Characterization of Togolese Gneisses and Granites by Rock Drilling Test

This paper introduces the study of Togolese gneiss and granites’ intrinsic properties such as mineralogical composition, density, porosity, homogeneity one the one hand, and their mechanical properties such as resistance to attrition, abrasion and puncturing depth on the other. After the correlation analysis, significant correlations between the mechanical properties of the rocks (Los Angeles and Micro-Deval) and the depth of perforation obtained by the rock drilling test were found, as well as the not significant correlations between the mineralogical composition and the physical properties of the rock were observed. Laboratories test often performed to obtain Los Angeles and Micro-Deval values are expensive and time consuming. For this, the depths (parallel and perpendicular to the foliation planes for the gneisses or two perpendicular planes for the granites) obtained during a rock drilling test will be used to estimate its coefficients (Los Angeles and Micro-Deval). This study, is based on a database of a sample size of 32 to determine the parameters of the multifactorial model of size 6 used for the validation tests.


Introduction
A longstanding a construction begins with the use of materials (sands, fine gravels, stones) coming from good quality natural rocks used as such or crushed. The aggregates are the prevalent materials composing the bed, base and surface course of roads, and are also used in fabricating concrete and mortar cement. The durability of the quality of these bases under the influence of the traffics depends on their mechanical and physical properties.
The principal specification for the use of the aggregates relates to their mechanical resistance: they must possess sufficient hardness to resist deterioration and fragmentation in consequence of load application. This is crucial because once in use these aggregates will be bound together, either by a hydraulic binder in the case of Portland cement concrete, either by a bitumen binder in the case of asphaltic concretes, or by forces of friction created by compaction in the case of road aggregates.
Currently in Togo, the aggregates most used in civil engineering come from the gneisses and the granites originating from careers used for industrial production and which function permanently, or from old careers exploited by the local population.
The current tests used to evaluate the quality and durability of these aggregates are expensive, complex and long in procedure, especially when installation of new production units is involved.
The intrinsic characteristics, such as the mineralogical composition, the porosity, the density and the homogeneity of the gneisses and the granites have been studied and their influence on the mechanical properties of the aggregates resulting from these rocks has been demonstrated [1,2,3,4]. The drillability test was used, for example in the characterization of limestones [5] and the statistics prove the correlation between the properties of the rocks and their drillability [6]. Several authors have proposed methods of predicting the rock drillibility based on cognitive systems of comparative or neural networks and wear factor using engineering properties of rocks analysis [7] and drilling rate (DR) using the rock mass drillability index (RDi) involved the intact rock mechanical properties structural properties of rock masses [8] but also many parameters including rock properties, machine parameters of the chosen rig and the working process [9].
In the attempt to reduce the rather high costs of traditional tests, we propose an approach based on drillability tests which would enable to determine the mechanical properties of the aggregates used in civil engineering in Togo.

Characteristics of the Rocks
The aims are, first to determine a correlation between the rock drillability and the characteristics of the sampled gneisses and granites; and second, to construct models of rock drillability according to the mechanical and physical properties, particularly the rock's resistance to abrasion by Los Angeles, resistance to attrition by Micro-Deval, its porosity, homogeneity and density. For these purposes, we look at the gneisses of the structural unit of the Bénino-Togolese plain and the granites of the West African craton [10]. In total, have been analyzed thirty-two (32) samples taken (  The characteristics of the studied rocks are summarized in table 1.
The essential intrinsic characteristics characterizing the samples are: the density, the mineralogical composition, porosity, the homogeneity [10]. The mechanical characteristics of the aggregates [11] consist of the resistance to abrasion using the Los Angeles machine and the resistance to attrition using the Micro-Deval machine [12,13].

The Rock Drillability Test
The main question is to find out whether there exist possible correlations between the rock drillability test and the intrinsic and mechanical characteristics of the aggregates. The rock drillability test consists in measuring the depth created by the drill in a rock during a fixed time (T), or in determining the time during which the drill leaves on the rock a print with a fixed depth.
The rock drilling test consisted in perforating the gneissic and granitic rocks using a drill of 6mm of diameter with the speed of 550 rpm under a load of 1daN. After the time of perforation fixed at 10 S, we measure the depth PF created by the drill in a sample of parallelepiped form.
To perform the perforation, a drill press CINCINNATI ( Figure 2) to which was hung a dynamometer applying a drilling force of 1 daN was used. On each sample, five perforations were made parallel to the layers of foliation and five perpendicularly to the foliation layers. By foliation we understand the entirety of the parallel plans according to which the new minerals crystallize.
After the perforation, a slide caliper was used to measure the depth of perforation obtained after 10 s.

Data Processing
Laboratory practices open a broad horizon of problems for which the use of statistical methods proves profitable and sometimes even indispensable. Among these methods, a paramount place is granted to the statistical study of the reciprocal connections between the variables. The mathematical tools used [14] in this field are primarily: correlation analysis and regression analysis.
The regression analysis enables to deduce an estimating equation which describes the functional nature of the relation between two variables, whereas the correlation analysis gives a measurement of the force of this relation.
In this study, the statistical analysis is used to determine the correlations between the rock drillability and other characteristics of the gneisses and granites, as well as the construction of models of rock drillability in correspondence with the mechanical properties of the rocks from which the gneisses and granites come.

The Drillability Test Results
The results of the tests made in accordance with the various directions in the foliation are presented on the figures 3 and 4. Figure 5 presents the variation of the characteristics of the rocks according to the average depth determined by the layers of foliation (both parallel and perpendicular).
The clouds of points on the figures bellow show that from the analyzed samples it is impossible to obtain significant correlations, and to delineate regressions whatever the perforation method. This is explained by the large variety of petrographic types of the sampled gneiss and granites.
Nevertheless, it is possible to make certain important observations in relation to the average depth of perforation the speed of 550 rpm.
(a) Relating to the mineralogical composition The data of perforation of the samples show that the depth of perforation depends on volume fraction of quartz in the rock. Thus, the rocks which depth of perforation is lower than 2mm have a volume fraction of quartz ≥10%.
There is a reduction of perforation depth with the increase of quartz fractions.
(b) Relating to the homogeneity The analysis of the samples in relation to the homogeneity shows that the samples of depth perforation lower than 3,5 mm have a high homogeneity.
(c) Relating to the aggregate's resistance to shock (coefficient LA) and wear (coefficient MD) One notices a marked tendency of the increase in the resistance of the aggregates when the depth of drilling rock decreases.
For the rocks of various types, the groups of dots are very dispersed. On the other hand, the analysis of tables 3 and 4 on the correlation of the foliated rocks and granites, shows strong intragroup correlations between the intrinsic properties (homogeneity and porosity), the mechanical properties (rock drillabilitty and LA, rock drillability MD, LA and MD) and between mineralogical and mechanical property (contain of quartz and LA, contain of quartz and MD, contain of quartz and rock drillability) for the average depth of perforation. This enables to determine: a) the homogeneity from the porosity, b) LA from the drilling property, c) MD starting from the rock drillability and d) the contain of quartz from the rock drillability.

Analyses Correlation and Mathematical Model
The analysis of correlation gives the measurement of the intensity of the dependence between two variables. This intensity is significant when the coefficient of correlation is close to the unit (r≥0.5).
The mathematical functions allowing the determination of these characteristics per rock drilling test are indicated on the diagrams of figure 4. The depth of drilling rests on several factors and a multifactorial mathematical model based on the characteristics of the rock such as the Los Angeles coefficient, the Micro-Deval coefficient, the density, the homogeneity, the porosity and the contain of quartz and biotite, use monofactorial models. The study of the connection between several factors, entitled multifactorial regression, can be presented by the following equation: This system is equivalent to the following: E1: -matrix of the Pm coefficient M1: intermediary matrix. This matrix is formed by the values of the mineralogical composition, the structure, the homogeneity and the density, corresponding to the samples for which one wishes to identify Pm C1: coefficients of the model The coefficients of the model are determined using the following equation: The system of equation (Eq. 3) being overdetermined, the criterion of minimization selected is that of least squares. The resolution of this system of equations is developed in the Matlab program [14] with the functions: pinv and lsqr on figure 6.
The gaps noticed in relation to the measured data are linked to the diversity of the types of studied rocks. When one applies this same model to the rocks of evident foliation texture or equate, one obtains more reliable results (figure 7) with the values of the obtained coefficients: α=0.241; β=-1.6628; γ=3.2627; λ=-1.5236; κ=0.11; δ=-0.034; ε=0.1366; ζ=-0.0472.  The simulation of the model applied to the six (06) granite and gneiss samples with foliated structure gave the results presented in Table 4.

Conclusion
The Togolese gneisses and granite were characterised by two types of properties: intrinsic with the porosity, the homogeneity, the mineralogical composition, the density, and mechanical with the Los Angeles coefficient, the Micro-Deval coefficient, and the rock drillability.
For the intrinsic properties, it is necessary to note the significant correlation between the homogeneity and the porosity of the rocks with evident foliated texture. For the mechanical properties, there is a significant correlation between the drilling property and the Los Angeles and Micro-Deval coefficients and finally between the Los Angeles coefficient and the Micro-Deval coefficient.
The significant correlations were observed between the rock drillability, the Los Angeles coefficient and the Micro-Deval coefficient and the contain of quartz.
The analysis of the regressions was permitted to construct mathematical models for estimation the intrinsic and mechanical properties the gneisses with evident foliated texture and granites by the rock drilling test.
The multifactorial analysis confirms the interdependence between the rock dryllability and the properties of the rocks.