Statistical analysis on the radiological assessment and geochemical studies of granite rocks in the north of Um Taghir area, Eastern Desert, Egypt

: Granite rocks are currently one of the foremost raw materials that can be used for various economic pur poses such as ornamentation and building materials, because they do not possess radioactive concentrations and have good physical and mechanical properties. The granite rocks of north Um Taghir are connected to neo proterozoic rocks and integrated to the north Arabian Nubian Shield ( ANS ) , which lies in Northeast Africa. Inductively coupled plasma mass spectrometry ( ICP - MS ) and X - ray ﬂ uorescence analysis, concurrent to some sta tistical analysis, have been carried for major oxides and some trace elements to extract much fundamental infor mation by following certain mathematical methods. The exposed granite rock units in north Um Taghir are classi ﬁ ed into four rock units represented by tonalite, grano diorite, monzogranite, and alkali - feldspar granite which are cut by di ﬀ erent types of dikes. The magma of tonalite and granodiorite is low - to - medium K calc - alkaline a ﬃ nity, while the magma of monzogranite and alkali - feldspar granite is medium - to - high K calc - alkaline a ﬃ nity, and of metaluminous to peraluminous nature. Granite rocks show a slightly depletion of fractionated patterns from light rare earth elements ( LREEs ) to heavy rare earth elements ( HREEs ) with slightly positive to negative Eu anomalies from tonalite granite. As stated by all results, it can be mentioned that the granite rocks have a worthy result of mechanical and physical properties. So that they can be used for various economic purposes.

Abstract: Granite rocks are currently one of the foremost raw materials that can be used for various economic purposes such as ornamentation and building materials, because they do not possess radioactive concentrations and have good physical and mechanical properties. The granite rocks of north Um Taghir are connected to neoproterozoic rocks and integrated to the north Arabian-Nubian Shield (ANS), which lies in Northeast Africa. Inductively coupled plasma mass spectrometry (ICP-MS) and X-ray fluorescence analysis, concurrent to some statistical analysis, have been carried for major oxides and some trace elements to extract much fundamental information by following certain mathematical methods. The exposed granite rock units in north Um Taghir are classified into four rock units represented by tonalite, granodiorite, monzogranite, and alkali-feldspar granite which are cut by different types of dikes. The magma of tonalite and granodiorite is low-to-medium K calc-alkaline affinity, while the magma of monzogranite and alkali-feldspar granite is medium-to-high K calc-alkaline affinity, and of metaluminous to peraluminous nature. Granite rocks show a slightly depletion of fractionated patterns from light rare earth elements (LREEs) to heavy rare earth elements (HREEs) with slightly positive to negative Eu anomalies from tonalite to monzogranite and alkali-feldspar granites. The statistical criteria have been achieved to explore the significant differences of radiological hazard parameters among samples. It is obvious that there is no homogeneity among samples; furthermore, in Kruskal-Wallis test, Mann-Whitney test, and Pearson correlation coefficient, it can be noticed that there are significant differences between each pair of samples: tonalite, monzogranite; tonalite, alkali-feldspar granite; granodiorite, monzogranite; and granodiorite, alkali-feldspar granite. There is a strong direct relationship among granodiorite and both tonalite and alkali-feldspar granite, and among alkali-feldspar granite and tonalite and granodiorite. There is a strong inverse relationship among monzogranite and tonalite, granodiorite, and alkali-feldspar

Introduction
Granites constitute about 60% of exposures neoproterozoic basement rock in the Eastern desert and Sinai as a part of the Arabian-Nubian shield (ANS) related to the pan African orogenic belt [1][2][3]. Due to the widespread distribution of granite in Egyptian basement rock units, numerous studies and works have been conducted to classify the various granitic rocks in Egypt, based on their geologic context, petrographic, geochemical, and geochronological characteristics [4][5][6][7][8]. It can be concluded that the granite rock can be classified into two major types: the first type is older granite (880-610 Ma); can be mentioned as gray granite, shaitian granite, syn-to late-tectonic, and G1 granites. It comprises mainly trondhjemite, quartz diorites, tonalities, and granodiorites with calc-alkaline affinity of subduction origin. Quartz-diorite and tonalite always older than dokhan volcanic (Pre-dokhan). The second type is younger granite (620-540 Ma), it also referred to as Post-orogenic and anorogenic. The second type is younger granite (620-540 Ma), it also referred to as post-orogenic and anorogenic, Guattarian Granite, G2 and G3 granite, and red to pink granite usually alkaline to per-alkaline are formed by suture-related and intraplate granites, likewise, is classified into three phases: phase I comprises granodiorites and monzogranites, phase II comprises mainly monzogranites and syeno-granites, and phase III comprises mainly alkali feldspar granites. As well as, Monzogranite and Syanogranite always younger than dokhan volcanic. The two types of granite rocks are related to I-type granite, but some of the younger granite are A-type, rift-related granites. Granite rocks are currently one of the most essential raw materials for various economic reasons, such as decorative and construction materials, assuming they do not contain substantial radioactive concentrations and have excellent physical and mechanical capabilities [9][10][11][12]. Granite rocks of the north Um Taghir area are restricted in the southern extreme boundary of the northeastern Desert of Egypt on the Qena-Safaga road ( Figure 1). It covers about 400 km 2 , between latitudes 26°35′00″-26°49′00″ and longitudes 33°35′00″-33°50′00″. It belongs to the North ANS, which constituent neoproterozoic evolution in northeast Africa [13][14][15][16][17][18]. Mostly, the ANS represents the largest area formed by the upper part of the mantle, with a length of 3,500 km and a width extending to 1,500 km; the African Orogen part (East African Orogeny) of ANS covers about 2.7 km 2 × 106 km 2 [7], as shown in Figure 2. Many researchers have been studied in the area along the road of Qena-Safaga [19,[20][21][22][23][24][25][26][27]. Simultaneously, the statistical analysis is one of the most significant applications that appertain to scientific research, through which the researcher collects a set of factors that control his scientific research and assemble the critical analysis, subsequently, extracting the essential information from them by following certain mathematical methods, besides drawing his conclusion and recommendations from numerous sources, where these relationships are sensibly related to the content, thus emerging a new meaning of importance from the relationships that have no meaning if they exist individually. Statistical analysis is one of the types of analysis that is carried out when planning to do a specific project, or when conducting scientific research, Indeed the statistical Figure 2: Geological map of Um Taghir area, created based on integrated processing of data from regional geological surveys, remote sensing, and field observations. Quaternary formations: 1 -(sand, pebbles, conglomerates). Neoproterozoic formations: 2schist; 3metagabbro; 4granodiorite; 5tonalite; 6gabbro; 7monzogranite, 8alkali-feldspar granite; 9 -Dokhan volcanics; (10) mafic dikes; 11felsic dikes; 12faults. analysis is one of the most important reasons for the success of the project or the scientific research presented by the researcher due to the great role that statistical analysis plays, from by providing important and valuable information that greatly helps the success of scientific research.

Materials and methods
About 28 samples of granite rocks have been collected from 20 sites in the north Um Taghir area. The samples (approximately 1 kg) were taken to the lab for sample preparation. Thin sections were performed at the Central Laboratory of Institute of the Earth Sciences, Southern Federal University, Russia. The mineral analyses were measured by microscopic modal analyses. The collected samples were dried and sieved through a fine mesh (<1 mm) (0.256 mm) for homologation. The samples were placed inside an oven for drying at 100°C for one day to completely remove moisture. The quantitative analyses were measured by ICP-MS, after digestion of the fused beads with HF + HNO 3 . The external of pure solution standers were selected for calibration. Measurements were performed on an ELAN-DRC-6100 ICP-MS at the Central Laboratory of Russian Geological Institute. Also, major oxides and some trace elements testing was carried out by X-ray fluorescence analysis at the Institute of Biology, Southern Federal University. The X-ray powder diffraction method works by collecting and analyzing the spectrum generated by exposing the test material to X-ray radiation. Set the voltage to 10 kV for light elements, 20-30 kV for medium components, and 40-50 kV for heavy elements.

Geological observations
The investigated granite rocks are affiliated with the Late Cryogenian-Ediacaran age magmatism of the East African Orogeny; they are represented by late to post-orogenic (Continental crust terrain) [7,28]. The granite rocks have a good result of mechanical and physical properties, so they can be used for various economic purposes [11]. We collected and prepared the representative samples from the different rock types from the investigated area in addition to using the QAP plutonic classification diagram [29]; the exposed rock units in the studied area have been classified into four distinct rock units represented by tonalite, granodiorite, monzogranite, and alkali-feldspar granite, which are traversed by different types of dikes as shown in Figures 2 and 4a. As Shown in Table 1 and          3 Results

Tonalite
It is located in the southeast of the study area, with distinguished gray color, jointed and low relief hills. It is intruded directly by monzogranite and crosscut in oldest rock (Figure 3a), on the other hand, monzogranite contains some xenolith of the tonalite rocks as big bodies (xenoliths; Figure 3b), nearby the contact with the quaternary rocks and monzogranite. Tonalite is represented essentially by plagioclase of andesine composition (∼50.3%), quartz (∼30%), and alkali-feldspar (∼3.15%), with some additional amount of biotite and hornblende, while sphene, zircon, and iron oxide occur as accessory minerals (Figure 4b).

Granodiorite
It is characterized by medium grained to coarse grained with greyish in color and moderate relief; it exhibits some foliation and joints. Nevertheless, monzogranite intruded in granodiorite with sharp contact, becomes visible especially at Abu Haweis granite (Figure 3c). Petrographically granodiorite occurs as medium-grained with a granular texture; it is composed mainly of plagioclase which ranges in composition between oligoclase and andesine (An 16 -An 36 ) with an amount of 45.9%, quartz (∼30.4%), and alkali-feldspar (∼16.3%) as essential minerals. At the same time, apatite, biotite, and iron oxide represent the accessory minerals ( Figure 4c).

Monzogranite
It covers about 30% of the investigation region and directly cuts granodiorite (Figure 3c), instead, monzogranite is intruded by alkali-feldspar granite by sharp contact. It is distinguished with white to pinkish in color, coarse-to-medium-grained massive rock, high relief, highly jointed in two trends E-W and N-S, and highly fractured due to the effect of numerous faults trends. On the other hand, cavernous cavity and exfoliation are very common. It often exhibits granite texture and consists predominantly of alkali-feldspar with an average ∼38.6% represented by microcline, orthoclase, and perthite, plagioclase of oligoclase in composition (∼29.7%), and anhedral grain quartz (∼27.8%). On the other hand, a negligible Table 3:  quantity of muscovite and biotite, while the accessory minerals are represented by zircon and iron oxides.

Alkali-feldspar granite
It represents the youngest unit of granite magma in the study area. The alkali-feldspar granite is characterized by an elongated NS belt extending from Abu Haweis in the north part of the study area to Wadi Um Taghir at the south (Figure 2). It shows high topographic relief up to ∼890 m in Abu Hawies. It is distinguished by massive, medium-to-coarse-grained pink to red color and less jointed. Moreover, it is intruded by the granodiorite and monzogranite with sharp contact between them (Figure 3d). Furthermore, it is composed mainly of alkalifeldspar minerals with an average ∼59.8% of perthite, microcline, and little amount of orthoclase, likewise quartz (∼33.2%) and noticeable amount as of plagioclase of albite in composition (∼3.4%), with addition small amounts of muscovite and iron oxide (Figure 4e).

Geochemistry of the investigated rock units
The results of the complete silicate analyses of the major oxides and trace elements of 28 samples were represented by 4 samples for tonalite, 6 samples for granodiorite, 13 samples for monzogranite, and 5 samples for alkali-feldspar granite (Tables 2 and 3).

Nomenclature of the investigated rock units
A lot of parameters are used to classify and follow up the chemical affinity of the investigated rocks. According to SiO 2 vs (Na 2 O + K 2 O) diagram [30], the investigated samples of granites are falling in tonalite, granodiorite, monzogranite, and alkali-feldspar granite fields as shown in Figure 5a. The geochemical classifications of granites are well coexisting petrographic classifications as shown in Figure 4a.

Magma type of the investigated rock units
The magma type of the studied rock units was discussed on the basis of the following proposed diagrams. According to Peccerillo and Taylor [31], K 2 O-SiO 2 binary diagram shows the tonalite and granodiorite are low-to-medium K calc-alkaline, where monzogranite and alkali-feldspar granite are medium-to-high K calc-alkaline as shown in Figure 5b, as well as according to ref. [32] used ANK versus ACNK variation diagram to show quite a variation of the examined granites, from metaluminous to peraluminous nature, actually tonalite and granodiorite are metaluminous, while monzogranite and alkali-feldspar granite are metaluminous to peralkaline in nature (Figure 5c).

Tectonic setting of the investigated granites
Pearce et al. [33] used Nb versus Y diagram to show the tectonic setting of oceanic ridge granite (ORG), syn-collision granites (Syn-COLG), volcanic arc granite, and within plate granite (WPG) fields, particularly the tonalite and granodiorite samples are falling in the volcanic arc field, while the monzogranite and alkali-feldspar granite samples are related to WPG field (Figure 5d).

Trace and rare earth elements of the investigated rock units
Based on the ORG normalizing diagram [33], the tonalite and granodiorite are enriched in some trace elements content (Figure 5e)  We note that P-value <5%; hence there is a significant difference between tonalite, granodiorite, monzogranite, and alkali feldspar granite. We performed Mann-Whitney test between every two samples together to determine the difference. The results are listed in: From Table 5, there is no significant difference between both tonalite, granodiorite and monzogranite, alkali-feldspar granite; this is clear of mean ranks for every two samples together. Also, this decision can be taken by comparing P-values with significance level of 5%, where P-value of 0.415 > 0.05 for tonalite and granodiorite and P-value of 0.367 > 0.05 for monzogranite and alkali-feldspar granite. While comparing P-values and mean rank of the remaining samples, we can notice that there are significant differences between each pair of samples [(tonalite, monzogranite), (tonalite, alkali feldspar granite), (granodiorite, monzogranite), and (granodiorite, alkali-feldspar granite)]. Table 6 shows the Pearson correlation among samples (tonalite, granodiorite, monzogranite, and alkalifeldspar granite). We can notice that there is a strong direct relationship between tonalite and both granodiorite, monzogranite, and alkali-feldspar granite with Pearson correlation coefficient (0.603**, 0.752**, 0.573**) significant at the 0.01, respectively. Also, there is a strong direct relationship among granodiorite and both tonalite and alkalifeldspar granite with Pearson correlation coefficients (0.603** and 0.723**) significant at the 0.01, respectively. Moreover, a strong direct relationship among alkali-feldspar granite and tonalite and granodiorite with 0.573** and 0.723** Pearson correlation coefficient significant at the 0.01, respectively. Also, one can see that there is a strong inverse relationship among monzogranite and tonalite, granodiorite, and alkali-feldspar granite with Pearson correlation coefficients (−0.752**, −0.485** and −0.598**) significant at the 0.01.

Conclusion
Granite rocks are currently one of the chief row materials that can be subjugated for various economic purposes such as ornamentation and building materials. They do not include radioactive concentrations and have good physical and mechanical properties. Granite rocks of north Um Taghir are appropriate to Neoproterozoic rocks related to the north ANS, which occurs in northeast Africa. The exposed rock units in the investigated area are classified into four rock units represented by tonalite, granodiorite, monzogranite, and alkali-feldspar granite, which are cut by different dikes. The magma of tonalite and granodiorite is low-to-medium K calc-alkaline affinity, while the magma of monzogranite and alkali-feldspar granite is medium-to-high K calc-alkaline affinity, metaluminous to peraluminous nature, and related to ORG, Syn-COLG, and WPG fields. The normalization of trace elements such as K, Rb, Sr, Th, Ce, and Sm compared to Nb, Hf, Zr, Y, and Yb with distinct troughs at Nb and Zr, reffered to the I-type granites that resulting from the subduction zones. However, monzogranite and alkali feldspar granite are enriched in Rb and Th relative to Nb and Ta; in addition, Ce and Sm are enriched relative to their adjacent elements. Granite rocks show a slight depletion of fractionated patterns from LREEs to HREEs with slightly positive to negative Eu anomalies from tonalite to monzogranite and alkali-feldspar granite. In contrast, the statistical criteria have been functioned to explore the significant differences among the sample. By probing the results, we establish that there is no homogeneity or normality among sample results. Furthermore, with Kruskal-Wallis test, Mann-Whitney test, and by comparing P-value with a significance level of 5%, we can notice that there are significant differences between each pair of samples [(tonalite, monzogranite), (tonalite, alkali-feldspar granite), (granodiorite, monzogranite), and (granodiorite, alkali-feldspar granite)]. With Pearson correlation coefficient, we can notice a strong direct relationship among granodiorite and both tonalite and alkali-feldspar granite, among alkali-feldspar granite and tonalite and granodiorite, there is a strong inverse relationship among monzogranite and tonalite, granodiorite and alkali-feldspar granite. Granitic rocks have outstanding mechanical and physical properties, as stated in all of the results, allowing them to be used as a raw material for a variety of economic purposes.