NAPOVED KALIFORNIJSKEGA INDEKSA NOSILNOSTI (CBR) IN LASTNOSTI ZGOSTITVE ZRNATIH ZEMLJIN Ključne besede CBR, regresija, model, napoved, karakteristike zgostitve Izvleček V pričujoči študiji je podan poskus korelacije indeksnih lastnosti zrnatih zemljin s kalifornijskim indeksom nosilnosti (CBR) in lastnosti zgostitve. Na naravnih in kompozitnih vzorcih peskov so bile skladno z ASTM metodami izvedene klasifikacija zemljin, modificirani Proctorjev preizkus in CBR preizkus. Rezultati laboratorijskih preiskav so pokazali, da vzorci v študiji spadajo med kategorije SW, SP in SP-SM, skladno s sistemom enotne klasifikacije zemljin in v skupini A-1-b in A-3, skladno z AASHTO klasifikacijskim sistemom. Na podatkih eksperimentov je bila izvedena multipla linearna regresijska analiza in razvite korelacije za napoved CBR, maksimalne suhe gostote in optimalne vlažnosti glede na indeksne lastnosti vzorcev. Med različnimi parametri so se za napovedovanje izkazali za najboljše koeficient enakomer-nosti (Cu), velikost zrn pri 30 % presejku (D30) in pri 50 % presejku (D50). Predlagani modeli za napoved zgornjih lastnosti so bili potrjeni na bazi neodvisnih podatkov CBR preizkusov peščenih zemljin. Primerjalni rezultati kažejo, da je variacija med eksperimentalnimi in napovedanimi rezultati za CBR znotraj ±4 % intervala zaupanja, in za maksimalno suho gostoto ter optimalno vlažnost znotraj ±2 %. Na osnovi korelacij, razvitih za CBR, maksimalno suho gostoto in optimalno vlažnost, so predlagane napovedovalne krivulje za hitro oceno teh lastnosti na osnovi Cu, D30 in D50. Predlagani modeli in napovedovalne krivulje za oceno CBR vrednosti in lastnosti zgostitve so lahko zelo uporabni v geotehničnem inženirstvu in dimenzioniranju voziščnih konstrukcij, ne da bi izvedli laboratorijske preiskave zgostitve in CBR preizkuse. Attique ul Rehman (vodilni avtor) University of Lahore, Department of Civil Engineering Lahore, Pakistan E-posta: attiq.engr@gmail.com Khalid Farooq University of Engineering and Technology, Department of Civil Engineering Lahore, Pakistan Hassan Mujtaba University of Engineering and Technology, Department of Civil Engineering Lahore, Pakistan 10. Acta Geotechnica Slovenica, 2017/1 PREDICTION OF CALIFORNIA BEARING RATIO (CBR) AND COMPACTION CHARACTERISTICS OF GRANULAR SOILS Keywords CBR, regression, model, prediction, compaction characteristics Abstract This research is an effort to correlate the index properties of granular soils with the California Bearing Ratio (CBR) and the compaction characteristics. Soil classification, modified proctor and CBR tests conforming to the relevant ASTM methods were performed on natural as well as composite sand samples. The laboratory test results indicated that samples used in this research lie in SW, SP and SP-SM categories based on Unified Soil Classification System and in groups A-1-b and A-3 based on the AASHTO classification system. Multiple linear regression analysis was performed on experimental data and correlations were developed to predict the CBR, maximum dry density (MDD) and optimum moisture content (OMC) in terms of the index properties of the samples. Among the various parameters, the coefficient of uniformity (Cu), the grain size corresponding to 30% passing (D30) and the mean grain size (D50) were found to be the most effective predictors. The proposed prediction models were duly validated using an independent dataset of CBR tests on sandy soils. The comparative results showed that the variation between the experimental and predicted results for CBR falls within ±4% confidence interval and that of the maximum dry density and the optimum moisture content are within ±2%. Based on the correlations developed for CBR, MDD and OMC, predictive curves are proposed for a quick estimation based on Cu, D30 and D50. The proposed models and the predictive curves for the estimation of the CBR value and the compaction characteristics would be very useful in geotechnical & pavement engineering without performing the laboratory compaction and CBR tests. Attique ul Rehman (corresponding author) University of Lahore, Department of Civil Engineering Lahore, Pakistan E-mail: attiq.engr@gmail.com Khalid Farooq University of Engineering and Technology, Department of Civil Engineering Lahore, Pakistan Hassan Mujtaba University of Engineering and Technology, Department of Civil Engineering Lahore, Pakistan 1 INTRODUCTION An appropriate and sound foundation is always required for the construction of all kinds of engineering projects, especially those involving large quantities of earth works, like pavements, runways, railway formations and pavement embankments, etc. Bearing capacity, swell potential and the settlement of different layers of pavements should be within tolerable limits. Therefore, it is necessary to have reliable methods to access the engineering properties of such projects. The California Bearing Ratio (CBR) is one of the most common methods to design and assess the strength of different pavement layers by comparing them with the strength of standard California crushed rock. The CBR value is used to determine the thickness of pavement layers and also to evaluate the shear strength and stiffness modulus of sub-grade material. Similarly, an evaluation of the compaction characteristics (OMC and MDD) for 10. Acta Geotechnica Slovenica, 2017/1 Attique et al.: Prediction of California Bearing Ratio (CBR) and Compaction Characteristics of granular soil projects involving large quantities of earthworks is also an essential requirement, and these parameters are also used in the evaluation of the CBR value. Both the CBR value and the compaction characteristics are very much dependent on soil gradation and other index properties in the case of granular soils. Engineers encounter many difficulties in obtaining a reliable CBR value because of insufficient soil investigation data and limited time during the pre-feasibility stages of the project. At least 4 days are required to generate a soaked CBR value for a single soil specimen and multiple CBR tests are required on subgrade samples along the length of the pavement to obtain a representative design CBR value. In order to save time during the pre-feasibility stages, researchers have therefore developed prediction models to correlate the CBR value with various index properties of the soils. As mentioned earlier, the CBR value is mainly dependent on various index properties of the soil; therefore, many researchers have conducted research studies to understand the effect of soil type and soil characteristics on the CBR value of both coarse-grained and finegrained soils. Based on their research, various researchers including Agarwal and Ghanekar [1], National Cooperative Highway Research Program(NCHRP)[2], Breytenbach [3], Roy et al. [4], Ferede [5], Patel and Desai [6], Saklecha et al. [7], Yildirim and Gunaydin [8], Singh et al. [9], Taha et al. [10] and Talukdar [11] have proposed correlations to predict the CBR value for vari- ous types of soils based on their index properties. These correlations are summarized in Table 1, followed by their relevant discussion. Agarwal and Ghanekar [1] used forty-eightfine-grained soil samples to correlate the CBR value with the liquid limit (LL) and optimum moisture content (OMC). The National Cooperative Highway Research Program (NCHRP) [2] presented a correlation between the grain size corresponding to 60% passing (D60) and the CBR value. The applicability of the proposed correlation is limited for D60 varying between 0.01 mm to 30 mm. The recommended value of CBR is 5 when D60 is less than 0.01 mm and the CBR value is 95 when D60 is greater than 30 mm. Breytenbach [3] correlated the CBR value with the plasticity index (PI) and grading modulus (GM) based on the research work conducted on a variety of soils present in various parts of South Africa. Roy et al. [4] proposed an equation to estimate the CBR value on the basis of the maximum dry unit weight, the unit weight of water and the optimum moisture content for fine-grained soils. Ferede [5] developed correlations to predict the CBR value using D6o , the optimum moisture content (OMC) and the maximum dry density (MDD) for granular soils and liquid limit (LL), plastic limit (PL), plasticity index (PI) and percentage of fines (F200) for fine-grained soils. Pateland Desai[6] proposed correlations to estimate the soaked and unsoaked CBR values based on compaction parameters (MDD and OMC) and the plasticity index of fine-grained soil. Saklecha et al. [7] performed multiple Table 1. Correlations for predicting CBR proposed by various researchers. Correlations Reference CBR = 2 - log(OMC) + 0.07 LL Agarwal and Ghanekar (1970) CBR = 28.09 (D60)0358 NCHRP (2001) CBR = 26.382 x (0.458 PI) + 5.278 GM Breytenbach (2009) log CBR = log(Ydmax / Yw) - log OMC Roy et al. (2009) CBR = 68.789 - 11.925 D60 + 0.897 D602 - 0.02 5 D603 CBR = -27.998 + 0.029 OMC2 + 4.796 MDD4 Ferede (2010) CBR = 4.175 - 0.029 LL- 0.009 F200 CBR(Soaked) = 43.907 - 0.093 Ip - 18.78 MDD - 0.3081 OMC Patel and Desai (2010) CBR(Unsoaked) = 17.009 - 0.0696 Ip - 0.296 MDD + 0.0648 OMC CBR = 0.26O MC + 42.55 MDD - 73.62 Saklecha et al. (2011) CBR = 0.22 G + 0.045 S + 4.739 MDD + 0.122 OMC Yildirim and Gunaydin (2011) CBR(Soaked) = -2.213 - 0.055[(MC/OMCjx100] + 0.328[(Density/MDD)x100] - 1.147 PL Singh et al. (2011) CBR = 0.025 F2004 + 30.130(MDD) - 25.813 Taha et al. (2013) CBR(Soaked) = 0.127 LL - 0.16 PI + 1.405 MDD - 0.259 OMC + 4.62 Talukdar (2014) CBR = California Bearing Ratio, LL = Liquid limit, PL = Plastic limit, PI = Ip = Plasticity index. OMC = Optimum moisture content, MDD = Maximum dry density, Ydmax = Maximum dry unit weight, yw = Unit weight of water, D60 = grain size corresponding to 60% passing, G = Percentage of gravels, S = Percentage of sand, F200 = Percentage of fines, GM = Grading modulus 64. Acta Geotechnica Slovenica, 2017/1 Attique et al.: Prediction of California Bearing Ratio (CBR) and Compaction Characteristics of granular soil regression analyses to correlate the CBR with the compaction parameters (MDD and OMC) of sub-grade soil. Yildirim and Gunaydin [8] utilized fine-grained as well as coarse-grained soils comprising a wide range of grain sizes to develop prediction models for the estimation of CBR values based on the compaction parameters (MDD and OMC), the percentage of gravel (G) and the sand content (S). Singh et al. [9] collected five different soils from West Bengal and tested them in the laboratory at four different compaction energy levels and five different moisture contents. A prediction model for soaked CBR was proposed by considering the effect of the degree of compaction and moisture content. Taha et al. [10] correlated the CBR value with the index properties of Egyptian soil. They found after their study that the percentage of fines (F2oo) and MDD are the most effective parameters to predict the CBR value. Talukdar [11] used multiple linear regression analysis (MLRA) to correlate the soaked CBR value with the index properties of fine-grained soil from the Assam state of India. Also, various researchers proposed correlations to predict the compaction characteristics based on soil index properties. Sivrikaya et al. [12] focused on the prediction of compaction parameters for granular soils and used two approaches, named multiple linear regression (MLR) and Genetic Expression Programming (GEP), to develop correlations. Mujtaba et al. [13] used granular soil samples to propose predictive models using gradation parameters and compaction energy (CE) for predicting the maximum dry unit weight (ydmax) and the optimum moisture content (OMC). The prediction models presented by [13] are given in Eq.(1)and Eq. (2), respectively. Omar et al.[14] developed prediction models to estimate the compaction characteristics of granular soil present in the United Arab Emirates.The prediction models developed in their research are presented in Eqs. (3) and (4). Noor et al. [15] collected 106 samples of fine-grained soils from various Indian Hydropower projects to develop prediction models for the estimation of compaction parameters given in Eq. (5) and Eq. (6). Boltz et al. [16] proposed correlations for fine-grained soil based on the liquid limit (LL) and the compaction energy (E), as presented in Eqs.(7) and (8). Sridharan and Nagaraj [17] found that only the plastic limit (op) can give good estimates of compaction parameters. Their proposed correlations are presented in Eqs. (9) and (10). Ydmax = 4.49 log(CJ + 1.51 log(CE) + 10.2 (1) log OMC (%) = 1.67 - 0.193 log(Cu) - 0.153 log(CE) (2) Pdmax(kg/m3) = [4804574 Gs - 195.55(LL2) + 156971(R#4) - 9527830] i0.5 (3) ln(o0) = 1.195x10-4 (LL2) - 1.964 Gs - (4) 6.617x10-3 (R#4) + 7.651 MDD = VPL - 0.089 LL + 33.97/(PL+1.37) + 19.05 (5) OMC = PI/G + 3.424 + 0.462 PL - G (6) MDD = (2.27 log LL - 0.94) log E - 0.16 LL + 17.02 (7) OMC = (12.39 - 12.21 log LL)log E + 0.67 LL + 9.21 (8) Ydmax = 0.23(93.3 - op) (9) OMC = 0.92 oP (10) The present research is mainly focused on proposing prediction models to estimate the CBR, the MDD and the OMC in the case of granular soils present in various areas of the Punjab province of Pakistan, based on their index properties. The index parameters including D50, D30 and Cu obtained from the results of grain size analysis were used for the estimation of the CBR, MDD and OMC of the coarse-grained soils. 2 MATERIALS AND METHODS_ The major sources of soil samples were local deposits of granular soils commercially known as Ravi, Chenab and Lawrencepur sands, which have been used in this study. A total of seventy soil samples were tested, including natural sand samples and composite sand samples prepared by mixing the above-mentioned sands in different proportions. The soil samples were classified as poorly graded sand (SP), well-graded sand (SW) and poorly graded sand with silt (SP-SM),as per the Unified Soil Classification System (USCS) [18]. Similarly, according to the AASHTO classification system, soil samples lie in A-1-b and A-3 groups [19]. All the tests were conducted on every sample according to the standard test procedures described in the relevant ASTM standards. The grain size analysis test was performed in accordance with ASTM-D422 [20], where a modified Proctor compaction test was carried out in the laboratory following the test procedure of ASTM-D1557 [21]. For the determination of the California Bearing Ratio (CBR), soil samples were compacted at optimum moisture content, corresponding to the maximum dry density, which was obtained by performing a modified Proctor test on every sample. Compacted soil samples were then soaked in water for 96 hours under excess weight as specified in a standard test procedure. Afterwards, the samples were tested in a CBR machine by penetrating a plunger in soil samples 64. Acta Geotechnica Slovenica, 2017/1 Attique et al.: Prediction of California Bearing Ratio (CBR) and Compaction Characteristics of granular soil at the specified rate stipulated in ASTM-D1883 [22]. All the experimentation was performed in the Geotechnical Engineering Laboratory of Civil Engineering Department, University of Engineering and Technology, Lahore, Pakistan. A summary of the results based on the above-mentioned tests is shown in Table 2. The outcomes of the laboratory tests were analyzed using multiple linear regression analysis to develop prediction models for the estimation of the California Bearing Ratio (CBR) and the compaction characteristics. A statistical package for the social sciences (SPSS) software was utilized to perform multiple linear regression analysis. Before starting the analysis process, data was divided into two categories, i.e., the input and the output parameters. For predicting the CBR value, the CBR value was considered as an output parameter and parameters like D30 , D50 , Dg0 , Cu , MDD and OMC were considered as probable input parameters. For predicting the compaction characteristics, OMC and MDD were the output parameters, whereas D30 , D50 , Dg0 and Cu were possible input parameters. The poten- tial input parameters for the prediction of the CBR value and the compaction characteristics were identified as D30 , D50 and Cu , on the basis of passing t-test, while the rest of the parameters were neglected. The formulated correlations were calibrated using simple linear regression analysis by having a plot between the experimental and the predicted results. The developed prediction models are validated using an independent database, which was not used in the development of the models. A correlation coefficient, a standard error of estimates and a relative error of estimates for every prediction model were examined to check the reliability of the developed models. 3 RESULTS AND DISCUSSIONS The laboratory test results and the classification group based on the USCS and AASHTO classification system of the tested soil samples are summarized in Table 2. Table 2. Test data used for the development of the predictive models. No D10 D30 D50 D60 g OMC MDD CBR USCS Clas- AASHTO ' mm mm mm mm_u_C_S_% kN/m3 %_sification Classification 51 0.10 0.18 0.25 0.36 3.79 0.95 2.67 15.4 18.4 13_SP_A-3 52 0.13 0.18 0.25 0.30 2.31 0.83 2.70 13.1 17.6 10_SP_A-3 53 0.11 0.19 0.24 0.32 2.91 1.03 2.66 12.2 18.6 13 SP-SM_A-3 54 0.30 1.00 2.20 2.40 8.00 1.39 2.72 8.2 21.9 24_SW_A-1-b 55 0.28 0.90 2.30 2.40 8.57 1.21 2.65 8.2 21.9 34_SW_A-1-b 56 0.21 0.48 0.74 0.90 6.00 1.22 2.60 12.0 20.0 21_SW_A-1-b 57 0.19 0.28 0.50 0.58 3.05 0.71 2.63 11.6 20.0 16_SP_A-1-b 58 0.17 0.27 0.45 0.60 3.53 0.71 2.71 12.4 20.1 14_SP_A-1-b 59 0.12 0.22 0.36 0.47 3.92 0.86 2.69 11.1 18.1 8_SP_A-3 510 0.17 0.30 0.73 1.30 7.65 0.41 2.72 11.2 20.3 20_SP_A-1-b 511 0.16 0.21 0.28 0.33 2.06 0.84 2.64 13.4 19.4 7_SP_A-3 512 0.15 0.20 0.27 0.45 3.00 0.59 2.70 14.8 19.2 13_SP_A-3 513 0.15 0.21 0.25 0.32 2.13 0.88 2.65 14.0 19.3 11_SP_A-3 514 0.16 0.21 0.28 0.32 1.97 0.88 2.60 13.5 19.2 12_SP_A-3 515 0.16 0.20 0.27 0.31 4.50 0.82 2.63 12.3 19.3 12_SP_A-3 516 0.14 0.19 0.26 0.29 2.07 0.89 2.71 13.1 19.5 7_SP_A-3 517 0.12 0.19 0.22 0.27 4.20 1.06 2.72 12.0 19.0 14 SP-SM_A-3 518 0.19 0.19 0.25 0.56 4.50 0.35 2.64 14.5 19.2 16_SP_A-3 519 0.13 0.20 0.26 0.48 3.69 0.61 2.70 13.8 19.4 6_SP_A-3 520 0.13 0.19 0.25 0.51 3.92 0.54 2.67 14.8 19.0 10_SP_A-3 521 0.10 0.17 0.21 0.25 2.60 1.20 2.65 11.9 18.5 12 SP-SM_A-3 522 0.12 0.18 0.23 0.27 2.35 1.04 2.60 13.7 18.6 12 SP-SM_A-3 523 0.12 0.19 0.24 0.28 2.33 1.07 2.63 14.0 18.7 12 SP-SM_A-3 524 0.13 0.20 0.25 0.30 2.27 0.99 2.71 13.8 18.8 12_SP_A-3 525 0.13 0.19 0.25 0.30 2.31 0.93 2.65 12.9 18.9 14_SP_A-3 526 0.16 0.22 0.33 0.43 2.74 0.73 2.61 11.6 19.4 12_SP_A-3 527 0.16 0.25 0.30 0.52 3.25 0.75 2.68 12.4 18.7 6 SP A-3 64. Acta Geotechnica Slovenica, 2017/1 Attique et al.: Prediction of California Bearing Ratio (CBR) and Compaction Characteristics of granular soil r No D10 D30 D50 D60 OMC MDD CBR USCS Clas- AASHTO ' ' mm mm mm mm u c s % kN/m3 % sification Classification 528 0.16 0.23 0.40 0.45 2.90 0.76 2.72 12.5 19.0 10_SP_A-3 529 0.17 0.19 0.88 1.00 5.88 0.20 2.65 12.8 19.8 18_SP_A-3 530 0.17 0.18 0.20 0.53 3.12 0.36 2.60 13.2 19.7 9_SP_A-3 531 0.13 0.17 0.22 0.25 1.92 0.89 2.63 13.7 17.8 11_SP_A-3 532 0.17 0.19 0.92 1.20 7.06 0.18 2.70 11.7 20.5 20_SP_A-3 533 0.14 0.19 0.22 0.27 7.96 1.01 2.63 13.5 18.4 12_SW_A-3 534 0.23 0.41 0.53 0.73 3.17 1.00 2.71 11.3 20.2 8 SP-SM_A-1-b 535 0.18 0.44 1.50 1.70 9.71 0.65 2.69 9.7 21.2 24_SP_A-1-b 536 0.16 0.20 0.75 0.80 5.00 0.30 2.72 13.0 18.9 9_SP_A-3 537 0.15 0.20 0.26 0.30 2.07 0.92 2.64 11.8 19.1 8_SP_A-3 538 0.16 0.21 0.90 1.20 7.50 0.22 2.65 11.6 19.4 14_SP_A-3 539 0.17 0.22 1.20 1.40 8.48 0.21 2.60 11.2 19.6 17_SP_A-3 540 0.15 0.22 0.70 1.00 6.67 0.32 2.63 11.6 18.9 9_SP_A-3 541 0.17 0.25 1.00 1.30 7.65 0.28 2.71 10.0 21.2 19_SP_A-3 542 0.18 0.27 1.40 1.70 9.71 0.25 2.63 10.1 20.4 21_SP_A-3 543 0.17 0.26 1.00 1.55 9.39 0.26 2.71 11.8 20.1 19_SP_A-3 544 0.23 0.30 0.56 0.76 3.30 0.51 2.69 10.3 20.8 10_SP_A-1-b 545 0.16 0.20 0.24 0.27 1.69 0.88 2.70 13.6 18.3 9_SP_A-3 546 0.17 0.20 0.80 1.10 6.47 0.20 2.63 14.6 18.5 13_SP_A-3 547 0.18 0.21 0.60 0.67 6.50 0.38 2.71 11.2 20.5 20_SP_A-3 548 0.16 0.22 0.30 0.37 2.31 0.82 2.69 11.2 19.0 13_SP_A-3 549 0.18 0.26 1.30 1.50 8.33 0.25 2.72 11.4 20.2 18_SP_A-3 550 0.18 0.30 0.54 0.71 3.94 0.70 2.64 11.2 20.4 12_SP_A-1-b 551 0.19 0.47 1.10 1.20 6.32 0.97 2.68 12.0 20.5 21_SP_A-1-b 552 0.20 0.50 0.90 1.30 6.50 0.96 2.63 11.0 20.8 20_SP_A-1-b 553 0.22 0.55 1.00 1.50 6.82 0.92 2.71 11.0 21.4 21_SP_A-1-b 554 0.21 0.57 1.30 1.70 8.10 0.91 2.69 9.2 21.0 29_SP_A-1-b 555 0.22 0.60 1.30 1.85 8.41 0.88 2.72 9.0 21.2 28_SP_A-1-b 556 0.28 0.88 1.40 1.80 6.43 1.54 2.64 9.3 21.6 24_SW_A-1-b 557 0.27 0.83 1.90 2.10 9.00 1.21 2.60 8.9 21.7 29_SW_A-1-b 558 0.33 1.10 2.20 2.60 7.88 1.41 2.63 8.2 21.0 34_SW_A-1-b 559 0.32 0.90 2.10 2.70 8.44 0.94 2.71 8.3 21.5 33_SP_A-1-b 560 0.30 1.00 2.20 2.80 9.33 1.19 2.68 8.1 21.9 35_SW_A-1-b 561 0.10 0.14 1.10 1.50 5.00 0.13 2.63 11.5 19.0 20_SP_A-3 562 0.17 0.12 1.60 2.40 4.12 0.04 2.70 11.0 18.5 27_SP_A-1-b 563 0.90 1.20 1.70 1.90 2.11 0.84 2.63 11.0 19.2 32_SP_A-3 564 0.07 0.11 1.50 1.80 5.71 0.10 2.71 11.0 19.6 33_SP_A-3 565 0.60 0.90 1.20 1.30 2.17 1.04 2.69 9.5 20.9 22 SP-SM_A-3 566 0.60 0.90 1.20 1.50 2.50 0.90 2.72 7.5 21.4 23_SP_A-3 567 0.40 0.60 2.20 2.50 6.25 0.36 2.64 6.5 21.6 32_SP_A-1-b 568 0.90 1.60 2.00 2.40 2.67 1.19 2.65 9.5 19.5 26 SP-SM_A-1-b 569 0.10 0.40 0.70 0.90 9.00 1.78 2.60 9.5 18.7 24_SW_A-3 570 0.70 1.10 1.40 1.60 7.29 1.08 2.63 7.5 20.7 32 SW A-1-b Based on the grain size analysis, it can be inferred that the samples used in the study contain a sand content (percent passing 4.75 mm, and percent retained on 0.075 mm) varying between 80 and 100 %. The gravel content (percent retained on 4.75 mm) in the samples varies from 0 to 20% and the fines (percent finer than 0.075 mm) vary from 0 to 7%. The mean grain size (D50) of all the samples is in the range 0.2 mm to 2.3 mm and the effective grain size (D10) is in the range 0.45 mm to 0.07 mm. The particle sizes at 30% and 60% passing (D30 and D60) were also determined from the grain size analysis curve. The coefficient of uniformity (Cu = D60/D30) of 64. Acta Geotechnica Slovenica, 2017/1 Attique et al.: Prediction of California Bearing Ratio (CBR) and Compaction Characteristics of granular soil the tested samples ranges from 1.7 to 9.7 and the coefficient of curvature (Cc=D302/D60xD10) varies in between 0.04 and 1.78. The specific gravity of the samples is in the range 2.60-2.72. The results of the modified Proctor and CBR tests presented in Table 2 indicated that the maximum dry density (MDD) ranges from 17.64kN/ m3 to 21.92kN/m3 and the optimum moisture content (OMC) ranges from 6.5% to 15.4% and the CBR values vary from 6 to 35. More specifically, the MDD for the SP samples varies from 17.64kN/m3 to 21.6kN/m3, while for the SP-SM samples it fall between 18.45kN/m3 and 20.89kN/m3 and for the SW samples it varies from 18.37kN/m3 to 21.92kN/m3. The OMC for the SP samples varies from 6.5% to 15.4%, while for the SP-SM samples it falls between 9.50% and 14%,and for SW samples it varies from 7.5% to 13.5%. Similarly, the CBR for the SP samples varies from 6% to 33%, while for the SP-SM samples it falls between 8% and 26%, and for the SW samples it varies from 12% to 35%. The laboratory test results mentioned in Table 2 were analyzed using multiple linear regression analysis to develop prediction models for the estimation of the California Bearing Ratio (CBR) and the compaction characteristics. A statistical package for the social sciences (SPSS) software was utilized to perform multiple linear regression analysis. The best-fit prediction models obtained as a result of the regression analysis carried out on the test data presented in Table 2 are as follows: SEE = CBR = 6.508D50 + 1.48Cu + 3.970 (R2 = 0.85) (11) MDD = 0.171Q + 2.408D30 + 18.168 (R2 = 0.81) (12) OMC = 0.026Cu - 2.53D50 + 13.456 (R2 = 0.74) (13) D50 and D30 are the grain sizes corresponding to 50% finer and 30% finer, respectively and D50 and D30 are in mm for the above-mentioned equations. The coefficient of determination is a quantitative measure to represent how well the predicted results are replicated by the model. The standard error of estimate (SEE) is a quantitative measure to check the variance between the predicted and the experimental results. The relative standard error of the estimate is obtained by dividing SEE by the mean of the output values to provide a standard measure of fit. The formulated correlations in the present research have high values for the coefficient of determination (R2) and relatively low values for the standard error of the estimate (SEE) and the relative standard error of the estimate. The SEE was computed mathematically; exp erimental -ypredicted f (14) where v = Degree of freedom = number observa- tions - number of variables y experimental = Experimental results ypredicted = Predicted results The SEEs for Eqs.(11), (12) and (13) are 3.13, 0.49 and 0.93, respectively. The SEE values indicate that the proposed models have a good prediction capability. Analysis of variance (ANOVA) is carried out to determine the F- statistic for the output parameters and the t-statistics for input parameters for Eqs. (11), (12) and (13). The model F value for Eq.(11) is 147.7,for Eq.(12) is 105.63 and for Eq.(13) is 69.35. These values of the F- statistic are greater than the critical F, indicating that Eq.(11), (12) and (13) are significant. Similarly, absolute t- statistics for the input parameters for these equations are greater than the t- significance of the model. Figures 1, 2 and 3 represent a comparison between the experimental and predicted results of CBR, MDD and OMC using equations (11), (12) and (13), respectively. These plots show that the variation between the experimental versus the predicted results for CBR are within ±4% confidence interval and within ±2% confidence interval for both the MDD and OMC. The prediction models developed in this research were validated using an independent database. For this purpose, laboratory test results from 37 samples were utilized, which were not used in the development process of the models. The experimental results from the laboratory data were plotted against the predicted values using the proposed models, as represented in Figures1, 2 and 3, which show that the predicted results almost fall within the confidence interval of ±4% for CBR and±2% for both MDD and the OMC. The correlations proposed by NCHRP (National Co-operative Highway Research Program) [2], Ferede [5] and Saklecha et al. [7] were used for comparison purposes of the CBR value. The predictions using the above-mentioned correlations are plotted in Figure 4. The predictions made by the NCHRP[2] correlation show that 7 out of 37 predictions fall outside ±4% confidence interval. The predictions made by Ferede's [5] correlation show that 10 out of 37 predictions fall outside ±4% confidence interval, and the predictions by Saklecha [7] correlation show that 11 out of 37 predictions fall outside ±4% confidence interval. The probable reason for this variation is the different v 68. Acta Geotechnica Slovenica, 2017/1 Attique et al.: Prediction of California Bearing Ratio (CBR) and Compaction Characteristics of granular soil 40 30 * 20 S3 U •o u o ¡3 2 10 PL, CBR = 1.48C„ + 6.508Dc„ + 3.97 .4 1:1 line 4"i 10 20 30 Experimental CBR (%) 40 Figure 1. Experimental vs Predicted values of CBR by Eq. (11). 8 10 12 14 Experimental OMC(%) Figure 3. Experimental vs Predicted OMC by Eq. (13). 17 18 19 20 21 22 23 24 Experimental MDD (kN/m3) Figure 2. Experimental vs Predicted MDD by Eq. (12). mineralogical composition, soil texture, fabric and deposition mode of the soils present in various regions of the world. The correlations presented by Mujtaba et al. [13] and Omer et al.[14] were used for predicting the compaction characteristics using validation data. It can be observed from Figures 5 and 6 that the predicted results of the MDD and OMC fall almost within the ±2% envelopes, except for a few predicted results that exceed the prediction band of ±2%. Figure 5 illustrates that the predictions by Eq. (3) show that 8 out of 37 predictions fall outside the ±2% confidence interval. Whereas the predictions by Eq. (1) show that 13 out of 37 predictions fall outside the ±2% confidence interval. The soil samples used in this ♦ Present work ANCHRPEq. OFerede Eq. □ Saklecha et al. Eq. 12 16 20 24 Experimental CBR (%) Figure 4. Experimental vs Predicted values of CBR by various models using the validation data. Acta Geotechnica Slovenica, 2017/1 69. Attique et al.: Prediction of California Bearing Ratio (CBR) and Compaction Characteristics of granular soil § S 13 28 26 - 24 - 22 - 20 - 1 18 £ 16 - 14 -' 12 ♦ Present Work □ Mujtaba et al., Eq. o Omer et al., Eq. 12 + 2 %, 14 16 26 28 18 20 22 24 Experimental MDD (kN/m3) Figure 5. Experimental vs Predicted MDD by various predictive equations using validation data. 21 19 17 15 13 11 9 7 5 3 1 ♦ Present Work □ Mujtaba et al., Eq, O Omer et al., Eq. + 2% O