Limestone reserve calculation for engineering purposes for the Nfayil Formation (middle Miocene) in Bahr Al-Najaf Depression, Iraq

Limestones have considerable commercial importance because they are used as building stones and are widely used for flooring and interior and exterior facings. On the other hand, the reserve calculation reveals the economic effectiveness of the investigation. This study aims to calculate the reserve of the middle Miocene limestone for engineering purposes. The limestone beds of the Nfayil Formation in Central Iraq have been studied over 15 outcrop sections. The Nfayil bed has an average thickness of about 1.64 m, while the overburden has an average of about 0.93 m. The average bulk density of limestone is 2.1 gm/cm 3 . Kriging and triangulation method has been adopted and used in the calculation and assessment of reserve. The industrial layer was calculated based on the American classification, where the assessment is from the inferred reserve, which is according to the geological characteristics of the industrial layer, as well as the presence of a few wells obtained for the studied area (15 wells). The industrial bed's total reserve (tonnage) is 253,245,195 tons, which is acceptable for accuracy and reliability compared to the American system. These values are acceptable for the number of


Physical properties tests
The basic physical properties are important to evaluate limestone rocks, giving an integrated description of the quality and extent of validity for the rocks as construction materials. Bulk density: Density is defined as the sample's weight to the total volume [6].
Weight of a submerged model (g) W sat Water saturated form weight (g) V t Total volume (cm 3 ) As density increases, the value of the mechanical properties of rocks will increase [7]. Such as the volume stability and heat capacity [8]. Ten limestone samples were tested for bulk density. They range from 1.8 gm/cm 3 to 2.6 gm/cm 3 whereas the average value is 2.1 gm/cm 3 . These values are compatible with the common densities of industry.

Engineering Properties
Uniaxial compressive strength: Compressive strength is defined as rock resistance to its stress. It is measured by applying continuous stress on the material in opposite directions until failure occurs. The stress represents the material resistance, and its unit of measurement is m2 / N or Pa (Pa), depending on the rock mineral composition, hardness, texture, and water content [7]. The uniaxial compressive strength shows the materials' stability in construction and their resistance to crushing, which mostly happens during transport. [8] Uniaxial compression strength according to ASTM C170-90 and according to the following formula:q u = W/A …………………(3) Where: q u Compression strength. W Projected load upon collapse. A Calculated surface area projected load upon collapse.

Estimation of Reserve
The reserve estimation shows the economic efficiency of investigation and provides the necessary information to evaluate through the geological exploration work [9]. The geologic exploration for natural resources is too expensive; however, it opens new opportunities and challenges. The geologic investigation follows a series of multidisciplinary activities: explorations, reconnaissance, prospecting, and economic mining. The investigation concept looks for the unique stratigraphic age of committed favourable rocks [10].

Mineral Deposit Geometry
The mineral deposits geometry means the location of these mineral deposits in the earth's crust, shape and size. They have irregular geometric forms depending on complex geological and sedimentary conditions, which have led to their three-dimensional origin. The two dimensions are the horizontal area (length and width), while the third dimension is the thickness of the mineral deposits Figure 2. [11] The three factors (length, width, and thickness) are significant in studying mining operations because of their effect on choosing the method of mining used in ore extractions. The main objectives of geological studies and explorations of mineral deposits are to identify the sediment thickness and side extensions to be transferred to the coming after phase of detailed studies and mineral assessments, which is a reserve account for mineral deposits.

Kriging Method
This method represents insertion data that gives predictions at the unsampled sites by using a linear combination of the observations at nearby sampled sites. The influence of each observable feature on the kriging prognostic is controlled by several factors: 1-the geographical proximity to the unsampled location. 2-the spatial arrangement of all observations. 3-the pattern of spatial correlation of the data.
Developing kriging methods and models is meaningful only when data are spatially correlated. The advantages of the kriging method are: 1-Providing the measurement of the uncertainty attached to the results. 2-The accounts for direction-dependent relationships. 3-Weights were assigned to observations based on the spatial correlation of data and information. 4-Kriging prognostics do not constrain the ranges of the observations used for interpolating. 5-The measured data can be combined and changed over different spatial supports [12].

Triangulation Method
The triangulation method is based on using multiple methods or data and information from the sources in qualitative research to develop a comprehensive understanding of phenomena [13]. It is also a qualitative strategy to test data validity and information from different sources. [13] Four types of triangulation are approved: (a) theory triangulation, (b) investigator triangulation, (c) method triangulation, and (d) data source triangulation. In the triangles method, the area is divided into triangles by connecting the adjacent columnar sections with straight lines and computing the data and information area for each mathematical triangle. The studied area is a semi-triangle area. This method divides the study area into 19 triangles to estimate the limestone reserve ( Figures 3&4). Each triangle represents three sections. The triangle sides are unequal, and the angle is unequal at 60°. The correction factor is recommended to correct the thickness of limestone beds in each triangle according to [11], [14], [15] and [16]. It was presented in (Table 1)  Average of corrected thickness for triangle (m). T1, T2 and T3: Thickness of the industrial bed in sections. F1, F2 and F3: Factors of correction for each triangle. n: Section numbers of and which equal 3

Discussion and Conclusion
Kriging method, one applications of Rockwork-15 which uses to calculate reserve. The expanding area is used according to the application of the extension rule to the impact site of the models. In this way, the statistical processing of wells is used to calculate the reserve and estimate its effect on distances from the studied well locations or sections. The average area thickness in each triangle is estimated, consisting of three wells located at the vertices of each triangle. The extension of the triangle datum covers the studied area. The effect of each triangle on the study area where the thicknesses of the industrial layer were relied upon ( Table  2). The geostatistical method, called the Kriking method, is one of the modern methods of calculating and estimating the reserves of the geological beds. At any location within the geological formation or the bedrock, it takes into account the location of each sample concerning the other in any location, as well as the relationship with each other within the extensions of the geological bed and even outside the sample location or boundaries of those extensions. In this study, the sample location and thickness were obtained. There is an extension of the bed thickness beyond the location of each sample, and for a certain distance that is estimated by the program depending on the sample value and the extent of each sample distance and their relationship. Therefore the method is used geostatistical in addition to other areas outside the boundaries of the sites up to the study area boundary according to the coordinates ( Figure  3). The reserve calculated based on this method is 749,712.0 confirmed tons. The reason for the exaggeration of the value of the reserve is due to the addition of these areas depending on the relationship of the extent of influence area of the locational impact of the samples within the study area. Table 2 represents the data and reserve values calculated using the triangulation method, which depends on dividing the study area into triangles. The sample location from the peak of the triangles and the correction factor was calculated to re-evaluate the extent of the positional influence of each sample in the case of large angles. In this method, the reserve for the Nfayil Formation was calculated manually depending on the triangle area multiplied by the weighted thickness value to get the reserve volume for each triangle. Then they are collected to obtain the volume of the total reserve. The volume is multiplied by the density rate to obtain the total reserve in tons. With the triangle method, a lower value for reserve estimation is obtained due to not adding areas outside the limits of the sampling sites, so this method gives a certain reserve, and this is the reason for the difference in the data obtained in calculating the reserve using these two methods.
The reserve estimation of the industrial class was calculated according to the U.S. classification. The estimation of the inferred reserve class depends on the geologic characteristics of the industrial layers, as well as the presence of fifteen wells. The accuracy and reliability are acceptable in comparison to the weighted reserve class used in the American system. The standard deviation ranges from about 0.3 m to the number of the studied wells.