Papers in Physics, vol. 12, art. 120005 (2020) Received: 25 April 2020, Accepted: 30 July 2020 Edited by: D. Peres Menezes Reviewed by: E. M. Yoshimura, Instituto de F́ısica da Univ. de São Paulo, Brazil Licence: Creative Commons Attribution 4.0 DOI: https://doi.org/10.4279/PIP.120005 www.papersinphysics.org ISSN 1852-4249 Optimizing the shielding properties of strength-enhanced concrete containing marble A. Abdel-Latif M.1,2*, M. I. Sayyed3, H. O. Tekin4,5, M. M. Kassab1 The purpose of this study is to develop a low cost, locally produced concrete mixture with optimum marble content. The resulting mixture would have enhanced strength properties compared to the non-marble reference concrete, and improved radiation shielding proper- ties. To accomplish these goals five concrete mixtures were prepared, containing 0, 5, 10, 15 and 20 % marble waste powder as a cement replacement on the basis of weight. These samples were subjected to a compressive strength test. The shielding parameters such as mass attenuation coefficients (µm), mean free path (MFP), effective atomic number (Zeff ) and exposure build-up factors (EBF) were measured, and results were compared with those obtained using the WinXcom program and MCNPX code in the photon energy range of 0.015 - 3 MeV. Moreover, the macroscopic fast neutron removal cross-section (neutron attenuation coefficient) was calculated and the results presented. The results show that the sample containing 10 % marble has the highest compressive strength and potentially good gamma ray and neutron radiation shielding properties. I. Introduction Radiation shielding has recently become an im- portant research topic in nuclear science, and is defined as the ability to reduce radiation effects through interaction with the shielding material. Several parameters such as attenuation effective- ness, strength, and thermal properties influence the * aam00@fayoum.edu.eg 1 Department of Mathematics and Eng. Physics - Fac- ulty of Engineering - Fayoum University, 63514 Fayoum, Egypt. 2 College of Industry and Energy Technology - New Cairo Technological University, Cairo, Egypt. 3 Department of Physics, Faculty of Science - University of Tabuk, Saudi Arabia. 4 Department of Radiotherapy, Vocational School of Health Services, Uskudar University, Turkey. 5 Medical Radiation Research Center (USMERA), Usku- dar University, Turkey. selection of radiation shielding materials. Concrete is one of the most widely used materials in reac- tor shielding due to its intrinsic properties, such as cheapness, and the ease of preparation of differ- ent compositions and forms. Moreover, its shield- ing properties depend strongly on the elemental composition of the prepared mixtures. An enor- mous amount of solid waste is generated annu- ally in Egypt as a by-product of mining, agri- cultural 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. Sev- eral researchers investigated the possible use of in- dustrial 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 fine or coarse aggregates in concrete, and their effects on mechanical and radiation shielding properties 120005-1 Papers in Physics, vol. 12, art. 120005 (2020) / A. Abdel-Latif M. et al. were evaluated. Among these mining and indus- trial by-products is marble dust powder, generated during the marble cutting process. Marble process- ing plants cannot store large amounts of marble dust powder, so reusing it is of great environmen- tal and economic benefit [5] and [6]. Corinaldesi et al. (2010) found that replacing sand with marble powder at a rate of 10 % provides maximum com- pressive strength [7]. Akkurt and Altindag (2012) determined, both experimentally and theoretically, the linear attenuation coefficients of concrete con- taining marble powder in its fine aggregate form. The measured and calculated linear attenuation co- efficients 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 mar- ble 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]. Ergün (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 workabil- ity of the mixture, while maintaining its compres- sive strength [12]. In a recent review it was found that as the amount of marble powder fine aggre- gate increases within the mixture, concrete work- ability decreases, and the compressive strength of the concrete increases because of its CaCO3 and SiO2 content [13]. Moreover, the cement with op- timal 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 op- timum marble content, which is stronger than or- dinary concrete and has enhanced gamma-ray and neutron shielding properties. II. Theoretical basis and calculations i. The mass attenuation coefficient, µm A mono-energetic gamma ray passing through mat- ter is attenuated due to photoelectric absorption, scattering, and pair-production. Attenuation be- havior follows Beer–Lambert’s law [8, 9, 16] I = I0e −µid, (1) where the incident and the transmitted photon intensities are denoted by I0 and I respectively. Moreover, d and µi are the thickness and the lin- ear attenuation coefficient, respectively. Also, the mass attenuation coefficient µm can be calculated by: µm = ∑ i ωi µi ρi (2) where ωi, µi and ρi are the weight fraction, linear attenuation coefficient, and the density of the ith constituent element. The mean free path (MFP) is the average distance traveled by a moving particle between successive impacts (collisions) MFP = 1 µ , (3) where µ is the linear attenuation coefficient. ii. Effective atomic number, Zeff The effective 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 un- certainties from pair production estimates are 2 to 3 percent, while above 100 MeV they are 1 to 2 percent [20]. Zeff = NA ∑ i fiAi µi ρi∑ i fi Ai Zi µi ρi , (4) where NA is Avogadro’s number, µi is the linear attenuation coefficient, ρi is the density, Ai is the atomic mass, Zi is the atomic number and fi is the mole fraction of the ith constituent element. Mole fraction fi is given by fi = (ωi/Ai)∑ i ( ω A ) i , (5) where omegai is the weight fraction. 120005-2 Papers in Physics, vol. 12, art. 120005 (2020) / A. Abdel-Latif M. et al. 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 is- sues 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 µm of different concrete mixtures [22,23]. The schematic diagram shows the MCNPX gamma ray attenuation setup with five 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 file. iv. Exposure build-up factor, EBF During the penetration of gamma photons through any material, they may be either absorbed or scat- tered by the atoms of this material. Secondary ra- diation may arise due to the build-up of scattered photons inside the material. Accordingly, it is nec- essary to estimate these build-up factors to deter- mine effective exposure and energy deposition in the shielding material. The build-up of secondary radiation is characterized by the exposure build- up factor (EBF), defined as the ratio of the to- tal gamma photon flux (absorbed and scattered) to the absorbed gamma photons of the incident beam [24, 25]. In this work, the geometrical progression (G-P) fitting method [26] was used due to a high level of accuracy. The ratio R = µcomp/µm, which represents the relative contribution of the mass at- tenuation coefficient due to Compton scattering in- teraction (µcomp), 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 equiva- lent atomic number (Zeq) for each sample was ob- tained using the following formula of interpolation by [24–26]: Zeq = Z1 log(R2/R) + Z2 log(R/R1) log(R2/R1) . (6) The build-up factors for each sample were calcu- lated using the geometrical progression fitting func- tion B(E,x) and K(E,x). B(E,x) = { 1 + (b− 1) (K x−1) (K−1) K 6= 1 1 + (b− 1)x K = 1 , (7) K(E,x) = cxa + d tanh ( x XK − 2 ) − tanh (−2) 1 − tanh (−2) , (8) 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 ob- tained in advance using the following interpolating formula: P = P1 log(Z2/Zeq) + P2 log(Zeq/Z1) log(Z2/Z1) , (9) where P stands for the required G-P fitting pa- rameter for the selected sample at a specific energy value, while P1 and P2 represent the values of the G-P fitting parameter corresponding to the atomic numbers Z1 and Z2, respectively. The G-P fitting parameters P1 and P2 can be obtained from the American National Standard database which con- tains the exposure buildup G-P fitting 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 ΣR The attenuation of neutrons in matter obeys the following law: I = I0 exp (−ΣR x) (10) 120005-3 Papers in Physics, vol. 12, art. 120005 (2020) / A. Abdel-Latif M. et al. The effective fast neutron removal cross-section (neutron attenuation coefficient), ΣR, for a com- pound or a homogeneous mixture may be calcu- lated using the values ΣR/ρ for various elements in the compound or mixture, using the following equations [27–34] ΣR/ρ = ∑ i Wi(ΣR/ρ)i, (11) ρ = ∑ i ρi(ΣR/ρ)i. (12) Where Wi is the weight percentage, and ρi and (ΣR/ρ)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 pro- cedures i. Materials The fine 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 mar- ble 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 shield- ing properties due to the incorporation of mar- ble dust as a partial replacement for cement, on a weight basis. In order to achieve these goals, five different 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 pre- pared mixtures. For each mixture nine cubic sam- ples (5 cm × 5 cm × 5 cm) were cast. Samples The first radioactive source (isotope) is placed in the device and then the unnnatenuated radiation intensity l 0 is measured One slice of the sample (1-1.5 cm thick) is placed and the transmitted radiation intensity is then measured Another slice of the same sample (1-1.5 cm thick) is added to the first one and the transmitted radiation intensity is measured again Continue adding slices and measuring the transmitted radiation intensity A linear regression is developed between the measured intensity and the overall thickness. The linear attenuatuation coefficient is calculated and hence the mass of sample CM1 Replace the radioactive source with another source and repeat the previous steps for all isotopes Repeat the previous steps for CM2, CM3, CM4 and CM5 Group the measured mass attenuation versus the energy lines and compare it with MCNPX and Xcom data Figure 2: A flowchart describing the steps followed in the experiment to measure the mass attenuation coef- ficients. used for measuring the linear attenuation coeffi- cient were then obtained by cutting the cubic sam- ples into slices with thicknesses varying from 1 to 1.5 cm, and the flowchart was followed, as shown, (see Fig. 2) to calculate the mass attenuation coef- ficients. The chemical composition of the constituent ma- terials of each sample were analyzed using the X- ray Fluorescence (XRF) technique; these composi- tions are listed in Table 1. 120005-4 Papers in Physics, vol. 12, art. 120005 (2020) / A. Abdel-Latif M. et al. 0 5 10 15 20 104 106 108 110 112 114 116 118 120 Region II C om pr es si ve s tr en gt h (K g/ cm 2 ) Marble Concentration (%) Compressive strength Polynomial Fit of Compressive strength Region I y = -0.0943x2 + 1.5857x + 110.29 R² = 0.9461 Figure 3: Compressive strength and marble concentra- tion. 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/cm 2 per minute until the specimen failed, and the average reading was registered. iv. Gamma ray shielding parameters ex- periment 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 mea- Table 1: XRF analysis of the prepared mixtures. Chemical Composition (% by weight) Element CM1 CM2 CM3 CM4 CM5 TiO2 0.27 0.33 0.37 0.33 0.24 Al2O3 2.88 3.27 3.38 2.86 2.53 Fe2O3 1.89 2.06 2.38 1.92 1.55 MnO 0.04 0.05 0.05 0.04 0.03 MgO - 0.14 0.64 0.11 0.03 CaO 19.26 18.69 20.28 16.95 15.09 Na2 O 0.14 0.24 0.11 0.08 0.15 SiO2 Balance Balance Balance Balance Balance Figure 4: The measured mass attenuation coefficient compared with that determined by MCNPX and WinX- Com. sure the linear gamma ray attenuation coefficient of each sample struck by gamma radiation. 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, max- imum 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. 120005-5 Papers in Physics, vol. 12, art. 120005 (2020) / A. Abdel-Latif M. et al. Figure 5: The effective atomic number, Zeff , as a func- tion of the incident photon energy. ii. Gamma ray shielding parameters The mass attenuation coefficient, µm, was experi- mentally measured at different 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 re- sults are displayed in Fig. 4. It can be clearly seen that there is good agreement between the the- oretically calculated µm and that measured exper- imentally. Moreover, for very low photon energy (E < 15 keV), the mass attenuation coefficient µm 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. Us- ing Eq. (4) together with the calculated mass at- tenuation coefficient, the effective 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 increas- ing again as the energy increased to 3 MeV, it was found that sample CM1 had the highest effective atomic number, followed by CM3. Moreover, it is worth noting that the addition of marble led to a decrease in the effective atomic number. The MFP values for the different marble concentrations were calculated using MCNPX simulation code at dif- ferent 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 Figure 6: MFP and marble concentration at different energy lines. lead to a significant 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 pho- ton increases, until it reaches a maximum value, after which it decreases as the penetration depth increases. At this peak point, the Compton scatter- ing interaction is the dominant mechanism. This is followed by a decrease in the build-up factors with 0.01 0.1 1 1 2 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 E B F Photon energy (MeV) (a) 1 MFP 0.01 0.1 1 1 10 Photon energy (MeV) (b) 5 MFP 0.01 0.1 1 1 10 E B F Photon energy (MeV) (c) 10 MFP 0.01 0.1 1 100 101 102 Photon energy (MeV) (d) 40 MFP Figure 7: The EBF as a function of photon energy at 1, 5, 10 and 40 MFP depth. 120005-6 Papers in Physics, vol. 12, art. 120005 (2020) / A. Abdel-Latif M. et al. 1 10 1.02 1.04 1.06 1.08 1.1 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 E B F Penetration depth (mfp) (a) 0.015MeV 1 10 1 10 100 Penetration depth (mfp) (b) 0.15MeV 1 10 1 10 100 E B F Penetration depth (mfp) (c) 1.5MeV 1 10 100 101 15 20 25 30 35 40 4 5 6 7 8 9 10 11 12 EB F E (MeV) R-CM1 R-CM2 R-CM3 R-CM4 R-CM5 Penetration depth (mfp) (d) 3MeV Figure 8: The EBF and penetration depth at photon energies 0.015, 0.15, 1.5 and 3 MeV. 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]. Variation in the EBF with penetration depth for the different concrete mixtures at an incident pho- ton 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 mecha- nism, 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 concentra- tion. iv. The effective removal cross section for fast neutrons (neutron attenuation co- efficient) The calculations of the fast neutron removal cross- section 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, numer- ically, 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. Figure 9: The Neutron MFP and marble concentra- tions. V. Conclusions The following conclusions can be drawn: � The replacement of cement by marble waste powder enhances compressive strength, as re- placing 10 % of cement with marble powder (CM3) led to an increase of 10 % in com- pressive 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 eco- nomically beneficial. � Based on the mass attenuation coefficients, the effective atomic number, Zeff , and the mean free path were calculated for the different mix- tures. It was found that sample CM3, which contained 10 % marble, had better gamma and neutron shielding properties (i.e., minimum MFP and maximum effective 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 bet- ter gamma ray shielding properties than the other samples, while for E > 0.015 MeV it is composition-independent. 120005-7 Papers in Physics, vol. 12, art. 120005 (2020) / A. Abdel-Latif M. et al. Table 2: Calculations of the fast neutron removal cross-section for the prepared samples. Element CM1 CM2 CM3 CM4 CM5 Part. dens. ΣRcm −1 Part. dens. ΣRcm −1 Part. dens. ΣRcm −1 Part. dens. ΣRcm −1 Part. dens. 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Dosim. 116, 489 (2005). 120005-9 https://doi.org/10.1088/0031-9155/53/20/N01 https://doi.org/10.1088/0031-9155/53/20/N01 https://doi.org/10.1016/j.jnucmat.2009.07.001 https://doi.org/10.1155/2014/725629 https://doi.org/10.1155/2014/725629 https://doi.org/10.1051/radiopro/2013090 https://doi.org/10.6028/NBS.NSRDS.29 https://doi.org/10.6028/NBS.NSRDS.29 https://inis.iaea.org/search/search.aspx?orig_q=RN:39098954 https://inis.iaea.org/search/search.aspx?orig_q=RN:39098954 https://doi.org/10.1016/j.jnoncrysol.2017.04.031 https://doi.org/10.1016/j.jnoncrysol.2017.04.031 https://doi.org/10.1007/s41365-017-0253-4 https://doi.org/10.1007/s41365-017-0253-4 https://doi.org/10.13182/NSE86-A17113 https://dx.doi.org/10.18434/T4D01F https://dx.doi.org/10.18434/T4D01F https://webstore.ansi.org/Standards/ANSI/ANSIANS1991-1534182 https://webstore.ansi.org/Standards/ANSI/ANSIANS1991-1534182 https://doi.org/10.1016/j.anucene.2009.01.013 https://doi.org/10.1016/j.anucene.2009.10.022 https://doi.org/10.1016/j.anucene.2009.10.022 https://doi.org/10.1016/j.anucene.2010.08.003 https://doi.org/10.1016/j.anucene.2010.08.003 https://doi.org/10.1016/j.anucene.2014.09.044 https://doi.org/10.1016/j.anucene.2014.09.044 https://doi.org/10.18576/jrna/020203 https://doi.org/10.18576/jrna/020203 https://dx.doi.org/10.26808/rs.ed.i8v4.02 https://dx.doi.org/10.26808/rs.ed.i8v4.02 http://www.scirp.org/journal/PaperInformation.aspx?PaperID=59708&#abstract http://www.scirp.org/journal/PaperInformation.aspx?PaperID=59708&#abstract https://doi.org/10.1093/rpd/nci192 https://doi.org/10.1093/rpd/nci192 Introduction Theoretical basis and calculations The mass attenuation coefficient, m Effective atomic number, Zeff MCNPX code (version 2.6.0) Exposure build-up factor, EBF The macroscopic effective removal cross-section for fast neutron R Materials and experimental procedures Materials Concrete sample preparation Compressive strength test Gamma ray shielding parameters experiment Results and discussion Compressive strength Gamma ray shielding parameters The energy exposure build-up factor, EBF The effective removal cross section for fast neutrons (neutron attenuation coefficient) Conclusions