## 1 Introduction  
Soil thermal conductivity has a wide interest in underground infrastructure engineering, such as sub-ground building [1], subsurface pipeline [2; 3] and cable networks [4; 5], underground transportation [6], and ground source heat pump systems [7; 8; 9]. Soil thermal conductivity depends on many factors, which may be primarily classified into three groups: the nature of soils, including the texture, mineral composition, shape and size of soil particles; the structural condition, including porosity and particle arrangement; and the physical condition, including water content, temperature, and pressure. In reality, all these influences work together making the evaluation of soil thermal conductivity a big challenge [10; 11; 12; 13; 14]. In order to understand the influences of structural and physical conditions, the study on the thermal conductivity of unsaturated sandy soils has raised particular interest [15; 16; 17; 18; 19]. [PERSON] [18] reported an experimental work using four different quartz sands, which had the same over 99% quartz content, but different particle size distribution. Using the transient thermal probe method, the thermal conductivity was measured at four different porosities and five water contents from dry to fully saturated. Based on the experimental result, he proposed an empirical thermal conductivity model for sandy soil, which took a logarithmic form containing the porosity and saturation. [PERSON] et al. [16] conducted a similar test on three standard sands, called Ottawa C-109, Ottawa C-190, and Toyoura,respectively. The Ottawa sands have 99.8% quartz content and a density of 2.65, while the Toyoura sand, which is mainly composed of quartz and some siliceous rocks and black shale, has a density of 2.63. Using the thermal probe method, they measured the thermal conductivity at two porosities and six degrees of water saturation from dryness to full saturation. For modelling, they used the de Vries model [20] to fit the measurements. Both of the two reported works took a similar procedure in sample preparation, in which, at first, a certain amount of sands of a specific water content were filled in a container. Thereafter the sands in the container were compacted to a certain volume to achieve a specific porosity. The two separately conducted works had obtained quite similar measurement results for the thermal conductivity of sandy soils at different porosity and water content conditions. The two models adopted had produced a good fitting result for the experimental measurements. The effect of the soil structural and physical conditions on soil thermal conductivity is a complicated problem because the two factors present a strongly coupled influence. It has been noticed before that there is an intrinsic link between thermal conductivity and the water retention characteristics of soils. The variation of thermal conductivity against the water saturation displays a resembling mirrored S-shape as the water retention curve of unsaturated soils [21] as illustrated in Figure 1. The resemblance is due to the variation of both thermal conductivity and matric suction of soils against the water content depending on the pore water distribution, which relates to the pore size distribution, and the configuration of the pore water interface, including the water film on pore wall surfaces and the air-water interface between soil particles. However, so far, most of the previous work evaluated the soil structural influence on thermal conductivity mainly based on porosity and particle size distribution. Seeing the fact that the pore water distribution of unsaturated soils depends on the soil pore size distribution, but the pore size distribution does not have a unique correlation to the soil porosity and particle size distribution, the effect of pore size distribution on the soil thermal conductivity at different water contents still needs more research for a deeper understanding.