts of diesel may facilitate the compaction of sandy soils, as diesel can provide a stronger interlock between particles and reduce the field effort required for compaction. This finding also agrees with Abousnina et al. (2015) and AbdelSalam and Hasan (2020).

Ultrasonic testing
The ultrasonic test was utilized in this study to obtain a correlation between the pulse wave velocity (V) and other main soil parameters, and that for clean and diesel-mixed clay and sand. The test was also used to determine the dynamic properties of the diesel-mixed soil. Samples were prepared following the previously described diesel-mixing procedures and using the actual unit weight of soil. The ultrasonic standard Pundit laboratory device was utilized, which consists of a transmitter and a receiver as shown in Fig. 9 a. Two frequencies equal to 24 and 500 kHz were attempted during testing. The ultrasonic testing on clay and sand samples is shown in Fig. 9 b and c, respectively, where samples were remolded in an open-ended stainless-steel frame with internal dimensions of 70 × 70 × 70 mm to expedite transmission of the pulse waves.
Results of the ultrasonic test for clean and diesel-mixed clays are presented in Fig. 10 using a frequency equal to 24 kHz using a recipient probe with precision equals to 0.5-µ second. Higher frequency of 500 kHz was attempted with clay, but ideal pulses were not clear, as the frequency of 24 kHz provided higher amplitude. Accordingly, the main   observations for clay were based on the lower frequency. Figure 10 shows the relation between time and amplitude, as a maximum amplitude of 2.4%, 2.54%, 16.8%, and 27% was respectively recorded for clays mixed with 0%, 2.5%, 5%, and 10% diesel. This means that the gained amplitude increased with adding diesel in clay until an optimum of 10%. Figure 11 a presents the measured pulse wave velocity (V) by time lapsed from the first wave front to appear, where V increased by increasing diesel to an optimum percentage of 10% then started to decline again following a parabolic curve. The fastest wave with V equal to 1200 m/s was recorded for clay mixed with 10% diesel. It is believed that using larger amount of diesel exceeding the optimum percentage enabled the fluid to govern the overall behavior of the material; this was also apparent during the mixing and remodeling processes. On the other hand, the wave velocity was correlated with M R for clays as shown in Fig. 11 b. The favored interpretation between V and M R was using two simplified linear correlations to account for the change that occurred in the clay behavior at 10% diesel. The correlations are provided in Fig. 11 b for D c ≤ 9% and > 9%.
The ultrasonic tests were conducted on sand based on the procedures summarized by AbdelSalam and Hasan (2020). The amplitude versus time for clean and dieselmixed sand was measured using frequencies of 24 and 500 kHz. A phase shift between both frequencies was detected, where the smaller frequency had a higher amplitude inside the soil mass. Accordingly, the main observations for sand samples were determined using a frequency of 24 kHz. For clean sand, the maximum amplitude at 24 kHz was around 22.5%.
Relation between pulse wave velocity, V, and percentage of diesel in sand is shown in Fig. 12 a. An increase in V was noticed by increasing diesel to a certain percentage, as peak wave velocity was about 484.1 m/s at 24 kHz, corresponding to an optimum diesel percentage ranging from 8 to 10%. After that, V started to slightly decrease by increasing the diesel percentage. Therefore, changing the amount of diesel in sand affected the wave velocity due to possible variations in the damping properties of the mix. It was also observed from the figure that changes in V resembled the correlation between CBR and diesel percentage. Accordingly, the relation between the pulse wave velocity in sand with respect to CBR at different percentages of diesel in the soil mix was calculated. Figure 12 b represents this relation, whereas a maximum CBR of about 25% was acquired at 10% diesel corresponding to a wave velocity of 490 m/s using a frequency of 24 kHz. It was believed that providing simplified equations of this relation may be more beneficial.
To determine CBR (in percentage) with respect to V at a certain pulse wave frequency, Eq. (2) can be used for sand mixed with diesel percentage, D s % ≤ 9%, and Eq. (3) for sand with diesel percentage, D s % > 9%. where V is wave velocity in m/sec and ω is frequency of source in kHz. As per Putri et al. (2012), an expression can be derived between CBR% and the soil modulus of elasticity, E. Accordingly, Eqs. (4)-(6) were obtained from the laboratory outcomes for sand samples at various ranges of Poisson's ratio, v, which can be eventually linked with Eqs. (2)-(3).
From the previous correlations, a rapid ultrasonic test can be conducted in situ to determine the CBR and modulus of elasticity of clean as well as diesel-mixed soils. This can also help enhance the quality control techniques used in projects that involve large amounts of soil backfill and compaction such as roadway embankments.

Damping based on ultrasonic wave decay
The damping coefficient can be obtained from the decay of a pulse wave with defined peaks, and this is typical for various materials such as concrete and steel. In this study, the damping coefficient for soil (ζ) was determined based on the ultrasonic test measurements in sand and clay, and that for clean as well as diesel-mixed samples. For example, Fig. 13 shows the wave decay envelop that occurred during a pulse wave for a clay mixed with 10% diesel, as this wave provided the highest peak. Accordingly, the rate of decay was defined and used to obtain ζ, where Eq. (7) for under damped vibrating systems with ζ < 1 was used after Chopra (2017).
where C(t) is the equation for the envelope of the received wave, ω n is undamped natural circular frequency, t is time in seconds, and parameter is represented by Eq. (8).
where u(0) is displacement of the received wave at time t = 0, which is the time prescribed at the highest peak that occur during a pulse wave.
(2) CBR% = 7e −4 V + 0.0167 + 0.14 V − 46 for D s % ≤ 9% (3) A received wave consists of a series of interfering frequencies, and it was challenging to determine a specific damped or undamped time periods. Hence, the correlation provided by Chopra (2017) between the damped and undamped natural frequencies (ω D and ω n ) was adopted in this study as presented in Eq. (9). The damped frequency ω D was determined from the wave decay envelop and used in the equation, then ζ was computed by substitution in Eqs. (7) and (8).
The decay envelope was extracted for all other clay samples mixed with diesel percentages equal to 0%, 2.5%, 5%, 10%, and 13.5% diesel, and the results were satisfactory with a high coefficient of determination equal to 0.98. As an example, decay curves for clay with 0% and 5% diesel are presented in Fig. 14 a and b, respectively. Using the available envelopes, the damping coefficient for clays was plotted as presented in Fig. 14 c, whereas a decline in ζ from 0.12 to 0.06 was apparent by changing the diesel percentage from 0 to 10%, though ζ started to increase again to reach 0.10 by adding 13.5% diesel. Values of ζ were comparable to what is stated in the literature for clean clay soils, as Lin et al. (1988) indicated that the damping values range from 0.02 to 0.08 for saturated clean clays under various shear strains using results from the resonant column test. Accordingly, the ultrasonic pulse wave can be used to determine the damping of clay in the case of clean as well as dieselmixed samples.
For the case of diesel-mixed sands, the shortage of a wave with defined peaks made the extraction of the decay envelops quite challenging. Chopra (2017) provided a correlation that requires only two peaks to calculate the damping coefficient. Therefore, the aim in this part was to detect these   Figure 15 b shows change in the damping coefficient with different percentages of diesel in sand. As expected, the trend of the curve is opposite to that previously acquired between diesel and CBR. This means that damping decreased by increasing diesel to an optimum percentage of 10%, then started to increase again after soil stiffness was reduced. Values of ζ varied from 0.18 to 0.26, which is quite different from what was stated in the literature for sands after Lin et al. (1988) who indicated damping values ranging from 0.01 to 0.10 at shearing strains between 0.1 and 10%. This difference could be due to the following: (1) damping acquired from resonant column test depend on cycles of shear strain, while the proposed ultrasonic approach depends on continuous dynamic excitation at a constant shear strain, and (2) damping in the ultrasonic approach is calculated based on the observed natural decay envelop after excitation, where defined peaks must be clear, and this is not the case in some soils with relatively large voids.

Fourier analysis of ultrasonic wave
Additional investigation for the resulted wave frequency was done using Fourier analysis. The analysis was performed using Fourier transform function (FFT). The result wave from the ultrasonic pulse for 24 kHz and 500 kHz for the sand with different percentages of diesel, and for 24 kHz for clay with different percentages of diesel. The analysis was performed to evaluate frequency spectrum, and the resulted spectrum for sand is presented in Fig. 16, the original FFT results domain of frequencies extended from 0 to 500 kHz, while only a small percentage of the resulted frequencies showed significance from 0 to 30 kHz. Two peaks can be observed for each curve, the peak frequency shifts with the increase of diesel content, while greater FFT values can be lined with the ultrasonic pulse wave velocity USPV. For clay, USPV for the 24-kHz pulses were available, whereas the results from FFT analysis are presented in Fig. 17. From the figure, it was clear that the same effect of peak frequency shift was associated with the increase in diesel, while the same double peaks can be observed.

Conclusions
An experimental program including soil basic classification, unconfined compression, direct shear, CBR, and ultrasonic tests was conducted on clean as well as diesel-mixed soils. A wide range of diesel was mixed with these soils starting from 0 to 13.5%. Correlations in the form of design charts and equations were developed for changes in various soil shear strength parameters and diesel percentages. Results were linked with ultrasonic outcomes based on a frequency of 24 kHz. The ultrasonic pulse wave was further analyzed to determine damping coefficient. The main outcomes of this study can be summarized as follows: • By adding 13.5% diesel in clay, plasticity index increased by 72%, unconfined compressive strength increased from 0.14 to 0.31 N/mm 2 , and resilient modulus (M R ) increased from 61.8 to 86.5 MPa. Also using only 5% diesel increased the clay cohesion by 63%. • The amplitude and velocity (V) of the ultrasonic pulse wave increased with increasing the amount of diesel in clay to an optimum value of 10%, after that V declined as diesel started to govern the behavior. A correlation between V and M R was developed to determine the soil modulus using the ultrasonic test. • The effect of adding diesel in sand had a slight effect on the shear failure envelop, as a limited increase of about 5% was noticed in ϕ by adding 13.5% diesel by weight. However, a quite evident enhancement in the CBR was recorded when the diesel percentage in SP was equal to an optimum value of about 10%. • Results from the ultrasonic test in sand showed a parabolic increase in V to 484.1 m/s with the increase in diesel to an optimum percentage of about 9%, also a maximum CBR of 25% was achieved at V equals to 490 m/s using a frequency of 24 kHz. • The damping coefficient (ζ) was determined for clay based on the wave decay envelopes from the ultrasonic test, where values of ζ ranged from 0.12 to 0.06 by changing the diesel percentage from 0 to 10%, respectively. • For sand samples, ζ was determined based on two wave peaks, and the correlation between the percentage of diesel with respect to ζ was opposite to that acquired with respect to CBR. • The introduction of diesel caused an increase in the peak frequency spectrum from the FFT for sand and clay.
Finally, mixing controlled percentages of diesel limited to 10% with soil can significantly enhance its mechanical properties, which is useful for construction and development at locations with already-contaminated soils and other applications such as soil compaction for remote highway embankments. Adding more than this optimum percentage of diesel enabled the fluid to govern the overall behavior of soil. The ultrasonic test was proposed as an uncomplicated

Conflict of interest
The authors declare no competing interests.
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