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www.etasr.com Alghamdi: Relationship between Grain Size Distribution and Radon Content in Surficial Sediments … 
 

Relationship between Grain Size Distribution and 
Radon Content in Surficial Sediments of Wadi Arar, 

Saudi Arabia  
 

Mohammed A. M. Alghamdi  
Engineering Geology, Earth Science Faculty 

King Abdulaziz University 
Jeddah, Saudi Arabia 

mmushrif@gmail.com 
 

 

Abstract—Surficial sediments with low radon content are 
desirable materials in construction applications. In this study, the 
relationship between grain size and radon content was 
investigated in sediments collected from seven sites in Wadi Arar, 
Saudi Arabia, with the intent of determining whether grain size 
analysis could be used for rapidly assessing the suitability of 
potential construction materials. Thirty-five samples were 
collected (five per site) and the grain size distribution was 
determined using sieves. Radon contents were measured on 
composite samples with a RAD7 radon detector. Among the 
sediment types (gravel, coarse sand, medium sand, fine sand, and 
silt and clay), the best linear correlations between grain size and 
radon contents were found for the coarse sand (negative slope, 
r=0.82) and fine sand (positive slope, r=0.78). Polynomial 
relationships were also tested. A fourth-degree polynomial 
equation effectively described the correlation between grain size 
and radon content (R2 = 0.933). As shown by this model, the 
highest correlations with radon contents were detected at grain 
sizes smaller than 2.0 mm. Thus, grain size may be useful for 
preliminary site assessment work. 

Keywords-grain size distribution; Rad7; Radon; construction 
material; polynomial 

I. INTRODUCTION 
Radon in construction materials can pose health hazards to 

building occupants. Thus, knowledge of radon contents in 
potential source materials would be valuable before natural 
resources are extracted from particular sites. The health hazard 
of radon gas is due to its radioactivity. The link between radon 
and lung cancer has been already established through 
epidemiological studies in many countries [1-3]. Moreover, 
authors in [4] correlated radon concentrations with 
geodynamic, volcanic, and tectonic events. Authors in [5] 
observed that the radon exhalation rate increases with grain 
size. Their estimated values of radon exhalation rates for all 
studied samples were found to be lower than the internationally 
accepted value of 57–60 Bq m-2 h-1. Authors in [6] presented an 
improvement on previous models of radon emanation from the 
soil by incorporating soil grain size in addition to moisture. 
Authors in [7] found that the correlations between raw values 

of radon concentrations, soil particle size fractions, and 
elevation were weak. Furthermore, as a result of differences in 
geological structure, lithology, and climate parameters, an 
anomaly of 222Rn around Uro in western Sudan was reported in 
[8]. Regarding construction material selection, authors in [9] 
found that dune sands located east of Jeddah city should be 
mixed with crushed fine aggregates prior to use as a 
construction material, and authors in [10] found that the 
addition of both lime and cement has a pronounced effect on 
soil stability by changing its mineralogy. This research 
therefore makes an important contribution to the literature by 
highlighting radon as another important factor affecting the 
selection of construction materials. Wadis in Saudi Arabia are a 
common source of sediments for construction applications. 
This study investigates the relationship between sediment grain 
size and radon contents in Wadi Arar in Saudi Arabia. The 
objective is to determine if grain size can be used as a rapid 
assessment technique for predicting radon contents and 
assessing the suitability of sediments for construction 
applications. 

II. METHODOLOGY 

A. Site and Sampling Description 
In this work, the relationship between radon content and the 

grain size of deposits along a 20 km stretch of Wadi Arar 
(Figure 1) was investigated. The radon content was measured 
using the RAD 7 technique. The soil is composed of 
Cretaceous sedimentary rocks such as sandstone, shale, and 
limestone. The Quaternary sediments within Wadi Arar have 
previously been investigated [11, 12] and classified as silty 
sand SM according to the unified soil classification system 
[11]. The CR-39 technique was previously used to determine 
the radon contents of Wadi Arar in northern Saudi Arabia [13, 
14]. This study expands the results of [14], in which author 
developed a polynomial equation to determine radon content 
by incorporating grain size. developed a polynomial equation 
to determine radon content by incorporating grain size. 



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B. Samples 
Thirty-five fresh surface disturbed samples were collected 

from seven locations labeled A, B, C, D, E, F, and G. Each 
location profile included five samples. Profile A was located at 
the NE point of Wadi Arar adjacent to Arar city, profile G was 
located in the SW direction facing Aljouf city. The remaining 
five profiles B, C, D, E, and F were located between A and G 
(Figure 1). A shovel was used to collect approximately 1 kg of 
sediment at each sampling point, and the samples were stored 
in 20 L plastic buckets and transported at room temperature to 
the laboratory of Northern Border University. The samples 
were analyzed within one week of collection. 

 

 
Fig. 1.  The seven sampled locations in the study area 

C. Radon Contents 
Radon content was measured with a RAD7 electronic radon 

detector according to the methods described in [13]. A single 
radon concentration value was measured in a composite sample 
created from portions of the five sediment samples taken at 
each site. To ensure environmental safety with regard to the 
radon hazards, the maximum readings for the radon contents 
(Bq/m3) were used. 

D. Grain Size Distribution  
The grain size distribution was determined using a 

mechanical shaker and a standard set of sieves, as in [14]. 
Percentages of the retained grains in nine sieves were 
calculated. The diameters of the used sieves were 4.75, 3.35, 
2.0, 1.0, 0.85, 0.425, 0.25, 0.15, and 0.075 mm. According to 
the unified soil classification system (USCS), the geometric 
means of each profile were grouped into five groups: gravel 
(G), coarse sand (CS), medium sand (MS), fine sand (FS), and 
silt & clay (SC), based on the following sizes in mm: 

G ≥ 4.75 

4.75 > CS ≥ 2 

2 > MS ≥ 0.425 

0.425 > FS ≥ 0.075 

0.075 > SC 

E. Data Analysis  
Microsoft Excel was used for the linear regressions and 

polynomial analysis. 

III. RESULTS 

A. Mean and Variability  
The harmonic mean of the maximum radon content was 

calculated and then the standard deviations (σ) and coefficients 
of variation (CV%) were determined. For the grain size 
distribution, the geometric means, σ, and CV% were 
constructed from [14] (Table I). According to statistical 
analysis of the geometric mean, σ and CV%, the relative 
quantitative distribution of different grain size fractions in 
Wadi Arar changes with location. Sites A and D show 
homogeneous grain size distributions, yet sites B, C, E, F, and 
G are characterized by significantly larger relative quantities of 
medium- sand, coarse sand, silt & clay, gravel and fine sand, 
respectively. Sites C, E, and F are also characterized by 
significant smaller relative quantities of fine sand, medium 
sand, and coarse sand, respectively. According to the 
coefficient of variation, the fine sand fraction is relatively more 
homogenous throughout the study area, whereas gravel is less 
homogeneous. According to harmonic mean, σ, and CV% 
values, high radon content was observed in location G. 

B. Correlation between Radon Content and Grain Size 
Correlation coefficients (r) were calculated to detect and 

compare the strength and direction of the linear relationship 
between radon content and various grain size fractions. Figure 
2 shows the correlation between radon content and grain size 
fractions. According to hypothesis testing, coarse sand and fine 
sand show a highly significant correlation with radon content 
(P-values less than 0.05) with correlation coefficient values 
equal to -0.82 and 0.78, respectively. All other fractions show a 
weak correlation. According to the negative and weak 
correlation results, all grain sizes except fine sand are suitable 
for use as a construction material. At a coefficient of 
determination (R2) equal to 0.93, and based on measurements 
obtained, the relationship between grain size and its correlation 
is a function of a fourth degree polynomial (Figure 3). 

C. Polynomial Relationship 
The main goal of this work is to find the best model for the 

maximum radon content in terms of various grain size class 
percentages because it is much simpler and cheaper to measure 
grain size percentage than radon content. The term ‘best model’ 
refers to the statistical polynomial fit between Rad7-max and 
grain size with the highest R2 value. To achieve that target, the 
following two parameters must be calculated: 

1. The degree of the polynomial 

2. The grain size fraction or fractions with the highest 
R2 value 

As there are only seven profiles, the highest possible 
polynomial degree is six. The polynomial fit used is a statistical 
polynomial fit with a 95% confidence interval. The relationship 
between radon content and different grain size fractions was 
plotted, and the best fit line of the data was deduced for 
different functions that could represent the relationship, such as 
linear, logarithmic, power, or polynomial functions. According 
to the highest values of the coefficient of determination (R2), 



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the polynomial function was selected as the best function to 
represent the relationship between radon content and grain size 
contents. Figure 4 shows the plots and equations for all grain 
size contents using the fourth degree polynomial function.  

TABLE I.  MAX RADON CONTENT AND PERCENTAGES OF GRAIN SIZE 
FRACTIONS FOR GRAVEL (G), COARSE SAND (CS), MEDIUM SAND (MS), FINE 
SAND (FS), AND SILT AND CLAY (SC).  

Site Rn G CS MS FS SC 
A 35 19.23 13.82 22.55 19.63 24.77 
B 35 10.57 14.63 27.91 18.98 27.91 
C 38 16.2 15.49 22.56 18.01 27.74 
D 40 13.13 13.1 20.71 19.88 33.18 
E 42 9.77 10.98 17.29 20.56 41.4 
F 43 31.62 7.57 20.56 20.45 19.8 
G 45 11.2 9.91 24.68 23.2 30.99 

Mean 39.38 16.29 12.17 22.49 20.32 28.73 
σ 3.9 7.68 2.84 3.37 1.62 6.82 

CV% 9.91 47.14 23.33 14.97 8 23.74 

 

 
Fig. 2.  Correlation between radon content and various grain size fraction 
(*Correlation is statistically significant at 0.05) 

 

 
Fig. 3.  Grain size vs. its correlation with radon content according to 
cumulative % passing 

 
Fig. 4.  Polynomial relationship between radon content and grain size 
contents 

D. R2 Versus Polynomial Degree 
The polynomial is more representative when the value of R2 

is high. According to the best fit line of R2 of each grain size 
fraction at different polynomial degrees (Figure 5), the 
relationship between R2 and the degree of the polynomial can 
be classified into two clusters. The first cluster indicates a 
straight line relationship, which includes coarse sand, fine sand, 
and silt and clay, while the second cluster describes a curved 
model that includes medium sand and gravel. For the straight 
line models, coarse and fine sand reflects strong R2 values for 
all polynomial degrees (>0.67 and 0.61, respectively), while 
the silt and clay fraction reflects strong R2 values for the 3rd 
degree polynomial (0.61). For the curved models, strong R2 
values are observed for medium sand at the 4th degree 
polynomial (0.93) and for gravel at the 6th degree polynomial 
(1.00). 

E. Relationship Strength 
According to the value of R2, the strength of the polynomial 

relationship between radon content and grain size can be 
classified into three categories: good, medium, and weak. Good 
relationships are observed for coarse and fine sand, which have 
the highest values of R2 at different polynomial degrees. 
Medium relationships are found for medium sand and silt and 
clay, which have high R2 values at the 4th or higher degree of 
the polynomial. A weak relationship is observed for the gravel 
fraction, which contains almost all the lowest R2 values (Figure 
5). 

 

 
Fig. 5.  R2 values for different degrees of the polynomial function and 
different grain sizes 

IV. STUDY COMPARISON 
 A comparison with [14] indicates that coarse sand and fine 

sand display highly significant correlations with both 
techniques used in these studies. The correlation between grain 
size and radon content measured using the Rad7 technique is 
generally higher than that measured using CR-39 (Figure 6). 
The relationship between the two correlations is linear, with an 
R2 of 0.97 (Figure 7). The relationship between the R2 values 
of both techniques is linear for fine sand and polynomial for all 
other fractions (Figure 8). 



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Fig. 6.  Correlation between radon content and various grain size fractions 
for both CR-39 and Rad 7 techniques 

 

 
Fig. 7.  Relationship between radon content and grain size correlations 
determined using CR-39 and Rad 7 techniques 

 

 
Fig. 8.  Relationship between R2 values for the correlations determined 
using Cr-39 and Rad7 techniques 

V. CONCLUSIONS 
The relationship between grain size and radon content was 

investigated in sediments collected from seven sites in Wadi 
Arar, Saudi Arabia, with the intent of determining whether 
grain size analysis could be used for rapidly assessing the 
suitability of potential construction materials.  The main 
conclusions are as follows: 

 The polynomial function is the best model to represent the 
relationship between radon content and grain size. 

 Coarse sand has a correlation coefficient of -0.82 with 
radon content, which is a strong negative relationship. 

 Fine sand has a highly positive correlation with radon 
content, with a correlation coefficient of 0.78. 

 According to R2 values, the strength of the polynomial 
relationship between radon content and grain size is good 
for coarse and fine sand, which have the highest R2 values 
at all polynomial degrees, medium for sand and silt and 
clay, and weak for gravel. 

 The relationship between the coefficient of determination 
R2, and the polynomial degree shows two different 
behaviors: a straight line relationship for coarse sand, fine 
sand, and silt and clay, and a curved relationship for 
medium sand and gravel. 

 According to the fraction type, both linear and polynomial 
relationships were representative. 

 The Rad7 technique reflects higher correlations between 
grain size and radon content than the CR-39 technique. 

 This research shows that fine sand grain size would make 
bad construction material. 

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