Modeling of morphometric parameters of gypsum sinkholes

Introduction
Maroon plain, located in Maroon basin is situated in Khuzestan, and Kohgiluyeh and Boyer-Ahmad provinces; and Jaber plain is positioned in northwest Ilam City in Ilam Province. The existence of Gachsaran Formation and gypsum karstic phenomena (the most important of which are sinkholes) in the mentioned plains, can have a very devastating effect on man-made structures. The morphometric study of these phenomena can allow comparison of various parameters of the sinkholes and lead to some hypotheses about their evolution. In this research, the sinkholes of both plains were classified according to Basu and Switch methods; based on Basu Model, they are categorized in elongated and bowl-shaped sinkholes, and on the basis of Switch method, they can be classified as bowl-shaped, pit-shaped and funnel-shaped groups. The results of the univariate linear regression analysis between the morphometric components of the sinkholes showed that the components of the area with large diameter, area with small diameter, depth with area, and depth with large diameter, indicate the highest values of significant correlation with determination coefficients of 0.922, 0.873, 0.699, 0.581, respectively. The maximum significant relationship at the error probability level, less than 0.1 is between the components of the area and large diameter for 2^nd-degree and 3^rd-degree relationships with determination coefficients of 0.997 and 0.998 and the estimation error of 0.07 and 0.08. The results of stepwise multiple linear regression analysis between the morphometric components of the sinkholes indicated that the highest value of determination coefficient is related to the area, small diameter, large diameter, and depth with determination coefficient of 0.997, and estimation error of 0.024, while the least values of determination coefficient is related to slope with depth, and large and small diameters with determination coefficient of 0.584 and the estimation error of 0.091. Therefore, the area, large and small diameters, and depth can be suitable parameters for modeling.
Karst is a geomorphic and hydrological system that is formed by the dissolution of soluble rocks such as limestone, dolomite, and gypsum (Eziot et al., 2014). Gypsum and anhydrite are among the rock types which can be karstified easily and quickly (White, 1988). Given the development of evaporate formations such as Gachsaran, Kalhor, Hith, salt domes, etc. in Iran and particularly Zagros basin, and as well, the presence of gypsum and anhydrite as their main constituents, their importance in engineering geological issues including dams, tunnels, roads and railways, structures, mines and so on is evident. There is a close relationship between karst geomorphology and its evolution, so that karst morphology phenomena are abundant and developed in the area (Karimi 2010, Ghobadi 2009). Generally speaking, four different mechanisms are characterized for the formation of sinkholes; they are as follows: solution from above, collapse from the bottom, soil transport, and removal of buoyant support. Sometimes the formation of the sinkholes is due to a combination of different mechanisms. It seems that the above-mentioned mechanisms can also be applied to gypsum sinkholes; the only difference is the formation speed of the landform (Gunay, 2002). In the present study, it is attempted to classify the various sinkhole types of Jaber and Maroon plains based on their morphology, and as well to determine the most suitable parameters for modeling.
Methodology
To survey the morphometry of gypsum sinkholes, after field studies and measuring the sinkhole characteristics of Maroon and Jaber plains, the required parameters were prepared by SPSS software (Table 1). Initially, using the obtained data, the sinkholes of two study areas were categorized by Basu and Switch methods, then the regression analysis of the morphometric parameters of the sinkholes was performed in SPSS software. For this purpose, univariate linear, 2^nd-degree, 3^rd-degree, and multivariate methods were used, and consequently, the most suitable models with higher preference values were presented.
Results and discussion
The results demonstrate that according to Basu method, the sinkhole types of the study area are circular and elongated. As well, based on the Switch method, and the diameter to depth ratio, the sinkholes of these areas are of bowl-shaped, funnel-shaped, and pit-shaped types; the number of pit-shaped sinkholes is greater than the other two types. The results of the univariate linear regression analysis between the morphometric components of the sinkholes show that the components of area with large diameter, area with small diameter, depth with area, and depth with large diameter, indicate the highest values of significant correlation by determination coefficients of 0.922, 0.873, 0.699, 0.581, respectively. The maximum significant relationship at the error probability level, less than 0.1 is between the components of area and large diameter for 2nd and 3rd degree relationships with coefficients of determination of 0.997 and 0.998 and the estimation error of 0.07 and 0.08. Also, the results show that the least significant 2^nd-degree and 3^rd-degree relationships are between environment and slope with determination coefficients of 0.025 and 0.081 and estimation error of 0.022 and 0.022. Besides, the results of stepwise multiple linear regression analysis between the morphometric components of the sinkholes demonstrated that the highest value of determination coefficient is related to the area, small diameter, large diameter, and depth with determination coefficient of 0.997, and estimation error of 0.024, while the least values of determination coefficient is related to the slope with depth, and large and small diameters with determination coefficient of 0.584 and the estimation error of 0.091.
Conclusion
According to the obtained results of the Basu method, the sinkholes of the Jaber plain are circular in shape and the Maroon plain sinkholes are classified among the elongated ones; certainly, the mechanism of formation of the sinkholes has directly influenced their shape and morphometry. The presence of creeks on the formations and gypsum layers has resulted in elongated sinkholes; in the Jaber plain where most of the sinkholes have been formed on the Knick line, the intersection point of a centralized slope flow and the gypsum layer has formed circular sinkholes. The results of field studies show that the depths of the Jaber plain are deeper; the reason can be the higher thickness of the gypsum layers of the Jaber plain compared with those of the Maroon plain and more importantly is that these layers are situated in Knick line and exposed to a powerful centralized slope flow. But the sinkholes of the Maroon plain are steeper, and the sinkholes of the Jaber plain enclose more area. After field observations as well as quantitative calculations of the ratio of the small and large diameters of the elongated sinkholes, the proportion of these two parameters is roughly calculated as 1/3. Quantitative results of univariate linear analysis between the morphometric components the sinkholes as well as the significant relationship at the error probability level, less than 0.1, for 2^nd-degree and 3^rd-degree relationships, and the results of stepwise multiple linear regression analysis between the morphometric components of the sinkholes express that the area, large and small diameters, and depth can be appropriate parameters for modeling.