I. Introduction

Radiation shielding has recently become an important research topic in nuclear science, and is defined as the ability to reduce radiation efects through interaction with the shielding material. Several parameters such as attenuation efectiveness, strength, and thermal properties in uence the selection of radiation shielding materials. Concrete is one of the most widely used materials in reactor shielding due to its intrinsic properties, such as cheapness, and the ease of preparation of diffierent compositions and forms. Moreover, its shielding properties depend strongly on the elemental composition of the prepared mixtures. An enormous amount of solid waste is generated annually in Egypt as a by-product of mining, agricultural and industrial processes. Due to various economic, social, and environmental restraints, the development of a suitable waste disposal method remains a top priority. The non-degradable waste by-products of mining and industry have long been targeted in research on concrete production. Several researchers investigated the possible use of industrial by-products such as steel shots [1], steel particulates, used steel ball-bearings [2], electric arc furnace slag [3] and stone slurry [4], either as ne or coarse aggregates in concrete, and their effects on mechanical and radiation shielding properties were evaluated. Among these mining and industrial by-products is marble dust powder, generated during the marble cutting process. Marble processing plants cannot store large amounts of marble dust powder, so reusing it is of great environmental and economic benet [5] and [6]. Corinaldesi et al. (²⁰¹⁰) found that replacing sand with marble powder at a rate of 10 % provides maximum compressive strength [7]. Akkurt and Altindag (2012) determined, both experimentally and theoretically, the linear attenuation coefficients of concrete containing marble powder in its ne aggregate form. The measured and calculated linear attenuation coefficients showed good agreement. Finally, they concluded that marble can be used as an aggregate in the production of shielding concrete [8]. Akkurt and EL-Khayatt (2013) also calculated the photon interaction parameters for concrete containing marble dust for the photon energy range of 1 keV-100 GeV [10]. Aliabdo et al. (2014) found that using marble powder as a partial replacement for cement or sand improves the physical properties of concrete [9]. Ergun (2015) utilized marble powder together with diatomite as a partial replacement for cement. He found that either 5 % marble powder alone or 5 % marble powder along with 10 % diatomite can be used to enhance the mechanical properties of concrete [¹¹]. Furthermore, it was found that up to 10 % marble powder enhances the workability of the mixture, while maintaining its compressive strength [12]. In a recent review it was found that as the amount of marble powder ne aggregate increases within the mixture, concrete workability decreases, and the compressive strength of the concrete increases because of its CaCO3 and SiO2 content [13]. Moreover, the cement with optimal concrete strength was obtained using 10 % waste marble as a replacement for cement [¹⁴] and [15]. The purpose of this study is to develop a low cost, locally produced concrete mixture with optimum marble content, which is stronger than ordinary concrete and has enhanced gamma-ray and neutron shielding properties.

II. Theoretical basis and calculations

i. The mass attenuation coefficient, um

A mono-energetic gamma ray passing through matter is attenuated due to photoelectric absorption, scattering, and pair-production. Attenuation behavior follows Beer-Lambert's law [8, 9, 16]

ii. Efective atomic number, Ze

The efective atomic number for low-Z elements due to the inelastic scattering of gamma rays with material atoms is given by Eq. 4 below [16-19], while for high-Z elements such as molybdenum through uranium, the uncertainties at low energies (10 keV to 1 MeV) range from 1 to 2 percent far from an absorption edge to 5 to 10 percent in the vicinity of an edge. In the range 1 to 100 MeV uncertainties from pair production estimates are 2 to 3 percent, while above 100 MeV they are 1 to 2 percent [20].

Figure 1: Schematic diagram of the modeled NaI (Tl) detector with simulation geometry. 

iii. MCNPX code (version 2.6.0)

The Monte Carlo method is often employed for issues with a probabilistic structure. In this study, MCNPX (Monte Carlo N-Particle Transport Code System-extended) version 2.6.0 [21] was used to investigate the um of different concrete mixtures [22,23]. The schematic diagram shows the MCNPX gamma ray attenuation setup with ve main pieces of simulation equipment: point isotropic radiation source, Pb collimator for primary radiation beam, attenuator concrete sample, Pb blocks to prevent scattered radiation and NaI (Tl) detector (see Fig. 1) [22, 23]. The relative error rate observed was less than 0.1 % in the output le.

iv. Exposure build-up factor, EBF

During the penetration of gamma photons through any material, they may be either absorbed or scattered by the atoms of this material. Secondary radiation may arise due to the build-up of scattered photons inside the material. Accordingly, it is necessary to estimate these build-up factors to determine efective exposure and energy deposition in the shielding material. The build-up of secondary radiation is characterized by the exposure buildup factor (EBF), defined as the ratio of the total gamma photon ux (absorbed and scattered) to the absorbed gamma photons of the incident beam [24, 25]. In this work, the geometrical progression (G-P) tting method [26] was used due to a high level of accuracy. The ratio R = ucomp=um, which represents the relative contribution of the mass attenuation coefficient due to Compton scattering interaction (comp), was obtained for each sample over the photon energy range of 0.015 - 3 MeV. The ratio R at a given energy value was then matched with the corresponding ratios R1 and R2 of known elements whose atomic numbers were Z1 and Z2, respectively, where R1 < R < R2. The equivalent atomic number (Zeq) for each sample was obtained using the following formula of interpolation by [24{26]:

The build-up factors for each sample were calculated using the geometrical progression tting function B(E; x) and K(E; x).

where Eq. (8) is valid for x 40 MFP and x is the source-to-detector distance in terms of the MFP. The geometrical progression parameters (b, c, a, XK and d) for the selected samples were obtained in advance using the following interpolating formula:

where P stands for the required G-P tting parameter for the selected sample at a specic energy value, while P1 and P2 represent the values of the G-P tting parameter corresponding to the atomic numbers Z1 and Z2, respectively. The G-P tting parameters P1 and P2 can be obtained from the American National Standard database which contains the exposure buildup G-P tting parameters for 23 different elements, one compound (water), and one mixture (concrete) for different energies [24-26].

v. The macroscopic effective removal cross- section for fast neutron ER

The attenuation of neutrons in matter obeys the following law:

The efective fast neutron removal cross-section (neutron attenuation coefficient), R, for a compound or a homogeneous mixture may be calculated using the values R= for various elements in the compound or mixture, using the following equations [27-34]

Where Wi is the weight percentage, and i and (R=)i are the partial density and the mass fast neutron removal cross-section (mass attenuation coefficient) of the ith constituent, respectively.

III. Materials and experimental procedures

i. Materials

The ne aggregate used is natural siliceous yellow sand with a particle size less than 0.6 mm, with Ordinary Portland Cement (OPC) produced by the Beni-Suef cement factory, in Egypt. Also, the marble powder is white-colored and odorless, with quite low porosity and a grain-size less than 0.365 mm.

ii. Concrete sample preparation

The experimental part of this study has three main goals: to analyze changes in the concrete chemical composition, to monitor the compressive strength, and evaluate the enhancement of the gamma shielding properties due to the incorporation of marble dust as a partial replacement for cement, on a weight basis. In order to achieve these goals, ve di erent concrete mixtures were prepared where marble was used at a rate of 0 %, 5 %, 10 %, 15 % and 20 %, and tagged as CM1, CM2, CM3, CM4 and CM5, respectively. The variation in the samples was carried out in such a way that when the marble proportion was increased, the cement proportion was decreased by the same proportion. Accordingly, the water to cement ratio (w/c) was varied with the varying marble content in the prepared mixtures. For each mixture nine cubic samples (5 cm 5 cm 5 cm) were cast. Samples used for measuring the linear attenuation coefficient were then obtained by cutting the cubic samples into slices with thicknesses varying from 1 to 1.5 cm, and the owchart was followed, as shown, (see Fig. 2) to calculate the mass attenuation coefficients.

Figure 2: A owchart describing the steps followed in the experiment to measure the mass attenuation coeffi cients. 

The chemical composition of the constituent materials of each sample were analyzed using the Xray Fluorescence (XRF) technique; these compositions are listed in Table 1.

Figure 3: Compressive strength and marble concentration. 

iii. Compressive strength test

For each mixture, three concrete samples were put to a compressive strength test using an ADR 2000 Standard Compression Machine (2000 kN/450000 lbf capacity, rated power of 1350 W). The load was applied gradually at the rate of 140 kg/cm2 per minute until the specimen failed, and the average reading was registered.

iv. Gamma ray shielding parameters experiment

The radiation shielding experiments were carried out with the samples placed between sources 133 Ba (0.356 MeV), 137Cs (0.662 and 0.911 MeV), 60Co (1.173 and 1.332 MeV), and 232Th (0.583 and 2.614 MeV); a NaI(TI) detector was connected to a Multi-Channel Analyzer (MCA) with PC to measure the linear gamma ray attenuation coefficient of each sample struck by gamma radiation.

Table 1: XRF analysis of the prepared mixtures. 

Figure 4: The measured mass attenuation coefficient compared with that determined by MCNPX and WinXCom. 

IV. Results and discussion

i. Compressive strength

The relationship between marble powder content and compressive strength is shown in Fig. 3. It can be seen that the compressive strength of concrete containing marble increases as the marble content increases, until it reaches an absolute maximum value at a marble cement-replacement ratio of 10 % (Region I), after which it starts to decrease as the marble content increases (Region II). Thus, maximum compressive strength is typically obtained with the use of 10 % waste marble powder, in good agreement with the literature [13{15]. This may be attributed to the higher content of Fe2O3 and CaO in sample CM3 than in the other samples, as well as its higher density.

Figure 5: The efective atomic number, Zeff , as a function of the incident photon energy. 

Figure 6: MFP and marble concentration at diferent energy lines. 

Figure 7: The EBF as a function of photon energy at 1, 5, 10 and 40 MFP depth. 

ii. Gamma ray shielding parameters

The mass attenuation coefficient, um, was experimentally measured at dffierent photon energy lines, and these results were then compared with those obtained theoretically using WinXCom software and the Monte-Carlo simulation code MCNPX for a photon energy range of 0.015 - 3 MeV. These results are displayed in Fig. 4. It can be clearly seen that there is good agreement between the theoretically calculated m and that measured experimentally. Moreover, for very low photon energy (E < 15 keV), the mass attenuation coefficient um has a very high value due to dominance of the photo-electric interaction. It then decreases as the incident photon energy increases, until it reaches a minimum value at a photon energy of 3 MeV. Using Eq. (4) together with the calculated mass attenuation coefficient, the efective atomic number is obtained over the photon energy range of 0.015 - 3 MeV and displayed in Fig. 5.

For very small decreases in energy down to a minimum value of 1.0 MeV, then slightly increasing again as the energy increased to 3 MeV, it was found that sample CM1 had the highest efective atomic number, followed by CM3. Moreover, it is worth noting that the addition of marble led to a decrease in the fective atomic number. The MFP values for the diferent marble concentrations were calculated using MCNPX simulation code at different energy lines within the range 0.015 - 3 MeV.

The values obtained (see Fig. 6) show where the mixture CM3 has the minimum numerical value for the MFP. However, the addition of marble did not lead to a signicant change in the MFP.

iii. The energy exposure build-up factor, EBF

Variation in the EBF with photon energy at the penetration depths of 1, 5, 10 and 40 MFP is shown in Fig. 7 (a-d). It is clear that the EBF value increases as the energy of the incident photon increases, until it reaches a maximum value, after which it decreases as the penetration depth increases. At this peak point, the Compton scattering interaction is the dominant mechanism. This is followed by a decrease in the build-up factors with any further increase in the energy of the incident photon, due to an increase in the contribution of the pair-production interaction at the expense of the Compton scattering [33, 35].

Figure 8: The EBF and penetration depth at photon energies 0.015, 0.15, 1.5 and 3 MeV. 

Figure 9: The Neutron MFP and marble concentrations. 

Variation in the EBF with penetration depth for the diferent concrete mixtures at an incident photon energy of 0.015, 0.15, 1.5 and 3 MeV is shown in Fig. 8 (a-d). It can be seen that the EBF increases with increased penetration depth for all concrete mixtures. At a photon energy of 0.015 MeV, where photoelectric absorption is the dominant mechanism, the EBF shows that CM3 has better gamma ray shielding properties than the other samples. In contrast, at the higher energies of 0.15, 1.5 and 3 MeV the EBF is independent of marble concentration.

iv. The efective removal cross section for fast neutrons (neutron attenuation coefficient)

The calculations of the fast neutron removal crosssection for the prepared samples are listed in Table 2. Variation in the neutron mean free path with marble powder concentration is illustrated in Fig. 9. The results show that sample CM3 has, numerically, the minimum value for the neutron mean free path. Similar to the case of gamma ray MFP, the addition of marble did not lead to a significant change in the fast neutron MFP.

V. Conclusions

The following conclusions can be drawn:

- The replacement of cement by marble waste powder enhances compressive strength, as replacing 10 % of cement with marble powder (CM3) led to an increase of 10 % in compressive strength with respect to the measured value for reference sample CM1. This may be attributed to the higher content of Fe2O3 and CaO than in the other samples, and is economically benecial.

- Based on the mass attenuation coefficients, the efective atomic number, Zeff , and the mean free path were calculated for the diferent mixtures. It was found that sample CM3, which contained 10 % marble, had better gamma and neutron shielding properties (i.e., minimum MFP and maximum efective atomic number Zeff than the other mixtures. This may be due to its higher density compared to the other mixtures.

- At the photon energy of 0.015 MeV, where photoelectric absorption is the dominant mechanism, the EBF shows that CM3 has better gamma ray shielding properties than the other samples, while for E > 0.015 MeV it is composition-independent.

Table 2: Calculations of the fast neutron removal cross-section for the prepared samples.