MODELING AND SIMULATION OF MECHANICAL PROPERTIES OF PULVERIZED COW BONE AND LATERITIC PAVING TILES

This study included the experimental production and investigation of the mechanical properties of paving tiles produced from a mixture of laterite, silica sand, pulverized cow bones, and cement. Empirical models of compressive and flexural strength were also developed and herein presented for the paving tiles. The maximum compressive strength of the paving tiles were obtained for 20, 15, and 10% cement content as 5.05, 5.05 and 3.08 MPa, while the maximum flexural strength for similar values of cement content were obtained as 1.83, 1.21 and 0.26 MPa respectively. The results indicate that there was no noticeable difference in the values of the compressive strength at 20 and 15% cement content, while a sharp reduction of the mechanical properties was experienced as the cement content reduces from 15 to 10%. Recommended composition for paving tiles with pulverized cow bones composite is cement, 15%; pulverized cow bones, 30%; laterite 35% and silica sand, 20% respectively. Sustainable production of paving tiles and a sustainable environment can, therefore, be enhanced by replacing granite constituent with waste cow bones, which can easily be replicated by the empirical models herein developed.


INTRODUCTION
Global consciousness on the environment has been on the increase in recent years, which has engineered several existing environmental protection programs not only to focus on protecting the natural resources, but also to instigate the judicious use of waste materials, and curtail the level of environmental damage. It is of good benefit and importance for developing countries around the world to seek means to create a sustainable development in order to key into such protection programs. The increasing population of the world has propelled both private and public organizations to constantly embark on infrastructural development, a scenario that has encouraged the use of building accessories and products such as paving tiles. It is therefore imperative to constantly explore sustainable materials to develop some of the infrastructural products that would guarantee a sustainable environment [1].
Several applications are being developed to make use of discarded animal bones, in the field of biomedical engineering; animal bones have been used as reinforcement and binding agents for different composite applications such as polyesters, epoxies etc. [2][3]. The potentials of pulverized animal bones as pozzolanic material was also established by Falade et al. [4] and was found to exhibit good pozzolan character. Therefore, recycled waste bones are considered as a composite material for the production of paving tiles in this study.
Paving tiles are usually of different shapes and sizes; they range from square, rectangle, star shape etc. The standard thicknesses are usually 60 mm with common dimensions of 60 x 30, 40 x 40, and 30 x 30 cm [5][6]. In Nigeria, the conventional materials used in the production of paving tiles are granite, silica sand, and cement as a binder. Making use of bones in the production of paving tiles will not only help clean the environment of the ugly pile of bones in abattoirs but would also provide a sustainable means of production, due to its availability. Furthermore, the breaking strength of 9.9 kg makes it a suitable substitute for granite particles in paving tiles productions [7]. Several works have been conducted on the use of readily available and affordable materials in the manufacturing of paving tiles. Ohijeagbon et al. [1] used laterite as a partial replacement of granite in the production of interlocking tiles due to the availability of laterite. Ajao and Ohijeagbon [8] successfully utilized corncobs, an agro-waste and charcoal to produce paving tiles, but the sustainability of corncobs waste presents a limitation due to the seasonal availability of agricultural wastes. Therefore this study aim at investing the impact of pulverized cow bones on the mechanical propertie of paving tiles and creating a model to predict the mechanical properties of produced paving tiles for future application.

Laboratory Experiment
The raw materials used were laterite, silica sand, pulverized cow bones and cement. The particle sizes of materials used were 1000, 500 and 4750 µm respectively. Mass of materials required to cast a unit tile were weighed according to the proportion of aggregate mix presented in Table 1. The constituents were thoroughly mixed together before the addition of water and further mixing was done to obtain a homogeneous mixture. Each unit of tile was mixed independently to avoid rapid setting of the mixture. A mold size of 200 × 100 × 60 mm was filled to its maximum volume, rammed with a 2.5 kg rammer with 28 blows; the surface was leveled and trimmed. This was done in accordance with Agunwa [9] and Omoniyi et al. [10].
Used automobile engine oil was used to smear the inner surfaces of the mold preceding the filling up of the mold in order to avoid adhesion of the cast to the walls of the mold when unmolding. The paving tiles were unmolded after 24 hours and cured in water for twenty-one days (21) then sundried for another seven (7) days, making up a total curing duration of twenty-eight (28) days [9,[11][12].

Compressive strength
The test specimen was loaded into a universal testing machine. The load was slowly and carefully applied centrally on the tile specimens until the first sign of crack was observed and the load was then recorded. The compressive strength of each tile specimen was carried out in accordance with Equation (1) [13]: (1) Where, Pc = maximum load on the specimen at failure, Ac = calculated cross-sectional area of the specimen and σ = compressive strength of the test specimen.

Flexural strength
Universal Testing Machine was used in accordance with [8,14] to determine the flexural test. The specimen was supported horizontally on two vertical supports of known span and was loaded with known values of masses until failure occurred. The flexural strength for each tile specimen was then obtained using Equation (2): (2) Where, R = modulus of rupture, P = applied load at failure, L = length between the supports, b = width of the specimen and d = thickness of the specimen

Analysis of modeling of paving tiles
When a function with two or more independent variables (multivariate function) is given, multivariate approximation is necessary for interpolation, differentiation and integration [15]. Also, quadratic interpolation is possible, if three points are available for a set of data. A polynomial equation represented by Equation (3) is suitable to develop the models of mechanical properties of produced tiles [16][17]: The dependent variable y denote compressive strength and modulus of rupture and independent variable X, is represented by the percentage of pulverized cow bones, which is the error term.
Simple linear regression, which is a tool in predictive analysis, could be found suitable for modeling analysis as represented by Equation (4).

(4)
Where, Y is the response variable, a, b are constants, x is the independent variable and is the error term.
Equations (6) to (11) which were generated using the EXCEL spreadsheet were used in the determination of empirical model curves for compressive strength and flexural strength of lateritic paving tiles as shown in Figures 1 and 2.

Coefficient of Correlation
The coefficient of correlation as a measure of the relationship between two variables and was determined for each curve in Figures 1 and 2 by using Equation (5): (5) Where, and are the mean value of X and Y respectively.

Fig. 1-Relationship between compressive strength and material composition
The compressive strength is shown in Figure 1 and Table 2 was found to decrease as the percentage of pulverized cow bones decreases in the composition of the paving tiles; this is due to the reinforcement the pulverized cow bones added to the strength of produced tiles. The reduction in compressive strength could also be attributed to the cement content, due to the fact that samples of paving tiles with 5-10% cement content had lower compressive strength. Samples with a laterite ratio of up to 25% and above exhibited an improved compressive strength due to the bonding properties of laterite. Equation (6) to (8), show the empirical model developed for determining the compressive strength of lateritic paving tiles at different cement composition of  ; , MPa (6) ; , MPa (7) ; , MPa (8)   Table 2 show the relationship between the flexural strength and composition of produced tiles at different cement compositions of 20, 15 and 10% respectively. Flexural strength was observed to decrease with an increase in silica sand addition, due to the grittiness of the material which reduces the bonding strength of the products. Conversely, flexural strength increases as the percentage composition of laterite and pulverized cow bones also increases. This was due to the adhesive properties of laterite and reinforcing properties of pulverized cow bones. Equations (9) and (11) represent the models of flexural strength and were observed to exhibit a linear relationship due to the close variation of the material composition at each mix.

CONCLUSION
Empirical models of the mechanical properties of paving tiles produced from aggregates of laterite, silica sand pulverized cow bones and cement, for cement addition of 20, 15 and 10% respectively were developed in this study and the models have been able to predict the trends of the mechanical properties of produced paving tiles. The maximum compressive and flexural strength of about 5.10 and 1.83 MPa were obtained at a composite composition of 30:10:40 of pulverized cow bones to silica sand to laterite. These were found to conform to the Nigerian Industrial Standard [18], which approves 2.5 MPa for load-bearing and 1.8 MPa for non-load bearing blocks. The higher the cement and pulverized cow bone content, the higher the compressive and flexural strength obtained. The use of pulverized cow bones as a constituent of paving tiles was found feasible and a viable means of reducing the environmental pollution. Also, replacing the more expensive granite constituent with waste cow bones would result in the cheaper production cost of paving tiles, creating a more sustainable environment. Developed empirical models from this study are useful for further investigation and product development of a similar nature.