The building materials samples to be analyzed are collected from large and important commercial suppliers in Morocco. As regards sand, samples are taken from seven different quarries in the Doukkala region. Before any analysis and to obtain homogeneous samples, these building materials are dried in an oven at 40˚C for 24 hours and then ground and sieved through a 100 μm mesh screen. The screened samples are packaged in radon-tight containers for at least 4 weeks to establish the secular equilibrium corresponding to seven half-lives of ²²²Rn.

The measurement of the natural radioactivity in the prepared samples is carried out by gamma ray spectrometer using the Broad Energy Germanium detector (BEGe) at Pluridisciplinary Institute Hubert Curien in Strasbourg, France. It is a planar type Hyper-Pure Germanium HPGe detector associated with a set of electronic modules for shaping the pulses, amplifying and storing the pulses delivered during the passage of the gamma rays through the detector. Its energy measurement range is 30 to 3000 keV with a resolution of 0.633 keV to 122 keV and from 1.934 keV to 1332 keV [12] .

As regards the energy and efficiency calibration of the BEGe detector, a multi-energy certified standard is analyzed under the same conditions and geometry as the samples studied. This standard contains several γ-emitting radionuclides such as ²⁴¹Am (60 keV), ¹⁰⁹Cd (88 keV), ⁵⁷Co (122, 136 keV), ¹³⁹Ce (165 keV), ⁵¹Cr (320 keV), ¹¹³Sn (391 keV), ⁸⁵Sr (514 keV), ¹³⁷Cs (661 keV), ⁸⁸Y (898, 1836 keV) and⁶⁰Co (1173, 1332 keV). Samples of building materials are packaged in SG50 geometry and counted for 172.800 seconds. The treatment of the amplitude spectra is carried out using automatic analysis software Genie 2000 [12] allowing to give directly the mass activity of each radioelement present in the sample.

The volumetric activities and the exhalation rate in terms of area and mass of the radon in the prepared samples are carried out using the alpha dosimetry. For this purpose, several pieces of 2 × 2 cm² of Solid State Nuclear Track Detector (SSNTD) LR115 type 2 non strippable, Kodak brand 12 µm thick, are exposed in sealed cylindrical “cans” of 5.5 cm diameter and 9.5 cm height by 50 g of each sample of building materials. After two months of irradiation, the LR115 are chemically treated in a 2.5 N sodium hydroxide solution during 100 min at a temperature of 60˚C. The developed films are read using an optical microscope. The density of traces per unit area and per unit time in LR115 and the volume activity of radon A V R n are determined according to [13] .

The specific activities of the radionuclides ²²⁶Ra, ²³²Th and ⁴⁰K are calculated by gamma spectrometry, after establishment of the secular equilibrium, in the various samples of building materials using the following ratios of energies:

• ²¹⁴Pb (295 keV and 352 keV) and ²¹⁴Bi (609 keV, 1120 keV and 1764 keV) for ²²⁶Ra;

• ²²⁸Ac (911 keV and 969 keV) and ²¹²Pb (239 keV) for ²³²Th;

• ⁴⁰K (1461 keV) from the emission intensity line 10.55%.

Figure 1 shows the minimum, the maximum and the average specific activities of ²²⁶Ra, ²³²Th and ⁴⁰K radionuclides measured in the different types of

building materials. It can be seen that the contribution of the activity of the ⁴⁰K is much greater than that contributed by the ²³⁸U and the ²³²Th. It should also be noted that the activity of ²³²Th in each sample is less than that of ²²⁶Ra except for the red brick, ceramic and granite samples.

From these values, it results that the low average specific activities are recorded in the gypsum for the radionuclides ²²⁶Ra and ²³²Th, and in the white cement for the ⁴⁰K with average activities of the order of 9 Bq/kg, 3 Bq/kg and 68 Bq/kg respectively. The highest average specific activities for the ²²⁶Ra, ²³²Th and ⁴⁰K radionuclides are recorded in the granite and are respectively of the order of 52 Bq/kg, 63 Bq/kg and 705 Bq/kg. All the specific activities of the measured ²²⁶Ra, ²³²Th and ⁴⁰K are within the permissible limits of 35 Bq/kg, 30 Bq/kg and 370 Bq/kg [4] , respectively, with the exception of a few samples of red brick, gray cement, ceramic and granite. Therefore, the choice of materials for building constructions should be monitored and adapted according to the criteria of the limitation of doses.

In Table 1, and for comparison with our results, the specific activities of natural radionuclides are grouped together in samples of building materials in Morocco and some other countries. Overall, the specific activities obtained in this study are comparable to those found in other countries, with the exception of a few activities that are remarkably higher than ours.

Due to the non-uniform distribution of natural radionuclides in building material samples, the radiological index radium equivalent Ra_eq is generally represented as the sum of the specific activities of ²²⁶Ra, ²³²Th and ⁴⁰K based on the assumption that 10 Bq/Kg of ²²⁶Ra, 7 Bq/kg of ²³²Th and 130 Bq/kg of ⁴⁰K would produce the same dose rate of gamma radiation. This is the most widely used index for radiological risk assessment. It is calculated using the following equation [5] [28] :

R a e q = A 226Ra + 1.43 A 232Th + 0.077 A 40K (1)

where A 226Ra , A 232Th and A 40K are the specific activities in (Bq/kg) of ²²⁶Ra, ²³²Th and ⁴⁰K in the samples analyzed.

In Table 2, the mean values of the radium equivalent Ra_eq varying from 19 to 196 Bq/kg, which are still below the permissible limit of 370 Bq/kg [5] , are grouped together for the samples analyzed. We note that the lowest value is found in the gypsum, while the highest is in the granite.

From these results, we can consider that these building materials do not present a significant radiological hazard to the population and can be used in various construction activities. However, it should be noted that the Ra_eq values vary considerably in the same type of building materials and may in some cases exceed the permissible limit. This is the case of granite where the maximum value of the equivalent radium Ra_eq is of the order of 382 Bq/kg. The use of the latter in construction activities must be moderate.

The calculation of the total activity of radionuclides in building materials alone does not make it possible to assess the radiological risks of gamma radiation. Other risk indices are also taken into account and are defined by a model taking into account the maximum activity of Ra_eq (370 Bq/kg). The external hazard index H_ex is defined by the following equation [5] [28] :

H e x = A 226Ra 370 + A 232Th 259 + A 40K 4810 (2)

In addition to this external hazard, the respiratory organs are threatened because of the decay of ²²⁶Ra into ²²²Rn and its descendants. To account for this threat, the maximum permissible activity for ²²⁶Ra is therefore reduced by half (185 Bq/kg). This internal hazard H_in is quantified by the following relation [5] [28] :

H i n = A 226Ra 185 + A 232Th 259 + A 40K 4810 (3)

Table 2 gives the internal and external hazard indices of the samples of the building materials studied. The values of the internal hazard index according to the materials vary between 0.08 and 0.67 while for the external hazard index they are between 0.05 and 0.53. The values are maximum for granite and minimum for gypsum. None of these values exceeds the unit, the maximum value of the internal (H_in) and external (H_ex) hazard indices allowed.

The absorbed dose rate Ḋ (nGy/h) due to the specific activity of natural radionuclides from building materials in air at 1 m height is defined by the following equation [5] :

D ˙ ( nGy / h ) = 0.462 A 226 Ra + 0.604 A 232 Th + 0.0417 A 40 K (4)

Table 2 summarizes the results of the absorbed dose rates in air for the analyzed building materials. We note that the highest value is attributed to granite (91 nGy/h) while the lowest value is gypsum (9 nGy/h). These values of absorbed dose rates are below the permissible limit (55 nGy/h) [5] with the exception of the granite sample.

To estimate the annual effective dose received by the population, we take into account the coefficient of conversion of dose rate absorbed in air in effective dose (0.7 Sv/Gy) and external occupancy factor (0.2) [5] . The annual effective doses are determined as follows [5] :

Ė e x ( mSv / y ) = D ˙ ( nGy / h ) × 8760 ( h ) × 0.2 × 0.7 ( Sv / Gy ) 10 − 6 (5)

Ė i n ( mSv / y ) = D ˙ ( nGy / h ) × 8760 ( h ) × 0.8 × 0.7 ( Sv / Gy ) 10 − 6 (6)

The results of the annual external (Ė_ex), internal (Ė_in) and total (Ė_tot) effective doses for the samples of building materials studied are given in Table 2. It is found that the total value for each sample is less than the annual effective dose limit set at 1 mSv/y [5] . Therefore, we consider that these building materials do not present a radiological risk to the population and can be used in the construction of buildings.

The Excess Lifetime Cancer Risk (ELCR) treats the probability of developing cancer during the life of a human being at a certain level of exposure. The ELCR is calculated using the following equation [29] :

ELCR = E ˙ t o t × DL × RF (7)

Or:

Ė_tot is the total annual effective dose (μSv/year);

DL (Duration of Life) is the average life span of a human being (70 years);

RF is the Risk Factor fatal by cancer (Sv⁻¹). For stochastic effects, the International Commission on Radiological Protection (ICRP) estimates the value of this factor to be 0.05 for the public [30] .

In Table 2, ELCR values range from 0.19 × 10⁻³ to 1.96 × 10⁻³ where the lowest value is found in the gypsum, while the highest is in the granite. The ELCR value at the granite sample far exceeds the permissible limit of 0.29 × 10⁻³ [29] . As a result, the risk of cancer increases with increasing exposure to these materials.

After calculating the density of traces per unit area and per unit time in the LR115, the volume activities of the radon A V R n are calculated using the detection efficiency equal to 0.0258 (traces∙cm⁻²∙j⁻¹)/(Bq∙m⁻³) [31] . The exhalation rate in terms of area (E_S in Bq∙m⁻²∙h⁻¹) and mass (E_M in Bq∙kg⁻¹∙h⁻¹) of ²²²Rn are determined by the following equation [32] [33] :

E S = A V R n V λ R n S e [ t + ( 1 λ R n ) ( e − λ R n t − 1 ) ] (8)

E M = A V R n V λ R n M [ t + ( 1 λ R n ) ( e − λ R n t − 1 ) ] (9)

With A V R n is the volume activity of radon (Bq∙m⁻³∙h); V is the volume of the enclosure (m³); λ R n is the ²²²Rn decay constant (h⁻¹); S_e is the area of the sample (m²); M is the mass of the sample in kg and t is the exposure time (h).

We present in Table 3 the average values of the volumetric activity and exhalation rate in terms of area and mass of radon measured in the samples of the building materials analyzed. These values vary respectively from (72 to 350 Bq/m³), (56 to 273 mBq∙m⁻²∙h⁻¹) and (3 to 15 mBq∙kg⁻¹∙h⁻¹) where the lowest values are identified in the gypsum, while the highest values are in the granite. All volumic activity values for radon are in the range of 100 to 300 Bq/m³ recommended by ICRP [34] with the exception of some samples of gray cement (191 to 366 Bq/m³), ceramic (159 to 322 Bq/m³) and granite (132 to 610 Bq/m³).

In Table 4, for comparison with our results, the volumetric activities and exhalation rates in terms of area and mass of radon in building materials samples in Morocco and some other countries. Overall, the obtained results in this study are comparable to those found in other countries, with the exception of a few values that are remarkably higher than ours.

A positive correlation is found between the specific activities of ²²⁶Ra on the one hand, it is determined by high resolution gamma spectrometry and the exhalation rates of ²²²Rn calculated with the alpha dosimetry based on the use of LR115 on the other hand. This correlation is illustrated in Figure 2 with a correlation coefficient in the order of 0.96.