Microsoft Word - 001.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 66, 2018 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Songying Zhao, Yougang Sun, Ye Zhou Copyright © 2018, AIDIC Servizi S.r.l. ISBN 978-88-95608-63-1; ISSN 2283-9216 Effects of Different Porosities on Shear Strength of Fiber Clay by Response Surface Methodology Chunpeng Hana, Jiayi Tiana, Jian Zhanga, Yulong Heb,* aSchool of Civil Engineering, Northeast Forestry University, Harbin 150040, China bChina School of Transportation, Jilin University, Changchun 130012, China heyl15@mails.jlu.edu.cn To study the effects of different factors (fiber length, fiber content and porosity) on the shear strength of fiber reinforced soil, the direct shear test of 3 levels and 3 factors was designed by response surface methodology (RSM) to explore the effects of different factors on the increment of shear strength parameters and construct polynomial regression equation of each effect factor. The test results showed that internal friction angles of fiber soil and plain soil were very close in different porosities, and increment of cohesion was changed after mixing fiber. From the analysis of variance (ANOVA), fiber content was the main factor, followed by porosity, and the fiber length and porosity had strong interaction significance; the validity of the theoretical model of fiber pull-out in soil was checked. From the test, the porosity variable influenced the effect of fiber reinforced soil cohesion, and porosity of soil should be considered in the engineering program of fiber reinforced soil. 1. Introduction Aim to fiber reinforced soil technology Researchers have studied how to obtain the optimum mix ratio of fiber soil by mixing different fibers in the different soils to enhance its strength and the ability to resist deformation. Y. Yilmaz (2015) investigated the effects of discrete polypropylene fibers and Class C fly ash on the stress–strain and shear strength behavior of clayey soil. Pradip et al., (2012) investigated the effects of random inclusion of polypropylene fibers on strength characteristics of cohesive soil. Shao et al., (2014) investigated the mechanical properties of sands reinforced with discrete randomly distributed fiber. Wu et al., (2015) investigated the mechanical properties of randomly distributed sisal fiber reinforced soil. Butt et al., (2016) investigated the strength behavior of clayey soil reinforced with human hair as natural fibers. Zaimoglu et al., (2012) investigated the strength behavior of fine-grained soil reinforced with randomly distributed polypropylene fibers. Qu and Sun, (2016) investigated the strength behavior of Shanghai clayey soil reinforced with wheat straw fibers. 2. Materials and methods 2.1 Materials Table 1: Physical properties of soil samples Specific gravity Gs Maximum dry density ρd(g/cm3) Optimum water content ωopt (%) Liquid limit ωL (%) Plastic limit ωP (%) Plasticity index IP (%) 2.65 1.86 11.4 33.3 24.0 9.3 Table 2: Physical and mechanical parameters of polypropylene Density (g/cm3) Breaking tensile strength (MPa) modulus of elasticity (MPa) elongation Diameter (μm) Melting point (℃) 0.96 500 3850 10-28 18-48 165 DOI: 10.3303/CET1866186 Please cite this article as: Han C., Tian J., Zhang J., He Y., 2018, Effects of different porosities on shear strength of fiber clay by response surface methodology, Chemical Engineering Transactions, 66, 1111-1116 DOI:10.3303/CET1866186 1111 The test soil sample was taken from a construction foundation pit in Harbin. The main physical parameters of sample soil used in test were provided in Table 1. Fiber used in the test is regular engineering polypropylene fibe. The main physical and mechanical parameters of the polypropylene fiber were given in Table 2. 2.2 Preparation of sample and test The soil samples obtained from the foundation pit were naturally air-dried, then crushed for screening with a 2mm sieve. The best water content of the soil compaction test was used, and water, soil and fiber were then mixed evenly. The fiber length was 3mm, 6mm, 9mm, 12mm and the quality percentage of the dry soil was regarded as fiber content. The preparations of samples were carried out by using the static pressure method. The diameter and height of sample was respectively 68.1mm and 20mm. The SDJ-Ⅱtype three-speed electric strain direct shear instrument was used to test. The controlling loading rate was 0.8mm/min for shearing, and the test last for3-5minutes, and 0.01mm dial indicator was used to control shear displacement measurement accuracy. Every group of the shear test took four of the same specimens, which were under the vertical cutting pressure of 50, 100, 200, and 300kPa. 2.3 Experimental design Previous trials (Tang et al., 2009) showed that the strength of fiber reinforced soil depended on the friction between fiber and soil particles mainly, so a Box-Behnken Design (BBD) was used to investigate the effects of 3 independent variables (porosity (X1), fiber content (X2) and fiber length (X3)) on the shear strength parameters. The independent variables were coded at three levels, and the complete design consisted of 17 experimental points carried out in a random order. The experimental design, including the uncoded and coded independent factors (Xi) and experimental levels, were showed in Table 3. Table 3: Coded levels for 3 variables formed by BBD Factors Codes coded levels -1 0 1 porosity 0.4 0.3 0.5 fiber content 1‰ 3‰ 5‰ fiber length 6 9 12 2.4 Statistical analysis In RSM, the relationship between input variables and the resulting response value were explained by the following equation.Where the output response value y depended on the input variables x1, x2,…, xi by the response surface f; and ε represented the statistical error. 1 2( , )iy f x x x  L (1) According to the formula (1), the behavior of the system was represented by the following formula. 1 2 0 1 1 1 1 k k k k i i ii ii ij i j i i i j i Y x x x x                   (2) Where Y represented the shear strength parameters (Δc,ΔФ) of 2 kinds of soil, β was the undetermined coefficients that were estimated by building response function with the commonest method to estimate β being the least square method, and β0 was the constant; βi(i=1,2,3) was the linear coefficient, βii was the quadratic coefficient of xii, βij was the coefficient of interaction effect. The accuracy of the response surface for the shear strength parameters could be analyzed by statistical analysis. ANOVA was used to evaluate the differences of test samples. According to the results obtained from the direct shear test, the test data was processed by ANOVA, and a fitting second-order regression model represented by formula (2) was constructed. Based on the obtained response surface equations, the optional conditions for fiber mixing were obtained. 3. Results and discussion 3.1 Single factor analysis 3.1.1 Fiber length According to reference (Wu and Zhang, 2010), 3‰ fiber content PP fibers were selected as initial experimental materials. Direct shear strength test was conducted on fiber soil specimens with different fiber lengths (3mm, 6mm, 9mm and 12mm) and results were compared with the direct shear test results of plain soil. Shear strength 1112 parameters, after data processing, were shown in Fig. 1. Figure 1: Shear strength parameters of polypropylene fiber reinforced soil with different lengths As shown in Fig. 1(a), there was a significant increase in the cohesion with increasing length of fiber from 3mm to 12mm, which peaked at a length of 9mm and then decreased. And it also could be seen from Fig. 1(b) that the internal friction angle of the fiber soil grew slowly with the increase of fiber strength. the 9mm fiber was selected as test materials. 3.1.2 Fiber content According to above test results, 9mm was the best length to improve shear strength of clay. So 9mm was selected as the testing fiber length. Direct shear tests were conducted on fiber soil specimens with different fiber contents (0‰, 1‰, 2‰, 3‰, and 4‰). Shear strength parameters could be determined by the results of direct shear tests, and the results were shown in Fig. 2. Figure 2: Shear strength parameters of polypropylene fiber reinforced soil with different fiber contents It could be seen from Fig. 3(a) that there was an obvious increment in cohesion along with the increase of fiber content up to 3‰ and then a decrease in cohesion was observed. And Fig. 2 showed that adding fiber would increase the cohesion, and the internal friction angle of fiber soil had little change with different contents. Part of the shear force was assumed by the soil itself in the process of shearing, and the others were transformed from the friction force between the soil particles and the fibers to the tensile force of the fibers. With the increment of fiber content, the distribution of fiber in soil increase, the total tensile strength of the fibers in the shear failure occurred, and the cohesion of the soil was greater. 3.1.3 Porosity Figure 3: Shear strength parameters of polypropylene fiber reinforced soil with different porosities 1113 The soil density at different porosities (0.3%, 0.4%, 0.5%, and 0.6%) was calculated, and the corresponding quality of the soil and fiber (9mm, 3‰) was taken out for the shear test. The trend of shear strength parameters of fiber soil and plain soil under different porosities was shown in Fig. 3. The cohesion of fiber soil and plain soil decreased exponentially with the increase of porosity, and cohesion of fiber soil was greater than that of plain soil; the internal friction angle of two soils decreased in the form of the power function, and the trend of internal friction angle of two soils under different porosities was almost coincident. With the increase of porosity, the reinforcement effect of the fiber on the cohesion of the soil increased at first and then decreased, and the fiber reinforcement effect was at its best when porosity was 0.4. 3.2 Response surface analysis Combined with single factor test results, fiber content, fiber length and porosity were used as response factors, with 3‰, 9mm, 0.4 used as a center, a direct shear test was carried out according to BBD design. The results of cohesion differences were displayed in the last column in Table 4. The maximum cohesion difference was 50.4kPa in run 14, while the minimum cohesion difference was 0.28kPa in run 7. Multiple regression analysis was used to analyze the cohesion differences from Table 4, and a quadratic polynomial equation was derived from regression analysis as follows: Table 4: Results of BBD of response surface methodology Factor 1 Factor 2 Factor 3 Response Std Run A:e B:l mm C:n ‰ Cohesion different kPa 16 1 0.40 9.00 3.00 39.07 1 2 0.30 6.00 3.00 15.25 12 3 0.40 12.00 5.00 20.39 2 4 0.50 6.00 3.00 20.72 8 5 0.50 9.00 5.00 19.39 11 6 0.40 6.00 5.00 15.03 4 7 0.50 12.00 3.00 22.28 15 8 0.40 9.00 3.00 38.89 6 9 0.50 9.00 1.00 14.02 3 10 0.30 12.00 3.00 25.19 14 11 0.40 9.00 3.00 40.1 5 12 0.30 9.00 1.00 14.81 7 13 0.30 9.00 5.00 14.68 13 14 0.40 9.00 3.00 40.4 9 15 0.40 6.00 1.00 12.66 17 16 0.40 9.00 3.00 38.14 10 17 0.40 12.00 1.00 21.23 Table 5: ANOVA for response surface quadratic model Source Sum of Squares Df Mean Square F Value p-value Prob > F Model 1783.39 9 198.15 227.23 < 0.0001 A-e 5.25 1 5.25 6.02 0.0439 B-l 80.84 1 80.84 92.69 < 0.0001 C-s 5.73 1 5.73 6.57 0.0374 AB 17.56 1 17.56 20.13 0.0028 AC 7.56 1 7.56 8.67 0.0216 BC 2.58 1 2.58 2.95 0.1294 A^2 423.69 1 423.69 485.85 < 0.0001 B^2 299.13 1 299.13 343.02 < 0.0001 C^2 774.63 1 774.63 888.28 < 0.0001 Residual 6.1 7 0.87 Lack of Fit 2.69 3 0.9 1.05 0.4621 Pure Error 3.41 4 0.85 Cor Total 1789.49 16 1 2 3 1 2 1 3 2 2 2 2 3 1 2 3 39.32 0.81 3.18 0.85 2.1 1.38 0.8 10.03 8.43 13.56 Y x x x x x x x x x x x x           (in coded term) (3) 2 2 3 1 2 1 3 2 2 2 2 3 1 2 3 262.10 852.83 21.11 19.22 6.98 6.86 0.134 1003.13 0.94 3.39 Y x x x x x x x x x x x x            (in actual factors) (4) 1114 Where Y was the response variable (cohesion difference), x1 was the coded value of porosity, x2 was the coded value of fiber length, and x3 was the coded value of fiber content. From Table 5, the model F value of 227.23 with a low probability P value indicated high significance of the model. And the viscosity variation coefficient C.V% of cohesion was 3.11, so the coefficient of variation was small. A plot of experiment results versus the predicated value was showed in Fig. 4, actual test results and predicated values were very close, indicating high reliability of test results so that the tests could be analyzed by a model of two regression equation instead of the real point test. As a further check, the normality test of residuals was carried out (see Fig.5). It was obvious that all the test points were approximated in a straight line, and the results were distributed as the normal distribution. Figure 4: Normal plot of residuals for Figure 5: Plot of predicted values versus actual values cohesion difference of cohesion difference According to the ANOVA results in Table 5, porosity, fiber length and fiber content were all significant factors that influence cohesion of fiber soil. And the result P(B)