## 1 Introduction  
Landfill settlement offers a significant opportunity for landfill operators to increase the potential disposal capacity of landfills. Because the majority of waste settlements occur very rapidly, a large settlement can be achieved during the filling process. Moreover, the decomposition process of organic components also increases landfill capacity. With a suitable model and the appropriate parameters, a landfill operator can estimate the actual remaining space of an existing landfill. In addition, the accurate estimation of the exact disposal capacity, including the extra volume achieved by the waste settlement, is also important for municipalities whose responsibility it is to develop an efficient waste management strategy for the local community [1]. Clearly, the prediction of a settlement cannot be more accurate than the data used in the corresponding settlement model. Therefore, in order to avoid inappropriate waste management strategies, the fundamental physical properties that govern landfill settlements (i.e., solid particle density and dry density) must be accurately established. Solid particle density (\(\rho_{s}\)) is a fundamental property which, in waste mechanics, is commonly used to determine the base phase relationships (i.e., void ratio, porosity, degree of saturation, and unit weight) of temporally stored or landfilled waste material [2]. Moreover, it is a fundamental property used in design calculations for predicting the behavior of sanitary landfills [3, 4]. It is defined as the ratio between dry mass (\(m_{s}\)) and the volume of solid particles (\(V_{\rm s}\)) as  
\[\rho_{s}=\frac{m_{s}}{V_{s}} \tag{1}\]  
Although the determination of mass particles (\(m_{s}\)) is straightforward, the determination of particle volume (\(V_{s}\)) is characterized by many difficulties. Specifically, an object such as a solid waste specimen is a multiphase material, which consists of various particles and voids. Voids that have a connection to the surface can be referred to as open pores, whereas the interior voids, inaccessible from the surface, can be considered to be closed pores. Consequently, various types of volumes can be defined, i.e., apparent particle volume and absolute volume. Although the apparent particle volume is defined as the total volume of all the particles, excluding the volume of open pores but including the volume of closed pores, the absolute volume is defined as the volume of solid matter after the exclusion of all the spaces [5]. Solid particle density is most commonly measured by a conical-topped pycnometer, in accordance with the ASTM D854 standard [6]. Although the mentioned method is capable of providing an accurate measurement of the solid particle density of soils, the application of this method to the measurement of the solid particle density of waste materials is overburdened with many difficulties. The particles with less specific gravity than water will float during the experiment. The heterogeneous nature of waste material, the relative specific gravity of individual waste particles, the size of waste particles, the amount of closed (intraparticle) voids, the compressibility, and the hydrophilic properties also have negative effects on the measurement accuracy. Air entrapment and various chemical and physical interactions between waste particles and measurement fluid (usually water) can also be anticipated. [PERSON] et al. [7] showed that the solid particle density of waste materials was dependent on the moisture content. With increasing moisture content, the solid particle density decreased due to a swelling of solid particles and the consequent increase in the volume of said particles. Moreover, in some cases, increased moisture content could weaken the particle's structure, causing the particle to collapse, which consequently reduced the solid particle's volume. [PERSON] et al. [2] reported that solid particle density was poorly determined for municipal solid waste (MSW), because it was linked to the specific solid particle density of each component.