## 1 Introduction  
Foamed concrete is a material classified as cellular lightweight concrete with entrained air voids. Foamed concrete is a versatile material with high flowability, low cement content and high thermal insulation [1; 2; 3]. Since energy efficiency has become an important issue in the civil construction engineering fields, foamed concrete has been widely produced and used as a promising building material due to its low energy consumption and high energy-saving characteristics [4; 5]. Foamed concrete is basically a porous material, and it contains numerous pores inside the material. The pore structure inside the material strongly affects the cell (solid) structure, as well as its characteristics and properties [6; 7; 8]. Like other types of concrete [9; 10; 11], the material properties of foamed concrete are significantly affected by the pore characteristics, and many studies have been reported about the pore characteristics of foamed concrete over the past few years. [PERSON] and [PERSON] [12] examined the porosity effect on the mechanical property of foamed concrete, and [PERSON] et al. [13] investigated the size distribution of the entrained pores in foamed concrete. [PERSON] et al. [14; 15] characterized and simulated the microstructure of foamed concrete. In particular, [PERSON] and [PERSON] [16], as well as [PERSON] et al. [17] examined the pore structure inside foam concrete and demonstrated that porosity is not sufficient to regulate the characteristics of foam concrete, and other pore characteristics, such as pore size, size distribution, shape and cell thickness, should also be considered for more detailed understanding of foam concrete material. In spite of this significance, the investigation of the relationship between the spatial distribution of pores and the physical properties of foamed concrete (i.e., thermal conductivity, elastic modulus and compressive strength) has rarely been performed. In this study, the correlation between the pore characteristics and material responses of foamed concrete is investigated using both numerical and experimental approaches. Particularly, the effects of local pore characteristics on the physical properties are examined from foamed concrete samples with different densities at the microstructure level. For that purpose, a set of foamed concrete samples with very low densities are produced by using the LithoFoam(r) (Luca Industries International, Berlin, Germany) foam agent. In general, the pores in foamed concrete are secured by using either the pre-foaming or mix foaming methods [2; 17]; the foamed concrete specimens used in this study are generated using the pre-foaming method. Pores in foamed concrete have a role to enhance the insulation effect, while the compressive strength and elastic stiffness decrease as the porosity increases. Thus, an appropriate investigation of the pore structure is required for better understanding the property characteristics of foamed concrete. Here, the pore distributions within foamed concrete samples are described using X-ray micro-computed tomography (micro-CT), which is a nondestructive method. From the micro-CT, a set of 2D images of a sample with pixel sizes in the micrometer range can be produced by X-rays without damaging the specimen [18; 19]. To classify the pores and the specimen, the image processing of converting the original CT images into binary images is utilized. Then, a 3D binary image of the sample is obtained by subsequent stacking of the converted cross-sectional images. In particular, a modified watershed 3D algorithm is used here for segmentation and identification of the pores with irregular shapes. For the characterization of the pore and cell characteristics of the foamed concrete specimens, probabilistic and quantitative methods are used. Probabilistic functions, two-point correlation [20; 21; 22] and lineal-path [23; 24] are used here for the description of the pore characteristics.