Prediction of Uniaxial Compressive Strength and Modulus of Elasticity for Some Sedimentary Rocks in Kurdistan Region- Iraq using Schmidt Hammer

Uniaxial compressive strength (UCS) and Modulus of Elasticity or Young’s Modulus (E) used in most of engineering projects in rock mechanics, are the most important mechanical parameters of rocks. The calculation of these parameters needs most cost, time and effort. There are indirect methods to estimate the (UCS) and (E) such as Schmidt Hammer, also known as a rebound number (RL), this indirect method is easily and quickly applicable in laboratory and in field and it is considered as a non-destructive method for evaluation of surface hardness. The aim of this paper is to establish a correlation between UCS, E and Schmidt Hammer rebound value and it has been carried out on forty-nine specimens of different sedimentary rock types that belong to three different formations in Kurdistan Region, Iraq (Pila Spi Formation, Fatha Formation “Lower Fars Formation” and Tanjero Formation) with ages (Middle-Late Eocene, Middle Miocene and Campaman-Maastrichtian) respectively. The samples were prepared as cuboids of size 5x5x10 cm. A new correlation with high accuracy level for prediction of (UCS) and (E) from Schmidt hammer of some sedimentary rocks is proposed for the first time in Kurdistan Region-Iraq.


Introduction
The Uniaxial Compressive Strength plays an important role in designing various geotechnical applications such as buildings, tunnels and dams [1]. Evaluation of this parameter and Modulus of Elasticity in laboratory by direct tests is expensive and needs time and effort. While quick determination of these mechanical properties of rocks with minimum cost, effort and time can be done by Schmidt hammer [2] which has been widely used to determine hardness and to predict the uniaxial compressive strength (UCS) of rocks. The Schmidt hammer test is easily and quickly applicable [3] in both laboratory and field and it is considered as a non-destructive method for evaluation of surface hardness [4]. Due to the non-destructive test, the same samples subjected to Scmidt hammer can be used to other tests and measurements. In present study, the same samples were used for both Scmidt hammer rebound value and compressive strength. The Fatha (Lower Fars) Formation was defined from the Fars Province in Iran and introduced to Iraq by Busk and Mayo in 1918 [9]. The type section has been located in the Al Fatha Gorge, 10 km north of Baiji town. The formation is an evaporitic sequence with thickness of 600 m and consists of repeated cycles of mudrock, marl, limestone and gypsum which is used for buildings decoration.
The Tanjero Formation mainly occurs in the Balambo-Tanjero Zone. It was defined by Dunnington, in 1952. The type section in the Sirwan valley (SE of Sulaimaniya) consists of two parts. The lower part consists of pelagic marl, and occasional beds of argillaceous limestone with siltstone beds in the upper part [9]. The upper part consists of silty marl, sandstone, conglomerates, and sandy or silty organic detrital limestones. The formation was deposited as flysch in a rapidly subsiding foredeep basin.

Previous studies
Due to the simplicity, speed, portability, minimum cost, effort and time the Schmidt hammer was used by many researchers who have studied the correlations between uniaxial compressive strength and Schmidt hammer rebound value.  (1), are in the form of linear, exponential, and power functions. In the present study, the empirical correlation is in the form of exponential function. Miller (1965) [12] studied the relationship between unit weight, UCS and Schmidt hammer. Later, Deere and Miller (1966) [13] proposed a correlation between rock density, Young's modulus and Schmidt hammer rebound values. Haramy and DeMarco (1985) [14] have determined the utility of the Schmidt hammer in designing underground coal mine pillars by testing 10 types of U.S. coals. Ghose and Chakrabarti (1986) [15] have proposed an empirical correlation between Schmidt rebound values and UCS for Indian coals. Xu et al. (1990) [16] estimate the mechanical properties of weak rocks using Schmidt hammer rebound value. The relationship between UCS and Schmidt hammer rebound value for different rock types can be found in works presented by [17, 18, 2, 19, 20, 21 and 22].

Methodology
The samples of sandstone and limestone of three geological formations (Tanjero, Pila Spi and Forty-nine specimens were tested for this study for Schmidt hammer rebound value and compressive strength testing. The Schmidt hammer and compressive testing were performed on the same samples. The samples were puted in water until they became saturated and the testing was performed in saturated condition. For Schmidt hammer test, the L type hammer was used with energy of 0.735 Nm and ten impact readings were recorded from each specimen Fig (2), the average of these readings was taken as a Schmidt rebound value.
Uniaxial compressive tests were performed on forty-nine cuboid samples, which had is the section area of specimen (mm 2 ).
Modulus of elasticity values were calculated using the following formula: where is the Modulus of elasticity, is the Uniaxial compressive strength and is the strain obtained from uniaxial compressive tests The lowest values of the mechanical properties found in the Lower Fars Formation limestone due to their high porosity and poor cementation.

Results and discussion
In order to describe the relationships between Schmidt hammer rebound value with uniaxial compressive strength and modulus of elasticity of the tested rocks, regression analysis was performed Fig. (3, 4, 5 and 6). The plot of the Schmidt hammer rebound value as a function of UCS is shown in Fig. (3) while this plot between Schmidt hammer rebound value and modulus of elasticity is shown in Fig. (4, 5 and 6) show the measured UCS and E versus predicted UCS and E. Fig. (3) shows that there is a power relationship between Schmidt  The correlation equation between measured and predicted UCS can be found from equation The correlation equation between measured and predicted Young' Modulus of Elasticity can be found from equation (4) with (R 2 =0.5999) As a result of this study, the UCS and E can be predicted using the Schmidt hammer rebound value.

Conclusions
Uniaxial Compressive Strength (UCS) and Modulus of Elasticity (E) of rocks play an important role in many rock engineering projects. As a simple tool for quick prediction of these parameters is using Schmidt hammer rebound value which has been widely used for this purpose. In this study the acceptable correlations were developed to predict the UCS and E Furthermore, a strong coefficient of correlation was found between UCS and Schmidt hammer rebound value (R 2 = 0.879).

Recommendations:
To reach better results, we suggest further research on different types of sedimentary rocks that are predominant in Iraq as these types of rocks cover most of Iraq's surface.