ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT AZOJETE, September 2019. Vol. 15(3) 777-791 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 777 ORIGINAL RESEARCH ARTICLE EFFECTS OF SOIL PROPERTIES AND OPERATIONAL VARIABLES ON THE COMPACTIBILITY OF A SANDY LOAM SOIL D. Audu1*, O. S. Balogun2, F. A. Adeniji3, and Y. Musa4 (1Department of Soil Science, Federal University of Kashere, Gombe State, Nigeria 2Department of Water Resources and Environmental Engineering, University of Ilorin, Ilorin, Nigeria 3Department of Food, Agriculture and Bio-Engineering, College of Engineering Technology, Kwara State University, Malete, Nigeria 4Department of Agricultural Education, Federal College of Education (Technical), Gombe, Nigeria) * Corresponding author’s email address: danladimsh@gmail.com ARTICLE INFORMATION Submitted 22 November, 2018 Revised 7 March, 2019 Accepted 10 March, 2019 Keywords: Soil Soil Properties Compaction Compaction Efforts Empirical Equation Statistical Significance ABSTRACT The evaluation of an empirical equation for the determination of degree of compaction of a sandy loam soil was carried out using seven soil physical properties and four compaction operational variables. The soil used was obtained from a borrow pit in Gombe. Five levels of compactive effort, E/A, using a drop-weight type compactor varying from 107.91 to 539.55 Nm was used to compact each of seven pairs of embankment and slice thicknesses (Z, z respectively) with Z varying from 210 to 450 mm and z from 30 to 210 mm. The developed empirical equation, π1 = Gπ2k in which π1 is the dimensionless degree of compaction and π2 is a dimensionless combination of the soil properties and the compaction operational variables, has a very high coefficient of determination, r2 varying from 98.8% to 98.9%. G and k are each polynomial functions of compactive effort per loading, eL. that is, G = αGeL2+βG eL + λG and k=αkeL2+βkeL+ λk. The values of the respective α, β and λ are highly statistically significant at 99.95 confidence level. The “dependent” variables (G and k) are highly correlated at 99.95% confidence level of statistical significance with the “independent” variable (eL). The multivariate expression of the degree of compaction obtained in this study shows that compaction depends, not only on cumulative compactive effort, E/A, but also on the compactive effort per loading (eL), embankment and slice thicknesses (Z and z respectively) as well as on easy-to-measure soil properties (i.e. soil texture, soil uniformity coefficient, antecedent soil moisture and antecedent bulk density). © 2019 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. 1.0 Introduction Appropriate response of an engineering soil to compaction is one of the most important qualities sought in civil and agricultural engineering construction activities such as those in building foundations for canals, railroad and highway works, earth embankments and dams, airport runways, sanitary landfills and excavation for structures and retaining walls (Jack, 2007; Davis, 2008). Identification and measurement of the interactions of all relevant factors governing soil compaction still remain major challenges in geotechnics. This study seeks to address some of these challenges. The bulk density (ρbc) of a soil is a measure of soil’s response to compaction mailto:danladimsh@gmail.com http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):777-791. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 778 through rolling, ramming, free falling loads or by consolidation. The degree of compaction or compactibility of a soil Cd is a function of compactive energy (E), the area (A) of the soil on which energy is exerted, soil moisture content (mc), density of water (ρw) in the soil, the mean soil particle size (φ50), thickness of the compaction slice (z), the coarseness of the soil (C/F), where C is coarse fraction of the soil and F is fine fraction, soil’s uniformity coefficient (Uc = φ60/φ10), the soil particle density (ρs), its antecedent bulk density (ρbc), acceleration due to gravity (g), and the time (t) of contact between the compacting load and the soil being compacted. By definition Cd is the ratio of the change in volume (ΔV = V1 – V2) where V1 is soil’s original volume and V2 is final soil volume after compaction to its original volume, V1. A universal function of the type: Cd = f[(E/A), t, C/F, mc, ρw, z, φ50, Uc, ρbc, ρs, g] (1) That simultaneously relates all the eleven independent variables believed to be influencing Cd has not been successfully determined so far. The common practice has been to rely on case- specific model studies for a given project and apply the results to that project type only. That approach lacks the capacity for general application. The determination of the function “f” in Equation 1 is the main problem that requires solution or solutions. The purpose of this study therefore is to evaluate the relationship between the degree of compaction and the easy-to-measure soil properties and compaction operational variables using a soil of given φ50, C/F and Uc. Equation 1, implicitly incorporating eleven independent variables, is a robust function, which has a potential for wide applicability in soil engineering works, such as the construction of canals, roads and earth dams, provided the constituent variables are known and measurable. Compaction is the process of increasing the density of a soil by packing the particles closer together with a reduction in the volume of air within the soil. Maximum compaction of a soil is achieved at the optimum moisture content of the soil (Timothy et al., 2012). This is the water content at which a maximum dry unit weight is reached (Craig, 1978; Sutton, 1986). Although this process involves the expulsion of air from the voids, the moisture content does not change significantly (Bell, 1993). Compaction results in increase in shear strength (Duncan, 1990). The increase in soil density according to Gray (2000) is as a result or consequence of compaction but not the goal. Density is used as a target in engineering soil compaction specifications. The purpose of compaction is to change engineering properties of a soil in a desirable direction. Optimally compacted materials display engineering properties that are substantially superior to the same materials in a loose state (Watson and Burnett, 1995; Werkmeister, 2003; Shestak et al., 2005). Quality of compacted fill is influenced by inter-related factors such as soil type, thickness of compacting layer and the compactive effort. Soil characteristics including grain size (φ50), gradation (Uc) and clay or fine content (C/F), play an important role in soil behaviour under compaction. In coarse-grained soils, there exists an inter-granular contact and compaction processes brings about re-arrangement of soil particle positions. The way in which these particles are arranged within the soil mass and the distribution of particle sizes throughout, will ultimately determine the degree of compaction and hence the density, stability and the bearing capacity of the soil. Therefore, the maximum compaction can be achieved by the best packing of well-graded soil where the fine grains fill the spaces between the large grains. However, surplus file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Audu, et al: Effects of soil properties and operational variables on the compactibility of a sandy loam soil. AZOJETE, 15(3):678-691. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 779 of fines can be detrimental by preventing inter-granular contact between coarse particles (Mosaddeghi et al., 2000; Shaqour, 2004). Effective compaction of earth materials can be achieved by applying the proper mechanical energy to a soil layer of suitably specified optimum thickness. An optimised compactive effort may be described as one that results in obtaining the compaction required from making the correct number of falls or passes, over a layer of optimum thickness. In a field, an optimum thickness, 200 to 300 mm is normally recommended (Watson and Burnett, 1995). The thickness of the compacting layer varies with grain size and compactive effort. Generally, coarse-grained soils compact more readily than fine grained ones and hence the finer the particles the thinner the maximum layer to be compacted (Shaqour, 2004; SCH., 2005). 2. Materials and Methods 2.1 The Study Area Gombe Metropolis is located between latitude 10° 0' N and 10° 20' N and longitude 11°01' E and 11° 19' E and lies in the stretch of Benue trough. It consists majorly two types of soils corresponding to the two geological formations from which they are derived; sandy soil found in the northwest underlain by keri keri formation and clayey soil which occurs to the south and southeast (Mbaya, 2012). Sandy loam soil could also be found in some parts of the metropolis, especially, in the north (Audu, 2014). Gombe Metropolis has two distinct climates: the dry season which begun from November to March and the rainy season, from April to October with an average rainfall of 969.7 mm (Yahaya, 2015). 2.2 Description of the Compaction Device Figure 1 shows the sketch of the compaction device that was constructed and used for this study. As depicted, it consists of the following components: (a) Compactor and bearings; (b) Mould; (c) Removable Plate; and (d) Steel Rod. Figure 1: The Compaction Device http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):777-791. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 780 2.2.1 The Compactor and bearings The compactor, cylindrical in shape, was constructed of concrete with cement, fines and coarse sand ratio of 1:2:4 by mixing 3.143 kg cement, 6.286 kg of fine sand and 12.571 kg of coarse sand with 2.2 litres of water and cured for 21 days, yielding 22 kg dry weight. The bearings were purchased. The cylindrical shaped compactor has a diameter of 305 mm and made 2 mm smaller than the diameter of the mould in order to allow its free in-and-out movement into the mould during compaction. The thickness of the compactor was 193 m with a circular hole at the centre to allow the steel rod to pass through and for the bearings to be situated inside as shown in Figure 1. The bearings slide along the steel rod up and down during compaction. This helps to reduce friction that may occur between the steel rod and the compactor during compaction process. 2.2.2 The mould This is also cylindrical in shape, and was constructed with 2 mm thick sheet metal according to the shape of the compactor. Its height was 500 mm and inner diameter was 307 mm, which was 2 mm larger than that of the compactor in order to allow free in-and-out movement of the compactor into it during the compaction process. It is built strong enough to withstand the pressure of the compacting force. 2.2.3 The removable plate This is of the same shape and diameter as the compactor and as the name implies, it is removable and constructed of the same material as the mould. It is placed at the base of the compactor to allow even distribution of compactive effort during the compaction process. It has a circular hole, 2 mm greater than the external diameter of the steel rod, at its centre, for the steel rod to pass through. 2.2.4 The steel rod This is a rigid, cylindrical structure placed vertically up at the bottom centre of the mould, passing through the drilled hole of the removable plate and the compactor, with an 85 mm thick (mahogany) wooden plate fixed at the base of the steel rod. The steel rod guides the compactor through the height of free fall during the compaction process. It was 1500 mm long. 2.3 Compaction Equipment The compaction facilities consist of the fabricated compaction device shown in Figure 1 and moisture sprayer, sieves, pestle, scoop, knife, mixing pan, balances, drying oven, cans and polythene bags (Mann, 2006). Table 1 lists the specifications of the compaction equipment. file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Audu, et al: Effects of soil properties and operational variables on the compactibility of a sandy loam soil. AZOJETE, 15(3):678-691. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 781 Table 1: Specifications of the Compaction Equipment S/N Definition/Description Quantity/value Units 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Cross sectional area Weight Height of drop Height of mould Height of rod Diameter of compactor Thickness of compactor Diameter of mould Cement : fine sand : coarse sand Water at 70% of the cement by wt. 0.07309 215.82 0.5 0.5 1.5 0.305 0.193 0.324 3.143 : 6.29 : 12.57 2.2 m2 N m m m m m m kg litres 2.4 Soil Sample Preparation The soil used was obtained in Federal College of Education (Technical), Duku road, Gombe, Nigeria. It was air-dried, aggregates present in the sample were broken down gently, using pestle and mortar to maintain the natural size of the individual particles. Soil particles larger than 76.2 mm are gravels and were discarded as the soil was characterized and classified geotechnically according to the system adopted by AASHTO Standard No. M 145–91 (1995). The soil samples were then kept in polythene bags for compaction. 2.5 Compaction Procedure A soil sample of 3.55 kg, whose physical characteristics such as texture was determined according to Braja (1986) was used to obtain uniformity coefficient and coefficient of curvature, particle density according to Blake (1965), bulk density according to Heed (1992), porosity by Nyle and Ray (1999) and moisture content by ASTM D 2216 (1998), was considered. The particle unit weight, bulk unit weight and unit weight of water were also calculated by multiplying the values of the particle density, bulk density and the moisture content by 9.81 m/s2. The soil sample was then taken and spread evenly over a flat surface of area, A = 0.07309 m2 in the mould, and its thickness, 30 mm was measured using a ruler placed vertically on the soil surface inside the mould. A compactor weight of 215.82 N was released from a height of 0.5 m, to drop one time on the soil layer; the new thickness was measured. Another soil “slice” (2 loadings), of thickness 30 mm was spread evenly on the previous slice, a new pre-compacted thickness was determined. Compactive effort was applied and a new compacted soil thickness was measured from which the new compaction was obtained. The above procedures were repeated until the desired “pavement” thickness of 210 mm was reached or slightly exceeded. The above procedures were repeated for 2, 3, 4 and 5 drops representing multiples of compacting energy per loading for the same soil thickness of 30 mm loaded in each case. The whole procedures were repeated for 60 mm, 90 mm and 120 mm, 150 mm, 180 mm and 210 mm soil thicknesses. From dimensional analysis, degree of compaction, π1=ΣΔZ/Z and the governing variables, π2 = (Ecφ50(C/F)Uc) (Aγbcz3Se) for the 5 levels of compactive effort per loading was established. Multiple regression analysis was used to analyse the data to estimate the connection between http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):777-791. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng 782 Corresponding author’s e-mail address: danladimsh@gmail.com degree of compaction, π1 and the governing variables, π2 and by how much. This provided an equation for the prediction and plotting of relationships. p-value and correlation coefficient were given to indicate the accuracy of the model. 3. Results and Discussions Table 2 shows the results of the dry-sieving test which is used to obtain the grading curve (Figure 2) by plotting % passing versus sieve opening. From the hydrometer analysis, silt and clay particles were found to be 8% and 19%, respectively. Table 2: Results of Sieve Analysis Sieve opening (mm) Soil weight retained (g) Soil weight passing (g) Percent retained (%) Percent passing (%) 14 131.8 3868.2 3.295 96.705 5 267.3 3600.9 6.683 90.023 1.18 556.8 3044.1 13.920 76.103 0.3 2055.4 988.7 51.385 24.718 0.075 636.6 352.1 15.915 8.803 Pan 349.6 0.0 0.0 0.0 From the grading curve (Figure 2), φ10 = 0.11, φ30 = 0.34, φ50 = 0.49 and φ60 = 0.68, all φ values are in mm. From these data, Uniformity coefficient Uc = φ60/φ10 = 0.68/0.11 = 6.18 and the coefficient of curvature, Cc = (φ30)2/(φ60φ10) = (0.342)/0.68 x 0.11 = 0.1156/0.0748 = 1.55. According to Budhu (2004), a well graded soil is a soil with a uniformity coefficient (Uc) greater than 6 and coefficient of curvature (Cc) greater than 1 but less than 3. From the result of this analysis, the soil used was a well graded sandy loam soil and indicated that there was a wide spread of soil particle distribution of sand, silt and clay in the soil used, which is expected to compact well. Figure 2: Percentage Soil Particle Size Distribution Table 3 below shows the physical properties of the soil used in the study. From the Table, the energy deliverable per drop by the compactor of weight 215.82 N from a height of 0.5 m (i.e. 215.82 N x 0.5 m) was 107.91 N. The Table also shows that the coarse to fine fraction ratio (C/F) https://www.statisticshowto.datasciencecentral.com/p-value/ https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/correlation-coefficient-formula/ file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Audu, et al: Effects of soil properties and operational variables on the compactibility of a sandy loam soil. AZOJETE, 15(3):678-691. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 783 was 2.7 and uniformity coefficient was 6.18; the unit weight of soil particle; bulk soil and water were 26045.55, 15882.5 and 9810 Nm-3 respectively. In table 4 column 8, the quantity of soil used for the compaction test was 1505 kg. Table 3: Soil Physical Properties S/N Item/Notation Definition/Description Quantity/Values Units 1. 2. 3. 4. 5. 6. 7. 8. 9. Texture φ50 Uc = φ60/φ10 C F C/F γbc γs γw Sandy loam Mean particle diameter Uniformity coefficient Coarse fraction Fine fraction Coarse:fine ratio Initial antecedent unit weight Particle unit weight Unit weight of water 1505 0.49 6.18 73% 27% 2.7 15882.5 26045.55 9810 kg mm - - - - Nm-3 Nm-3 Nm-3 3.1 Processed Compaction Data Table 4 shows the compaction test data for 7 levels of soil slice thicknesses, LST 1–7 and 5 levels of compactive effort per loading, LEL 1–5. According to the table, one drop of the compactor released an energy, eL of 107.91 Nm per loading or 755.37 Nm at the end of the 7th loading. Thus, the cumulative compactive effort, Ec, was 755.37 Nm achieving a cumulative soil compaction ΣΔZ = 49.5 mm from Z = 210 mm thick of uncompacted soil at 15882.5 Nm3 unit weight to a “pavement” of thickness Z′ = 160.5 mm at 19677.3 Nm-3 unit weight. The last column shows the loading-by-loading computed degrees of compaction ΔZ/Zι varying from 18.33% to 5.31% for LST = 1 and loading ι = 1 to ι = 7. Increasing values of eL at multiples of 107.91 Nm per loading carry similar information as described above. Table 4: Test Data Record “Matrix” for 7 Levels of Soil Slice Thickness (LST) for the 1st Level of Compactive effort (eL) per Loading LEL & eL (1) 107.91 Nm/Loading LST z Z Ɩ Ec ZƖ ΔZ m γbc Se ΔZ/ZƖ x102 1 30 210 1 107.91 30.0 5.50 3.55 15882.5000 0.0469 18.3333 2 215.82 54.5 6.00 7.10 17485.3000 0.0557 11.0092 3 323.73 78.5 6.50 10.65 18209.2000 0.0608 8.2803 4 431.64 102.0 7.00 14.20 18685.2130 0.0648 6.8627 5 539.55 125.0 7.50 17.75 19058.8641 0.0682 6.0000 6 647.46 147.5 8.00 21.30 19381.9568 0.0715 5.4237 7 755.37 169.5 9.00 24.85 19677.3295 0.0748 5.3097 mc = 1.83% http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):777-791. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng 784 Corresponding author’s e-mail address: danladimsh@gmail.com 2 60 300 1 107.91 60.0 8.50 7.10 15882.4737 0.0989 14.1667 2 215.82 111.5 9.50 14.20 17093.2452 0.1123 8.5202 3 323.73 162.0 11.00 21.30 17647.1930 0.1197 6.7901 4 431.64 211.0 11.50 28.40 18065.3729 0.1260 5.4502 5 539.55 259.5 12.00 35.50 18361.2412 0.1308 4.6243 mc = 3.86% 3 90 450 1 107.91 90.0 12.00 10.65 15882.4737 0.0551 13.3333 2 215.82 168.0 13.50 21.30 17016.9361 0.0620 8.0357 3 323.73 244.5 14.50 31.95 17538.9280 0.0658 5.9305 4 431.64 320.0 15.00 42.60 17867.7829 0.0685 4.6875 5 539.55 395.0 16.00 53.25 18093.9573 0.0704 4.0506 mc = 2.15% 4 120 360 1 107.91 120.0 14.50 14.20 15882.4737 0.0794 12.0833 2 215.82 225.5 17.50 28.40 16903.7414 0.0883 7.7605 3 323.73 328.0 18.00 42.60 17431.9833 0.0937 5.4878 mc = 3.10% 5 150 450 1 107.91 150.0 16.50 17.75 15882.4737 0.1207 11.0000 2 215.82 284.0 17.00 35.50 16777.2609 0.1324 5.9859 3 323.73 417.5 18.00 53.25 17118.8339 0.1374 4.3114 mc = 4.71% 6 180 360 1 107.91 180.0 18.50 21.30 15882.4737 0.2132 10.2778 2 215.82 343.0 20.50 42.60 16669.6317 0.2311 5.9767 mc = 8.32% 7 210 420 1 107.91 210.0 19.00 24.85 15882.4737 0.1545 9.0476 2 215.82 403.0 22.00 49.70 16552.4539 0.1654 5.4591 mc= 6.03% Se = ((γbc/γw)/(1-(γbc/γs))*mc, mc=gravimetric dry weight soil moisture content, γw, γs and γbc are as given in Table 3. Test data record matrix for 7 levels of soil slice thickness (LST) for the 2nd, 3rd, 4th and 5th levels of compactive effort (eL) per loading convey the same trend of information with increasing relative magnitude of the coefficients in the polynomial function and power functions as the compactive effort increased. file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Audu, et al: Effects of soil properties and operational variables on the compactibility of a sandy loam soil. AZOJETE, 15(3):678-691. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 785 3.2 Dimensionless Degrees of Compaction Functions 3.2.1 The version of π1 versus π2 relationship Table 5: Input - Output Data for Computing π1 and π2 LEL 1 2 3 4 5 LST eL , Nm 107.91 215.82 323.73 431.64 539.55 1 z = 30, Z = 210 Se 0.0469 0.0469 0.0469 0.0469 0.0469 Ec 755.37 1510.74 2266.11 3021.48 3776.85 ƩΔZ 49.5 59 63.5 69 71.5 2 z = 60, Z = 300 Se 0.0989 0.0989 0.0989 0.0989 0.0989 Ec 539.55 1079.1 1618.65 2158.2 2697.75 ƩΔZ 52.5 57.5 59.5 61.5 63.5 3 z = 90, Z = 450 Se 0.0551 0.0551 0.0551 0.0551 0.0551 Ec 539.55 1079.1 1618.65 2158.2 2697.75 ƩΔZ 71 80 85.5 87 92 4 z = 120, Z = 360 Se 0.0794 0.0794 0.0794 0.0794 0.0794 Ec 323.73 647.46 971.19 1294.92 1618.65 ƩΔZ 50 54 61 66 69.5 5 z = 150, Z = 450 Se 0.1207 0.1207 0.1207 0.1207 0.1207 Ec 323.73 647.46 971.19 1294.92 1618.65 ƩΔZ 51.5 61.5 70 77 82 6 z = 180, Z = 360 Se 0.2132 0.2132 0.2132 0.2132 0.2132 Ec 215.82 431.64 647.46 863.28 1079.1 ƩΔZ 39 46 51 54.5 56.5 7 z = 210, Z = 420 Se 0.1545 0.1545 0.1545 0.1545 0.1545 Ec 215.82 431.64 647.46 863.28 1079.1 ƩΔZ 41 50.5 57.5 62.5 64.5 π1 = ƩΔZ/Z; π2 = [Ucφ50 (C/F)/(Aγbc)](Ec/(Sez3)); where z=Soil Slice Thickness, mm; Z = Total Soil Thickness in mm to be compacted; Ec=Cumulative Compactive effort, Nm. Table 5, derived from Table 4, contains the information required to compute the degree of compaction, http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):777-791. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng 786 Corresponding author’s e-mail address: danladimsh@gmail.com π1=ΣΔZ/Z (2) and the governing variables, π2 = (Ecφ50(C/F)Uc) (Aγbcz3Se) (3) for the 5 levels of compactive effort per loading. Here, the cumulative compactive efforts, Ec was used. The version of π1 versus π2 was discussed hereunder. From Table 5, another table, Table 6 was derived to determine the version of the multivariate soil compaction function. 3.2.2 Function “weighted” by compactive effort per loading, eL and its use Each of the five pairs of columns in the main entries in Table 6 showing π1 and π2 also has its own unique characteristics namely, its magnitude of compactive effort per loading, eL in Nm/loading. This is reflected in the “best fit” regression curves, also power curves of the type: π1 = Gπ2k π2 = ΔZ = G(Ecφ50(C/F)Uc)/(Aγbcz3Se)b (4) Where: π1 and π2 are as defined in Table 7, “G” is the coefficient and “k” the exponent which took different values as MEL varied. As in section 3.2.3, G and k were regressed, but this time both on eL from 107.91 to 539.55 Nm/loading. Figures 3 to 7 derived from Table 6 show the coefficients “G”, exponents “k”, determination coefficients r2 varying from 0.925 to 0.985, averaging 0.955 and each with its own “G” and “k” as listed in Table 7. Table 6: The Values of π1 (Y) and π2 (X) for 7 Levels of Soil Slice Thickness (LST) and 5 Levels of Compactive effort per Loading (LEL) LEL 1 2 3 4 5 MEL = eL 107.91 215.82 323.73 431.64 539.55 LST MST, mm π1x104 π2 π1x104 π2 π1x104 π2 π1x104 π2 π1x104 π2Z Z 1 30 210 2357 4201.466 2810 8402.932 3024 12604.400 3286 16805.860 3405 21007.330 2 60 300 1750 177.853 1917 355.705 1983 533.558 2050 711.410 2117 889.263 3 90 450 1578 94.613 1778 189.227 1900 283.840 1933 378.453 2044 473.066 4 120 360 1389 16.619 1500 33.237 1694 49.856 1833 66.475 1931 83.093 5 150 450 1144 5.597 1367 11.194 1556 16.791 1711 22.388 1822 27.985 6 180 360 1083 1.222 1278 2.445 1417 3.667 1514 4.890 1569 6.112 7 210 420 976 1.062 1202 2.124 1369 3.186 1488 4.249 1536 5.311 Notations: π1 = ΣΔZ/Z for C/F = 2.7, A = 0.07308895m2, Uc = 6.18, φ50 = 0.49 mm, γbc = 15882.5 N, π2 = Ec(C/F)φ50Uc/(SeγbcAz3) becomes π2 = ((C/F) φ50Uc/Aγbc)(Ec/Sez3)) = 7.043325 x 10-6(Ec/Sez3). file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Audu, et al: Effects of soil properties and operational variables on the compactibility of a sandy loam soil. AZOJETE, 15(3):678-691. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 787 Figure 3: π1 vs π2 for 107.91 Nm compactive effort Figure 4: π1 vs π2 for 215.82 Nm compactive effort Figure 5: π1 vs π2 for 323.73 Nm compactive effort Figure 6: π1 vs π2 for 431.64 Nm Compactive effort Figure 7: π1 vs π2 for 539.55 Nm compactive effort Table 7: Power Function π1 = G π2k, Coefficient “G”, Exponent “k” Determination Coefficient r2 and eL for the eL-Governed Variations S/N From Figures 3 – 7 Compactive Effort per Loading “G” “k” r2 eL, Nm 1. 2. 3. 4. 5. 1006 1104 1211 1276 1310 0.102 0.097 0.089 0.086 0.086 0.985 0.981 0.966 0.925 0.927 107.91 215.82 323.73 431.64 539.55 http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):777-791. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng 788 Corresponding author’s e-mail address: danladimsh@gmail.com With the data derived from Figures 3 to 7 and listed in Table 7 above, both “G” and “k” were regressed on eL as polynomial expressed in the following equations G = αG eL2+βGeL+λG (5) and shown in Figure 8, and k = αk eL2+βkeL+λk (6) shown in Figure 9 where: αG = -0.001, βG = 1.398, λG = 862.4, r2 = 0.996 for “G”; and αk = 9x10-8, βk = -1x10-4, λk = 0.112, r2 = 0.975 for “k”. Within the limits of dependability of r2 from 0.975 to 0.996, equations (5) and (6) can be used to obtain best values for “G” and “k” for specified values of “eL”. From that, π1 = ΣΔZ/Z can be computed for specified values of the governing variables in π2. Figure 8: Coefficient “G” of π1 versus π2 against eL Figure 9: Exponent “k” of π1 versus π2 against eL 3.2.3 Coefficient in the polynomials Table 8 shows the respective values of α, β and λ for G and k. The correlation coefficient of Y with X varied from 0.987 to 0.988 each indicating a high confidence level of statistical significance. Table 8: The Polynomial Coefficients Data Matrix for Calculating the Coefficients and Exponents of Sandy Loam Soil Degree of Compaction Equation: π1 = Gπ2k Function Y = αX2+βX+λ Correlation Y X Α Β Λ R t-test G K eL eL -0.001 9x10-8 1.398 -1x10-4 862.4 0.112 0.988 0.987 HS* HS * = Highly significant at 99.95 Confidence Level. 3.3 Comparison of the Estimator with the Measured Values of Degree of Compaction Table 9 shows the calculated values of the degree of compaction (π1)c (i) = Gπ2k and its corresponding ratio with measured value (π1)m= ΣΔZ/Z. file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng Audu, et al: Effects of soil properties and operational variables on the compactibility of a sandy loam soil. AZOJETE, 15(3):678-691. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 789 Table 9: Comparison of Estimated Values with Measured Value of Degree of compaction of Sandy Loam soil S/No Variables Validation Test 1 2 1. 2. 3. Measured π1 = ΣΔZ/Z Gπ2k Ratio, %100[Gπ2k/(ΣΔZ/Z)] 0.2357 0.2167 97.79 0.2357 0.1745 97.98 From the above data, it is obvious that the function Gπ2k estimated the degree of compaction of sandy loam soil accurately; G and k could be correlated significantly with eL in this study. 4. Conclusion The foregoing has described a study of compaction behaviour of a sandy loam soil. Among many others, eleven quantifiable factors believed to be governing the compaction, ΣΔV of the soil volume V have been identified and grouped to develop a multivariate compaction function using a “drop-weight” compactor designed and constructed for this study. From Table 8, G and k can be computed for use in estimating the degree of compaction π1 = ΣΔZ/Z = ΣΔV/V for any combination of the eleven governing factors encapsulated in π2 as π1 = Gπ2k. The other estimator aπ2b is weak. It needs more data from many other soils to characterize “a” and “b” more vigorously. Two validation test results show that the procedure is durable for a large number and a wide range of operating variables with respect to sandy loam soil and “drop- weight” compactor. The two estimators passed the t-test of statistical significance of correlation r of estimator with measured values of degree of sandy loam soil compaction. The usefulness of the procedure is that one does not need to carry out trial compaction tests to know the degree of compaction of sandy loam soil from a given borrow site before knowing its response to a given set of operating conditions, provided the easy-to-measure variables in π2 are known. References AASHTO 1995. 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Thesis, Department of Agricultural and Environmental Resources Engineering, University of Maiduguri, pp. 41. http://www.ohioagriculture.gov/pubs/curr/rules http://www.astm/standards/D698.htm http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2019; Vol. 15(3):777-791. ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng Corresponding author’s e-mail address: danladimsh@gmail.com 790 Bell, FG. 1993. Engineering Treatment of Soils. E and IN Spon, an Imprint of Chapman and Hall, London, pp. 302. Blake, GR. 1965. Particle Density. In: Black, C. A. Ed., Methods of Soil Analysis, Part I, Physical and Mineralogical Properties. American Society of Agronomy. Madison, Wisc. pp. 371-373. Braja, MD. 1986. Soil Mechanics. 2nd Edition. Engineering Press, Russia. pp. 96. Budhu. M. 2004. Soil Mechanics and Foundations. 3rd Edition. John Wiley and Sons: NY 2000. pp. 350-352. Craig, RF. 1978. Soil Mechanics. Van Nostrand. Reinhold Ltd; London, pp. 317. 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Watson, I. and Burnett, AD. 1995. Hydrology and Environmental Approach. Buchanam Books, Cambridge, pp.702. Werkmeister, S. 2003. Permanent Deformation Behaviour of Unbound Granular Materials in Pavement Construction. M. Sc. Thesis in University of Technology, Dresden, Germany, 10th February, 2013. pp.79 http://www.azojete.com.ng