## 1 Introduction  
Since the second half of the 19 th century, considerable attention has been paid to the use of coarse-grained soil in the construction of embankment dams. Then, improvements in the density methods and the use of coarse-grained soil meant that engineers were able to design and construct higher rockfill dams [1]. In order to control the functions of dams, their behaviour must be examined at the time of construction, and considerable data need to be gathered. Observations reveal that, with the first impoundment or heavy rain, not only long-term deformation (creep) [2] but also sudden settlements occur [3]. Sudden settlement during the first impoundment is a salient feature of central core clay dams with rockfill shells. This sudden settlement, which is referred to as collapse settlement, is ascribed to the impacts of floods in the upstream rockfill [4]. Collapse settlement is a dangerous geotechnical phenomenon that can damage dams and their equipment. However, it is hard to predict the collapses resulting from collapsible soil for various reasons, such as soil deformability, the degree of saturation, and the variable loading conditions [5]. Previous studies have indicated that most soils can be exposed to collapse [6; 7; 8; 9]. In other words, if poorly graded unsaturated soil is excessively saturated under the loading process, it is likely to collapse. However, there must be poor binding between the grains for it to be destroyed as a result of saturation and, consequently, the soil weakens [10]. Destruction of this binding reduces the shear strength of the soil and finally leads to significant deformations. Studies have demonstrated that factors such as the size of particles, Afterberg limits, and the moisture content of fine-grained particles affect the collapse failure [11]. In order to look into the reasons for collapse and the considerable deformations of rockfill dams, many researchers conducted different experiments on soil in the 1960s and 1970s [12; 2]. One of these experiments was the one-dimensional odometer test, which is widely used to estimate the collapse potential of soils. It can also be used to calculate soil collapse settlement [5; 13; 14]. The results of these experiments revealed that the fracture of coarse grains under considerable stress leads to the rearrangement of soil grains and collapse settlement. Comprehensive studies were undertaken in this regard by running several three-dimensional and one-dimensional investigations [15]. The results of sieving before and after the experiments indicated that soil grains were shattered during the experiment. Thus, it was understood that wetting of soil reduces the strength of particles. Various reasons, such as spreading of cracks in grains [16], suction reduction, and reduction of the energy level of minerals [17], have been suggested to illuminate the fracturing of grains [18]. In response to the reduction of matrix suction, collapsible soils undergo three distinct phases: the pre-collapse phase, collapse phase, and post-collapse phase. In the pre-collapse phase, collapsible soils may expand, maintain a constant volume, or collapse slightly, and the soil structure is intact in this phase. In the post-collapse phase, soil may collapse with the same intensity as in the collapse phase, slow down, or stop collapsing [19]. Previous studies have revealed that various parameters, such as moisture content, level of normal and shear stresses, sand content, clay content, and relative density, can influence the collapse phenomenon [10; 20; 21; 22]. Collapse criteria have been developed based on two parameters, dry density and saturation degree [5]. It is understood that, as dry density is reduced in terms of fixed moisture content (fixed matrix suction), the collapse potential of soils increases [5; 14; 23; 24]. Further, as the moisture percentage increases in terms of the fixed dry unit weight, collapse potential decreases [5; 14; 24; 25].