2.1 Experimental procedure

The collected samples were pulverized, sieved through a 0.2 mm mesh, sealed in standard 1 L Marinelli beakers, dry-weighed and stored for 4 weeks before counting in order to allow the attainment of equilibrium between ²²⁶Ra and ²²²Rn and its decay products. In equilibrium, the activity of each daughter is equal to that of the initial isotope of the series [8]. The gamma-ray spectra of the prepared samples were measured using a typical high-resolution gamma spectrometer based on a coaxial P-type shielded high-purity germanium (HPGe) detector, with a relative photo peak efficiency of 80% and energy resolution of 1.80 keV (FWHM) at 1332 keV, coupled to a high count-rate Multi-Task 16 k MCA card. Commercial software Gamma Genie-2000 was used for data analysis [6].

The ²²⁶Ra activities were calculated from the short-lived daughters ²¹⁴Pb (295.2 and 351.9 keV) and ²¹⁴Bi (609.3 keV). Similarly, ²³²Th activities were measured by taking the mean activity of photo peaks of the daughter nuclides ²²⁸Ac (338.40, 911.07 and 968.90 keV) and ²¹²Pb (238.63 keV). Activities of ⁴⁰K were determined directly from its 1460.83 keV gamma-ray. Quality assurance of the measurements was determined by using of Standard Reference Material IAEA Soil-375 [10].

The density of all the granite samples was estimated at 2580 kg·m⁻³ in average. The granite stones in markets are usually sized at 30 cm × 50 cm× 3 cm [11]. The granites differ from one type to another in their compositions. Table 1 shows the composition of a typical granite stone.

Calculation of the dose rate conversion factors was done based on the point kernel integration method for floors covered with 3.0 cm thick granite. The free-in-air absorbed dose rate (nGy·h⁻¹) in the room center can be expressed as Eq. (1) [4]:

where A_K, A_Ra and A_Th are the activity concentrations (Bq·kg⁻¹) of ⁴⁰K, ²²⁶Ra and ²³²Th, respectively.

To calculation the effective annual dose rate (mSv), we consider the conversion factor 0.7 Sv·Gy⁻¹ for adult categories. The indoor occupancy factor is 0.8 given by UNSCEAR report and the allowed indoor dose is 1 mSv·y⁻¹ [5]. The effective annual dose rate is by Eq. (2):

2.2 Theoretical procedure

3.1 Experimental and Simulation Results

The measured activities of ²³²Th, ²²⁶Ra and ⁴⁰K in the granite samples are 6.5–172.2, 3.8–94.2 and 556.9–1529.2 Bq·kg⁻¹, respectively. They are shown in Table 3, together with measurement and simulation results of the absorbed dose rate (dD/dt) and effective annual dose rate (dE/dt) due to ²²⁶Ra, ²³²Th and ⁴⁰K in air.

The absorbed dose rate is calculated by using DFn (Dose Function), DEn (Dose Energy) cards and tally F4 operations. Suppose one wanted to compute a dose rate of some type associated with a flux tally, either total or by energy group. This feature allows one to enter a point-wise response function (such as flux-to-dose conversion factors) as a function of energy to modify a regular tally. The energy points are specified on the DEn card and the corresponding values of the dose function are identified on the DFn card.

The calculated dose rate distributions due to ²³²Th, ²²⁶Ra and ⁴⁰K in the room floor are shown in Fig 1. As can be seen, the dose rate in the floor center is the maximum. The dose rate decreases with increasing height (the Z direction, not shown).

Fig. 1Full-screen View

The absorbed dose rate distribution in the room floor, due to ²³²Th, ²²⁶Ra and ⁴⁰K.

The simulated dose rates are 26.3–184.4 nGy·h⁻¹, averaged at 90.7 nGy·h⁻¹, while the measured dose rates are 27.7–204.2 nGy·h⁻¹, averaged at 104.9 nGy·h⁻¹.The two sets of minimum-maximum range and average value overlap closely. Thus the simulation method is suitable to any kind of dwelling places with the use of granite stones. The uncertainties calculation are calculated within 1σ (standard deviation) and simulation uncertainties calculated fewer than 5% errors by code. The uncertainty is calculated by:

where X_mean is the mean value, N is number of data and X_i is data. (i=1,2,3…,N).

The approximations errors are expressed by:

where, X_T is the true value and X_A is the approximate value.

The measured ²³²Th, ²²⁶Ra and ⁴⁰K activities of the samples are used to calculate the effective annual dose rates, which are. 0.14–1.00 mSv·y⁻¹, while the simulated effective annual dose rates are 0.13 – 0.92 mSv·y⁻¹.